What is the domain of the function y=^3/x-1?
The domain of the function y = (3/x) - 1 is all real numbers except x = 0
The domain of a function consists of all the valid input values for which the function is defined. In the case of the function y = (3/x) - 1, the only restriction on the domain arises from the presence of the variable x in the denominator.
To determine the domain, we need to find the values of x for which the expression 3/x is defined. Division by zero is undefined, so we must exclude any value of x that makes the denominator equal to zero.
In this case, we set the denominator, x, equal to zero and solve for x:
x = 0
Therefore, x cannot be equal to zero. All other real numbers are valid input values for this function. Therefore, the domain of the function y = (3/x) - 1 is all real numbers except x = 0. In interval notation, we can represent the domain as (-∞, 0) ∪ (0, ∞).
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Calcula el trabajo realizado al elevar 75cm sobre el piso unas
pesas de 90 kg
The work done to lift a 90 kg weight by 75 cm is approximately 661.5 joules.
How to calculate work?Para calcular el trabajo realizado al elevar una pesa de 90 kg a una altura de 75 cm sobre el piso, necesitamos conocer la fuerza necesaria para levantar la pesa y la distancia que recorre la pesa para llegar a su altura máxima.
El trabajo se define como la energía necesaria para mover un objeto a través de una distancia determinada, y se calcula como el producto de la fuerza aplicada y la distancia recorrida.
En este caso, la fuerza necesaria para levantar la pesa es igual a su peso, que se calcula como su masa multiplicada por la aceleración debido a la gravedad (9.8 m/s²):
peso = masa x gravedad
= 90 kg x 9.8 m/s²
= 882 N
La distancia que recorre la pesa para elevarse 75 cm (o 0.75 m) es:
distancia = 0.75 m
Por lo tanto, el trabajo realizado al elevar la pesa es:
trabajo = fuerza x distancia
= 882 N x 0.75 m
= 661.5 J
Por lo tanto, se requiere un trabajo de 661.5 J para elevar una pesa de 90 kg a una altura de 75 cm sobre el piso.
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What is the area of a 125 degree sector for a circle with a radius of 12 m, rounded to the nearest whole number
The area of the 125 degree sector for a circle with a radius of 12 m is approximately 158 square meters.
To find the area of a 125 degree sector of a circle with a radius of 12 m, we need to use the formula for the area of a sector:
Area of sector = (θ/360) x πr², where θ is the central angle of the sector, r is the radius of the circle, and π is a constant equal to approximately 3.14.
Substituting the given values, we get: Area of sector = (125/360) x π x 12² = (0.3472) x π x 144 = 158.03
Rounding to the nearest whole number, we get the area of the sector as 158 square meters. Therefore, the area of the 125 degree sector for a circle with a radius of 12 m is approximately 158 square meters.
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What is the mean absolute deviation of 10 10 9 8 10 5 6 4 8 4
The mean absolute deviation of the given data set is approximately 2.16.
To find the mean absolute deviation (MAD), we first need to calculate the mean of the data set:
Mean = (10 + 10 + 9 + 8 + 10 + 5 + 6 + 4 + 8 + 4) / 10 = 7.4
Next, we calculate the absolute deviation of each data point from the mean:
|10 - 7.4| = 2.6
|10 - 7.4| = 2.6
|9 - 7.4| = 1.6
|8 - 7.4| = 0.6
|10 - 7.4| = 2.6
|5 - 7.4| = 2.4
|6 - 7.4| = 1.4
|4 - 7.4| = 3.4
|8 - 7.4| = 0.6
|4 - 7.4| = 3.4
Then, we find the average of these absolute deviations:
MAD = (2.6 + 2.6 + 1.6 + 0.6 + 2.6 + 2.4 + 1.4 + 3.4 + 0.6 + 3.4) / 10 ≈ 2.16
Therefore, the mean absolute deviation of the given data set is approximately 2.16.
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A store has two large vats of juice
containing a total of 28 gallons of juice.
One-eighth of container A is orange juice.
Three-fourths of container B is orange
juice. Together the two containers hold 11
gallons of orange juice. Which system of
equations can be used to determine a and
b, the total amounts of juice, in gallons, in
containers A and B?
