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Lena is on a two week bicycle trip. After 5 days she had ridden 212 miles. Express Lena’s rate as a unit rate

Answers

Answer 1

Answer:

Answer:

42.4 miles per day

Step-by-step explanation:

212 miles ÷ 5 (days) = 42.4 miles

which means Lena can go at the rate of

42.4 miles per day

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Decorating your house for Christmas takes 106ft of lights. You use two lengths of lights,the short length of lights is 5 ft and the long length of lights is 11 ft. The total number of
strings of lights you use is 14. How many of each type of light do you have?

Answers

Answer:

8 short and 6 long strings

Step-by-step explanation:

Let the number of lights are short = s and long = l.

According to question we have:

s + l = 14
5s + 11l = 106

Subtract 5 times the first equation from the second one to solve for l:

5s + 11l - 5s - 5l = 106 - 5*14
6l = 36
l = 36/6
l = 6

Find s:

s = 14 - 6 = 8

Answer:

A good rule of thumb is 100 lights for every 1.5 feet of tree. However, if you love lights, you may want to double, or even triple, that amount.

Step-by-step explanation:

Just a guess because you gave no answer choices

I need help with these questions

Answers

Answer:

1)10 months 2) 40 cm 3)8in

Step-by-step explanation:

1)1year =12 months

5/6year=?months

cross multiply

5x2=10

------

6x2=12

answer 12months

2)100cm in a meter

100divided by 5=20

1/5=20cm

2/5=40cm

answer:40 cm

3)12in in a foot

12divided by 3=4

1/3=4in

2/3=8 in

answer=8 in

thats all the time I have for now bye

The percent of fat calories that a person consumes each day is normally distributed with a mean of 35 and a standard deviation of 10. Suppose that 16 individuals are randomly chosen. Let X = average percent of fat calories. (a) For the group of 16 individuals, find the probability that the average percent of fat calories consumed is more than thirty-seven. (Round your answer to four decimal places.) b) Find the first quartile for the average percent of fat calories. (Round your answer to two decimal places.) percent of fat calories

Answers

Answer:

a) 0.2119 = 21.19% probability that the average percent of fat calories consumed is more than thirty-seven.

b) The first quartile for the average percent of fat calories is 33.31

Step-by-step explanation:

To solve this question, we have to understand the normal probability distribution and the central limit theorem.

Normal probability distribution:

Problems of normally distributed samples are 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:

$Z = (X - \mu)/(\sigma)$

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.

Central limit theorem:

The Central Limit Theorem estabilishes that, for a random variable X, with mean $\mu$ and standard deviation $\sigma$ , a large sample size can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = (\sigma)/(√(n))$

In this problem, we have that:

$\mu = 35, \sigma = 10, n = 16, s = (10)/(√(16)) = 2.5$

(a) For the group of 16 individuals, find the probability that the average percent of fat calories consumed is more than thirty-seven. (Round your answer to four decimal places.)

This is the 1 subtracted by the pvalue of Z when X = 37. So

$Z = (X - \mu)/(\sigma)$

By the Central Limit Theorem

$Z = (X - \mu)/(s)$

$Z = (37 - 35)/(2.5)$

$Z = 0.8$

$Z = 0.8$ has a pvalue of 0.7881

1 - 0.7881 = 0.2119

0.2119 = 21.19% probability that the average percent of fat calories consumed is more than thirty-seven.

b) Find the first quartile for the average percent of fat calories. (Round your answer to two decimal places.) percent of fat calories

The 1st quartile is the 25th percentile. So this is the value of X when Z has a pvalue of 0.25. So it is X when Z = -0.675. So

$Z = (X - \mu)/(s)$

$-0.675 = (X - 35)/(2.5)$

$X - 35 = -0.675*2.5$

$X = 33.31$

The first quartile for the average percent of fat calories is 33.31

If log(x+3)-log(x-5)=log2What is the value of x?

Please answer with explanation and process

Answers

We use log(x) - log(y) = log(x/y) and log(x) = log(y) ⇔ x = y

$\displaystyle\log(x+3) - \log(x-5) = \log 2 \implies \log\left( (x+3)/(x-5) \right) = \log 2 \implies \n \n (x+3)/(x-5) = 2 \impliesx+3 = 2(x-5) \n \nx = 13$

Help please whats the answer

Answers

Answer:

12 students

Explanation:

40% earned a B; 20% earned an A, so (40%+20% =) 60% got a "B or better."

60% of 20 students is ...

... 60/100 × 20 students = 1200/100 students = 12 students

(02.05)The figure shows three quadrilaterals on a coordinate grid: A coordinate plane is shown. Quadrilateral D has sides measuring 3 units and 1 unit. Quadrilateral F has sides measuring 3 units and 1 unit. Quadrilateral E has sides measuring 2 units and 6 units. Which of the following statements is true about the three quadrilaterals? D and E are similar but not congruent. E and F are similar and congruent. D and E are similar and congruent. F and D are similar but not congruent.

Answers

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