A windshield wiper is 45 cm long and
creates a central angle of 120° in one
wipe. what is the sector area?

Answers

Answer 1

The windshield sector area is 706.86 cm².

To calculate the sector area of the windshield wiper, we need to use the formula for the area of a sector of a circle. The formula is:

A = (θ/360°) x πr²

where A is the area of the sector, θ is the central angle of the sector in degrees, and r is the radius of the circle.

In this problem, we are given that the windshield wiper has a length of 45 cm, which means that the radius of the circle traced by the wiper is 45 cm/2 = 22.5 cm.

We are also given that the wiper creates a central angle of 120° in one wipe. Substituting these values into the formula, we get:

A = (120°/360°) x π(22.5 cm)²

A = (1/3) x π x (22.5 cm)²

A ≈ 706.86 cm²

Therefore, the sector area of the windshield wiper is approximately 706.86 square centimeters.

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Related Questions

What is the missing step in solving the inequality 4(x – 3) 4 < 10 6x? 1. the distributive property: 4x – 12 4 < 10 6x 2. combine like terms: 4x – 8 < 10 6x 3. the addition property of inequality: 4x < 18 6x 4. the subtraction property of inequality: –2x < 18 5. the division property of inequality: ________ x < –9 x > –9 x < x is less than or equal to negative startfraction 1 over 9 endfraction. x > –x is greater than or equal to negative startfraction 1 over 9 endfraction.

Answers

The missing step in solving the inequality 4(x – 3) /4 < 10/6x is to divide both sides by 2.

Apply the distributive property to get 4x - 12 /4 < 10/6x.

Combine like terms to obtain 4x - 3 < 5/3x.

Add 3/3x to both sides to get 4x < 8/3x + 3.

Subtract 8/3x from both sides to get 4/3x < 3.

Divide both sides by 4/3 to get x < -9/4.

Simplify the result by dividing both sides by 2 to get x < -9/2 or x > -4/3.

Therefore, the missing step is to divide both sides by 2, which gives x < -9/2 or x > -4/3.

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Susan’s weekly earnings were proportional to the number of hours she worked. this table shows


the number of hours susan worked and the amount she earned. how much money did susan


earn per hour?


hours earnings ($)


5 $47.50


7 $66.50


9 $85.50


11 $104.50

Answers

Susan earns $9.50 per hour. This is found by dividing her earnings by the number of hours worked for each corresponding row in the table.

To find how much money Susan earned per hour, we need to divide the total earnings by the total number of hours worked. For finding the Total earnings we need to add the money earned in every hour,

Total earnings = $47.50 + $66.50 + $85.50 + $104.50 = $304

Total hours worked = 5 + 7 + 9 + 11 = 32

Money earned per hour = Total earnings / Total hours worked

= $304 / 32

= $9.50

Therefore, Susan earned money of $9.50 per hour.

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Taylor is making a large banner that
measures 6 yards in length. He split the
banner into 18 sections for him and
some of his friends to work on. How
many inches long is each section?

Answers

Answer:

12 is the answer

Step-by-step explanation:

6 y = 6 × 36 in. ( y = yards, in = inches )

do the math:

6(36) ÷ 18 = 12 ( for 18 sections of course )

12 × 18 = 6 × 36

becuase;

12 × 18 = 216 \

                       ——- They are the same

6 × 36 = 216  /

= 216

Divide

216 ÷ 18 = 12

12 being the answer

Answer:

12 inches long

Step-by-step explanation:

One yard is equal to 36 inches, so 6 yards is equal to:

[tex]\sf:\implies 6 \times 36 = 216\: inches[/tex]

To find the length of each section, we need to divide the total length of the banner (216 inches) by the number of sections (18):

[tex]\sf:\implies 216 \div 18 = \boxed{\bold{\:\:12\:\:}}\:\:\:\green{\checkmark} [/tex]

Therefore, each section is 12 inches long.

HELP!! 50 points !!



13. An online job - seeking service allows job - seekers to post their resumés for free. The service charges employers looking for applicants a fee to look through the resumés. The fee is based on how long the employer wants the employer wants to consider. The fees are $585 for a 100 - mile radius for access to the resumés , and how many miles from the workplace address 3 weeks and $675 for a 150-mile radius for 3 weeks. A If there are 98 resumés within a 100 - mile radius , what is the average cost to b. If there are 208 resumés within a 150 - mile radius , what is the average cost. Under the 150 - mile radius option , an employer would see the same 98 resumés from part a that he would have seen under the 100 - mile radius option. What is the average cost to the employer for looking at the extra resumés he would see if he opted for the more expensive plan ? Explain. The nearest cent to the employer for looking at each resume ? to the employer for looking at each resumé? d. Give an advantage and a disadvantage of opting for the more expensive plan.

