The circumference of the base of a cylinder is 24π mm. A similar cylinder has a base with circumference of 60π mm. The lateral area of the larger cylinder is 210π mm2. What is the lateral area of the smaller cylinder? 17.1π mm2 33.6π mm2 60π mm2 84π mm2

Answer:

Dian has $250 originally.

Step-by-step explanation:

Let the total money Dian has originally = $S

Dian gave [tex]\frac{2}{5}[/tex] of her total money to Justin,

Money given to Justin = [tex]\frac{2}{5}(\text{S})[/tex]

Money left with Dian = S - [tex]\frac{2}{5}(\text{S})[/tex]

                                   = [tex]\frac{\text{5S-2S}}{5}[/tex]

                                   = [tex]\frac{3S}{5}[/tex]

Since Dian has $150 left then the equation will be,

[tex]\frac{3S}{5}=150[/tex]

S = [tex]\frac{150\times 5}{3}[/tex]

S = $250

Therefore, Dian has $250 originally.

Answer:

i think (d) one i think it will help you

Complete Question

If w'(t) is the rate of growth of a child in pounds per year, what does

[tex]\int\limits^{7}_{4} {w'(t)} \, dt[/tex]  represent?

a) The change in the child's weight (in pounds) between the ages of 4 and 7.

b) The change in the child's age (in years) between the ages of 4 and 7.

c) The child's weight at age 7.

d) The child's weight at age 4. The child's initial weight at birth.

Answer:

The correct option is  option a

Step-by-step explanation:

From the question we are told that

       [tex]w'(t)[/tex] represents the rate of growth of a child in   [tex]\frac{pounds}{year}[/tex]

So      [tex]{w'(t)} \, dt[/tex]  will be in  [tex]pounds[/tex]

Which then mean that this  [tex]\int\limits^{7}_{4} {w'(t)} \, dt[/tex]  the change in the weight of the child between the ages of  [tex]4 \to 7[/tex] years

Answer:

A

Step-by-step explanation:

[tex]g(x) = \frac{3}{{x}^{2} + 2x} \\ {x}^{2} + 2x - \frac{3}{g(x)} = 0 \\ x = \frac{1}{2} \Big( - 2 + \sqrt{12 + \frac{12}{g(x)} }\Big) \\ x = - 1 + \sqrt{1 \pm \frac{3}{g(x)} } [/tex]

Now replace $x$ by $g^{-1}(x)$ and $g(x)$ by $x$ and you have your answer.

Answer:

It is unlikely.

Step-by-step explanation:

Certain = 100%

Impossible = 0%

Likely = more than 50%

Unlikely = less than 50%

It is less than 50%, so it is unlikely.

Answer:

(A) it is likely

Step-by-step explanation:

i took the test on edge

Answer:

a. p`± z₀.₀₂₅[tex]\sqrt{ \frac{p`q`}{n}[/tex]  

b.0.6 ±  1.96 [tex]\sqrt \frac{0.6* 0.4}{1000}[/tex]  

c. { -1.96 ≤  p`± z₀.₀₂₅[tex]\sqrt{ \frac{p`q`}{n}[/tex]     ≥ 1.96} = 0.95  

Step-by-step explanation:

Here the total number of trials is n= 1000

The number of successes is p` = 600/1000 = 0.6. The q` is 1 - p`= 1- 0.6 = 0.4

The degree of confidence is 95 %  therefore z₀.₀₂₅ = 1.96 ( α/2 = 0.025)

a.  The formula used will be

p`± z₀.₀₂₅[tex]\sqrt{ \frac{p`q`}{n}[/tex]       ( z with the base alpha by 2 (α/2 = 0.025))

b. Putting the values

0.6 ±  1.96 [tex]\sqrt \frac{0.6* 0.4}{1000}[/tex]  

c. Confidence Interval in Interval Notation.

{ -1.96 ≤  p`± z₀.₀₂₅[tex]\sqrt{ \frac{p`q`}{n}[/tex]     ≥ 1.96} = 0.95  

{ -z( base alpha by 2) ≤  p`± z₀.₀₂₅[tex]\sqrt{ \frac{p`q`}{n}[/tex]     ≥ z( base alpha by 2)  } = 1- α

Answer:

A. 0.89.

Step-by-step explanation:

The value of correlation coefficient ranges from -1 to 1. Any value outside this range cannot possibly be correlation coefficient of a scatter plot representing relationship between two variables.

