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Sergeeva-Olga [200]
2 years ago
15

If the area of a square with side x is equal to the area of a triangle with base x, then find the altitude of the triangle.

Mathematics
1 answer:
zhannawk [14.2K]2 years ago
3 0

Answer:

h= 2x

Step-by-step explanation:

Given

Square

Side = x

Triangle

Base = x

Altitude = h

Required

Find h, if both shapes have the same area

The area of the square is:

Area = x * x

Area = x^2

The area of the triangle is:

Area = \frac{1}{2} * Base*Height

Area = \frac{1}{2} * x*h

Equate both areas

x^2 = \frac{1}{2} * x*h

Divide both sides by x

x = \frac{1}{2} *h

Multiply both sides by 2

2*x = \frac{1}{2} *h*2

2x = h

h= 2x

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The product of a number, x, and six is four more than the product of the number and three-eighths. Which answer represents this
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Answer:

6x = 3/8x + 4

Step-by-step explanation:

The product of a number (x) and 6 ... 6x

is ... =

four more than ... ___ +4

the product of the number and 3/8 ... 3/8x . . . . (goes in the blank that is added to 4).

Thus, this statement is directly translated to ...

... 6x = 3/8x + 4

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3 years ago
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A survey asked whether respondents favored or opposed the death penalty for people convicted of murder. Software shows the resul
pav-90 [236]

Answer:

95% confidence interval for the proportion of the adults who were opposed to the death penalty is (0.668, 0.704).

Step-by-step explanation:

We are given that a survey asked whether respondents favored or opposed the death penalty for people convicted of murder. Software shows the results below, where X refers to the number of the respondents who were in favor.

X = 1,790

N = 2,610

\hat p = Sample proportion = X/N = 0.6858

Firstly, the pivotal quantity for 95% confidence interval for the population proportion  is given by;

     P.Q. = \frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }  ~ N(0,1)

where, \hat p = sample proportion = 0.6858

           n = sample of respondents = 2,610

           p = population proportion

<em>Here for constructing 95% confidence interval we have used One-sample z proportion statistics.</em>

So, 95% confidence interval for the population​ proportion, p is ;

P(-1.96 < N(0,1) < 1.96) = 0.95  {As the critical value of z at

                                   2.5% level of significance are -1.96 & 1.96}

P(-1.96 < \frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } } < 1.96) = 0.95

P( -1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } } < {\hat p-p} < 1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } } ) = 0.95

P( \hat p-1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } < p < \hat p+1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } } ) = 0.95

<u>95% confidence interval for p</u> = [ \hat p-1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } , \hat p+1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} }]

  = [ 0.6858-1.96 \times {\sqrt{\frac{0.6858(1-0.6858)}{2610} } , 0.6858+1.96 \times {\sqrt{\frac{0.6858(1-0.6858)}{2610} } ]

  = [0.668 , 0.704]

Therefore, 95% confidence interval for the population proportion of the adults is (0.668, 0.704).

3 0
3 years ago
A square has a perimeter of 28 centimeters.<br> What is the square's area, in square centimeters?
fiasKO [112]

Answer:

The answer is 49

Step-by-step explanation:

The perimeter is the sum of all four sides so 28 divided by 4 would be 7 and 7 x 7 = 49

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5 0
3 years ago
Whats the density of an object with the length of 5.0 cm a height of 3.0 and width of 15.0 cm and a mass of 24 grams
Sphinxa [80]

Answer:

The density of the object is 0.1067 grams per cubic centimeter. (Rounded off to 4th decimal)

Step-by-step explanation:

Density = [Mass/Volume]

Here we have been given the dimensions of the object.

Volume = Height * Width * Length

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Now we can substitute the Mass and the Volume to the density equation.

Density = [Mass/Volume]

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3 x + 2 y = − 6.<br><br> help me find the y and the x<br><br> x y<br> -4<br> 0<br> 0 –3
Maru [420]

Answer:

x = 0 and y = -3

Step-by-step explanation:

3 (0) = 0

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5 0
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