Answers

a. The cost for a 100-mile radius for 3 weeks is $585, and there are 98 resumes within this radius, so the average cost per resume would be:

$585 / 98 = $5.96 per resume

b. The cost for a 150-mile radius for 3 weeks is $675, and there are 208 resumes within this radius, so the average cost per resume would be:

$675 / 208 = $3.25 per resume

c. If an employer opts for the 150-mile radius option instead of the 100-mile radius option, they would pay an extra $90 ($675 - $585) to see an additional 110 resumes (208 - 98).

The average cost to the employer for looking at each extra resume would be:

$90 / 110 = $0.82 per resume

d. An advantage of opting for the more expensive plan is that the employer would have access to a larger pool of potential candidates, which could increase the likelihood of finding a qualified applicant.

A disadvantage is that the employer would have to pay more money, which could be a significant expense for smaller businesses or those with limited budgets.

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In a certain high school, a survey revealed the mean amount of bottled water consumed by students each day
was 153 bottles with a standard deviation of 22 bottles. assuming the survey represented a normal distribution,
what is the range of the number of bottled waters that approximately 68.2% of the students drink?

Answers

68.2% confidence of the students drink between: 131 and 175 bottles of water per day.

We can use the empirical rule, also known as the 68-95-99.7 rule, to determine the range of values that contain 68.2% of the data in a normal distribution. According to the rule, approximately 68.2% of the data falls within one standard deviation of the mean.

We know that the mean amount of bottled water consumed is 153 bottles, with a standard deviation of 22 bottles. Therefore, one standard deviation below the mean is 153 - 22 = 131 bottles, and one standard deviation above the mean is 153 + 22 = 175 bottles.

Thus, we can say with 68.2% confidence that the number of bottled water consumed by students each day falls between 131 and 175 bottles.

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Question 6 of 20 :

Select the best answer for ige question. 6. Simplify (4x 4)-3. O B. 2

O C. -8x12

0D. -64x9

Answers

The correct answer is (C) -8x12.

To simplify (4x^4)^-3, we use the power of a power rule which states that (a^m)^n = a^(mn), where a is a non-negative number and m and n are integers. Applying this rule, we get:

(4x^4)^-3 = 4^(-3) x^(4 x -3) = (1/64)x^(-12) = -8x^12 (using the negative exponent rule, which states that a^(-n) = 1/a^n)

Therefore, the simplified form of (4x^4)^-3 is -8x^12.

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In a school of 580 students, one class was asked which hand they write with.
• “L” means they use their left hand.
• “R” means they use their right hand.
Here are the results:
L, R, R, R, R, R, R, R, R, L, R, R, R, R, R

1) Based on this sample, estimate the proportion of students at the school who write with their left hand.
2) Estimate the number of students at the school who write with their left hand.
3) A different class of `18` students is surveyed. Estimate how many write with their left hand.

Answers

1.  The proportion of students at the school who write with their left hand is 2/15 OR 13.3%

2. The estimated number of students who write with their left hand is 77 students

3. The estimated number of students in the different class of 18 students who write with their left hand is 2

Estimating the number of students that write with their left hand

From the question, we are to estimate the proportion of students who write with their left hand

To estimate the proportion of students at the school who write with their left hand, we need to count the number of students in the sample who write with their left hand and divide by the total number of students in the sample.

From the given sample, there are 2 students who write with their left hand and 13 students who write with their right hand. So the estimated proportion of students who write with their left hand is:

2/15 = 0.133

OR

13.3%

2.

To estimate the number of students at the school who write with their left hand, we can multiply the proportion by the total number of students in the school

That is,

2/15 x 580 = 77.33

Thus, about 77 students write with their left hand

3.

To estimate how many students in a different class of 18 students write with their left hand, we can apply the proportion to the new sample:

2/15x 18 = 2.4

Hence, about 2 students in the different class write with their left hand.

