if ∫5-1f(x)dx = 12 and ∫5-4f(x)=3.6, find ∫4-1f(x)dx

Answer:

28

Step-by-step explanation:

Since the perimeter is the width + width + length + length, we know that there 2 of the 8 millimeter width in the perimeter. So multiply 8 by 2, which is 16. So 16 of the 72 represents both widths. So subtract 16 from 72. You're left with 56, which represents 2 of the length. So divide 56 by 2, and you get one of the length, which is 28.

Answer:

28 ^^

Step-by-step explanation:

Good Luck!!!

Answer: After 7 years the population will be one-half the initial amount.

Step-by-step explanation:

Given: Initial population = 500,000

The population declines according to the equation:

\(P(t) = 500,000e^{ -0.099t}\), where P is the population in t years later.

One-half the initial amount = 0.5 x 500,000

= 250,000

Put P(t)=250,000, we get

\(250000=500000e^{-0.099t}\\\\\Rightarrow\ \frac{500000e^{-0.099t}}{500000}=\frac{250000}{500000}\\\\\Rightarrow\ e^{-0.099t}=\frac12\\\\\Rightarrow\ -0.099t=\ln \left(\frac{1}{2}\right)\\\\\Rightarrow\ t=\frac{1000\ln \left(2\right)}{99}=\frac{1000(0.69314)}{99}\\\\\Rightarrow\ t=7.00148\approx7\)

Hence, After 7 years the population will be one-half the initial amount.

Answer:

so each chair will cost 205

205 will be our cost C this is our dependent due to the entire cost being base on how many chairs that will get order

the independent variable will be how many chairs that will be ordered and there are 34 chairs being ordered

34*205= 6970

the total cost will be 6970

Answer:

the answer is certainly A

Answer:

The area is 12.56 units^2 (same as circumference?)

Step-by-step explanation:

Assuming pi is 3.14, the equation for the circumference is C = 2 pi r

Fill it out for the radius (r)

12.56 = 2 3.14 r

12.56 = 6.28 r

r = 2

With the radius, the equation for the area is A = pi r^2

Fill it out for the area

A = 3.14 2^2

A = 3.14 4

A = 12.56

Answer:

8

Hope this helps!

The discriminant of the given quadratic equation is 8.

The discriminant determines the type and number of solutions that the equation has.

If the discriminant is positive, the equation has two distinct real solutions. If the discriminant is zero, the equation has one repeated real solution. If the discriminant is negative, the equation has no real solutions.

Given is a quadratic equation -x²+4x-2 = 0, we need to find the discriminant of the quadratic equation,

So,

D = b²-4ac

Here,

a = -1, b = 4 and c = -2

Therefore,

D = 4² - 4(-1)(-2)

D = 16 - 8

D = 8

Hence, the discriminant of the given quadratic equation is 8.

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The value of the standard deviation of the weekly earnings of the bus drivers is $14.57.

To solve this problem, we can use the standard normal distribution table or a calculator that provides the inverse of the standard normal distribution. Let X be the weekly earnings of the bus drivers, then we have:

P(X > $429.35) = 0.011

Using the standard normal distribution table or calculator, we can find the z-score that corresponds to a probability of 0.011, which is approximately -2.33. We can then use the formula for standardizing a normal variable:

z = (X - μ) / σ

where μ is the mean and σ is the standard deviation of the distribution. Substituting the given values, we have:

-2.33 = ($429.35 - $395) / σ

Solving for σ, we get:

σ = ($429.35 - $395) / (-2.33) = $14.57

Therefore, the value of the standard deviation of the weekly earnings of the bus drivers is $14.57.

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After finding the derivative of f(x) and setting it equal to the average rate of change, we find that there is only one solution in the open interval (0, 1.565). Therefore, the answer is (B) one

To determine the number of values of x in the open interval (0, 1.565) where the instantaneous rate of change of f is equal to the average rate of change of f on the closed interval [0, 1.565], we can use the Mean Value Theorem for Derivatives.

According to the Mean Value Theorem for Derivatives, if f(x) is a differentiable function on the closed interval [a, b], where a < b, then there exists a point c in the open interval (a, b) such that the instantaneous rate of change of f at c is equal to the average rate of change of f on [a, b].

