Which of the following proportions is false
12/15 = 20/25
25/45 = 50/90
20/50 = 40/100
18/48 = 30/50

Yes we should be concerned; the probability that we get a sample of 5 with a mean salary of $49,000 or greater is 0.0083.

How to determine if a sample accurately reflects a population using sample means and standard deviation ?

We can use a t-test to determine if the sample accurately reflects the population. The null hypothesis is that the sample mean is equal to the population mean, and the alternative hypothesis is that the sample mean is greater than the population mean.

t = (sample mean - population mean) / (standard deviation / square root of sample size)

Determine if a sample accurately reflects a population :

Plugging the given values in the above formula, we get:

\(t = (49000 - 43000) / (5600 / \sqrt{5}) = 2.60\)

Using a t-distribution table with 4 degrees of freedom (sample size - 1), we can find the probability of getting a t-value of 2.60 or greater. The probability is 0.0083, which is less than the usual significance level of 0.05.

Therefore, we can reject the null hypothesis and conclude that the sample mean of $49,000 is significantly different from the population mean of $43,000.

This suggests that the sample may not accurately reflect the population, and we should be concerned about the validity of our sample.

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Answer:

→ -9

Step-by-step explanation:

Solution,

\(\hookrightarrow x+69=60[Alternate\:angles\:are\:equal]\\\\\hookrightarrow x=60-69=-9\)

Interference is a property of ALL the given wave options, which are light waves, sound waves, and water waves.

Interference is the phenomenon of two or more waves combining to form a resultant wave of greater, lower, or the same amplitude.

When two waves meet at the same point at the same time, they either combine constructively (resulting in the formation of a wave of greater amplitude) or destructively (resulting in the formation of a wave of lower amplitude).

For instance, when two sound waves or light waves meet, they create a resultant wave whose amplitude is equal to the sum of the two original waves.

This is known as constructive interference.

On the other hand, when two waves meet and their amplitudes are in opposite directions, they produce a resultant wave whose amplitude is equal to the difference between the two waves.

This is known as destructive interference.

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Answer:

24/49

Step-by-step explanation:

The options to get 2 of different color is picking blue then red or red then blue.  

Starting with picking blue then red.

The chance to pull blue first is 3/7.  Then since the marble is replaced the chance to pull red next is 4/7.  

The chance to get those in that specific order is the product of the two fractions.   (3/7) * (4/7) = 12 / 49

The second option of getting red then blue will be the same as above but 4/7 then 3/7 with the same result of 12/49.  

To finish, add the two probabilities together 12/49 + 12/49 = 24/49.  

So, we can estimate with 95% confidence that the proportion of Broward College students who are employed is between 77.3% and 82.7%.

onstruct a 95% confidence interval estimate for the proportion of Broward College students who are employed. In this survey, we have a sample size (n) of 835 students, of which 668 are employed.

To calculate the sample proportion (p), we divide the number of employed students by the total sample size:

p = 668 / 835 ≈ 0.8

To construct a 95% confidence interval, we need the standard error (SE) of the proportion. We can calculate SE using the following formula:

SE = sqrt(p(1 - p) / n) ≈ sqrt(0.8(1 - 0.8) / 835) ≈ 0.014

Next, we need the critical value (z) for a 95% confidence interval, which is approximately 1.96. Now, we can calculate the margin of error (ME):

ME = z * SE ≈ 1.96 * 0.014 ≈ 0.027

Finally, we can construct the 95% confidence interval by adding and subtracting the margin of error from the sample proportion:

Lower bound: p - ME ≈ 0.8 - 0.027 ≈ 0.773
Upper bound: p + ME ≈ 0.8 + 0.027 ≈ 0.827

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dy/dx = (1/(e^(x^2)+1)) * (e^(x^2) * 2x) + e*cos(x)

This is the derivative of the given function y with respect to x.

We want to find the derivative dy/dx of the function y = ln(e^(x^2)+1) + e*sin(x). To do this, we will apply the rules of differentiation.

First, we'll differentiate the function term-by-term. For the natural logarithm function, the derivative is (1/u) * du/dx, where u is the function inside the natural logarithm. In our case, u = e^(x^2) + 1.

