evaluate y=3^x for x=2

Answer:

Time= [tex]10[/tex] years

Step-by-step explanation:

Let total time[tex]=t[/tex]

Initial Amount[tex]=5000[/tex]

Final Amount[tex]=10000[/tex]

Total interest = Final Amount - Initial Amount

                      [tex]=10000-5000\\=5000[/tex]

Simple Interest [tex]=\frac{Initial Amount\times time\times rate}{100} \\\\5000=\frac{5000\times t \times 10}{100}\\\frac{t}{10} =1\\t=10 \ years[/tex]

Answer

given,

average rent of one bed room = $1229

sample size = n = 15

Sample mean rent = $1350

Assuming standard deviation equal to $250

the test hypothesis is

H o: µ=1229

H a: µ not equal to 1229

now we know,

[tex]t = \dfrac{\bar{x}-\mu}{\dfrac{\sigma}{\sqrt{n}}}[/tex]

[tex]t = \dfrac{\$ 1350-\$ 1229}{\dfrac{250}{\sqrt{15}}}[/tex]

     t = 1.875

from t- table

a=0.05, the critical value is  |t(0.025, d f= n-1 = 14)|=2.14

since t= 1.875 which is less than 2.14 we do not reject H o.

So we can not conclude that the monthly rent outside San Francisco differs from that in the city

At a 0.05 significance level, we cannot conclude that the monthly rent outside San Francisco differs from that in the city, based on the given data and hypothesis test.

To determine if the monthly rent outside San Francisco differs from that in the city based on the sample provided, we perform a hypothesis test. Our null hypothesis (H0) states that the mean rent outside San Francisco is equal to the average rent in San Francisco, i.e., $1229. The alternative hypothesis (Ha) posits that the mean rent outside San Francisco is different from $1229.

Calculate the test statistic: We use a Z-test since the population standard deviation is known. The formula for the Z-score is:
[tex]Z = \frac{\bar{X} - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
where X_bar = 1350, μ = 1229, σ = 250, and n = 15. Plugging in these values:
[tex]Z = \frac{1350 - 1229}{\frac{250}{\sqrt{15}}} = \frac{121}{64.55} \approx 1.87[/tex]

Determine the critical value: At α = 0.05, the critical values for a two-tailed test are approximately ±1.96.

Compare the test statistic to the critical value: Since 1.87 is less than 1.96, we fail to reject the null hypothesis.

Conclusively, at the 0.05 significance level, we do not have enough evidence to say that the monthly rent outside San Francisco differs from that in the city.

Complete question:

The average monthly rent for a one-bedroom home in San Francisco is $1229. A random sample of 15 one-bedroom homes about 15 miles outside of San Francisco had a mean rent of $1350. The population standard deviation is $250. At α = 0.05, can we conclude that the monthly rent outside San Francisco differs from that in the city?

Answer:

Step-by-step explanation:

We will first find the slope of the line from those 2 points, then write the equation of the line in slope-intercept form, solving for b, the y-intercept.

[tex]m=\frac{13-19}{6-(-3)}=-\frac{6}{9}=-\frac{2}{3}[/tex]

So the slope is -2/3.  We will choose a point now to use in the slope-intercept equation.  I'm picking the one with no negatives (cuz who likes negatives!?).

[tex]13=-\frac{2}{3}(6)+b[/tex] which simplifies down to

13 = -4 + b so

b = 17

The y-intercept of the line that goes through those 2 points is (0, 17)

Answer:

Therefore the distance across the patch of swamp water is 50 ft

Step-by-step explanation:

Given:

VW = 100 ft

WX = 60 ft

XZ = 30 ft

To Find:

ZY = l = ?

Solution:

In  Δ VWX and Δ YZX

∠W ≅ ∠ Z    …………..{measure of each angle is 90° given}

∠VXW ≅ ∠YXZ      ..............{vertically opposite angles  are equal}

Δ ABC ~ Δ DEC ….{Angle-Angle Similarity test}

If two triangles are similar then their sides are in proportion.

[tex]\frac{VW}{YZ} =\frac{WX}{ZX} =\frac{VX}{YX}\ \textrm{corresponding sides of similar triangles are in proportion}\\[/tex]  

On substituting the given values we get

[tex]\frac{100}{l} =\frac{60}{30}\\\\l=\frac{3000}{60}=50\ ft[/tex]

Therefore the distance across the patch of swamp water is 50 ft

Answer:

There was 10° F change in temperature in Fairbanks, Alaska.

Step-by-step explanation:

Given:

Temperature change from = -1° F.

Temperature change to = 9° F

We need to find the change in temperature.

Change in temperature can be calculated by subtracting Temperature change from with Temperature change to.

Framing in equation form we get;

Change in temperature = Temperature change to - Temperature change from

Substituting the values we get;

Change in temperature = [tex]9-(-1)= 9+1=10\° F[/tex]

Hence There was 10° F change in temperature in Fairbanks, Alaska.