The scatter plot given shows a positive correlation between average daily temperatures and number of visitors, as the trend shows the two variables are moving in the same direction. As daily temperature increases, visitors also increases.

From the options given, the only plausible correlation that can represent this positive relationship is A. 0.89.

Answer:

In Table C, y vary inversely with x.

1×18 = 18

2×9 = 18

3×6 = 18

18 = 18 = 18

Step-by-step explanation:

We are given four tables and asked to find out in which table y vary inversely with x.

We know that an inverse relation has a form given by

y = k/x

xy = k

where k must be a constant

Table A:

x     |      y

1     |      3

2     |     9

3     |    27

1×3 = 3

2×9 = 18

3×27 = 81

3 ≠ 18 ≠ 81

Hence y does not vary inversely with x.

Table B:

x     |      y

1     |     -5

2     |     5

3     |    15

1×-5 = -5

2×5 = 10

3×15 = 45

-5 ≠ 10 ≠ 45

Hence y does not vary inversely with x.

Table C:

x     |      y

1     |      18

2     |     9

3     |     6

1×18 = 18

2×9 = 18

3×6 = 18

18 = 18 = 18

Hence y vary inversely with x.

Table D:

x     |      y

1     |      4

2     |     8

3     |    12

1×4 = 4

2×8 = 16

3×12 = 36

4 ≠ 16 ≠ 36

Hence y does not vary inversely with x.

Answer:C

Step-by-step explanation:

Pemdas

3+5(10)

5*10=50

3+50=53

Answer:

8lb of the cheaper Candy

17.5lb of the expensive candy

Step-by-step explanation:

Let the cheaper candy be x

let the costly candy be y

X+y = 25.5....equation one

2.2x +7.3y = 25.5(5.7)

2.2x +7.3y = 145.35.....equation two

X+y = 25.5

2.2x +7.3y = 145.35

Solving simultaneously

X= 25.5-y

Substituting value of X into equation two

2.2(25.5-y) + 7.3y = 145.35

56.1 -2.2y +7.3y = 145.35

5.1y = 145.35-56.1

5.1y = 89.25

Y= 89.25/5.1

Y= 17.5

X= 25.5-y

X= 25.5-17.5

X= 8

Answer:

I think that is the C

Step-by-step explanation:

Answer:

Option B is the correct answer.

Step-by-step explanation:

here, arc RT =162°

as in question given that the value of arc RT is 162° the value of angle RST is 1/2 of 162°.

so, its value must be 81°only.

hope it helps..

Answer:

33800

Step-by-step explanation:

100 x 338 = 33800

Answer:

33800

Step-by-step explanation:

338x10=3380 then 3380x10=33800

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

Good luck with your assignment...

Answer:

(a) The probability of getting someone who was not sent to prison is 0.55.

(b) If a study subject is randomly selected and it is then found that the subject entered a guilty plea, the probability that this person was not sent to prison is 0.63.

Step-by-step explanation:

We are given that in a study of pleas and prison sentences, it is found that 45% of the subjects studied were sent to prison. Among those sent to prison, 40% chose to plead guilty. Among those not sent to prison, 55% chose to plead guilty.

Let the probability that subjects studied were sent to prison = P(A) = 0.45

Let G = event that subject chose to plead guilty

So, the probability that the subjects chose to plead guilty given that they were sent to prison = P(G/A) = 0.40

and the probability that the subjects chose to plead guilty given that they were not sent to prison = P(G/A') = 0.55

(a) The probability of getting someone who was not sent to prison = 1 - Probability of getting someone who was sent to prison

      P(A') = 1 - P(A)

               = 1 - 0.45 = 0.55

(b) If a study subject is randomly selected and it is then found that the subject entered a guilty plea, the probability that this person was not sent to prison is given by = P(A'/G)

We will use Bayes' Theorem here to calculate the above probability;

    P(A'/G) =  [tex]\frac{P(A') \times P(G/A')}{P(A') \times P(G/A') +P(A) \times P(G/A)}[/tex]      

                 =  [tex]\frac{0.55 \times 0.55}{0.55\times 0.55 +0.45 \times 0.40}[/tex]

                 =  [tex]\frac{0.3025}{0.4825}[/tex]

                 =  0.63

Answer:

lmkjhvjgcfnhjkhbmgnc gfghh

Step-by-step explanation:

Answer:

Step-by-step explanation:

The average salary in this city is $45,600.

