4. Simplify the following.
3
a. 2-X5-:11
3
x5
5
6
7​

Answer:

decreases.

Step-by-step explanation:

Type II error is one in which we fail to reject the null hypothesis that is actually false. Null hypothesis is a statement that is to be tested against the alternative hypothesis and then decision is taken whether to accept or reject the null hypothesis. The power of Type II error is 1 - [tex]\beta[/tex]. As the power increases the probability of Type II error decreases.

Answer:

200 N/m

Step-by-step explanation:

Rearranging the formula F = kx, you find that k = F/x. For the first spring,

F = 36 N and x = 0.06 m (6 cm). So the spring constant, F/x, is 36N/0.06m = 600 N/m

For the second spring, F = 36 N and x = 0.09 m. F/x = 36N/0.09m = 400 N/m

The difference between these values is 200 N/m, and that's the answer.

Your integrand is missing some symbols. My best interpretation is the following integral:

[tex]I=\displaystyle\int\frac{x^4+18x^2+4}{x^5+30x^3+20x}\,\mathrm dx[/tex]

Decompose into partial fractions; we're looking for an expansion of the form

[tex]\dfrac{x^4+18x^2+4}{x^5+30x^3+20x}=\dfrac ax+\dfrac{bx^3+cx^2+dx+e}{x^4+30x^2+20}[/tex]

Now:

[tex]x^4+18x^2+4=a(x^4+30x^2+20)+(bx^3+cx^2+dx+e)x[/tex]

[tex]=(a+b)x^4+cx^3+(30a+d)x^2+ex+20a[/tex]

Matching up coefficients tells us that

[tex]\begin{cases}a+b=1\\c=0\\30a+d=18\\e=0\\20a=4\end{cases}\implies a=\dfrac15,b=\dfrac45,d=12[/tex]

so that

[tex]I=\displaystyle\frac15\int\frac{\mathrm dx}x+\frac45\int\frac{x^3+15x}{x^4+30x^2+20}\,\mathrm dx[/tex]

The integral is trivial:

[tex]\displaystyle\frac15\int\frac{\mathrm dx}x=\frac15\ln|x|+C[/tex]

For the second integral, notice that

[tex]\mathrm d(x^4+30x^2+20)=(4x^3+60x)\,\mathrm dx[/tex]

Distribute the 4 over the numerator, then substitute [tex]u=x^4+30x^2+20[/tex] and [tex]\mathrm du=(4x^3+60x)\,\mathrm dx[/tex]:

[tex]\displaystyle\frac15\int\frac{4x^3+60x}{x^4+30x^2+20}\,\mathrm dx=\frac15\int\frac{\mathrm du}u=\frac15\ln|u|+C=\frac15\ln(x^4+30x^2+20)+C[/tex]

So we have

[tex]I=\dfrac15\ln|x|+\dfrac15\ln(x^4+30x^2+20)+C[/tex]

and with some simplification,

[tex]I=\boxed{\ln\sqrt[5]{|x^5+30x^3+20x|}+C}[/tex]

Answer:

[tex]A = A_c-A_t=4\pi -8=4.5664cm^2[/tex]

Step-by-step explanation:

The area of the shaded region can be calculated as the area of the semicircle less the area of the right triangle.

The area of the right triangle can be calculated as:

[tex]A_t=\frac{b*h}{2} =\frac{LM*MN}{2}[/tex]

Where LM and MN have the same length because the internal angles are L=45°, M=90°, and N=45°. So the area is:

[tex]A_t=\frac{4*4}{2}=8[/tex]

The diameter of the circle can be calculated using the Pythagorean theorem as:

[tex]D=\sqrt{(LM)^2+(MN)^2} =\sqrt{4^2+4^4}=4\sqrt{2}[/tex]

So, the radius is [tex]r=2\sqrt{2}[/tex]

Finally, the area of the semicircle is:

[tex]A_c=\frac{\pi*r^2 }{2}=\frac{\pi*(2\sqrt{2})^2 }{2}=4\pi[/tex]

So, the area of the shaded region is:

[tex]A = A_c-A_t=4\pi -8=4.5664cm^2[/tex]

The formula C = π2r

Is used for the circumference.

