Two random samples are taken from private and public universities
(out-of-state tuition) around the nation. The yearly tuition is recorded from each sample and the results can be found below. Test to see if the mean out-of-state tuition for private institutions is statistically significantly higher than public institutions. Assume unequal variances. Use a 1% level of significance.
Private Institutions (Group 1 )
43,120
28,190
34,490
20,893
42,984
34,750
44,897
32,198
18,432
33,981
29,498
31,980
22,764
54,190
37,756
30,129
33,980
47,909
32,200
38,120
Public Institutions (Group 2)
25,469
19,450
18,347
28,560
32,592
21,871
24,120
27,450
29,100
21,870
22,650
29,143
25,379
23,450
23,871
28,745
30,120
21,190
21,540
26,346
Hypotheses:
H0: μ1 (?) μ2
H1: μ1 (?) μ2
What are the correct hypotheses for this problem?
-A. H0: μ1 = μ2 ; H1: μ1 ≠ μ2
-B. H0: μ1 = μ2 ; H1: μ1 > μ2
-C. H0: μ1 ≤ μ2 ; H1: μ1 ≥ μ2
-D. H0: μ1 < μ2 ; H1: μ1 = μ2
-E. H0: μ1 ≠ μ2 ; H1: μ1 = μ2
-F. H0: μ1 ≥ μ2 ; H1: μ1 ≤ μ2

Answer:

width = 8 inches; length = 13 inches

Step-by-step explanation:

(x + 5)x = 104

x^2 + 5x - 104 = 0

(x - 8)(x + 13) = 0

x - 8 = 0 or x + 13 = 0

x = 8 or x = -13

Since the width of a rectangle cannot be a negative number, we discard the answer x = -13.

x = 8

The width is 8 inches.

The length is 8 + 5 = 13.

The length is 13 inches.

Answer:

For lines A and B to be parallel, the Same Side Interior angles must be supplementary which means:

2x + 10 + 4x + 80 = 180

6x + 90 = 180

6x = 90

x = 15°

Answer:I think it's TRUE not sure

Step-by-step explanation:

The correct answer is A. The 200 randomly selected students

Explanation:

In most studies, the complete population is not surveyed or studied instead, a specific number of individuals are selected, this group is known as the sample. Additionally, the sample represents the population, and due to this, their answers are used to make inferences about all the population.

According to this, the population is all the students in the school, while the sample is the 200 randomly selected students because this is the group that is going to be studied to make conclusions and inferences about all the population.

Answer:

(a)

Step-by-step explanation:

Answer:

d. 0.459 < p < 0.603

Step-by-step explanation:

We have to calculate a 90% confidence interval for the proportion.

The sample proportion is p=0.531.

[tex]p=X/n=69/130=0.531[/tex]

The standard error of the proportion is:

[tex]\sigma_p=\sqrt{\dfrac{p(1-p)}{n}}=\sqrt{\dfrac{0.531*0.469}{130}}\\\\\\ \sigma_p=\sqrt{0.001916}=0.044[/tex]

The critical z-value for a 90% confidence interval is z=1.645.

The margin of error (MOE) can be calculated as:

[tex]MOE=z\cdot \sigma_p=1.645 \cdot 0.044=0.072[/tex]

Then, the lower and upper bounds of the confidence interval are:

[tex]LL=p-z \cdot \sigma_p = 0.531-0.072=0.459\\\\UL=p+z \cdot \sigma_p = 0.531+0.072=0.603[/tex]

The 90% confidence interval for the population proportion is (0.459, 0.603).

Answer:

1/81.

Step-by-step explanation:

3^-4 = 1 /3^4

= 1/81.

Answer:

[tex]\frac{5x-11}{\left(2x-3\right)\left(x+2\right)}[/tex]

Step-by-step explanation:

[tex]\frac{5x-11}{2x^2+x-6}[/tex]

Factor the denominator.

[tex]\frac{5x-11}{\left(2x-3\right)\left(x+2\right)}[/tex]

The fraction cannot be simplified further.