F
H
+
b = 11
a
a + b 28
a + b = 28
320
b = 28
J
+ b = 28
4
a + b = 11
a + b = 11
The system of equations can be used to determine the gallons of juice in container A and the gallon of juice in container B is A + B = 28 and A + 6B = 88
Total amount of juice in both the vats is 28
Let the first container = A
second container = B
A + B = 28
Orange juice in A = 1/8 of A
Orange juice in B = 3/4 of B
Total orange juice in container A and B = 11
(1/8)A + (3/4)B = 11
A + 6B = 88
Hence the two equations will be A + B = 28 and A + 6B = 88
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PLEASE ANSWER!!! FOR BRAINLY!!! ASAP!!
A system of linear equations is shown on the graph.
The graph shows a line that passes through negative 10 comma 10, negative 5 comma 9, and 0 comma 8. The graph also shows another line that passes through negative 8 comma 12, negative 5 comma 9, and 0 comma 4.
What is the solution to the system of equations?
A There are infinitely many solutions.
B There is no solution.
C There is one unique solution (−5, 9).
D There is one unique solution (0, 8).
Answer:
(-1/5)x + 8 = -x + 4
(4/5)x + 8 = 4
(4/5)x = -4
x = -5, so y = 9
C. There is one unique solution (-5, 9).
In a hypothesis test for a mean in one population, where you have H subscript 0 colon space mu space equals space 40 comma space H subscript A colon space mu space not equal to space 40 and the population standard deviation is sigma space equals space 12, what are the critical value(s) of the sample mean x with bar on top if your sample size is 36 and the significance level alpha = 0. 05?
Group of answer choices
Using the t-distribution table with a sample size of 36 and a significance level of 0.05, we find the critical t-value to be ±2.03 (with 34 degrees of freedom, which is n-1).
What are the critical values of the sample mean for a hypothesis test with a sample size of 36, population standard deviation of 12, significance level of 0.05, and null hypothesis of μ = 40?
To explain, we use the t-distribution to find the critical values because the population standard deviation is known. Since the alternative hypothesis is two-tailed (H_A: μ ≠ 40), we need to find two critical values.
With a sample size of 36, the degrees of freedom are 34 (n-1), so we use a t-distribution table with 34 degrees of freedom and a significance level of 0.05. From the table, we find the critical t-value to be ±2.03.
Therefore, if the calculated t-value falls outside of this range, we can reject the null hypothesis H0: μ = 40 in favor of the alternative hypothesis H_A: μ ≠ 40.
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Please answer the question with the image provided.
Based on the information on the number line, the numbers that represent the percentages are: 42 (100%), 21 (50%), 63 (150%).
How to calculate the number that equals each percentage?To calculate the number that is equivalent to each percentage we must carry out the following procedure: Rule of three. In this case we must take into account that 42 represents 100% of the people.
100% = 42 people100% = ? people100 * 42 / 100 = 42 people100% = 42 people50% = ? people50 * 42 / 100 = 21 people100% = 42 people150% = ? people150 * 42 / 100 = 63 peopleLearn more about rule of three at: https://brainly.com/question/9264846
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Helps me please What is most likely to push the price of a company's stock higher?
O A. An increase in demand for the company's stock
OB. An increase in demand for the company's products
O C. An increase in tariffs paid by the company's competitors
O D. An increase in the exchange rate for the US dollar
SUBMIT
PREVIOUS
e to search
O
RI
The most likely factor to push the price of a company's stock higher is an increase in demand for the company's stock. Option A.
A stock's price will often increase when there is greater demand than there is supply. Various things, such as good news about the company's financial performance, new product releases or innovations, positive analyst reports, or general market trends, can contribute to this increased demand.
The company's financial performance may benefit from a rise in product demand, but if investors do not view it as a key growth engine for the business, it may not necessarily transfer into a higher stock price.
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Buy-Rite Pharmacy has purchased a small auto for delivering prescriptions. The auto was purchased for $26,000 and will have a 6-year useful life and a $5,500 salvage value. Delivering prescriptions (which the pharmacy has never done before) should increase gross revenues by at least $33,500 per year. The cost of these prescriptions to the pharmacy will be about $28,000 per year. The pharmacy depreciates all assets using the straight-line method. The payback period for the auto is closest to (Ignore income taxes. ): (Round your answer to 1 decimal place. )
The payback period for the auto is approximately 8 years.