We know that the number π is defined as the quotient between the circumference of a circle and its diameter, so we can write:

C/d = π

And remember that the diameter is twice the radius, so we can write:

d = 2r

Then we can rewrite the equation for the circumference as:

C = π2r

Then we conclude that the correct option is B.

If you want to learn more about circles:

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Answer: 0.0548

Step-by-step explanation:

Given, A research study investigated differences between male and female students. Based on the study results, we can assume the population mean and standard deviation for the GPA of male students are µ = 3.5 and σ = 0.05.

Let [tex]\overline{X}[/tex] represents the sample mean GPA for each student.

Then, the probability that the random sample of 100 male students has a mean GPA greater than 3.42:

[tex]P(\overline{X}>3.42)=P(\dfrac{\overline{X}-\mu}{\dfrac{\sigma}{\sqrt{n}}}>\dfrac{3.42-3.5}{\dfrac{0.5}{\sqrt{100}}})\\\\=P(Z>\dfrac{-0.08}{\dfrac{0.5}{10}})\ \ \ [Z=\dfrac{\overline{X}-\mu}{\dfrac{\sigma}{\sqrt{n}}}]\\\\=P(Z>1.6)\\\\=1-P(Z<1.6)\\\\=1-0.9452=0.0548[/tex]

hence, the required probability is 0.0548.

Answer:

Step-by-step explanation:

Hello,

First of all, we need to find the equation of the line.

It will be something like y = ax + b (we need to find a and b).

Then the graph is the part of the plan which is above this line, so the inequality will be

[tex]\large \boxed{\sf \ \ y\geq ax+b \ \ }[/tex]

There is only one line passing by two different points, right?

We need to find two points of this line, the x-axis gives the x of the point and the y-axis give the y of the point.

We can see on the graph that (-1,-1) and (6,13) are two points of this line.

I attached a graph with the two points A (-1,-1) and B (6,13).

We need to solve y = ax + b to find a and b which means:

(-1) = a(-1 )+ b <=> -1 = -a + b <=> -a + b = -1

(13) = a(6) + b <=> 6a + b = 13

To eliminate b, we can subtract the first equation from the second one.

6a + b -(-a) - b = 13 - (-1) = 13 + 1 = 14

<=> 6a + a = 7a = 14 we can divide by 7 both parts of the equation.

[tex]\large \boxed{\sf \ \ a=\dfrac{14}{7}=2 \ \ }[/tex]

And then, b = -1 + a = -1 + 2 = 1

[tex]\large \boxed{\sf \ \ b=1 \ \ }[/tex]

The equation of the line is then [tex]y=2x+1[/tex]

So, the inequality is:

[tex]\Large \boxed{\sf \ \ y\geq 2x+1 \ \ }[/tex]

And this is the answer of the question 1.

2. First, we find the equation of the line by finding two points on this line. Then, we deduce the inequality from the equality as the graph is all the points above the line (as explained above).

3. A real-life example is the following.

My parents gave $1 to my sister and they will give her $2 every day.

So today at x = 0 she has $1 and her pocket money will be represented by the line. And I told my parents that there were no way I can get less than my little sister. To help them understand what can be an acceptable deal I provided this graph, and I told them to only look for t positive of course.

The label for the x-axis is the time.

The label for the y-axis is the pocket money in $

After one day x = 1 my sister has $3 (point on the line), a possible solution for my pocket money is $6, $14 (two points from the graph) is also a solution of course :-)

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Answer:

[tex]\boxed{\sf x - 5 = 10}[/tex]

Step-by-step explanation:

Taking away 5 from x ⇒ subtracting 5 from x

[tex]\large {\sf x - 5[/tex]

Gives 10 ⇒ result is 10

[tex]\large {\sf x - 5 = 10[/tex]

Answer:

-1.031 m/s or  [tex]\frac{-\sqrt{17} }{4}[/tex]

Step-by-step explanation:

We take the length of the rope from the dock to the bow of the boat as y.

