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The height of the inverted image representing segment [is 0.75 cm.

More than one triangle are said to be similar when the corresponding sides and angles have relatable properties. The length of segment A′B′ is 0.75 cm.

it can be observed that; △ABC ≅ △A′B′C′

Given that: BC = 100cm, B′C′ = 2.5 cm; AB = 30 cm,

A′B′  = ?

Comparing the corresponding sides of the similar triangles, we have:[tex]\frac{AB}{A^{I}B^{I} }[/tex] = [tex]\frac{BC}{B^{I}C^{I} }[/tex][tex]\frac{30}{A^{I}B^{I} }[/tex] = [tex]\frac{100}{2.5}[/tex][tex]A^{I}B^{I}[/tex] = [tex]\frac{30*2.5}{100}[/tex]  = 0.75[tex]

A^{I}B^{I}[/tex] = 0.75

Thus the height of the inverted image representing segment [tex]A^{I}B^{I}[/tex] is 0.75 cm.

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Answer: 400 points

Step-by-step explanation:

500 x 80 =  40,000

40,000/100 = 400 points

The association between days absent and test score is described by weak negative association.

The discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.

We need to find the association between days absent and test score.

From the graph we know that the x axis is represented by the average number of days absent and y axis is represented by the Average test score.

The association is depended on the correlation.

The correlation will positive increasing when the values of x axis are increasing and the value of y is increasing.

In the given graph as the values are decreasing the x values are increasing.

Which means it is a negative association.

Hence, weak negative association is describes the association between days absent and test score.

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The image created by the scale factor of 1 will be same as the pre-image

The scale factor of the image = 1

The ratio between the new size of the figure and the original figure = 1 : 1

The scale factor is the ratio between the dimensions of the new figure and the dimensions of the original figure.

The image in the dilation is the new/final figure and the pre-image is the original figure before dilation

Here, the size of the image and pre-image will be same because the ratio is 1 : 1, image and pre-image has same dimensions

Therefore, the image and the pre-image will be same

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Answer:

4.125 rounded to 4.13 = the price of tax.

4.13 + 55 = 59.13

The width at the instant the width is decreasing at .5 units/sec is increasing 5 units per/sec.

How to find change in length or width?

Given:

Area of triangle = 100 units²

Area of triangle = Length * Width

Length * Width = 100

dl / st = 2 unit/sec

a) Find length

when dw/dt = -0.5 unit/sec

l * w = -0.5

l dw/dt + w dl/dt = 0

100/w (-0.5) + w(2) = 0

(- 50+ 2w²) / w = 0

2w² = 50

w² = 25

w = 5

Hence, the width at the instant the width is decreasing at .5 units/sec is increasing 5 units per sec.

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The domain, range and asymptotes of the exponential function y = -2^(-x+2)+1 are given as follows:

The function in this problem is defined as follows:

y = -2^(-x+2)+1.

It is an exponential function, hence it has no restrictions, meaning that:

The range of the function is the set that is composed by all the output values of the function.

Due to the multiplication by the negative number, the function is reflected over the x-axis, and the addition by 1 means that the function is shifted up 1 unit, thus:

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Answer:

Step-by-step explanation:

Gradient of a line that is perpendicular to another line is always the negative reciprocal.

So:

the gradient perpendicular to -0.25x is 4

to find the y-intercept (c), you need to substitute x and y into the equation:

5 = 2(4) + c

5 = 8 + c

c = -3

hence:

y = 4x -3

Answer:

2, 3, and 7 are not function

The rest are

Step-by-step explanation:

In a function every X has one and only one y

2 is not a function because X=5 has 2 different y's

3 is not a function because X=2 has 2 different Y's

7 is not a function because X=b has 2 different Y's

By means of the law of cosine, the missing side of the triangle has a length of approximately 6.502 units.