The derivative of e^(x^2) is found by applying the chain rule, which gives us (e^(x^2) * 2x). The derivative of 1 is 0. Therefore, the derivative of u is (e^(x^2) * 2x). Now we can find the derivative of ln(u):

d[ln(u)]/dx = (1/(e^(x^2)+1)) * (e^(x^2) * 2x)

Next, we will differentiate e*sin(x). The derivative of e*sin(x) is found by applying the product rule. The derivative of e is e, and the derivative of sin(x) is cos(x). Applying the product rule, we have:

d[e*sin(x)]/dx = e*cos(x) + e*sin(x) * 0 = e*cos(x)

Now, adding the derivatives of both terms, we get:

dy/dx = (1/(e^(x^2)+1)) * (e^(x^2) * 2x) + e*cos(x)

This is the derivative of the given function y with respect to x.

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Answer:

7. -4/5

8. 1

9. 0

10. 3/4

11. undefined/nonlinear

12. -9/4

13. parallel

The general solution of the given differential equation is:

\(y = (3/8)T^8 + C\)

The given equation is\(T^(-7)y' = 3.\) To find the general solution, we first need to isolate y' by multiplying both sides by T^7:

\(y' = 3T^7\)

Now we can integrate both sides with respect to the independent variable (let's call it x) to obtain:

\(y = ∫3T^7 dx + C\)

where C is the constant of integration. We can evaluate the integral as:

\(y = (3/8)T^8 + C\)

Therefore, the general solution of the given differential equation is:

\(y = (3/8)T^8 + C\)

where C is an arbitrary constant. Note that the solution is expressed explicitly as a function of the independent variable T. Also, the initial condition y(0) = 0 is satisfied by taking C = 0.

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A. To save for her payout annuity with an ordinary annuity set up thirty years before her retirement, Holly Krech must make a monthly payment of $175.97.

B. If she sets up the ordinary annuity twenty years before her retirement, Holly Krech must make a monthly payment of $432.00.

To calculate the monthly payment for an ordinary annuity set up thirty years before retirement, we can use the formula for the present value of an ordinary annuity. Given the deposit amount of $218,437.048 and the total amount received from the annuity of $432,000, and solving for the monthly payment, we find that Holly must make a monthly payment of $175.97.

For an ordinary annuity set up twenty years before retirement, we use the same formula for present value. With the deposit amount and total amount received unchanged, we solve for the monthly payment, which comes out to be $432.00.

It's important to note that the monthly payment increases when the annuity is set up closer to the retirement date. This is due to the shorter time period available for saving, resulting in a higher required contribution to reach the desired payout amount.

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The claim we need to check is that 16 is the 50% of 36.

Recall that if we add 50% and 50%, we should end up with 100%. In our case, we have that our 100% is 36. So, if it was true that 16 is the 50% of 36, then it should happen that if we add 16 with itself, we should get 36.

Note that

Since 16+16 is not 36, it is not true that 16 is the 50% of 36.

The volume of the given rectangular prism is 315\(cm^3\)

We have the information from the question:

A right rectangular prism has a height of 17.5 cm.

The area of the base of the prism is 18 square cm.

To find the volume, in cubic cm of the right rectangular prism.

We know that the volume of a right rectangular prism is given by-

Volume = A × h

Volume = (18)(17.5)

Volume = 315\(cm^3\)

So the volume of the given rectangular prism is 315\(cm^3\)

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Answer:

f=-27, hope this helped my love have a good rest of your day ^^

Step-by-step explanation:

subtract 24 from both sides

the you get f=-27

Answer:

What is the question?!

Step-by-step explanation:

Answer:

x+4

.....................

Answer

\( \boxed{x + 4}\)

Option C is the correct option

Step by step explanation

Let's find the expression which represents the length of the box:

\( \mathsf{length \times width \times height \: of \: prism \: = \: volume \: of \: prism}\)

\( \mathsf{lengh \times \: (x - 1) \times (x + 8) = {x}^{3} + 11 {x}^{2} + 20x - 32}\)

\( \mathsf{length = \frac{ {x}^{3} + 11 {x}^{2} + 20x - 32 }{(x - 1)(x + 8)} }\)

Write 11x² as a sum

\( \mathsf{ = \frac{ {x}^{3} - {x}^{2} + 12 {x}^{2} + 20x - 32 }{(x - 1)(x + 8)} }\)

