The area of the first triangle is 0 square feet.
To find the area of the first triangle with the given side lengths of 1 ft, 3 ft, and 4 ft, you can use Heron's formula.
Calculate the semi-perimeter (s) of the triangle:
s = (a + b + c) / 2
where a, b, and c are the side lengths of the triangle.
s = (1 + 3 + 4) / 2 = 8 / 2 = 4 ft
Apply Heron's formula to find the area (A) of the triangle:
A = √(s * (s - a) * (s - b) * (s - c))
A = √(4 * (4 - 1) * (4 - 3) * (4 - 4))
A = √(4 * 3 * 1 * 0)
A = √0 = 0
The area of the first triangle is 0 square feet. This means that the given side lengths do not form a valid triangle, as two sides' lengths (1 ft and 3 ft) do not add up to be greater than the length of the third side (4 ft).
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Bailey has a sheet of plywood with four right angles. She saws off one of the angles and turns the plywood one-half turn clockwise
How many right angles are there on the plywood now?
Enter the correct answer in the box.
Answer:For each figure, which pair of angles appears congruent? How could you check?
Figure 1
3 angles. Angle A B C opens to the right, angles D E F and G H L open up.
Figure 2
3 angles. Angles M Z Y and P B K open up, angle R S L opens to the right.
Figure 3
Identical circles. Circle V with central angle GVD opens to the right, circle J with central angle LJX opens to the left and circle N with central angle CNE opens up.
Figure 4
A figure of 3 circles. H. B. E.
Step-by-step explanation:
On a coordinate plane, 2 triangles are shown. Triangle D E F has points (6, 4), (5, 8) and (1, 2). Triangle R S U has points (negative 2, 4), (negative 3, 0), and (2, negative 2).
Triangle DEF is reflected over the y-axis, and then translated down 4 units and right 3 units. Which congruency statement describes the figures?
ΔDEF ≅ ΔSUR
ΔDEF ≅ ΔSRU
ΔDEF ≅ ΔRSU
ΔDEF ≅ ΔRUS
The congruency statement that describes the figures is:
ΔDEF ≅ ΔRSU
To answer your question, let's first find the image of triangle DEF after reflecting over the y-axis and then translating down 4 units and right 3 units.
1. Reflect ΔDEF over the y-axis:
D'(−6, 4), E'(−5, 8), F'(−1, 2)
2. Translate ΔD'E'F' down 4 units and right 3 units:
D''(−3, 0), E''(−2, 4), F''(2, −2)
Now, we have ΔD''E''F'' with points (−3, 0), (−2, 4), and (2, −2). Comparing this to ΔRSU with points (−2, 4), (−3, 0), and (2, −2), we can see that:
ΔD''E''F'' ≅ ΔRSU
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Answer:
ΔDEF ≅ ΔRSU
Step-by-step explanation:
Find the area of the shaded region. Provide an answer accurate to the
nearest tenth.
18 ft
10 ft
Thus, the area of the shaded part is found to be 50 sq. ft.
Define about area of the shaded region:The shaded region's area is most frequently found in common geometry problems. Such problems always have a minimum of two forms, and you must determine the area for each shape as well as the darkened zone by deducting the smaller shape's area from the larger.
Rectangle's area :
Area has two dimensions: length and width. Square units like square inches, square feet, or square metres are used to measure area.
Multiply its length by the width to determine the area of a rectangle. A is equal to L * W, where * denotes multiplication, L is the length, W is the breadth, and A is the area.Length of shaded part = 5 ft
width of shaded part = 10 ft
Area = 5*10
Area = 50 sq. ft
Thus, the area of the shaded part is found to be 50 sq. ft.
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Correct question:
For the given figure find the area of the shaded region.
Length BC = 18 ft
Length CD = 10 ft
A set of data is represented in the stem plot below.
Key: 315= 35
Part A: Find the mean of the data. Show each step of work. (2 points)
Part B: Find the median of the data. Explain how you determined the median. (2 points)
Part C: Find the mode of the data. Explain how you determined the mode. (2 points)
Part A: The mean of the data is approximately 5.79. Part B: The median is 6.5. Part C: The mode of the data is the set of values {5, 9}.