Using the formula

z score = x - u /(sd/√n)

Where x is 46,356, u is 45,600 sd is 15,930 and n is 53.

z = 46,356 - 45600 / (15930/√53)

z = 756/(15930/7.2801)

z = 756/(2188.1568)

z = 0.3455

To draw a conclusion, we have to determine the p value, at 0.05 level of significance for a two tailed test, the p value is 0.7297. The p value is higher than the significance level, thus we will fail to reject the null and can conclude that there is not enough statistical evidence to prove that the average is any different for single people.

Answer:

[tex] S.A = 246.6 in^2 [/tex]

Step-by-step explanation:

The figure given above is a square pyramid, having a square base and 4 triangular faces on the sides that are of the same dimensions.

Surface area of the square pyramid is given as: [tex] B.A + \frac{1}{2}*P*L [/tex]

Where,

B.A = Base Area of the pyramid = 9*9 = 81 in²

P = perimeter of the base = 4(9) = 36 in

L = slant height of pyramid = 9.2 in

Plug in the values into the given formula to find the surface area

[tex] S.A = 81 + \frac{1}{2}*36*9.2 [/tex]

[tex] = 81 + 18*9.2 [/tex]

[tex] = 81 + 165.6 [/tex]

[tex] S.A = 246.6 in^2 [/tex]

Answer: 680

Step-by-step explanation:

When order doesn't matter,then the number of combinations of choosing r things out of n = [tex]^nC_r=\dfrac{n!}{r!(n-r)!}[/tex]

Given: Total participants = 17

From these, a group of 3 participants is to be tested under a special condition.

Number of groups of 3 participants chosen = [tex]^{17}C_3=\dfrac{17!}{3!(17-3)!}\[/tex]

[tex]^{17}C_3=\dfrac{17!}{3!(17-3)!}\\\\=\dfrac{17\times16\times15\times14!}{3\times2\times14!}\\\\=680[/tex]

Hence, there are 680 groups of 3 participants can  be chosen,.

Answer:

(H1, T1)

Step-by-step explanation:

Since we know that the only number option is 1, we can cancel out the first 3 options. and obviously, there are only heads, and tails. So, using only the # 1 and heads and tails, we can conclude that the answer is (H1, T1).

Answer:

D. (H1, T1)

Step-by-step explanation:

Since all outcomes require card #1 is chosen, so any answer with 2 or 3 can be rejected, therefore the answer is

D. (H1, T1)

Answer: The length of the line B'C" is 1 unit.

Step-by-step explanation:

Given: Triangle ABC is dilated by a scale factor of 0.5 with the origin as the center of dilation , resulting in the image Triangle A'B'C'.

If A (2,2), B= (4,3) and C=(6,3).

Distance between (a,b) and (c,d): [tex]D=\sqrt{(d-b)^2+(c-b)^2}[/tex]

Then, BC [tex]=\sqrt{(3-3)^2+(6-4)^2}[/tex]

[tex]\\\\=\sqrt{0+2^2}\\\\=\sqrt{4}\\\\=2\text{ units}[/tex]

Length of image = scale factor x length in original figure

B'C' = 0.5 × BC

= 0.5 × 2

= 1 unit

Hence, the length of the line B'C" is 1 unit.

Answer: 0.9964

Step-by-step explanation:

Consider,

P (disk failure) = 0.06

q = 0.06

p = 1- q

p = 1- 0.06,

p = 0.94

Step 2

Whereas p represents the probability that a disk does not fail. (i.e. working entire year).

a)

Step 3

a)

n = 2,

let x be a random variable for number...