Herein we find the case of a triangle with two known side lengths and a known measure of an angle between the two given sides. The measure of the unknown side is determined by the law of cosine, whose definition is shown below:

x² = a² + b² - 2 · a · b · cos θ

If we know that a = 15, b = 12 and θ = 25°, then the equation for the triangle is:

x² = 12² + 15² - 2 · 12 · 15 · cos 25°

Now we proceed to simplify and find the resulting value of x by algebra properties:

x² = 369 - 360 · cos 25°

x² = 369 - 326.271

x² = 42.279

x ≈ 6.502

The length of missing side of the triangle is approximately equal to 6.502 units.

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To find the average rate of change of a function over an interval, we need to calculate the slope of the secant line connecting the points on the function at the two endpoints of the interval.

The equation of a line in slope-intercept form is y = mx + b, where m is the slope of the line and b is the y-intercept. In the case of a secant line, we can calculate the slope by using the formula:

m = (y2 - y1) / (x2 - x1)

For the function y = x^2 + 4x - 1, we can plug in the values of x and y at the two endpoints of the interval, (-4 and 1), to find the slope of the secant line:

m = [(1)^2 + 4(1) - 1] - [(-4)^2 + 4(-4) - 1] / (1 - (-4))

Simplifying this expression, we get:

m = (1 + 4 - 1) - (16 + 16 - 1) / (-3)

This simplifies to:

m = -20 / -3

Therefore, the average rate of change of the function y = x^2 + 4x - 1 over the interval -4 ≤ x ≤ 1 is 6.5.

The linear function that has a slope of -4 and goes to point (9,-10) will be y = -4x - 50.

A straight line on the coordinate plane is represented by a linear function.

A linear function always has the same and constant slope.

The formula for a linear function is f(x) = ax + b, where a and b are real values.

Suppose that the linear function is y = mx + c

As per the given, slope m = -4

Put (9,-10)

-10 = -4 x -10 + c

c = -50

Thus, y = -4x - 50

Hence "y = -4x - 50 is the equation for the linear function with a -4 slope that leads to point (9,-10) in the graph.".

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The coordinates of the point on the directed line segment from (−3,4) to (3,8) partitions the segment into a ratio of 1 to 3 is given as follows:

(-1.5, 1).

The coordinates of the point are applied using proportions, as the fact that the point partitions the segment into a ratio of 1 to 3 means that the following equation is built:

Point - Initial Coordinate = 1/4(Final Coordinate - Initial Coordinate).

This equation is used to find both the x-coordinate and the y-coordinate of the point.

The x-coordinate of the point is obtained as follows:

x + 3 = 1/4(3 + 3)

x + 3 = 1.5

x = -1.5.

The y-coordinate of the point is obtained as follows:

y - 4 = 1/4(-8 - 4)

y - 4 = -3

y = 1.

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The probability that the sample mean will be less than 318 is 0.0011.

Mean is defined as the average of given numbers i.e. sum of all numbers divided by the total number of numbers. The Mean is denoted as m or μ. Standard deviation is the measure which it shows the variation from the mean exists or not. The standard deviation is denoted as σ.

We know that,

                 P ( x  <  n  )   =   P (   z     <     x  -  μ / ( σ / √n )   )    →   1  

where,     z   =       x - μ / ( σ / √n )  

As per the given question,

                                    P ( x  <  318 ) = ?

Substitute the values in 1,

P ( x < 318 )   =   P ( z < x - μ / ( σ / √n ) )

                      =   P ( z  <   318 - 330 / ( 35 / √80 )

                      =   P ( z < -12 / ( 35 / 8.94 )

                      =   P ( z < -12 / 3.91 )

                      =   P ( z < -3.069 )

                      =   P ( z < -3.07 )

P ( x < 318 )   =   0.0011

Therefore, 0.0011 is the probability that the sample mean will be less than 318. Hence Option a is correct.

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The complete question is

A certain brand of electric bulbs has an average life of 330 hours with a standard deviation of 35. A random sample of 80 bulbs is tested. What is the probability that the sample mean will be less than 318?

a.) 0.0011

b.) 0.9989

c.) 0.0006

d.) 0.0127

A function formula y = f(x) defines the relation between input values and output values.

