Which equation represents the function on the graph?

ANSWER CHOICES
A: f(x)= cos 1/4x
B: f(x)= sin 4x
C: f(x)= cos 4x
D: f(x)= sin 1/4x

The statements that are true about the triangle f d e and its dilated counterpart f' d' e' are: (1) The center of dilation was (0, 0). (2) The coordinates of f' d' e' are (negative 3, 1), (negative 3, 3), and (negative 2, 2). (3) f' d' e' is a similar triangle to f d e.

The triangle f d e and its dilated counterpart f' d' e' have specific properties that make them similar triangles. The center of dilation for the transformation was (0, 0). This means that the distance from the center of dilation to each point before and after the dilation was the same. The coordinates of triangle f d e were (negative 9, 3), (negative 9, 9), and (negative 6, 6). In order to obtain the coordinates of f' d' e', the dilation rule one-third(x,y) (one-third x, one-third y) was used. This means that the x and y coordinates of each point were divided by three. The result is that the new coordinates of f' d' e' are (negative 3, 1), (negative 3, 3), and (negative 2, 2). These new coordinates demonstrate that the triangle f d e and its dilated counterpart f' d' e' are similar triangles.

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Answer:

A. ∠F corresponds to ∠F'.

C. The distance from point D' to the origin is 1/3 the distance of point D to the origin.

E. △DEF ~△D'E'F'

Step-by-step explanation:

got it right on edge 23

As per given digits of integers, the largest number of possible integers are 84.

Here we have given that the number is a multiple of 5 and the units digit must be 0 or 5.

Then let us consider that if 5 is the units digit then the thousands digit can be 1,2,3, or 4 so here we have 4 options.

Then let us consider that the hundreds digit also has 4 options because it can have 0.

Then the tens digit has 3 options which is written as,

=> 4*4*3 = 48

Similarly, let us consider that if 0 is the units digit, then 5 is the largest digit, there must be a 5 in the integer.

Here we have also note that if the 5 is the hundreds digit, then there are 12 ways.

And here there are 3 places the 5 could be so it can be written as

=> 12*3=36.

Therefore, the total possible numbers are written as

=> 48+36=84 Integers

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the fox population in a certain region has an annual growth rate of 8 percent per year. it is estimated that the population in the year 2000 was 7600.

(a) function model for the t year after 2000 (exponential model):

[tex]p(t) = 7600 (1.08)^t[/tex]

The function is a mathematical phrase, rule, or law that establishes the connection between an independent variable and a dependent variable (the another variable).

A function is described as a relationship between a group of inputs and one output each. A function is, to put it simply, a connection between inputs in which each input is connected to exactly one output.

Population in 2000,

P(0) = 7600

Growth rate = 8% each year

(a) function model for the t year after 2000 (exponential model):

[tex]p(t) = 7600 (1.08)^t[/tex]

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By applying a linear equation, it is concluded that the slope of the line is 2 and the y-intercept is -4

A linear equation is an equation that has the variable of the highest power of 1. The standard form of a linear equation is y = mx + k, where m is the slope of the line and k is the y-intercept.

First, we draw a triangle ABC whose vertices are A(0, 8), B(2, 0),C(8, 0)

Then we determine point D as the midpoint of AC, so D(4,4)

Now we use B(2,0) and D(4,4) to determine slope of the line (m):

m = (y₂-y₁) / (x₂-x₁)

    = (4-0) / (4-2)

    = 4/2  

    = 2

To find the y-intercept of the line, we pick one of the points on the line. Let's say we pick point (6,8). Then we put those values into the equation:

y = mx + k

8 = 2*6 + k

8 = 12 + k

k = -4

Thus the y-intercept of the line is - 4

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The relation in this problem that is a function is given as follows:

D. (3, 4), (-5, 2), (5, 1), (-8, 2).

To verify whether a relation represents a function, we need to observe if each input is mapped to only one output.

The relationships that are not functions in this problem, along with the justification, are given as follows:

Hence the relationship that is a function is given by option D, as the inputs 3, -5, 5 and -8 are each mapped to a single output.

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A set of reflections that would carry hexagon ABCDEF onto itself would be "x-axis, y=x, x-axis" or "y=x, x-axis, y-axis".

What is a combination of reflections?

Combination of Two Reflections. A point or object once reflected can further be reflected to form a new image. The axes of these reflections may be parallel to each other or they intersect each other at a point.

Given the coordinates of hexagon ABCDEF, it can be determined that a set of reflections that would carry the hexagon onto itself would be a combination of reflections over the x-axis and y-axis.

One possibility would be to reflect over the x-axis, then reflect over the y=x line, and finally reflect over the x-axis again.

This would take the hexagon from its original position to itself.

Another possibility would be to reflect over the y = x line, then reflect over the x-axis, and finally reflect over the y-axis.