Buy-Rite Pharmacy has purchased an auto for delivering prescriptions. The auto was purchased for $26,000, and it has a useful life of 6 years with a $5,500 salvage value. By delivering prescriptions, the pharmacy aims to increase gross revenues by at least $33,500 per year. The pharmacy will incur a cost of $28,000 per year for these prescriptions.
Using the straight-line method, the annual depreciation of the auto is ($26,000 - $5,500) / 6 = $3,917. This means that the total cost of the auto over 6 years will be $26,000 - $5,500 + ($3,917 x 6) = $43,502.
To calculate the payback period, we need to determine how long it will take for the increased gross revenues to cover the cost of the auto.
The net increase in revenues will be $33,500 - $28,000 = $5,500 per year. Therefore, the payback period is $43,502 / $5,500 = 7.9 years, which is rounded to 8 years.
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The FBI wants to determine the effectiveness of their 10 Most Wanted list. To do so, they need to find out the fraction of people who appear on the list that are actually caught. Step 2 of 2 : Suppose a sample of 455 suspected criminals is drawn. Of these people, 109 were captured. Using the data, construct the 85% confidence interval for the population proportion of people who are captured after appearing on the 10 Most Wanted list. Round your answers to three decimal places
The 85% confidence interval for the population proportion of people who are captured after appearing on the 10 Most Wanted list falls between 0.194 and 0.286.
To construct the 85% confidence interval for the population proportion of people who are captured after appearing on the 10 Most Wanted list, we can use the following formula:
[tex]\hat{p} \pm z^* \sqrt{\frac{\hat{p} (1 - \hat{p})}{n}}[/tex]
where [tex]$\hat{p}$[/tex] is the sample proportion, [tex]$n$[/tex] is the sample size, and [tex]$z^*$[/tex] is the z-score corresponding to the desired level of confidence. Since we are looking for an 85% confidence interval, the z-score is 1.440.
First, we can calculate the sample proportion:
[tex]\hat{p} = \frac{109}{455} = 0.240[/tex]
Next, we can plug in the values into the formula:
[tex]$$ 0.240 \pm 1.440 \sqrt{\frac{0.240 (1 - 0.240)}{455}} $$[/tex]
Simplifying this expression, we get:
[tex]$$ 0.240 \pm 0.046 $$[/tex]
Therefore, the 85% confidence interval for the population proportion of people who are captured after appearing on the 10 Most Wanted list is [tex]$(0.194, 0.286)$[/tex].
We can interpret this interval as follows: if we were to draw many samples of size 455 from the population of people who appear on the 10 Most Wanted list, and construct a 85% confidence interval for the proportion of people who are captured based on each sample, about 85% of these intervals would contain the true population proportion.
Furthermore, we are 85% confident that the true population proportion of people who are captured after appearing on the 10 Most Wanted list falls between 0.194 and 0.286.
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A line shape like a trapezoid has an area of 337. 5ft^2 if the length of the bases are 25 fr and 20 ft then the perpendicular distance between bases would be
The perpendicular distance between the bases of a trapezoid with an area of 337.5 ft² and base lengths of 25 ft and 20 ft is 15 ft.
Area = (1/2) * (Base1 + Base2) * Height
In this case, the area is 337.5 ft², Base1 is 25 ft, and Base2 is 20 ft. We need to solve for the height, which represents the perpendicular distance between the bases.
Plugging in the known values into the formula:
337.5 = (1/2) * (25 + 20) * Height
Simplifying the expression:
337.5 = (1/2) * (45) * Height
Multiplying both sides of the equation by 2 to get rid of the fraction:
675 = 45 * Height
Dividing both sides by 45 to solve for the height:
Height = 675 / 45
Height = 15 ft
Therefore, the perpendicular distance between the bases of the trapezoid is 15 ft.
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Jamie mixes 2 parts of red paint with 3 parts of blue paint to make purple paint.
He uses 12 cans of blue paint.
How many cans of red paint does he use?
coordinate grid by equation y=4 what line would represent a row parallel to it ?
A row parallel to the line y = 4 on a coordinate grid would be represented by a line with an equation of the form y = c.
