What is the measure of the angle in red?
70°

Answer:

0.5675 = 56.75% probability that at least 22 of the 44 students selected are non-history majors.

Step-by-step explanation:

The students are chosen without replacement from the sample, which means that the hypergeometric distribution is used to solve this question. We are working also with a sample with more than 10 history majors and 10 non-history majors, which mean that the normal approximation can be used to solve this question.

Hypergeometric distribution:

The probability of x successes is given by the following formula:

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]

In which:

x is the number of successes.

N is the size of the population.

n is the size of the sample.

k is the total number of desired outcomes.

Combinations formula:

[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Approximation:

We have to use the mean and the standard deviation of the hypergeometric distribution, that is:

[tex]\mu = \frac{nk}{N}[/tex]

[tex]\sigma = \sqrt{\frac{nk(N-k)(N-n)}{N^2(N-1)}}[/tex]

In this question:

88 + 88 = 176 students, which means that [tex]N = 176[/tex]

88 non-history majors, which means that [tex]k = 88[/tex]

44 students are selected, which means that [tex]n = 44[/tex]

Mean and standard deviation:

[tex]\mu = \frac{44*88}{176} = 22[/tex]

[tex]\sigma = \sqrt{\frac{44*88*(176-88)*(176-44)}{176^2(175-1)}} = 2.88[/tex]

What is the probability that at least 22 of the 44 students selected are non-history majors?

Using continuity correction, as the hypergeometric distribution is discrete and the normal is continuous, this is [tex]P(X \geq 22 - 0.5) = P(X \geq 21.5)[/tex], which is 1 subtracted by the p-value of Z when X = 21.5. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{21.5 - 22}{2.88}[/tex]

[tex]Z = -0.17[/tex]

[tex]Z = -0.17[/tex] has a p-value of 0.4325

1 - 0.4325 = 0.5675

0.5675 = 56.75% probability that at least 22 of the 44 students selected are non-history majors.

Answer:

95% provides more information

Step-by-step explanation:

The confidence interval is obtained by using the relation :

Xbar ± Zcritical * σ/√n

(Xbar - (Zcritical * σ/√n)) = 5.22 - - - (1)

(Xbar + (Zcritical * σ/√n)) = 5.98 - - (2)

Adding (1) and (2)

2xbar = 5.22 + 5.98

2xbar = 11.2

xbar = 11.2 / 2 = 5.6

Margin of Error :

Xbar - lower C.I = Zcritical * σ/√n

Zcritical at 90% = 1.645

5.6 - 5.22 = 1.645 * (σ/√n)

0.38 = 1.645 * (σ/√n)

(σ/√n) = 0.38 / 1.645 = 0.231

Therefore, using the se parameters to construct at 95%

Zcritical at 95% = 1.96

Margin of Error = Zcritical * σ/√n

Margin of Error = 1.96 * 0.231 = 0.45276

C.I = xbar ± margin of error

C. I = 5.6 ± 0.45276

C.I = (5.6 - 0.45276) ; (5.6 + 0.45276)

C. I = (5.147 ; 6.053)

Hence, 95% confidence interval provides more information as it is wider.

Answer:

Step-by-step explanation:

You have not provided the answers to choose from.

The expression can be simplified to δ⁴/a, but I cannot tell if that is one of the choices.

Given:

A credit card advertises an annual interest rate of 23%.

To find:

The equivalent monthly interest rate.

Solution:

We know that,

1 year = 12 months

It is given that, the credit card advertises an annual interest rate of 23%. So, the equivalent monthly interest rate is:

[tex]\dfrac{23\%}{12}=1\dfrac{11}{12}\%[/tex]

[tex]\dfrac{23\%}{12}\approx 1.9167\%[/tex]

Therefore, the equivalent monthly interest rate is [tex]1\dfrac{11}{12}\%[/tex] and the approximate equivalent monthly interest rate is 1.9167%.