Describe Mean?In statistics, mean is a measure of central tendency that represents the average of a set of numbers. The mean is calculated by adding up all the values in a data set and dividing by the total number of values.
The formula for calculating the mean of a set of n numbers is:
mean = (x1 + x2 + ... + xn) / n
where x1, x2, ..., xn are the individual values in the data set.
Part A:
To find the mean of the data, we need to add up all the values and divide by the total number of values:
3 + 4 + 4 + 5 + 5 + 5 + 6 + 7 + 7 + 8 + 8 + 9 + 9 + 9 = 81
There are 14 values in the data set, so we divide the sum by 14 to get:
81/14 ≈ 5.79
Therefore, the mean of the data is approximately 5.79.
Part B:
To find the median of the data, we need to arrange the values in order from lowest to highest:
3, 4, 4, 5, 5, 5, 6, 7, 7, 8, 8, 9, 9, 9
There are 14 values, so the median is the middle value. Since there is an even number of values, we need to find the average of the two middle values, which are 6 and 7. Thus, the median is:
(6 + 7)/2 = 6.5
Therefore, the median of the data is 6.5.
Part C:
To find the mode of the data, we need to look for the value(s) that occur most frequently. From the stem plot, we can see that the values 5 and 9 occur three times each, while all other values occur either once or twice. Therefore, the mode of the data is:
5 and 9
Thus, the mode of the data is the set of values {5, 9}.
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Solve the trigonometric equation in the interval [0, 2π). give the exact value, if possible; otherwise, round your answer to two decimal places. (enter your answers as a comma-separated list.) 2 cos2(x) + cos(2x) = 0 x =
To solve the trigonometric equation 2cos^2(x) + cos(2x) = 0 in the interval [0, 2π), we will first use the double angle formula for cos(2x) and then solve for x. Recall that cos(2x) = 2cos^2(x) - 1.
Substitute this into the equation: 2cos^2(x) + (2cos^2(x) - 1) = 0 Combine the terms: 4cos^2(x) - 1 = 0 Now, isolate cos^2(x): cos^2(x) = 1/4 Take the square root of both sides: cos(x) = ±√(1/4) = ±1/2 Now, find the values of x in the interval [0, 2π) that satisfy the equation: For cos(x) = 1/2: x = π/3, 5π/3 For cos(x) = -1/2: x = 2π/3, 4π/3 Combine the answers as a comma-separated list: x = π/3, 2π/3, 4π/3, 5π/3
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A number 5 times as big as M
Answer:
Step-by-step explanation:
If we let M be a number, then 5 times as big as M would be 5M. Not that hard :/
Let a,b,c and d be distinct real numbers. Show that the equation (x-b)(x-c) (x-d) + (x-a)(x-c)(x - d) + (x-a) (x-b)(x-d) + (x - a)(x-b)(x-c) has exactly 3 distinct roul solutions (Hint: Let p(x)= (x-a)(x-b)(x-c)(x-d). Then p(x) = 0 has how many distinct real solutions? Then use logarithmic differentiation to show that p'(x) is given by the expression on the left hand side of (1). Now, apply Rolle's theorem. )
There exists at least one c in the open interval (a, b) such that f'(c) = 0.
There are 3 distinct points where p'(x) = 0, which corresponds to the 3 distinct real solutions of the given equation.
To prove that the given equation has exactly 3 distinct real solutions, let's follow the steps mentioned in the question.
First, consider the polynomial p(x) = (x-a)(x-b)(x-c)(x-d). Since a, b, c, and d are distinct real numbers, p(x) has 4 distinct real roots, namely a, b, c, and d.
