How do I solve this? Trying to help my son but he didn’t take any notes! Help please!

Step-by-step explanation:

67yd² is the answer...........

Answer:

4^5

Step-by-step explanation:

8×4³+2×4⁴

4×2×4^3+2×4^4

4^4×2+2×4^4

4^4(2+2)

4^4×4

4^5

So answer is 4^5

Answer:

$473

Step-by-step explanation:

We divide 5676 by 12 and we get 473

$473 they lose each month (?)

Step-by-step explanation:

calculator

Answer:

y = 10.5x - 8.25

Step-by-step explanation:

m = (44.25 - 12.75)/(5 - 2) = 10.5

y = mx + b

y = 10.5x + b

12.75 = 10.5 × 2 + b

b = -8.25

y = 10.5x - 8.25

To find the local and absolute maximum and minimum points of the function f(x) = (3/5)x^5 - 9x^3 + 2 on the closed interval [-4,5], we need to follow these steps:

a) Find all critical numbers (x-coordinates only):

To find the critical numbers, we need to identify where the derivative of the function is zero or undefined. Let's find the derivative of f(x) first:

f'(x) = 3x^4 - 27x^2

Now, set the derivative equal to zero and solve for x:

3x^4 - 27x^2 = 0

Factoring out a common factor of 3x^2, we get:

3x^2(x^2 - 9) = 0

This equation is satisfied when either 3x^2 = 0 or x^2 - 9 = 0.

For 3x^2 = 0, we have x = 0.

For x^2 - 9 = 0, we have x = -3 and x = 3.

Therefore, the critical numbers (x-coordinates) are 0, -3, and 3.

b) Find the intervals on which the graph is increasing (mark critical numbers):

To determine the intervals of increasing, we need to analyze the sign of the derivative on each side of the critical numbers. We create a sign chart for f'(x):

Interval (-∞, -3): Choose a test point x < -3, e.g., x = -4

f'(-4) = 3(-4)^4 - 27(-4)^2 = 768 > 0

The derivative is positive, indicating the graph is increasing.

Interval (-3, 0): Choose a test point x between -3 and 0, e.g., x = -1

f'(-1) = 3(-1)^4 - 27(-1)^2 = -24 < 0

The derivative is negative, indicating the graph is decreasing.

Interval (0, 3): Choose a test point x between 0 and 3, e.g., x = 1

f'(1) = 3(1)^4 - 27(1)^2 = -24 < 0

The derivative is negative, indicating the graph is decreasing.

Interval (3, ∞): Choose a test point x > 3, e.g., x = 4

f'(4) = 3(4)^4 - 27(4)^2 = 768 > 0

The derivative is positive, indicating the graph is increasing.

Therefore, the graph is increasing on the intervals (-∞, -3) and (3, ∞).

c) Find the intervals on which the graph is decreasing (mark critical numbers):

From the analysis above, we can see that the graph is decreasing on the intervals (-3, 0) and (0, 3).

d) Find all local maximum points:

To find the local maximum points, we need to examine the points where the graph changes from increasing to decreasing. By observing the sign changes in the derivative, we can identify potential local maximum points.

From our analysis in part b, we can see that the graph changes from increasing to decreasing at x = -3 and x = 0. Therefore, these are the local maximum points.

e) Find all local minimum points:

To find the local minimum points, we need to examine the points where the graph changes from decreasing to increasing. By observing the sign changes in the derivative, we can identify potential local minimum points.

From our analysis in part c, we can see that the graph changes.

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Answer:

1+tan2x=sec2x.

Explanation: Change to sines and cosines then simplify.

Answer:

F(-x) = 0

Step-by-step explanation:

What is F(-x)?

F(-x) = F(-1)

F(x) = x³ + 1                              F(-1)

F(-1) = -1³ + 1

F(-1) = -1 + 1

F(-1) = 0

So, F(-x) = 0

Answer:

f(-1) = 0

Step-by-step explanation:

Evaluating a function for f(-x) is the same as evaluating it for f(-1).

So we plug in -1 instead.

f(-1) = x³ + 1  

      = (-1)³ + 1 (here we cube -1)

      = -1 + 1     (here we subtract)

      = 0           (and, this is the answer)

\(\therefore\) The answer is f(-1) = 0

Answer:

A: Ben has been a member longer because 1 year, 2 weeks, 3 days is longer than 372 days.

