Find the values of x and y.

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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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

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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Answer:

Option c) I have 2 and you have 3

Answer:

H (13, -16)

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{7.4 cm}\underline{Midpoint between two points}\\\\Midpoint $=\left(\dfrac{x_2+x_1}{2},\dfrac{y_2+y_1}{2}\right)$\\\\\\where $(x_1,y_1)$ and $(x_2,y_2)$ are the endpoints.\\\end{minipage}}[/tex]

Given:

Substitute the given endpoint G and midpoint M into the midpoint formula:

[tex]\implies M=\left(\dfrac{x_H+x_G}{2},\dfrac{y_H+y_G}{2}\right)[/tex]

[tex]\implies (3, 4)=\left(\dfrac{x_H-7}{2},\dfrac{y_H+24}{2}\right)[/tex]

x-value of endpoint H:

[tex]\implies 3=\dfrac{x_H-7}{2}[/tex]

[tex]\implies 6=x_H-7[/tex]

[tex]\implies x_H=13[/tex]

y-value of endpoint H:

[tex]\implies 4=\dfrac{y_H+24}{2}[/tex]

[tex]\implies8=y_H+24[/tex]

[tex]\implies y_H=-16[/tex]

Therefore, the coordinates of endpoint H are:

Answer: 13 -16

Step-by-step explanation: Edge 2023

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"

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

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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A set of distinct numerical expressions known as simplify algebraic expressions in mathematics has been deconstructed by numerous philosophers and intellectuals throughout history. Speaking of algebra, it is a discipline of mathematics that deals with geometry and number theory, two of the oldest ideas in mathematics.

1. Group like terms: Combining all the terms that have the same variables and coefficients to form a single term.

2. Factor out the greatest common factor (GCF): Factoring out the greatest common factor from each of the terms in the equation.

3. Use the distributive property: Rewriting an expression using the distributive property to make it easier to solve.

4. Combine like terms: Summing or subtraction the same terms on both sides of the equation.

5. Use factoring techniques: Factoring a polynomial equation to make it easier to solve.

6. Use the addition or subtraction principle: Rewriting an equation so that all the terms are on the same side of the equation.

7. Use the multiplication or division principle: Rewriting an equation so that all the terms are on the same side of the equation, multiplied or divided by the same number.

8. Use substitution: Replacing an unknown with a known value in an equation.

9. Use the quadratic equation: Solving an equation with a quadratic equation if it can be written in the form of ax2 + bx + c = 0 by simplify.

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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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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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Using a system of equations and solving them via simultaneous method, we determined that Bo bought 3 soda and 4 juice.

What is System of Equations?

A system of equations, also known as a set of simultaneous or an equation system, is a finite set of equations for which we sought the common solutions. A system of equations can be classified in a similar manner as single equations.

We can write out the equations and proceed to solve this problem.

Let;

x = soda

y = juice

x + y = 7 ...eq(i)

50x + 25y = 250 ...eq(ii)

Solving equation (i) and (ii)

The value of x and y are 3 and 4 respectively

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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.

The quotient of the fractions  is 42/55

The quotient of a fraction is the value that is obtained when you simplify the fraction

Given: 5 3/5 ÷ 7 1/3

5 3/5 = 28/3 and 7 1/3 = 22/3

5 3/5 ÷ 7 1/3 = 28/5 ÷ 22/3

                    = 28/5 × 3/22

                    = 84/110

                    = 42/55

Thus, the quotient is 42/55

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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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Answer: the price is 1,5 8-ounce price

Step-by-step explanation: The unitary price is the same, but the quantity is  12/8 = 1,5.

The 12-ounce price should be 1,5 more than the 8-ounce price.

Answer:

The distance between boat A and boat B will be 7.2 units apart.

What is the distance between two points?

It is the measure of distance between the two points and is known as length. The length is measured in meters generally. Let one point be (x, y) and another point be (h, k).

Then the distance between the points will be

D² = (x - h)² + (y - k)²

A marina is looking like a direction framework. Boat An is moored at (3.1, −1) and Boat B is moored at (−4.1, −1).

Then the distance between the points (3.1, −1) and (−4.1, −1) will be given as,

D² = (-1 + 1)² + (3.1 + 4.1)²

D² = (7.2)²

D = 7.2 units

The distance between boat A and boat B will be 7.2 units apart.

Answer:

7 Units

Step-by-step explanation:

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 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:

c

Step-by-step explanation:

Answer:Use the model to t = predict the population of each country in 2030.

Step-by-step explanation:

We can infer from the graph that is attached that (D) the function decreases when x is between -6 and 0.

A function in mathematics from a set X to a set Y allocates exactly one element of Y to each element of X.

The sets X and Y are collectively referred to as the function's domain and codomain, respectively.

So, consider the given chart.

For a certain period of points, the function is decreasing.

Attach the point to the x-axis and we will get that between the x-axis -6 and 0, the function is decreasing.

Therefore, we can infer from the graph that is attached that (D) the function decreases when x is between -6 and 0.

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Complete question:
This shows a graph of a function.

Where is the function decreasing?

a. The function decreases when x is less than –7.

b. The function decreases when x is greater than –6.

c. The function decreases when x is between 0 and 4.

d. The function decreases when x is between –6 and 0.

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:

9 pies per hour

Step-by-step explanation:

If Janelle can make 10 pies in 2 hours

10 divided by 2 is 5

so she can make 5 pies per hour

If hector can make 9 pies in 3 hours

9 divided by 3 is 3

so he can make 3 pies per hour

so 3 + 5 is 9 pies per hour

together they they can make 9 pies per hour

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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Answer:

------------------------

Given:

Find the missing leg, using Pythagorean:

Answer:

Multiply 5 5 by −4 - 4 . Multiply 2 2 by −5 - 5 . Multiply −5 - 5 by 5 5 . Subtract 10y 10 y from −20y - 20 y .