Now, let's find the derivative p'(x) using logarithmic differentiation. Taking the natural logarithm of both sides, we have:
[tex]ln(p(x)) = ln((x-a)(x-b)(x-c)(x-d))[/tex]
Differentiating both sides with respect to x, we get:
[tex]p'(x)/p(x) = 1/(x-a) + 1/(x-b) + 1/(x-c) + 1/(x-d)[/tex]
Multiplying both sides by p(x) and simplifying, we have:
[tex]p'(x) = (x-b)(x-c)(x-d) + (x-a)(x-c)(x-d) + (x-a)(x-b)(x-d) + (x-a)(x-b)(x-c)[/tex]
Now, we apply Rolle's Theorem, which states that if a function is continuous on the closed interval [a, b], differentiable on the open interval (a, b), and f(a) = f(b), then there exists at least one c in the open interval (a, b) such that f'(c) = 0.
Since p(x) has 4 distinct real roots, there must be 3 intervals between these roots where the function p(x) satisfies the conditions of Rolle's Theorem. Therefore, there are 3 distinct points where p'(x) = 0, which corresponds to the 3 distinct real solutions of the given equation.
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What is the percent of change in 6 yards to 36 yards - - - 7th-grade math show the work
Answer:
Step-by-step explanation:
Rounded percent of change = 500.0% Therefore, the percent of change is an increase of 500.0%.
I think sorry if I’m wrong
Sebastian is 12 34 years old. camden is 1 38 years older than sebastian and jane is 1 15 years older than camden. how old is jane?
Jane is 14 years old, if Sebastian is 12 34 years old. Camden is 1 38 years older than Sebastian and Jane is 1 15 years older than Camden.
To find out how old Jane is, we will first determine the ages of Sebastian and Camden, then add the additional years to find Jane's age.
Sebastian is 12 34 years old, but the correct age should be 12 years old (ignoring the typo).
Camden is 1 38 years older than Sebastian, which should be correctly written as 1 year older. So, Camden's age is 12 (Sebastian's age) + 1 = 13 years old.
Jane is 1 15 years older than Camden, which should be correctly written as 1 year older. Therefore, Jane's age is 13 (Camden's age) + 1 = 14 years old.
So, Jane is 14 years old.
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Find the length of the radius r
Step-by-step explanation:
Use Pythagorean theorem for right triangles
c^2 = a^2 + b^2 where c = hypotenuse and a and b are the legs
8.6^2 = 5^2 + r^2
8.6^2 - 5^2 = r^2
r = ~ 7 units
Natalie saves money in her piggy bank. Maria saves money in a savings account at a bank.
Which statement about the savings plans is true?
Responses
Natalie uses a safer way to save money because she can protect her piggy bank.
Maria's way of saving money allows her to earn interest and make her money grow.
Maria will have less money because she must pay sales tax on her money.
Natalie's method of saving is better because Maria must pay interest on her money.
In a case whereby Natalie saves money in her piggy bank. Maria saves money in a savings account at a bank the statement about the savings plans that is true is B.Maria's way of saving money allows her to earn interest and make her money grow.
What is savings account ?An efficient approach to keep your money safe and earning interest is in a savings account. You can keep your savings in a liquid state with a savings account, which allows you to access your money anytime you need to, while also creating some breathing room between your savings and your daily spending requirements.
Because of their safety, liquidity, and potential for collecting interest, savings accounts are a suitable way to put money set aside for future use. These accounts are perfect for saving for short-term objectives like a trip or home repair or for your emergency fund.
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Liang wants to form a chess club. His principal says that he can do that if Liang can find six players, including himself. How would you conduct a simulated model that estimates the probability that Liang will find at least five other players to join the club if he asks eight players who have a 70% chance of agreeing to join the club? Suggest a simulation model for Liang by describing how you would do the following parts
To conduct a simulated model that estimates the probability that Liang will find at least five other players to join the chess club if he asks eight players who have a 70% chance of agreeing to join.
We can use the following steps:
1. Define the variables:
- n: the number of trials (i.e., the number of times Liang asks eight players to join)
- p: the probability of success (i.e., the probability that a player agrees to join the club, which is 0.7)
- k: the number of successes needed (i.e., the number of players, excluding Liang, that he needs to find to form the club, which is 5)
- success: a counter to keep track of the number of successful trials (i.e., the number of times Liang finds at least five players to join)
2. Set the initial value of the success counter to 0.
3. Start a loop that runs n times. In each iteration of the loop:
- Generate a random number between 0 and 1 using a random number generator.
