A homogeneous second-order linear differential equation, two functions y1 and y2 , and a pair of initial conditions are given below. First verify that y1 and y2 are solutions of the differential equation. Then find a particular solution of the form
y = c1y1 + c2y2 that satisfies the given initial conditions.
y'' + 49y = 0; y1 = cos(7x) y2 = sin(7x); y(0) = 10 y(0)=-4
y(x)=?

Answer:

36

Step-by-step explanation:

Answer:

Yes because yes.

Step-by-step explanation:

Y + e + s = Yes

Answer:

The correct answer is:

r + 0.50 = 10.25: Subtract .50 from both sides. The answer is $9.75.

This is because Juan got a $0.50 raise which means that his new rate will be $0.50 more than his original rate (r).

Answer:

$9.75

Step-by-step explanation:

Answer:

15 is the answer to the question

Answer:

15, which for some reason does not seem to be an option.

Step-by-step explanation:

Product means to multiply to numbers, items etc.

5 times 3, as you should know, is 15.

Hope this helps.

Answer:

The expected number of adult workers with a high school diploma is 4.

Step-by-step explanation:

This random variable X can be modeled with the binomial distribution, with parameters n=10 (the sample size) and p=0.4 (the probability that a adult worker have a high school diploma).

The expected value of X is then the mean of the binomial distribution with the parameters already mentioned.

This is calculated as:

[tex]E(X)=\mu_b=n\cdot p=10\cdot0.4=4[/tex]

Answer:

Step-by-step explanation:

Step 1: Consider P(1) that is n = 1

[tex]1^2 = \frac{1(1+1)(2*1+1)}{6}=\frac{6}{6}=1 \checkmark[/tex]

Step 2: Suppose the equation is true up to n. That is

[tex]1^2 + 2^2+3^2+........+n^2 = \dfrac{n(n+1)(2n+1)}{6 }[/tex]

Step 3: Prove that the equation is true up to (n+1). That is

[tex]1^2 + 2^2+3^2+........+n^2 + (n+1)^2 = \dfrac{(n+1)(n+2)(2n+3)}{6 }[/tex]

The easiest way to prove it is to expend the right hand side and prove that the right hand side = the right hand side of step 2 + (n+1)^2

From step 2, add (n+1)^2 both sides. The left hand side will be the left hand side of step 3, now, the right hand side after adding.

[tex]\dfrac{n(n+1)(2n+1)}{6 }+(n+1)^2 = \dfrac{2n^3+3n^2+n}{6}+\dfrac{6n^2+12n+6}{6}[/tex]

[tex]=\dfrac{2n^3+9n^2+13n+6}{6}[/tex]

If you expend the right hand-side of the step 3, you will see they are same.

Proof done

Answer:

see below

Step-by-step explanation:

1^2+2^2+3^2+...+n^2=n(n+1)(2n+1)/6

Step1

Verify it for n=1

1^2= 1(1+1)(2*1+1)/6= 1*2*3/6= 6/6=1 - correct

Step2

Assume it is correct for n=k

1^2+2^2+3+2+...+k^2= k(k+1)(2k+1)/6

Step3

Prove it is correct for n= k+1

1^2+2^2+3^2+...+(k+1)^2= (k+1)(k+2)(2k+2+1)/6

prove the above for k+1

1^2+2^2+3^2+...+k^2+(k+1)^2= k(k+1)(2k+1)/6 + (k+1)^2=

= 1/6(k(k+1)(2k+1)+6(k+1)^2)= 1/6((k+1)(k(2k+1)+6(k+1))=

=1/6((k+1)(2k²+k+6k+6))= 1/6(k+1)(2k²+4k+3k+6))=

= 1/6(k+1)(2k(k+2)+3(k+2))=

=1/6(k+1)(k+2)(2k+3)

Proved for n= k+1 that:

the sum of squares of (k+1) terms equal to  (k+1)(k+2)(2k+3)/6

Answer:

B. Length A of Rasheeda’s garden is 27 ft.

C. Length B of the book’s garden is 12 ft.

E. Length A of the book’s garden is 9 ft longer than length A of Rasheeda’s garden.

Step-by-step explanation:

step 1

Find the dimension of the book's garden

we know that

Book scale: 1 inch = 2 feet

That means

1 inch in the drawing represent 2 feet in the actual

To find out the actual dimensions, multiply the dimension in the drawing by 2

so

Length A of the book’s garden

Width B of the book’s garden

step 2

Find the dimension of Rasheeda’s garden

we know that

Rasheeda's Scale: 2 inch = 3 feet

That means

2 inch inches the drawing represent 3 feet in the actual

To find out the actual dimensions, multiply the dimension in the drawing by 3 and divided by 2

so

Length A of Rasheeda's garden

Width B of Rasheeda's garden

Verify each statement

A. Length A of the book’s garden is 18 ft.

The statement is false

Because, Length A of the book’s garden is 36 ft (see the explanation)

B. Length A of Rasheeda’s garden is 27 ft.

The statement is true (see the explanation)

C. Length B of the book’s garden is 12 ft

The statement is true (see the explanation)

D. Length B of Rasheeda’s garden is 6 ft.

The statement is false

Because, Length B of Rasheeda’s garden is 9 ft. (see the explanation)

E. Length A of the book’s garden is 9 ft longer than length A of Rasheeda’s garden.

The statement is true

Because the difference between 36 ft and 27 ft is equal to 9 ft

F. Length B of the book’s garden is 3 ft shorter than length B of Rasheeda’s garden.

The statement is false

Because, Length B of the book’s garden is 3 ft greater than length B of Rasheeda’s garden.

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Answer:

B. Length A of Rasheeda’s garden is 27 ft.

C. Length B of the book’s garden is 12 ft.

E. Length A of the book’s garden is 9 ft longer than length A of Rasheeda’s garden.

(second, third, and fifth choices)

Explanation: I did the quiz and got it right.

Hope this Helps!

Answer:

Initial Value Problem: [tex]\frac{d^2 x}{dt^2} = -32, x(0) = 200, \frac{dx}{dt}(0) = 40[/tex]

[tex]x(t) = -16t^2 + 40t +200[/tex]

Step-by-step explanation:

The ball is thrown vertically downward, this means that acceleration due to gravity, [tex]g = \frac{dx^{2} }{dt^{2} } = - 32 ft/s^2[/tex]

The height of the ball at time, t = 0 at the top of the building will be: [tex]x(0) = 200 ft[/tex]

The velocity at which the ball is thrown from the top of the building, [tex]\frac{dx}{dt} (0)= 40 ft/s[/tex]

Therefore the initial value problem is written below:

[tex]\frac{d^2 x}{dt^2} = -32, x(0) = 200, \frac{dx}{dt}(0) = 40[/tex]

Let us solve for x(t)

[tex]\frac{d^2 x}{dt^2} = -32\\d(\frac{dx}{dt} )= -32 dt\\[/tex]

Integrate both sides

[tex]\frac{dx}{dt} = -32t + k_1\\\frac{dx}{dt} (0) = 40\\40 = -32(0) + k_1\\k_1 = 0\\\frac{dx}{dt} = -32t + 40[/tex]

Integrate both sides

[tex]x(t) = -16t^2 + 40t + k_2\\x(0) = 200\\200 = -16(0) + 40(0) + k_2\\k_2 = 200\\x(t) = -16t^2 + 40t +200[/tex]

Answer:

  a = -2; b = 5

Step-by-step explanation:

Expanding the right side of the given equation, we have ...

  x^2 -4x +9 = x^2 +2ax +a^2 +b

Comparing coefficients, we see ...

  -4 = 2a . . . . . coefficient of x term

  9 = a^2 +b . . . constant term

The first of these tells us ...

  -2 = a . . . . divide by 2

The second of these tells us ...

  9 = (-2)^2 +b . . . substitute for a

  5 = b . . . . subtract 4

The values of a and b are (a, b) = (-2, 5).

