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Savatey [412]
1 year ago
13

Example 4

Mathematics
1 answer:
Vesnalui [34]1 year ago
7 0

Answer: Part a: b represents the base fee charged for the "house call" job

m is the hourly rate.

x is the number of hours at the job.

y represents the total cost for the job.

Part b:. The y-intercept is 65

The equation follows y=mx+b

Y= 42x + 65

Part c:. $275

Step-by-step explanation:

The difference between the two total costs, (Camilla 191 - Connor 107)

= $84. That is the rise. The run is the difference in time, 2 hours. 84/2 = 42.

m= 42

42 from 107 to find b, the base fee, 65 This is the y-intercept.

The equation is y= 42x + 65

Quick check using Camilla's bill: 191 = (42)(3) + 65

191 = 126 + 65 True!

Part C:

To find the total cost of the plumber's 5 hour job,

Y = 42(5) + 65

Y= 210 + 65

Y= $275

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Tara owes $14,375 in credit card debt. The interest accrues at a rate of 5.3%. She is also borrowing $570 each month for rent fr
siniylev [52]

Answer:

(f + g)(t) = f(t) + g(t) = 14375 (1 + \frac{5.3}{100})^{t} + 6840t

$29619.13

Step-by-step explanation:

a. Tara has $14375 in credit card debt and the interest rate is 5.3%.

Now, if f(t) represent the amount of money Tara have in credit card debt, where t is the number of years after after interest begins to accrue, then  

f(t) = 14375 (1 + \frac{5.3}{100})^{t} ......... (1)

Again Tara borrows $570 each month for rent from her parents without any interest.  

If g(x) represent the amount of money Tara owes to her parents, where t represents the number of years passed,then we can write  

g(t) = 570 × 12t = 6840t ........ (2)

Therefore, (f + g)(t) = f(t) + g(t) = 14375 (1 + \frac{5.3}{100})^{t} + 6840t

b. So, for t = 2 years,  

(f + g)(t) = 14375 (1 + \frac{5.3}{100})^{2} + 6840 \times 2 = $29619.13

So, Tara has to repay $29619.13 if she continues this way without any repayment for 2 years. (Answer)

7 0
1 year ago
In ΔABC, and m∠ABC = 90°. D and E are the midpoints of and , respectively. If the length of is 9 units, the length of is units a
jok3333 [9.3K]
This is an isosceles right triangle (AB = BC & ∠ B=90° - Given)
Then the angles at the base are equal and ∠ CAB = ∠ ACB = 45°

Theorem: Segment DE, joining the midpoints of 2 sides is:
1st) parallel to the 3rd side and
2nd) equal to half the measurement of the 3rd side
So if the 3rd side (hypotenuse) = 9 units, DE = 9/2 = 4.5 units
3 0
2 years ago
Use the table and the data provided to analyze the following data. During gym class, the pulse rate was recorded for 19 students
nexus9112 [7]

Answer:

Part A

Please see attached the required stem and leaf plot

For the stem and leaf plot, the nonsplit system is used because of clarity for analysis

Part B:

From the shape of the stem and leaf plot we have that there is an average increase of pulse rate of 20 pulses in all the 19 students after the exercise

The shape of the plot is relatively the same for the before and after exercise save for the decrease in the third to the last row by one and the increase in the second to the last roe by one student

The spread remained relatively constant in both cases with the most being in the 60s range having 7 students in the before exercise and the 80s range having 8 students in the after exercise leaf plot.

Step-by-step explanation:

The given data are;

67{}                                    87

67{}                                    88

67 {}                                   89

68 {}                                   89

71 {}                                    91

72                                   93

72                                   93

75                                   95

77                                   96

77                                   97

79                                   98

81                                    98

85                                   101

87                                   105

87                                   105

91                                    119

97                                   125

103                                  125

121                                  147

3 0
2 years ago
Kevin has a spinner that has 10 equal sections and 2 sections of each color—red, blue, green, yellow, and purple. Kevin spins th
IrinaK [193]

Answer:  2nd answer

Step-by-step explanation:

Kevin should have used a 4 in the numerator because there are 2 red sections and 2 green sections.

6 0
1 year ago
Read 2 more answers
A standard weight known to weigh 10 grams. Some suspect bias in weights due to manufacturing process. To assess the accuracy of
notsponge [240]

Answer:

a) The 98% confidence interval for the mean weight is between 10.00409 grams and 10.00471 grams

b) 49 measurements are needed.

Step-by-step explanation:

Question a:

We have that to find our \alpha level, that is the subtraction of 1 by the confidence interval divided by 2. So:

\alpha = \frac{1 - 0.98}{2} = 0.01

Now, we have to find z in the Ztable as such z has a pvalue of 1 - \alpha.

That is z with a pvalue of 1 - 0.01 = 0.99, so Z = 2.327.

Now, find the margin of error M as such

M = z\frac{\sigma}{\sqrt{n}}

In which \sigma is the standard deviation of the population and n is the size of the sample.

M = 2.327\frac{0.0003}{\sqrt{5}} = 0.00031

The lower end of the interval is the sample mean subtracted by M. So it is 10.0044 - 0.00031 = 10.00409 grams

The upper end of the interval is the sample mean added to M. So it is 10 + 0.00031 = 10.00471 grams

The 98% confidence interval for the mean weight is between 10.00409 grams and 10.00471 grams.

(b) How many measurements must be averaged to get a margin of error of +/- 0.0001 with 98% confidence?

We have to find n for which M = 0.0001. So

M = z\frac{\sigma}{\sqrt{n}}

0.0001 = 2.327\frac{0.0003}{\sqrt{n}}

0.0001\sqrt{n} = 2.327*0.0003

\sqrt{n} = \frac{2.327*0.0003}{0.0001}

(\sqrt{n})^2 = (\frac{2.327*0.0003}{0.0001})^2

n = 48.73

Rounding up

49 measurements are needed.

7 0
1 year ago
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