Find the y-intercept of the line on the graph.

a. The probability that the sample proportion will be within ±0.02 of the population proportion - 0.5223

b. The probability that the sample proportion will be within 0.05 of the population proportion - 0.9232

[tex]Given, \\$P=0.2 a$ \\$n=200$ \\mean, \ $\mu \hat{p}=p$ \\$=0.20$ \\Standard deviation, $\sigma_p=\sqrt{\frac{p(1-p)}{n}}$ \\$=\sqrt{\frac{0.20(1-0.20)}{208}}$ \\$=\sqrt{\frac{0,20(0,80)}{200}}$ \\$=\sqrt{\frac{0.16}{200}}$. \\$=0.0283$ \\a) $p(|x-\mu|=\pm 0.02)=f\left(\frac{-|x-\mu|}{\sigma \hat{p}} < z < \frac{|x-\mu|}{\sigma_{\hat{p}}}\right)$ \\$=1\left(\frac{-0.02}{0.0283} < = < \frac{0.02}{0.0283}\right)$ \\$=P(-0,71 < z < 0,71)$[/tex]

[tex]$$\begin{gathered}=p(z < 0,71)-p(z < -0,71) \\=0,7612-0.2389 \\=0,5223 } \\\therefore P(|x-\mu|=\pm 0.021=0,5223)\end{gathered}$$[/tex]

[tex]b)\\$$\begin{aligned}p(|x-\mu|=\pm 0.05)=p\left(\frac{|x-\mu|}{\sigma \hat{p}} < z < \frac{|x-\mu|}{\sigma \hat{p}}\right) \\=p\left(\frac{-0.05}{0.0283}-z < \frac{0.05}{0.0283}\right) \\=& p(-1.77 < z < 1.77) \\=& P(z < 1.77)-p(z < -1.77) \\\therefore p(i x-\mu \mid&=\pm 0.05)=0.9232\end{aligned}$$[/tex]

A population is a complete  group of individuals, regardless of whether that group consists of a nation or a group of people with a common characteristic.

In statistics, a population is a group of individuals from which a statistical sample is taken for research. Thus, any selection of individuals grouped together on the basis of some common characteristic can be called a population. A sample may also refer to a statistically significant portion of the population rather than the entire population. Therefore, statistical analysis of a sample must report the approximate standard deviation or standard error of the results for the entire population. Only the whole population analysis has no standard error

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Notice that the first number is 4, that would be the missing number.

The complete expression is

Remember that the associative property just groups the numbers differently.

To find:

The angular velocity of the point.

Solution:

Given the wheel moves with a velocity of 95 feet per second and the diameter is 5 feet.

So, the radius of the wheel is 5/2 feet.

The formula used to find the angular velocity of the wheel is given by:

So, by the given information is:

Thus, the angular velocity is 38 radians per second.

Answer:

If you are talking about a triangle XYZ

<x + <y + <z = 180

73 + 90 + z =180

<z = 17

Latoya's Coffee Shop makes a blend that is a mixture of two types of coffee. Type A coffee costs Latoya $5.85 per pound, and type B coffee costs $4.30 per pound.

This month's blend used four times as many pounds of type B coffee as type A, for a total cost of $553.20.

Let, a pounds of type A coffee and b pounds of type B coffee were used.

Then,

Substituting in the first equation,

Hence, 24 pounds of type A coffee were used.

Correct graph: C

Explanation

Given

Therefore;

Answer:

To solve the exercise you can use the point-slope formula, that is,

So, in this case, you have

Then,

We have

So we must replace the value of y of the second equation in the first equation

So, the answer is 9x - 6 = 50. Last option.

Part a:  Average rate of change = 7.2 m/sec(going downward)

part b: Instantaneous rate of change = -7.6 m/sec

For the given question;

The height of ball kicked is given by equation;

h(t) = -4.9t^2 + 12t + 0.5

Where,  h(t) = -4.9t^2 + 12t + 0.5

Part a: Average rate of change of the height of the ball from 1s to 3s.

For t = 1 sec

h(1) =  -4.9(1)^2 + 12(1) + 0.5

h(1) = 7.6 m

For t = 3 sec

h(3) =  -4.9(3)^2 + 12(3) + 0.5

h(3) = -7.6

Average rate of change = -7.6 - 7.6 m/3 - 1

Average rate of change = - 15.2/2

Average rate of change = 7.2 m/sec(going downward)

Part b : instantaneous rate of change at 3s.

h(3) =  -4.9(3)^2 + 12(3) + 0.5

h(3) = -7.6

instantaneous rate of change = -7.6 m/sec

Thus, the instantaneous rate of change of the ball at 3s -7.6 m/sec.

