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2 years ago

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Errol's bike ride from home to school can be modeled by the equation d(t) = - 1/4 * t + 2 where d(t) is his distance from school

in miles, at t minutes. Errol's friend Daniel lives 4 miles away from school. It takes Daniel twice as long to get to school if he bike rides at the same pace as Errol. What can be said about the graph of the equation that models Daniel's bike rides?

1 answer:

Aleks04 [339]2 years ago

8 0

Answer:

Daniel's equation will have a vertical translation by 2 units in the positive direction.

Step-by-step explanation:

Errol's bike ride can be modeled by the equation,

$d(t)=-\frac{1}{4}t+2$

Slope of the equation = $-\frac{1}{4}$

Here slope defines the rate of change of distance from Errol's house.

Y-intercept = 2, which represents the distance of the school from his home.

Let the equation that represents the equation is,

d(t) = mt + b

Errol's friend Daniel lives 4 miles away from school that means y intercept of the equation (b) = 4

Since Daniel drives his bike at the same pace as Errol, slope will be same.

Equation that models the distance will be

$d(t)=-\frac{1}{4}t+4$

If we compare both the equations, slopes are same but y-intercepts have a difference of 2 units

Therefore, the graph from the Daniel's equation will have a vertical translation by 2 units in the positive direction.

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What is the sum of the distinct prime factors of 315

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Answer: The exponents in the prime factorization are 2, 1, and 1. Adding one to each and multiplying we get (2 + 1)(1 + 1)(1 + 1) = 3 x 2 x 2 = 12. Therefore 315 has exactly 12 factors.

Step-by-step explanation: First, the exponents in the prime factorization are 2, 1, and 1. Then adding one to each and multiplying we get (2 + 1)(1 + 1)(1 + 1) = 3 x 2 x 2 = 12. Finally, 315 has exactly 12 factors.

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1 year ago

Sean has 15,000 to invest she will put some of it into a fund that pays 4.5% annual interest in the rest in a certificate of dep

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Answer:$12500 was invested into the account that pays 4.5% annual interest..

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Step-by-step explanation:

Let x represent the amount invested into the account that pays 4.5% annual interest.

Let y represent the amount invested into the certificate of deposit that pays 1.8% annual interest.

Sean has 15,000 to invest. She will put some of it into a fund that pays 4.5% annual interest and the rest in a certificate of deposit that pays 1.8% annual interest. This means that

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if she wants to earn 4.05% annual interest on the total amount, the amount would be

4.05/100 × 15000 = 607.5

Therefore,

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Substituting x = 15000 - y into equation 1, it becomes

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1 year ago

Read 2 more answers

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malfutka [58]

Answer:

A 95% confidence interval for this population proportion is [0.081, 0.159].

Step-by-step explanation:

We are given that a market research company conducted a survey to find the level of affluence in a city.

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Firstly, the pivotal quantity for finding the confidence interval for the population proportion is given by;

P.Q. = $\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ ~ N(0,1)

where, $\hat p$ = sample proportion of people who are considered affluent = $\frac{32}{267}$ = 0.12

n = sample of persons = 267

p = population proportion

<em>Here for constructing a 95% confidence interval we have used One-sample z-test for proportions.</em>

<u>So, 95% confidence interval for the population proportion, p is ;</u>

P(-1.96 < N(0,1) < 1.96) = 0.95 {As the critical value of z at 2.5% level

of significance are -1.96 & 1.96}

P(-1.96 < $\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ < 1.96) = 0.95

P( $-1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ < ${\hat p-p}$ < $1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ ) = 0.95

P( $\hat p-1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ < p < $\hat p+1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ ) = 0.95

<u>95% confidence interval for p</u> = [ $\hat p-1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ , $\hat p+1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ ]

= [ $0.12-1.96 \times {\sqrt{\frac{0.12(1-0.12)}{267} } }$ , $0.12+1.96 \times {\sqrt{\frac{0.12(1-0.12)}{267} } }$ ]

= [0.081, 0.159]

Therefore, a 95% confidence interval for this population proportion is [0.081, 0.159].

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2 years ago

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VARVARA [1.3K]

Answer:

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Step-by-step explanation:

He lost 80%.

750000*80%

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= $ 600,000

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