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2 years ago

Daniel's yard is perfectly rectangular. It has a length of 28 yards and a perimeter of 88 yards. Find the width of his yard.

1 answer:

8 0

Draw a picture of the yard, rectangle. On the two long sides, write 28 yards and on the two shorter ones, just write a question mark.

To figure out perimeter, you need to add up each side.

P = Perimeter

L = Length

W = Width

P = L(2) + W(2)

If the length is 28, double it. = 56

Now subtract that from the perimeter - 88-56=32

32 is what you have left, so now split that, and replace the question marks.

All-in-all each width is 16 yards, while each length is 28, making the whole rectangle have a perimeter of 88 yards.

You might be interested in

What is −34, 0.5, 23,−73, 1.2 in order from least to greatest?

denpristay [2]

Answer:

-73, -34, 0.5, 1.2, 23

Step-by-step explanation:

In Mathematics, the set of numbers are arranged in two ways. It means that the numbers can be arranged either in ascending order or descending order. If the numbers are arranged from the least to the greatest, then it is called ascending order. In this form, the numbers are in increasing order. The first number should be lesser than the second number.

If the numbers are arranged from the greatest to the least, then it is called descending order. In this form, the numbers are in decreasing form. The first number should be greater than the second number.

Also, read: Descending Order

Standard Form

<em>The standard form to represent the least to the greatest arrangement </em>of numbers is given by:

a < b < c < d < …..

Here,

a, b, c, d represent the numbers

Example: 2 < 5 < 7 < 8

5 0

2 years ago

Kat has 19 coins, all quarters and dimes, that are worth a total of $4. The system of equations that can be used to find the num

lorasvet [3.4K]

Since q+d=19, we can re-write this as d=19-q. Using the second equation 0.25q+0.1d=4 we can multiply both sides by 100. So we get 25q+10d=400. So now we can plug d=19-q into 25q+10d=400. So now we get, 25q+190-10q=400. Subtracting both sides by 190, we get 15q=210 and that q=14 plugging that in d=5

3 0

2 years ago

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

Which expression is equivalent to (4 + 7i)(3 + 4i)? –16 + 37i 12 – 28i 16 – 37i 37 + 16i

ASHA 777 [7]

Answer:

The equivalent expression is $\Rightarrow -16+37i$

A is correct

Step-by-step explanation:

We are given two complex number and need to multiply it. To find equivalent fraction.

$(4+7i)(3+4i)$

Using Binomial product property: (a+b)(c+d)=ab+ad+bc+bd

$\Rightarrow (4+7i)(3+4i)$

$\Rightarrow 4(3)+4(4i)+7i(3)+7i(4i)$

$\Rightarrow 12+16i+21i+28i^2$

Combine the like term and simplify

$\Rightarrow 12-28+37i$ $\because \ \ i^2=-1$

$\Rightarrow -16+37i$

Hence, The equivalent expression is $\Rightarrow -16+37i$

4 0

2 years ago

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ΔABC and ΔXYZ are similar triangles. If BC = x + 7, AC = x + 6, YZ = 4 − x, and XZ = 3 − x, find the value of x.

Montano1993 [528]

I believe the answer is B) -3/2 or -1.5.

Please give a heart and rating if this is right!

3 0

2 years ago

Read 2 more answers