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700,000,000

+

60,000,000

+

8,000,000

+

90,000

+

20,000

+

50

+

4

____________

768,110,054

When a point is reflected across the line, y = x, the x and y coordinates changes places. Given that the coordinates of the original point is (a, b), the coordinate of the new point would be (b, a)

Again, this new point was reflected across the x axis. Recall, if reflection is done across the x axis, the sign of the x coordinate remains the same while the sign of the y coordinate is reversed,

Therefore, the coordinates of its final image point in terms of a and b is (b, - a)

The correct option is number 3

The co-ordinates when reflected over the y-axis are (-2,1), (-5,1) and (-2,4).

The co-ordinates of the figure given are (2,1), (5,1), and (2,4). It is clear that the figure is a triangle as (2,1) and (2,4) has same x-co-ordinates and (2,1) and (5,1) has same y-co-ordinates.

So this figure is reflected over the y-axis and we need to find the co-ordinates of the new transformed figure.

The reflection over y-axis does not change the y-co-ordinates but the x-co-ordinates are changed into their corresponding opposite signs. That is,

x ----> -x.

So the reflection over y-axis can be represented as (x, y) ----> (-x, y)

Hence the co-ordinates of the reflected figure are:

(-2,1), (-5,1), and (-2,4).

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Answer:

85

Explanation:

First, recall the formula for Z-Score.

Substitute the given values:

A z-score of -1.5 represents ​an IQ score of 85.

Answer:

C

Step-by-step explanation:

Just divide 48/120.

Those are like terms because are constants

Those aren't like terms because 25 is a constant, x is a variable, and 3x² is a quadratic variable

The ratio OQ/QN would not give a correct calculation of K

Here, we want to select which of the options would be a wrong calculation for k which is the scale factor

Any of the ratios that would measure k should be such a ratio that compares similar distances

The correct answer in this case is OQ/QN

The reason why it is wrong is that while OQ meaures the distance from the center of dilation to the first segment, QN should also have measured a comparable distance

Thus, ON should have been what to use if we are to compare both distances since they would have measured the distances from the center of dilation which is the origin in this case

1) In this question, we can see that a point has been given. So let's plot that point that belongs to the function:

We can tell that this point is part of the function by plugging it into the given function:

2) So let's plot the graph:

Now, we can find another point by moving one unit down and three to the right.

3) Thus, the answer is:

The volume of the cone is 36,960km³.

What is a cone?

A cone is a three-dimensional solid geometric shape having a circular base and a pointed edge at the top called the apex.

The volume of a cone defines the space or the capacity of the cone. It is calculated using:

Vol. of a cone=1/3×π×r²h

where π=22/7

r     = raπius of the base of the cone

h= height of the cone

Thus, vol. of the cone=1/3×22/7×21²×80

                                   =  776160/21

                                    =36,960km³

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Answer:

What is the relationship between altitude and boiling point of a liquid?

At a higher elevation, the lower atmospheric pressure means heated water reaches its boiling point more quickly—i.e., at a lower temperature. Water at sea level boils at 212 degrees Fahrenheit; at 5,000 feet above sea level, the boiling point is 203 degrees F. Up at 10,000 feet, water boils at 194 degrees F.

Step-by-step explanation:

Answer:

[tex]\textsf{Equation}: \quad b=-0.0019a+214[/tex]

209.44 °F

Step-by-step explanation:

Define the variables:

Given:

If the relationship between altitude (a) and boiling point (b) is linear, this can be modelled as:

[tex]\boxed{b=ma+c}[/tex]

where:

Find the slope of the linear equation by substituting the given ordered pairs into the slope formula:

[tex]\implies \textsf{slope}\:(m)=\dfrac{b_2-b_1}{a_2-a_1}=\dfrac{205.45-198.61}{4500-8100}=\dfrac{6.84}{-3600}=-0.0019[/tex]

Substitute the found slope and one of the ordered pairs into the point-slope formula:

[tex]\implies b-b_1=m(a-a_1)[/tex]

[tex]\implies b-205.45=-0.0019(a-4500)[/tex]

[tex]\implies b-205.45=-0.0019a+8.55[/tex]

[tex]\implies b=-0.0019a+214[/tex]

Therefore, an equation giving the boiling point (b) of the​ liquid in terms of altitude​ (a) is:

[tex]\boxed{b=-0.0019a+214}[/tex]

To find the boiling point of the liquid at 2400 ​ft, substitute a = 2400 into the found equation:

[tex]\implies b=-0.0019(2400)+214[/tex]

[tex]\implies b=-4.56+214[/tex]

[tex]\implies b=209.44[/tex]

Therefore, the boiling point of the liquid at 2400 ft is 209.44 °F.

