Read the following scenario, and then answer the question.

Juan assumes that the temperature of the hot tea cooling on his desk can be modeled with an exponential function like this one: T(t)=179(0.92)t. He bases his assumption on the following: The tea cools about 8% every minute. The tea's current temperature is around 179 degrees Fahrenheit.

Which explanation correctly addresses Juan's assumption?

He is incorrect. The tea will cool linearly since it cools at the same number of degrees every minute.
He is correct. The tea will cool exponentially since it cools at a percentage rate every minute.
He is incorrect. The tea will cool along the curve of a parabola since it cools at an increasing percentage rate every minute.

Answer:

g(x) is obtained by shift the function f(x) down 7 units by subtracting 7 units from f(x).

Step-by-step explanation:

We are given that

[tex]g(x)=f(x)-7[/tex]

We have to identify  the transformation that occurs to create the graph of g(x).

To identify  the transformation that occurs to create the graph of g(x)

We will subtract the 7 from f(x).

Let f(x) be any function

[tex]g(x)=f(x)-k[/tex]

It means g(x) obtained by  shift the function f(x) down  k units by subtracting k units from f(x).

Therefore, g(x) is obtained by shift the function f(x) down 7 units by subtracting 7 units from f(x).

Answer:

19.3 miles per gallon

Step-by-step explanation:

First, subtract 54,042.8-53,737.7. The answer is 305.1

Then, find the unit rate. 305.1/15.8

You get 19.31012658. The prompt says to round to the nearest tenth, so round, and you get 19.3.

That's your answer!

Answer:

where is the statement

Step-by-step explanation:

its incomplete po

Answer:

The standard error of your estimate of the average height in the city is 0.5 inches.

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.

You begin by collecting the heights of a random sample of 196 people from the city.

This means that [tex]n = 196[/tex]

The standard deviation of the heights in your sample is 7 inches.

This means that [tex]\sigma = 7[/tex]

The standard error of your estimate of the average height in the city is

[tex]s = \frac{\sigma}{\sqrt{n}} = \frac{7}{\sqrt{196}} = 0.5[/tex]

The standard error of your estimate of the average height in the city is 0.5 inches.

Answer:

-90.625

Step-by-step explanation:

Answer:

[tex]-90~5/8\\[/tex]

[tex]Decimal=-90.625[/tex]

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

~HOPE IT HELP....~

~HAVE A GREAT DAY!!~

Answer:

[tex] - \frac{ \sqrt{3} }{2} [/tex]

Step-by-step explanation:

Unit circle

Answer:

A) P(Type I error) = 0.045

B) P(Type II) error = 0.1

Step-by-step explanation:

We are told that the reliability of the test is 90% reliable.

Also, we are told that the probability that the test erroneously detects a lie even when the individual is actually telling the truth is 0.045.

Thus;

A) To calculate the probability of type I error:

From statistics, in this question we can say that the probability of a type I error is the probability that the test will erroneously detect a lie even though the individual is actually telling the truth. Thus;

Probability of (type I error) = P(rejecting true null) = 0.045

B) For probability of type II error, it is defined as the error where we accept a null hypothesis that is false. We can say that it produces a false negative and the formula is;

P(Type II) error = 1 - reliability

Reliability in the question is 0.90

Thus;

P(Type II) error = 1 - 0.9

P(Type II) error = 0.1

Answer:

0.9984

Step-by-step explanation:

we have shape parameter for the first component as 2.1

characteristics life = 100000

for this component

we have

exp(-2000/100000)².¹

= e^-0.0002705

= 0.9997

for the second component

shape parameter = 1.8

characteristic life = 80000

= exp(-2000/80000)¹.⁸

= e^-0.001307

= 0.9987

the reliability oif the system after 2000  events

= 0.9987 * 0.9997

= 0.9984

Answer:

y = 64/3

x = -119/3

Step-by-step explanation:

3х + 6у = 9 => 5*3x+5*6у = 9*5 => 15x+30у=45 (1)

5х + 7y = -49 => 3*5x + 3*7y = -49*3 => 15x+21y=-147 (2)

(1)-(2) => 9y = 192 => y = 64/3

x = -119/3

Answer: 5,987

Step-by-step explanation:

Answer:

angles A and C are congruent

Answer:

1) 5.64

2) 17.321

1) [tex]\frac{21}{28}[/tex]

2) [tex]\frac{16}{34}[/tex]

3) [tex]\frac{28}{35}[/tex]

4) [tex]\frac{32}{24}[/tex]

Step-by-step explanation:

SOH - CAH - TOA

Sin = [tex]\frac{O}{H}[/tex]   Cos = [tex]\frac{A}{H}[/tex]  Tan = [tex]\frac{O}{A}[/tex]      

O = opposite, A = adjacent, H = hypotenuse

First two,  use Pythagorean Theorem

If you want to calculate the angle on the last 4, use inverse of function and put in the ratio.