Answer:

solution,

[tex] \frac{5x - 11}{2 {x}^{2} + x - 6} \\ = \frac{5x - 11}{2 {x}^{2} + (4 - 3)x - 6} \\ = \frac{5x - 11}{2 {x}^{2} + 4x - 3x - 6 } \\ = \frac{5x - 11}{2x(x + 2) - 3(x + 2)} \\ = \frac{5x - 11}{(x + 2)(2x - 3)} [/tex]

Hope this helps..

Answer:

61% of the time a person will wait at least 1.872 seconds before the wave crashes in.

Step-by-step explanation:

An uniform probability is a case of probability in which each outcome is equally as likely.

For this situation, we have a lower limit of the distribution that we call a and an upper limit that we call b.

The probability that we find a value X lower than x is given by the following formula.

[tex]P(X \leq x) = \frac{x - a}{b-a}[/tex]

Uniform distribution from 0 to 4.8 seconds.

This means that [tex]a = 0, b = 4.8[/tex]

61% of the time a person will wait at least how long before the wave crashes in?

This is the 100 - 61 = 39% percentile, which is x for which [tex]P(X \leq x) = 0.39[/tex]. So

[tex]P(X \leq x) = \frac{x - a}{b-a}[/tex]

[tex]0.39 = \frac{x - 0}{4.8 - 0}[/tex]

[tex]x = 4.8*0.39[/tex]

[tex]x = 1.872[/tex]

61% of the time a person will wait at least 1.872 seconds before the wave crashes in.

Hey there! :)

Answer:

x = 18 minutes.

Step-by-step explanation:

To solve this equation, set up a ratio.

# of towels over time taken:

[tex]\frac{6}{3} = \frac{36}{x}[/tex]

Cross multiply:

6x = 108

Divide both sides by 6:

6x/6 = 108/6

x = 18 minutes.

Answer:

In eighteen minutes she will have folded all 36

Answer:

Experiment

Time..

Step-by-step explanation:

It is an experimental study. An experimental study is a type of study in which all conditions are under the control of the researcher.

The control factor in this case may includes the time...before measurements.

Here we must answer different things about the experiment that the farmer performed. We will see that this is an experiment and the controlled factors are:

What he did is divide his land in two equal parts, and then use different types of seeds in each one of the two parts.

After 3 months, he measures the height of the crops.

The questions are:

Is the study observational or experimental?

It is experimental, because the farmer assigned two areas and he decided what type of seed went into each area.

If it is an experiment, what are the controlled factor?

The controlled factors are the things that are the same for both of the groups of sections and that are relevant for the growth of the seeds. These things are:

If you want to learn more about experiments, you can read:

https://brainly.com/question/11256472

Answer:

Pair of compasses.

Step-by-step explanation:

These are used to inscribe circles/arcs.

Compasses are used in maths, navigation,e.t.c.

Hope it helps.

Answer: (a) The chart is in the first attachment named table frequency.

(b) The histogram is in the second attachment named frequency vs. enrollment

(c) Mode

(d) x = 9071.4

(e) s = 6677.64

(f) It is -0.16 standard deviation away

Step-by-step explanation:

(c) Mode is the number in the data set which appears more often. When thinking about builiding a new community college, if you choose mode will have which college enrollment will appear more often, i.e., which courses have more students wanting to enroll.

(d) To calculate sample mean of a frequency data:

1) Find the midpoint for each interval;

2) Multiply each midpoint for its correspondent frequency;

3) Sum up each multiplication obtained in the previous step;

4) Sum up all the frequencies;

5) Divide the sum in step 3 by the sum in step 4;

For this chart:

x = [tex]\frac{3000.10+7500.16+12500.3+17500.3+22500.1+27500.2}{35}[/tex]

x = 9071.4

(e) To find the standard deviation:

1) With each midpoint, calculate its square;

2) Multiply the midppoint square by its correspondent frequency;

3) Use the following formula to determine the sample standard:

s = √∑f.M²  - n(μ)² / n-1

For this chart:

s = [tex]\sqrt{\frac{4396250000 - 35*(9071.4)^{2}}{34} }[/tex]

s = 6677.64

(f) To find how many standard deviations away is the enrollment:

z = [tex]\frac{8000-9071.4}{6677.64}[/tex]

z = - 0.16

8000 enrollments are -0.16 standard deviations away from the mean.