We take x be the horizontal  distance from the dock to the boat.

We know that the rate of change of the rope length is [tex]\frac{dy}{dt}[/tex] = -1 m/s

We need to find the rate of change of the horizontal  distance from the dock to the boat =  [tex]\frac{dx}{dt}[/tex] = ?

for x = 4

Applying Pythagorean Theorem we have

[tex]1^{2} +x^{2} =y^{2}[/tex]    .... equ 1

solving, where x = 4, we have

[tex]1^{2} +4^{2} =y^{2}[/tex]

[tex]y^{2} = 17[/tex]

[tex]y = \sqrt{17}[/tex]

Differentiating equ 1 implicitly with respect to t, we have

[tex]2x\frac{dx}{dt} = 2y\frac{dy}{dt}[/tex]

substituting values of

x = 4

y = [tex]\sqrt{17}[/tex]

[tex]\frac{dy}{dt}[/tex] = -1

into the equation, we get

[tex]2(4)\frac{dx}{dt} = 2(\sqrt{17} )(-1)[/tex]

[tex]\frac{dx}{dt} = \frac{-\sqrt{17} }{4}[/tex] = -1.031 m/s

Answer:

$10 to rent shoes for 9 people

Step-by-step explanation:

Total amount of the party = $140

A bowling lane = $50

$140 - $50 = $90

$90 divided by 9 = 10

$10 to rent shoes for 9 people

Answer:

y=0.5x+40

Step-by-step explanation:

Copy the  equation.

x-2y=8

Subtract x from both sides.

-2y=-x-8

Divide both sides by -2.

y=0.5x+4

Now we know the slope is 0.5.

Any line with a slope of 0.5 will be perpendiculr to the original line.

One that you can use is y=0.5x+40.

Answer:

C) 24/25

Step-by-step explanation:

did the quiz and got it right

The value of the sine theta in the first quadrant in the diagram given is [tex]\mathbf{\dfrac{24}{25}}[/tex]

The explanation of the trigonometric functions (i.e cosine, sine, tangent) in respect of point coordinates on the unit circle informs us of the signs and meanings of the trigonometric functions for each of the four(4) quadrants, depending on the signs of the x, as well as, y coordinates in each quadrant.

In the first quadrant;

Thus, we have a positive x and y-axis.

Taking the forms x and y, i.e. (x, y) = (cos θ, sin θ)

The value of sine theta in [tex]\mathbf{(\dfrac{7}{25}, \dfrac{24}{25} ) = \dfrac{24}{25} }[/tex]

Learn more about Trigonometric functions here:

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Answer:

The given data is:

30, 32, 11, 14, 40, 37, 16, 26, 12, 33, 13, 19, 38, 12, 25, 15, 39, 11, 37, 17, 27, 14, 36

We will fill the table with the relevant information:

Question 1: 21 - 25 (because the previous range stops at 20 and the following range starts at 26)

Question 2: III (write 3 as a tally)

Question 3: II (write 2 as a tally)

Question 4: 8 (write the tally as a number)

Question 5: 4 (write IIII as a number)

Answer:

[tex]\large \boxed{\sf \text{The rate of the boat is } 53 \ km/h \text{, the rate of the current is }8\ km/h \ \ }[/tex]

Step-by-step explanation:

Hello, let's note v the rate of the boat and r the rate of the current. We can write the following

[tex]\dfrac{135}{v-r}=3=\dfrac{183}{v+r}[/tex]

It means that

[tex]135(v+r)=183(v-r)\\\\135 v + 135r=183v-183r\\\\\text{ *** We regroup the terms in v on the right and the ones in r to the left***}\\\\(135+183)r=(183-135)v\\\\318r=48v\\\\\text{ *** We divide by 48 both sides ***}\\\\\boxed{v = \dfrac{318}{48} \cdot r= \dfrac{159}{24} \cdot r}[/tex]