Answer:

9.725%

Step-by-step explanation:

(1.0475)^2 =1.09725

one year 2 periods 4.75% per period

Answer:

sin A = 4/5

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

sin A = opp / hyp

sin A = 24/ 30

Dividing the top and bottom by 6

sin A = 4/5

sinØ=Perpendicular/Hypotenuse

Answer:

25, 33

Step-by-step explanation:

let the length of the one with equal sides be x

third side = x+8

x+x+x+8 = 83

3x+8 = 83

3x = 75

x = 25

x+8 = 25+8 = 33

QUESTION:- SOLVE EQUATION BY FACTORISATION

EQUATION:-

[tex] {x}^{2} + x - 72 = 0[/tex]

ANSWER:-

[tex] {x}^{2} + x - 72 = 0\\{x}^{2} + 9x - 8x - 72 = 0 \\ x(x + 9) - 8(x +9) = 0 \\ (x - 8)(x + 9) = 0 \\ [/tex]

NOW FOR VALUE OF X ->

[tex]x - 8 = 0 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: x + 9 = 0\\ x = 8 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: x = - 9[/tex]

Answer:

3.) A,B,AB,O

Step-by-step explanation:

Non-numeric data refers to categorical data, or data that is not expressed quantitatively. Answers (1) and (2) contain quantitative data, so they would be eliminated as potential answer choices and therefore (4) would also be eliminated. This leaves answer (3), which does not have quantitative data and is therefore non-numeric.

Answer:

Range is (-8,00)

Step-by-step explanation:

Answer:

48degrees

Step-by-step explanation:

From the circle geometry shown, traingle BDC is an isosceles triangle which shows means that their base angels are the same. Hence;

<B = <C

<CBD + <BCD + <D = 180

<BCD + <BCD + <D =180

2<BCD + <BDC = 180

Get <BCD;

<BCD+ <ECB = 90

<BCD + 48 = 90

<BCD = 90 - 48

<BCD = 42degrees

Get <BDC

2<BCD + <BDC = 180

2(42)+ <BDC = 180

84 + <BDC = 180

<BDC = 180 - 84

<BDC = 96

Since angle at the centre is twice that at the circumference, then;

<BAC = 1/2(<BDC )

<BAC = 96/2

<BAC = 48degrees

Answer:

12

Step-by-step explanation:

12

The given table represents Exponential growth.

The process of Quantity rising over time is called exponential growth. An exponential function is used to create an exponential growth curve, which represents a pattern of data that shows a rise over time. Where the Exponential decay helps to understand the rapid decrease in a period of time

Here we have

The table

х     1       2       3       4          5  

у    14     56    224    896    3584  

From the given table, we can observe that

[tex]\frac{14}{56} = \frac{56}{224} = \frac{896}{3584} = \frac{1}{4}[/tex]    

Since the absolute value of the common ratio is less than 1 i.e 1/4

And the values are increasing

Therefore,

The given table represents Exponential growth.

Learn more about Exponential growth at

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We have two lines from the same point.

These two lines are also tangents to same circle which implies that they are of the same length.

That is 2x - 1 = 9

2x = 9 +1 = 10

x =10/2

x = 5

Answer:I just need points

Step-by-step explanation:

Hey

Answer:

yes

Step-by-step explanation:

o

Answer:

7 7/80 or 7.0875

Step-by-step explanation:

product is the result of multiplication

7/8 * 81/10 = 567/80 = 7 7/80 or 7.0875

Answer:

44.85

Step-by-step explanation:

There are two ways to do it, you can either multiply 0.3 by 34.5 and then add it to 34.5 to get 44.85, or you can add the 30% to 100% and get 1.3 which you multiply by 34.5 and that gets you 44.85

Answer:

b = h*D +hg^3

Step-by-step explanation:

b/h = D +g^3

Multiply each side by h

h* b/h = h*D +hg^3

b = h*D +hg^3

Answer:

5/8 ft^2

Step-by-step explanation:

The area of a rectangle is given by

A = l*w  where l is the length and w is the width

A = 5/6 * 3/4

A = 3/6 * 5/4

A = 1/2 * 5/4

A = 5/8 ft^2

Answer:

0.9894 = 98.94% probability that he does not have a TBI.

Step-by-step explanation:

Conditional Probability

We use the conditional probability formula to solve this question. It is

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]

In which

P(B|A) is the probability of event B happening, given that A happened.

[tex]P(A \cap B)[/tex] is the probability of both A and B happening.

P(A) is the probability of A happening.

In this question:

Event A: Negative screen

Event B: Does not have a TBI.