B: 10 days longer

Step-by-step explanation:

1 year, 2 weeks, 3 days is 382 days -> 365 + 14 + 3 = 382

Answer:

1/ N = 1 / 5 + 1/ 4 - 1/ 3 + 1/12

taking L.C.M

Then,

or, 1/N = 5 + 6 / 20 - 13+ 4 / 12

or, 1/N = 11/ 20 - 7/12

or, 1/N = 14 - 12 / 60

or, 1/N = 2 / 60

NOW,

Do cross multiplication,

60 = 2N

or, 60 / 2 = N

so, N = 30

ANS

Answer:

D.) 4

Step-by-step explanation:

Answer:

8

Step-by-step explanation:

scince it has the lines that mean that it will always be positive.

Answer:

8

Step-by-step explanation:

Have a nice day!

The solution of the expression is,

a) 3,724

b) 2,784

We have to given that,

a) Divide 70,756 by 19.

b) Subtract 940 from your answer to part a).​

Now, We can simplify as,

a) Divide 70,756 by 19.

⇒ 70,756 ÷ 19

⇒ 3,724

And, Subtract 940 from your answer to part a).​ that is, 3724

⇒ 3724 - 940

⇒ 2,784

Therefore, The solution of the expression is,

a) 3,724

b) 2,784

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Answer:

84.41 miles

Step-by-step explanation:

For this one, all you have to do is set up a proportion. You can do that by setting it as (39.25/x)=(46.5/100). You cross multiply to get 39.25(100)=46.5(x). From there, you simplify to get 3,925=46.5x. Divide both sides by 46.5 to get x alone, and you should get your answer, 84.41.

Answer: 117 days (3.9 months)

Step-by-step explanation:

Los Angeles is approximately 787 miles away from Colardo. A comfortable walking speed is around 3 miles per hour. Consider hiking from Colarado to Los Angeles. This would take about 250 hours (10 days).

Answer:

67

Step-by-step explanation:

NO HAHAHAHAHAHAHAHAAH

The logically equivalent statement to p → q is:

~q → ~p

The conditional statement:

p → q

Assuming p and q are propositions, the conditional statement may be expressed as:

"If p holds true, then q follows suit. "

'

Whenever p is true, q is true as well. This implies that if q is false, then p must also be false.

We can rephrase this statement cleverly using the negative propositions, which include the opposite or contradictory statements.

~p  and ~q

These mean:

Not p and Not q respectively.

Then the statement:

"If q is not true, then p is not true"

Is written as:

~q → ~p

So this is the logically equivalent statement.

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The Complete Question

Given a conditional statement p → q, which statement is logically equivalent?

~p → ~q

~q → ~p

q → p

p → ~q

We can conclude that with 95 percent confidence, the sample means will fall within the interval of approximately (0.9534, 0.9566).

To determine the interval within which 95 percent of the sample means will fall, we need to calculate the margin of error using the standard deviation and the desired level of confidence.

The formula to calculate the margin of error is given by:

Margin of Error = Z * (Standard Deviation / √n)

Where:

Z is the critical value corresponding to the desired level of confidence

Standard Deviation is the standard deviation of the population

n is the sample size

Since the sample size is 41 and we want to find the interval at a 95 percent confidence level, we need to find the critical value corresponding to a 95 percent confidence level.

The critical value can be found using a standard normal distribution table or a calculator. For a 95 percent confidence level, the critical value is approximately 1.96.

Now we can calculate the margin of error:

Margin of Error = 1.96 * (0.0050 / √41)

Calculating this, we find:

Margin of Error ≈ 0.001624

To find the interval within which 95 percent of the sample means will fall, we need to subtract and add the margin of error to the true mean:

Interval = True Mean ± Margin of Error

Interval = 0.9550 ± 0.001624

Calculating this, we find:

Interval ≈ (0.9534, 0.9566)

Therefore, we can conclude that with 95 percent confidence, the sample means will fall within the interval of approximately (0.9534, 0.9566).

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The area of the composite figure is 122.24 units².

The composite figure consist of a rectangle and two semi circles. Therefore, the area of the composite figure is the sum of the area of the individua shapes.

Hence,

area of the composite figure = area of the rectangle + 2(area of semi circle)

Therefore,

area of the composite figure = 9 × 8 + 2(1 / 2 πr²)

area of the composite figure = 72 + πr²

where

r = 8 / 2 = 4 units

Therefore,

area of the composite figure = 72 + 3.14 × 4²

area of the composite figure = 72 + 3.14 × 16

area of the composite figure = 72 + 50.24

area of the composite figure = 122.24 units²

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a) Comparing the two functions, Scooter's business has a lower slope of 15 compared to Karissa's business with a slope of 35. b) Both Scooter and Karissa earned a total of $500 in that month. Therefore, they had an equal month in terms of total money earned.

a) In the context of Scooter's business, the slope of the function f(x) = 200 + 15x represents the rate at which the total money earned increases with each additional sale. Each unit increase in x (number of sales) results in an increase of $15 in total money earned. The y-intercept of 200 represents the initial amount of money Scooter already had before making any sales.

