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2 years ago

10

Marvin has a coupon the discount is the rental of a full-size car by $25 they decide to buy insurance for each day if the cost i

s $465 how much days dear well they rent the car right and solve the equation

2 answers:

ipn [44]2 years ago

7 0

Answer: Marvin needs approximately 19 days to rent the car.

Step-by-step explanation:

Since we have given that

Amount Marvin get on a discount coupon = $25

She decided to buy insurance for each day.

Let the number of days be x

cost of insurance = $465

According to question, it becomes,

$25x=465\\\\x=\frac{465}{25}\\\\x=18.6\\\\x=19\ days$

Hence, Marvin needs approximately 19 days to rent the car.

beks73 [17]2 years ago

6 0

Answer: 9 is the answer

You might be interested in

Rocky Mountain National Park is a popular park for outdoor recreation activities in Colorado. According to U.S. National Park Se

Ugo [173]

Answer:

a) 0.6628 = 66.28% probability that at least 85 visitors had a recorded entry through the Beaver Meadows park entrance

b) 0.5141 = 51.41% probability that at least 80 but less than 90 visitors had a recorded entry through the Beaver Meadows park entrance

c) 0.5596 = 55.96% probability that fewer than 12 visitors had a recorded entry through the Grand Lake park entrance.

d) 0.9978 = 99.78% probability that more than 55 visitors have no recorded point of entry

Step-by-step explanation:

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

Can be approximated to a normal distribution, using the expected value and the standard deviation.

The expected value of the binomial distribution is:

$E(X) = np$

The standard deviation of the binomial distribution is:

$\sqrt{V(X)} = \sqrt{np(1-p)}$

Normal probability distribution

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

When we are approximating a binomial distribution to a normal one, we have that $\mu = E(X)$ , $\sigma = \sqrt{V(X)}$ .

In this problem, we have that:

$n = 175$

(a) What is the probability that at least 85 visitors had a recorded entry through the Beaver Meadows park entrance?

46.7% of visitors to Rocky Mountain National Park in 2018 entered through the Beaver Meadows. This means that $p = 0.467$ . So

$\mu = E(X) = np = 175*0.467 = 81.725$

$\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{175*0.467*0.533} = 6.6$

This probability, using continuity correction, is $P(X \geq 85 - 0.5) = P(X \geq 84.5)$ , which is 1 subtracted by the pvalue of Z when X = 84.5. So

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{84.5 - 81.725}{6.6}$

$Z = 0.42$

$Z = 0.42$ has a pvalue of 0.6628.

66.28% probability that at least 85 visitors had a recorded entry through the Beaver Meadows park entrance.

(b) What is the probability that at least 80 but less than 90 visitors had a recorded entry through the Beaver Meadows park entrance?

Using continuity correction, this is $P(80 - 0.5 \leq X < 90 - 0.5) = P(79.5 \leq X \leq 89.5)$ , which is the pvalue of Z when X = 89.5 subtracted by the pvalue of Z when X = 79.5. So

X = 89.5

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{89.5 - 81.725}{6.6}$

$Z = 1.18$

$Z = 1.18$ has a pvalue of 0.8810.

X = 79.5

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{79.5 - 81.725}{6.6}$

$Z = -0.34$

$Z = -0.34$ has a pvalue of 0.3669.

0.8810 - 0.3669 = 0.5141

51.41% probability that at least 80 but less than 90 visitors had a recorded entry through the Beaver Meadows park entrance

(c) What is the probability that fewer than 12 visitors had a recorded entry through the Grand Lake park entrance?

6.3% of visitors entered through the Grand Lake park entrance, which means that $p = 0.063$

$\mu = E(X) = np = 175*0.063 = 11.025$

$\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{175*0.063*0.937} = 3.2141$

This probability, using continuity correction, is $P(X < 12 - 0.5) = P(X < 11.5)$ , which is the pvalue of Z when X = 11.5. So

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{11.5 - 11.025}{3.2141}$

$Z = 0.15$

$Z = 0.15$ has a pvalue of 0.5596.

55.96% probability that fewer than 12 visitors had a recorded entry through the Grand Lake park entrance.

(d) What is the probability that more than 55 visitors have no recorded point of entry?

