What is the value of a in the right triangle shown below?

Answer:

The proportion of borrowers who owe more than 54,000 is 0%.

Step-by-step explanation:

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.

Researchers found that the average student loan balance per borrower is $23,300.

This means that [tex]\mu = 23300[/tex]

They also reported that about one-quarter of borrowers owe more than $28,000.

This means that the 1 subtracted by the p-value of Z is 0.25 when X = 28000, that is, when X = 28000, Z has a p-value of 0.75, so when X = 28000, Z = 0.675. We use this to find [tex]\sigma[/tex]

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

[tex]0.675 = \frac{28000 - 23300}{\sigma}[/tex]

[tex]0.675\sigma = 4700[/tex]

[tex]\sigma = \frac{4700}{0.675}[/tex]

[tex]\sigma = 6963[/tex]

Estimate the proportion of borrowers who owe more than 54,000.

This is 1 subtracted by the p-value of Z when X = 54000. So

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

[tex]Z = \frac{54000 - 23300}{6963}[/tex]

[tex]Z = 4.41[/tex]

[tex]Z = 4.41[/tex] has a p-value of 1

1 - 1 = 0

The proportion of borrowers who owe more than 54,000 is 0%.

Answer:

Step-by-step explanation:

C isnt an interval and the function is always decreasing

Answer:

1808.64 IN^3

Step-by-step explanation:

Helium needed = volume of spherical shaped ice cream + volume of cone

Volume of a sphere = 4/3 x pi x r^3

4/3 x 3.14 x 6^3 = 904.32 ft^3

Volume of a cone 1/3 x (nr^2h)

n = 22/7

r = radius  = 12/2 = 6

the diameter is the straight line that passes through the centre of a circle and touches the two edges of the circle.

h = height

1/3 x 3.14 x 6^2 x 24 = 904.32

helium needed = 2 x 904.32 = 1808.64 in^3

Answer:

17+19i

Step-by-step explanation:

[tex](3-2i)(1+7i) =3+21i-2i-14i^2=3+19i+14=17+19i[/tex]

Answer:

what are we supposed to do

Step-by-step explanation:

im confused

Answer:

0.108

Step-by-step explanation:

Using the poisson probability process :

Where :

P(x =x) = (e^-λ * λ^x) ÷ x!

Given that :

Each batch of bread = 3 loaves

Each loaf = 15 slices

Total slice per batch = 15 * 3 = 45 slices

Number of raising added = 100

Average number of raisin per slice, λ = 100/45 = 20/9

Hence,

Probability that a randomly chosen slice has no raising :

P(x = 0) = (e^-λ * λ^x) ÷ x!

P(x = 0) = (e^-(100/45) * (100/45)^0) ÷ 0!

P(x = 0) = (0.1083680 * 1) / 1

P(x = 0) = 0.108

Answer:

H  0

​ :μ=18.2  ∘  C

H  a

 :μ>18.2  ∘  C

​

Step-by-step explanation:

Khan............... The null hypothesis has a statement of equality, and the direction of alternative hypothesis (>)(>)left parenthesis, is greater than, right parenthesis matches her belief that last year was warmer.

The three conditions for hypothesis testing are approximately met, and the null hypothesis is that the population mean daily high temperature in Buenos Aires is 18.2∘C.

Hypothesis Testing is a type of statistical analysis in which you put your assumptions about a population parameter to the test. It is used to estimate the relationship between 2 statistical variables.

here, we have,

The three conditions for hypothesis testing are approximately met based on the information given.

Null hypothesis (H0) is that the population mean daily high temperature in Buenos Aires is 18.2∘C. Alternative hypothesis (Ha) is that the population mean daily high temperature in Buenos Aires is greater.

The test statistic is calculated as (sample mean - population mean) / (sample standard deviation / sqrt(sample size)).

The p-value is the probability of obtaining a test statistic as extreme or more extreme than the observed test statistic, assuming the null hypothesis is true. It can be calculated using a t-distribution with degrees of freedom equal to the sample size minus one.

