If f (x) is an exponential function where f(-2.5) = 9 and f(7) = 91, then find
the value of f(12), to the nearest hundredth.

Answer:

0.8665 = 86.65% probability that the sample proportion of Democrats will be greater than 52%.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

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

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]

Suppose 54% of the registered voters in a country are Democrats. Sample of 770.

This means that:

[tex]p = 0.54, s = \sqrt{\frac{0.54*0.46}{770}} = 0.01796[/tex]

What is the probability that the sample proportion of Democrats will be greater than 52%?

This is 1 subtracted by the p-value of Z when X = 0.52. So

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

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{0.52 - 0.54}{0.01796}[/tex]

[tex]Z = -1.11[/tex]

[tex]Z = -1.11[/tex] has a p-value of 0.1335

1 - 0.1335 = 0.8665

0.8665 = 86.65% probability that the sample proportion of Democrats will be greater than 52%.

Answer:

242.4

Step-by-step explanation:

y = 500×sin 29°

= 500× 0.4848

= 242.4 ft

Answer:

C) 1/16

Step-by-step explanation:

2*2*2*2=16

Therefore, 2^(-4)=1/16.

Answer:

C) [tex]\frac{1}{16}[/tex]

Step-by-step explanation:

2⁻⁴

2⁴ = 2 × 2 × 2 × 2 = 16

[tex]\frac{1}{16}[/tex]

5.7

Step-by-step explanation:

Lean- 6x

Hayden- x

x+ 6x=40 Equation

7x=40 Added the x and 6x

x= 5.7 Divided from each side

Answer:

10,361 dolls were sold in 2001.

Step-by-step explanation:

Number of dolls sold in x years after 1993:

The number of dolls sold in x years after 1993 is given by:

[tex]f(x) = -0.002x^4 - 0.025x^3 - 0.364x^2 - 7.243x + 86.993[/tex]

Estimate how many dolls were sold in 2001.

2001 is 2001 - 1993 = 8 years after 1993, so this is f(8).

[tex]f(8) = -0.002*8^4 + 0.025*8^3 - 0.364*8^2 - 7.243*8 + 86.993 = 10.361[/tex]

10,361 dolls were sold in 2001.

===============================================

Explanation:

When you list out the perfect squares, notice that 49 and 64 are on that list.

These are values we focus on because 49 < 52 < 64

We'll apply the square root to all three sides

[tex]49 < 52 < 64\\\\\sqrt{49} < \sqrt{52} < \sqrt{64}\\\\7 < \sqrt{52} < 8\\\\[/tex]

This shows that [tex]\sqrt{52}[/tex] is between 7 and 8

A calculator helps confirm this

[tex]\sqrt{52} \approx 7.2111\\\\[/tex]

Answer:

5.9 years.

Step-by-step explanation:

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]

In this question:

Mean of the population is [tex]\mu = 5.9[/tex]

If a sampling distribution is created using samples of the ages at which 69 children begin reading, what would be the mean of the sampling distribution of sample means?

By the Central Limit Theorem, the same population mean, of 5.9 years.

Answer:

3

9

21

Step-by-step explanation:

For the first one use the law of total probability

B=A∩B+A'∩B

12=9+A∩B

A∩B= 3

For this one you should use demorgans law and the union formula

(A'∩B')=(AUB)'

AUB= A+B-A∩B

6+12-3=15

15'= 24-15 = 9

For this one use demorgans law again

(A'UB')=(A∩B)'

(A∩B)'= 24-A∩B= 24-3= 21

Answer:

[tex]A(2,4)<-3,-2)A'(-1,2)>A''(-4,8)[/tex]

[tex]B)(5,2)-> B'(2,0)->B''(8,0)[/tex]

[tex]C(3,1)->C'(0,-1)->C''(0,-4)[/tex]

[tex](x,y)->(x-3,y-2)->([(x-3)*4],[(y-2)*4])[/tex]

Answer:

[22 x 21] / 2=231 or "c"

Step-by-step explanation:

When using GeoGebra, I'm getting the regression curve to be roughly

h(t) = 1.67*(1.4)^t

I'm not sure how your teacher got 1.64 instead of the 1.67, but it's fairly close. So it seems like choice B is the best answer for the first part.

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

Once we know the regression equation, we plug in t = 14 to find that,

h(t) = 1.64*(1.4)^t

h(14) = 1.64*(1.4)^(14)

h(14) = 182.236911939151

h(14) = 182.2

If 14 days have gone by, then we estimate the height is roughly 182.2 inches.

Compared to what the table says, which is 190 inches, we see that we have an underestimate. The error is about 190-182.2 = 7.8 which is under 10.

Answer: Choice C

The model under-predicts the actual height by less than 10 inches

9514 1404 393

Answer:

 5

Step-by-step explanation:

Put the numbers where the letters are and do the arithmetic.

  5(3) -2(5) = 15 -10 = 5

Answer:

5

Step-by-step explanation:

5m - 2n

Where, we have given ; m = 3 & n = 5

plug the value in the equation

Answer:

A) 1.7 inches of lumber is left.