How to find a row parallel to y=4 on a coordinate grid?A coordinate grid is a two-dimensional plane consisting of a horizontal x-axis and a vertical y-axis. The point where the x and y-axes intersect is called the origin, and it has coordinates (0, 0).
An equation in the form y = c, where c is a constant, represents a horizontal line parallel to the x-axis. In this case, the equation y = 4 represents a horizontal line that intersects the y-axis at 4, as all points on the line have a y-coordinate of 4.
To find a row parallel to this line, we need to look for another line that also has a constant y-coordinate of 4. One way to represent this line is by the equation y = 4 again, since all points on this line have a y-coordinate of 4.
Alternatively, we can look for an equation in the form y = mx + b, where m is the slope of the line (which is zero for a horizontal line), and b is the y-intercept (which is 4 in this case). Thus, the equation for the row parallel to y = 4 would also be y = 4, since its slope is zero and it intersects the y-axis at y = 4, just like the line y = 4.
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If a couch measures 10ft across in real life, what would it's measurement be in the scale drawing (in)
Explain
the measurement of the couch in the scale drawing would be 15 inches.
what is scale drawing?We can precisely portray locations, areas, structures, and details in scale drawings at a scale that is either smaller or more feasible than the original.
When a drawing is said to be "to scale," it signifies that each piece is proportionate to the real or hypothetical entity; it may be smaller or larger by a specific amount.
When something is described as being "drawn to scale," we assume that it has been printed or drawn to a conventional scale that is accepted as the norm in the construction sector.
When our awareness of scale improves, we are better able to quickly recognize the spaces, zones, and proposed or existent spatial relationships when looking at a drawing at a given scale.
One metre is equivalent to one metre in the actual world. When an object is depicted at a 1:10 scale, it is 10 times smaller than it would be in real life.
You might also remark that 10 units in real life are equivalent to 1 unit in the illustration.
To determine the measurement of the couch in the scale drawing, we can use the scale factor provided:
1/4 inch = 2 feet
This means that every 1/4 inch in the drawing represents 2 feet in real life.
To find the measurement of the couch in the drawing, we need to convert its actual size to the corresponding size in the drawing using the scale factor.
First, we can convert the actual size of the couch to feet:
10 ft = 10 ft x 12 inches/ft = 120 inches
Next, we can use the scale factor to convert the actual size to the corresponding size in the drawing:
1/4 inch = 2 feet
1 inch = 8 feet (multiplying both sides by 4)
So, 120 inches in real life is equal to:
120 inches / 8 feet per inch = 15 inches in the drawing
Therefore, the measurement of the couch in the scale drawing would be 15 inches.
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Data was taken on carpooling in Tallahassee,
Florida. For each person's daily commute, the number
of people in the car was recorded. The results are
summarized in the bar graph at left. What is the
median number of people in the car?
100
80
60-
Percent of population
20
0+
2
3 4 or more
Number of people in car
Answer:34
Step-by-step explanation:
Charity can make 36 cupcake in 45 minutes. If she continues at this rate, how many cupcakes can she make in 8 hours?
a. 280 cupcakes b. 384 cupcakes c. 360 cupcakes d. 300 cupcakes
The total number of cupcakes charity can make in 8 hours is 384
The total number of cupcakes she can make in 45 minutes is 36
Cupcakes she can make in 1 minute = 36/45
Cupcakes she can make in 1 minute = 0.8
Cupcakes she can make in 8 hours
We will convert hours into minutes
1 hour = 60 min
8 hour = 8 × 60 min
8 hour = 480 min
Cupcakes she can make in 8 hours that is 480 min = 480 × 0.8
Cupcakes she can make in 8 hours = 384
Total number of cupcakes she can make is 384
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Find the volume and surface area of the composite figure. Give your answer in terms of π.
The figure shows a compound solid that consists of a hemisphere with a right cone on top of it. The radii of both the hemisphere and the right cone are equal to 6 centimeters. The slant of the right cone is equal to 8 centimeters.
I WILL GIVE BRAINLIST,
To find the volume and surface area of the composite figure, we need to first find the individual volumes and surface and the right cone, and then add them together.
The volume of a hemisphere with radius r is (2/3)πr^3, and the surface area is 2πr^2.
The volume of a right cone with radius r, height h, and slant s is (1/3)πr^2h, and the surface area is πr^2 + πrs.