In the context of Karissa's business, the slope of the function f(x) = 80 + 35x represents the rate at which the total money earned increases with each additional repair job. Each unit increase in x (number of repairs) results in an increase of $35 in total money earned. The y-intercept of 80 represents the initial amount of money Karissa already had before doing any repair jobs.

Comparing the two functions, Scooter's business has a lower slope of 15 compared to Karissa's business with a slope of 35. This means that Karissa's business earns more money per repair job compared to Scooter's business per t-shirt sale.

b) To determine who had the better month, we need to calculate the total money earned by each individual based on the given sales/repairs.

For Scooter, with x = 20 (number of shirts sold):

f(x) = 200 + 15x

f(20) = 200 + 15 * 20

f(20) = 200 + 300

f(20) = 500

For Karissa, with x = 12 (number of repairs):

f(x) = 80 + 35x

f(12) = 80 + 35 * 12

f(12) = 80 + 420

f(12) = 500

Both Scooter and Karissa earned a total of $500 in that month. Therefore, they had an equal month in terms of total money earned.

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Answer:  = approx 0.2006

Step-by-step explanation:

The probability that first 1 randomly selected  calculator is defective is

P(1st defect)= 42/(42+20)=42/62=21/31

If the first calculator is defective the residual number of defective calculators is 42-1=41. The residual total number  number of calculators is 62-1=61

So the probability that second calculator is defected

P(2nd defective)=41/61

If both previous calculators are defective the residual number of defective calculators is 42-2=40.  Total residual number of calculators is 62-2=60

So the probability that third calculator is defected

P(3rd defective)=40/60=2/3

Finally the probability that also fourth calculator is defective is 39/59

P(4th defective)=39/59

The resulted probability that all 4 calculators are defective is

P(all 4 are defective)= P(1st defect)* P(2nd defect) * P(3rd defect)* P(4th defect)=21*41*2*39/(31*61*3*59)=67158/334707=0.200647... = approx 0.2006

The probability of observing at least one head in 10 tosses of a fair coin is approximately 0.999 or 99.9%.

When you flip a fair coin, there are two possible outcomes: heads or tails. Since the coin is fair, the probability of observing heads is the same as the probability of observing tails, and each individual coin toss is independent of all the others.

To find the probability of observing at least one head in 10 coin tosses, we can use the complement rule. The complement of the event "observing at least one head" is the event "observing no heads" or "observing all tails."

The probability of observing all tails in 10 coin tosses is (1/2)^10, since the probability of observing tails on any given toss is 1/2, and the tosses are independent.

Therefore, the probability of observing at least one head in 10 coin tosses is:

1 - (1/2)^10

This is the probability of the complement of the event "observing all tails," which is the event "observing at least one head."

We can calculate this probability using a calculator or by simplifying the expression:

1 - (1/2)^10 = 1 - 1/1024

= 1023/1024

≈ 0.999

So the probability of observing at least one head in 10 coin tosses is approximately 0.999, or 99.9%. This means that it is very likely (but not guaranteed) that you will observe at least one head if you flip a fair coin 10 times.

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Answer:

y= -3x +40

Step-by-step explanation:

Properties of perpendicular bisector:

• perpendicular to the given line

• cuts through the center of the given line

The equation of a line can be written in the form of y=mx +c, where m is the gradient and c is the y -intercept.

Let's find the gradient of the given line first.

\(\boxed{gradient = \frac{y1 - y2}{x1 - x2} }\)

Gradient of given line

\( = \frac{6 - 2}{18 - 6} \)

\( = \frac{4}{12} \)

\( = \frac{1}{3} \)

The product of the gradients of perpendicular lines is -1.

m(⅓)= -1

m= -1(3)

m= -3

Substitute m= -3 into the equation:

y= -3x +c

To find the value of c, substitute a pair of coordinates in which the perpendicular bisector passes through into the equation. Since perpendicular bisectors passes through the center of the segment, we can find the point in which the perpendicular bisector passes through using the mid- point formula.

\(\boxed{midpoint = ( \frac{x1 + x2}{2} , \frac{y1 + y2}{2} )}\)

Midpoint

\( = ( \frac{6 + 18}{2} , \frac{6 + 2}{2} )\)

\( = ( \frac{24}{2} , \frac{8}{2} )\)

\( = (12,4)\)

y= -3x +c

when x= 12, y= 4,

4= -3(12) +c

4= -36 +c

c= 4 +36

c= 40

Thus, the equation of the perpendicular bisector is y= -3x +40.