- If the random number is less than or equal to p, increment a "success count" variable.
- If the success count variable reaches k, break out of the loop.
4. After the loop finishes, divide the success count variable by n to get the simulated probability that Liang will find at least five players to join the chess club.
5. Repeat the simulation multiple times (e.g., 1000 times) to obtain a distribution of simulated probabilities.
6. Calculate the mean and standard deviation of the simulated probabilities to estimate the most likely probability that Liang will find at least five players to join the chess club, and the range of probabilities that he is likely to obtain.
Note: This simulation model assumes that each player's decision to join the club is independent of the other players' decisions and that the probability of success (i.e., agreeing to join) is the same for each player. These assumptions may not always be accurate in practice.
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Please help solve
Use Mean value theorem to prove √ 6a+3
1. Using methods other than the Mean Value Theorem will yield no marks
The Mean Value Theorem can be used to prove that the square root of 6a+31 lies between two values, where one value is equal to the function evaluated at a divided by the square root of 6, and the other value is equal to the function evaluated at a plus one divided by the square root of 6.
Let f(x) = √(6x + 31) and choose any value of a such that a > -31/6.
By the Mean Value Theorem, there exists some c in (a, a+1) such that:
f(a+1) - f(a) = f'(c)
where f'(c) is the derivative of f(x) evaluated at c.
We have:
f'(x) = 3/√(6x+31)
Thus, we can write:
f(a+1) - f(a) = (3/√(6c+31)) * (a+1 - a)
Simplifying, we get:
f(a+1) - f(a) = 3/√(6c+31)
Since a < c < a+1, we have:
a < c
√(6a+31) < √(6c+31)
√(6a+31) < (3/√(6c+31)) * √(6c+31)
√(6a+31) < f(a+1) - f(a)
Therefore, we can write:
f(a) < √(6a+31) < f(a+1)
f(a) = √(6a + 31)/√6
f(a+1) = √(6(a+1) + 31)/√6
Substituting these values, we get:
(√(6a + 31))/√6 < √(6a+31) < (√(6(a+1) + 31))/√6
Simplifying, we get:
√(6a + 31)/√6 < √(6a+31) < √(6a + 37)/√6
Hence, we have shown that the square root of 6a+31 lies between two values, where one value is equal to the function evaluated at a divided by the square root of 6, and the other value is equal to the function evaluated at a plus one divided by the square root of 6.
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Antonia read an article that said 26% of Americans can speak more than one language. She was curious if
this figure was higher in her city, so she tested H, :p=0. 26 vs. H, :p > 0. 26, where p represents the
proportion of people in her city that can speak more than one language.
Antonia took a sample of 120 people in her city found that 35% of those sampled could speak more than
one language. The test statistic for these results was z ~ 2. 25, and the corresponding P-value was
approximately 0. 1. Assume that the conditions for inference were met.
Is there sufficient evidence at the a= 0. 05 level to conclude that the proportion of people in her city
that can speak more than one language is greater than 26%?
There is not sufficient evidence at the α=0.05 level to conclude that the proportion of people in Antonia's city that can speak more than one language is greater than 26%.
Here's a step-by-step explanation:
1. Identify the null hypothesis (H₀) and the alternative hypothesis (Hₐ): H₀: p = 0.26, Hₐ: p > 0.26.
2. Determine the significance level (α): α = 0.05.
3. Calculate the test statistic (z): In this case, z ≈ 2.25.
4. Determine the P-value: The P-value is given as approximately 0.1.
5. Compare the P-value to the significance level: If the P-value is less than or equal to the significance level (α), reject the null hypothesis. In this case, 0.1 > 0.05, so we do not reject the null hypothesis.
Based on the information provided, there is not sufficient evidence at the α=0.05 level to conclude that the proportion of people in Antonia's city that can speak more than one language is greater than 26%.