In this case, the radius r and slant s are both 6 cm, and the height h of the cone can be found using the Pythagorean theorem: h = √(s^2 - r^2) = √(8^2 - 6^2) = √28 ≈ 5.29 cm.
So, the volume of the hemisphere is (2/3)π(6 cm)^3 = 72π/3 = 24π cubic cm, and the surface area is 2π(6 cm)^2 = 72π square cm.
The volume of the right cone is (1/3)π(6 cm)^2(5.29 cm) = 62.83π/3 ≈ 20.94π cubic cm, and the surface area is π(6 cm)^2 + π(6 cm)(8 cm) = 36π + 48π = 84π square cm.
Therefore, the total volume of the composite figure is 24π + 20.94π = 44.94π cubic cm, and the total surface area is 72π + 84π = 156π square cm.
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A computer can download 3 megabytes in 5 seconds. If the computer downloads data at a constant rate, what is the linear equation that represents the number of megabytes downloaded per second?
A. y = −1.67x
B. y = −0.6x
C. y = 0.6x
D. y = 1.67x
The slope of the equation is 0.6, which means that for every second, the computer downloads 0.6 megabytes of data, option C is correct.
The linear equation that represents the number of megabytes downloaded per second can be determined by dividing the total amount of data downloaded (3 MB) by the time taken to download it (5 seconds). This gives us the rate of download in megabytes per second (MB/s). Therefore, the equation is:
y = 0.6x
where y represents the number of megabytes downloaded per second and x represents the time taken to download the data. The negative slope values in the other options do not make sense, as the number of megabytes downloaded per second should be a positive value, option C is correct.
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Adam is purchasing a new television that costs $2,187. 96 after tax. He borrowed the money from his parents and must pay back the full amount plus simple interest at the rate of 3. 5%. What is the interest he will pay if he takes 2 years to pay his parents back? (Include Decimal with the cents; No Commas)
and
Adam is purchasing a new television that costs $2,187. 96 after tax. He borrowed the money from his parents and must pay back the full amount plus simple interest at the rate of 3. 5%. What is the total amount he will pay if he takes 2 years to pay his parents back? (Include Decimal with the cents; No Commas)
please
he interest he will pay if he takes 2 years to pay his parents back is $153.16. The total amount he will pay if he takes 2 years to pay his parents back is $2,341.12.
To calculate the interest Adam will pay, we need to use the simple interest formula:
Interest = Principal x Rate x Time
The principal is the amount borrowed, which is $2,187.96. The rate is 3.5% per year, or 0.035 in decimal form. The time is 2 years.
Interest = $2,187.96 x 0.035 x 2 = $153.16
Therefore, Adam will pay $153.16 in interest if he takes 2 years to pay his parents back.
To calculate the total amount he will pay, we need to add the interest to the principal:
Total amount = Principal + Interest
Total amount = $2,187.96 + $153.16 = $2,341.12
Therefore, Adam will pay a total of $2,341.12 if he takes 2 years to pay his parents back.
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A forester is 50 m from the base of a tree and measures the angle between the ground and the top of the tree. If the angle is 768, fi nd the height of the tree. Round your answer to the nearest meter
The height of the tree is approximately equal to the tangent of 768 radians multiplied by 50 meters, rounded to the nearest meter.
How to determine the height of a tree using trigonometry and angle measurement?To find the height of the tree, we can use trigonometry. Let's assume that the height of the tree is represented by the variable "h."
In a right triangle formed by the forester, the base of the tree, and the top of the tree, the tangent of the angle is equal to the opposite side (height of the tree, h) divided by the adjacent side (distance from the base of the tree, 50 m).
Using the tangent function, we can write:
tan(angle) = [tex]\frac{h }{ 50}[/tex]
We can rearrange this equation to solve for h:
h = tan(angle) * 50
Now we can substitute the given angle into the equation and calculate the height:
h = tan(768) * 50
Calculating this in degrees might result in an error because the tangent function expects the angle to be in radians.
Therefore, we need to convert the angle to radians before evaluating the tangent.