After evaluating the limit we have came to find that the limit of   [tex]\lim_{x\rightarrow \left(1/2)^-} $$|2x-1| 2x-1[/tex]    as x approaches 1/2- is -1.

In mathematics, a limit is the value that a function, sequence, or index approaches as an input or as an index approaches a specific value. Limits, which are fundamental to calculus and mathematical analysis, are required for the definitions of continuity, derivatives, and integrals.

The concept of a limit of a sequence is further generalized to include the concept of a limit of a topological network, in addition to having a connection to the category theory concepts of limit and direct limit.

A function's limit is typically expressed in formulas as

[tex]{\displaystyle \lim _{x\to c}f(x)=L}[/tex]

We need to solve the given equation

⇒ [tex]\lim_{x\rightarrow \left(1/2)^-} $$|2x-1| 2x-1[/tex]

⇒ [tex]\lim_{x\rightarrow \left(1/2)^-} $$(2\times|2x-1| x) + \lim_{x\rightarrow \left(1/2)^-}}$$( -1)[/tex]

⇒ Evaluate for x

⇒ [tex]0+ \lim_{x\rightarrow \left(1/2)^-}}$$( -1)[/tex]

⇒ 0 - 1

⇒ -1

Thus, after evaluating the limit we have came to find that the limit of   [tex]\lim_{x\rightarrow \left(1/2)^-} $$|2x-1| 2x-1[/tex]    as x approaches 1/2- is -1

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Using the Factor Theorem, the equation of the quartic polynomial in standard form is given by:

y = 4(x^4 + x³ - 13x² - x + 12).

The Factor Theorem states that a polynomial function with roots(also called zeros) [tex]x_1, x_2, \codts, x_n[/tex] is given by the rule given as follows:

[tex]f(x) = a(x - x_1)(x - x_2) \cdots (x - x_n)[/tex]

In which a is the leading coefficient of the polynomial, determining if it is positive(a positive) or negative(a negative).

From the given table, the roots are given by the values of x when y = 0, hence they are given by:

[tex]x_1 = -4, x_2 = -1, x_3 = 1, x_4 = 3[/tex]

Hence the function is given by:

f(x) = a(x + 4)(x + 1)(x - 1)(x - 3)

f(x) = a(x² + 5x + 4)(x² - 4x + 3)

f(x) = a(x^4 + x³ - 13x² - x + 12).

From the table, we also have that when x = 0, y = 48, hence the leading coefficient a can be found as follows:

12a = 48

a = 48/12

a = 4.

Hence the equation is:

y = 4(x^4 + x³ - 13x² - x + 12).

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answer: x = 3.27

Answer:

Solution examples: (5,0) and (5,5)

Not a Solution (1,5) and (5, 10)

Explanation:

The graph and the points inside and outside the solution set are given below.

The grey-blue region is the solution to the system and the region outside it is not.

Therefore, the point (5, 0) is a solution and (1, 5) is not a solution.

Using simple interest, we know that the principal (p) is $6000.

OR

Using simple interest formula, we have:

To find a principal we have

Hence the value of the principal or p is $6000.

Therefore, using simple interest, we know that the principal (p) is $6000.

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In linear equation, 432 milliliters of water does he use .

What are a definition and an example of a linear equation?

Nick bakes 3 dozen cookies for the bake sale.

1 cookie  requires 12 milliliters of water.

water does he use = 3 × 12 × 12

                                = 432 milliliters of water

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SOLUTION

Given the question in the image, the following are the solution steps to answer the question.

STEP 1: Write the given points

STEP 2: Write the formula for finding the modulus

STEP 3: Substitute the values into the formula to get the answer

Hence, the required modulus is approximately 3.6 to the nearest tenth.

We know that figure I and figure II are similar, which means that:

-The corresponding angles are equal

-The corresponding sides are at the same ratio.

The ratios between the corresponding sides are:

You have to compare the determined ratios with the given options to find the true statement.

The only given proportion that is true is the first one

Number of candy's Bev has left with her is 12 .

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Given:

No. of candy Bev has= 24

She gave 1 /3 of candy to Jamie.

No. of candy Jamie got = 1 /3 of total candy

                                       = 1 /3 * 24

                                       = 8 candy

No. of candy she remained = total no. of candy - no of candy she gave to Jamie:

                                            =24 - 8

                                            =16

No. of candy Selena got = 1 /4 of remaining candy

                                           =1 /4 ×16

                                            =4

No. of candy left = total candy - (candy Jamie got +candy Selena got)

                                             = 24-(8+4)

                                              = 12 candy

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ANSWER

EXPLANATION

We are given that the radius of the circle is 3 inches and the length of the arc that subtends the angle is 3π inches.

We can find the angle subtended by the arc by using the formula for length of an arc:

Therefore, we have that:

That is the angle subtended by the arc.