Answer:

first second third

Step-by-step explanation:

Answer:

A,B,C

Step-by-step explanation:

I took the course

Answer:

to determine the inverse of the given function, change f(x) to y, switch [tex]\boxed{x}[/tex] and y and solve for [tex]\boxed{y}[/tex]

The resulting function can be written as

[tex]f^{-1}(x)=x^2+\boxed{4}[/tex] where [tex]x\geq\boxed{0}[/tex]

Step-by-step explanation:

Hello,

f is defined for [tex]x\geq 4[/tex] as x-4 must be greater or equal to 0

and [tex]f(x)\geq 0[/tex]

so [tex]f^{-1}[/tex] is defined for [tex]x\geq 0[/tex]

and then we can write

[tex]x=(fof^{-1})(x)=f(f^{-1}(x))=\sqrt{f^{-1}(x)-4} \ so\\f^{-1}(x)-4=x^2 <=> f^{-1}(x)=x^2+4[/tex]

hope this helps

Answer:

116370.197$

Step-by-step explanation:

Jimmie invested $13,000 at 5.23% compounded monthly.

Jimmie's account balance (B) after 42 years:

B = principal x (1 + rate)^time

  = 13000 x (1 + (5.23/100)/12)^(42 x 12)

  = 116370.197$

Answer:

0.42

Process:

1 - 0.58

0.42

Answer:

Yes. At the 0.05 significance level, there is enough evidence to support the claim that the proportion that support the candidate has significantly changed.

Step-by-step explanation:

This is a hypothesis test for the difference between proportions.

The claim is that the proportion that support the candidate has significantly changed.

Then, the null and alternative hypothesis are:

[tex]H_0: \pi_1-\pi_2=0\\\\H_a:\pi_1-\pi_2\neq 0[/tex]

The significance level is 0.05.

The sample 1, of size n1=800 has a proportion of p1=0.58.

[tex]p_1=X_1/n_1=460/800=0.58[/tex]

The sample 2, of size n2=1000 has a proportion of p2=0.52.

[tex]p_2=X_2/n_2=520/1000=0.52[/tex]

The difference between proportions is (p1-p2)=0.05.

[tex]p_d=p_1-p_2=0.58-0.52=0.05[/tex]

The pooled proportion, needed to calculate the standard error, is:

[tex]p=\dfrac{X_1+X_2}{n_1+n_2}=\dfrac{464+520}{800+1000}=\dfrac{980}{1800}=0.54[/tex]

The estimated standard error of the difference between means is computed using the formula:

[tex]s_{p1-p2}=\sqrt{\dfrac{p(1-p)}{n_1}+\dfrac{p(1-p)}{n_2}}=\sqrt{\dfrac{0.54*0.46}{800}+\dfrac{0.54*0.46}{1000}}\\\\\\s_{p1-p2}=\sqrt{0.00031+0.000248}=\sqrt{0.000558}=0.02[/tex]

Then, we can calculate the z-statistic as:

[tex]z=\dfrac{p_d-(\pi_1-\pi_2)}{s_{p1-p2}}=\dfrac{0.05-0}{0.02}=\dfrac{0.05}{0.02}=2.33[/tex]

This test is a two-tailed test, so the P-value for this test is calculated as (using a z-table):

[tex]\text{P-value}=2\cdot P(z>2.33)=0.02[/tex]

As the P-value (0.02) is smaller than the significance level (0.05), the effect is significant.

The null hypothesis is rejected.

There is enough evidence to support the claim that the proportion that support the candidate has significantly changed.