There are 180 degrees in pi radians, so we can convert the angle as follows:
angle_radians = [tex]\frac{768 \* \pi }{ 180}[/tex]
Substituting this value into the equation:
h = tan(angle_radians) * 50
Now we can calculate the height using a calculator:
h ≈ [tex]tan(\frac{768 \pi }{ 180}) 50[/tex]
After evaluating this expression, we get the height of the tree. Rounding the answer to the nearest meter will give us the final result.
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A manufacturer makes sneakers in six colors, available in four styles, with three choices of
fabrics. how many unique types of sneakers does the manufacturer make?
To find the number of unique types of sneakers, we need to multiply the number of options for each characteristic:
Number of colors: 6
Number of styles: 4
Number of fabrics: 3
Total number of unique types of sneakers = 6 x 4 x 3 = 72
Therefore, the manufacturer makes 72 unique types of sneakers.
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Question
The figure is made up of a rectangle, 2 right triangles and a 3rd triangle.
What is the area of the figure?
Responses
46 in2
136 in2
34 in, 2
52 in2
The area of the polygon composed of rectangles and triangle is 52 in²
What is area?Area is the amount of space occupied by a two dimensional shape or object.
For the first right triangle:
base = 2 in, height = 6 in
Area of first right triangle = 1/2 * base * height = 0.5 * 2 in * 6 in = 6 in²
For the second right triangle:
base = 2 in, height = 6 in
Area of second right triangle = 1/2 * base * height = 0.5 * 2 in * 6 in = 6 in²
For the triangle:
base = (2 + 4 + 2) = 8 in, height = 4 in
Area of triangle = 1/2 * base * height = 0.5 * 8 in * 4 in = 16 in²
For the rectangle:
length = 4 in, width = 6 in
Area of rectangle = length * width = 4 in * 6 in = 24 in²
Area of polygon = 6 + 6 + 16 + 24 = 52 in²
The area of the polygon is 52 in²
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Find the values of U and d for an arithmetic sequence with U20 = 100 and U25 = 115.
The values of U and d for an arithmetic sequence with U20 = 100 and U25 = 115 is U = 43 and d = 3.
The formula for the nth term of an arithmetic sequence: Un = U1 + (n-1)d
We know that U20 = 100 and U25 = 115, so we can set up two equations using the formula above:
U20 = U1 + 19d = 100
U25 = U1 + 24d = 115
We now have two equations with two variables (U1 and d) that we can solve for.
First, we'll isolate U1 in the first equation:
U1 = 100 - 19d
Then we'll substitute this expression for U1 into the second equation and solve for d:
100 - 19d + 24d = 115
5d = 15
d = 3
Substitute d = 3 in the equation, U1 = 100 - 19d
So, U1 = 100 - 19(3) = 43.
Therefore, the values of U and d for the arithmetic sequence are U= 43 and d = 3.
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The town of Madison has a population of
25
,
000
25,00025, comma, 000. The population is increasing by a factor of
1.12
1.121, point, 12 each year.
Write a function that gives the population
P
(
t
)
P(t)P, left parenthesis, t, right parenthesis in Madison
t
tt years from now.
Do not use commas in your answer.
The function for the population of Madison t years from now is:[tex]p(t) = 25000 (1.12)^{t}[/tex]
To write a function that gives the population P(t) in Madison t years from now, considering the town has an initial population of 25,000 and an annual increase factor of 1.12, you can use the formula:
[tex]p(t) = P_{0} (1 + r)^{t}[/tex]
Where:
- P(t) is the population at time t
- P_0 is the initial population (25,000)
- r is the annual increase factor (1.12 - 1 = 0.12)
- t is the number of years
So, the function for the population of Madison t years from now is:
[tex]p(t) = 25000 (1.12)^{t}[/tex]
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Which equation has a focus at (–6, 12) and directrix of x = –12?
1. ) ( y - 12)^2 = 1/12 ( x + 9 )
2. ) ( y - 12 )^2 = -1/12 ( x + 9 )
3. ) ( y - 12)^2 = 12 ( x+9 )
4. ) ( y - 12)62 = -12 (x + 9 )
Answer: C
None of the given options have a focus at (-6, 12) and directrix of x = -12,so none of the option is correct.
To find the equation with a focus at (-6, 12) and directrix of x = -12, we can use the general equation for a parabola with a vertical axis of symmetry:
(y - k)^2 = 4p(x - h)
where (h, k) is the focus and x = h - p is the directrix.