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Just-in-time (JIT) delivery: Increases physical distribution costs for business customers. Requires that a supplier be able to respond to the customer's production schedule. Usually does not require e-commerce order systems and computer networks. Means that deliveries are larger and less frequent. Shifts greater responsibility for physical distribution activities from the supplier to the business customer

Answers

Just-in-time (JIT) delivery is a supply chain management strategy that aims to improve efficiency and reduce inventory costs by having materials and goods delivered exactly when they are needed in the production process.

This approach requires suppliers to be able to respond to the customer's production schedule, ensuring timely deliveries to prevent disruptions. As a result, JIT delivery shifts greater responsibility for physical distribution activities from the supplier to the business customer, who needs to closely monitor inventory levels and maintain efficient communication with suppliers.

However, JIT delivery does not typically lead to larger, less frequent deliveries, nor does it inherently increase physical distribution costs. In fact, it may reduce costs by minimizing inventory storage expenses. Additionally, e-commerce order systems and computer networks are often utilized to facilitate the communication and coordination required for effective JIT delivery.

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A poll used a sample of randomly selected car owners. Within the​ sample, the mean time of ownership for a single car was years with a standard deviation of years. Test the claim by the owner of a large dealership that the mean time of ownership for all cars is less than years. Use a 0. 05 significance level

Answers

If t is less than -1.699, we reject the null hypothesis.

To test the claim by the owner of the large dealership, we will use a one-sample t-test with the following hypotheses:

Null Hypothesis: H0: µ >= µ0 (The population mean time of ownership is greater than or equal to µ0)

Alternative Hypothesis: Ha: µ < µ0 (The population mean time of ownership is less than µ0)

where µ is the population mean time of ownership, µ0 is the claimed mean time of ownership by the owner of the dealership.

The significance level is α = 0.05.

We can calculate the t-value as:

t = ([tex]\bar{x}[/tex] - µ0) / (s / √n)

where [tex]\bar{x}[/tex] is the sample mean time of ownership, s is the sample standard deviation, n is the sample size.

Plugging in the values given in the problem, we get:

t = ([tex]\bar{x}[/tex] - µ0) / (s / √n) = (5.7 - µ0) / (1.8 / √n)

Since the alternative hypothesis is one-tailed (less than), we need to find the critical t-value from the t-distribution table with n-1 degrees of freedom and a significance level of 0.05. For a sample size of n = 30 (assuming it is large enough), the critical t-value is -1.699.

If the calculated t-value is less than the critical t-value, we reject the null hypothesis and conclude that there is evidence to support the claim that the mean time of ownership for all cars is less than the claimed mean time of ownership by the owner of the dealership.

If the calculated t-value is greater than the critical t-value, we fail to reject the null hypothesis and conclude that there is not enough evidence to support the claim that the mean time of ownership for all cars is less than the claimed mean time of ownership by the owner of the dealership.

So, if we assume that the sample is representative of the population and meets the assumptions of the t-test, we can calculate the t-value as:

t = (5.7 - µ0) / (1.8 / √30)

If t is less than -1.699, we reject the null hypothesis. Otherwise, we fail to reject the null hypothesis.

Note that we don't have any information about the claimed mean time of ownership by the owner of the dealership, so we cannot calculate the t-value or make any conclusions.

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Write two numbers that multiply to the value on top and add to the value on bottom.

Answers

Answer:

-17 and -5

Step-by-step explanation:

-5 x -17 = 85

-5 + -17 = -22

A random sample of 100 stores from a large chain of 1,000 garden supply stores was selected to determine the average number of lawnmowers sold at an end-of-season clearance sale. The sample results indicated an average of 6 and a standard deviation of 2 lawnmowers sold. A 95% confidence interval (5. 623 to 6. 377) was established based on these results. True or False: Of all possible samples of 100 stores taken from the population of 1,000 stores, 95% of the confidence intervals developed will contain the true population mean within the interval

Answers

The statement is True.

The statement "95% confidence interval (5.623 to 6.377)" means that if we were to repeat this process of taking 100 samples from the population and constructing a confidence interval for each sample, then about 95% of those intervals would contain the true population mean.

This is the definition of a confidence interval at a certain level of confidence (in this case, 95%). Therefore, the statement is true.

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What is the anwser to number 3

Answers

The volume of a triangular prism in question number 3, obtained from the product of the area of a triangle and the thickness of the prism is 1,728 mi³

What is a triangular prism?

A triangular prism consists of two triangular bases and three sides that are rectangular.

The solid in the figure in question number 3 is a triangular prism, with the following dimensions.

