HELP GIVING BRAINIEST

1 If angle DAC is 40 degrees how many degrees is Angle ACD. Show all of your work. Show Your work​

Answers

Answer 1

Answer:

m<ACD = \(50^{o}\)

Step-by-step explanation:

From the question given, ΔACD is a right angled triangle. Then we can apply one of the properties of a triangle to it.

In the triangle ACD:

<ACD + <DAC + <ADC = 180 (sum of angles in a triangle)

<ACD + 40 + 90 = 180

<ACD + 130 = 180

<ACD = 180 - 130

<ACD = \(50^{o}\)

With the application of the property of the sum of interior angles of a triangle, the measure of <ACD is \(50^{o}\).


Related Questions

A bee flies at feet per second directly to a flowerbed from its hive. The bee stays at the flowerbed for ​minutes, and then flies directly back to the hive at feet per second. It is away from the hive for a total of minutes. a. What equation can you use to find the distance of the flowerbed from the​ hive? b. How far is the flowerbed from the​ hive?

Answers

Answer:

Step-by-step explanation:

The question is incomplete. Here is the complete question.

A bee flies at 12 feet per second directly to a flowerbed from its hive. The bee stays at the flowerbed for 14 ​minutes, and then flies directly back to the hive at 8 feet per second. It is away from the hive for a total of 18 minutes. A. Write the equation. Let d be the distance of the flowerbed from the hive. B. how far away is the hive from the flower bed.

First we need to calculate the time taken by the bee to fly to a flowerbird to its hive using the formula;

Speed = Distance/Time

Time = Distance/Speed

If a bee flies at 12 feet per second directly to a flowerbed from its hive, then the time taken by the bee is expressed as;

t1 = d/12 ....... 1

If the bee then flies directly back to the hive at 8 feet per second, the time taken by the bird will be:

t2 = d/8 ....... 2

Total time taken by the bee to and fro will be the sum total of both times;

t1+t2 = d/12+d/8

t11+t2 = 2d+3d/24

t1+t2 = 5d/24 ........ 3

If the bee stays at the bee stays at the flowerbed for 14 ​minute and away from the hive for 18minutes, the total time used by the bird during the journey will be 18-14 = 4 minutes

converting 4 minutes to seconds

4 minutes = 4*60 = 240seconds

The equation that can be used to find the distance of the flowerbed from the​ hive is gotten by equating equation 3 to  the total time used by the bird during the journey i.e;

5d/24 = 240

5d = 24*240

5d = 5760

b) To know how far is the flowerbed from the​ hive, we will solve the resulting equation in a for the value of d as shown

Given 5d = 5760

Divide both sides by 5

5d/5 = 5760/5

d = 1152ft

Hence the distance of the flowerbed from the​ hive is 1152ft

Solve the system of equations:

y = x + 2
y = x2 + 5x + 6

A.
(0, 2) and (2, 4)

B.
(–2, 0) and (–3, 0)

C.
(–2, 0)

D.
(0, 2)

Answers

Answer: C

Step-by-step explanation:

Since both equations are set equal to y, it follows that

\(x+2=x^2 + 5x+6\\\\x^2 +4x+4=0\\ \\ \\(x+2)^2 = 0\\\\x=-2\\\\\implies y=-2+2=0\)

So, the solution is (-2, 0).

If the observations have weights of 2, 3 and 1 respectively, solve these equations for the most probable values of A and B using weighted least squares method. Solve the problem using both algebraic approach and matrices and compare your results.
A+2B=10.50+V1
2A-3B=5.55+V2
2A-B=-10.50+V3

Answers

The results obtained using the algebraic approach and the matrix approach should be the same. Both methods are mathematically equivalent and provide the most probable values of A and B that minimize the sum of squared weighted residuals.

To solve the system of equations using the weighted least squares method, we need to minimize the sum of the squared weighted residuals. Let's solve the problem using both the algebraic approach and matrices.