In this case, we are given that the closed interval is [0, 1.565] and the open interval is (0, 1.565), so we need to find if there exists any point c in (0, 1.565) where the instantaneous rate of change of f is equal to the average rate of change of f on [0, 1.565].

To do this, we can first find the average rate of change of f on [0, 1.565] by using the formula:

average rate of change = (f(1.565) - f(0))/(1.565 - 0)

Next, we can find the derivative of f(x) and set it equal to the average rate of change to find any possible values of c that satisfy the Mean Value Theorem for Derivatives.

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The answer is (C) Three, as there will be three points of intersection.

To answer this question, we need to first understand what the instantaneous rate of change and average rate of change mean. The instantaneous rate of change of a function at a particular point is the slope of the tangent line to the graph of the function at that point. The average rate of change of a function over a closed interval is the slope of the secant line connecting the two endpoints of the interval.

In this case, we are looking for values of x in the open interval (0, 1.565) where the instantaneous rate of change of f is equal to the average rate of change of f over the closed interval [0, 1.565].

Since f(x) is not given, we cannot determine the instantaneous and average rate of change of f directly. However, we can use the Mean Value Theorem for Derivatives to help us solve the problem. The Mean Value Theorem states that if f is a continuous function on the closed interval [a, b] and differentiable on the open interval (a, b), then there exists a number c in the open interval (a, b) such that:

f'(c) = (f(b) - f(a))/(b - a)

In this case, we can apply the Mean Value Theorem to the closed interval [0, 1.565] and the open interval (0, 1.565) to get:

f'(c) = (f(1.565) - f(0))/(1.565 - 0)

Simplifying, we get:

f'(c) = f(1.565)/1.565

So, we need to find values of x in the open interval (0, 1.565) where f(x)/x = f(1.565)/1.565.

To solve this equation, we can graph y = f(x)/x and y = f(1.565)/1.565 on the same set of axes and look for points of intersection. The number of intersection points will be the number of values of x in the open interval (0, 1.565) where the instantaneous rate of change of f is equal to the average rate of change of f over the closed interval [0, 1.565].

Therefore, the answer is (C) Three, as there will be three points of intersection.

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Answer:

N = 33

Step-by-step explanation:

N = D + 19

.05N + .10 D = 3.05

N = 33

D = 14

Answer:

x = 21 degrees!

Step-by-step explanation:

3x + x + 96 = 180

4x +96 = 180

Subtract 96 from both sides!

4x = 84

Divide by 4 from both sides!

x = 21 degrees

Answer:

x=21°

Step-by-step explanation:

3x+x+96°=180°

4x=180°-96°

4x=84°

x=84°/4

x=21°

I need only one brainliest to complete my challenge so please give me a brainliest

Answer:

I can’t see the picture well please make it more detailed

Step-by-step explanation:

Answer: Its A

explanation:

Im good at math

Can i have brainliest please?

Answer:

I'm pretty sure its 0...since anything multiplied by zero is 0

Answer:

(8,2)

Step-by-step explanation:

Rotating a point 180° basically puts it in the quadrant across from it, in this case, the (x,y) quadrant.

The sign of coordinate will changes as (8,2) after 180° rotation about the origin.

A pair of numbers that employ the horizontal and vertical distinctions from the two reference axes to represent a point's placement on a coordinate plane. typically expressed by the x-value and y-value pairs (x,y).

As per the given coordinate (–8, –2).

If we rotate it by 180° about the origin no matter clockwise or anti-clockwise the coordinate will shifts in the first quadrant at (8,2) as shown below.

Hence "The sign of coordinate will changes as (8,2) after 180° rotation about the origin".

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SOLUTION:

Case: Proportions

Method:

The recommended dosage of a drug for pediatric patients is 200 mg per kilogram

We calculate John's weight in kg

Since

Next, the drug should he receive

Final an

Answer:

x*(x+3)*(x^2)

Step-by-step explanation:

Width: x meters, length: x + 3 meters, height x^2 meters

It's an expression, so there's no simplifying needed.

x(x+3)(x^2)

But if I'm wrong and it's supposed to be simplified, Read the rest.