Answer:

[tex]z=\frac{0.849 -0.8}{\sqrt{\frac{0.8(1-0.8)}{232}}}=1.869[/tex]  

[tex]p_v =2*P(Z>1.869)=0.0616[/tex]  

If we compare the p value obtained and the significance level given [tex]\alpha=0.05[/tex] we see that [tex]p_v>\alpha[/tex] so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can said that at 5% of significance the proportion of adults were no longer smoking after one month is not significantly different from 0.8 or 80% .  

Step-by-step explanation:

1) Data given and notation

n=232 represent the random sample taken

X represent the adults were no longer smoking after one month

[tex]\hat p=0.849[/tex] estimated proportion of adults were no longer smoking after one month

[tex]p_o=0.80[/tex] is the value that we want to test

[tex]\alpha=0.05[/tex] represent the significance level

Confidence=95% or 0.95

z would represent the statistic (variable of interest)

[tex]p_v[/tex] represent the p value (variable of interest)  

2) Concepts and formulas to use  

We need to conduct a hypothesis in order to test the claim that the true proportion is 0.8.:  

Null hypothesis:[tex]p=0.8[/tex]  

Alternative hypothesis:[tex]p \neq 0.8[/tex]  

When we conduct a proportion test we need to use the z statistic, and the is given by:  

[tex]z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}[/tex] (1)  

The One-Sample Proportion Test is used to assess whether a population proportion [tex]\hat p[/tex] is significantly different from a hypothesized value [tex]p_o[/tex].

3) Calculate the statistic  

Since we have all the info requires we can replace in formula (1) like this:  

[tex]z=\frac{0.849 -0.8}{\sqrt{\frac{0.8(1-0.8)}{232}}}=1.869[/tex]  

4) Statistical decision  

It's important to refresh the p value method or p value approach . "This method is about determining "likely" or "unlikely" by determining the probability assuming the null hypothesis were true of observing a more extreme test statistic in the direction of the alternative hypothesis than the one observed". Or in other words is just a method to have an statistical decision to fail to reject or reject the null hypothesis.  

The significance level provided [tex]\alpha=0.05[/tex]. The next step would be calculate the p value for this test.  

Since is a bilateral test the p value would be:  

[tex]p_v =2*P(Z>1.869)=0.0616[/tex]  

If we compare the p value obtained and the significance level given [tex]\alpha=0.05[/tex] we see that [tex]p_v>\alpha[/tex] so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can said that at 5% of significance the proportion of adults were no longer smoking after one month is not significantly different from 0.8 or 80% .  

The given relation is a function

Step-by-step explanation:

When a relation is given in the form of ordered pairs, for each ordered pair, the first element of ordered pair represents elements of domain and the second element represents elements of set of range.

In order for a relation to be a function, there should be no repetition in domain i.e. every element should be unique.

Given relation is:

{(2, 2), (3, 2), (4, 3), (5,4)}

As we can see that the domain of given relation is:

{2,3,4,5} i.e. every element is unique

So,

The given relation is a function

Keywords: Relations, functions

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The provided set of ordered pairs {(2, 2), (3, 2), (4, 3), (5,4)} represents both a relation and a function. This holds because each input maps to exactly one output, with no repeating input values.

In mathematics, a set of ordered pairs is a relation if input values (also known as the domain or x-values) may have any number of corresponding output values (the range or y-values). A set of ordered pairs is a function if each input value maps to exactly one output value.

Considering the set of ordered pairs: {(2, 2), (3, 2), (4, 3), (5,4)}, we can see that each input (x-value) matches with one corresponding output (y-value) and none of the input values is repeating. Hence, according to the definition, this set of ordered pairs represents both a relation and a function.

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Answer:

solve using long division.

75/4

what is the largest whole number smaller than 75 that 4 can go into?

72.

how many times can 4 go into 72?

18.

so then subtract 72 from 75 to get 3.

the new equation is

3/4

how many times can 3 go into 4?

0.75 times.

so add the 2 answers to get

18.75

4 can go into 75 18.75 times.

To determine how many times 4 can go into 75, you divide 75 by 4. The result is 18 with a remainder of 3. Thus, 4 can go into 75 a total of 18 full times.

To find out how many times 4 can go into 75, we need to perform a division. Specifically, we need to divide 75 by 4.

This means that 4 goes into 75 exactly 18 times with a remainder of 3. So, 4 fully fits into 75 for 18 full times.

Answer:

The correct answer is D. 114

Step-by-step explanation:

There are 252 students of twelfth grade at Vista View High School.