Answer:

50 miles

Step-by-step explanation:

hello,

let's note x the number of miles travelled heading west,

it takes 1 hour to travel 25 miles

so it takes x/25 hours to travel x miles

we know that in total it travels 7 hours so it will travel 7-x/25 hours heading North, then heading North it takes 1 hour to travel 19 miles

so in 7-x/25 hours it travels 19(7-x/25) miles

we can write, as the total distance is 145 miles

[tex]x+19(7-\dfrac{x}{25})=145\\<=> 25x+3325-19x=3625\\<=> 6x=300\\<=> x = 50[/tex]

we can verify

50 miles heading West takes 2 hours

in 5 hours it travels 19*5 = 95 miles

the total is 145 miles

so this is correct

hope this helps

Answer:

2,022,456 committees

Step-by-step explanation:

From the above question, we are given the following information:

Number of women = 20

Number of men = 17

In order to form a committee of six members with at least 2 men, the number of ways we can do this is 5 ways and they are:

a) A committee of 6 men

b) A committee of 5 men and 1 woman

c) A committee of 4 men and 2 women

d) A committee of 3 men and 3 women

e) A committee of 2 men and 4 women

To solve for this we use the combination formula which is given as:

C(n, r) = nCr = n!/r!(n - r)!

Hence, the number of committees that are possible if the committee must have at least two men is calculated as

A committee of 6 men or A committee of 5 men and 1 woman or A committee of 4 men and 2 women or A committee of 3 men and 3 women or A committee of 2 men and 4 women

=[C(17, 6)]+ [C(17,5) × C(20,1)] + [C(17,4) × C(20,2)] + [C(17,3) × C(20,3)] + [C(17,2) × C(20,4)]

= [17!/6!(17 - 6)!] + [17!/5!(17 - 5)! × 20!/1!(20 - 1)!] + [17!/4!(17 - 4)! × 20!/2!(20 - 2)!] + [17!/3!(17 - 3)! × 20!/3!(20 - 3)!] + [17!/2!(17 - 2)! × 20!/4!(20 - 4)!]

= [12376] + [ 6188 × 20] + [2380 × 190] + [680 × 1140] + [ 136 ×4845]

= 2,022,456 committees

Answer:

m∠A = 17 degrees       m∠B = 73 degrees     m∠C = 90 (given)    a =   12 (given)    b =  40           c = 42 (given)

Step-by-step explanation:

Use sin to solve m∠A

sin x = 12/42     Simplify

sin x = 0.2857   Use the negative sin to solve for x

sin^-1 x =  17 degrees

Add together all of the angle measures to solve for m∠B

17 + 90 + x = 180    Add

107 + x = 180

-107        -107

x = 73 degrees

Use Pythagorean Theorem to solve for b

12^2 + x^2 = 42^2     Simplify

144 + x^2 = 1764

-144            -144

x^2 = 1620               Take the square root of both sides

x = 40

Answer:

Hello, your answer is:

B. 3²×5

Step-by-step explanation:

Prime factorization of 45 is:

45 = 9 x 5

= 3²×5

Hope this helps you.. Good Luck

Answer:

B. 3² × 5

Step-by-step explanation:

45 can be written as a product of its prime factors.

45 = 3 × 3 × 5

45 = 3² × 5

Answer:

  41°, 56°, 83°

Step-by-step explanation:

We can find the largest angle from the law of cosines:

  c² = a² +b² -2ab·cos(C)

  C = arccos((a² +b² -c²)/(2ab))

  C = arccos((4² +5² -6²)/(2(4)(5))) = arccos(5/40) ≈ 82.8192°

Then the second-largest angle can be found the same way:

  B = arccos((4² +6² -5²)/(2·4·6)) = arccos(27/48) ≈ 55.7711°

Of course the third angle is the difference between the sum of these and 180°:

  A = 180° -82.8192° -55.7711° = 41.4096°

Rounded to the nearest degree, ...

  the angles of the triangle are 41°, 56°, 83°.

Answer:y times 20 p

Step-by-step explanation:

Answer:124

Step-by-step explanation:

2x + 8 + x - 2 = 180

Add like terms

3x + 6 = 180

Subtract the 6 from both sides

3x + 6 - 6 = 180 - 6

3x = 174

Divide by 3

x = 58

Now we have to find the measure of angle ACD

2(58) + 8 = 124

Answer:

2 ft by 6

Step-by-step explanation:

The dimensions of the table are either 2 feet by 6 feet or 6 feet by 2 feet.