Continuation in the attached document

Answer:

2 inches

Step-by-step explanation:

x= smallest

3x=largest

2x=medium

x+3x+2x=12

6x=12

x=2

so smallest is 2

largest is 6 (3x)

medium is 4 (2x)

2+6+4=12

Answer:

x = 3 ± sqrt(11)

Step-by-step explanation:

x^2 - 6x + 9 = 11

Recognizing  that this is a perfect square trinomial

(x-3) ^2 =11

Taking the square root of each side

sqrt((x-3) ^2) = ± sqrt(11)

x-3 =± sqrt(11)

Add 3 to each side

x = 3 ± sqrt(11)

Answer:

[tex]\large\boxed{\sf \ \ x = 3+\sqrt{11} \ \ or \ \ x = 3-\sqrt{11} \ \ }[/tex]

Step-by-step explanation:

Hello,

   [tex]x^2-6x+9=11\\<=> x^2-2*3*x+3^2=11\\<=>(x-3)^2=11\\<=> x-3=\sqrt{11} \ or \ x-3=-\sqrt{11}\\<=> x = 3+\sqrt{11} \ or \ x = 3-\sqrt{11}[/tex]

Do not hesitate if you have any question

Hope this helps

You want to end up with [tex]A\sin(\omega t+\phi)[/tex]. Expand this using the angle sum identity for sine:

[tex]A\sin(\omega t+\phi)=A\sin(\omega t)\cos\phi+A\cos(\omega t)\sin\phi[/tex]

We want this to line up with [tex]2\sin(4\pi t)+5\cos(4\pi t)[/tex]. Right away, we know [tex]\omega=4\pi[/tex].

We also need to have

[tex]\begin{cases}A\cos\phi=2\\A\sin\phi=5\end{cases}[/tex]

Recall that [tex]\sin^2x+\cos^2x=1[/tex] for all [tex]x[/tex]; this means

[tex](A\cos\phi)^2+(A\sin\phi)^2=2^2+5^2\implies A^2=29\implies A=\sqrt{29}[/tex]

Then

[tex]\begin{cases}\cos\phi=\frac2{\sqrt{29}}\\\sin\phi=\frac5{\sqrt{29}}\end{cases}\implies\tan\phi=\dfrac{\sin\phi}{\cos\phi}=\dfrac52\implies\phi=\tan^{-1}\left(\dfrac52\right)[/tex]

So we end up with

[tex]2\sin(4\pi t)+5\cos(4\pi t)=\sqrt{29}\sin\left(4\pi t+\tan^{-1}\left(\dfrac52\right)\right)[/tex]

Answer:

Step-by-step explanation:

In the form ...

  y(t) = Asin(ωt +φ)

you have ...

The translation from ...

  y(t) = 2sin(4πt) +5cos(4πt)

is ...

  A = √(2² +5²) = √29 . . . . the amplitude

  ω = 4π . . . . the angular frequency in radians per second

  φ = arctan(5/2) ≈ 1.1903 . . . . radians phase shift

Then, ...

  y(t) = √29·sin(4πt +1.1903)

_____

Comment on the conversion

You will notice we used "2" and "5" to find the amplitude and phase shift. In the generic case, these are "coefficient of sin( )" and "coefficient of cos( )". When determining phase shift, pay attention to whether your calculator is giving you degrees or radians. (Set the mode to what you want.)

If you have a negative coefficient for sin( ), you will need to add 180° (π radians) to the phase shift value given by the arctan( ) function.

Answer:

z(c)  = - 1,64

We reject the null hypothesis

Step-by-step explanation:

We need to solve a proportion test ( one tail-test ) left test

Normal distribution

p₀ = 63 %

proportion size  p = 51 %

sample size  n = 114

At 5% level of significance   α = 0,05, and with this value we find in z- table z score of z(c) = 1,64  ( critical value )

Test of proportion:

H₀     Null Hypothesis                        p = p₀

Hₐ    Alternate Hypothesis                p < p₀

We now compute z(s) as:

z(s) =  ( p - p₀ ) / √ p₀q₀/n

z(s) =( 0,51 - 0,63) / √0,63*0,37/114

z(s) =  - 0,12 / 0,045

z(s) = - 2,66

We compare z(s) and z(c)

z(s) < z(c)      - 2,66 < -1,64

Therefore as z(s) < z(c)  z(s) is in the rejection zone we reject the null hypothesis

Answer:

The  probability is  [tex]P(X < 900 ) = 0.0918[/tex]

Step-by-step explanation:

From the question we are told that

   The sample mean is  [tex]\= x = 1100[/tex]