Base length = 30 mi.

Thickness (depth of the prism) = 8 mi

Shape of the triangles = Right triangles

Leg lengths of the right triangles = 18 miles and 24 miles

The volume of the triangular prism = Area of the cross section of the triangular prism × Depth of the prism

Area of the triangular cross section of the triangular prism = (1/2) × 18 × 24 = 216 mi²

Volume of the triangular prism = 216 mi² × 8 mi = 1728 mi³

The volume of the triangular prism in the figure is therefore; 1,728 mi³

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Mariana tiene un peso de 175 libras y su nutrióloga le ha otorgado una nueva dieta y ella misma a creado una nueva rutina de ejercicio su comida semanal consiste en lo siguiente 3 libras de pollo, 9 libras de frutas, 15 libras de verduras cocinadas o crudas y solo 1 libra de tortilla o pollo

¿cual es el peso en kilogramos de mariana?

¿cuantos kilos debe conseguir de pollo a la semana?

¿cuantos de fruta?

¿cuantos kg de verduras deberá consumir?

plis es para hoy​

Answers

El peso de Mariana en kilogramos es aproximadamente 79.378 kg. Debe conseguir 1.361 kg de pollo a la semana, 4.082 kg de frutas y 6.803 kg de verduras.

How to convert Mariana's weight from pounds to kilograms?

Para convertir el peso de Mariana de libras a kilogramos, debemos recordar que 1 libra equivale a aproximadamente 0.4536 kilogramos. Por lo tanto:

Peso de Mariana en kilogramos = 175 libras * 0.4536 kg/libra ≈ 79.3792 kg

Entonces, el peso de Mariana es aproximadamente 79.3792 kilogramos.

En cuanto a la cantidad de pollo que Mariana debe conseguir a la semana, la dieta establece que debe consumir 3 libras de pollo. Para convertirlo a kilogramos:

Cantidad de pollo a la semana = 3 libras * 0.4536 kg/libra ≈ 1.3618 kg

Por lo tanto, Mariana debe conseguir aproximadamente 1.3618 kilogramos de pollo a la semana.

De manera similar, para las frutas, la dieta establece 9 libras. Convertimos a kilogramos:

Cantidad de frutas a la semana = 9 libras * 0.4536 kg/libra ≈ 4.0824 kg

Por lo tanto, Mariana debe conseguir aproximadamente 4.0824 kilogramos de frutas a la semana.

Para las verduras, la dieta establece 15 libras. Convertimos a kilogramos:

Cantidad de verduras a la semana = 15 libras * 0.4536 kg/libra ≈ 6.804 kg

Por lo tanto, Mariana debe consumir aproximadamente 6.804 kilogramos de verduras (cocinadas o crudas) a la semana.

En resumen, el peso de Mariana es de aproximadamente 79.3792 kilogramos. Debe conseguir alrededor de 1.3618 kilogramos de pollo, 4.0824 kilogramos de frutas y 6.804 kilogramos de verduras a la semana.

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Third-, fourth-, and fifth-grade students collected food items to be sent to 2 different food pantries. The third-grade students collected 35 items and the fourth-grade students collected 25 items. each food pantry was given 50 items. write and solve an equation to find how many items fifth-grade collected

Answers

Answer: 35 + 25 + 50 / 2 = 85

Step-by-step explanation: You would have to add them all together and then divide them by 2.

In my class, everyone studies French or German, but not both languages.



One third of the girls and the same number of boys study German.



Twice as many boys as girls study French.



Which of these could be the total number of boys and girls in my class?

Answers

The possible total number of boys and girls in the class is 21, and

the answer is b).

Let's denote the number of girls in the class as 'g' and the number of

boys as 'b'.

We know that all students in the class study either French or German,

but not both.

Therefore, the total number of students in the class is equal to the sum

of the number of students who study French and the number of students

who study German

From the given information, we can write the following equations:

g + b = total number of students

(1/3)g = (1/3)b (one third of the girls and the same number of boys

        study German

2(1/3)g = b (twice as many boys as girls study French)We can simplify the second equation by multiplying both sides by 3:g = b

Substituting this into the first equation, we get:

2g = total number of studentsSubstituting the second equation into

the third equation, we get:

2g = b (twice as many boys as girls study French)

Substituting this into the first equation, we get:

3g = total number of students

Therefore, the total number of students in the class must be a multiple

of 3.