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A student at a local high school claimed that three-
quarters of 17-year-old students in her high school had
their driver's licenses. To test this claim, a friend of hers
sent an email survey to 45 of the 17-year-olds in her
school, and 34 of those students had their driver's
license. The computer output shows the significance test
and a 95% confidence interval based on the survey data.
Test and Cl for One Proportion
Test of p = 0. 75 vs p +0. 75
Sample X N Sample p 95% CI Z-Value P-Value
1
34 45 0. 755556 (0. 6300, 0. 086 0. 9315
0. 8811)
Based on the computer output, is there convincing
evidence that p, the true proportion of 17-year olds at this
high school with driver's licenses, is not 0. 75?
O No, the P-value of 0. 9315 is very large.
Yes, the P-value of 0. 9315 is very large.
O Yes, the 95% confidence interval contains 0. 75.
No, the incorrect significance test was performed.
The alternative hypothesis should be p > 0. 75.
No, the incorrect significance test was performed.
The alternative hypothesis should be p<0. 75.
No, there is not convincing evidence that p, the true proportion of 17-year-olds at this high school with driver's licenses, is not 0.75.
This is because the P-value of 0.9315 is very large, and the 95% confidence interval contains 0.75 (0.6300, 0.8811). This means that there is not enough evidence to reject the null hypothesis that the true proportion of 17-year olds with driver's licenses is 0.75. The 95% confidence interval also supports this, as it includes 0.75. Therefore, there is no convincing evidence to suggest that the student's claim is incorrect.
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Be Precise The base of a triangle is 2 ft. The
height of the triangle is 15 in. What is the area
of the triangle in square inches?
Thus, the area of triangle for the given values of height and base is found as: 180 sq. in.
Explain about the conversion units:A number of steps are involved in the Unit of Conversion process, which involves multiplying or dividing by a numerical factor. There are numerous ways to measure things like weight, separation, and temperature.
Unit conversion is the process of changing the unit of measurement for a comparable quantity by multiplying or dividing by conversion factors.
Scientific notation is used to express the units, which are then translated into numerical values in accordance with the amounts.
Given data:
base of triangle b = 2 ft.Height h = 15 in.We know that,
1 foot = 12 in.
2 feet = 12*2 = 24 in.
Area of triangle = 1/2 * b * h
Area of triangle = 1/2 * 24 * 15
Area of triangle = 12* 15
Area of triangle = 180 sq. in
Thus, the area of triangle for the given values of height and base is found as: 180 sq. in.
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In a recent election 59% of people supported re-electing the incumbent. Suppose a poll is done of 1230 people. If we used the normal as an approximation to the binomial, what would the mean and standard deviation be? Please show formulas used in excel
The mean is 725.7 and the standard deviation is 13.55.
To find the mean and standard deviation using the normal approximation to the binomial, we will use the following formulas in Excel:
Mean = np
Standard Deviation = sqrt(np(1-p))
Where n = sample size, p = proportion of success, and sqrt = square root.
Using the information given in the question, we can plug in the values:
n = 1230
p = 0.59
Mean = np = 1230*0.59 = 725.7
Standard Deviation = sqrt(np(1-p)) = sqrt(1230*0.59*(1-0.59)) = 13.55
Therefore, the mean is 725.7 and the standard deviation is 13.55.
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There are 7 purple flowers, 9 yellow flowers, and 12 pink flowers in a bouquet. You choose a flower to give to a
friend, then choose another flower for yourself. Is this an independent or dependent event? Explain how you
know.
Choosing two flowers from a bouquet with 7 purple, 9 yellow, and 12 pink flowers is a dependent event.
This is a dependent event. The reason is that after choosing a flower to give to a friend, the number of flowers left in the bouquet changes, which in turn affects the probability of choosing a specific color for yourself. Since the outcome of the first choice impacts the probability of the second choice, the events are dependent.
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Can someone please help me ASAP? It’s due tomorrow. Show work please
The number of possible outcomes of the compound event of selecting a card, spinning the spinner, and tossing a coin is B. 72 outcomes.
