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NikAS [45]
2 years ago
11

Find the missing value for the exponential function represented by the table below x -2 -1 0 1 2 y 29 20.3 14.21 6.9629

Mathematics
1 answer:
andre [41]2 years ago
5 0

Answer:

y=4.8710 is the missing value

Step-by-step explanation:

The first step in approaching this question is determining the exponential equation that models the set of data. This can easily be done in Ms.Excel application. We first enter the data into any two adjacent columns of an excel workbook. The next step is to highlight the data, click on the insert tab and select the x,y scatter-plot feature. This creates a  scatter-plot for the data.

The next step is to click the Add chart element feature and insert an exponential trend line to the scatter plot ensuring the display equation on chart is checked.

The exponential regression equation for the data set is given as;

y=12.321e^{-0.464x}

To find the missing y value, we simply substitute x with 2 in the regression equation obtained;

y=12.321e^{-0.464(2)}\\\\y=4.8710

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A researcher wants to estimate the mean weekly family expenditure on clothing purchases and maintenance. First, she needs to det
Blizzard [7]

Answer: C. 461

Step-by-step explanation:

We know that the formula to find the sample size is given by :-

n=(\dfrac{z^*\cdot \sigma}{E})^2

, where \sigma = Population standard deviation from prior study.

E = margin of error.

z* = Critical value.

As per given , we have

\sigma=125

E= 15

Significance level : \alpha=0.01

Critical value (Two tailed)=z^*=z_{\alpha/2}=z_{0.005}=2.576

Now , Required sample size = n=(\dfrac{(2.576)\cdot 125}{15})^2

n=(21.4666666667)^2\\\\ n=460.817777779\approx461 [Round to next integer]

Hence, the required sample size to be taken is 461.

Correct answer = C. 461

3 0
2 years ago
Aramp is 17 feet long, rises 8 feet above the floor, and covers a horizontal distance of 15 feet, as shown in the figure.
bonufazy [111]

Answer:

The ratio of Tan B is

\tan B= \dfrac{AC}{BC}=\dfrac{8}{15}

OR

\tan A= \dfrac{BC}{AC}=\dfrac{15}{8}

Step-by-step explanation:

In Right Angle Triangle ABC

angle C = 90°

AB = Ramp = 17 feet

BC =Horizontal distance = 15 feet

AC = Height from floor = 8 feet

To Find:

Ratio of Tan B = ?

Solution:

In Right Angle Triangle ABC By Tangent Identity we have

\tan B= \dfrac{\textrm{side opposite to angle B}}{\textrm{side adjacent to angle B}}

Substituting the given values we get

\tan B= \dfrac{AC}{BC}=\dfrac{8}{15}

OR

\tan A= \dfrac{BC}{AC}=\dfrac{15}{8}

5 0
2 years ago
Victor is enlarging a poster for a school baseball match. The graph below shows the size y of the poster after x enlargements: g
Norma-Jean [14]
For this case we have the following function:
 y = 1.8 ^ x
 The intersection with the y axis occurs when x = 0.
 We have then:
 y = 1.8 ^ 0
 y = 1
 In this case, the intersection with the y-axis represents the original size of the poster.
 Answer:
 
the y-intercept of the graph represents:
 
the original size of the poster.
3 0
2 years ago
Read 2 more answers
Mike earned x dollars the first week of his new job. He earned 5% more the second week than the first week. Which expression rep
gregori [183]

The expression represents the total amount of money Mike earned for both weeks is 2.05x dollars

<em><u>Solution:</u></em>

Given that, Mike earned x dollars the first week of his new job

He earned 5% more the second week than the first week

To find: Total amount earned in both weeks

From given,

Amount earned in first week = "x" dollars

Amount earned in second week = 5 % more than first week

Therefore,

Amount earned in second week = x + 5 % of x

\rightarrow x + 5 \% \times x\\\\\rightarrow x + \frac{5}{100} \times x\\\\\rightarrow x + 0.05x = 1.05x

Thus amount earned in second week = 1.05x dollars

<em><u>The total amount earned in both weeks:</u></em>

Total amount = Amount earned in first week + Amount earned in second week

Total\ Amount = x + 1.05x = 2.05x

Thus the expression represents the total amount of money Mike earned for both weeks is 2.05x dollars

5 0
2 years ago
What equation can pair with x +2y=5 to create an inconsistent system a. 2x+4y=3 b.5x+2y=3 c.6x+12y=30 d.3x+4y=8
Aneli [31]

Answer: A

Hope this is helpful.

Step-by-step explanation:

Try to solve using simultaneous equations with each answer given.  

x + 2y = 5  

x = 5 - 2y  

Plug this into each equation  

A 2(5 - 2y) + 4y = 3  

10 - 4y + 4y = 3  

10 = 3 in consistent  

B 5(5 - 2y) + 2y = 3  

25 - 10 y + 2y = 3  

25 - 8y = 3  

8y = 22  

y = 2.75  

Using original equation solve for x  

5x + 2(2.75) = 3  

5x + 5.5 = 3  

5x = -2.5  

x = -0.5  

Using original equation,  

(-0.5) + 2 (2.75) = 5  

-0.5 + 5.5 = 5 consistent  

C 6x + 12y = 30  

6(5 - 2y) + 12y = 30  

30 - 12y + 12 y = 30 consistent for every value of y  

D 3(5 - 2y) + 4y = 8  

15 - 6y + 4y = 8  

- 2y = -7  

y = 3.5  

x = 5 - 2y  

x = 5 - 7  

x = -2  

Solving for x  

3(-2) + 4(3.5) = -6 + 14 = 8 consistent  

So A is the correct answer

4 0
2 years ago
Read 2 more answers
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