3(x+9)-4x=11x-13x+23

Answer:

x = 20.8

y = 22.3

Step-by-step explanation:

tan(21) = 8/x

or, x = 8/tan(21)

or, x = 20.8 (rounded to the nearest tenth)

sin(21) = 8/y

or, y = 8/sin(21)

or, y = 22.3 (rounded to the nearest tenth)

Answered by GAUTHMATH

Answer:

a) 0.0749 = 7.49% probability that the student makes more than $15,000.

b) 0.227 = 22.7% probability that the student makes between $13,000 and $14,000.

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.

Full-time Ph.D. students receive an average of $12,837 per year.

This means that [tex]\mu = 12837[/tex]

Standard deviation of $1500

This means that [tex]\sigma = 1500[/tex]

a. The student makes more than $15,000.

This is 1 subtracted by the p-value of Z when X = 15000.

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

[tex]Z = \frac{15000 - 12837}{1500}[/tex]

[tex]Z = 1.44[/tex]

[tex]Z = 1.44[/tex] has a p-value of 0.9251.

1 - 0.9251 = 0.0749

0.0749 = 7.49% probability that the student makes more than $15,000.

b. The student makes between $13,000 and $14,000.

This is the p-value of Z when X = 14000 subtracted by the p-value of Z when X = 13000.

X = 14000

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

[tex]Z = \frac{14000 - 12837}{1500}[/tex]

[tex]Z = 0.775[/tex]

[tex]Z = 0.775[/tex] has a p-value of 0.7708.

X = 13000

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

[tex]Z = \frac{13000 - 12837}{1500}[/tex]

[tex]Z = 0.11[/tex]

[tex]Z = 0.11[/tex] has a p-value of 0.5438.

0.7708 - 0.5438 = 0.227

0.227 = 22.7% probability that the student makes between $13,000 and $14,000.

7.49% of the student makes more than $15,000, while 23.85% of the student makes between $13,000 and $14,000

Z score is used to determine by how many standard deviations the raw score is above or below the mean. It is given by:

z = (raw score - mean) / standard deviation

Given that:

Mean = $12837, standard deviation = $1500

a) For >15000:

z = (15000 - 12837)/1500 = 1.44

P(z > 1.44) = 1 - P(z < 1.44) = 1 - 0.9251 = 0.0749

b) For >13000:

z = (13000 - 12837)/1500 = 0.11

For <14000:

z = (14000 - 12837)/1500 = 0.78

P(0.11 < z < 0.78) = P(z < 0.78) - P(z < 0.11) = 0.7823 - 0.5438 = 0.2385

7.49% of the student makes more than $15,000, while 23.85% of the student makes between $13,000 and $14,000

Find out more on z score at: https://brainly.com/question/25638875

Answer:

b

Step-by-step explanation:

i had it

Answer:

Step-by-step explanation:

Hello!

          2          4              5          ∟ 70

        -2           1                                 3, 5

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

                      3              5        0

                      3              5       0

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

                     0                0        0

Asnwer: C

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

Answer:

C

Step-by-step explanation:

3.8 is the answer

68.4÷18=3.8

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: $1,223.40.

Step-by-step explanation:

Since she earns $22.5 per hour, for 34 hours, she would earn:

$22.5 × 34 = $765

She earn 3% of her sales, therefore find 3% of $15,280:

$15280(3%) = $15280(0.03) = $458.4

Add them together:

$765 + $458.4 = $1223.4

9514 1404 393

Answer:

  $1,223.40

Step-by-step explanation:

Zoe's total pay is the sum of the products of hours and hourly rate, and sales and commission rate.

  Pay = (34 h)($22.50/h) +($15,280)(.03) = $765.00 +458.40

  Pay = $1,223.40

Zoe's pay for the week is $1,223.40.

Answer:

18

Step-by-step explanation:

Because angle A and C are equal, it is an isoceles traingle.

This means that side BA is equal to side BC.

Thus, you can set 6x equal to 3x + 9.

Solving that gives you x = 3.

6(3) = 18    3(3) +9 = 18

Answer:

B. 18

Step-by-step explanation:

Since angles A and C are congruent, then sides BA and BC are congruent.

6x = 3x + 9

3x = 9

x = 3

AB = 6x = 6(3) = 18

Answer: B. 18

Answer:

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

Step-by-step explanation:

The equation of a circle is given by

(x-h)^2 + (y-k)^2 = r^2 where (h,k) is the center and r is the radius

(x-5)^2 + (y- -6)^2 = 2^2

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

Answer:

a) The 90% confidence interval for the mean amount owed in student loans of graduates of four-year business colleges is ($13,600, $15,162), having a margin of error of $781.

b) We are 90% sure that the mean amount owed in student loans of graduates of  all four-year business colleges is between $13,600 and $15,162.

