Please help me answer this

Andy is building a model of a square pyramid for a class project. The side length of the square base is 11 inches and the slant

Wewaii [24]

Answer:

The surface area of the model pyramid is $451\ in^{2}$

Step-by-step explanation:

we know that

The surface area of the pyramid is equal to

$SA=B+LA$

where

B is the area of the base of the pyramid

LA is the lateral surface of the pyramid

Find the area of the base B

$B=11^{2}=121\ in^{2}$ -----> is a square

Find the lateral surface area of the pyramid LA

we know that

The lateral surface area is equal to the area of its four triangular faces

$LA=4[\frac{1}{2}(11)(15)]=330\ in^{2}$

Find the surface area of the pyramid

Substitute the values

$SA=121+330=451\ in^{2}$

6 0

3 years ago

A professor of women's studies is interested in determining if stress affects the menstrual cycle. Ten women are randomly sample

BabaBlast [244]

Answer:

Null hypothesis: $\mu_1 = \mu_2$

Alternative hypothesis: $\mu_1 \neq \mu_2$

$t=\frac{(20.4 -27.6)-(0)}{\sqrt{\frac{2.074^2}{5}}+\frac{2.702^2}{5}}=-4.73$

$df=5+5-2=8$

$t_{crit}=\pm 2.306$

Reject H0: stress affects the menstrual cycle

Step-by-step explanation:

The statistic is given by the following formula:

$t=\frac{(\bar X_1 -\bar X_2)-(\mu_{1}-\mu_2)}{\sqrt{\frac{s^2_1}{n_1}}+\frac{s^2_2}{n_2}}$

Where t follows a t distribution with $n_1+n_2 -2$ degrees of freedom

The system of hypothesis on this case are:

Null hypothesis: $\mu_1 = \mu_2$

Alternative hypothesis: $\mu_1 \neq \mu_2$

Or equivalently:

Null hypothesis: $\mu_1 - \mu_2 = 0$

Alternative hypothesis: $\mu_1 -\mu_2 \neq 0$

Our notation on this case :

$n_1 =5$ represent the sample size for group 1

$n_2 =2$ represent the sample size for group 2

Tha data given is:

Group 1 (High stress) : 20,23,18,19,22

Group 2 (Relatively stress free): 26,31,25,26,30

We can calculate the sample mean and the sample deviation with the following formulas:

$\bar X =\frac{\sum_{i=1}^n x_i}{n}$

$s=\sqrt{\frac{\sum_{i=1}^n (x_i -\bar X)^2}{n-1}}$

$\bar X_1 =20.4$ represent the sample mean for the group 1

$\bar X_2 =27.6$ represent the sample mean for the group 2

$s_1=2.074$ represent the sample standard deviation for group 1

$s_2=2.702$ represent the sample standard deviation for group 2

And now we can calculate the statistic:

$t=\frac{(20.4 -27.6)-(0)}{\sqrt{\frac{2.074^2}{5}}+\frac{2.702^2}{5}}=-4.73$

Now we can calculate the degrees of freedom given by:

$df=5+5-2=8$

Now we can calculate the critical value since the confidence is 95% the value for the significance would be $\alpha=1-0.95=0.05$ and the value for $\alpha/2 =0.025$ and if we find a critical value on th t distribution with 8 degrees of freedom that accumulates 0.025 of the area on each tail we got $t_{crit}=\pm 2.306$

Since our calculated value is lower than the critical value, we have enough evidence to reject the null hypothesis. And makes sense say that the difference between the two means are different at 5% of significance.

Reject H0: stress affects the menstrual cycle

5 0

3 years ago

Which would be appropriate compatible numbers to use to estimate (19 4/5) (4/6) A. 16(1/3) B. 19(2/3) C. 20(1/2) D. 20(1)

podryga [215]

Answer:

C. 20(1/2)

Step-by-step explanation:

Let's find the value of the expression before looking for the nearest estimate

(19 4/5) (4/6) = 19 *(4/5)(4/6)

(19 4/5) (4/6) = 19(16/30)

(19 4/5) (4/6) = 19(8/15)

(19 4/5) (4/6) = (19*8)/15

(19 4/5) (4/6) = 152/15

(19 4/5) (4/6) = 10(2/15)

A. 16(1/3) =5.33

B. 19(2/3) = 12.667

C. 20(1/2) = 10

D. 20(1)= 20

The nearest to the expression is C. 20(1/2)

6 0

3 years ago

Determine if the listed line is tangent to the circle

777dan777 [17]

Answer:

SEG KL is not a tangent coz Pythagoras theorem doesn't apply here
SEG GH is not a tangent coz Pythagoras theorem doesn't apply here
SEG GF is not a tangent coz Pythagoras theorem doesn't apply here
SEG FG is not a tangent coz Pythagoras theorem doesn't apply here
SEG XY is a tangent Pythagoras theorem apply here 24²+7²=25²
SEG XY is not a tangent coz Pythagoras theorem doesn't apply here

8 0

3 years ago

Victor is picking out some movies to rent, and he is primarily interested in comedies and mysteries. He has narrowed down his se

aliya0001 [1]

Answer: 1020 ways

Step-by-step explanation:

Let C= comedy

Let M= Mystery

Number of movies(comedy) = 10

Number of movies (mystery) = 10

The total number of movies from which selection is to be made is 10 + 10

= 20

We want to pick 3 movies from 10 comedies and 10 mysteries with at least one mystery.

The selection will be from;

Unconditional selection - (0 mysteries)

=unconditional selection - ( all comedy included)

= 20C3 - 10C3 For combination, [nCr = n! /(n-r) r! ]

= [20!/(20-3)!3!] - [10!/(10-3)!3!

= (6840/6) - (720/6)

= 1140 - 120

= 1020 ways

3 0

3 years ago