Answer:

c = 49

b = 131

Step-by-step explanation:

c and 49 are vertical angles and vertical angles are equal

c = 49

b and 49 are supplementary angles and supplementary angles add to 180 degrees

b+49 = 180

b = 180-49

b =131

Answer:

Hello!

c = 49

b = 131

explanation: 131 + 131 + 49 + 49 = 360

hope that helps!

Answer:

C the one with the 12

so the 3 turn into 1/3 now 1/3 times 1/4 = 1/12

now turn the 1/12 into the outside of the sign

Step-by-step explanation:

Answer: Yes since its + (-5/12) each time

Step-by-step explanation:

Answer:

You don't have your options listed but if one of them is Point L is the midpoint of the segment, that would be your answer.

Step-by-step explanation:

Answer:

Since there are 2 sides, a front & back, and a top & bottom, you must find the surface area of each of those 3 surfaces and multiply by 2.

Step-by-step explanation:

The formula would be:

Top & Bottom - 5 × 4 (multiply by 2 for top AND bottom)

Front & Back - 5 × 7 (multiply by 2 for front AND back)

Sides - 4 × 7 (multiply by 2 for BOTH sides)

___________________________________________________

Once you find the 3 surface areas, add the areas all together for the total. (I did not show the answer because that is for you to do on your own.)

Ex. Top & Bottom + Front & Back + Sides

Answer:

166 is the answer.

Answer:

85º and 95º

Step-by-step explanation:

supplementary angle total 180

(8x – 3) + (7x + 18)  = 180

Combine like terms

15x + 15 = 180

15x = 165

x = 11

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

8x – 3

8(11) - 3

88 - 3

85º

7x + 18

7(11) + 18

77 + 18

95º

Answer:

Two terms

Step-by-step explanation:

First, we have to simplify reducing the number of terms, since there are like terms

x-5+16x+4-2x-3

Eventually, you'll get 15x-4,  thus there are two terms.

Please correct me if I'm incorrect, and I'll change the answer, but I hope I helped :)

Answer:

[tex] \cos(A + B) = \cos A \cos B - \sin A \sin \: B \\ but : \cos \: A = \sqrt{1 - ({ \frac{3}{5} })^{2} } = \frac{4}{5} \\ : \sin B = \sqrt{1 - {( \frac{ - 12}{13} })^{2} } = \frac{5}{13} \\ \therefore \cos(A + B) = ( \frac{4}{5} )( \frac{ - 21}{13} ) - ( \frac{3}{5} )( \frac{5}{13} ) \\ = \frac{ - 84}{65} - \frac{3}{13} \\ = \frac{ - 99}{65} \\ = - 1.52[/tex]

Answer:

100 in 10 theaters. 100÷10=10 44÷4=11

Answer:

I'm not sure if you have the question quite right.  Whenever you multiply x and y by something, it is a dilation.  So 3 of those are dilations.  If you add or subtract something from x, it is a translation.

Hope that helps.

Step-by-step explanation:

Answer:

I think it's a square or maybe a rhombus?

Step-by-step explanation:

Answer:

if 25c + 15d = 0, then d = -25/15c

Step-by-step explan

just yes, that

The percent change from the $2000 per month will be 4%.

The quantity of anything is stated as though it were a fraction of a hundred. A quarter of 100 can be used to express the ratio. Per 100 is what the term percent signifies. The symbol ‘%’ is used to symbolize it.

A woman making $2000 per month has her salary reduced by 20% because of sluggish sales. Then her salary will be

⇒ $2,000 × (1 - 0.20)

⇒ $1,600

One year later, after a dramatic improvement in sales, she is given a 30% raise over her reduced salary. Then her salary will be

⇒ $2,000 × (1 + 0.30)

⇒ $2,080

Then the percent change from the $2000 per month will be

P = [(2080 - 2000) / 2000] × 100

P = (80 / 2000) × 100

P = 0.04 × 100

P = 4%

The percent change from the $2000 per month will be 4%.

More about the percentage link is given below.

https://brainly.com/question/8011401

#SPJ2

Answer:

What is the value of x?

Whenever we have a problem to solve we assume the unknown quantity(or value to be identified) as x. This is just a convention followed in algebra by using a variable to denote the unknown quantity and then arrive at the solution.

What is the value of X?

What's the value of X?

X + X = X, what is the value of X?

What is the value of x ? How can I find it?

Do you know the value of x?

Value of X can be any numerical value or anything but depends solely on your question .But I find no question ok lets take an example .

If an equation is given ,

X+2=4

=> X=4–2

=>X=2

We X's value as 2 .

Now another ,

X + Y = 5 , 2X + 5Y = 10

Now taking first equation

X = 5-Y ………………………..(1)

Now taking second equation

X= 10–5Y/2…………………(2)

Now,

2(5-Y) = 10–5Y

=> 10–2Y = 10–5Y

=> 2Y = 5Y

Y has no value here because this equation not correctly represented .

Hence ,

We conclude the value of X varies with equation .

Thank You ,

Answer:

28.61258...

Step-by-step explanation:

Don't really know how to explain this over a computer, but it is correct.

Hope that this helps!