Algebraic Approach:

We have the following equations:

A + 2B = 10.50 + V1 ... (1)

2A - 3B = 5.55 + V2 ... (2)

2A - B = -10.50 + V3 ... (3)

To minimize the sum of squared weighted residuals, we square each equation and multiply them by their respective weights:

\(2^2 * (A + 2B - 10.50 - V1)^2\)

\(3^2 * (2A - 3B - 5.55 - V2)^2\\1^2 * (2A - B + 10.50 + V3)^2\)

Expanding and simplifying these equations, we get:

\(4(A^2 + 4B^2 + 10.50^2 + V1^2 + 2AB - 21A - 42B + 21V1)\\9(4A^2 + 9B^2 + 5.55^2 + V2^2 + 12AB - 33A + 16.65B - 11.1V2)\\(A^2 + B^2 + 10.50^2 + V3^2 + 2AB + 21A - 21B + 21V3)\\\)

Now, let's sum up these equations:

\(4(A^2 + 4B^2 + 10.50^2 + V1^2 + 2AB - 21A - 42B + 21V1) +\\9(4A^2 + 9B^2 + 5.55^2 + V2^2 + 12AB - 33A + 16.65B - 11.1V2) +\\(A^2 + B^2 + 10.50^2 + V3^2 + 2AB + 21A - 21B + 21V3)\int\limits^a_b {x} \, dx\)

Simplifying further, we obtain:

\(14A^2 + 31B^2 + 1113 + 14V1^2 + 33V2^2 + 14V3^2 + 14AB - 231A - 246B + 21V1 - 11.1V2 + 21V3 = 0\)

Now, we have a single equation with two unknowns, A and B. We can use various methods, such as substitution or elimination, to solve for A and B. Once the values of A and B are determined, we can substitute them back into the original equations to find the most probable values of A and B.

Matrix Approach:

We can rewrite the system of equations in matrix form as follows:

| 1 2 | | A | | 10.50 + V1 |

| 2 -3 | | B | = | 5.55 + V2 |

| 2 -1 | | -10.50 + V3 |

Let's denote the coefficient matrix as X, the variable matrix as Y, and the constant matrix as Z. Then the equation becomes:

X * Y = Z

To solve for Y, we can multiply both sides of the equation by the inverse of X:

X^(-1) * (X * Y) = X^(-1) * Z

Y = X^(-1) * Z

By calculating the inverse of X and multiplying it by Z, we can find the values of A and B.

Comparing Results:

The results obtained using the algebraic approach and the matrix approach should be the same. Both methods are mathematically equivalent and provide the most probable values of A and B that minimize the sum of squared weighted residuals.

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Is (1,5) (9,12) (12,27) (19,33) a function?

Answers

Answer:

Yes

Step-by-step explanation; vertical line test!!! have a great day

The area of a door is 3024 square inches. If
the length of the door is 48 inches longer
than the width of the door, what is the
width of the door?
A: Translate the problem into an equation.
B: Solve

Answers

Answer:

Lets take all factors into consideration first

The door is a rectangle and the area of a rectangle is length times width

Let the width be w

Let the length be l

Equation length × breadth = area

(w+48)w = 3024

w^2 + 48w = 3024

w^2 + 48w - 3024 = 0

w^2 + 84w - 36w - 3024 = 0

w(w + 84) -36 ( w + 84) = 0

(w + 84) (w - 36) = 0

w + 84 = 0 AND w - 36 =0

w = -84 and w = 36

Since width cannot be negative, the right answer is 36

How did I get 84 and 36? Well, I had to factorize 3024 and since 84 times 36 is 3024 and 84 minus 36 is 48, I chose them.

Cual transformación produce acercamientos de las gráficas al eje de Y en el plano de coordenadas

Answers

Answer:

El eje horizontal en el plano de coordenadas se llama eje-x. El eje vertical se llama eje-y. El punto en el que los dos ejes se intersectan se llama origen.

Step-by-step explanation:

El plano de coordenadas se desarrolló hace cientos de años y fue refinado por el matemático Francés René Descartes. En su honor, se le conoce también como sistema de coordenadas Cartesianas. El plano de coordenadas puede usarse para graficar puntos y rectas. Este sistema nos permite describir relaciones algebraicas de una manera visual, y también nos ayuda a interpretar conceptos algebraicos.

solve the following equation. 3112x=46,866 question content area bottom part 1 x≈enter your response here (do not round until the final answer. then round to the nearest whole number as needed.)

Answers

Answer:

Substitute the value of the variable into the equation and simplify.

866

Step-by-step explanation:

La suma entre 1,3 y su inverso​

Answers

Answer:

bbvfvnjjggfx

ghjjggffcvvvchjvvnbb

El número decimal 1,3 lo expresamos en fracción como 13/10

El inverso de esa fracción es otra fracción pero los números de arriba y abajo se intercambian

→ El inverso de 13/10 es 10/13

Ahora hacemos la suma

\( \frac{13}{10} + \frac{10}{13} \)

\( \frac{13\cdot 13+ 10 \cdot 10}{10\cdot 13}\)

\( \frac{169+ 100}{130}\)

\( \boxed{\frac{269}{130}}\)

El valor decimal

\( \boxed{2,0\overline{692307}} \)

Urgent please help..