Step-by-step explanation:

Question a:

We have the standard deviation for the sample, which means that the t-distribution is used to solve this question.

The first step to solve this problem is finding how many degrees of freedom,which is the sample size subtracted by 1. So

df = 25 - 1 = 24

90% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 24 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.9}{2} = 0.95[/tex]. So we have T = 2.0639

The margin of error is:

[tex]M = T\frac{s}{\sqrt{n}} = 2.0639\frac{1892}{\sqrt{25}} = 781[/tex]

In which s is the standard deviation of the sample and n is the size of the sample.

The lower end of the interval is the sample mean subtracted by M. So it is 14381 - 781 = $13,600

The upper end of the interval is the sample mean added to M. So it is 14381 + 781 = $15,162

The 90% confidence interval for the mean amount owed in student loans of graduates of four-year business colleges is ($13,600, $15,162), having a margin of error of $781.

b) Interpret the confidence interval you have computed.

We are 90% sure that the mean amount owed in student loans of graduates of  all four-year business colleges is between $13,600 and $15,162.

9514 1404 393

Answer:

  d) Listen to his suggestions to see what might work

Step-by-step explanation:

A supervisor or team leader cannot be expected to know everything, or be completely up-to-date with the latest innovations. A lot of what comprises "best practice" is developed on the job, or propagated by personnel transfers or word of mouth. A different point of view can often be beneficial, planting the seed for a beneficial change, even if the specific suggestion is not workable.

Ursula should pay attention to all of her team members, Tom included.

Answer:

Hes correct ^

Step-by-step explanation:

Answer:

B - They are symmetric over the y-axis

Step-by-step explanation:

A - I couldn't find a way to explain this one

B - Even functions have graph symmetry across the y-axis, I'm not sure if you looking for multiple answers, but I got B as one of them.

C - An odd function has rotational symmetry, and even function has reflects

D - An even function is symmetric over the y-axis not the x-axis

Answer:

A. A critical value is how far away our sample statistic can be from the true population parameter with a certain level of confidence.

Step-by-step explanation:

Test of a hypothesis:

When we are testing a hypothesis, we have a null hypothesis and an alternative hypothesis, and the conclusion depends on the test statistic, given by:

[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.

The test statistic measures the number of standard errors that we have to move away from the sample mean, and the critical value is how much we can be far from the population parameter with a certain level of confidence, that is, before a certain value we do not reject the null hypothesis, after the value we reject, and this value is the critical value, and thus the correct answer is given by option a.

Answer:

MD = 2

SS = 18

SAMPLE VARIANCE = 2.25

STANDARD ERROR = 0.5

Step-by-step explanation:

Given :

A 8 7

B 7 5

C 6 6

D 7 6

E 9 7

F 8 5

G 5 4

H 9 4

I 7 4

Difference, d = Before - After

______ d

A 8 7 __ 1

B 7 5 __ 2

C 6 6 __ 0

D 7 6 __ 1

E 9 7 __ 2

F 8 5 __ 3

G 5 4 __ 1

H 9 4 __5

I 7 4 ___3

The mean of difference, MD ;

MD = Σd/ n = (1+2+0+1+2+3+1+5+3) / 9 = 18 / 9 = 2

The sum of square, SS ;

(1 - 2)^2 + (2 - 2)^2 + (0 - 2)^2 + (1 - 2)^2 + (2 - 2)^2 + (3 - 2)^2 + (1 - 2)^2 + (5 - 2)^2 + (3 - 2)^2 = 18

Sample variance, S² = SS/(N-1) = 18 / (9 - 1) = 18 / 8 = 2.25

Sample standard deviation, S = √Variance = √2.25 = 1.5

Standard Error, S.E = S / √n = 1.5 / √9 = 0.5

Test statistic : MD / S.E = 2 / 0.5 = 4

We test at α = 0.05 since no α - value is stated in the question.

Critical value at 0.05, df = 8 ;

Critical value = 2.306

Since; Test statistic > Critical value, then result is significant at α = 0.05

Answer:

The 100 trees closest to a ranger station are assessed for damage.

Step-by-step explanation:

Convenience samples are samples taken from only around the focal point.

Option B is correct, The 100 trees closest to a ranger station are assessed for damage.

Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.

A convenience sample is a non-random method of sampling that involves selecting subjects that are easy to access or readily available.

Of the methods listed, the convenience sample is the one where the trees are selected based on their proximity to a ranger station:

The 100 trees closest to a ranger station are assessed for damage.

This method is a convenience sample because it does not involve random selection of trees.

Instead, the trees are chosen based on their proximity to a specific location.

This can introduce bias into the sample, as trees near the ranger station may not be representative of the overall health of white pine trees in the state park.