Answer:

a=-2

b=5

Step-by-step explanation:

type this on mathswatch and you will get it right

Answer:

The large sample size 'n' =  199.6569≅ 200

Step-by-step explanation:

Step(i):-

Given Standard deviation of salary for all baseball players for 2015 is about $5,478,384.55

Standard deviation of  of salary for all baseball players for 2015

  (S.D ) σ =  $5,478,384.55

Given estimate of this average salary for all baseball players for 2015

                          =  $497,000

Given Margin of error of error is  =  $497,000

Level of significance ∝ = 80%

The critical value Z₀.₂₀ = 1.282  

Step(ii):-

Margin of error of error is  determined by

          [tex]M.E = \frac{Z_{0.20} S.D}{\sqrt{n} }[/tex]

         [tex]497,000 = \frac{1.282 X 5,478,384.55}{\sqrt{n} }[/tex]

Cross multiplication , we get

 [tex]\sqrt{n} = \frac{1.282 X 5,478,384.55}{497,000 }[/tex]

On calculation , we get

√n = 14.13

Squaring on both sides, we get

n = 199.6569

Conclusion:-

The large sample size 'n' =  199.6569≅ 200

The graph of the compound inequality can be seen at the end.

Here we have two inequalities that depend on p, these are:

4p + 1 > -15

6p + 3 < 45

First, we need to isolate p on both inequalities.

4p + 1 > -15

4p > -15 - 1

p > -16/4

p > - 4

6p + 3 < 45

6p < 45 - 3 = 42

p < 42/6 = 7

So we have the compound inequality:

p > -4

p < 7

or:

-4 < p < 7

Then this represents the set (-4, 7) where the values -4 and 7 are not included, so we should graph them with open circles.

The graph of the inequality is something like the one below.

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Answer:

he domain of the composition is all real x values except for x = -1

In other words: [tex]\left \{ x \, |\, x \neq -1} \right \}[/tex]

Step-by-step explanation:

Let's find the composition [tex]f(g(x))[/tex] in order to answer about its domain (where on the Real number set the function is defined), give the two functions:

[tex]f(x)= \frac{1}{x+4}[/tex]    and    [tex]g(x)=\frac{8}{x-1}[/tex]  :

[tex]f(g(x))=\frac{1}{g(x)+4} \\f(g(x))=\frac{1}{\frac{8}{x-1} +4} \\f(g(x))=\frac{1}{\frac{8+4(x-1)}{x-1} }\\f(g(x))=\frac{x-1}{8+4x-4} \\f(g(x))=\frac{x-1}{4+4x} \\[/tex]

This rational function is defined for every real number except when the denominator adopts the value zero. Such happens when:

[tex]4+4x=0\\4x=-4\\x=-1[/tex]

So the domain of the composition is all real x values except for x = -1

Answer:

Step-by-step explanation:

Using the one sample proportion test:

z = (p-P) / √{P (1-P)/n}

Where p = 709/2640= 0.27, P = 0.29, n= 2640

Thus z = (0.27-0.29) / √{0.29 (1-0.29) / 2640}

z = (-0.02) / √{0.29(0.71) /2640}

z = (-0.02) / √0.00007799

z = (0.02) / 0.0088

z = 2.27

To be able to draw a conclusion, lets find the p value at the 0.1 level of significant: p value is 0.2327. The result is significant as the p value is greater than 0.1 thus we will fail to reject the null and conclude that there is not enough statistical evidence to prove that the true percentage of all firms that announced one or more acquisitions during the year 2000 is less than 29%

Answer:

a) P(Y=10)=0.0013

b) P(Y≤5)=0.00000035

c) Mean = 17.5

S.D. = 2.29

Step-by-step explanation:

We can model this as a binomial random variable with n=25 and p=0.7.