But we can as well use the second equation:

[tex]3(v+r)=183\\\\v+r=\dfrac{183}{3}=61\\\\\dfrac{159}{24}r+r=61\\\\\dfrac{159+24}{24}r=61\\\\\boxed{r = \dfrac{61*24}{183}=8}[/tex]

and then

[tex]\boxed{v=\dfrac{159*8}{24}=53}[/tex]

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Answer:

linear

Step-by-step explanation:

Answer:

[tex] c = 15.5 [/tex]

Step-by-step explanation:

Using the Law of Cosines, c² = a² + b² - 2ab*cos(C), let's find c.

Where,

a = 15 ft

b = 20 ft

C = 50°

Thus:

[tex] c^2 = 15^2 + 20^2 - 2*15*20*cos(50) [/tex]

[tex] c^2 = 625 - 600*0.6429 [/tex]

[tex] c^2 = 625 - 600*0.6429 [/tex]

[tex] c^2 = 625 - 385.74 [/tex]

[tex] c^2 = 239.26 [/tex]

[tex] c = \sqrt{239.26} [/tex]

[tex] c = 15.5 [/tex] (nearest tenth)

Answer:

c sorry gotta get points.

Step-by-step explanation:

Answer:

The probability that at least 4 of them use their smartphones is 0.1773.

Step-by-step explanation:

We are given that when adults with smartphones are randomly selected 15% use them in meetings or classes.

Also, 15 adult smartphones are randomly selected.

Let X = Number of adults who use their smartphones

The above situation can be represented through the binomial distribution;

[tex]P(X = r) = \binom{n}{r}\times p^{r} \times (1-p)^{n-r} ; n = 0,1,2,3,.......[/tex]

where, n = number of trials (samples) taken = 15 adult smartphones

           r = number of success = at least 4

           p = probability of success which in our question is the % of adults

                 who use them in meetings or classes, i.e. 15%.

So, X ~ Binom(n = 15, p = 0.15)

Now, the probability that at least 4 of them use their smartphones is given by = P(X [tex]\geq[/tex] 4)

P(X [tex]\geq[/tex] 4) = 1 - P(X = 0) - P(X = 1) - P(X = 2) - P(X = 3)

= [tex]1- \binom{15}{0}\times 0.15^{0} \times (1-0.15)^{15-0}-\binom{15}{1}\times 0.15^{1} \times (1-0.15)^{15-1}-\binom{15}{2}\times 0.15^{2} \times (1-0.15)^{15-2}-\binom{15}{3}\times 0.15^{3} \times (1-0.15)^{15-3}[/tex]

= [tex]1- (1\times 1\times 0.85^{15})-(15\times 0.15^{1} \times 0.85^{14})-(105 \times 0.15^{2} \times 0.85^{13})-(455 \times 0.15^{3} \times 0.85^{12})[/tex]

= 0.1773

Answer:

y-intercept is (0,-10) and x-intercept is (-6,0).  Connect them by a straight line to graph the given equation.

Step-by-step explanation:

The given equation of line is

[tex]3y=-5x-30[/tex]

For x=0,

[tex]3y=-5(0)-30[/tex]

[tex]3y=-30[/tex]

[tex]y=-10[/tex]

So, y-intercept is at point (0,-10).

For y=0,

[tex]3(0)=-5x-30[/tex]

[tex]0=-5x-30[/tex]

[tex]5x=-30[/tex]

[tex]x=-6[/tex]

So, x-intercept is at point (-6,0).

Now, plot the point (0,-10) and (-6,0) on a coordinate plane and connect them by a straight line to graph the given line as shown below.

Answer:

3/11

Step-by-step explanation:

There are eleven equal parts.

So the denominator is 11.

He copies 8 parts on Sunday.

11-8=3.

He copied 3 parts on Saturday.