Urgent please help..

Answers

Answer:

Anong grade lalaki or babae

Answer:
The area of the other one is 140 in.² .

Explanation:

Let y in.² be the area of the other one.

15/21 = y/196

15 x 196 = y x 21

2940 = 21y

21y = 2940

y = 140

Ue the given condition to write an equation for the line in​ point-lope form and in​ lope-intercept form. Slope​ = 1/2​, paing through the origin

Answers

The equation of the line in point-slope form and in​ slope-intercept form are both y = 1/2x.

There are three common forms of the equation of a line:

1. Point-Slope Form: y - y1 = m(x - x1), where m is the slope of the line and (x1, y1) is a point on the line.

2. Slope-Intercept Form: y = mx + b, where m is the slope of the line and b is the y-intercept.

3. Standard Form: Ax + By = C, where A and B are coefficients that define the slope and y-intercept of the line.

If a line has a slope of 1/2 and passing through the origin, then:

m = 1/2

(x1, y1) = (0,0)

Plug in the values in the point-slope form and in​ slope-intercept form.

point-slope form

y - y1 = m(x - x1)

y - 0 = 1/2(x - 0)

y = 1/2x

slope-intercept form

y = mx + b

y = 1/2x + b

Substitute the values of x and y and solve for the y-intercept, b.

0 = 1/2(0) + b

b = 0

y = 1/2x + 0

y = 1/2x

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The minor arc measures of circle Z are shown in the figure.

Circle Z is shown. Radii Z Y, Z X, Z W, Z V, Z U, and Z T are shown. The arc measure of Y X is 71 degrees, the arc measure of X W is 32 degrees, the arc measure of W V is 71 degrees, the arc measure of V U is 78 degrees, the arc measure of U T is 54 degrees, and the arc measure of T Y is 54 degrees.

Use the drop-down menus to complete each statement.

Angle UZT is congruent to angle

.

Angle VZW is congruent to angle

.

Answers

The completed statement are:

Angle UZT is congruent to angle TZY.Angle VZW is congruent to angle YZX.

What is the angle about?

Part A:

Angle UZT is congruent to angle TZY.

Using the image attached figure, we can see that:

∠UZT = 54°

∠TZY = 54°

Hence one can say that ∠TZY = ∠UZT are both congruent angles.

Part B:

Angle VZW is congruent to angle YZX.

Using the image attached attached, we can see that:

∠VZW = 71°

∠YZX = 71°

Hence, ∠YZX = ∠VZW are both  regarded as congruent angles .

Therefore, The completed statement are:

Angle UZT is congruent to angle TZY.Angle VZW is congruent to angle YZX.

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The minor arc measures of circle Z are shown in the figure.Circle Z is shown. Radii Z Y, Z X, Z W, Z

Answer: a, c

Step-by-step explanation:

7 47/50 as a decimal​

Answers

Answer:

0.94

Step-by-step explanation:

You just divide 47 by 50 and you get 0.94 bam!

Point B lies between points A and C on Line segment A C . Let x represent the length of segment AB in incUse the segment to complete the statements.Hes.

Answers

Answer:

x = 5,  AB = 5 inches, BC = 15 inches

Step-by-step explanation:

The segment addition postulate states that for line AC having point B between point A and point C, the distances between the point satisfy the equation:

AB + BC = AC

Given that AB = x and BC = 3x, also AC = 20 inches

AB + BC = AC

x + 3x = 20

4x = 20

Dividing through by 4:

4x/4 = 20/4

x = 5

Therefore AB = x = 5 inches, BC = 3x = 3 * 5 = 15 inches

Answer, please Please

Answer, please Please

Answers

Answer:

18

Step-by-step explanation:

9+(-15)+4+20

9-15+4+20

18 ans

Answer:
18

Explanation:

9 + (-15) + 4 + 20

(+- = -)

9 - 15 + 4 + 20

=18

A 2 quart container of window cleaner cost $6.96. What is the price per cup?

Answers

Answer:

$0.87

Step-by-step explanation:

2 quarts = 8 cups

$6.96 ÷ 8 = $0.87

Answer:

0.87 cents

Step-by-step explanation:

The price per cup is 87 cents because 4 cups goes into one quart. Therefore, you have to divide by eight because 2 quarts is $6.96, and you get $0.87. Hope this helps! have a great day!!

