2.5 in.
7.5 in.
A = 54 in.²
A = ?
The 2 pentagons above are similar. What is the area of the smaller pentagon?
27 in 2
18 in 2
6 in 2
9 in 2

Answer:

A) (1 s, 2.3 s)

B) (-4 m/s², 3.8 m/s²)

Step-by-step explanation:

The car's position which is the distance is given by the equation;

s(t) = t³ - 5t² + 7t

A) Velocity is the first derivative of the distance. Thus;

v(t) = ds/dt = 3t² - 10t + 7

At v = 0, we have;

3t² - 10t + 7 = 0

Using quadratic formula, we have;

t = 1 and t = 2.3

Thus, time at velocity of 0 is t = (1 s, 2.3 s)

B) acceleration is the derivative of the velocity. Thus;

a(t) = dV/dt = 6t - 10

At velocity of 0, we got t = 1 and t = 2.3

Thus;

a(1) = 6(1) - 10 = -4 m/s²

a(2.3) = 6(2.3) - 10 = 3.8 m/s

Thus, a(t) at v = 0 gives; (-4 m/s², 3.8 m/s²)

Answer:

Let's assume that the total number of students in the school is "x". We can create a proportion to estimate how many students would choose the aquarium based on the given information:

Number of students who chose aquarium / Total number of students in the school = Percentage of students who chose aquarium / 100

We can plug in the values we know:

80 / x = p / 100

where "p" is the percentage of students who would choose the aquarium if the entire school were surveyed.

We can solve for "x" by cross-multiplying and simplifying:

8000 = px

x = 8000 / p

Now, we need to estimate the value of "p". We can do this by finding the average percentage of students who chose the aquarium, science center, planetarium, and farm:

(80 + 60 + 30 + 40) / x = (210 / x) = Average percentage of students who chose an attraction

This tells us that, on average, 210 out of every "x" students would choose one of the attractions. We can estimate that a similar percentage of the entire school would choose the aquarium:

p / 100 = 80 / 210

p = 38.1

So, we can estimate that approximately 38.1% of the students in the whole school would choose the aquarium. To find the estimated number of students who would choose the aquarium, we can plug in this value for "p" in our original proportion:

80 / x = 38.1 / 100

Cross-multiplying and solving for "x", we get:

x = 209.71

Rounding to the nearest whole number, we can estimate that approximately 210 students in the whole school would choose the aquarium.

Step-by-step explanation:

Answer:

The teacher surveyed a total of:

80 + 60 + 30 + 40 = 210 students.

If we assume that the sample of 210 students surveyed is representative of the entire population of 1000 students at Lake Middle School, we can use the relative frequency of students choosing the aquarium in the sample to estimate the number of students in the whole school who would choose the aquarium.

The relative frequency of students choosing the aquarium in the sample is:

80/210 = 0.38

This means that approximately 38% of the students in the sample chose the aquarium.

To estimate the number of students in the whole school who would choose the aquarium, we can multiply the relative frequency by the total number of students at the school:

0.38 x 1000 = 380

Therefore, the teacher can estimate that approximately 380 students out of 1000 at Lake Middle School would choose the aquarium for a field trip.

Answer: no one cares

Step-by-step explanation:

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

The final expression of -16\(x^{8}\) / -8\(x^{9}\) is 2/x.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

-16\(x^{8}\) / -8\(x^{9}\)

= (-16/-8)\(x^{8 - 9}\)

= 2 \(x^{-1}\)

= 2/x

Thus,

The final expression of -16\(x^{8}\) / -8\(x^{9}\) is 2/x.

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Answer:

Step-by-step explanation:

I and II

Pages in a book and leaves on a tree can be counted precisely. They are discrete.

The height of a person cannot be measured exactly. We can get very good

approximations (to a lot of decimal places) but never exact. This is continuous.

Answer:

Definitely nonlinear - this is because we are dealing with 3 variables, x, y and xy. If we just had x and y then it would be linear, but the xy makes the function have a vertical asymptote at 3.

Step-by-step explanation:

Answer:

Non-linear

Step-by-step explanation:

This is because this cannot be written in standard form or slope-intercept. y and x cannot be multiplied together if the equation is linear.

4x - 5y + 2xy = 0

4x - y(5 - 2x) = 0

-y(5 - 2x) = -4x

-y = -4x / (5 - 2x)

y = 4x / (5 - 2x)

[when y is isolated to set a linear equation to slope-intercept, m is not constant, and there is no constant term]

This is a hyperbola and not a linear equation.

When y is isolated on the left side to set a linear equation to slope intercept, it must follow the form

y = mx + b.

Where m is the slope, b is the constant that is the y intercept.

The slope of the lines on the graph are:

Line AB = 2

Line CD = -1/3.