This would also take the hexagon from its original position to itself.

Hence, a set of reflections that would carry hexagon ABCDEF onto itself would be "x-axis, y=x, x-axis" or "y=x, x-axis, y-axis".

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The equation x(2x+3) = x² + 1 is the quadratic equation and the remaining equation (x²)² + 1 = 2x³, (x +  1) + 8 = (x²)(x²), and (x²)³ = (x³)⁴ are not in quadratic equation.

The term quadratic equation in math is defined as an equation containing one term in which the unknown is squared and no term in which it is raised to a power higher than 2.

Here we have to find the equation that was not in the form of the quadratic equation.

As per the definition, we have know that the quadratic equation must be in the form of

=> ax² + bx + c = 0

So, here we have to look into the given expression, then w e have identified that only the equation x(2x+3) = x² + 1 is in the quadratic form.

Because the quadratic equation only have the highest power value of 2.

And the remaining are not the quadratic equation.

Therefore, option (a), (b) and (d) are the resulting options.

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Buffalo Mild Wings offers the lowest price per wing.

Lowest Price:

Demands for the lowest possible price are more commonly seen in markets with limited liquidity or low trading volume, or from traders in companies with very small market caps. This is because investors trading illiquid securities are less likely to fill buy and sell orders. Markets for less traded securities are more limited and other parties can charge prices that may not be ideal for investors. For example, investors who want to trade currency options in foreign currencies (i.e. currencies other than dollars, euros, pounds or yen) often use the lowest possible price.

According to the Question:

Given:

Buffalo Bills has 8 wings for $7.

Buffalo Mild Wings has 12 wings for $10.

Wingers has 20 wings for $17.

To Find:

Which restaurant offers the lowest price per wing?

Solution:

Find the price per wing in Buffalo Bills:

8 wings = $7

1 wing = 7 ÷ 8

1 wing = $0.875

Find the price per wing in Buffalo Mild Wings:

12 wings = $10

1 wing = 10 ÷ 12

1 wing = $0.833

Find the price per wing in Wingers:

20 wings = $17

1 wing = 17 ÷ 20

1 wing = $0.85

Now,

Comparing  $0.875 , $0.833 and $0.85:

$0.833 < $0.85 < $0.875

⇒ $0.833 is the cheapest

⇒ Buffalo Mild Wings is the cheapest

Answer: Buffalo Mild Wings offers the lowest price per wing

Complete Question:

Leah loves chicken wings and is comparing the deals at three different restaurants. Buffalo Bills has 8 wings for $7. Buffalo Mild Wings has 12 wings for $10. Wingers has 20 wings for $17. Which restaurant offers the lowest price per wing?

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Answer:

-1233

Step-by-step explanation:

Step 1.) Plug in the orresponding number to letter

- |135+ -2| 2- -7.

Step 2.) Find absolute value

-| 137 | 2- -7

Step 3.) Solve

-137 × 9

= -1233

Answer: 14.7

Step-by-step explanation:

The remaining interior angle is [tex]135^{\circ}[/tex].

[tex]\frac{x}{\sin 19^{\circ}}=\frac{32}{\sin 135^{\circ}}\\ \\ x=\frac{32 \sin 19^{\circ}}{\sin 135^{\circ}} \\ \\ x \approx 14.7[/tex]

Step-by-step explanation:

(e) = number of erasers she had originally.

now she has 38.

so,

A

38 = (e) + 10

B

38 - 10 = (e) + 10 - 10

28 = (e)

she had originally 28 erasers.

The test statistic of -0.03 is compared to a critical value to determine if the null hypothesis can be rejected. If the test statistic is less than or equal to the critical value, the null hypothesis is rejected and the 90% figure is not accurate.

Calculate the sample proportion:

Sample Proportion

= 657/750

= 0.87

Calculate the test statistic:

Test Statistic

= 0.87 - 0.90

= -0.03

Compare the test statistic to a critical value:

If the test statistic is less than or equal to the critical value, then we can reject the null hypothesis. If the test statistic is greater than the critical value, then we cannot reject the null hypothesis.

The null hypothesis is that the percentage of adults in the region who drink milk is equal to 90%, while the alternative hypothesis is that the percentage is not equal to 90%. A sample of 750 adults is polled and the sample proportion is calculated to be 0.87.

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Answer:

Say you take a pizza and cut it perfectly down the middle so there are two slices. Each slice is a half or 1/2 of the pizza.

a). 115.26 is the upper bound of a 98% band (b). 93.36 to 116.63 is the 98% confidence interval (c). We have 98% confidence that the collected sample data will include the true worth of the population parameter.

By multiplying the total number of numbers by amount of all the numbers, one can approximate the average. A mean can be established by the average of such probabilities in a survey of data. In other words, an average is also known as the arithmetic mean. The average is referred to as having a mean.