For example :

1) Tan Z = [tex]\frac{21}{28}[/tex]

   [tex]Tan^{-1}[/tex] ( [tex]\frac{21}{28}[/tex])

Z = 36.9°

Answer:

6

Step-by-step explanation:

Hello!

log₃(x) + log₃(x - 6) = log₃(7) <=>

<=> log₃(x * (x - 6)) = log₃(7) <=>

<=> log₃(x² - 6x) = log₃(7) <=>

<=> x² - 6x = 7 <=>

<=> x² - 6x - 7 = 0 <=>

<=> x² + x - 7x - 7 = 0 <=>

<=> x * (x + 1) - 7 * (x + 1) = 0 <=>

<=> (x + 1) * (x - 7) = 0 <=>

<=> x + 1 = 0 and x - 7 = 0 <=>

<=> x = -1 and x = 7, x ∈ { 6; +∞ } <=>

<=> x = 7

Good luck! :)

Answer:

n = 4 is 10

hope it helps and have a good day

Answer:

0.5217

Step-by-step explanation:

P(more than 5 customer arrive):

P(X>=6)=1-P(X<=5)=  1-∑x=0x e-λ*λx/x!= 0.5217

Answer:

hgfyjtdjtrxgfyfguktfkgh

Step-by-step explanation:

hgfytrdutrc

Step-by-step explanation:

Since an interior angle is 150 degrees, its adjacent exterior angle is 30 degrees.  Exterior angles of any polygon always add up to 360 degrees.  With the polygon being regular, we can just divide 360 by 30 to get 12 sides.

Step-by-step explanation:

x=-6 y= 0

x0 y= -1

y=mx+b

b= -1

0= -6m -1

-6m= 1

m= -1/6

parallel lines have the same slope

slope = -1/6

Answer:

A = (2, 2)

B = (3, -1)

C = (-1, 0)

Step-by-step explanation:

To translate a point, you have to translate each individual point. At the bottom it shows <-2,3>, therefore you have to translate x 2 units to the left (because it's negative meaning the number is going away from 0, and 3 units to the right because 3 is a positive number.)

First Point A:

x: 4 - 2 = 2; y: -1 + 3 = 2

Second Point B:

x: 5 - 2 = 3; y: -4 + 3 = -1

Lastly, Point C:

x: 1 - 2 = -1, y: -3 + 3 = 0

I hope this helps!

Answer:

Range: { 0,3,5,7,9}

Step-by-step explanation:

The range is the values that y takes

Range: { 0,3,5,7,9}

Now we have to find,

The range of the table of values,

→ Range = ?

Then the range will be the numbers that is in the Y column.

→ Range = ?

→ Range = (value that Y takes)

→ Range = 0,3,5,7,9

Therefore, the range is 0,3,5,7,9.

Answer:

False because $296=$296

Answer:

[tex]\frac{AB}{BC} = \frac{CE}{ED}[/tex]

Step-by-step explanation:

Given

The attached proof

Required

Complete the missing piece

In (a), we have:

[tex]\triangle ABC \to \triangle CED[/tex]

This implies that, the following sides are similar:

[tex]AB \to CE[/tex]

[tex]AC \to CD[/tex]

[tex]BC \to ED[/tex]

An equation that compares the triangle can be any of:

[tex]\frac{AB}{BC} = \frac{CE}{ED}[/tex]

[tex]\frac{AB}{AC} = \frac{CE}{CD}[/tex]

.....

From the options;

[tex]\frac{AB}{BC} = \frac{CE}{ED}[/tex] is true

Answer:

Number of pineapples= 10

number of pears = 19

number of kiwis = 10 -2 = 8

Step-by-step explanation:

Cost of a pear = $ 0.50

Cost of a pineapple = $ 1.5

cost of a kiwi = $ 0.3

Let the pineapples = p

Number of pears = 9 + p

Number of kiwis = p - 2

The cost is

0.15 p + 0.5 (9 + p) + 0.3 (p - 2) = 13.50

0.15 p + 4.5 + 0.5p + 0.3 p - 0.6 = 13.50

0.95 p = 9.6

p = 10

Answer: There is 3 pineapples, 12 pears and 10 kiwis

Hope this help :)

Answer: The graph moved left 3 units.

