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tamaranim1 [39]
2 years ago
9

Multi step problems what is -10(10+b)=5(3b+5)

Mathematics
1 answer:
Alla [95]2 years ago
5 0

Answer:

b= -5

Step-by-step explanation:

-10(10+b)=5(3b+5)

Distribute

-100 -10b = 15b +25

Add 10b to each side

-100-10b+10b = 15b+10b +25

-100 = 25b+25

Subtract 25 from each side

-100-25 = 25b+25-25

-125 = 25b

Divide by 25

-125/25 =25b/25

-5 =b

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A diving board is 10 feet above the surface of the water. At time t = 0, the board propels Chris upward at a rate of 12 feet per
Art [367]

Answer:

Chris will take 0.75 seconds to return to his starting height of 10 feet.

Step-by-step explanation:

Let the height of Chris be represented by h(t) = -16\cdot t^{2}+12\cdot t +10, where h(t) is the height in feet and t, the time in seconds. First, we equalize the formula to a height of 10 feet and simplify the resulting expression, that is:

-16\cdot t^{2}+12\cdot t +10 = 10

-16\cdot t^{2}+12\cdot t = 0

Then, we simplify the expression by algebraic means:

-16\cdot t\cdot \left(t-\frac{3}{4} \right) = 0

Roots of the polynomial are, respectively:

t = 0\,s\,\lor \,t = 0.75\,s

First root represents the initial height of Chris, whereas the second one represents the instant when Christ returns to the same height above the surface of the water. Hence, Chris will take 0.75 seconds to return to his starting height of 10 feet.

5 0
2 years ago
1. A trapezoid has an area of 91 m2. The height of the trapezoid is 7 m and the measure of one base is twice the height. What is
Lynna [10]
The area of the trapezoid is given by:
 A = (1/2) * (b1 + b2) * (h)
 Where,
 b1, b2: bases of the trapezoid
 h: height
 Substituting values we have:
 91 = (1/2) * ((2 * 7) + b2) * (7)
 Rewriting we have:
 91 = (1/2) * (14 + b2) * (7)
 (2/7) * 91 = 14 + b2
 b2 = (2/7) * 91 - 14
 b2 = 12 m
 Answer:
 
The measure of the other base of the trapezoid is:
 
b2 = 12 m
6 0
2 years ago
Read 2 more answers
3h-2(4h-5)=10-5h A-0 B-4 C-infinity many solutions D-no solutions​
Crank

Answer:

Step-by-step explanation:

3h - 8h + 10 = 10 - 5h

-5h + 10 = 10 - 5h

10 = 10

infinitely many solutions

7 0
2 years ago
Ricardo and Tammy practice putting golf balls. Ricardo makes 47% of his putts and Tammy makes 51% of her putts. Suppose that Ric
yaroslaw [1]

Answer:

0.3821 = 38.21% probability that Ricardo makes a higher proportion of putts than Tammy.

Step-by-step explanation:

To solve this question, we need to understand the normal distribution, the central limit theorem, and subtraction of normal variables.

Normal probability distribution

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.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean \mu and standard deviation \sigma, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \mu and standard deviation s = \frac{\sigma}{\sqrt{n}}.

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean \mu = p and standard deviation s = \sqrt{\frac{p(1-p)}{n}}

Subtraction of normal variables:

When we subtract normal variables, the mean of the subtraction will be the subtraction of the means, while the standard deviation will be the square root of the sum of the variances.

Ricardo makes 47% of his putts, and attempts 25 putts.

By the Central Limit Theorem, we have that:

\mu_R = 0.47, s_R = \sqrt{\frac{0.47*0.53}{25}} = 0.0998

Tammy makes 51% of her putts, and attempts 30 putts.

By the Central Limit Theorem, we have that:

\mu_T = 0.51, s_T = \sqrt{\frac{0.51*0.49}{30}} = 0.0913

What is the probability that Ricardo makes a higher proportion of putts than Tammy?

This is the probability that the subtraction of R by T is larger than 0. The mean and standard deviation of this distribution are, respectively:

\mu = \mu_R - \mu_T = 0.47 - 0.51 = -0.04

s = \sqrt{s_R^2 + s_T^2} = \sqrt{0.0998^2 + 0.0913^2} = 0.1353

This probability is 1 subtracted by the pvalue of Z when X = 0. So

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

By the Central Limit Theorem

Z = \frac{X - \mu}{s}

Z = \frac{0 - (-0.04)}{0.1353}

Z = 0.3

Z = 0.3 has a pvalue of 0.6179

1 - 0.6179 = 0.3821

0.3821 = 38.21% probability that Ricardo makes a higher proportion of putts than Tammy.

6 0
2 years ago
Read 2 more answers
What is fifteen cube​
gulaghasi [49]

Answer:

3375

Step-by-step explanation:

15 times 15 times 15 = 3375

6 0
3 years ago
Read 2 more answers
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