[tex]\begin{aligned}& \mu=105 \\& \sigma_x=\frac{\sigma}{\sqrt{n}}=\frac{15}{\sqrt{9}}=5\end{aligned}[/tex]

(a). The maximum 98% interval

[tex]=\mu+Z_{0.02} * S D=105+2.0537 * 5=115.2685[/tex]

(b). 98 percent confidence band

[tex]\begin{aligned}& \left(\mu-Z_{\frac{0.02}{2}} * S D, \mu+Z_{\frac{0.02}{2}} * S D\right) \\& (105-2.3263 * 5,105+2.3263 * 5)=(93.3685,116.6315)\end{aligned}[/tex]

(c). We have 98% confidence that the collected random sample would also include the true value of said population parameter.

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The complete question is-

Suppose you administer a certain aptitude test to a simple random sample of 9 students in your school, and that the average score is 105 . From past experience, scores on such a test among students like those at your school follow a Normal distribution. We want to determine the mean score [tex]$\mu$[/tex] of the population. Assume a standard deviation of [tex]$\sigma=15$[/tex] for the test.

(a). What is the upper critical value for a 98% confidence interval? (Show the key numbers in the sketch of the distribution.)

(b). Construct and interpret a 98% confidence interval for the mean score [tex]$\mu$[/tex]. Follow the Inference Toolbox.

(c). Explain the meaning of 98 % confident.

Answer:

Step-by-step explanation:

a. To model the population of Western Lowland Gorillas after 5, 10 and 20 years, we can use an exponential decay model. This model assumes that the population of the gorillas is decreasing at a constant rate over time.

Let y equal the population of the gorillas and x represent the number of years since 2022.

The exponential decay model is represented by the equation:

y = a*e^(-rt)

Where a is the initial population, r is the decay rate and t is the number of years.

If we assume that the initial population of gorillas in 2022 is 1000, the decay rate is 0.1, and we can calculate the population of gorillas after 5, 10, and 20 years.

For 5 years after 2022:

y = 1000e^(-0.15) = 810 gorillas

For 10 years after 2022:

y = 1000e^(-0.110) = 648 gorillas

For 20 years after 2022:

y = 1000e^(-0.120) = 404 gorillas

b. Table:

Years Gorilla Population

5            810

10            648

20            404

c. The table shows that the population of gorillas is decreasing over time, which is an example of exponential decay. This decrease is consistent with the exponential decay model which we used. Exponential decay models are often used to predict population changes in endangered species as they assume a constant rate of decrease in population. Scientists can use this model to predict future populations, as well as estimate the rate of population decline. Based on this information, conservation efforts can be better planned, and resources can be allocated more effectively to prevent the extinction of endangered species.

Answer:

125 miles per week

Step-by-step explanation:

He is running: 100 x (100 + 20)% = 100 x 120% = 100 x 6/5 = 125 miles
He is running 125 miles per week

=> r = 125 miles

Step-by-step explanation and Answer

Since the interest rate is 5%, and the first loan was borrowed on May 1, we can calculate the interest on the first loan by using the formula:

Interest = Principal x Rate x Time

In this case, the principal is 2000, the rate is 5% (expressed as a decimal), and the time is (September 24 - May 1) = 4.5 months

So, Interest = 2000 x 0.05 x 4.5/12 = 50

The same applies to the second loan of 1000, so the interest on this loan is:

Interest = 1000 x 0.05 x (4.5/12) = 25

To find the total amount returned, we add the interest on both loans to the total principal borrowed:

total = 2000 + 1000 + 50 + 25 = 3075

Therefore, the total amount returned is Ks 3075

Step-by-step explanation:

a. To find dy/dx when y = 2xlog e (2x), we can use the chain rule. First, we rewrite the function as y = 2x(ln(2x) + 1) where ln is the natural logarithm. Then, we can take the derivative of y with respect to x:

dy/dx = 2(ln(2x) + 1) + 2x(1/2x) = 2ln(2x) + 2 + 2/x

b. To find f′(0) when f(x) = e^x^2/e^x+1, we can take the derivative of the function with respect to x:

f′(x) = (2xe^x^2(e^x+1) - e^x^2(e^x+1)) / (e^x+1)^2

Setting x = 0, we get:

f′(0) = 2e^0(e^0 + 1) - e^0(e^0 + 1) / (e^0 + 1)^2 = 1 / (e^0 + 1)^2 = 1 / 2^2 = 1/4

The number of ways in which exactly one of the toddler triplets to end up with their coat is given as follows:

3.

A sample space is a set that contains all possible outcomes in the context of an experiment.

The cardinality of the sample space in this problem, considering the Fundamental Counting Theorem, is obtained as follows:

N = 3 x 2 x 1

N = 6.