First, multiply x by x + 3

x(x + 3)

x^2 + 3x

Now, multiply x^2 + 3x by x^2

(x^2)(x^2 + 3x)

x^4 + 3x^3

Null hypothesis: The population median is equal to 22.

Alternative hypothesis: The population median is not equal to 22.

To perform the hypothesis test, we can use the Wilcoxon signed-rank test, which is a non-parametric test suitable for testing the equality of medians.

Null hypothesis (H0): The population median is equal to 22.

Alternative hypothesis (H1): The population median is not equal to 22.

Next, we calculate the test statistic S. The Wilcoxon signed-rank test requires the calculation of the signed ranks for the differences between each observation and the hypothesized median (22).

Arranging the differences in ascending order, we have:

-9, -6, -5, -4, -3, -2, 12, -8.

The absolute values of the differences are:

9, 6, 5, 4, 3, 2, 12, 8.

Assigning ranks to the absolute differences, we have:

2, 3, 4, 5, 6, 7, 8, 9.

Calculating the test statistic S, we sum the ranks corresponding to the negative differences:

S = 2 + 8 = 10.

To determine the p-value, we compare the calculated test statistic to the critical value from the standard normal distribution. Since the sample size is small (n = 8), we look up the critical value for α/2 = 0.025 in the Z-table. The critical value is approximately 2.485.

If the absolute value of the test statistic S is greater than the critical value, we reject the null hypothesis. Otherwise, we fail to reject the null hypothesis.

In this case, S = 10 is not greater than 2.485. Therefore, we fail to reject the null hypothesis. The p-value is greater than 0.05 (the significance level α), indicating that we do not have sufficient evidence to conclude that the population median is different from 22.

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15/19 + 14/19 = 29/19

Step-by-step explanation:

Add the number of balls in the basket together.

Subtract the number of white balls from the sample space ( the total amount of balls) your answer is written over the sample space and the same process is done for the green ball

Answer:

.50$

Step-by-step explanation:

When you add 1/2, 1/4, and 1/8 you get 7/8. We now know that Quinn spent 7/8 of 4.00$. We multiply 7/8 and 400 and we get 350. That means he spent 3.50$. 4.00-3.50= .50$

Answer:

3.50

Step-by-step explanation:

2.00+1.00+.50=3.50

Answer:

10t - 16

Step-by-step explanation:

4(t + 2)+ 6(t - 4)

4t + 8 + 6t -24

10t - 16

The mean of the five numbers 223, 264, 216, 218, and 229 is 230.

To calculate the mean, follow these steps:
1. Add the numbers together: 223 + 264 + 216 + 218 + 229 = 1150
2. Divide the sum by the total number of values: 1150 / 5 = 230
The mean represents the average value of the dataset. In this case, the mean value of the five numbers provided is 230, which gives you a central value that helps to understand the general behavior of the dataset. Calculating the mean is a bused in statistics to summarize data and identify trends or patterns within a set of values.

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Answer:

try both -1, if I'm wrong I am sorry

The most sensible average to use in this case would be the mode, which is the value that appears most frequently in the data set. In this case, the mode is 2, which appears 9 times in the data set. This means that the most common number of children in a family in the class is 2.

In this case, the most sensible average to use would be the mode, which is the number that appears most frequently in the data set. This is because the mode represents the most common number of children in the families of the children in the class, which is likely to be a more accurate representation of the typical family size in the class than the mean or median.

To find the mode, we first need to count how many times each number appears in the data set. In this case, the numbers 1, 2, 3, and 4 appear in the data set as follows:

1: 7 times

2: 11 times

3: 3 times

4: 1 time

We can see that the number 2 appears most frequently, with a count of 11. Therefore, the mode in this case is 2, and this is the most sensible average to use in this situation.

Thus, distribution is a function that shows the possible values for a variable and how often they occur and categorical values are summarized by counts and/or percents

In statistics, the distribution is a function that shows the possible values for a variable and how often they occur.