Hope this helps ;) ❤❤❤

The answer is 86.4 km

Explanation:

The graph shows the gift shop is to the east of the science lab, and, between the gift shop and the science lab it is the art supply. Besides this, the description of the graph provides the distance between the art supply and the science lab, which is 40.0, as well as, the distance between the art supply and the gift shop, which is 46.4 kilometers.

In this context, it is possible to calculate the distance from the science lab to the gift shop by adding the partial distances, considering the art supply as a middle point in the map. This means the distance from the lab to the gift shop = 40.0 km (distance from the lab to the art supply) + 46.4 km (distance from the art supply to the gift shop) = 86.4 km.

Answer:  203,280

Step-by-step explanation:

Given: A catering service offers 11 appetizers, 12 main courses, and 8 desserts.

Number of combinations of choosing r things out of n = [tex]^nC_r=\dfrac{n!}{r!(n-r)!}[/tex]

A customer is to select 9 appetizers, 2 main courses, and 3 desserts for a banquet.

Total number of ways to do this: [tex]^{11}C_9\times ^{12}C_2\times^{8}C_3[/tex]

[tex]=\dfrac{11!}{9!2!}\times\dfrac{12!}{2!10!}\times\dfrac{8!}{3!5!}\\\\=\dfrac{11\times10}{2}\times\dfrac{12\times11}{2}\times\dfrac{8\times7\times6}{3\times2}\\\\= 203280[/tex]

hence , this can be done in 203,280 ways.

Answer:

(x – 4)^2 + (y + 7)^2 = 16

Step-by-step explanation:

The formula of a circle is:

(x – h)^2 + (y – k)^2 = r^2

(h, k) represents the coordinates of the center of the circle

r represents the radius of the circle

If you plug in the given information, you get:

(x – 4)^2 + (y – (-7))^2 = 4^2

which simplifies into:

(x – 4)^2 + (y + 7)^2 = 16

Answer:

Option D

Step-by-step explanation:

A type I error occurs when you reject the null hypothesis when it is actually true.

The null hypothesis in this case is minimum breaking strength is less than or equal to 0.5.

A type one error would be allowing the production process to continue when the true breaking strength is below specifications.

Answer:

A) 0.99413

B) 0.00022

Step-by-step explanation:

A) First of all let's find the total grading time from 6:50 P.M to 11:00 P.M.:

Total grading time; X = 11:00 - 6:50 = 4hours 10minutes = 250 minutes

Now since we are given an expected value of 5 minutes, the mean grading time for the whole population would be:

μ = n*μ_s ample = 42 × 5 = 210 minutes

While the standard deviation for the population would be:

σ = √nσ_sample = √(42 × 6) = 15.8745 minutes

To find the z-score, we will use the formula;

z = (x - μ)/σ

Thus;

z = (250 - 210)/15.8745

z = 2.52

From the z-distribution table attached, we have;

P(Z < 2.52) ≈ 0.99413

B) solving this is almost the same as in A above, the only difference is an additional 10 minutes to the time.

Thus, total time is now 250 + 10 = 260 minutes

Similar to the z-formula in A above, we have;

z = (260 - 210)/15.8745

z = 3.15

P(Z > 3.15) = 0.00022

Answer:

a) We reject H₀ we have enough evidence for that

b) 1.-The survey was made over a district, results will surely be different if the survey is carried out over a whole state ( considering urban and rural areas)

2.-In a district we find an equalized level of salaries, which could be associated with a similar level of habits

Step-by-step explanation:

We have to develop a proportion test. One tail-test

Population proportion mean (national proportion)  p₀  = 72 %

Sample information

sample proportion  271/300         p = 0,90      p = 90 %

We assume Confidence Interval  90 %     then α = 0,1

Test Hypothesis

Null Hypothesis                                 H₀     p   =  p₀

Alternative Hypothesis                       Hₐ    p   >  p₀

As  α = 0,1 and    

We look at z-table for z(c) and find     z(c) = 1,28

And we compute z(s)  as

z(s) = ( p - p₀ ) √  (p₀q₀/n

z(s) =  ( 0,9 - 0,72 ) /√(0,72)*(0,28)/300

z(s) =  0,18 / √0,1296/300

z(s) =  0,18/ 0,026

z(s) =   6,92

z(s) > z(c)      6,92 > 1,28

As z(s) is bigger than z(c), z(s) is in the rejection region, so we reject the null hypothesis. We have enough evidence to claim that the proportion in the district is bigger than the national one.