Write 20x as a sum

\( \mathsf{ = \frac{ {x}^{3} - {x}^{2} + 12 {x}^{2} - 12x + 32x - 32 }{(x - 1)(x + 8)}}\)

Factor out x² from the expression

\( \mathsf{ = \frac{ {x}^{2}(x - 1) + 12 {x}^{2} - 12x + 32x - 32 }{(x - 1)(x + 8)} }\)

Factor out 12 from the expression

\( \mathsf{ = \frac{ {x}^{2}(x - 1) + 12x(x - 1) + 32x - 32 }{(x - 1)(x + 8)} }\)

Factor out 32 from the expression

\( \mathsf{ = \frac{ {x}^{2}(x - 1) + 12x(x - 1) + 32(x - 1) }{(x - 1)(x + 8)} }\)

Factor out x+1 from the expression

\( \mathsf{ = \frac{(x - 1)( {x}^{2} + 12x + 32) }{(x - 1)(x + 8)} } \)

Factor out 12x as a sum

\( \mathsf{ = \frac{(x - 1)( {x}^{2} + 8x + 4x + 32) }{(x - 1)(x + 8)} }\)

Reduce the fraction with x-1

\( \mathsf{ = \frac{ {x}^{2} + 8x + 4x + 32 }{(x + 8)} }\)

Factor out x from the expression

\( \mathsf{ = \frac{x(x + 8) + 4x + 32}{(x + 8)} }\)

Factor out 4 from the expression

\( \mathsf{ = \frac{x(x + 8) + 4(x + 8)}{x + 8} }\)

Factor out x+8 from the expression

\( \mathsf{ = \frac{(x + 8)(x + 4)}{x + 8} } \)

Reduce the fraction with x+8

\( \mathsf{ = x + 4}\)

hence, x+4 is the expression that represents the length of a box.

Hope I helped!

Best regards!

When analyzing a consumer's utility function: preferences, marginal utility, optimal consumption, and substitution and income effects.

From a consumer's utility function alone, you may determine the following:

1. Preferences: A consumer's utility function represents their preferences for different goods and services. By analyzing the function, you can determine which items the consumer prefers and how much they value them.

2. Marginal utility: The marginal utility is the additional satisfaction a consumer receives from consuming one more unit of a good or service. It can be derived from the utility function by taking its first derivative with respect to the quantity of the good or service.

3. Optimal consumption: By analyzing a consumer's utility function and taking into account their budget constraint, you can determine the optimal consumption bundle that maximizes their utility.

4. Substitution and income effects: The utility function can also help you analyze how changes in prices or income will affect a consumer's consumption choices, through the substitution and income effects.

Remember to keep these terms in mind when analyzing a consumer's utility function: preferences, marginal utility, optimal consumption, and substitution and income effects.

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Answer:

draw a graph and plot the points to make it linear

Step-by-step explanation:

\(\lim \limits_{x \to \infty} \sqrt{x^2 +x(2a+2b) +4ab-x}\\\\\\=\lim \limits_{x \to \infty} \sqrt{x^2 \left( 1 + \dfrac{2a+2b}{x}+ \dfrac{4ab}{x^2} - \dfrac 1{x} \right)}\\\\\\=\sqrt{\lim \limits_{x \to \infty} x^2 \cdot \lim \limits_{x \to \infty} \left( 1 + \dfrac{2a+2b}{x}+ \dfrac{4ab}{x^2} - \dfrac 1{x} \right)}}\\\\\\=\sqrt{ \infty \cdot (1+0+0-0)}\\\\=\sqrt{ \infty \cdot 1}\\\\=\infty\)

Answer: $25

Step-by-step explanation: 25 times 3(because there are three people) =75 - 45(the amount they spent)=30 the amount they are left with all together.

it took me awhile to answer so sorry for the wait but i hope this helps.

Answer:

\(\sum {{n} \atop {1}} \right 6n+2n^2\)

Step-by-step explanation:

Given the series 8 + 12 + 16 + 20+ ...