Hence, Option B is correct, The 100 trees closest to a ranger station are assessed for damage.

To learn more on Statistics click:

https://brainly.com/question/29093686

#SPJ7

9514 1404 393

Answer:

Step-by-step explanation:

The sides of the triangle can be read from the figure:

The ratios tell you ...

  long leg = x√3 = 12

  x = 12/√3 = 4√3 . . . . . divide by √3. (same as multiply by (√3)/3)

  2x = 2·4√3 = 8√3

Then the missing sides are ...

The null and alternate hypotheses are

H0 : u = 0.44  vs   Ha: u > 0.44

Null hypothesis: 44% of readers own a personal computer.

Alternate Hypothesis : greater than 44% of readers own a personal computer.

This is one tailed test and the critical region for this one tailed test for the significance level 0.1 is  Z >  ±1.28

The given values are

p1= 0.54 , p2= 0.44 ; q2= 1-p2= 0.56

Using z test

Z = p1-p2/√p2(1-p2)/n

Z= 0.54-0.44/ √0.44*0.56/200

z= =0.1/ 0.03509

z=  2.849

Since the calculated value of Z=  2.849 is greater than Z= 1.28  reject the null hypothesis therefore there is sufficient evidence to support the executive's claim.

Null hypothesis is rejected

There is sufficient evidence to support the executive's claim at 0.10 significance level.

https://brainly.com/question/2642983

if the formula is [tex]\frac{(B+b)}{2} .h[/tex] we just need to plug in the values

21/2 = 10.5 x 5 = 52.5

hope it helps :)

Answer:

A = 52.5 in^2

Step-by-step explanation:

The area of a trapezoid is

A = 1/2 (b1+b2)h

where b1 and b2 are the bases and h is the height

A = 1/2 ( 14+7)*5

A = 105/2

A = 52.5 in^2

Answer:

a = 50t

Step-by-step explanation:

A function is rise over run, or y/x.

In this graph, the rise (y) is the account balance, while the run (x) is time. To solve for the slope, or the "equation modeled by the graph," we need to divide the rise by the run.

The graph is shown in terms of (a, t). If we look at the first point, (50,1), the rise is 50 and the run is 1. 50/1 is 50. Therefore, a = 50t, since a = 50 and t = 1.

To check, we can try another point, (100, 2). The rise is 100 and the run is 2. Divide these together and you still get 50. You are multiplying the "t" value by 50 to get the "a" value.

Therefore, it's a = 50t

Answer:

The answer is "[tex]7.21 \times 10^{37}[/tex]".

Step-by-step explanation:

[tex]\to ^{n}_{C_r}=\frac{n!}{r!(n-r)!}[/tex]

       [tex]=^{66}_{C_{33}} \times ^{66}_{C_{22}} \times ^{55}_{C_{1}} \\\\=\frac{66!}{33! (66-33)!} \times \frac{66!}{22! (66-22)!} \times \frac{55!}{1! (55-1)!}\\\\=\frac{66!}{33! (33)!} \times \frac{66!}{22! (44)!} \times \frac{55!}{1! (54)!}\\\\=\frac{66!}{33! (33)!} \times \frac{66!}{22! (44)!} \times \frac{55\times 54!}{1! (54)!}\\\\=\frac{66!}{33! (33)!} \times \frac{66!}{22! (44)!} \times 55\\\\= 7219428434016265740 \times 182183167981760400\times 55\\\\[/tex]

       [tex]= 7.21 \times 10^{18} \times 1.82\times10^{17}\times 55\\\\= 7.21 \times 10^{35} \times 1.82\times 55\\\\=721.721 \times 10^{35}\\\\=7.21\times 10^{37}[/tex]

Answer:

There can be several such functions; however, the basic condition that needs to be met for a function to be positive for the interval [–3, –2] is that it should be multiplied by (-1) Hence, one such function that is positive for the entire interval is f(x) = -x

Step-by-step explanation:

Answer:

I wish I knew that answer

Step-by-step explanation:

Answer:

it's no solution

Step-by-step explanation:

3(x^2 - 2*1/3*x+1/9) + 11/3 > 0

so it's no solution

9514 1404 393

Answer:

  (f•g)(x) = -16x^3 +10x^2 -14x

Step-by-step explanation:

  (f•g)(x) = f(x)•g(x) = (-2x)(8x^2 -5x +7)

Use the distributive property:

  (f•g)(x) = -16x^3 +10x^2 -14x

Answer:

2abc

Step-by-step explanation:

●●●●○○○○□□□□■■■■

Answer:

=> 2abc

Step-by-step explanation:

=> (abc - 4d) + (abc + 4d)

=> abc - 4d + abc + 4d

=> abc + abc

=> 2 abc