Answer:

4/15

Step-by-step explanation:

Bag A

3 red marbles and 6 blue marbles.  = 9 marbles

P(blue) = blue/total =6/9 = 2/3

Bag B

6 green marbles and 4 yellow marbles.  = 10 marbles

P(yellow) = yellow/total=4/10 = 2/5

P(blue,yellow) = 2/3 * 2/5 = 4/15

Answer:

a) The null and alternative hypothesis are:

\(H_0: \mu=13.04\\\\H_a:\mu< 13.04\)

b) P-value = 0.0151

c) We reject the null hypothesis.

We conclude that the cost of a restaurant meal is significantly cheaper than a comparable meal fixed at home.

Step-by-step explanation:

This is a hypothesis test for the population mean.

The claim is that the mean cost of a restaurant meal is significantly less than fixing a comparable meal at home.  

Then, the null and alternative hypothesis are:

\(H_0: \mu=13.04\\\\H_a:\mu< 13.04\)

The significance level is 0.05.

The sample has a size n=100.

The sample mean is M=12.6.

As the standard deviation of the population is not known, we estimate it with the sample standard deviation, that has a value of s=2.

The estimated standard error of the mean is computed using the formula:

\(s_M=\dfrac{s}{\sqrt{n}}=\dfrac{2}{\sqrt{100}}=0.2\)

Then, we can calculate the t-statistic as:

\(t=\dfrac{M-\mu}{s/\sqrt{n}}=\dfrac{12.6-13.04}{0.2}=\dfrac{-0.44}{0.2}=-2.2\)

The degrees of freedom for this sample size are:

\(df=n-1=100-1=99\)

This test is a left-tailed test, with 99 degrees of freedom and t=-2.2, so the P-value for this test is calculated as (using a t-table):

\(\text{P-value}=P(t<-2.2)=0.0151\\\)

As the P-value (0.0151) is smaller than the significance level (0.05), the effect is significant.

The null hypothesis is rejected.

There is enough evidence to support the claim that the mean cost of a restaurant meal is significantly less than fixing a comparable meal at home.  

There is enough evidence to support the claim that the mean cost of a restaurant meal is significantly less than fixing a comparable meal at home.

The null hypothesis is always represented by the equality sign.

So, the null hypothesis is:

\(H_o : \mu = 13.04\)

For the meal to be cheaper, then the less than inequality sign would be used.

So, the alternate hypothesis is:

\(H_a : \mu < 13.04\)

Hence, the null and the alternate hypotheses are:

\(H_o : \mu = 13.04\) and \(H_a : \mu < 13.04\)

The given parameters are:

n = 100

\(\sigma = 2\)

\(\bar x = 13.04\)

\(\mu = 12.60\)

Start by calculating the standard error

\(\sigma_x = \frac{\sigma}{\sqrt n}\)

This gives

\(\sigma_x = \frac{2}{\sqrt {100}}\)

\(\sigma_x = 0.2\)

Next, calculate the test statistic

\(t = \frac{\mu - \bar x}{\sigma_x}\)

This gives

\(t = \frac{12.60 - 13.04}{0.2}\)

\(t = -2.2\)

Calculate the degrees of freedom

\(df = n - 1\)

\(df = 100 - 1\)

\(df = 99\)

Next, we calculate the p-value as follows:

\(p = P(t < -2.2)\)

At a degree of freedom of 99, the p value when the t value is less than -2.2 is:

\(p = 0.0151\)

Hence, the p value for a sample size of 100

We have:

The significance level, α = 0.05

The p-value in b, 0.0151 is lesser than the significance level, 0.05.

This means that we reject the null hypothesis

So, the conclusion is:

There is enough evidence to support the claim that the mean cost of a restaurant meal is significantly less than fixing a comparable meal at home.

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Answer: 12

Step-by-step explanation:

Answer:

it would be 9

Step-by-step explanation:

All but nine died means "everything except nine goats died"

All 12 goats died.

The completed table of values for the equation 4x + 2y = 64 is provided .

To complete the table of values for the equation 4x + 2y = 64, we can assign different values to x and solve for y. Let's choose a range of values for x and calculate the corresponding values of y.

Table of Values:

x y

0 32

4 28

8 24

12 20

16 16

20 12

24 8

28 4

32 0

To find the values of y, we substitute each x-value into the equation and solve for y. For example, when x is 0, we have 4(0) + 2y = 64, which simplifies to 2y = 64 and y = 32. Similarly, for x = 4, we have \(4(4) + 2y = 64\), which simplifies to \(16 + 2y = 64\) and\(y = 28.\)

By continuing this process for the remaining values of x, we can complete the table of values for the equation 4\(x + 2y = 64.\)

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Answer:

the answered is a

Step-by-step explanation:

hope this helps