(the first chosen has 3 possible options, the second has two and the third has one).

The six possible outcomes are given as follows, considering the order Red - Green - Blue:

Hence there are three outcomes for exactly one of the toddler triplets to end up with their coat.

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According to the concept of inverse function, the domain of the function is explained below.

The term inverse function is defined as a function which is a square of a linear function.

Here we have know that we will restrict the domain of the function so that the function is one to one.

And then we will find the inverse and then we will find the domain of the inverse function.

Here we have given that the function is not one-to-one and then delete part of the domain so that the function that remains is one-to-one.

As we all know that a function is the set of inputs accepted by the function.

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Answer:

Step-by-step explanation:

Step-by-step explanation:

You will get the x and y interceptions by substituting. To make it easier, put x=0 , 3, -3 and solve the equation.

Hope this helps you.

Therefore ,performance task is indeed a learning project where students are required to perform in order to show their understanding, knowledge, and skill.

Your knowledge is lacking. Consequently, a summary will be provided. A function and variable performance task evaluates a student's ability to use their prior knowledge to interpret a novel phenomena.

Here,

It should be noted that performance tasks yield a tangible product and performance that serve as evidence of learning.

In those other words, the student must put what they have learned into practice.

These assignments often result in a physical output (such as a graphic display, blog post, or performance, such as an oral presentation or debate) that serves as proof of their knowledge and skill.

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The complete question is "What is Performance Task: Super Survey Simulator ?"

Answer:Its domain is all real numbers. Its range is all real numbers greater than or equal to zero. Its graph lies completely above the x-axis.

The rate of change of the volume at that particular instant is - 62.8 m^3/h.

How to get the rate of change of the volume?

First, we can write the dimensions as:

radius = R = (5m + 1m/h*t)

height = H = (8m - 4 m/h*t)

Where t is the time in hours.

Then the volume of the cylinder will be:

V = pi*R^2*H = 3.14*(5m + 1m/h*t)^2*(8m - 4 m/h*t)

To get the rate of change, we need to differentiate it with respect to t, we will get:

V' = 3.14*(2*(5m + 1m/h*t)*(1m/h)*(8m - 4 m/h*t) + (5m + 1m/h*t)^2*(-4m/h))

V' = 3.14*( (2 m/h)*(5m + 1m/h*t)*(8m - 4 m/h*t) - (4m/h)*(5m + 1m/h*t)^2)

V' = 3.14*(2m/h)*( (5m + 1m/h*t)*(8m - 4 m/h*t) - 2*(5m + 1m/h*t)^2)

As you can see the rate of change depends on t, but we want the rate of change at this instant, then we use t = 0, replacing that on the above equation we get:

V'(0) = 3.14*(2m/h)*( (5m + 1m/h*0)*(8m - 4 m/h*0) - 2*(5m + 1m/h*0)^2)

V'(0) = 3.14*(2m/h)*( (5m)*(8m ) - 2*(5m)^2)=  -62.8 m^3/h

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Answer: I think it is the first one

Step-by-step explanation:

Answer:

I'm pretty sure it's x^2 - 4x

Step-by-step explanation:

a. To prove the product property for logarithms using a base of 3 and solutions of 3, 9, 27, 81, and 243, we can start with the equation: log3(xy) = log3x + log3y

Let's say we want to find log3(81 * 27)
We know that log3(81) = 4, and log3(27) = 3
So, log3(81 * 27) = log3(81) + log3(27) = 4 + 3 = 7

We can verify this by using the fact that we know the solution of log3(81*27) is 243, and 3^7 = 243.

b. To prove the quotient property for logarithms using a base of 3 and solutions of 3, 9, 27, 81, and 243, we can start with the equation: log3(x/y) = log3x - log3y

Let's say we want to find log3(81 / 27)
We know that log3(81) = 4, and log3(27) = 3
So, log3(81 / 27) = log3(81) - log3(27) = 4 - 3 = 1

We can verify this by using the fact that we know the solution of log3(81/27) is 9, and 3^1 = 9.

c. To prove the power property for logarithms using a base of 3 and solutions of 3, 9, 27, 81, and 243, we can start with the equation: log3(x^n) = n*log3x

Let's say we want to find log3(81^3)
We know that log3(81) = 4
So, log3(81^3) = 3 * log3(81) = 3 * 4 = 12

We can verify this by using the fact that we know the solution of log3(81^3) is 243, and 3^12 = 243.

In all the above examples, we can see that the properties are upheld, and we can use the log3(y) values of 3, 9, 27, 81, and 243 to prove the Product, Quotient and Power property of logarithms with base 3.

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Degree: 2

Leading coefficient: -1 (The leading coefficient is the coefficient of the term with the highest degree in the polynomial, in this case, the coefficient of u², which is -1)