    The  standard deviation is  [tex]\sigma = 150[/tex]

     The random number value is  x =900

The probability that a trainee earn less than 900 a month is mathematically represented as

       [tex]P(X < x) = P(\frac{X -\= x}{\sigma} < \frac{x -\= x}{\sigma} )[/tex]

Generally the z-value for the normal distribution is mathematically represented as

       [tex]z = \frac{x -\mu }{\sigma }[/tex]

So From above we have

      [tex]P(X < 900 ) = P(Z < \frac{900 -1100}{150} )[/tex]

      [tex]P(X < 900 ) = P( Z <-1.33)[/tex]

Now from the z-table

    [tex]P(X < 900 ) = 0.0918[/tex]

Answer: Price-earnings ratio= 22.0

Step-by-step explanation:

Given: A company had a market price of $38.50 per share, earnings per share of $1.75, and dividends per share of $0.90

To find: price-earnings ratio

Required formula: [tex]\text{price-earnings ratio }=\dfrac{\text{ Market Price per Share}}{\text{Earnings Per Share}}[/tex]

Then, Price-earnings ratio = [tex]\dfrac{\$38.50}{\$1.75}[/tex]

⇒Price-earnings ratio = [tex]\dfrac{22}{1}[/tex]

Hence, the price-earnings ratio= 22.0

Answer:

The probability that no more than 70% would prefer to start their own business is 0.1423.

Step-by-step explanation:

We are given that a Gallup survey indicated that 72% of 18- to 29-year-olds, if given choice, would prefer to start their own business rather than work for someone else.

Let [tex]\hat p[/tex] = sample proportion of people who prefer to start their own business

The z-score probability distribution for the sample proportion is given by;

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

where, p = population proportion who would prefer to start their own business = 72%

            n = sample of 18-29 year-olds = 600

Now, the probability that no more than 70% would prefer to start their own business is given by = P( [tex]\hat p[/tex] [tex]\leq[/tex] 70%)

       P( [tex]\hat p[/tex] [tex]\leq[/tex] 70%) = P( [tex]\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] [tex]\leq[/tex] [tex]\frac{0.70-0.72}{\sqrt{\frac{0.70(1-0.70)}{600} } }[/tex] ) = P(Z [tex]\leq[/tex] -1.07) = 1 - P(Z < 1.07)

                                                                       = 1 - 0.8577 = 0.1423

The above probability is calculated by looking at the value of x = 1.07 in the z table which has an area of 0.8577.

Answer:

(0,-2)

Step-by-step explanation:

The y-intercept is simply when the function touches or crosses the y-axis.

We're told that the graph crosses the y-axis at -2. In other words, the y-intercept is at -2.

The ordered pair would be (0,-2)

Answer:

0.0668 or 6.68%

Step-by-step explanation:

Variance (V) = 10,000

Standard deviation (σ) = √V= 100

Mean score (μ) = 500

The z-score for any test score X is:

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

For X = 650:

[tex]z=\frac{650-500}{100}\\z=1.5[/tex]

A z-score of 1.5 is equivalent to the 93.32nd percentile of a normal distribution. Therefore, the probability that he or she will make a score of 650 or more is:

[tex]P(X\geq 650)=1-P(X\leq 650)\\P(X\geq 650)=1-0.9332\\P(X\geq 650)=0.0668=6.68\%[/tex]

The probability is 0.0668 or 6.68%

The probability that he or she will make a score of 650 or more is 0.0668.

Let X = Scores made on a certain aptitude test by nursing students

X follows normal distribution with mean = 500 and variance of 10,000.

So, standard deviation = [tex]\sqrt{10000}=100[/tex].

z score of 650 is = [tex]\frac{\left(650-500\right)}{100}=1.5[/tex].

The probability that he or she will make a score of 650 or more is:

[tex]P(X\geq 650)\\=P(z\geq 1.5)\\=1-P(z<1.5)\\=1-0.9332\\=0.0668[/tex]

Learn more: https://brainly.com/question/14109853

Add the top and bottom numbers together, divide that by 2 then multiply by the height.

15.3 + 19.5 = 34.8

34.8/2 = 17.4

17.4 x 11.1 = 193.14

Answer is 193.1 m^2