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1 year ago

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Jesus wants to start saving for college. His parents started an account for him that currently holds $325. Jesus adds $50 each m

onth. Label the y-intercept, the slope, and your axes

1 answer:

erma4kov [3.2K]1 year ago

7 0

Answer:

y-intercept, c = 325

Slope, m = 50

The x-axis represents the number of months and y-axis represents the total amount in saving accounts.

Step-by-step explanation:

We are given the following in the question:

A saving account currently holds $325. Jesus adds $50 each month.

Let x be the number of months and y be the total money n the saving account.

Then, we can use a linear function to represent the money in the account.

$y(x) = 325 + 50x$

Comparing to general linear function,

$y = mx + c$

where m is the slope and tells the rate of change and c is the y-intercept that is the value when x is zero.

Comparing we get:

m = 50

c = 325

y-intercept = c = 325

Slope, m = 50

The x-axis represents the number of months and y-axis represents the total amount in saving accounts.

The attached image shows a graph for the same.

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A manufacturer of paper coffee cups would like to estimate the proportion of cups that are defective (tears, broken seems, etc.)

Maksim231197 [3]

Answer:

a

The 95% confidence interval is $0.0503 < p < 0.1297$

b

The sample proportion is $\r p = 0.09$

c

The critical value is $Z_{\frac{\alpha }{2} } = 1.96$

d

The standard error is $SE =0.020$

Step-by-step explanation:

From the question we are told that

The sample size is n = 200

The number of defective is k = 18

The null hypothesis is $H_o : p = 0.08$

The alternative hypothesis is $H_a : p > 0.08$

Generally the sample proportion is mathematically evaluated as

$\r p = \frac{18}{200}$

$\r p = 0.09$

Given that the confidence level is 95% then the level of significance is mathematically evaluated as

$\alpha = 100 - 95$

$\alpha = 5\%$

$\alpha = 0.05$

Next we obtain the critical value of $\frac{ \alpha }{2}$ from the normal distribution table, the value is

$Z_{\frac{\alpha }{2} } = 1.96$

Generally the standard of error is mathematically represented as

$SE = \sqrt{\frac{\r p (1 - \r p)}{n} }$

substituting values

$SE = \sqrt{\frac{0.09 (1 - 0.09)}{200} }$

$SE =0.020$

The margin of error is

$E = Z_{\frac{ \alpha }{2} } * SE$

=> $E = 1.96 * 0.020$

=> $E = 0.0397$

The 95% confidence interval is mathematically represented as

$\r p - E < \mu < p < \r p + E$

=> $0.09 - 0.0397 < \mu < p < 0.09 + 0.0397$

=> $0.0503 < p < 0.1297$

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1 year ago

Dylan has a total of 25 marbles. He gives 5 marbles to his sister, Jane. What

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1/5th of the marbles

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Harriet has a square piece of paper. She folds it in half again to form a second rectangle (the high is not a square). The perim

dlinn [17]

Answer:

The area of the original piece of paper is 60cm

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1 year ago

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If 2A:3B=5:6 and 3B:2C=36:15 then find A:C

Aleonysh [2.5K]

Answer:

A: C = 2: 1

Step-by-step explanation:

Please see the attached pictures for the full solution.

Further explanantion (2nd image):

The reason why the ratio of A: C is equal to the ratio if 2A: 2C is that the number of parts of A and C is equal, which is 2 parts. If I were to divide both 2A and 2C by 2 to find the ratio of A: C, I would obtain 15: 15/2. However, ratios are expressed as whole numbers and thus, we would multiply the whole ratio by 2 again and the answer would still be 30: 15. This ratio is not in the simplest form since both can be divided by 15. Thus, dividing both sides of the ratio by 15 will leave us with the final answer of

A: C= 2: 1.

☆ An alternative method is to simplify the ratio 3B: 2C at the beginning.

3B: 2C

= 36: 15

= 12: 5

Multiply the first ratio by 2 so 3B has 12 parts in both ratios:

2A: 3B

= 10: 12

Combining the 2 ratios together,

2A: 3B: 2C

= 10: 6: 5

2A: 2C

= 10: 5

= 2: 1

A: C= 2: 1

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1 year ago

L = loudness, in decibels (dB); I = sound intensity, in watts/m2; I0 = 10−12 watts/m2

irina [24]

The sound intensity of the Pile Driver is 39.5
or nearly 40 times the sound intensity of the jackhammer.

Given with Loudness in dB for pile driver = 112 dB
We have to convert it in terms of sound intensity.
First,
112dB/10 = 11.2

Then we'll use this as exponent of 10
(10)^(11.2) = 1.5849 * 10 ^ 11

Then use the equation of Watts per square meter to find the intensity:
I / (10^-12 W/m^2) =1.5849 * 10 ^ 11
I = sound intensity = 0.158

Then compare:

Sound intensity of Pile Driver/ Sound intensity of Jackhammer
(0.158) / (0.004)
= 39.5
or nearly 40 times the jackhammer.

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