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gulaghasi [49]
3 years ago
12

He histogram shows the finishing times of runners in a race.

Mathematics
1 answer:
kobusy [5.1K]3 years ago
4 0
11 runners took at least 30 minutes to finish the race. (:
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Find the volume of the solid under the plane 5x + 9y − z = 0 and above the region bounded by y = x and y = x4.
svp [43]
<span>For the plane, we have z = 5x + 9y

For the region, we first find its boundary curves' points of intersection.
x = x^4 ==> x = 0, 1.

Since x > x^4 for y in [0, 1],

The volume of the solid equals

\int\limits^1_0 { \int\limits_{x^4}^x {(5x+9y)} \, dy } \, dx = \int\limits^1_0 {\left[5xy+ \frac{9}{2} y^2\right]_{x^4}^{x}} \, dx  \\  \\ =\int\limits^1_0 {\left[\left(5x(x)+ \frac{9}{2} (x)^2\right)-\left(5x(x^4)+ \frac{9}{2} (x^4)^2\right)\right]} \, dx  \\  \\ =\int\limits^1_0 {\left(5x^2+ \frac{9}{2} x^2-5x^5- \frac{9}{2} x^8\right)} \, dx =\int\limits^1_0 {\left( \frac{19}{2} x^2-5x^5- \frac{9}{2} x^8\right)} \, dx \\  \\ =\left[ \frac{19}{6} x^3- \frac{5}{6} x^6- \frac{1}{2} x^9\right]^1_0

=\frac{19}{6} - \frac{5}{6} - \frac{1}{2} =\bold{ \frac{11}{6} \ cubic \ units}</span>
8 0
3 years ago
Johnny spend 1/7 of his income on Food, 1/10 of his income on gas, and 3/8 of his income on rent. What percentage of his income
Agata [3.3K]

Answer:

  38.2%

Step-by-step explanation:

1/7 ≈ 14.29%

1/10 = 10.00%

3/8 = 37.50%

The total that Johnny has allocated for food, gas, and rent is ...

  14.29% + 10.00% + 37.50% = 61.79%

So, the remaining amount is ...

  100% -61.79% = 38.21%

About 38.2% of Johnny's income remains.

7 0
3 years ago
Which of the following is a reasonable estimate for the weight capacity of an elevator that can carry up to 15 people?
Bas_tet [7]

A is the most common

6 0
3 years ago
Read 2 more answers
Find the size of each of two samples (assume that they are of equal size) needed to estimate the difference between the proporti
hodyreva [135]

Answer:

The sample size n = 4225

Step-by-step explanation:

We will use maximum error formula = \frac{z_{a} S.D}{\sqrt{n} }

but we will find sample size "n"

\sqrt{n}  = \frac{z_{a} S.D}{maximum error}

Squaring on both sides , we get

n  = (\frac{z_{a} S.D}{maximum error})^2

Given 99% confidence interval (z value) = 2.56

given maximum error = 0.02

n  = (\frac{z_{a} p(1-p)}{maximum error})^2

n≤ (\frac{2.56X\frac{1}{2} }{0.02}) ^{2}    ( here S.D = p(1-p) ≤ 1/2

on simplification , we get n = 4225

<u>Conclusion</u>:

The sample size of two samples is  n = 4225

<u>verification</u>:-

We will use maximum error formula = \frac{z_{a} S.D}{\sqrt{n} } = \frac{2.56 1/2}{\ \sqrt{4225} }  = 0.0196

substitute all values and simplify we get maximum error is 0.02

4 0
3 years ago
Can someone help me with this question
Flura [38]
The answer is A or c I’m probs wrong
7 0
3 years ago
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