The probability that k students from the sample are foreign students can be calculated as:

[tex]P(y=k) = \dbinom{n}{k} p^{k}(1-p)^{n-k}\\\\\\P(y=k) = \dbinom{25}{k} 0.7^{k} 0.3^{25-k}\\\\\\[/tex]

a) Then, for Y=10, the probability is:

[tex]P(y=10) = \dbinom{25}{10} p^{10}(1-p)^{15}=3268760*0.0282475249*0.0000000143\\\\\\P(y=10)=0.0013\\\\\\[/tex]

b) We have to calculate the probability P(Y≤5)

[tex]P(y\leq5)=P(Y=0)+P(Y=1)+...+P(Y=5)\\\\\\P(x=0) = \dbinom{25}{0} p^{0}(1-p)^{25}=1*1*0=0\\\\\\P(y=1) = \dbinom{25}{1} p^{1}(1-p)^{24}=25*0.7*0=0\\\\\\P(y=2) = \dbinom{25}{2} p^{2}(1-p)^{23}=300*0.49*0=0.0000000001\\\\\\P(y=3) = \dbinom{25}{3} p^{3}(1-p)^{22}=2300*0.343*0=0.0000000025\\\\\\P(y=4) = \dbinom{25}{4} p^{4}(1-p)^{21}=12650*0.2401*0=0.0000000318\\\\\\P(y=5) = \dbinom{25}{5} p^{5}(1-p)^{20}=53130*0.16807*0=0.0000003114\\\\\\\\[/tex]

[tex]P(y\leq5)=0+0+0.0000000001+0.0000000025+0.0000000318+0.00000031\\\\P(y\leq5)= 0.00000035[/tex]

c) The mean and standard deviation for this binomial distribution can be calculated as:

[tex]\mu=np=25\cdot 0.7=17.5\\\\\sigma=\sqrt{np(1-p)}=\sqrt{25\cdot0.7\cdot0.3}=\sqrt{5.25}=2.29[/tex]

Answer:

It will take to long to type it all but i think i figured it out. The children would have to take several trips. 2 kids would go, then one kid goes back to get the other kid, crosses again, then goes back, gets out, and two witches go (the parents of the kids on the other side), leaving one set of witch and child still needing to cross. One of the children on the other side brings the boat back and picks up the left over kid, now just one witch needing to cross, the two kids cross then the one kid with his mother on the other side takes the boat back again to get his mom.

And then when it gets to the other side the witch there eats it

Step-by-step explanation:

To safely cross the river, the witches and children can follow these steps:

Two witches (W1 and W2) cross the river, leaving one witch (W3) behind.

W1 returns alone to the starting side.

W1 and one child (C1) cross the river, leaving C1 on the other side.

W2 takes two children (C2 and C3) across the river, leaving them on the starting side.

W1 and W3 cross the river, leaving C2 and C3 behind.

W1 returns alone to the other side.

W1 and C1 cross the river, leaving W3 on the other side.

W2 and W3 cross the river.

W2 returns alone to the starting side.

W2 and C2 cross the river, leaving C3 behind.

W1 and C3 cross the river

To solve this puzzle, the witches and children can follow these steps to cross the river without any harm coming to the children:

Two witches cross the river: Two witches (W1 and W2) row the boat to the other side of the river, leaving one witch (W3) on the starting side.

One witch returns alone: W1 leaves the other witch (W2) on the other side and rows back alone to the starting side of the river.

One witch and one child cross the river: W1 takes one child (C1) with her and they both row across the river to the other side. W1 leaves C1 on the other side and rows back alone to the starting side.

Two children cross the river: W2, who has been waiting on the other side, takes two children (C2 and C3) and rows across the river to the starting side. W2 leaves C2 and C3 on the starting side and rows back alone to the other side.

Two witches cross the river: W1 returns to the other side and picks up the remaining witch (W3). They both row across the river to the starting side, leaving C2 and C3 on the other side.

One witch returns alone: W1 rows back alone to the other side.

One witch and one child cross the river: W1 takes C1 and rows across the river to the starting side, leaving W3 on the other side.

Two witches cross the river: W2 returns to the starting side and picks up W3. They both row across the river to the other side.

One witch returns alone: W2 rows back alone to the starting side.

One witch and one child cross the river: W2 takes C2 and rows across the river to the other side, leaving C3 on the starting side.

Two children cross the river: W1 returns to the starting side and picks up C3. They both row across the river to the other side.

Now, all three witches and all three children have safely crossed the river without any harm coming to the children.