Given the focus (-6, 12) and directrix x = -12, we can determine the value of p:
p = h - (-12) = -6 - (-12) = 6
Now, we can plug in the values of h, k, and p into the equation:
(y - 12)^2 = 4(6)(x + 6)
Simplify the equation:
(y - 12)^2 = 24(x + 6)
Now, let's compare this equation to the given options:
1. (y - 12)^2 = 1/12 (x + 9)
2. (y - 12)^2 = -1/12 (x + 9)
3. (y - 12)^2 = 12 (x + 9)
4. (y - 12)^2 = -12 (x + 9)
None of the given options match the equation we found. Therefore, none of the given options have a focus at (-6, 12) and directrix of x = -12
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Dig deeper! a police dog spends of his workday in a police car, of his workday in public, and the rest of his workday
at the police station. what fraction of the dog's day is spent at the police station?
fraction of workday
The police dog spends 1/6 of its workday at the police station.
To find the fraction of the police dog's workday spent at the police station, we need to add up the fractions of time spent in each location and subtract them from 1, since the dog spends the rest of the day at the police station.
Fraction of time spent in police car = [tex]1/3[/tex]
Fraction of time spent in public = [tex]1/2[/tex]
To add these fractions, we need to find a common denominator:
[tex]1/3 = 2/6\\1/2 = 3/6[/tex]
So, the fraction of the dog's day spent at the police station is:
[tex]1 - (2/6 + 3/6) = 1 - 5/6[/tex]
= [tex]1/6[/tex]
Therefore, the police dog spends 1/6 of its workday at the police station.
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1. A company is testing a new energy drink. Volunteers are asked to rate their energy one hour
after consuming a beverage. Unknown to them, some volunteers are given the real energy
drink and some are given a placebo-a drink that looks and tastes the same, but does not have
the energy-producing ingredients. Show your work using the following list of random digits to
assign each participant listed either the real drink or the placebo.
69429 86140 11625 87049 23167
Volunteer
Abby
Barry
87524 24575 87254 97801 82231
Callie
Dion
Ernie
Falco
Garrett
Hallie
Indigo
Jaylene
Real or Placebo
2. The local water authority has received complaints of high levels of iron in the drinking water.
They decide to randomly select 20 houses from each subdivision of 100 houses to visit and test
their water. Describe how to use random numbers to select the 20 houses in each division.
3. A couple is willing to have as many children as necessary to have two girls.
a) Describe a simulation that can be performed to estimate the average number of children
required to have two girls.
What is the volume of the following rectangular prism?
2 units and 7 1/3 units
The volume of a rectangular prism is calculated by multiplying the length, width, and height. In this case, we are given the length and width, but not the height. So, we cannot calculate the exact volume without knowing the height.
To find the volume of a rectangular prism, we need to multiply its length, width, and height.
Given:
Length = 2 units
Width = 7 1/3 units
To calculate the volume, we first need to convert the mixed fraction to an improper fraction.
7 1/3 = (7 * 3 + 1) / 3 = 22/3 units.
Now, we can calculate the volume:
Volume = Length * Width * Height
= 2 units * (22/3 units) * Height.
Since the height is not provided, we cannot calculate the exact volume without that information. However, if you provide the height of the rectangular prism, I can help you find the volume by substituting the value into the formula.
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The table shows the amount of time, in minutes, it takes to walk a given distance, in miles, along each path. complete the table to show the average walking rate, in miles per hour, for each path. path distance (mi) time (min) walking rate (mph) a 0.5 12 b 1.5 45 с 0.75 15
The average walking rate for Path A is 2.5 mph, path B's is 2 mph and path C's is 3 mph.
Average walking rate = distance/time
for path A = 0.5/12 = 0.0416 mpm
To convert miles per meter into miles per hour it we will multiply the equation by 60 because 1 hour has 60 min
so, for path A = 0.0416 × 60 = 2.5 mph
Similarly , for path B = (1.5/45) × 60 = 2 mph
For path C = (0.75/15)×60 = 3 mph
Table to show the average walking rate
Path Distance(mi) Time(min) Walking rate (mph)
A 0.5 12 2.5
B 1.5 45 2
C 0.75 15 3
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