How to find the number of possible outcomes ?To determine the number of possible outcomes for the compound event, we need to multiply the number of outcomes for each individual event.
There are 12 cards labeled 1 through 12, so there are 12 possible outcomes for selecting a card. The spinner is divided into three equal-sized portions, so there are 3 possible outcomes for spinning the spinner. There are 2 possible outcomes for tossing a coin (heads or tails).
the total number of possible outcomes for the compound event:
12 (selecting a card) x 3 (spinning the spinner) x 2 (tossing a coin) = 72
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Solve for x.
Round to the nearest tenth.
The measure of the angle x in the circle is 65 degrees
Solving for x in the circleFrom the question, we have the following parameters that can be used in our computation:
The circle
On the circle, we have the angle at the vertex of the triangle to be
Angle = 100/2
Angle = 50
The sum of angles in a triangle is 180
So, we have
x + x + 50 = 180
Evaluate the like terms,
2x = 130
So, we have
x = 65
Hence, the angle is 65 degrees
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A. The mean selling price (in $ thousands) of the homes was computed earlier to be $357. 0, with a standard deviation of $160. 7. Use the normal distribution to estimate the percentage of homes selling for more than $500. 0. Compare this to the actual results. Is price normally distributed? Try another test. If price is normally distributed, how many homes should have a price greater than the mean? Compare this to the actual number of homes. Construct a frequency distribution of price. What do you observe?
b. The mean days on the market is 30 with a standard deviation of 10 days. Use the normal distribution to estimate the number of homes on the market more than 24 days. Compare this to the actual results. Try another test. If days on the market is normally distributed, how many homes should be on the market more than the mean number of days? Compare this to the actual number of homes. Does the normal distribution yield a good approximation of the actual results? Create a frequency distribution of days on the market. What do you observe?
a) The mean is the midpoint of the distribution, the percentage of homes with a price greater than the mean is 19.7%.
b) The percentage of homes on the market for more than the mean number of days is 72.1%.
a) Firstly, the mean selling price of homes is $357.0 thousand, with a standard deviation of $160.7 thousand. To estimate the percentage of homes selling for more than $500.0 thousand, we can use the normal distribution. This assumes that the distribution of home prices is approximately normal. Using the standard normal distribution table, we can find the z-score for a price of $500.0 thousand.
z = (500.0 - 357.0) / 160.7 = 0.88
Using the z-score, we find that the percentage of homes selling for more than $500.0 thousand is approximately 19.7%.
b) Moving on to the days a home spends on the market, the mean is 30 days and the standard deviation is 10 days. To estimate the number of homes on the market for more than 24 days, we can again use the normal distribution. Assuming that the distribution of days on the market is approximately normal, we can find the z-score for 24 days as:
z = (24 - 30) / 10 = -0.6
Using the z-score, we find that the percentage of homes on the market for more than 24 days is approximately 72.1%.
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the battery life of the iphone has an approximately normal distribution with a mean of 10 hours and a standard deviation of 2 hours. if you randomly select an iphone, what is the probability that the battery will last more than 10 hours?
If you randomly select an iphone, The probability that the battery will last more than 10 hours is 0.5000.
Population mean, µ = 10
Population standard deviation, σ = 2
The likelihood that the battery will survive more than 10 hours is equal to
[tex]= P( X > 10)\\= P( (X-\mu)/\sigma > (10 - 10)/2)\\= P( z > 0)\\= 1- P( z < 0)\\[/tex]
Using excel function:
= 1- NORM.S.DIST(0, TRUE)
= 0.5000
The normal distribution, also known as the Gaussian distribution, is a continuous probability distribution that describes a large class of phenomena observed in nature, social sciences, and engineering. It is often called the bell curve because of its characteristic shape, which is symmetric and bell-shaped.
The mean and the standard deviation are the two factors that define the normal distribution. The mean is the center of the distribution, and the standard deviation measures how much the data varies from the mean. The normal distribution has several important properties, including that approximately 68% of the data falls within one standard deviation of the mean, 95% falls within two standard deviations, and 99.7% falls within three standard deviations.