b)1. The survey was made over a district, results will surely be different if the survey is carried out over a whole state ( considering urban and rural areas)

2.-In a district we find an equalized level of salaries, which could be associated with a similar level of habits

To write an inequality and show on a number line all numbers: greater than (−3) but less than or equal to 3

Let n be the number, then -3 < n ≤3 .

On number line we mark open circle at -3 (since it has a strictly less than sign) and a closed circle at 3  (since it has a less than and equal to sign) .

To the required inequality that shows all the numbers greater than (−3) but less than or equal to 3 : -3 < n ≤3 and the number line is represented below.

Answer:

37.7

Step-by-step explanation:

Well use the formula for the volume of a cylinder which is,

,[tex]\pi r^2 h[/tex]

So the radius is 2 and the height is 3, so we plug those numbers into the formula,

(pi)(2)^2(3)

2^2 is 4 4*3 is 12

12*pi is about 37.7 rounded to the nearest tenth.

If you would like to check look at the image below.

Answer:

see explanation

Step-by-step explanation:

The median is the middle value of the data set in ascending order. If there is no exact middle then the median is the average of the values either side of the middle.

Given

3   8   14   19   22   29   33   37   43   49

                            ↑ middle is between 22 and 29

median = [tex]\frac{22+29}{2}[/tex] = [tex]\frac{51}{2}[/tex] = 25.5

The upper quartile [tex]Q_{3}[/tex] is the middle value of the data to the right of the median.

29   33   37   43   49

               ↑

[tex]Q_{3}[/tex] = 37

The lower quartile [tex]Q_{1}[/tex] is the middle value of the data to the left of the median.

3   8   14   19   22

           ↑

[tex]Q_{1}[/tex] = 14

The min is the smallest value in the data set, that is 3

The max is the largest value in the data set, that is 49

The 5 number summary is

3,  14,  25.5,  37,  49

Answer:

0.0414 with an upper tailed test

Step-by-step explanation:

Claim: P1P1 = P2P2

The above is a null hypothesis

The alternative hypothesis for a two-tailed test would be:

P1P1 \=/ P2P2

Where "\=/" represents "not equal to".

Using a z-table or z-calculator, we derive the p-value (probability value) for the z-score 2.04

With an upper tailed test, the

2 × [probability that z>2.04] = 2[0.0207] = 0.0414

This is the p-value for the test statistic.

Focus is on the alternative hypothesis.

Answer:

83.0°

Step-by-step explanation:

Given ∆XYZ, with 3 known sides, to find angle X, apply the Law of Cosines, c² = a² + b² - 2ab*cos(C).

For convenience sake, this formula can be rewritten to make the angle we are looking for the subject of the formula.

Thus, we would have this following:

[tex] cos(C) = \frac{a^2 + b^2 - c^2}{2ab} [/tex]

Where,

C = X = ?

a = 8 ft

b = 16 ft

c = 17 ft

Plug in the stated values into the formula and solve for X

[tex] cos(X) = \frac{8^2 + 16^2 - 17^2}{2*8*16} [/tex]

[tex] cos(X) = \frac{320 - 289}{256} [/tex]

[tex] cos(X) = \frac{31}{256} [/tex]

[tex] cos(X) = 0.1211 [/tex]

[tex] X = cos^{-1}(0.1211) [/tex]

[tex] X = 83.0 [/tex] (to nearest tenth)

Answer:

its actually 83 not 83.0

Step-by-step explanation:

im only saying this bc i know people with type 83.0 in the box