Sum of nth term Sn = n/2[2a+(n-1)d]

a is the first term = 8

d is the common difference = 12 - 8 = 16 - 12 = 4

Substitute

Sn = n/2[2(8)+(n-1)(4)]

Sn = n/2[16+4n-4]

Sn = n/2[12+4n]

Sn  2n/2[6+2n]

Sn = n(6+2n)

Sn = 6n + 2n²

Hence the sigma representation is expressed as;

\(\sum {{n} \atop {1}} \right 6n+2n^2\)

The probabilities are calculated assuming independence of each call and that the success probability remains constant throughout the calls.

a. The probability that, among five voters the student calls, exactly one supports candidate Smith can be calculated using the binomial probability formula. With a success probability of 64% (0.64) and exactly one success (k = 1) out of five trials (n = 5), the probability can be calculated as follows:

\[

P(X = 1) = \binom{5}{1} \times (0.64)^1 \times (1 - 0.64)^4

\]

The calculation results in approximately 0.369, or 36.9%.

b. The probability that, among five voters the student calls, at least one supports candidate Smith can be calculated as the complement of the probability that none of the voters support Smith. Using the binomial probability formula, with a success probability of 64% (0.64) and no success (k = 0) out of five trials (n = 5), the probability can be calculated as follows:

\[

P(X \geq 1) = 1 - P(X = 0) = 1 - \binom{5}{0} \times (0.64)^0 \times (1 - 0.64)^5

\]

The calculation results in approximately 0.997, or 99.7%.

c. The probability that the first voter supporting candidate Smith is reached on the fifth call can be calculated as the probability of not reaching a Smith supporter in the first four calls (0.36) multiplied by the probability of reaching a Smith supporter on the fifth call (0.64):

\[

P(\text{{First Smith Supporter on Fifth Call}}) = (1 - 0.64)^4 \times 0.64

\]

The calculation results in approximately 0.014, or 1.4%.

d. The probability that the third voter supporting candidate Smith is reached on the fifth call can be calculated as the probability of reaching two Smith supporters in the first four calls (0.64 for the first call, 0.36 for the second call, and 0.36 for the third call) multiplied by the probability of reaching a Smith supporter on the fifth call (0.64):

\[

P(\text{{Third Smith Supporter on Fifth Call}}) = (0.64)^2 \times (1 - 0.64) \times 0.64

\]

The calculation results in approximately 0.147, or 14.7%.

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The probabilities are calculated assuming independence of each call and that the success probability remains constant throughout the calls. The calculation results in approximately 0.369, or 36.9%.

a. The probability that, among five voters the student calls, exactly one supports candidate Smith can be calculated using the binomial probability formula. With a success probability of 64% (0.64) and exactly one success (k = 1) out of five trials (n = 5), the probability can be calculated as follows:

[P(X = 1) = \binom{5}{1} \times (0.64)^1 \times (1 - 0.64)^4\]

The calculation results in approximately 0.369, or 36.9%.

b. The probability that, among five voters the student calls, at least one supports candidate Smith can be calculated as the complement of the probability that none of the voters support Smith. Using the binomial probability formula, with a success probability of 64% (0.64) and no success (k = 0) out of five trials (n = 5), the probability can be calculated as follows:

[P(X \geq 1) = 1 - P(X = 0) = 1 - \binom{5}{0} \times (0.64)^0 \times (1 - 0.64)^5\]

The calculation results in approximately 0.997, or 99.7%.

c. The probability that the first voter supporting candidate Smith is reached on the fifth call can be calculated as the probability of not reaching a Smith supporter in the first four calls (0.36) multiplied by the probability of reaching a Smith supporter on the fifth call (0.64):

\[

P(\text{{First Smith Supporter on Fifth Call}}) = (1 - 0.64)^4 \times 0.64

\]

The calculation results in approximately 0.014, or 1.4%.

d. The probability that the third voter supporting candidate Smith is reached on the fifth call can be calculated as the probability of reaching two Smith supporters in the first four calls (0.64 for the first call, 0.36 for the second call, and 0.36 for the third call) multiplied by the probability of reaching a Smith supporter on the fifth call (0.64):

\[

P(\text{{Third Smith Supporter on Fifth Call}}) = (0.64)^2 \times (1 - 0.64) \times 0.64

\]

The calculation results in approximately 0.147, or 14.7%.