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Find the number(s)
b
such that the average value of
f(x)=6x 2
−38x+40
on the interval
[0,b]
is equal to 16 . Select the correct method. Set
b
1
f(3)=16
and solve for
b
Set
f(b)=16
and solve for
b
Set
∫ 0
b
f(x)dx=16
and solve for
b
Set
b
1
∫ 0
b
f(x)dx=16
and solve for
b
b=
Use a comma to separate the answers as needed.
The value(s) of b that satisfies the given condition is/are 0.506 and 5.327.
How to find the average value of a given function over the interval?We can use the method of setting the integral of f(x) over [0,b] equal to 16 and solving for b.
[tex]\begin{equation}\int 0 b f(x) d x=16\end{equation}[/tex]
Substituting [tex]f(x) = 6x^2 - 38x + 40[/tex], we get:
[tex]\begin{equation}\int 0 b\left(6 x^{\wedge} 2-38 x+40\right) d x=16\end{equation}[/tex]
Integrating with respect to x, we get:
[tex][2x^3 - 19x^2 + 40x]0b = 16[/tex]
Substituting b and simplifying, we get:
[tex]2b^3 - 19b^2 + 40b - 16 = 0[/tex]
Using numerical methods or polynomial factorization, we can find that the solutions to this equation are approximately 0.506 and 5.327.
Therefore, the value(s) of b that satisfies the given condition is/are 0.506 and 5.327.
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A school wants to rent out a laser tag arena the table shows the cost of renting the arena for different numbers of hours suppose the arena charges a constant hourly rate fill in the missing value in the table
hours _______ 5 9 -___________
cost (in dollars ) 500 1,250 __________ 3,500
The constant hourly rate using the given data points is $100 per hour.
To calculate the constant hourly rate, we can use the given data points. For example, let's use the 5-hour rental for $500:
Hourly rate = Total cost / Number of hours
Hourly rate = $500 / 5 hours
Hourly rate = $100 per hour
Now, we can use this hourly rate to find the cost for the missing hour value in the table:
Cost = Hourly rate × Number of hours
Cost = $100 per hour × 9 hours
Cost = $900
So, the table will look like this:
Hours: _______ 5 | 9 | _______
Cost (in dollars): 500 | 1,250 | 3,500
Now we can calculate the missing hours for the $3,500 cost:
Number of hours = Total cost / Hourly rate
Number of hours = $3,500 / $100 per hour
Number of hours = 35 hours
Now, the completed table is:
Hours: _______ 5 | 9 | 35
Cost (in dollars): 500 | 1,250 | 3,500
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Assume that demand equation is given by q=6000-100p. Find the marginal revenue for the given production levels (values of q). (Hint: Solve the demand equation for p and use R(q)=qp)
a). 1000 units
The marginal revenue at 1000 units is ____. (simplify your answer)
b). 3000 units
The marginal revenue at 3000 units is ____. (simplify your answer)
c). 6000 units
The marginal revenue at 6000 units is ____. (simplify your answer)
The marginal revenue at 1000 units is 40, at 3000 units is 0, and at 6000 units is -60.
Find the marginal revenue?
To find the marginal revenue for the given production levels, we first need to solve the demand equation for p and then derive the revenue function R(q).
Solve the demand equation for p.
q = 6000 - 100p
100p = 6000 - q
p = (6000 - q) / 100
Find the revenue function R(q) using R(q) = qp.
R(q) = q * ((6000 - q) / 100)
Derive the marginal revenue function MR(q) by taking the derivative of R(q) with respect to q.
MR(q) = dR(q)/dq = d(q * (6000 - q) / 100)/dq
Using the product rule:
MR(q) = (1 * (6000 - q) - q * 1) / 100
MR(q) = (6000 - 2q) / 100
Now, we can plug in the given production levels to find the marginal revenue at each level.
The marginal revenue at 1000 units is:
MR(1000) = (6000 - 2 * 1000) / 100 = (6000 - 2000) / 100 = 4000 / 100 = 40.
