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antoniya [11.8K]

2 years ago

10

Claire mowed 7 lawns last week. She mowed each lawn in 7/18 hour. She mowed the same lawns this week in 5/18 hour. How many time

s longer was claires time to mow all the lawns last week than this week?1

1 answer:

Wittaler [7]2 years ago

7 0

I think it’s 2 hours

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Pam served her apple pie on a 13 inch diameter dish. She wanted to tie a ribbon around the dish to make it a little more festive

zlopas [31]

Answer:

Length of ribbon = 40.86 inches

Step-by-step explanation:

Length of the ribbon = circumference of the dish = πD

D = diameter = 13 inches

Length of ribbon = 22/7 x 13 = 40.857143 inches

8 0

2 years ago

Read 2 more answers

Which system of equations can you use to find the roots of the equation 2x3 + 4x2 – x + 5 = –3x2 + 4x + 9? y = 2x3 + x2 + 3x +5

Alona [7]

Answer:The answer is y = 2x3 + 4x2 – x + 5 and y = –3x2 + 4x + 9

Roots are both: x=-4, x= -1/2 , x= 1

Proof:

Solve for x over the real numbers:

2 x^3 + 4 x^2 - x + 5 = -3 x^2 + 4 x + 9

Subtract -3 x^2 + 4 x + 9 from both sides:

2 x^3 + 7 x^2 - 5 x - 4 = 0

The left hand side factors into a product with three terms:

(x - 1) (x + 4) (2 x + 1) = 0

Split into three equations:

x - 1 = 0 or x + 4 = 0 or 2 x + 1 = 0

Add 1 to both sides:

x = 1 or x + 4 = 0 or 2 x + 1 = 0

Subtract 4 from both sides:

x = 1 or x = -4 or 2 x + 1 = 0

Subtract 1 from both sides:

x = 1 or x = -4 or 2 x = -1

Divide both sides by 2:

Answer: x = 1 or x = -4 or x = -1/2

Step-by-step explanation:

4 0

1 year ago

Read 2 more answers

At a financial institution, a fraud detection system identifies suspicious transactions and sends them to a specialist for revie

labwork [276]

Answer:

a. E(X) = 54.4

b. E(X) = 2.5

c. P(Y=2) = .0116

Step-by-step explanation:

a.

E(X) = np = .40 probability * 136 trials = 54.4 blocked transmissions

To get the expected value, we simply multiply probability times number of trials. You can look at it in simple terms by thinking if there's a 50% chance of flipping heads and you flip a coin twice, in an ideal world you will have .5*2 = 1 head.

b.

i. Let X represent the number of suspicious transmissions reviewed until finding the first blocked one. We will use a geometric distribution to model the "first" transmission. Whenever we're looking for the "first" time something happens, we use geometric.

ii. E(X) = 1/p , according to the geometric model.

= 1/.4 = 2.5.

We expect that the specialist will review 2.5 suspicious transactions <em>on average </em>before finding the first transmission that will be blocked.

c.

i. Let Y represent the exact number of blocked transmissions out of 10. We will use a binomial distribution to model the "fixed" number of transmissions. Whenever we're looking for a "fixed" number of times something happens, we use binomial.

ii. P(Y=k) = (n choose k)(p^k)(q^n-k)

P(Y=2) = (¹⁰₂)(.4^2)(.6^10-2)

= 45 (.4^2)(.6^10-2) = .0016

As for calculator notation, the n choose k can be accessed on a TI-84 via MATH -> PRB -> nCr. It looks like 10 nCr 2 on the display.

Hence the probability that two transactions out of ten will be blocked is .0016 by the binomial model.

5 0

2 years ago

An experiment was performed to compare the wear of two different laminated materials. Twelve pieces of material 1 were tested by

GenaCL600 [577]

Answer:

At 0.05 level of significance, the abrasive wear of material 1 exceeds that of material 2 by more than 2 units

Step-by-step explanation:

We hypothesize that mean difference between abrasive wear of material 1 and material 2 is greater than 2.

So we write the null hypothesis $H_0 : \mu_1 - \mu_2 >2$ ,

and the alternative hypothesis $H_1: \mu_1 - \mu_2 \leq 2$ .

We will find the T-score as well as the p-value. If the p-value is less than the level of significance, we will reject the null hypothesis, i.e. we will conclude that the abrasive wear of material 1 is less than that of material 2. Otherwise, we will accept the null hypothesis.

Since the variance is unknown and assumed to be equal, we will use the pooled variance

$s_p^2 = \frac{(n_1-1)s_1^2 + (n_2-1)s_2^2}{n_1+n_2-2} = 20.05$ ,

where $n_1 = 12, n_2 =10, s_1 =4, s_2 = 5$ .

The mean of material 1 and material 2 are $\mu_1 =85, \mu_2=81$ respectively and mean difference $d$ is equal to 4. The hypothesize difference $d_0$ is equal to 2.

To find the T-score, we use the following formula

$T = \frac{d - d_0}{\sqrt{\frac{s_p^2}{n_1} + \frac{s_p^2}{n_2} }}$

Substituting all the values into the T-score formula gives us $T = 1.04$ , and the respective p-value is equal to 0.31. This means we have enough statistical evidence not to reject the null hypothesis, and at 5% significance level, the abrasive wear of material 1 exceeds that of material 2 by more than 2 units.

6 0

2 years ago

Peter wants to fence the park in front of his home on three sides which measure 152m 40cm, 205m 10cm, 310m 39cm. What is the tot

Tpy6a [65]

One centimenter is 0.01 meters. So, you can write the measures as

$152.40\text{m},\quad 205.10\text{m},\quad 310.39\text{m}$

Once this rewriting is done, getting the total length $T$ is quite trivial, since all measurements are in the same unit, and we can simply sum everything:

$T = 152.40+205.10+310.39 = 667.89$

8 0

2 years ago