The distribution of a data set is the shape of the graph when all possible values are plotted on a frequency graph. Usually, we are not able to collect all the data for our variable of interest. Therefore we take a sample. This sample is used to make conclusions about the whole data set.

The categorical variable is a data in which individuals are placed into groups or categories.

One way to summarize categorical data is to simply count (frequency), or tally up, the number of individuals that fall into each category. Another way is to show the percentage of individuals who fall into each category, thereby creating a relative frequency.

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You must use the t-distribution table when working problems when the population standard deviation (σ) is not known and the sample size is small (n<30). General Correct Rule: If σ is not known, then using t-distribution is correct. If σ is known, then using the normal distribution is correct.

Normal distribution, also known as the Gaussian distribution, is a probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean.

In graphical form, the normal distribution appears as a "bell curve".

The normal distribution is the proper term for a probability bell curve.

In a normal distribution the mean is zero and the standard deviation is1. It has zero skew and a kurtosis of 3.

Normal distributions are symmetrical, but not all symmetrical distributions are normal.

The t-distribution describes the standardized distances of sample means to the population mean when the population standard deviation is not known, and the observations come from a normally distributed population.

Therefore,

You must use the t-distribution table when working problems when the population standard deviation (σ) is not known and the sample size is small (n<30). General Correct Rule: If σ is not known, then using t-distribution is correct. If σ is known, then using the normal distribution is correct.

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Answer:

Lashawn used 15, $0.50 stamps, 21, $0.35 stamps, and 8, $0.02 stamps to mail the package

Step-by-step explanation:

The given parameters are;

The number of stamps Lashawn used to mail the small package = 44

The price of the combination of 44 stamp = $15.01

The price categories of the stamps are $0.50, $0.35, and $0.02

The number of $0.35 stamps = 2 × The number of $0.50 stamps - 9

Let, x represent the number of $0.50 stamps Lashawn used to mail the package

We have;

The number of $0.50 stamps Lashawn used to mail the package = x

The number of $0.35 stamps = 2 × x - 9 = 2·x - 9

The number of $0.35 stamps = 2·x - 9

The number of $0.02 stamps = 44 - x - (2·x - 9) = 44 - x - 2·x + 9 = 53 - 3·x

The number of $0.02 stamps = 53 - 3·x

Which gives;

0.5 × x + 0.35 × (2·x - 9) + 0.02 × (53 - 3·x) = 15.01

0.5·x + 0.7·x - 3.15 + 1.06 - 0.06·x = 15.01

1.14·x - 2.09 = 15.01

1.14·x = 15.01 + 2.09 = 17.1

x = 17.1/1.14 = 15

x = 15

The number of $0.50 stamps Lashawn used to mail the package = x = 15 stamps

The number of $0.50 stamps Lashawn used = 15 stamps

The number of $0.35 stamps Lashawn used = 2·x - 9 = 2 × 15 - 9 = 21 stamps

The number of $0.02 stamps Lashawn used = 53 - 3·x = 53 - 3 × 15 = 8 stamps.

Answer:

Let's identify what we know and what we are looking for. To start off, the question states that there is a flat rate of 500. This is the y intercept, because you start off with 500. It also states that it charges a fee of 50 per hour, which is your slope. So what we have now is y=50x+500. We know that A is asking how much it will be for 20 hours. We simply plug 20 into x, so we do y=50(20)+500 which gives 1500. For C, we repeat the same step and just plug in 50.

Answer:The second one is better

Step-by-step explanation:

Amy is left with 60% of the money she had initially.

Let's break down the problem step by step:

Amy had $80 to spend on a filter.

She spent 20% of the money on a filter, which is 0.20 * $80 = $16.

After purchasing the filter, she paid $16 to a plumber to install it.

So far, Amy has spent a total of $16 + $16 = $32.

To find out how much money Amy is left with, we subtract the amount she has spent from the initial amount she had:

$80 - $32 = $48

Amy is left with $48.

To determine the percentage of the money she is left with, we can calculate what portion of the initial amount she still has:

($48 / $80) * 100 = 60%

Therefore, Amy is left with 60% of the money she had initially.

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