Probability of a negative screen:

93 are negative and do not have a TBI.

1 is negative and has a TBI.

Out of 112.

So

[tex]P(A) = \frac{93+1}{112} = \frac{94}{112}[/tex]

Probability of a negative screen and not having a TBI:

93 are negative and do not have a TBI, out of 112, so:

[tex]P(A \cap B) = \frac{93}{112}[/tex]

One of the veterans has a negative screen and wants to know the probability that he does not have a TBI.

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{\frac{93}{112}}{\frac{94}{112}} = \frac{93}{94} = 0.9894[/tex]

0.9894 = 98.94% probability that he does not have a TBI.

Answer:

Step-by-step explanation:

a) categorical

b) add all of the numbers and divide by how many numbers there were.

c) outliers means any that were far away from the rest of the data

d) not entirely, you can make an estimate based on it, but nat an exact answer.

Hence, the probability that all four students select the same tire is [tex]\frac{1}{16}[/tex].

What is the probability?

Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one.

Probability has been introduced in Maths to predict how likely events are to happen. The meaning of probability is basically the extent to which something is likely to happen.

Here given that,

Four students drive to school in the same car. The students claim they were late to school and missed a test because of a flat tire.

On the makeup test, the instructor asks the students to identify the tire that went flat; front driver's side, front passenger's side, rear driver's side, or rear passenger's side.

So, the probability of one person picking the tire is [tex]\frac{1}{4}[/tex].

Here four students so their probability is

[tex]\frac{1}{4(4)}=\frac{1}{16}[/tex]

Hence, the probability that all four students select the same tire is [tex]\frac{1}{16}[/tex].

To know more about the probability

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Answer:

1  3 5 2 4 6

Step-by-step explanation:

Answer:

q/N = g

Step-by-step explanation:

q = Ng

Divide each side by N

q/N = Ng/N

q/N = g

Answer:

f(x) = 40(1 + 0.13)^x

Step-by-step explanation:

The general formula for an exponential growth function is;

f(x) = a(1 + r)^x

Where;

a= initial population of the city

r= population growth rate

x = number of years

Given that;

a= 40,000

r= 0.13

The population of the city in thousands of people in terms of x is;

f(x) = 40(1 + 0.13)^x

Answer:

Friday

Step-by-step explanation:

you need to count the number of circles, the half circle represents 5 skirts

Answer by Gauthmath

Answer:

The function with blue line (see attachment) represents the graph of [tex]f(x) = -4\cdot |x|[/tex] after it is translated 3 units down.

Step-by-step explanation:

Mathematically speaking, a translation in the y-direction is defined by the following expression:

[tex]g(x) = f(x) + k[/tex] (1)

Where:

[tex]g(x)[/tex] - Resulting function.

[tex]f(x)[/tex] - Original function.

[tex]k[/tex] - Translation factor ([tex]k > 0[/tex] - Translation in the +y direction/[tex]k< 0[/tex] - Translation in the -y direction).

If we know that original function is translated 3 units down and [tex]f(x) = -4\cdot |x|[/tex], then the resulting function is:

[tex]g(x) = -4\cdot |x|-3[/tex]

Lastly, we graph both original and resulting functions with the help of a graphing tool, whose outcome is presented in the image attached below:

Please notice that the red line represents the original function, whereas the blue line represents the resulting function.

Answer:

520 feets

Step-by-step explanation:

The height of the building, h can be obtuined using trigonometry ;

From the attached diagram, opposite side = 300 feets ; height, h = adjacent side

Hence,

Tan θ = opposite / Adjacent

Tan 30° = 300 / height

0.5773502 = 300 / height

Height = 300 / 0.5773502

Height = 519.615

Height = 520 feets

Answer:

D.) y = 2x + 2

Step-by-step explanation:

First, we need to find the slope.

Lets use the points (0, 2) and (-2, -2).

Using the formula for calculating slope, we get 2 as our slope.

Since the equation should be in slope-intercept form, we use this formula.

y = mx + b

We'll use our first point (0, 2) to substitute for x and y and use 2 to substitute for m (slope):

2 = 2(0) + b

2 x 0 = 0

2 = 0 + b

-0 = -0

= 2 = b

Now, substitute b for 2 for 2 for m.

= y = 2x + 2.

Hope this helps!

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