(x, y) = (x - 3, y)

Answer:

0.1003 = 10.03% probability that a simple random sample of size n= 10 results in a sample mean greater than 40 inches.

Gestation periods:

1) 0.3539 = 35.39% probability a randomly selected pregnancy lasts less than 260 days.

2) 0.0465 = 4.65% probability that a random sample of 20 pregnancies has a mean gestation period of 260 days or less.

3) 0.004 = 0.4% probability that a random sample of 50 pregnancies has a mean gestation period of 260 days or less.

4) 0.9844 = 98.44% probability a random sample of size 15 will have a mean gestation period within 10 days of the mean.

Step-by-step explanation:

To solve these questions, 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

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

The height, X, of all 3-year-old females is approximately normally distributed with mean 38.72 inches and standard deviation 3.17 inches.

This means that [tex]\mu = 38.72, \sigma = 3.17[/tex]

Sample of 10:

This means that [tex]n = 10, s = \frac{3.17}{\sqrt{10}}[/tex]

Compute the probability that a simple random sample of size n= 10 results in a sample mean greater than 40 inches.

This is 1 subtracted by the p-value of Z when X = 40. So

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

By the Central Limit Theorem

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

[tex]Z = \frac{40 - 38.72}{\frac{3.17}{\sqrt{10}}}[/tex]

[tex]Z = 1.28[/tex]

[tex]Z = 1.28[/tex] has a p-value of 0.8997

1 - 0.8997 = 0.1003

0.1003 = 10.03% probability that a simple random sample of size n= 10 results in a sample mean greater than 40 inches.

Gestation periods:

[tex]\mu = 266, \sigma = 16[/tex]

1. What is the probability a randomly selected pregnancy lasts less than 260 days?

This is the p-value of Z when X = 260. So

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

[tex]Z = \frac{260 -  266}{16}[/tex]

[tex]Z = -0.375[/tex]

[tex]Z = -0.375[/tex] has a p-value of 0.3539.

0.3539 = 35.39% probability a randomly selected pregnancy lasts less than 260 days.

2. What is the probability that a random sample of 20 pregnancies has a mean gestation period of 260 days or less?

Now [tex]n = 20[/tex], so:

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

[tex]Z = \frac{260 - 266}{\frac{16}{\sqrt{20}}}[/tex]

[tex]Z = -1.68[/tex]

[tex]Z = -1.68[/tex] has a p-value of 0.0465.

0.0465 = 4.65% probability that a random sample of 20 pregnancies has a mean gestation period of 260 days or less.

3. What is the probability that a random sample of 50 pregnancies has a mean gestation period of 260 days or less?

Now [tex]n = 50[/tex], so:

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

[tex]Z = \frac{260 - 266}{\frac{16}{\sqrt{50}}}[/tex]

[tex]Z = -2.65[/tex]

[tex]Z = -2.65[/tex] has a p-value of 0.0040.

0.004 = 0.4% probability that a random sample of 50 pregnancies has a mean gestation period of 260 days or less.

4. What is the probability a random sample of size 15 will have a mean gestation period within 10 days of the mean?

Sample of size 15 means that [tex]n = 15[/tex]. This probability is the p-value of Z when X = 276 subtracted by the p-value of Z when X = 256.

X = 276

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

[tex]Z = \frac{276 - 266}{\frac{16}{\sqrt{15}}}[/tex]

[tex]Z = 2.42[/tex]

[tex]Z = 2.42[/tex] has a p-value of 0.9922.

X = 256

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

[tex]Z = \frac{256 - 266}{\frac{16}{\sqrt{15}}}[/tex]

[tex]Z = -2.42[/tex]

[tex]Z = -2.42[/tex] has a p-value of 0.0078.

0.9922 - 0.0078 = 0.9844

0.9844 = 98.44% probability a random sample of size 15 will have a mean gestation period within 10 days of the mean.

Least to greatest: 20,564 22,755 2,3805

Answer:

115

Step-by-step explanation:

Hello!

3(x + 2) - 4x = 8 <=>

<=> 3x + 6 - 4x = 8 <=>

<=> -x + 6 = 8 <=>

<=> -x = 8 - 6 <=>

<=> -x = 2 <=>

<=> x = -2

Good luck! :)