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Answer:

30 Skittles

Step-by-step explanation:

12 = .4 x S

12/.4 = S

30

taste the rainbow

Answer:

a) 5p (or 5q)

b) 5p ( or 5q)

c) 10p (or 10q)

Step-by-step explanation:

We will use the following information for solving and using the given figure

Preliminary computation

We have \(\overrightarrow{AB} = \overrightarrow{BC}\)

Therefore 4p + q = 5p

5p = 4p + q

5p-4p = q

p = q

\(\overrightarrow{AB} = 4p + q = 4p + p = 5p = 5q\\\)

So each side is 5p in length which is also equal to 5q since p = q

Part a

\(\overrightarrow{AO} = \overrightarrow{OA} = \overrightarrow{AB} = 5p\)  (same as 5q)

Part b

\(\overrightarrow{OB} = \overrightarrow{OA} = 5p\)   (same as 5q)

Part c
\(\overrightarrow{EB} = 2 \cdot \overrightarrow{OB} = 2 \cdot 5p = 10p\)   (also 10q)

The truth values of the statements are:

The complete question is added as an attachment, where we have the following parameters:

Height, h = 2.5 feet

Diameter, d = 4

The base area is then calculated as

Area = п(r²)

So, we have

Area = п(2²)

The volume is then calculated as

Volume = Base area * Height

So, we have

Volume = п(2²) * 2.5

Evaluate

Volume = 31.4

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The probability that is lower than 63 grams is 95%

Given that,

X~ Normal ( 67 grams, 5 grams ) , n = 5

=> E( x ) = 67 grams , Var( X ) =5 grams

* ~ Normal ( 67 grams , 1 grams )

We know that, if X~ Normal ( E ( x) = a . Val (x ) = b)

Then X~ Normal ( E(x) = a, √Var (x)/n = √b/n)

E(x) = a, Var (x)/ = √b/n

Probability that sample mean X , is blw 65 and 70 grams

P ( 65< X<70 ) =

= P(Z<1. 76 ) - P(Z≤-2.65)

Using standard normal table values represent area

left of the Z- score, we get

= 0.96080 - 0.00402

= 0 .95678

=0.9568

So,The probability that is lower than 63 grams is 95%

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The area of the regular polygons with 12 sides(dodecagon) and 5 sides (pentagon) are 389.06 in² and 19.87 in² respectively.

Area of regular polygon = 1/2 × apothem × perimeter

perimeter = (s)side length of octagon × (n)number of side.

apothem = s/[2tan(180/n)].

11 = s/[2tan(180/12)]

s = 11 × 2tan15

s = 5.8949

perimeter = 5.8949 × 12 = 70.7388

Area of dodecagon = 1/2 × 11 × 70.7388

Area of dodecagon = 389.0634 in²

Area of pentagon = 1/2 × 5.23 × 7.6

Area of pentagon = 19.874 in²

Therefore, the area of the regular polygons with 12 sides(dodecagon) and 5 sides (pentagon) are 389.06 in² and 19.87 in² respectively.

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Given:

The number of children =12

Probability that children under 10 years old lived with their father only is 4%.

It follows the binomial distribution,

Answer:

10 points

Step-by-step explanation:

Points scored in each of the first 3 quarter = x

Total points scored in the first 3 quarter = x + x + x

= 3x

Points scored in the fourth quarter = 14

Total points scored = 44 point

Total points scored = Total points scored in the first 3 quarter + Points scored in the fourth quarter

44 = 3x + 14

Subtract 14 from both sides

44 = 3x + 14

44 - 14 = 3x + 14 - 14

30 = 3x

Divide both sides by 3

x = 30/3

= 10

x = 10 points

Points scored in each of the first 3 quarter = x = 10 points

The school football team scored 10 points points in the first quarter

Answer:

Option B is the correct option.

Step-by-step explanation:

We know that the vertex form of a quadratic's equation is generally expressed as

y = a(x - h)² + k

where (h, k) is called the vertex of the quadratic function

In our case, given the function

\(f\left(x\right)=-\frac{1}{2}\left(x+3\right)^2+\frac{25}{2}\)

now comparing the equation with y = a(x - h)² + k

Here:

h = -3

k = 25/2

Therefore, the vertex of the function \(f\left(x\right)=-\frac{1}{2}\left(x+3\right)^2+\frac{25}{2}\) is:

(h, k) = (-3, 25/2)

Thus,

The  \(f\left(x\right)=-\frac{1}{2}\left(x+3\right)^2+\frac{25}{2}\)  form most quickly reveals the vertex.

Hence, option B is the correct option.