99 walked to school

11 went by bicycle

28 used the school bus

To find the amount of twelfth graders that rode in a car, we do this calculation:

Amount of twelfth graders that rode in a car = Total of twelfth graders - those who walked - those who went by bicycle - those who used the bus

Replacing with the real values, we have:

Amount of twelfth graders that rode in a car = 252 - 99 - 11 - 28 = 252 - 138 = 114

The correct answer is D. 114

Answer:

114

Step-by-step explanation:

Answer:A

Step-by-step explanation:

no need for this you only look at the answers

Answer:13hrs

Step-by-step explanation:

Initial Temperature = 21°c

final temperature = -18°c

rate of decrease = 3°c/hr

for every hour the temperature decreases by 3°c.

What time does it take to get to 0c  = . 21(°c) / 3(°c/hr)  = . 7hr

what time does it take to get to -18c  = 18(°c) / 3(°c/hr)   = . 6hr

Total Time taken  = . 7hr + 6hr = 13hr

Alternative solution

Initial Temperature = 21°c

final temperature = -18°c

rate of decrease = 3°c/hr

(21 + 18)°c/ 3(°c/hr) . = . 13hr

To cool a freezer from 21℃ to -18℃ at a rate of 3℃ per hour, it would take 13 hours for the freezer to reach -18℃.

The question asks how long it will take for a freezer to cool down from 21℃ to -18℃ if the temperature decreases at a rate of 3℃ per hour. To find the time it takes, you'll need to calculate the total temperature change required and then divide by the rate of temperature change.

First, calculate the total temperature difference:

21℃ (starting temperature) - (-18℃ target temperature) = 39℃ total temperature change.

Next, divide the total temperature change by the rate of temperature change:

39℃ total change / 3℃ per hour = 13 hours required

for the freezer to cool from 21℃ to -18℃.

Answer:

-5

Step-by-step explanation:

-7u+9=2

-7u=2-9

-7u=-7

7u=7

u=7/7

u=1

3(1)-8=3-8=-5

Line XD equals line XE and is also equal to line XF that proved by using AAS postulate of congruence ⇒ B

Step-by-step explanation:

Let us revise the cases of congruence

In Δ ABC

∵ Ray AL bisects ∠A ⇒ (divides it into two equal angles)

∴ m∠DAX = m∠EAX

∵ Ray BM bisects ∠B ⇒ (divides it into two equal angles)

∴ m∠EBX = m∠FBX

∵ XD ⊥ AC

∴ m∠XDA = 90°

∵ XE ⊥ AB

∴ m∠XEA = 90°

∵ XE ⊥ BC

∴ m∠XFB = 90°

Now lets prove that Δ ADX and ΔAEX are congruent

In Δs ADX and AEX

∵ m∠ADX = m∠AEX ⇒ (their measures are 90°)

∵ m∠DAX = m∠EAX ⇒ proved

∵ AX is a common side in both triangles

- By using the AAS postulate of congruence

∴ Δ ADX ≅ Δ AEX

∴ XD = XE

Let us do the same with Δ BEX and Δ BFX

In Δs BEX and BFX

∵ m∠BEX = m∠BFX ⇒ (their measures are 90°)

∵ m∠EBX = m∠FBX ⇒ proved

∵ BX is a common side in both triangles

- By using the AAS postulate of congruence

∴ Δ BEX ≅ Δ BFX

∴ XE = XF

∵ XE = XD

∵ XE = XF

- If one side is equal two other sides then the two other sides are

  equal, that means the three sides are equal

∴ XD = XF

∴ XD = XE = XF

Line XD equals line XE and is also equal to line XF that proved by using AAS postulate of congruence

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Answer:

10

Step-by-step explanation:

Given

[tex]x+y=8\\ \\4x-y=22[/tex]

Add these two equations:

[tex]x+y+4x-y=8+22\\ \\5x=30\\ \\x=6[/tex]

Substitute it into the first equation:

[tex]6+y=8\\ \\y=8-6\\ \\y=2[/tex]

Then

[tex]2x-y=2\cdot 6-2=12-2=10[/tex]

Answer:

-51/21

The first step in this equation would be to add -2/3 to 1/7

-2/3 and 1/7 need to have the same denominator, which 7 and 3 both go into 21

-2/3 converted to have the denominator, you would have to times top and bottom by 7, so you then get 14/21

Then you want to get the 1/7 with a denominator of 21 also, so you would times top and bottom by 3, so you get 3/21

Now you add 14/21 to 3/21 to get 17/21

-1/3h=17/21

You want to times by the reciprocal of -1/3 which would just be -3/1 so,

17/21*-3/1= -51/21 which is already simplified

So your answer would be -51/21

To check your work you would plug in -51/21 in for h

Step-by-step explanation:

To find the area of this rectangle, we first solve for the width using the given perimeter, yielding 4 inches. The length, three times this, is 12 inches. Multiplying these values together gives an area of 48 square inches.