22.7% of visitors had no recorded point of entry to the park. This means that $p = 0.227$

$\mu = E(X) = np = 175*0.227 = 39.725$

$\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{175*0.227*0.773} = 5.54$

Using continuity correction, this probability is $P(X \leq 55 + 0.5) = P(X \leq 55.5)$ , which is the pvalue of Z when X = 55.5. So

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{55.5 - 39.725}{5.54}$

$Z = 2.85$

$Z = 2.85$ has a pvalue of 0.9978

0.9978 = 99.78% probability that more than 55 visitors have no recorded point of entry

8 0

2 years ago

Three students, Linda, Tuan, and Javier, are given five laboratory rats each for a nutritional experiment. Each rat's weight is

Liula [17]

Answer:

The variance in weight is statistically the same among Javier's and Linda's rats

The null hypothesis will be accepted because the P-value (0.53 ) > ∝ ( level of significance )

Step-by-step explanation:

considering the null hypothesis that there is no difference between the weights of the rats, we will test the weight gain of the rats at 10% significance level with the use of Ti-83 calculator

The results from the One- way ANOVA ( Numerator )

with the use of Ti-83 calculator

F = .66853

p = .53054

Factor

df = 2 ( degree of freedom )

SS = 23.212

MS = 11.606

Results from One-way Anova ( denominator )

Ms = 11.606

Error

df = 12 ( degree of freedom )

SS = 208.324

MS = 17.3603

Sxp = 4.16657

where : test statistic = 0.6685

p-value = 0.53

level of significance ( ∝ ) = 0.10

The null hypothesis will be accepted because the P-value (0.53 ) > ∝

where Null hypothesis H0 = ∪1 = ∪2 = ∪3

hence The variance in weight is statistically the same among Javier's and Linda's rats

7 0

1 year ago

A building has an entry the shape of a parabolic arch 84 ft high and 42 ft wide at the base, as shown below. A parabola opening

Gala2k [10]

Since the parabola passes by the center its equation is:

y = ax². But it opens downward, that means the coefficient a is negative.

Then the equation becomes:

y = - ax², with x = 0 as its axis of symmetry.

We are given that the height is 84 ft when the opening downward is 42 ft.
That means to the (height) y, corresponds x =+21 & x=-21 (due to symmetry).
In order to calculate a let's plug y & x with their related values:

y = - ax²

84 = - a(21)²

84 = - a(441) and a = - 84/441 ↔ a = - 4/21

And the final equation is : y = -4/21. x²

3 0

2 years ago

Find the probability of rolling divisors of 12

AVprozaik [17]

If you're talking about dice than there are six sides of a die, right? 5 of those 6 numbers are divisors of 12. 1,2,3,4, and 6. 5/6 is 0.833... which is 83% of 6. So the probability of rolling divisors of 12 is 83%.

5 0

2 years ago

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Which graph represents the solution set for the inequality StartFraction one-half EndFraction x is less than or equal to 18.x ≤

Mrrafil [7]

Answer:

A number line from 0 to 60 in increments of 6. A point is at 36 and a bold line starts at 36 and is pointing to the left. ⇒ last answer

Step-by-step explanation:

* <em>Lets explain how to solve the problem</em>

- <u><em>When solving an inequality, there are some important points:</em></u>

# If the inequality is x > a, then it represented on the number line by

a ray with empty small circle as end starts at a and pointed to

the right (⇒ ∞)

# If the inequality is x ≥ a, then it represented on the number line by

a ray with bold small circle as end starts at a and pointed to the

right (⇒ ∞)

# If the inequality is x < a, then it represented on the number line

by a ray with empty small circle as end starts at a and pointed to

the left (⇒ -∞)

# If the inequality is x ≤ a, then it represented on the number line by

a ray with bold small circle as end starts at a and pointed to the

left (⇒ -∞)

* <em>Lets solve the problem</em>

∵ 1/2 x ≤ 18

- Multiply both sides by 2

∴ x ≤ 36

- To represent it draw a number line from 0 to 60 and the counted

by 6 as 0, 6, 12, 18, 24, 30, 36, 42, 48, 54, 60

- Draw a ray with bold end starts at 36 and pointed to the left

∴ A number line from 0 to 60 in increments of 6. A point is at 36 and

a bold line starts at 36 and is pointing to the left.

3 0

2 years ago

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