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notsponge [240]
3 years ago
15

A large pizza has a diameter of 16 inches. What is the area of the top of the pizza?

Mathematics
2 answers:
Slav-nsk [51]3 years ago
8 0
The diameter of the large pizza is 16 inches, so its radius is 8 inches. The diameter of the small pizza is 8 inches, so its radius is 4 inches. Area of large pizza = pi(r2) = pi(82) = 64pi square inches.
blondinia [14]3 years ago
3 0

Answer:

64pi square inches

Step-by-step explanation:

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Is there statistically significant evidence that the districts with smaller classes have higher average test​ scores? The t​-sta
Musya8 [376]

Complete Question

The complete question is shown on the first uploaded image

Answer:

The  95% confidence interval is [670.03  , 673.97 ]

The  test statistics is t = 7.7

The  p-value  is    p-value  =  0

The <u>p-value</u>  suggests that the null hypothesis is<u> rejected </u>with a high degree of confidence. Hence  <u>there is</u> statistically significant evidence that the districts with smaller classes have higher average test score  

Step-by-step explanation:

From the question we are told that

   The sample size is  n =  408

    The sample mean is  \= y  =  672.0

   The standard deviation is  s = 20.3

Given that the confidence level  is 95% then the level of significance is  

   \alpha = (100 -95 )\% = 0.05

From the normal distribution table  the critical value of \frac{\alpha }{2} = \frac{0.05 }{2} is  

    Z_{\frac{\alpha }{2} } =  1.96

Generally  the margin of error is mathematically represented as  

     E  =  Z_{\frac{\alpha }{2} } *  \frac{s}{\sqrt{n} }

=>   E  =  1.96 *  \frac{20.3}{\sqrt{408} }

=>     E  =  1.970

Generally the 95% confidence interval is mathematically represented as

       \= y -E  < \mu <  \= y + E

=>     672.0 -1.970  < \mu < 672.0 +1.970

=>     670.03  < \mu < 673.97

=>     [670.03  , 673.97 ]

From the question we are told that

   Class size                                  small                                      large

  Avg.score(\= y)         \= y_1 = 683.7   \= y_2 =  676.0

   S_y                          S_{y_1} =20.2    S_{y_2} = 18.6

   sample size                             n_1 = 229        n_2 =  184

The  null hypothesis is  H_o :  \mu_1 - \mu_2 = 0

The alternative hypothesis is  H_a :  \mu_1 - \mu_2 > 0

Generally the standard error for the difference in mean is mathematically represented as

       SE =  \sqrt{\frac{S_{y_1}^2 }{n_1} +\frac{S_{y_2}^2 }{n_2}   }

=>     SE =  \sqrt{20.2^2 }{229} +\frac{18.6^2 }{184_2}   }

=>     SE =  1.913

Generally the test statistics is mathematically represented as

      t = \frac{\= y _1 - \= y_2 }{SE}

=>    t = \frac{683.7 - 676.0 }{1.913}

=>   t = 7.7

Generally the p-value is mathematically represented as

    p-value  =  P(t >  7.7 )

From the  z-table

        P(t >  7.7 ) =  0

So

   p-value  =  0

From the values we obtained and calculated we can see that p-value  <  \alpha

This mean that

The p-value  suggests that the null hypothesis is rejected with a high degree of confidence. Hence  there is statistically significant evidence that the districts with smaller classes have higher average test score  

4 0
3 years ago
Hunter wants to draw an obtuse equilateral triangle, but hes's having trouble drawing it. Is sush a triangle possible to draw? E
zavuch27 [327]

let's recall that the sum of all interior angles in a triangle is 180°.

an equi-lateral, equal sides, triangle has all sides that are equal.

sides that are equal will yield an equal opposite angle.

so if all sides are equal, all angles are equal, for a sum of 180°, that's only possible with 60°, 60° and 60° angles, and all of them are acute, none obtuse.

7 0
2 years ago
Is 4.0 27 greater than or less than 4.00 92?
Morgarella [4.7K]
Isnt it less ? Correct me if im wrong
8 0
3 years ago
Read 2 more answers
In a fruitsurvey 30 children choose their favorite fruit out of apples bananas and watermelon 10% shows up 30% shows bananas how
BlackZzzverrR [31]

Answer: 40%

Step-by-step explanation:

3 0
2 years ago
What is the equation of this graphed line?
Veseljchak [2.6K]

Answer:

Slope Intercept form of the equation is y  = \frac{1}{3} x - 9

Step-by-step explanation:

Here,  the two point line are given as  is A(-6,-3) and B(6,-7)

The slope of the line AB =  m = \frac{y_2 - y_1}{x_2 - x_1}

m = \frac{-7-(-3)}{6-(-6)}   = \frac{-7 + 3}{6 + 6}   = \frac{4}{12} \\\implies m = \frac{1}{3}

⇒ the slope of AB  is m =  (4/3)

By SLOPE  INTERCEPT FORMULA:

The equation of a line with slope m and a point (x0, y0) is given as

(y-y0)=  m (x-x0)

⇒ The equation of line with point (6,-7) is:  

y + 7 = \frac{1}{3} (x-6)  \implies  3y + 21  - x + 6 - 0\\or, -x + 3y + 27 = 0

Now, the given equation is -x + 3y  = -27

Convert it in the  SLOPE INTERCEPT FORM  y = mx + c

We get, 3y = x - 27

or, y = \frac{1}{3} x - \frac{27}{3} \\\implies y = \frac{1}{3} x - 9

Hence, the Slope Intercept form of the equation is y  = \frac{1}{3} x - 9

3 0
3 years ago
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