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matrenka [14]
1 year ago
10

The following table shows the cost for a person to go to the 4 - H Fair to go on a certain number of rides: Develop an equation

to represent the scenario. A. y = 2x + 5B. y = 6x C. y = -2.5xD. y = 8x + 26E. None of the above

Mathematics
1 answer:
PtichkaEL [24]1 year ago
3 0

In order to develop an equation, let's use the slope-intercept form of the linear equation:

y=mx+b_{}

Using the points (3, 13.5) and (5, 18.5) from the table, we have:

\begin{gathered} (3,13.5)\colon \\ 13.5=3m+b \\ (5,18.5)\colon \\ 18.5=5m+b \end{gathered}

Subtracting the second and the first equation:

\begin{gathered} 5m+b-(3m+b)=18.5-13.5 \\ 2m=5 \\ m=2.5 \end{gathered}

Now, finding the value of b:

\begin{gathered} 13.5=3m+b \\ 13.5=7.5+b \\ b=13.5-7.5 \\ b=6 \end{gathered}

So the equation that represents this table is y = 2.5x + 6

Looking at the options, the correct one is E (none of the above).

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3 years ago
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In a study of parents' perceptions of their children's size, researchers asked parents to estimate their youngest child's height
tatyana61 [14]

Answer:

Test statistic t=6.505

P-value=0

Step-by-step explanation:

This is a hypothesis test for the population mean.

The claim is that parents tend to underestimate their youngest child's size.

Then, the null and alternative hypothesis are:

H_0: \mu=0\\\\H_a:\mu> 0

The significance level is assumed to be 0.05.

The sample has a size n=39.

The sample mean is M=7.5.

As the standard deviation of the population is not known, we estimate it with the sample standard deviation, that has a value of s=7.2.

The estimated standard error of the mean is computed using the formula:

s_M=\dfrac{s}{\sqrt{n}}=\dfrac{7.2}{\sqrt{39}}=1.153

Then, we can calculate the t-statistic as:

t=\dfrac{M-\mu}{s/\sqrt{n}}=\dfrac{7.5-0}{1.153}=\dfrac{7.5}{1.153}=6.505

The degrees of freedom for this sample size are:

df=n-1=39-1=38

This test is a right-tailed test, with 38 degrees of freedom and t=6.505, so the P-value for this test is calculated as (using a t-table):

P-value=P(t>6.505)=0

As the P-value (0) is smaller than the significance level (0.05), the effect is  significant.

The null hypothesis is rejected.

There is  enough evidence to support the claim that parents tend to underestimate their youngest child's size.

5 0
3 years ago
Andrea calls two truck rental companies to compare costs. Action trucks charges $80 for the day plus $0.22 per kilometer and tru
Amanda [17]

Answer:it will take 200 kilometers for the costs to be the same.

Step-by-step explanation:

Let x represent the number of kilometers that Andrea would have to drive for the total cost of renting from both companies to be the same.

Action trucks charges $80 for the day plus $0.22 per kilometer. It means that the total cost of x miles would be

80 + 0.22x - - - - - - - - - 1

Truck experts charges $100 for the day plus $0.12 per kilometer. It means that the total cost of x miles would be

100 + 0.12x - - - - - - - - - 2

Therefore, for the cost of renting from both companies to be the same,

80 + 0.22x = 100 + 0.12x

0.22x - 0.12x = 100 - 80

0.1x = 20

x = 20/0.1 = 200

4 0
3 years ago
The equation represents the proportional
zloy xaker [14]

Answer:

No, more than one hamburger was sold

5 0
3 years ago
Learning Theory Students in a psychology experiment were given an exam and then retested monthly with equivalent exams. The aver
forsale [732]

Answer:

Step-by-step explanation:

The average scores s (on a 100 point scale) for the students can be modeled by

s = 75 - 6 In(t + 1), 0 < t < 12

where t is the time in months.

a) Since the students were given an exam and then retested monthly with equivalent exams, then,

For the original exam, t = 0

Therefore,

s = 75 - 6 In(0 + 1) = 75 - 6 In1

s = 75 - 6 × 0 = 75

b) the average score after 4 months, t = 4

Therefore,

s = 75 - 6 In(4 + 1) = 75 - 6 In5

s = 75 - 9.66 = 65.34

c) s = 60

Therefore,

60 = 75 - 6 In(t + 1)

6 In(t + 1) = 75 - 60 = 15

In(t + 1) = 15/6 = 2.5

t + 1 = e^2.5 = 12.18

t = 12.18 - 1 = 11.18

t = 11 approximately

8 0
3 years ago
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