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Mkey [24]
3 years ago
6

A tent forms an equilateral triangular prism, with both triangular faces exposed. each side of the triangular face has a length

of 196196196 centimeters (\text{cm})(cm)left parenthesis, c, m, right parenthesis, and the tent is 250\,\text{cm}250cm250, space, c, m long. what is the height, in centimeters, of the tent?

Mathematics
1 answer:
Soloha48 [4]3 years ago
6 0
Given:
Equilateral Triangular Prism
Each side of the triangular face has a length of 196cm
The tent is 250cm long

I have attached an image of the tent. Since the height of the tent is also the height of the triangle, I will solve for the height of the triangle using Pythagorean theorem.

I divided the equilateral triangle into 2 right triangle. The height then becomes the long leg of the triangle. The hypotenuse is 196cm and the short leg is 98cm, half of one side of the triangle.

a² + b² = c²
a² = c² - b²
a² = (196cm)² - (98cm)²
a² = 38,416cm² - 9,604cm²
a² = 28,812cm²
a = √28,812cm² 
a = 169.74cm

The height of the tent is 169.74 centimeters. 

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Answer: (0.760, 0.820)

Step-by-step explanation:

Let p be the population proportion of all adults feel that "education and our schools" is one of the top issues facing California.

Given : 79% (actual results are 400 out of 506 surveyed) of California adults feel that "education and our schools" is one of the top issues facing California.

i.e.Sample size : n= 506

Sample proportion : \hat{p}=0.79

Critical value for 90% confidence interval ( Using z-value table) :

z=1.645

Now, the 90% confidence interval for the population proportion will be :

\hat{p}\pm z\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}

i.e. 0.79\pm (1.645)\sqrt{\dfrac{0.79(1-0.79)}{506}}

i.e. 0.79\pm (1.645)(0.0181)

\approx0.79\pm 0.030=(0.79-0.030,\ 0.79+0.030)\\\\=(0.760,\ 0.820)

Hence, the 90% confidence interval for the population proportion= (0.760, 0.820)

7 0
4 years ago
A taxi ride cost a flat fee of of $4.00 plus an additional $1.25 per mile. How many miles would a person travel if they paid $19
PIT_PIT [208]

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12 miles

Step-by-step explanation:

Subtract 19-4 to get you the price without the intial fee. The answer is 15. Then divide 15/1.25 to get you 12 miles.

6 0
3 years ago
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I really need help here ASAP​
AlexFokin [52]

Answer:

D. x=\frac{-4-\sqrt{31}}{3} or  x=\frac{-4+\sqrt{31}}{3}

Step-by-step explanation:

The given equation is:

3x^2+8x=5

Divide through by 3;

x^2+\frac{8}{3}x=\frac{5}{3}

Add the square of half the coefficient of x to both sides.

x^2+\frac{8}{3}x+(\frac{4}{3})^2=\frac{5}{3}++(\frac{4}{3})^2

x^2+\frac{8}{3}x+\frac{16}{9}=\frac{5}{3}+\frac{16}{9}

The left hand side is now a perfect square:

(x+\frac{4}{3})^2=\frac{31}{9}

Take square root

x+\frac{4}{3}=\pm \sqrt{ \frac{31}{9}}

x=-\frac{4}{3}\pm \sqrt{ \frac{31}{9}}

x=-\frac{4}{3}\pm \frac{\sqrt{31}}{3}

D. x=\frac{-4-\sqrt{31}}{3} or  x=\frac{-4+\sqrt{31}}{3}

5 0
3 years ago
At midnight what temperature is -6C. At midday the temperature is -9C. By how much did the temperature rise ?
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The polynomial equation x^4 + x^3 + x^2 + x + 1 = 0 has zero positive real roots. Please select the best answer from the choices
const2013 [10]

There are zero positive real roots for the given polynomial equation x^4 + x^3 + x^2 + x + 1 = 0. This is explained by Descarte's rule of signs. So, the best choice is T (true).

<h3>What is Descarte's rule of signs?</h3>
  • Descarte's rule of signs tells about the number of positive real roots and negative real roots.
  • The number of changes in signs of the coefficients of the terms of the given polynomial f(x) gives the positive real zeros of the polynomial.
  • The number of changes in signs of the coefficients of the terms of the given polynomial when f(-x) gives the negative real zeros of the polynomial.

<h3>Calculation:</h3>

The given polynomial equation is x^4 + x^3 + x^2 + x + 1 = 0

On applying Descarte's rule of signs,

f(x)=x^4 + x^3 + x^2 + x + 1

Since there are no changes in the signs of the coefficients of any of the terms in the above polynomial, the polynomial has no positive real roots.

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Since there are four changes in the signs of the coefficients of the terms of the given polynomial when f(-x), the polynomial has 4 negative real roots.

Therefore, the given polynomial equation has zero positive real roots. So, the correct choice is T(true).

Learn more about Descarte's rule of signs here:

brainly.com/question/11590228

#SPJ1

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