We know that the function defines relation between the input values and the output values. A relation is a function if and only of for each input there is exactly one output.

A mathematical equation which involves x and y, i.e., a function, can be written in the form y = an expression involving x

y = f (x).

The function formulas are used for calculating the x-intercept, y-intercept and slope in any function.

We can find the x-intercept of a function by substituting the value of f(x) as 0. Similarly, the y-intercept of a function by substituting the value of x is 0. We can calculate the slope of a linear function by rearranging the function to the form, f(x) = mx + c; where m is the slope and c is the y-intercept.

Therefore, the function formulas are used to determine the x-intercept, y-intercept and slope in any function.

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Answer:

A credit report is not useful for lenders and borrowers because it does not provide detailed information about a person's financial history.

Answer: x=45 degrees

Step-by-step explanation:

125+x+10=180

all triangles add up to 180 degrees

135+x=180

x=45

Using the t-distribution, it is found that the p-value is of 0.

[tex]H_{0\\}[/tex] : μ₁ - μ₂ ≥ 0

[tex]H_{1}[/tex] : μ₁ - μ₂ < 0

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Assuming that the population proportion of blue eyes is accurately reflected in each sample, about 380 of the 400 confidence intervals should cover the population proportion.

The confidence interval for the proportion of blue eyes in the population is calculated as follows:

Proportion of blue eyes in the population = sample mean +/- (1.96* Standard Error)

Where Standard Error = sqrt[(proportion of blue eyes in the population)*(1-proportion of blue eyes in the population)/sample size]

At a 95% confidence level, the confidence interval should cover the population proportion 95% of the time. Therefore, 95% of the 400 confidence intervals should cover the population proportion, which is approximately 380 intervals.

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Rhombus is 4 pairs of congruent sides.

Congruent triangles are triangles that are precisely the same size and shape. The word congruent has the sign ≅. When the three sides and three angles of one triangle match the same dimensions as the three sides and three angles of another triangle, two triangles are said to be congruent.

A rhombus is a parallelogram with four congruent sides.

All the characteristics of a parallelogram are present in a rhombus, plus the following: The diagonals intersect at right angles.

Square and rhombus are the only two quadrilateral shapes that consistently have four congruent sides. Note that congruent sides refer to sides that are of the same length. A quadrilateral having four equal sides and four equal angles is called a square (90 degrees). It combines a rhombus and a right-angled rectangle ( equal side ).

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12620256  different combinations of 31 balloons can be chosen

What are combinations?

Combinations are mathematical operations that count the variety of configurations that can be made from a set of objects, where the order of the selection is irrelevant. You can choose any combination of the things in any order.

From the question, we understand that; a combination of 31 is to be selected. Because the order is not important, we make use of combination.

Also, because repetition is allowed; different balloons of the same kind can be selected over and over again.

So:

n= 31 +8-1 = 38

r=31

Selection =  [tex]^{38}C_{31}[/tex]

Use the formula:

[tex]^{n}C_{r}=\frac{n!}{(n-r)! r!}[/tex]

= > [tex]^{38}C_{31}=\frac{38!}{(38-31)! 31!}[/tex]

[tex]^{38}C_{31}=\frac{38!}{7! 31!}[/tex]

         = [tex]\frac{38*37*36*35*34*33*32*31!}{7*6*5*4*3*2*1* 31!}[/tex]

         = 12620256

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Answer:

222 grams.

Step-by-step explanation:

If it is 20% more, then it is 1.2 times more. 1.2*185=222, so the cereal box comes with 222 g of cereal.

If Jerald keeps going at this rate, the miles that he will ride in 2 hours is 30 miles.

Rate demonstrates how many times one number can fit into another number. It should be noted that they contrast two numbers by ordinarily dividing them. A/B will be the formula if one is comparing one data point (A) to another data point (B).

In this case, Jerald is cycling for a race and he rides 3/4 of a mile in 1/20 of an hour. The miles in an hour will be:

= 3/4 ÷ 1/20

= 3/4 × 20

= 15 miles..