Let's try the answer choices:

a) 15 students (total number of students is not a multiple of 3)

b) 21 students (total number of students is a multiple of 3 and the

number of girls is a multiple of 3, so this is a possible solution)

c) 24 students (total number of students is a multiple of 3 and the

number of girls is not a multiple of 3)

d) 30 students (total number of students is a multiple of 3 but the

number of girls is not a multiple of 3)

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What capital letter that has more than two right angles.​

Answers

Answer:

E,F,H

Step-by-step explanation:

Answer:

B = 2 (could be 4, like with this font)

E = 4

F = 3

H = 4

P = 0 (could be 3, like this this font)

R = 0 (could be 3, like with this font)

X = (could be 4)

Other right angles:

D = 0 (could be 2, like with this font)

L = 1

T = 2

Y = (could be 1)

For the given cost and demand functions, find the production level that will maximize profit. (Round your answer to the nearest whole number.)C(q) = 660 + 5q + 0.03q^2, p = 10 − q/400

Answers

The production level that will maximize profit is 80 units

To find the production level that will maximize profit given the cost function C(q) = 660 + 5q + 0.03q^2 and demand function p = 10 - q/400, follow these steps:

1. Write down the revenue function: Revenue (R) is the product of price (p) and quantity (q). So, R(q) = p * q.

2. Substitute the demand function into the revenue function: R(q) = (10 - q/400) * q

3. Simplify the revenue function: R(q) = 10q - q^2/400

4. Write down the profit function: Profit (P) is the difference between revenue and cost. So, P(q) = R(q) - C(q).

5. Substitute the revenue and cost functions into the profit function: P(q) = (10q - q^2/400) - (660 + 5q + 0.03q^2)

6. Simplify the profit function: P(q) = 10q - q^2/400 - 660 - 5q - 0.03q^2

7. Combine like terms: P(q) = 5q - q^2/400 - 0.03q^2 - 660

8. Differentiate the profit function with respect to q to find the first derivative: P'(q) = 5 - q/200 - 0.06q

9. Set the first derivative equal to 0 and solve for q: 5 - q/200 - 0.06q = 0

10. Solve for q: q ≈ 80

The production level that will maximize profit is approximately 80 units (rounded to the nearest whole number).

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A town’s population doubles in 23 years. Its percentage growth rate is approximately *


23% per year.


70/23 per year


23/70 per year

Answers

The answer is that the town's percentage growth rate is approximately 3% per year.

What is the approximate percentage growth rate per year of a town whose population doubles in 23 years?

To find the town's percentage growth rate, we can use the formula:

growth rate = (final population - initial population) / initial population * 100%

Let P be the initial population of the town, and let t be the time it takes for the population to double, which is 23 years in this case. We know that:

final population = 2P (since the population doubles)

t = 23 years

Substituting these values into the formula, we get:

growth rate = (2P - P) / P * 100% / 23

= P / P * 100% / 23

= 100% / 23

≈ 4.35%

However, this is the annual growth rate that would result in a doubling of the population in exactly 23 years. Since the question asks for the approximate percentage growth rate per year.

We need to find the equivalent annual growth rate that would result in a doubling time of approximately 23 years.

One way to do this is to use the rule of 70, which states that the doubling time (t) of a quantity growing at a constant percentage rate (r) is approximately equal to 70 divided by the growth rate:

t ≈ 70 / r

In this case, we want t to be approximately 23 years, so we can solve for r:

23 ≈ 70 / r

r ≈ 70 / 23

r ≈ 3.04%

Therefore, the town's percentage growth rate is approximately 3% per year.

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Answer quickly please
Given that A is a constant, the general solution to the differential equation dy dt -5y is Select one O a. 3t2 2 Ob. 3= Ae-56 Ос. y = Aest Od y=est +A The solution to the exact differential equati

Answers

The general solution to the differential equation dy/dt - 5y = A is y = Ce^(5t) + A/5, where C is a constant of integration. The general solution is y = (A/5) + Ce^(5t). so, the correct answer is D).

The general solution to the differential equation dy/dt - 5y = A, where A is a constant, is

y = Ce^(5t) + A/5

where C is an arbitrary constant determined by any initial or boundary conditions given.

The general solution is a combination of the homogeneous solution y_h = Ce^(5t) (which satisfies the differential equation without the constant term A) and the particular solution y_p = A/5 (which satisfies the differential equation with A but without any initial or boundary conditions).

so, the correct option is D).

