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2 years ago

15

Denise wants to burn at least 5000 calories a week through running. Based on her running speed, she estimates that she can burn

550 calories per hour.
If Denise runs for one half hour each week day and one hour each weekend day, will she meet her goal? Justify your answer.

1 answer:

Firdavs [7]2 years ago

8 0

Answer:

She will not meet her goal.

Step-by-step explanation:

There are 5 weekdays, so she will run for 0.5 * 5 = 2.5 hours over the weekdays

There are 2 weekends, so she will run for 2 * 1 = 2 hours over the weekend.

In total, this means she will run for 4.5 hours.

4.5 hours * 550 calories per hour = 2475 calories.

She will not meet her goal.

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3 years ago

Which ordered pair (a, b) is a solution to the given system of linear equations? -2a+3b=14

Stels [109]

Answer:

The solution of the system is the ordered pair (-13,-4)

Step-by-step explanation:

we have

$-2a+3b=14$ -----> equation A

$a-4b=3$ ----> equation B

Solve the system by elimination

Multiply by 2 both sides equation B

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$2a-8b=6$ ----> equation C

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3 years ago

Read 2 more answers

4 questions 20 points

Dvinal [7]

1. Cross multiply
35x = 5(11)
35x = 55
Divide both sides by 35
x = 55/35
x = 11/7

2. (x - 2)/x = 3/8
Cross multiply
3x = 8(x - 2)
3x = 8x - 16
Subtract 8x from both sides
-5x = -16
divide both sides by -5
x = -16/-5
x = 16/5 OR 3 1/5

3. (a + 1)/(a - 1) = 5/6
cross multiply
6(a + 1) = 5(a - 1)
distribute
6a + 6 = 5a - 5
subtract 5a from both sides
a + 6 = -5
subtract 6 from both sides
a = -11

4. (1/3)x - 4 = (2/3)x + 6
multiply each term by 3 to clear the fractions
x - 12 = 2x + 18
subtract x from both sides
-12 = x + 18
subtract 18 from both sides
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3 0

3 years ago

The following data comparing wait times at two rides at Disney are listed below: Position Pirates Splash Mountain Sample Size 32

myrzilka [38]

Answer:

a) $(14.68 -18.77) - 2.39 \sqrt{\frac{11.87^2}{32}+\frac{16.79^2}{30}} =-12.968$

$(14.68 -18.77) + 2.39 \sqrt{\frac{11.87^2}{32}+\frac{16.79^2}{30}} =4.788$

b) $t=\frac{14.68-18.77}{\sqrt{\frac{11.87^2}{32}+\frac{16.79^2}{30}}}}=-1.10$

Step-by-step explanation:

Data given and notation

$\bar X_{A}=14.68$ represent the mean for Pirates

$\bar X_{B}=18.77$ represent the mean for Splash Mountain

$s_{A}=11.87$ represent the sample standard deviation for the sample Pirates

$s_{B}=16.79$ represent the sample standard deviation for the sample Slpash Mountain

$n_{A}=32$ sample size selected for Pirates

$n_{B}=30$ sample size selected for Splash Mountain

$\alpha=0.02$ represent the significance level for the hypothesis test.

t would represent the statistic (variable of interest)

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

Part a

The confidence interval would be given by:

$(\bar X_A -\bar X_B) \pm t_{\alpha/2} \sqrt{\frac{s^2_{A}}{n_{A}}+\frac{s^2_{B}}{n_{B}}}$

The degrees of freedom are given by:

$df = n_A +n_B -2 = 32+30-2 = 60$

Since we want 98% of confidence the significance level is $\alpha =1-0.98 =0.02$ and $\alpha/2 =0.01$ , we can find in the t distribution with df =60 a critical value that accumulates 0.01 of the area on each tail and we got:

$t_{\alpha/2}= 2.39$

And replacing we got for the confidence interval:

$(14.68 -18.77) - 2.39 \sqrt{\frac{11.87^2}{32}+\frac{16.79^2}{30}} =-12.968$

$(14.68 -18.77) + 2.39 \sqrt{\frac{11.87^2}{32}+\frac{16.79^2}{30}} =4.788$

Part b

State the null and alternative hypotheses.

We need to conduct a hypothesis in order to check if the means are equal, the system of hypothesis would be:

Null hypothesis: $\mu_{A} = \mu_{B}$

Alternative hypothesis: $\mu_{A} \neq \mu_{B}$

the statistic is given by:

$t=\frac{\bar X_{A}-\bar X_{B}}{\sqrt{\frac{s^2_{A}}{n_{A}}+\frac{s^2_{B}}{n_{B}}}}$ (1)

t-test: "Is used to compare group means. Is one of the most common tests and is used to determine whether the means of two groups are equal to each other".

Calculate the statistic

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

$t=\frac{14.68-18.77}{\sqrt{\frac{11.87^2}{32}+\frac{16.79^2}{30}}}}=-1.10$

6 0

2 years ago