The miles in 2 hours will be:

= 2 × 15

= 30 miles.

The miles is 30 miles.

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The kinematic equation of the motion of the paintbrush dropped 35 feet height from the ground and the 1.85 seconds reaction time of the 6 feet person standing directly below, indicates that they will be hit  by the paintbrush before they can move out of the way.

The kinematic equation of motion describe the motion of a body that moves under constant acceleration, without consideration of the forces causing the body to move.

The height from which the paintbrush is dropped from the roof to the ground = 35 feet

Height of the person standing directly below where the brush falls = 6 feet

The reaction time of the person = 1.85 seconds

The kinematic equation of motion of free fall of an object is presented as follows;

s = u·t + 0.5·g·t²

Where; s = The height through which the paintbrush falls

u = The initial velocity of the paintbrush = 0

g = The acceleration due to gravity ≈ 32.1741 ft/s²

The height the paintbrush falls before meeting the 6 feet tall person, s = 35 feet - 6 feet = 29 feet

Therefore, we get;

29 = 0 × t + 0.5 × 32.1741 × t²

t² = 29 ÷ (0.5 × 32.1741) ≈ 1.803

The time it takes the paintbrush to fall 29 feet, t, is therefore;

t = √(29 ÷ (0.5 × 32.1741)) ≈ 1.343

It takes the paintbrush to reach the height of the person standing directly below in just about 1.3 seconds after it is dropped, before the person can react to move away in 1.85 seconds, therefore, they will be hit by the paintbrush before they can move out of the way.

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Three types of infinitives in Spanish are the word that ends with the letters -er , -ar, and -ir.

Explanation:

Infinitive : In general sense infinitive represent the action or the purpose.

Infinitive in Spanish are generally non -conjugated verbs and they are ending with -er , -ar , -ir.

Basically infinitive in Spanish classified into three groups.

-er : Aprender meaning camping.

-ar : Acampar meaning Camping and so on.

Therefore, the three types of Spanish infinitives are word ends with -er , -ar, and -ir.

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Answer:

Option c) I have 2 and you have 3

The sample space for this experiment contains a total of 120 possible outcomes. This is because there are 10 possible balls to be drawn, and each of them can be chosen in 3 different ways. Thus, 10 x 10 x 10 = 1,000 possible combinations. However, since the order of the selected numbers does not matter, the number of possible outcomes is reduced to 1,000 / 6 = 120.

Mathematical explanations of the likelihood that an event will occur or that a statement is true are referred to as probabilities. A value between 0 and 1 represents the likelihood of an event, with 0 basically denoting impossibility and 1 generally indicating certainty.

Subtract the total number of events from the total number of outcomes. Divide the total number of ways the event could occur by the total number of possible outcomes once the probability event has been identified and its corresponding consequences have been determined.

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The Interest Rates are 2% and 5% respectively

What is Simple Interest?

Simple interest is a quick and straightforward way to calculate the interest on a loan. Simple interest is calculated by multiplying the daily interest rate by the principle multiplied by the number of days between payments.

Solution:

Let, the lesser interest rate be x

Simple Interest = Principal*Time*Rate/100

Total Interest = $166

166 = 2300*x*1/100 + 2400*(x + 3)*1/100

166 = 2300x + 2400x + 7200 / 100

16600 = 4700x + 7200

9400 = 4700x

x = 2%

and the Higher Interest Rate = 5%

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The expression equivalent to the statement raise p to the 7th power, then add q to the result is p⁷ + q

From the question, we have the following mathematical statement that can be used in our computation:

raise p to the 7th power, then add q to the result

When p is raised to the power of 7, we have the following representation

p⁷, then add q to the result

When q is added to p⁷ above, we have

p⁷ + q

Hence, the expression is p⁷ + q

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answer: b "the ratio of cranberry juice to fruit punch is 1:4"

C "The ratio of cranberry juice to orange juice is 1 to 4."

D "There is 1 cup of cranberry juice for every 4 cups of fruit punch. E. There are 4 cups of orange juice for every 5 cups of fruit punch"