Line EF = 0

Line GH = 1/5

Line IJ = -5/2

Line KL = -2/7

Line MN = undefined

Line PQ = 1

Tp find the slope of a line on a graph, find the ratio of the ris to the run along the line on the graph.

Declining line has a negative slope while a rising line has a positive slope. Therefore:

Line AB = rise / run = 4/2 = 2

Line CD = rise/run = -2/6 = -1/3.

Line EF = rise/run = 0/4 = 0

Line GH = rise/run = 1/5

Line IJ = rise/run = -5/2

Line KL = rise/run = -2/7

Line MN = rise/run = 3/0 = undefined

Line PQ = rise/run = 3/3 = 1

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Given:

The triangle ABC is reflected over the x-axis.

The distance between point A and A’ is 14.

To find:

The distance between the x-axis and A’.

Solution:

If a figure is reflected across the x-axis then the corresponding parts are mirror image of each other about the x-axis.

It means the distance between A and x-axis is same as the distance between x-axis and A'.

The distance between point A and A’ is 14.

Let d be the distance between the x-axis and A’. Then,

\(d+d=14\)

\(2d=14\)

\(d=\dfrac{14}{2}\)

\(d=7\)

Therefore, the correct option is 1.

Answer:

37

Step-by-step explanation:

All those can have equal rows with leaving the one out and with five equal groups it would leave 2

Six (6) confidence intervals or hypothesis tests would need to be done to make significant statements for each pair-wise comparison.

In an ANOVA F test, the null hypothesis is that the means of all the treatments are equal, and the alternative hypothesis is that at least two of the means are different. If the null hypothesis is rejected at the 5% significance level, this means that the differences between the means are statistically significant and the treatments can be considered different.

Since there are four treatments, there are 6 possible pairs of treatments. These tests would determine whether the means of each pair of treatments are significantly different from each other.

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Answer:

Step-by-step explanation:

A company produces steel rods. The lengths of the steel rods are normally distributed with a mean of 142.7-cm and a standard deviation of 2.2-cm.

Find the probability that the length of a randomly selected steel rod is between 137.6-cm and 143.6-cm.

P(137.6-cm < X < 143.6-cm) =

Enter your answer as a number accurate to 4 decimal places. Answers obtained using exact z-scores or z-scores rounded to 3 decimal places are accepted.

Answer:

9.1s

Step-by-step explanation:

Since we know that velocity is uniformly decelerating, we can take the average velocity: Letting Vf equale 0 /ms, we get 1/2 21.8ms or 10.9ms. Now we know V = D/T and rearranging this gives T = D/V. Substitute our velocity of 10.9m/s for V and 99m for D: T = 99m/ 10.9ms. finally we get T = 9.1s                

Hope This Helps :)

The time in which Anny drives in the rain is 90 minutes. This is calculated by using the speed-distance-time formula.

Speed is the ratio of distance traveled to the time taken for traveling.

Speed=distance/time

Unit: m/s

It is given that,

Anny drives at a speed of 50 miles per hour if it is not raining and drives at a speed of 30 miles per hour.

Today she drove in the sun in the morning and the rain in the afternoon, for a total of 120 miles in 180 minutes.

Consider x be the time required to drive not in the rain and y be the time required to drive in the rain

So, the distance covered (not in the rain) = 50x (since the speed is 50 mile/h), and the distance covered (in the rain) =30y (since the speed is 30 miles/h)

Therefore, the total distance covered both in rain and without rain is:

50x+30y=120 (since the total distance she drove is 120 miles)

And the total time required for driving in rain and without rain is:

x + y=3 (since 180 minute = 3 hours)

On solving the above equations we get,

x=\(\frac{3}{2}\) and y=\(\frac{3}{2}\)

Then,

y=\(\frac{3}{2}\)×60(minute)=90 minute

Therefore, the time taken for her to drive in rain is 90 minutes.

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Answer:

$48.91

Step-by-step explanation:

$45.50 * 1.075 or 7.5% = $48.91

The only possible value of "a" that satisfies the given equations is a = 5.

The possible values of "a" that satisfy the given equations, let's solve the system of equations:

a + ab = 250 ---(1)

a - ab = -240 ---(2)

We can solve this system by using the method of substitution. Rearranging equation (2), we get:

a = ab - 240 ---(3)

Substituting equation (3) into equation (1), we have:

(ab - 240) + ab = 250

2ab - 240 = 250

2ab = 250 + 240

2ab = 490

ab = 490/2

ab = 245

Now we have the value of "ab."

We can substitute this back into equation (3) to solve for "a":

a = (245) - 240

a = 5

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Answer:

a. 1,323,002

Step-by-step explanation:

Answer:

lilet is 7 and margie is 21?

