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2 years ago

Tell whether the angles are complementary or supplementary. Then find the value of x.

Mathematics

1 answer:

juin [17]2 years ago

6 0

Answer:

The angles are supplementary. X = 31

Step-by-step explanation:

The angles sum to equal 180 degrees, menaing they are supplementary. Add the degrees of each side 3x + 25 + 2x = 180 and solve for x. X should equal 31.

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Subtract the binomials. On simplifying (-3y2 − 8) − (-5y2 + 1), we get ____ y2 −______ .

Gala2k [10]

(-3y^2 − 8) − (-5y^2 + 1)
= -3y^2 − 8 + 5y^2 - 1
= 2y^2 - 9

answer is

2y^2 - 9

6 0

3 years ago

Read 2 more answers

Mopeds (small motorcycles with an engine capacity below 50cm3) are very popular in Europe because of their mobility, ease of ope

d1i1m1o1n [39]

Answer:

a) 96.64% probability that maximum speed is at most 50 km/h

b) 24.67% probability that maximum speed is at least 48 km/h

c) 86.64% probability that maximum speed differs from the mean value by at most 1.5 standard deviations

Step-by-step explanation:

When the distribution is normal, we use 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.

In this question, we have that:

$\mu = 46.8, \sigma = 1.75$

A. What is the probability that maximum speed is at most 50 km/h?

This is the pvalue of Z when X = 50. So

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

$Z = \frac{50 - 46.8}{1.75}$

$Z = 1.83$

$Z = 1.83$ has a pvalue of 0.9664

96.64% probability that maximum speed is at most 50 km/h.

B. What is the probability that maximum speed is at least 48 km/h?

This is 1 subtracted by the pvalue of Z when X = 48.

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

$Z = \frac{48 - 46.8}{1.75}$

$Z = 0.685$

$Z = 0.685$ has a pvalue of 0.7533

1 - 0.7533 = 0.2467

24.67% probability that maximum speed is at least 48 km/h.

C. What is the probability that maximum speed differs from the mean value by at most 1.5 standard deviations?

Z = 1.5 has a pvalue of 0.9332

Z = -1.5 has a pvalue of 0.0668

0.9332 - 0.0668 = 0.8664

86.64% probability that maximum speed differs from the mean value by at most 1.5 standard deviations

6 0

3 years ago

Find the domain of the function

aev [14]

Domain are those values of x for which function is defined. f(x) is not defined at x = 3. Therefore Domain is

x∈ (⁻∞, +∞) - {3}

8 0

3 years ago

On April 1, 1986, Casey deposited $1150 into a savings account paying 9.6% interest, compounded quarterly. If he hasn't made any

dalvyx [7]

According to the 72 rule
72/rate=time
72÷9.6=7.5 years

Another way to solve by using the main equation
2300=1150(1+0.096/4)^4t
Solve for t
t=((log(2,300÷1,150)÷log(1+(0.096÷4))÷4))=7.31years

Hope it helps :-)

7 0

3 years ago

Read 2 more answers

How many subsets of {1, 2, 3, 4, 6, 8, 10, 15} are there for which the sum of the elements is 15?

stepladder [879]

Answer:

512

Step-by-step explanation:

Suppose we ask how many subsets of {1,2,3,4,5} add up to a number ≥8. The crucial idea is that we partition the set into two parts; these two parts are called complements of each other. Obviously, the sum of the two parts must add up to 15. Exactly one of those parts is therefore ≥8. There must be at least one such part, because of the pigeonhole principle (specifically, two 7's are sufficient only to add up to 14). And if one part has sum ≥8, the other part—its complement—must have sum ≤15−8=7

For instance, if I divide the set into parts {1,2,4}

and {3,5}, the first part adds up to 7, and its complement adds up to 8

Once one makes that observation, the rest of the proof is straightforward. There are 25=32

different subsets of this set (including itself and the empty set). For each one, either its sum, or its complement's sum (but not both), must be ≥8. Since exactly half of the subsets have sum ≥8, the number of such subsets is 32/2, or 16.

8 0

3 years ago