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Marrrta [24]
3 years ago
7

What exponential function is the best fit for the data in the table?

Mathematics
2 answers:
Ratling [72]3 years ago
8 0

the answer is D fx=1/2(1/2)^x

gogolik [260]3 years ago
6 0
Answer: fourth option

\frac{1}{4} 4^{x-1}-4

Explanation:

1) the pair x = 3 f(x) = 0, leads you to probe this:

f(3) = 0 = A [4 ^ (3 - 1) ] + C = 0

=> A [4^2] = - C

A[16] = - C

if A = 1/4

16 / 4 = 4 => C = - 4

That leads you to the function f(x) = [1/4] 4 ^( x - 1) - 4

2) Now you verify the images for that function for all the x-values of the table:

x = 2 => f(2) + [1/4] 4 ^ (2 - 1) - 4 = [1/4] 4 - 4 = 4 / 4 - 4 = 1 - 4 = - 3 => check

x = 3 => f(3) = [1/4] 4^ (3 - 1) - 4 = [1/4] 4^2 - 4 = 16 / 4 - 4 = 4 - 4 = 0 => check

x = 4 -> f(4) = [1/4] 4^ (4-1) - 4 = [1/4] 4^(3) - 4 = (4^3) / 4 - 4 = 4^2 - 4 = 16 - 4 = 12 => check.

Therefore, you have proved that the answer is the fourth option.
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What is the value of y
guajiro [1.7K]

Answer:

<h2>              y = 5.6</h2>

Step-by-step explanation:

From Thales' theorem:

                                        \dfrac y7\ =\ \dfrac45\\\\y=\dfrac45\cdot7\\\\y = \dfrac{28}5\\\\y = 5.6

5 0
3 years ago
Granola Crunch cereal is packaged in 1 pound boxes. Susan Torres, a quality control analyst who works for the manufacturer of th
sineoko [7]

Answer:

z=\frac{1.02-1}{\frac{0.04}{\sqrt{40}}}=3.162    

p_v =2*P(z>3.162)=0.0016    

If we compare the p value and the significance level given \alpha=0.05 we see that p_v so we can conclude that we have enough evidence to to reject the null hypothesis, so we can conclude that the true mean is different from 1 pound at 5% of signficance.

Step-by-step explanation:

Data given and notation    

\bar X=1.02 represent the sample mean

\sigma=0.04 represent the population standard deviation    

n=40 sample size    

\mu_o =1 represent the value that we want to test  

\alpha=0.05 represent the significance level for the hypothesis test.    

z would represent the statistic (variable of interest)    

p_v represent the p value for the test (variable of interest)    

State the null and alternative hypotheses.    

We need to conduct a hypothesis in order to check if the true mean is equal to 1 pound or no :    

Null hypothesis:\mu =1    

Alternative hypothesis:\mu \neq 1    

Since we know the population deviation, is better apply a z test to compare the actual mean to the reference value, and the statistic is given by:    

z=\frac{\bar X-\mu_o}{\frac{\sigma}{\sqrt{n}}} (1)    

z-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".    

Calculate the statistic    

We can replace in formula (1) the info given like this:    

z=\frac{1.02-1}{\frac{0.04}{\sqrt{40}}}=3.162    

P-value    

Since is a two-sided test the p value would be:    

p_v =2*P(z>3.162)=0.0016    

Conclusion    

If we compare the p value and the significance level given \alpha=0.05 we see that p_v so we can conclude that we have enough evidence to to reject the null hypothesis, so we can conclude that the true mean is different from 1 pound at 5% of signficance.    

5 0
3 years ago
In one neighborhood, it is estimated that 20% of the people live in one-person households, 32% of the people live in two-person
MAXImum [283]

Answer:

The answer to this is 2.54

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3 years ago
Kristin graphed the locations of several places in her school on the coordinate plane shown below. Determine if each statement a
wel

Answer:

Step-by-step explanation:

1). Coordinates of Art → (1, -5).

   Coordinates of Library → (1, 9)

   Coordinates of Science → (-5, -5)

   Distance between Art and Library = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}

                                                             = \sqrt{(1-1)^2+(9+5)^2}

                                                             = 14 units

   Distance between Art and Science = \sqrt{(1+5)^2+(-5+5)^2}

                                                               = 6 units

   Since 14 > 6,

   Art is closer to Science than Library.

   Answer is False.

2). Coordinates of Cafeteria → (-7, 9)

    True.

5 0
3 years ago
Read 2 more answers
Solve the system of equations below. Enter your answer in the boxes.
Vesna [10]
Simplifying
8a + 12b = 92

Solving
8a + 12b = 92

Solving for variable 'a'.

Move all terms containing a to the left, all other terms to the right.

Add '-12b' to each side of the equation.
8a + 12b + -12b = 92 + -12b

Combine like terms: 12b + -12b = 0
8a + 0 = 92 + -12b
8a = 92 + -12b

Divide each side by '8'.
a = 11.5 + -1.5b

Simplifying
a = 11.5 + -1.5b
3 0
2 years ago
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