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--The given question is incomplete, the complete question is given

" Answer quickly please

Given that A is a constant, the general solution to the differential equation dy/dt -5y = A is Select one O a. 3t2 2 Ob. 3= Ae-56 Ос. y = Aest Od y = Ce^(5t) +A/5 The solution to the exact differential equation"--

The graph represents the distance the Pennsylvania Train traveled over 8 hours.
The Baltimore Train traveled 1,020 miles in 12 hours. Both trains traveled at a constant rate. Which sentence is true?

A. The Baltimore Train was faster by 10 miles per hour.
B. The Baltimore Train was faster by 15 miles per hour.
C. The Pennsylvania Train was faster by 10 miles per hour.
D. The Pennsylvania Train was faster by 15 miles per hour.

Answers

Answer:

Baltimore Train: 1,020 mi/12 hr = 85 mph

Pennsylvania Train: 75 mph

So the correct answer is A.

Find the indicated length

Answers

Answer:

y = 32/3 or  10.67 units

------------------------------

The two smaller right triangles are similar by AA property.

Use ratios of corresponding sides to get:

8/y = 6/8

Simplify and solve for y:

8/y = 3/4y = 8*4/3y = 32/3 ≈ 10.67

A hummingbird flaps its wings 80 times in one second. A bumblebee flutters its wings 7,800 times in 1 minute. Which animal flutters its wings more times in 1 minute?

Answers

Answer:

Step-by-step explanation:

The bumblebee flutters its wings more times in 1 minute, as it flutters its wings 7,800 times in one minute, whereas the hummingbird flaps its wings 80 times in one second, which translates to 4,800 times in one minute.

To understand this calculation in more detail, we can use unit conversions and multiplication. Since the hummingbird's wing flaps are given in seconds and the bumblebee's wing flutters are given in minutes,

we convert the hummingbird's wing flaps from seconds to minutes by multiplying by 60. We then compare the total number of wing flaps for each animal and find that the bumblebee flutters its wings more times in one minute than the hummingbird flaps its wings.

This is due to the bumblebee's higher frequency of wing movement, which enables it to achieve more wing flutters in a given amount of time.

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Select the correct answer.
What is the domain of the exponential function shown in the graph?
A. x ≥ -1
B.-∞ < x <∞
C. x< 0
D.x ≤ -1

Answers

Answer:

Step-by-step explanation:

cle Graphs MC)The circle graph describes the distribution of preferred transportation methods from a sample of 400 randomly selected San Francisco residents.circle graph titled San Francisco Residents' 9, 70 to 79, 80 to 89, 90 to 99, 100 to 109, 110 to 119. The y-axis is labeled Frequency and begins at 0 with tick marks every one unit up to 14. A shaded bar stops at 10 above 60 to 69, at 9 above 70 to 79, at 5 above 80 to 89, at 4 above 90 to 99, and at 2 above 100 to 109. There is no shaded bar above 110 to 119. The graph is titled Temps in Sunny Town.A graph with the x-axis labeled Temperature in Degrees, with intervals 60 to 69, 70 to 79, 80 to 89, 90 to 99, 100 to 109, 110 to 119. The y-axis is labeled Frequency and begins at 0 with tick marks every one unit up to 16. A shaded bar stops at 2 above 60 to 69, at 4 above 70 to 79, at 12 above 80

PLEASEEE SHOW ALL WORK THANK
YOUUUUUUUUUUUUUUUUUUUUU!!!!!!!!!!!!!!!!!!!!!!!!!!!!
LQ - 10.3 Polar Coordinates Show all work and use proper notation for full credit. Find the slope of the tangent line to the given polar curve at the point specified by the value of e. TT r = 1-2sine,

Answers

To find the slope of the tangent line to the polar curve, we need to find the derivative of the equation with respect to θ.

