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3 years ago

14

During week one of his training Conrad did 10 push-ups every day. He increased his daily number of push-ups by 5 every week afte

r that. How many push-ups did Conrad do every day during week 25?

1 answer:

Nonamiya [84]3 years ago

6 0

He starts with 10, +5 after every week
week 2=10+5
week 3=10+5*2
...
week 25 =10+5*24
f(x)=10+5(x-1)
so during the 25th week=10+5*24=10+120=130

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Solve the following for the specified variable<br><br> Z=s/2(P+p); for P

lapo4ka [179]

Answer:

$\boxed{\sf P = \frac{2Z}{s} - p}$

Step-by-step explanation:

$\sf Solve \ for \ P: \\ \sf \implies Z = \frac{s}{2} (P + p) \\ \\ \sf Z = \frac{s}{2} (P + p) \ is \ equivalent \ to \ \frac{s}{2} (P + p) = Z: \\ \sf \implies \frac{s}{2} (P + p) = Z \\ \\ \sf Divide \ both \ sides \ by \ \frac{s}{2} : \\ \sf \implies P + p = \frac{2Z}{s} \\ \\ \sf Substrate \ p \ from \ both \ sides: \\ \sf \implies P = \frac{2Z}{s} - p$

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2 years ago

What is the scale factor for the set of similar figures?

Oksanka [162]

$k=\dfrac{7}{20}$

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2 years ago

A toy manufacturer wants to know how many new toys children buy each year. A sample of 1492 children was taken to study their pu

julia-pushkina [17]

By assuming the standard deviation of population 2.2 the confidence interval is 8.67 toys,8.94 toys.

Given sample size of 1492 children,99% confidence interval , sample mean of 8.8, population standard deviation=2.2.

This type of problems can be solved through z test and in z test we have to first find the z score and then p value from normal distribution table.

First we have to find the value of α which can be calculated as under:

α=(1-0.99)/2=0.005

p=1-0.005=0.995

corresponding z value will be 2.575 for p=0.995 .

Margin of error=z*x/d

where x is mean and d is standard deviation.

M=2.575*2.2/ $\sqrt{1492}$

=0.14

So the lower value will be x-M

=8.8-0.14

=8.66

=8.67 ( after rounding)

The upper value will be x+M

=8.8+0.14

=8.94

Hence the confidence interval will be 8.67 toys and 8.94 toys.

Learn more about z test at brainly.com/question/14453510

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8 0

1 year ago

Find the area of each figure

Anon25 [30]

Area of trapezoid = a + b/2 * h
a = 20, b = 9, h = 21/-16
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Area of the rectangle = l * w
l = 16, w = 20
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7 0

2 years ago

f(x) = 3 cos(x) 0 ≤ x ≤ 3π/4 evaluate the Riemann sum with n = 6, taking the sample points to be left endpoints. (Round your ans

Kruka [31]

Answer:

$\int_{0}^{\frac{3 \pi}{4}}3 \cos{\left(x \right)}\ dx\approx 3.099558$

Step-by-step explanation:

We want to find the Riemann sum for $\int_{0}^{\frac{3 \pi}{4}}3 \cos{\left(x \right)}\ dx$ with n = 6, using left endpoints.

The Left Riemann Sum uses the left endpoints of a sub-interval:

$\int_{a}^{b}f(x)dx\approx\Delta{x}\left(f(x_0)+f(x_1)+2f(x_2)+...+f(x_{n-2})+f(x_{n-1})\right)$

where $\Delta{x}=\frac{b-a}{n}$ .

Step 1: Find $\Delta{x}$

We have that $a=0, b=\frac{3\pi }{4}, n=6$

Therefore, $\Delta{x}=\frac{\frac{3 \pi}{4}-0}{6}=\frac{\pi}{8}$

Step 2: Divide the interval $\left[0,\frac{3 \pi}{4}\right]$ into n = 6 sub-intervals of length $\Delta{x}=\frac{\pi}{8}$

$a=\left[0, \frac{\pi}{8}\right], \left[\frac{\pi}{8}, \frac{\pi}{4}\right], \left[\frac{\pi}{4}, \frac{3 \pi}{8}\right], \left[\frac{3 \pi}{8}, \frac{\pi}{2}\right], \left[\frac{\pi}{2}, \frac{5 \pi}{8}\right], \left[\frac{5 \pi}{8}, \frac{3 \pi}{4}\right]=b$

Step 3: Evaluate the function at the left endpoints

$f\left(x_{0}\right)=f(a)=f\left(0\right)=3=3$

$f\left(x_{1}\right)=f\left(\frac{\pi}{8}\right)=3 \sqrt{\frac{\sqrt{2}}{4} + \frac{1}{2}}=2.77163859753386$

$f\left(x_{2}\right)=f\left(\frac{\pi}{4}\right)=\frac{3 \sqrt{2}}{2}=2.12132034355964$

$f\left(x_{3}\right)=f\left(\frac{3 \pi}{8}\right)=3 \sqrt{\frac{1}{2} - \frac{\sqrt{2}}{4}}=1.14805029709527$

$f\left(x_{4}\right)=f\left(\frac{\pi}{2}\right)=0=0$

$f\left(x_{5}\right)=f\left(\frac{5 \pi}{8}\right)=- 3 \sqrt{\frac{1}{2} - \frac{\sqrt{2}}{4}}=-1.14805029709527$

Step 4: Apply the Left Riemann Sum formula

$\frac{\pi}{8}(3+2.77163859753386+2.12132034355964+1.14805029709527+0-1.14805029709527)=3.09955772805315$

$\int_{0}^{\frac{3 \pi}{4}}3 \cos{\left(x \right)}\ dx\approx 3.099558$

5 0

2 years ago