We are dealing with a rectangle whose length is three times its width. If we call the width of the rectangle 'w', then its length is '3w'. The perimeter of a rectangle is 2 times the sum of its length and width.

So 2*(w+3w) = 32. This simplifies to 8w = 32. Solving for 'w', we find that the width of the rectangle is 4 inches. Then, the length would be three times the width, which is 12 inches.

Having determined these dimensions, we can find the area of the rectangle. The area of a rectangle is its length multiplied by its width. So in this case, it would be 4 inches (width) times 12 inches (length) to give us an area of 48 square inches.

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Answer:

Step-by-step explanation:

(8,-3),(8,4)

since both points have the same x value, this means you have a vertical line with an undefined slope...so ur equation would be x = 8....because no matter what y is, x will always be 8

Answer:

$25.24

Step-by-step explanation:

If Tim earns $45.19 each month multiply by 3 which gives you $135.57 take $211.29 subtract $135.57, you get $75.72 which is the total amount that Tom needs to give. Divide that by 3 and get $25.64 which is the amount Tom needs in 3 months.

$45.19 x 3 = $135.57

$211.29 - $135.57 = $75.72

$75.72/3 = $25.24

Answer:

Lack of information.

Step-by-step explanation:

We can't get the answer because this question haven't provide the information enough.

Have a nice day and hope it helps ;)

Answer:

28 - 7x =< 28x + 28

28 - 35x =< 28

-35x =< 0

x >= 0

the answer is the fourth one

x is greater than or equal to 0

This is the new equation obtained after performing the subtraction.

[tex]\[ 9x - 2y = 0 \][/tex]

When subtracting one equation from another, we subtract the corresponding elements of the equations. Here's the step-by-step process:

Given the two equations:

1. [tex]\( x - 3y = 6 \)[/tex] (First equation)

2. [tex]\( -8x - y = 6 \)[/tex] (Second equation)

We want to subtract the second equation from the first. We do this by subtracting each term of the second equation from the corresponding term in the first equation:

Step 1: Subtract the x-terms:

[tex]\[ x - (-8x) = x + 8x = 9x \][/tex]

Step 2: Subtract the y-terms:

[tex]\[ -3y - (-y) = -3y + y = -2y \][/tex]

Step 3: Subtract the constants:

[tex]\[ 6 - 6 = 0 \][/tex]

So after subtracting the second equation from the first, the result is:

[tex]\[ 9x - 2y = 0 \][/tex]

This is the new equation obtained after performing the subtraction.

Answer:

30

Step-by-step explanation:

2m+180=8m

180=8m-2m

180=6m

m=180/6

m=30

Because the two lines are not parallel, we conclude that the system will have a solution.

Remember that the solution of a system of equations is the point where the graphs of the functions intersect.

In this case we have two linear functions:

f = 2m + 180

f = 8m

Notice that the slopes are different, this means that the lines are not parallel, and because of that, we know that the lines will intersect at some point. That is enough to know that the system has a solution.

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Answer:

130 is close to 128, so 128 is a reasonable answer.

Step-by-step explanation:

Consider the provided information.

We need to Use the estimation to check weather 128 is a reasonable answer in the example above:

p=200-72

Round to the nearest ten:             p = 200 - 70

Subtract the rounded numbers:   200-70=130

130 is close to 128, so 128 is a reasonable answer.

874.18

Step-by-step explanation:if you multiply 800 by1.03 it will increase by 3% then repeat step two more times

Answer:

b. Right, isosceles

Step-by-step explanation:

right because it has a right angle at the top corner

isosceles because two sides of the triangle are equal to each others

Answer:

1,3,5

Step-by-step explanation:

The domain is the set of all first elements of ordered pairs (x-coordinates).

The range is the set of all second elements of ordered pairs (y-coordinates).

Answer:

Step-by-step explanation:

y = 7 - 2x

x =1; y = 7 - 2*1 = 7- 2 = 5

x = 2; y = 7 - 2*2 = 7 - 4 = 3

x = 3; y = 7 - 2*3 = 7- 6 = 1

Range = { 1,3,5}

Answer:

The product is [tex]x^3+5x^2[/tex]

Step-by-step explanation:

This is because we apply the distributive property of multiplication.

Thus from [tex]x(5x+x^2)[/tex]

we get this:

[tex]x*5x+x*x^2[/tex]

[tex]x*5x[/tex] is [tex]5x^2[/tex] and [tex]x*x^2[/tex] is [tex]x^3[/tex]

Answer: -30.75=-75

Step-by-step explanation: Multiply -6.15 by 5.

Hope this helps you out.

Answer:

1

Step-by-step explanation:

4/4=1

5-1-3=4-3=1

Answer:

Below.

Step-by-step explanation:

-1 + r ≥ 4

Add 1 to both sides:

r  ≥ 5.

The  graph will have a filled circle on the number 5 and a  heavy line to the right.