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Answer:

The 1st graph

Step-by-step explanation:

The quickest and easiest way is to just graph y < x² + 4x + 5. When you do so you should be able to see your answer.

Answer:

[tex]=\frac{-209}{29}y[/tex]

I hope this help you :)

Answer:

The relative change from Ohio to Indiana is 49.04

Step-by-step explanation:

Answer:

40.5 ft

162 ft

16 in

7.2 in

13.9 ft

Step-by-step explanation:

1) V=√32d

d= ?

V=36 ⇒ 36²= 32d  ⇒ d= 1296/32=40.5 feet

2) S= 5.5√d

S= 70 mph, d=?

70²= 5.5²d ⇒ d= 4900/ 30.25≈ 162 feet

3) d= 0.25√h

d= 1 mile, h=?

1²= 0.25²h ⇒ h= 1/0.0625= 16 in

4) a= 4, b= 6, c=?

c²= a²+b² ⇒ c= √a²+b²= √4²+6² = √52≈ 7.2 in

5) c= 16 foot, b= 8 feet, a=?

c²= a²+b² ⇒ a= √c² - b²= √16²-8²= √256- 64= √192≈13.9 feet

Answer:

Step-by-step explanation:

Hello!

Since you didn't upload the data, I'll use my own data to solve the example. The steps will be the same, only the results will change. (see attachment) The hypothesis test will be made using a 5% significance level.

The objective of this exercise is to test if there is an association between two variables:

X₁: The subject is vaccinated, categorized "Yes" and "No"

X₂: The subject got the disease, categorized "Yes" and "No"

These two variables of interest are qualitative categorical and each one of them has two categories.

To test if the variables are associated, considering the type of variables they are, you have to apply a Chi Square test of Independence, where the statistic hypotheses are:

H₀: [tex]P_{ij}= P_{i.} * P_{.j}[/tex] ∀ i= 1, 2 and j= 1, 2

H₁: The variables, vaccination and disease status, are not independent.

α: 0.05

The statistic is

X²= [tex]{r} \atop {i=1} \right.[/tex]∑[tex]{c} \atop {j=1} \right.[/tex]∑[tex]\frac{(O_{ij}-E_{ij})^2}{E_{ij}}[/tex]≈[tex]X^2_{(r-1)(c-1)}[/tex]

i= values in rows

j= values in columns

r= total number of rows

c= total number of columns

This type of test is always one-tailed to the right, meaning that you will reject the null hypothesis to high values of Chi Square. There is only one critical value:

[tex]X^2_{(r-1)(c-1);1-\alpha }= X^2_{(2-1)(2-1);1-0.05}= X^2_{1*1;0.95}= 3.841[/tex]

The decision rule will be:

If [tex]X^2_{H_0}[/tex] ≥ 3.841, reject the null hypothesis.

If [tex]X^2_{H_0}[/tex] < 3.841, do not reject the null hypothesis.

Using the p-value approach, the decision rule is always the same:

If p-value ≤ α, reject the null hypothesis.

If p-value > α, do not reject the null hypothesis.

Before calculating [tex]X^2_{H_0}[/tex], you have to calculate the expected frequencies for all categories using the formula:

Ê[tex]_{ij}[/tex]= [tex]\frac{O_{i.}*O_{.j}}{n}[/tex]

Ê₁₁= [tex]\frac{O_{1.}*O_{.1}}{n}= \frac{82*100}{200} = 41[/tex]

Ê₁₂= [tex]\frac{O_{1.}*O_{.2}}{n}= \frac{82*100}{200} = 41[/tex]

Ê₂₁= [tex]\frac{O_{2.}*O_{.1}}{n}= \frac{118*100}{200} = 59[/tex]

Ê₂₂= [tex]\frac{O_{2.}*O_{.2}}{n}= \frac{118*100}{200} = 59[/tex]

[tex]X^2_{H_0}= \frac{(42-41)^2}{41} + \frac{(40-41)^2}{41} + \frac{(58-59)^2}{59} + \frac{(60-59)^2}{59}= 0.0827[/tex]

The p-value for this test is the probability of obtaining a value as extreme as [tex]X^2_{H_0}[/tex]= 0.0827:

P(X₁² ≥ 0.0827)= 1 - P(X₁² < 0.0827)= 1 - 0.2264= 0.7736

Ata 5% significance level, the decision is to not reject the null hypothesis. You can conclude that the vaccination and the disease status of the subjects are not related. The new vaccine does not affect the chances of the subjects getting the disease.