First, we can convert the polar equation into rectangular coordinates using the conversions rcos(θ) = x and rsin(θ) = y:
rcos(θ) = (1-2sin(θ))cos(θ)
r = x/cos(θ)
x/cos(θ) = 1 - 2sin(θ)
x = cos(θ) - 2sin(θ)cos(θ)
y = sin(θ) - 2sin^2(θ)

Next, we can find the derivative of y with respect to x using the chain rule:
dy/dx = (dy/dθ) / (dx/dθ)
dy/dθ = cos(θ) - 4sin(θ)cos(θ)
dx/dθ = -sin(θ) - 2cos^2(θ)
Plugging in the value of e for θ, we get:
dy/dθ = cos(e) - 4sin(e)cos(e)
dx/dθ = -sin(e) - 2cos^2(e)

Finally, we can find the slope of the tangent line by taking the ratio of dy/dθ to dx/dθ:
slope = (cos(e) - 4sin(e)cos(e)) / (-sin(e) - 2cos^2(e))
This is the slope of the tangent line to the polar curve at the point specified by the value of e.
Hi! I'd be happy to help you with your question. To find the slope of the tangent line to the polar curve r = 1 - 2sin(θ) at a specific value of θ, we'll first need to convert the polar equation into Cartesian coordinates.
Let's recall the conversion formulas:
x = r*cos(θ)
y = r*sin(θ)

Now, substitute the polar curve equation into these formulas:
x = (1 - 2sin(θ))*cos(θ)
y = (1 - 2sin(θ))*sin(θ)
To find the slope, we need the derivative of y with respect to x, which is dy/dx. To do this, we'll first find dy/dθ and dx/dθ.
Differentiating both x and y with respect to θ:
dx/dθ = -2cos(θ)^2 + 2sin(θ)cos(θ)
dy/dθ = -2sin(θ)^2 + 2sin(θ) - 2sin(θ)cos(θ)
Now, we find the derivative of y with respect to x:
dy/dx = (dy/dθ) / (dx/dθ)
dy/dx = (-2sin(θ)^2 + 2sin(θ) - 2sin(θ)cos(θ)) / (-2cos(θ)^2 + 2sin(θ)cos(θ))

Now, you can plug in the specific value of θ for which you want to find the slope of the tangent line to the polar curve, and simplify the expression to obtain the final answer.

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Micayla wants the print shop to reduce the size of there painting but keep the same ratio of length to width so that it will fit into her frame. Study the scale drawings to determine the proportional relationship between her painting and the frame she wants to use. What is the width of Micayla's frame?

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The width of Micayla's frame is Wf = (Lf x Wp) / Lp

Let's say that the painting has a length of Lp and a width of Wp, and the frame has a length of Lf and a width of Wf. We want to find the width of the frame, which we can call x. We know that Micayla wants to keep the same ratio of length to width between the painting and the frame, so we can set up the following equation:

Lp/Wp = Lf/Wf

This equation states that the ratio of the length to the width of the painting is equal to the ratio of the length to the width of the frame. We can use this equation to solve for x, the width of the frame. First, we can cross-multiply to get:

Lp x Wf = Lf x Wp

Then, we can solve for x by isolating it on one side of the equation:

Wf = (Lf x Wp) / Lp

This equation tells us that the width of the frame is proportional to the length of the frame and the width of the painting, divided by the length of the painting. By plugging in the appropriate values for Lp, Wp, and Lf, we can solve for x and determine the width of the frame.

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help me with pythagorean therom pleaseeeeeeeeeeeee i will legit do anything if someone can help i will give brainliest just help me pleaseeeeeeeeeeee

Answers

6.6,your answer is correct.

As the theorem is a^2+b^2=c^2 you first must assign the proper components to each variable. Since 12 is the longest since it is the hypotenuse that means it is c so in this case 144. And since 10 is the leg it is a.

To solve you must take

10^2+b^2=12^2

100+b=144

144-100=44

Since b^2 is 44 you must find the square root [tex]\sqrt{44}[/tex]=6.6

Question In this circuit, three resistors receive the same amount of voltage (24 volts) from de source Calculate the amount of current "drawn by each resistor, as well as the amount of power dissipated by each TT riston 192 w 222 w 352 w HH 24 volts

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The current drawn by each resistor is: R1: 8 A R2: 9.25 A R3: 14.67 A And the power dissipated by each resistor is: R1: 192 W R2: 222 W R3: 352 W

To calculate the current drawn by each resistor and the power dissipated by each, we will use Ohm's Law and the Power formula.

Ohm's Law is V = IR, and the Power formula is P = IV.

