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yuradex [85]
3 years ago
14

A lawn in the shape of a trapezoid has an area of 1,800 square meters. The length of one base is 50 meters, and the length of th

e other base is 40 meters. What is the width of the lawn?​
Mathematics
1 answer:
Alona [7]3 years ago
6 0

9514 1404 393

Answer:

  40 m

Step-by-step explanation:

The area is given by the formula ...

  A = 1/2(b1 +b2)h

Using the given values, we can find h to be ...

  1800 = 1/2(50 +40)h

  3600 = 90h . . . . . . . . . multiply by 2

  40 = h . . . . . . . . . . . divide by 90

The width of the lawn is 40 meters.

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You need a 15% acid solution for a certain test, but your supplier only ships 5% solution and 17.5% solution. If you need 20 lit
Nimfa-mama [501]

Answer:

4 liters of 5% and 16 liters of 17.5%

Step-by-step explanation:

Let quantity of 5% be x liters and of 17.5% be y liters

x+y=20 hence y=20-x

Introducing percentages

0.05x+0.175(20-x)=0.15*20

0.05x+3.5-0.175x=3

-0.125x=-0.5

x=\frac {-0.5}{-0.125}=4

Therefore, y=20-x=20-4=16

You need 4 liters of 5% and 16 liters of 17.5% to achieve 20 liters of 15% acid solution

6 0
3 years ago
Read 2 more answers
Several years​ ago, 39​% of parents who had children in grades​ K-12 were satisfied with the quality of education the students r
BaLLatris [955]
<h2>Answer with explanation:</h2>

Let p be the population proportion  of parents who had children in grades​ K-12 were satisfied with the quality of education the students receive.

Given : Several years​ ago, 39​% of parents who had children in grades​ K-12 were satisfied with the quality of education the students receive.

Set hypothesis to test :

H_0: p=0.39\\\\H_a :p\neq0.39

Sample size : n= 1055

Sample proportion : \hat{p}=\dfrac{466}{1055}=0.441706161137\approx0.44

Critical value for 95% confidence : z_{\alpha/2}=1.96

Confidence interval : \hat{p}\pm z_{\alpha/2}\sqrt{\dfrac{p(1-p)}{n}}

0.44\pm (1.96)\sqrt{\dfrac{0.39(1-0.39)}{1055}}\\\\0.44\pm0.0299536805135\\\\0.44\pm0.03\\\\=(0.44-0.03, 0.44+0.03)\\\\=(0.41,\ 0.47)

Since , Confidence interval does not contain 0.39.

It means we reject the null hypothesis.

We conclude that 95​% confidence interval represents evidence that​ parents' attitudes toward the quality of education have changed.

8 0
3 years ago
a spherical balloon is deflated at a rate of 256pi/3 cm^3/sec. at what rate is the radius of the balloon changing when the radiu
Hunter-Best [27]
What you need to look for is \frac { dr }{ dt } when r=8.

Now:

Volume\quad of\quad a\quad sphere:\\ \\ V=\frac { 4 }{ 3 } \pi { r }^{ 3 }

\therefore \quad \frac { dV }{ dr } =\frac { 4 }{ 3 } \pi \cdot 3{ r }^{ 2 }=4\pi { r }^{ 2 }\\ \\ \therefore \quad \frac { dr }{ dV } =\frac { 1 }{ \frac { dV }{ dr }  } =\frac { 1 }{ 4\pi { r }^{ 2 } }

And:\\ \\ \frac { dV }{ dt } =-\frac { 256\pi  }{ 3 } \\ \\ Therefore:\\ \\ \frac { dr }{ dt } =\frac { dr }{ dV } \cdot \frac { dV }{ dt }

\\ \\ =\frac { 1 }{ 4\pi { r }^{ 2 } } \cdot -\frac { 256\pi  }{ 3 } \\ \\ =-\frac { 256 }{ 12 } \cdot \frac { \pi  }{ \pi  } \cdot \frac { 1 }{ { r }^{ 2 } }

\\ \\ =-\frac { 64 }{ 3{ r }^{ 2 } } \\ \\ When\quad r=8,\\ \\ \frac { dr }{ dt } =-\frac { 64 }{ 3\cdot { 8 }^{ 2 } } =-\frac { 1 }{ 3 } \\ \\ Answer:\quad -\frac { 1 }{ 3 } \quad cm/sec
3 0
4 years ago
The first four terms of an arithmetic sequence are -11,-5,1,7. what is the equation for an
mr_godi [17]

Answer:

y = 6x - 11

Step-by-step explanation:

An arithmetic sequence is a linear function. This means it steadily increases or decreases through addition/subtraction by a constant amount. Here the sequence grows by adding 6 each time.

-11 + 6 = -5

-5 + 6 = 1

1 + 6 = 7

etc....

Since this is linear, its equation has the form y = mx + b where m is the slope and b is the y-intercept. The slope is m = 6 and b = -11.

y = 6x - 11

7 0
3 years ago
What is the solutions for y=3x-5 and y=x-3
MArishka [77]

Answer: x=1, y=-2

Step-by-step explanation:

System

y=3x-5

y=x-3

3x-5=x-3

3x-x=-3+5

2x=2

x=2:2=1

y=x-3=1-3=-2

4 0
3 years ago
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