I hope this helps!

Answer:

  $106.67

Step-by-step explanation:

Using the example, for 3 hours work, Alex would be paid ...

  (2 hr)($30/hr) +(1 hr)($20/hr) = $60 +$20 = $80

At the same rate of pay, for 4 hours work, the pay would be ...

  pay/(4 hr) = $80/(3 hr)

  pay = $80(4/3) ≈ $106.67

Alex's pay for 4 hours of work is $106.67.

Answer:

a = 30

b = 6/7

Step-by-step explanation:

The number of yeast cells after t hours is modeled by the following equation:

[tex]f(t) = a(1 + be^{-0.7t})[/tex]

In which a is the initial number of cells.

At time t = 0 the population is 30 cells

This means that [tex]a = 30[/tex]

So

[tex]f(t) = 30(1 + be^{-0.7t})[/tex]

And increasing at a rate of 18 cells/hour.

This means that f'(0) = 18.

We use this to find b.

[tex]f(t) = 30(1 + be^{-0.7t})[/tex]

So

[tex]f(t) = 30 + 30be^{-0.7t}[/tex]

Then, it's derivative is:

[tex]f'(t) = -30*0.7be^{-0.7t}[/tex]

We have that:

f'(0) = 18

So

[tex]f'(0) = -30*0.7be^{-0.7*0} = -21b[/tex]

Then

[tex]-21b = 18[/tex]

[tex]21b = -18[/tex]

[tex]b = -\frac{18}{21}[/tex]

[tex]b = \frac{6}{7}[/tex]

Answer: the answer is c (the third answer ) ‼️

Step-by-step explanation:

The data in the given residual plot shows that model C has the best fit.

A straight line that minimizes the gap between it and some data is called a line of best fit. In a scatter plot containing various data points, a relationship is expressed using the line of best fit.

Given:

The residual plot of the values in the graph,

The points in the first graph are very far from the x-axis and y-axis so, it is not the best fit,

The points in the second graph are very far from the x-axis and y-axis, and they are symmetric to the y-axis but not the best fit.

Most of the points are close to the x-axis, so it is the best fit,

Thus, the third graph is the best line of fit.

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Answer:

It's D: No, there is not enough information given.

Step-by-step explanation:

just took the quiz

The correct answer option D which is No, there is not enough information given.

A parallelogram is a quadrilateral having four sides with two opposite sides parallel to each other. The sum of the angles suspended by all the four sides of the parallelogram is 360.

Using VX = WZ and m∠ZVX = m∠XWZ, we have a side and an angle. In order to prove the triangles congruent by SAS, we must have two sides and the angle between them. With the information we have now, we would have to have VZ = WX. However, we are not given that information.

We do have that ZX = ZX by the reflexive property, but this is not SAS, as the angle we have is not between the two sides.

Therefore correct answer option D which is No, there is not enough information given.

The complete figure is attached with the answer below.

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Answer:

b. Skewed-left

Step-by-step explanation:

The histogram will be expressed with the x-axis representing the salaries, in growing amount to the right. The y-axis will represent the relative or absolute frequency.

We know that most of the players earn the minimum league wage. Then, we will have a high frequency in the low salaries classes, at the left of the histogram. A few players earn very high salaries, so we will have a right tail with high values for the salaries a little frequency.

There is no symmetry in this histogram and it is not uniform, as there is no representative mean salary.

As most of the data will be close to the left side, we can conclude that the histogram will be skewed-left.

The Histogram of salary data, with most having less salary is RIGHT Skewed

Given : Data of players' salary is concentrated towards towards most players having less ( minimum ) salary.

Right Skewness denotes a distribution where Tail is on the right side. This implies data is highly concentrated toward left side, ie lower independent variable (x - here 'salary') values.