I need help with question i went to a 81 to a 57 and know that i think about it i should have kept the 81 but PLEASE help me

I need help with question i went to a 81 to a 57 and know that i think about it i should have kept the

Answers

Answer:

The = sign

Step-by-step explanation:

\(\frac{7}{8} -\frac{9}{12} =\frac{1}{8}\)

1/8 = 1/8

Answer: =

Step-by-step explanation:

\(\frac{7}{8}-\frac{9}{12} ?\frac{1}{8}\)

We need to find a common denominator for the two

which will be 24

But we need to multiply the numerators as well to change them.

\(\frac{7}{8}(\frac{3}{3})-\frac{9}{12} (\frac{2}{2} )?\frac{1}{8}\\\frac{21}{24}-\frac{18}{24}? \frac{1}{8}\\\frac{3}{24} ?\frac{1}{8}\\Simplify\\\frac{1}{8} =\frac{1}{8}\)

10. If the radius of a circle is 40 inches, what is the area of the circle? *

Answers

Answer:

The formular for the area of a circle is as follows;

\(area = \pi {r}^{2} \)

r » radius, r is 40 in

[taking π to be 3.14]

substitute:

\(area = (3.14) \times ( {40)}^{2} \\ \\ { \boxed{ \boxed{area = 5024 \: \: in {}^{2} }}}\)

What is the difference?

74 – 26 =

47
48
52
58

Answers

48 is the correct answer

The second one 48 is the answer

5)
Function J is shown on the coordinate grid below.
3
2
1
1
2
5 4 3 2 1
3 4 5
-5
If the y-intercept of Ranction is a greater than the y-intercept of function I, which
equation could represent function R?
A y = -x + 4.5
0,5x + 3

5)Function J is shown on the coordinate grid below.321125 4 3 2 13 4 5-5If the y-intercept of Ranction

Answers

Answer:

i think the 2nd one

Step-by-step explanation:

Rey collected Three glasses of colored marbles.The first glass bas 27 red marbles the second one 36 green marbles and the third has 54 blue marbles he set the marbles into a set of boxes of each kind. What is the greatest number of marbles that he can put equally inside eaxh box

What is Asked:
What is Given:
What is operation:
What is number sentence:
What is Solution:
Check and look back:​

Answers

. What is asked: It asks us to find out the greatest number of marbles that rey can put equally inside each box.

■. What is it's Solution:

Before, i will start the solution first you shall need to know about, what is GCF ?GCF stands for the Greatest common factor. Now, i shall ask you: What is the GCF of 36 and 60. The ans will be: 12. How did i get answer 12 ? For that, find the factors of both numbers 36 and 60. then for finding GCF, multiply those factors which are common in both 36 and 60. ( See in the above attachment )

■. Now the Solution Starts:

Find the GCF of 27, 36 and 54. ( See in my right side of the attachment ).You will find the GCF = 9. That means, 9 is the greatest number of marbles that he can put equally inside each box.Hence, the required ans: 9.

Things you should know about:

What is HCF, GCD ( or GCF ) and LCF ? ( in my answer, I had explained GCF ).Don't confuse that HCF and GCF are same. HCF is mathematical term used in British English ( UK ) and GCF is also a mathematical term similar to HCF used in American English ( USA ). HCF = Highest Common Factor, GCF = Greatest Common Factor and LCF = Lowest Common Factor.

If you find anymore doubts regarding on my answer. then plz send your queries to the comment section. i will help you ;))

Rey collected Three glasses of colored marbles.The first glass bas 27 red marbles the second one 36 green
Rey collected Three glasses of colored marbles.The first glass bas 27 red marbles the second one 36 green

what is the x in 4x + 8 = 7.2+5x

Answers

Answer:

x = 0.8

Step-by-step explanation:

Answer:

0.8 i think

Step-by-step explanation:

Step 1: So i subtracted 8 from the postive 8 and 7.2

Step 2: Then I got 4x= -0.8 + 5x

Step 3: Now that were left with thart i subtracted 5 from the postive 5x and from the postive 4x

Step 4: I have -1 = -0.8

Step 5: subtract the -1 from the -1 and the -0.8 which will equal... a postive 0.8!

hope this helped and don't remove this pls

if a probability of a single birth resulting in a boy is 51%, what is the probability of a single birth resulting in a girl? (

Answers

The probability of a single birth resulting in a girl if the probability of a single birth resulting in a boy is 51% is 49%

Probability is the measure of the likelihood of an event occurring. The probability of an event occurring ranges from 0 to 1. If an event is impossible, the probability of its occurrence is 0, and if the event is certain to occur, the probability is 1. The probabilities of the complement of an event equal one minus the probability of the event. For instance, the probability of the complement of an event A, denoted as A', is 1 - P(A). If the probability of an event A is P(A), then the probability of the complement of A is 1 - P(A).