Given: Resistor 1 (R1) = 192 W Resistor 2 (R2) = 222 W Resistor 3 (R3) = 352 W Voltage (V) = 24 V

Step 1: Calculate the current (I) drawn by each resistor using the Power formula (P = IV):

For R1: I1 = P1 / V = 192 W / 24 V = 8 A

For R2: I2 = P2 / V = 222 W / 24 V = 9.25 A

For R3: I3 = P3 / V = 352 W / 24 V = 14.67 A

Step 2: Calculate the power (P) dissipated by each resistor using the Power formula (P = IV):

For R1: P1 = I1 × V = 8 A × 24 V = 192 W

For R2: P2 = I2 × V = 9.25 A × 24 V = 222 W

For R3: P3 = I3 × V = 14.67 A × 24 V = 352 W

So, the current drawn by each resistor is: R1: 8 A R2: 9.25 A R3: 14.67 A And the power dissipated by each resistor is: R1: 192 W R2: 222 W R3: 352 W

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true or false, Inflation occurs in an economy when there's a reduction in the total amount of money.

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Answer:

False.

Inflation occurs in an economy when there is an increase in the overall price level of goods and services over time. It is usually caused by factors such as an increase in the money supply, higher demand for goods and services, or a decrease in the supply of goods and services. Therefore, a reduction in the total amount of money in an economy would generally lead to deflation, which is the opposite of inflation.

work out minimum and maximum number of hikers who could have walked between 7 miles and 18 miles

Answers

(a) The minimum number of hikers who could have walked between 7 miles and 18 miles: at least 5 hikers and at most 13 hikers.

(b) The maximum number of hikers who could have walked between 7 miles and 18 miles:  at most 15 hikers.

According to the question and given conditions, we need to find the cumulative frequency of the distance intervals that fall within the range of 7 miles and 18 miles, to find the minimum number of hikers and the maximum number of hikers who could have walked between 7 miles and 18 miles.

The sum of the frequencies up to a certain point in the data is the cumulative frequency. By adding the frequency of the current interval to the frequency of the previous interval, we can calculate the cumulative frequency.

a) To find the minimum number of hikers who could have walked between 7 miles and 18 miles, we will find the cumulative frequency of the intervals from 5 miles to 10 miles and then from 10 miles to 15 miles.

Cumulative frequency for 5 < x <= 10: 2 + 3 = 5

Cumulative frequency for 10 < x <= 15: 5 + 8 = 13

Therefore, we find that at least 5 hikers and at most 13 hikers could have walked between 7 miles and 18 miles.

b) To find the maximum number of hikers who could have walked between 7 miles and 18 miles, we will find the cumulative frequency of the intervals from 10 miles to 15 miles and from 15 miles to 20 miles.

Cumulative frequency for 10 < x <= 15: 8

Cumulative frequency for 15 < x <= 20: 8 + 7 = 15

Therefore, we can conclude that at most 15 hikers could have walked between 7 miles and 18 miles.

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The complete question is "a) work out the minimum number of hikers who could have walked between 7 miles and 18 miles b) work out the maximum number of hikers who could have walked between 7 miles and 18 miles."

Find the interquartile range (IQR) for the data. 18, 16, 7, 5, 8, 6, 4, 3, 2, 12, 17, 18, 20, 4, 22

Answers

The interquartile range for the data 18, 16, 7, 5, 8, 6, 4, 3, 2, 12, 17, 18, 20, 4, 22 is 14.

How to find the interquartile range (IQR)?

1. Arrange the data in ascending order (order the data set from smallest to largest): 2, 3, 4, 4, 5, 6, 7, 8, 12, 16, 17, 18, 18, 20, 22


2. Determine the median (Q2):

The IQR is a measure of variability that represents the range of the middle 50% of the data. To find it, we need to first calculate the median of the entire data set. Since we have an even number of data points, we take the average of the two middle values:

Median = (8 + 12) / 2 = 10

Next, we need to find the median of the lower half of the data set (also called the first quartile, or Q1). To do this, we take the median of the values below the overall median:

Q1 = (4 + 4) / 2 = 4

Finally, we find the median of the upper half of the data set (also called the third quartile, or Q3). To do this, we take the median of the values above the overall median:

Q3 = (18 + 18) / 2 = 18


3. Find the lower quartile (Q1):

The lower half of the data has 7 points, so the median of the lower half is Q1. Q1 is the 4th value, which is 4.


4. Find the upper quartile (Q3):

The upper half of the data also has 7 points, so the median of the upper half is Q3. Q3 is the 12th value, which is 18.


5. Calculate the interquartile range (IQR) by subtracting Q1 from Q3:

IQR = Q3 - Q1

= 18 - 4

= 14.

The interquartile range (IQR) for the given data is 14.

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