Left Skewness denotes a distribution where Tail is on the left side. This implies data is highly concentrated towards right side, ie higher independent variable (x - here 'salary') values.

In this case : As more players have lower values of independent variable ie salary, so the data will be concentrated at left - having tail at right.

Hence, it will be Skewed Right

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Answer:

[tex]\frac{1}{12}[/tex]

Step-by-step explanation:

The number with the smallest denominator is the larger number and [tex]\frac{1}{12}[/tex] is the number with the smallest denominator out of [tex]\frac{1}{12} , \frac{1}{32} , \frac{1}{48} , \frac{1}{18}[/tex].

Answer:

1/12

Step-by-step explanation:

Start with a number, for example 100.

Now divide 100 by several numbers which are greater and greater:

100/1 = 100

100/2 = 50

100/4 = 25

100/10 = 10

100/100 = 1

As you divide the same number, 100, by a greater number, the result becomes smaller.

As we divide 100 by 1, then by 2, then by 4, etc., we are always dividing 100 by a greater and greater number. The result is smaller and smaller, 100, 50, 25, etc. If you always divide the same number by other numbers, the larger the number you divide by, the smaller the result.

Numbers in order from greatest to smallest:

1/12, 1/18, 1/32, 1/48

Answer: The greatest number is 1/12

Answer:

[tex] z = \frac{500-520}{\frac{90}{\sqrt{100}}}= -2.22[/tex]

And we can find this probability using the normal standard distribution and we got:

[tex] P(z<-2.22) =0.0132[/tex]

Step-by-step explanation:

For this case we have the foolowing parameters given:

[tex] \mu = 520[/tex] represent the mean

[tex] \sigma =90[/tex] represent the standard deviation

[tex] n = 100[/tex] the sample size selected

And for this case since the sample size is large enough (n>30) we can apply the central limit theorem and the distribution for the sample mean would be given by:

[tex] \bar X \sim N(\mu , \frac{\sigma}{\sqrt{n}}) [/tex]

And we want to find this probability:

[tex] P(\bar X <500)[/tex]

We can use the z score formula given by:

[tex] z = \frac{500-520}{\frac{90}{\sqrt{100}}}= -2.22[/tex]

And we can find this probability using the normal standard distribution and we got:

[tex] P(z<-2.22) =0.0132[/tex]

Answer:

X=12

Step-by-step explanation:

Given that: X:24 = 6:X

Then:

[tex]\dfrac{X}{24}= \dfrac{6}{X}\\$Cross multiply\\X^2=24 \times 6\\X^2=144\\X=\pm\sqrt{144}\\X=\pm 12[/tex]

Since we require the positive value of X

X=12.

Answer:

We conclude that older people are more likely to be victimized.

Step-by-step explanation:

We are given that a survey shows that 10% of the population is victimized by property crime each year.

A random sample of 527 older citizens (65 years or more of age) shows a victimization rate of 12.35%

Let p = population proportion of people who are victimized.

So, Null Hypothesis, [tex]H_0[/tex] : [tex]p \leq[/tex] 10%      {means that older people are less likely to be victimized or remains same}

Alternate Hypothesis, [tex]H_A[/tex] : p > 10%      {means that older people are more likely to be victimized}

The test statistics that would be used here One-sample z-test for proportions;

                             T.S. =  [tex]\frac{\hat p-p}{\sqrt{\frac{p(1-p)}{n} } }[/tex]  ~  N(0,1)

where, [tex]\hat p[/tex] = sample proportion of older people who are victimized = 12.35%

            n = sample of older citizens = 527

So, the test statistics  =  [tex]\frac{0.1235-0.10}{\sqrt{\frac{0.10(1-0.10)}{527} } }[/tex]  

                                       =  1.798

The value of z-test statistics is 1.798.

Since in the question, we are not given with the level of significance so we assume it to be 5%. Now at 5% level of significance, the z table gives a critical value of 1.645 for right-tailed test.

Since our test statistics is more than the critical value of z as 1.798 > 1.645, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region.

Therefore, we conclude that older people are more likely to be victimized.