To learn more about hypothesis testing please click on below link.

brainly.com/question/29607047

#SPJ3

Answer:

48pi

Step-by-step explanation:

pi x 8² - pi x 4²

64pi - 16pi

48pi

Answer: 5.32 × 10^12

Step-by-step explanation:

This is a question relating to indices. In indices, we add the power given for question relating to multiplication. Hence, this will be:

= (2.8•10^8)(1.9•10^4)

= (2.8 × 1.9) × 10^8+4

= 5.32 × 10^12

Therefore, the answer to the question will be 5.32 × 10^12.

Answer:

the second set of numbers are in least to greatest.

Step-by-step explanation:

Since it is negative -2.5 is farther away from zero than -2.3

Answer:

The limit of the (228.533, 234.735)

Step-by-step explanation:

The values are missing in the given question. Therefore, in order to attempt this question, we will make assumptions.

So, let's assume that:

sample size of the journal article that was reported = 5

which is applied for determining a 95% CI

Also, assuming that the resulting interval = (229.764, 233.504)

However, if we are to use a 99% CI which we deemed to be more appropriate;

Then, our objective is to find the limits of this particular interval in question.

To do that:

We need to first find the sample mean at 95% CI by using the formula:

[tex]\Big ( \bar {x} - t_{\alpha/2, df} \ \dfrac{s}{\sqrt{n}}}, \bar x + t_{\alpha/2, df} \ \dfrac{s}{\sqrt{n}}} \Big) = (229.764,233.504)[/tex]

Since; df = n - 1

df = 5 - 1

df = 4

Then;

[tex]\Big ( \bar {x} - t_{\alpha/2, 4} \ \dfrac{s}{\sqrt{n}}}, \bar x + t_{\alpha/2, 4} \ \dfrac{s}{\sqrt{n}}} \Big) = (233.504+229.764)[/tex]

[tex]2 \bar {x} = (463.268)[/tex]

[tex]\bar {x} =\dfrac{463.268}{2 }[/tex]

[tex]\bar {x} =231.634[/tex]

Sample mean = 231.634

Using the same formula to determine the standard deviation, we have:

[tex]\Big ( \bar {x} - t_{\alpha/2, df} \ \dfrac{s}{\sqrt{n}}}, \bar x + t_{\alpha/2, df} \ \dfrac{s}{\sqrt{n}}} \Big) = (229.764,233.504)[/tex]

[tex]\Big ( \bar {x} - t_{\alpha/2, 4} \ \dfrac{s}{\sqrt{n}}}, \bar x + t_{\alpha/2, 4} \ \dfrac{s}{\sqrt{n}}} \Big) = (233.504-229.764)[/tex]

[tex]\Big ( (\bar x + t_{\alpha/2, 4} \ \dfrac{s}{\sqrt{n}}} )- (\bar {x} - t_{\alpha/2, 4} \ \dfrac{s}{\sqrt{n}}}) \Big) = (233.504-229.764)[/tex]

[tex]\Big ( (\bar x + t_{0.05/2, 4} \ \dfrac{s}{\sqrt{4}}} )- (\bar {x} - t_{0.05/2, 4} \ \dfrac{s}{\sqrt{5}}}) \Big) = (233.504-229.764)[/tex]

At t = 0.025 and df = 4; = 2.776

[tex]2\times 2.776 \dfrac{s}{\sqrt{5}}= 3.74[/tex]

[tex]5.552 \dfrac{s}{\sqrt{5}}= 3.74[/tex]

[tex]\dfrac{s}{\sqrt{5}}= \dfrac{ 3.74}{5.552}[/tex]

[tex]\dfrac{s}{\sqrt{5}}= 0.6736[/tex]

[tex]s = 0.6736 \times \sqrt{5}[/tex]

s = 1.5063

The 99% CI is:

[tex]\implies \Big(\bar x \pm t_{\alpha/2,4} \dfrac{s}{\sqrt{n}} \Big)[/tex]

At t =0.005 and df =4; = 4.604

[tex]\implies \Big(231.634 \pm 4.604 \dfrac{1.5063}{\sqrt{5}} \Big)[/tex]

[tex]\implies \Big(231.634 \pm 4.604 (0.67364) \Big)[/tex]

[tex]\implies \Big(231.634 \pm 3.1014 \Big)[/tex]

[tex]\implies \Big((231.634 - 3.1014), (231.634 + 3.1014) \Big)[/tex]

[tex]\implies \Big( 228.533, 234.735 \Big)[/tex]

Answer:

64 times bigger

Step-by-step explanation:

I will use random values for this explanation to make it more understandable.

Lets say the length of the box is 1 inch, width is 1 inch, and height is 1 inch.

The volume would be l*w*h = 1*1*1 = 1 cubic inch

If the dimensions were 4 times bigger, the length, width and height would all be 4 inches.

4*4*4 = 64 cubic inches, which is 64 times bigger than the smaller box with a volume of 1 cubic inch.

Hope this answer helped! :)

Answer:

It’s C

Step-by-step explanation:

When the outlier is on the right of the rest then it’s going to be positively skewed

Answer:

Probability = 0.01531

Step-by-step explanation:

Prob (Getting 92 out of 100 germinated seeds) follows binomial probability distribution.

N = Number of seeds = 100. r = Number of success (germination) = 92

r = No. Success = Seed germination, Prob (Success) ie P = 85% =  0.85 , Prob (non success ie non germination) ie Q = 1 - 85% = 15% = 0.15

Probability = N c r . (P)^r . (Q)^(n-r)  

= 100c92 (0.85)^92  (0.15)^8

=  186087894300 (0.000000321026708) (0.000000256289062)

= 0.01531 {Approx}

Answer: Bottom left

Step-by-step explanation:

Answer:

Bottom Left

Step-by-step explanation:

Im near 100% sure if im wrong im very sorry

The formula for the area of a rectangular room is width x length, as shown in the figure below: This is the equation used in our square footage calculator as well.

Answer:

Step-by-step explanation:

1/3 bh=96 pi/3=32 pi

Answer:

[tex]\displaystyle V = 32\pi \ in^3[/tex]

General Formulas and Concepts:

Symbols

Pre-Algebra

Order of Operations: BPEMDAS

Geometry

Volume of a Cone Formula: [tex]\displaystyle V = \frac{1}{3} \pi r^2h[/tex]

Step-by-step explanation:

Step 1: Define

Identify

r = 4 in

h = 6 in

Step 2: Find Volume

Answer:

x > 3/5

Step-by-step explanation:

x > 3/5 has an open circle because 3/5 is not included

if it was x ≥ 3/5 then that would include 3/5 and the circle would be closed

Answer: Volume = 48

Step-by-step explanation:

V = L * W * H

V = 4 * 6 * 2

V = 48

Answer:

(7 - i) and (5 + i) with multiplicity 1 are also roots of this polynomial. The complete set of roots are: Therefore the polynomial is: The correct choice is C

Answer:

(-4, 2)

Step-by-step explanation:

this is a simultaneous equation;

solving by substitution method, we have;

since y= ¼x + 3 and the same y= 2x + 10

therefore we combine both equations;

¼x + 3= 2x+10

3-10=2x-¼x

to clear out fraction, multiply throughout by 4

-28= 8x-x

-28= 7x

x= -28/7

x= -4

since x is -4, therefore All we have to do is to substitute x into y, doing this, we have;

y=2x+10

y= 2(-4) + 10

y= -8 + 10

y= 2

therefore y= 2 and x= -4

so the values are (-4, 2)

if you still don't understand, check your NGM SS2 textbook or make a comment and I will explain better

Answer:

1 r 4

Step-by-step explanation:

 0 1

6 1 0

− 0  

 1 0

−   6

   4