Step-by-step explanation:

36-15=21

21÷3=7

21 would be Margies age since its the older age, maybe im wrong i dont know

Step-by-step explanation:

70 to 85 % of his maximum

Maximum is estimated to be 220 - age  = 220 - 42 = 178

70% of this is 125

85 % is 89  151  

I believe I would go with the third choice  116-160 bpm

In order to find what factors could represent the length and the width, we need to factor the polynomial that represents the area.

To do so, first let's find the zeros a1 and a2, then we can factor as follows:

Where k is the coefficient of the quadratic term (so k = 12).

Using the quadratic formula, we have:

Then, we have:

Therefore the factors are 2a-1 and 6a+5.

\(35 cm ^{3}\) is the volume of the prism displayed. The triangular cross section is 1.25 cm tall.

length , l = 7 cm , width w = 4 cm , height , h= 1.25 ,diagonal ,   d=8.15858444 cm , total surface area, \($S_{\text {tot }}=83.5 \mathrm{~m}^2$\) , lateral surface area , \($S_{\text {lat }}=27.5 \mathrm{~m}^2$\) , top surface area , \($S_{\text {top }}=28 \mathrm{~m}^2$\) , bottom surface area , \($S_{\text {bot }}=28 m^2$\) , volume \($V=35 \mathrm{~m}^3$\) .

To calculate the height of a prism, divide its volume by its area at the base. Let's say that the prism has a volume of 600 cubic inches to wrap up this scenario. The height is determined by multiplying 600 cubic inches by 100 square inches.

A prism's volume is calculated using the formula V=Bh, where B denotes the base area and h the height. A rectangular area makes up the prism's base. The rectangle's dimensions are 9 cm long by 7 cm wide. The formula V=Bh, where V stands for volume, B for the prism's area at its base, and h for its height, can be used to determine a prism's volume. B should be replaced with the area of a rectangle formula because this is a rectangular prism.

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Answer:

Mistake is that "y" and "x" were substituted by the wrong values. Instead, Greyson should have written the following:

\(y = mx + b\\ \\8 = (\frac{1}{2})(-6) + b\\ \\8 = -3 + b\\ \\b=8+3\\ \\b=11\)

Answer:

0.9940

Step-by-step explanation:

P(at least 1) = 1 − P(zero)

P(at least 1) = 1 − (1 − 0.64)⁵

P(at least 1) = 1 − (0.36)⁵

P(at least 1) = 0.9940

The probability that at least one of them has been vaccinated is 0.9939.

The binomial distribution is the discrete probability distribution that gives only two possible results in an experiment, either success or failure. It helps to check the probability of getting “x” successes in “n” independent trials of a binomial experiment.

For the given situation,

Number of people vaccinated = 64% = 0.64

The formula of binomial distribution is

\(P(x:n,p) = nC_{x} p^x (1-p)^{n-x}\)

Here x is the number of successes, x ≤ 1

n is the number of trials, n = 5

p is the probability of a success on a single trial, p = 0.64 and

where, \(nC_{x}=\frac{n!}{x!(n-x)!}\)

The probability is \(P(X \leq 1)=1-P(X=0)\)

\(P(X=0)= 5C_{0} (0.64)^{0} (1-0.64)^{5-0}\)

⇒ \(P(X=0)= 1(1) (0.36)^{5}\)

⇒ \(P(X=0)= 0.0060\)

Thus, \(P(X \leq 1)=1-P(X=0)\\\)

⇒ \(P(X \leq 1)=1-0.0060\)

⇒ \(P(X \leq 1)=0.9939\)

Hence we can conclude that the probability that at least one of them has been vaccinated is 0.9939.

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Answer:

$1.50 per jar

Step-by-step explanation:

4.50 / 3 = 1.50

Answer:-20=41

Step-by-step explanation:

3(-2-21)-7=41

We need to first make these improper fractions. 5 = 40/8, so 40/8+6/8 = 46/8. Similarly, 4 = 20/5, so 20/5+4/5=24/5.

So we need to find the value of 46/8+24/5. Multiply the first fraction by 5/5 and second fraction by 8/8 to get the same denominator. We get (46*5+24*8)/8*5 = 422/40. This is equal to 400/40 + 22/40 = 10+22/40.

So the third answer choice is correct.

Hope that helped!

Answer:

75%

Step-by-step explanation:

Formula:
P = (x/y) * 100

where x is 6 dollars and y is 8 dollars.

P = (6/8) * 100
P = 0.75 * 100
P = 75%

I believe that it is 2x^2+1x-2

Answer: No

To check if (-5,6) is a solution to the equation y=-7, we need to substitute -5 for x and 6 for y in the equation.

If the equation is true, then the ordered pair is a solution to the equation.

If we put (-5,6) into y=-7, we get 6=-7, which is not true.

So, (-5,6) is not a solution to the equation y=-7.