The marginal revenue at 3000 units is:
MR(3000) = (6000 - 2 * 3000) / 100 = (6000 - 6000) / 100 = 0 / 100 = 0.
The marginal revenue at 6000 units is:
MR(6000) = (6000 - 2 * 6000) / 100 = (6000 - 12000) / 100 = -6000 / 100 = -60.
So, the marginal revenue at 1000 units is 40, at 3000 units is 0, and at 6000 units is -60.
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What is the area of the trapezoid?
Answer:
33
Step-by-step explanation:
Pythagorean theorem:
6,5^ - 2.5^2= 36
✓36=6 second leg
3×6=18 square area
0,5×6×2,5=7,5 area of a triangle
2×7,5 + 18= 33
Question 10 9 pts 1 De Let f(x) = 2.3 + 6x? - 150 +3. (a) Compute the first derivative of f'(x) = (c) on what interval is f increasing? interval of increasing = (d) On what interval is f decreasing? interval of decreasing = **Show work, in detail, on the scrap paper to receive full credit.
The First derivative: f'(x) = 12x - 15 and the Interval of increasing: (5/4, ∞) and the Interval of decreasing: (-∞, 5/4)
Hi! I'd be happy to help you with your question. Let's compute the first derivative, and then determine the intervals of increasing and decreasing:
Given function: f(x) = 2.3 + 6x^2 - 15x + 3
(a) Compute the first derivative, f'(x):
f'(x) = d(2.3)/dx + d(6x^2)/dx - d(15x)/dx + d(3)/dx
f'(x) = 0 + 12x - 15 + 0
f'(x) = 12x - 15
(c) To find the interval where f is increasing, we need to find where f'(x) > 0:
12x - 15 > 0
12x > 15
x > 15/12
x > 5/4
So, the interval of increasing is (5/4, ∞).
(d) To find the interval where f is decreasing, we need to find where f'(x) < 0:
12x - 15 < 0
12x < 15
x < 15/12
x < 5/4
So, the interval of decreasing is (-∞, 5/4).
Your answer:
- First derivative: f'(x) = 12x - 15
- Interval of increasing: (5/4, ∞)
- Interval of decreasing: (-∞, 5/4)
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please help.................................
Answer:
plugging in those values you get 40+(81/9)=40+9=49.
50 POINTS ASAP Polygon D has been dilated to create polygon D′.
Polygon D with top and bottom sides labeled 8 and left and right sides labeled 9.5. Polygon D prime with top and bottom sides labeled 9.6 and left and right sides labeled 11.4.
Determine the scale factor used to create the image.
Scale factor of 1.6
Scale factor of 1.2
Scale factor of 0.9
Scale factor of 0.8
Answer:
1.2
Step-by-step explanation:
based on your description the top sides are corresponding pairs, the bottom sides are corresponding sides, the left sides are corresponding sides, and the right sides are corresponding sides between the 2 polygons.
the dilation (scaling) is happening for all points on the polygon with the same scaling factor.
so, we only need to find the scaling factor f between one of these corresponding pairs.
8×f = 9.6
f = 9.6/8 = 1.2
Answer: The answer is 1.2
Step-by-step explanation:
Just trust me.
If the arc length of a circle with a radius of 5 cm is 18.5 cm, what is the area of the sector, to the nearest hundredth
i need it quick please
The area of the sector, to the nearest hundredth, is 45.87 cm^2.
The formula for the length of an arc of a circle is L = rθ, where L is the arc length, r is the radius, and θ is the angle in radians subtended by the arc.
We solve for θ by dividing both sides by r: θ = L/r.
In this case, r = 5 cm and L = 18.5 cm, so θ = 18.5/5 = 3.7 radians.
The formula for the area of a sector of a circle is A = (1/2)r^2θ.
Plugging in the values, we get A = (1/2)(5^2)(3.7) ≈ 45.87 cm^2.
Therefore, the area of the sector, to the nearest hundredth, is 45.87 cm^2.
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