A rectangle is a two dimension figure with 4 sides, 4 corners and 4 right angles. The opposite sides of the rectangle are equal and parallel to each other.

Since, the area of a rectangle is:

Area = length x width

We know that the area of the table is 12 square feet,

So, we can write:

12 = length x width

And, use the formula for the perimeter of a rectangle:

Perimeter = 2 x length + 2 x width

We know that the perimeter of the table is 16 feet, so we can write:

16 = 2 x length + 2 x width

Now we have two equations with two variables (length and width), which we can solve simultaneously as.

Let's rearrange the second equation to solve for length:

16 = 2 x length + 2 x width

16 - 2 x width = 2 x length

8 - width = length

Now we can substitute this expression for length into the first equation:

12 = length x width

12 = (8 - width) x width

12 = 8w - w²

We can rearrange this equation into standard quadratic form:

w² - 8w + 12 = 0

Now we can use the quadratic formula:

where a = 1, b = -8, and c = 12

w = (-(-8) ± √((-8)² - 4(1)(12))) / 2(1)

w = (8 ± √(16)) / 2

w = 4 ± 2

Hence, w = 2

w = 6

So the possible values for the width are 2 and 6.

If the width is 2 feet, then the length is:

length = 8 - width = 6 feet

If the width is 6 feet, then the length is:

length = 8 - width = 2 feet

Therefore, the dimensions of the table are either 2 feet by 6 feet or 6 feet by 2 feet.

Learn more about the rectangle visit:

https://brainly.com/question/2607596

#SPJ3

Answer: 5182

To get the value of all 100 numbers you would need to multiply.

Step-by-step explanation:

51.82x100= 5182

Answer:

Option (C)

Step-by-step explanation:

Given expression is,

[tex]4+4\times \text{log}_2(x)=14[/tex]

By subtracting 4 from both the sides of the equation.

[tex]4\times \text{log}_2(x)=14-4[/tex]

Now divide the equation by 4

[tex]\text{log}_2(x)=\frac{10}{4}[/tex]

[tex]\text{log}_2(x)=2.5[/tex]

[If [tex]\text{log}_ab=x[/tex] , then [tex]b=a^{x}[/tex]]

[tex]x=(2)^{2.5}[/tex]

[tex]x = 5.657[/tex]

x ≈ 5.66

Therefore, Option C will be the correct option.

4+4•log2 x=14

x= 5.66

Answer:

873116133

Step-by-step explanation:

18576939 × 47

Multiply the numbers.

= 873116133

Answer: 873116133

Step-by-step explanation:

‘Hope this helps:)

Answer:

0

Step-by-step explanation:

3 cards

P( odd) = 1 odd/ 3 cards = 1/3

No replacement

2 cards 6,8

No odds

P( odd) = 0/2

P( odd, no replacement, odd) = 1/2 * 0 = 0

Answer:

The height of the hill is 116.9 meters.

Step-by-step explanation:

The diagram depicting this problem is drawn and attached below.

From Triangle ABC

[tex]\tan 22^\circ=\dfrac{h}{150+x}\\\\h=\tan 22^\circ(150+x)[/tex]

From Triangle XBC

[tex]\tan 40^\circ =\dfrac{h}{x}\\\\h=x\tan 40^\circ[/tex]

Therefore:

[tex]h=\tan 22^\circ(150+x)=x\tan 40^\circ\\150\tan 22^\circ+x\tan 22^\circ=x\tan 40^\circ\\x\tan 40^\circ-x\tan 22^\circ=150\tan 22^\circ\\x(\tan 40^\circ-\tan 22^\circ)=150\tan 22^\circ\\x=\dfrac{150\tan 22^\circ}{\tan 40^\circ-\tan 22^\circ} \\\\x=139.30[/tex]

Therefore, the height of the hill

[tex]h=139.3\times \tan 40^\circ\\=116.9$ meters( correct to 1 d.p.)[/tex]

The height of the hill is 116.9 meters.