Here, the probability of a single birth resulting in a boy is 51%. Therefore, the probability of a single birth resulting in a girl is the complement of this event, which is 49%. Hence, the main answer is that the probability of a single birth resulting in a girl if the probability of a single birth resulting in a boy is 51% is 49%.

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Which equation is most likely used to determine the acceleration from a velocity vs. time graph?
O a=
Om=
O a=
Om =
Δν
V2 - V1
X2-X1
Av
m
X2-X1
V2 - V1

Answers

We can calculate acceleration (a) by using the following equation: a = Δv/m.

The equation most likely used to determine the acceleration from a velocity vs. time graph is: a = Δv/m. This equation states that the acceleration (a) is equal to the difference in velocity (Δv) divided by the time (m). To solve this equation, we must find the change in velocity (Δv) and the time (m). To find the Δv, we can subtract the final velocity (V2) from the initial velocity (V1). To find the time (m), we can subtract the final time (t2) from the initial time (t1).

Therefore, we can calculate acceleration (a) by using the following equation: a = Δv/m.

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"Your question is incomplete, probably the complete question/missing part is:"

Which equation is most likely used to determine the acceleration from a velocity vs. time graph?

a= 1/Δv

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

a = Δv/m

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

Consider a standard deck of 52 playing cards with 4 suits. If A is the event of drawing a 6 from the deck, and B is the event of drawing a black playing card from the deck, what is the intersection of A and B? (Remember that the black cards are spades and clubs.)

Answers

Answer: Intersection of A and B = 2

Step-by-step explanation:

Total cards = 52

Let A is the event of drawing a 6 from the deck, and B is the event of drawing a black playing card from the deck.

Total cards having 6 on them = 4

[There are 4 suits of two different colors red and black.]

Total  black playing card =26

Intersection of A and B = Black cards having 6 = 2

hence, Intersection of A and B = 2

Those methods involving the collection, presentation, and characterization of a set of data in order to properly describe the various features of that set of data are called?

Answers

Those methods involving the collection, presentation, and characterization of a set of data in order to properly describe the various features of that set of data are called descriptive statistics.

Descriptive statistics:- Descriptive statistics helps to describe, summarize and organize the set of data efficiently and in an informative way, so that it'll be easier to make conclusion about the data in order to make rational decisions. This method describes the characteristics of a dataset.

Example:- The average test score for the students of a particular class, gives descriptive sense of the typical scores.

There are three types of descriptive statistics-

Univariate statistics:- It summarizes only one variable at a time.Bivariate statistics:- It compares between two variables.Multivariate statistics:- It compares between more than two variables.

Thus we can conclude that, those methods involving the collection, presentation, and characterization of a set of data in order to properly describe the various features of that set of data are called descriptive statistics.

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!!30 Points, Pls help ASAP!!
Divide using synthetic division
x^4 – 3x^3 – 7x + 1 ÷ x + 2

Answers

The quotient of x⁴ – 3x³ – 7x + 1 ÷ x + 2 is x³ - 5x² + 3x and the remainder is 5

How to perform the synthetic division?

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

x^4 – 3x^3 – 7x + 1 ÷ x + 2

Rewrite as

x⁴ – 3x³ – 7x + 1 ÷ x + 2

This means that

Divisor = x + 2

Dividend = x⁴ – 3x³ – 7x + 1

Using the synthetic division, we have the following setup

-2 |    1     -3    -7     1

Bring down the first factor

-2 |    1     -3    -7     1

        1

Multiply by -2

-2 |    1     -3    -7     1

              -2

        1

Repeat the above steps as follows

So, we have

-2 |    1     -3    -7     1

              -2    10    -6

        1      -5    3    5

The last number represents the remainder of the division

This means that

Remainder = 5

Quotient = x³ - 5x² + 3x

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Which of the following ordered pair is a solution of the equation x minus 2 y 6?

Answers

The ordered pair of the solution of the equation, x - 2y - 6 = 0 is d. (4,-1).

