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Arlecino [84]
3 years ago
6

Tim is choosing between two cell phone plans that offer the same amount of free minutes. Cingular's plan charges $39.99 per mont

h with additional minutes costing $0.45. Verizon's plan costs $44.99 with additional minutes at $0.40. How many additional minutes, a, will it take for the two plans to cost the same?
Mathematics
1 answer:
Eduardwww [97]3 years ago
8 0

Answer:

It will take 100 additional minutes for the two plans to cost the same.

Step-by-step explanation:

Tim is choosing between two cell phone plans, Cingular and Verizon. They offer the same amount of free minutes.

Cingular's plan charges $39.99 per month with additional minutes costing $0.45.

Verizon's plan costs $44.99 with additional minutes at $0.40

Let a = the number of additional units that it will take the two plans to cost the same.

This means total cost of Cingular's plan additional minutes will be 0.45a and total cost of Verizon's plan additional minutes will be 0.4a

For the two plans to cost the same,

39.99 + 0.45a = 44.99 + 0.4a

0.45a - 0.4a = 44.99 - 39.99

0.05a = 5

a = 5/0.05 = 100

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Which situation could best be represented by the integer 120
ASHA 777 [7]
Which situation could best be represented by the integer 120?

1. could be negative but the likely of losing 120 pounds is very low

2. this number would be positive

3. could be between -1 to - infinity

answer: 3. the number of feet below a surface
8 0
2 years ago
The thickness of a plastic film (in mils) on a substrate material is thought to be influenced by the temperature at which the co
statuscvo [17]

Answer:

Step-by-step explanation:

Hello!

The objective is to test if rising the process temperature reduces the thickness of the plastic film that coats a substrate material To do so, two samples of substrates are coated at different temperatures:

Sample 1

X₁: Thickness of the plastic film after the substrate is coated at 125F

n₁=11

X[bar]₁= 101.28

S₁= 5.08

Sample 2

X₂: Thickness of the plastic film after the substrate is coated at 150F

n₂= 13

X[bar]₂= 101.70

S₂= 20.15

Does the data support this claim? Use the P-value approach and assume that the two population standard deviations are not equal.

Now if the higher the heat, the thinner the thickness of the plastic coating, then the average thickness of the coating done at 150F should be less than the average thickness of the coating done at 125F, symbolically: μ₂ < μ₁

Then the hypotheses are:

H₀: μ₂ ≥ μ₁

H₁: μ₂ < μ₁

α:0.05 (there is no α level stated so I've chosen the most common one)

Assuming that both variables have a normal distribution since the population standard deviations are not equal, the statistic to use is the Welch's t-test:

t= \frac{(X[bar]_2-X[bar]_1)-(Mu_1-Mu_2)}{\sqrt{\frac{S^2_1}{n_1} +\frac{S^2_2}{n_2} } } ~~t_w

t_{H_0}= \frac{(101.7-101.28)-0}{\sqrt{\frac{(20.15)^2}{13} +\frac{(5.08)^2}{11} } } = 0.072

This test is one-tailed to the left, meaning that you'll reject the null hypothesis at small values of t. The p-value is also one-tailed and has the same direction as the test. To calculate it you have to first calculate the degrees of freedom of the Welch's t:

Df_w= \frac{(\frac{S^2_1}{n_1} +\frac{S^2_2}{n_2} )^2}{\frac{(\frac{S^2_1}{n_1})^2 }{n_1-1}+\frac{(\frac{S^2_2}{n_2} )^2}{n_2-1}  }

Df_w= \frac{(\frac{5.08^2}{11} +\frac{20.15^2}{13} )^2}{\frac{(\frac{5.08^2}{11})^2 }{10} +\frac{(\frac{20.15^2}{13} )^2}{12} } = 13.78

The distribution is a Student's t with 13 degrees of freedom, then you can calculate the p-value as:

P(t₁₃≤0.072)= 0.4718

Using the p-value approach, the decision rule is:

If the p-value ≤ α, the decision is to reject the null hypothesis.

If the p-value > α, the decision is to not reject the null hypothesis.

The p-value is greater than the significance level, so the decision is to nor reject the null hypothesis.

Using a significance level of 5%, there is no significant evidence to support the claim that the average thickness pf the plastic coat processed at 150F is less than the average thickness pf the plastic coat processed at 125F.

I hope you have a SUPER day!

4 0
3 years ago
Evaluate 0.53n+5 when n=3
Alex777 [14]
0.53(3) + 5 = <span>6.59
</span><span>6.59 is the answer.
</span>
6 0
3 years ago
Find the function rule
dybincka [34]
1/-5, because when x increases by 1, y decreases by 5
6 0
3 years ago
Is x = 7 a solution to the equation 3x - 4 = 15? No Yes
Elis [28]

Answer:

No, because 3 x 7 = 21 - 4 = 17

Step-by-step explanation:

8 0
2 years ago
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