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3 years ago

Find the area of a circle with a circumference of 31.4 units.

Mathematics

2 answers:

Elden [556K]3 years ago

3 0

Answer:

area = 78.46

Step-by-step explanation:

31.4 = 2pi * r

divide 31.4 by 2 and get 15.7

15.7 = pi * r

divide 15.7 by pi and get

4.997 = r

(4.997^2) * pi = 78.46

Alexandra [31]3 years ago

3 0

Answer:

I agree with you. that is what I got too

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A pizza shop delivered 17 pepperoni pizzas to a college on the first night of final exams. The total cost of the pizzas was &amp

Allushta [10]

Answer:

Step-by-step explanation:

Let x = number of small pizzas

Let y = number of medium pizzas

Let z = number of large pizzas

Total weight of pizza = 9 *16 +8 = 152

Total pizza = 17

Total amount = $153

x + y + z = 17 - equation 1

4x + 6y + 15z = 153 - equation 2

3x + 9y + 14z = 152 - equation 3

from equation 1, x = 17 -y -z - equation *

substitute in both 2 and 3

4(17 -y -z) + 6y + 15z = 153 ---- 1

3(17 -y -z) +9y +14z = 152 --- 2

68 - 4y - 4z +6y + 15z = 153 ----i

51 - 3y - 3z + 9y + 14z = 152 ---ii

2y + 11z = 85 ---1

6y +11z = 101 ----2

equation 2 minus equation 1

4y = 16 => y = 4

substitute y in equation 1

8 + 11z = 85 => 11z = 77 => z = 7

subtitute y as 4 and z as 7 in equation *

x = 17 - 4 -7 => x = 6

So, 6 small pizzas, 4 medium and 7 big pizzas were delivered

8 0

4 years ago

Suppose μ1 and μ2 are true mean stopping distances at 50 mph for cars of a certain type equipped with two different types of bra

Stella [2.4K]

Answer:

The 95% confidence interval would be given by $-23.44 \leq \mu_1 -\mu_2 \leq -8.16$

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

$\bar X_1 =114.1$ represent the sample mean 1

$\bar X_2 =129.9$ represent the sample mean 2

n1=5 represent the sample 1 size

n2=2 represent the sample 2 size

$s_1 =5.08$ sample standard deviation for sample 1

$s_2 =5.37$ sample standard deviation for sample 2

$\mu_1 -\mu_2$ parameter of interest.

Confidence interval

The confidence interval for the difference of means is given by the following formula:

$(\bar X_1 -\bar X_2) \pm t_{\alpha/2}\sqrt{\frac{s^2_1}{n_1}+\frac{s^2_2}{n_2}}$ (1)

The point of estimate for $\mu_1 -\mu_2$ is just given by:

$\bar X_1 -\bar X_2 =114.1-129.9=-15.8$

In order to calculate the critical value $t_{\alpha/2}$ we need to find first the degrees of freedom, given by:

$df=n_1 +n_2 -1=5+5-2=8$

Since the Confidence is 0.95 or 95%, the value of $\alpha=0.05$ and $\alpha/2 =0.025$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.025,8)".And we see that $t_{\alpha/2}=\pm 2.31$