Solution of a Linear equation:

The solution of a linear equation is the points or the set of all possible values for the variables that satisfy the specified linear equation is the solution set of the system of linear equations.

Here we have  

Equation x - 2y - 6 = 0 ----- (1)

Now we need to find the solution to the equation from the given points  

Substitute each given point in equation (1) and check which point will satisfy equation (1)

Checking For a. (2,4)

=> 2 - 2(4) - 6 = 0

=> 2 - 8 - 6 = 0

=> -12 ≠ 0

Checking For b. (0,3)

=> 0 - 2(3) - 6 = 0

=> - 6 - 6 = 0

=> -12 ≠ 0

Cheking For c. (-4,1)

=> - 4  - 2(1) - 6 = 0

=> - 12  = 0

=> -12 ≠ 0

Cheking For d. (4,-1)

=> 4 - 2(-1) - 6 = 0

=> 4 + 2 - 6 = 0

=> 0 = 0  

By the above calculation,

The Equation x - 2y - 6 = 0 is satisfied only at d. (4,-1)

Therefore,

The ordered pair of the solution of the equation, x - 2y - 6 = 0 is d. (4,-1).

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Complete Question:

Which of the following ordered pairs is the solution of the equation

x - 2y - 6 = 0

a. (2,4)   b. (0,3)   c. (-4,1)     d. (4,-1)

Look at the data points on the graph

Is this relationship a function?

Look at the data points on the graphIs this relationship a function?

Answers

It issssssssssssssssss 1,1
No, usint the vertical line test, the dots on 2A and 2B will line up with each other, proving it isnt a function.

what is the simplified form of y^2 -y -12/ y^2 +8y+15​

Answers

Answer:

(y - 4)/(y + 5)

Step-by-step explanation:

Simplify by factoring both trinomials:

(y^2 - y - 12)/ (y^2 +8y + 15)​ = (y - 4)(y + 3) /(y + 5)(y + 3) =(y - 4)/(y + 5)

SAT Scores: A college admissions officer sampled 116 entering freshmen and found that 45 of them scored more than 590 on the math SAT. Part 1 of 3 (a) Find a point estimate for the proportion of all entering freshmen at this college who scored more than 590 on the math SAT. Round the answer to at least three decimal places The point estimate for the proportion of all entering freshmen at this college who scored more than 590 on the math SATIS 0.388 Part 2 of 3 (b) Construct a 98% confidence interval for the proportion of all entering freshmen at this college who scored more than 590 on the math SAT. Round the answer to at least three decimal places. A 9896 confidence interval for the proportion of all entering freshmen at this college who scored more than 590 on the math SAT IS 0.283

Answers

The 98% confidence interval for the proportion of all entering freshmen at this college who scored more than 590 on the math SAT is approximately 0.283 to 0.493.

To find the point estimate for the proportion of all entering freshmen at this college who scored more than 590 on the math SAT, we divide the number of freshmen who scored more than 590 by the total sample size.

Point Estimate = Number of freshmen who scored more than 590 / Total sample size

In this case, the number of freshmen who scored more than 590 on the math SAT is 45, and the total sample size is 116.

Point Estimate = 45 / 116 ≈ 0.388

Rounded to three decimal places, the point estimate for the proportion of all entering freshmen at this college who scored more than 590 on the math SAT is approximately 0.388.

To construct a 98% confidence interval for the proportion of all entering freshmen at this college who scored more than 590 on the math SAT, we can use the following formula:

Confidence Interval = Point Estimate ± (Critical Value * Standard Error)

The critical value corresponds to the desired confidence level and is obtained from the standard normal distribution. For a 98% confidence level, the critical value is approximately 2.326.

The standard error can be calculated using the following formula:

Standard Error = sqrt((Point Estimate * (1 - Point Estimate)) / Sample Size)

Using the point estimate from part (a) as 0.388 and the sample size as 116, we can calculate the standard error:

Standard Error = sqrt((0.388 * (1 - 0.388)) / 116) ≈ 0.050

Now we can construct the confidence interval:

Confidence Interval = 0.388 ± (2.326 * 0.050)

Lower Bound = 0.388 - (2.326 * 0.050) ≈ 0.283

Upper Bound = 0.388 + (2.326 * 0.050) ≈ 0.493

Rounded to three decimal places, the 98% confidence interval for the proportion of all entering freshmen at this college who scored more than 590 on the math SAT is approximately 0.283 to 0.493.

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