I really need help on both of these please.

What is the length of the missing leg? If necessary, round to the nearest tenth.

Marrrta [24]

Answer:

The length of the hypotenuse is 33 yards.

Step-by-step explanation:

We can solve for 'a' using Pythagoras theorem. Let's solve it.

65² = b² + 56²
=> 4225 = b² + 3136
=> b² = 1089
=> b = 33

Hence, the length of the hypotenuse is 33 yards.

Hoped this helped.

$BrainiacUser1357$

7 0

2 years ago

The data represents the number of runs allowed by 8 college softball pitchers. {18, 49, 38, 41, 33, 44, 42, 22}

lawyer [7]

This Question is incomplete

Complete Question:

The data represents the number of runs allowed by 8 college softball pitchers. {18, 49, 38, 41, 33, 44, 42, 22}

What is the five number summary:

a) Minimum

b) Q₁

c) Median

d) Q₃

e) Maximum

Answer:

a) Minimum = 18

b) Q₁ = 27.5

c) Median = 39.5

d) Q₃ = 43

e) Maximum = 49

Step-by-step explanation:

From the above diagram, we were given the following set of data.

{18, 49, 38, 41, 33, 44, 42, 22}

Before answering any of the questions, we have to rearrange the data from the lowest to the highest (ascending order). Hence, we have:

{18, 22, 33, 38, 41, 42, 44, 49}

a) Minimum

{18, 22, 33, 38, 41, 42, 44, 49}

Looking at this set of arranged data, the minimum number is the least or lowest number.

This number is 18

b) Q₁

{18, 22, 33, 38, 41, 42, 44, 49}

Q₁ means First Quartile. The formula is = ¼(n + 1)th value

n = Number of terms in the data set = 8

= ¼(8 + 1)th value

= ¼(9)th value

= 2 1/4 value

= 2.25 value

In the above Question, the 2.25 value is the value between the second and third number.

Hence:

22+33/2 = 55/2 = 27.5

Therefore, Q₁ = 27.5

c) Median

{18, 22, 33, 38, 41, 42, 44, 49}

The median of the number is the number in the middle

For this data, we have 8 number, Hence the median is the sum of the 4th and 5th term divided by 2

4th term = 38

5th term = 41

= 38 + 41/ 2 = 79/2

= 39.5

Hence, the median = 39.5

d) Q₃

{18, 22, 33, 38, 41, 42, 44, 49}

Q₃ means Third Quartile. The formula is = ¾(n + 1)th value

n = Number of terms in the data set = 8

= ¾(8 + 1)th value

= ¾(9)th value

= 6 3/4 value

= 6.75 value

In the above Question, the 6.75 value is the value between the sixth and seventh number.

Hence:

42+44/2 = 86/2 = 43

Therefore, Q₃ = 43

e) Maximum

{18, 22, 33, 38, 41, 42, 44, 49}

Looking at this set of arranged data, the Maximum number is the highest number.

This number is 49

6 0

3 years ago

A teacher was interested in finding out whether a special study program would increase the scores of students on a national exam

bija089 [108]

Answer:

Check the explanation

Step-by-step explanation:

Going by the first attached image below we reject H_o against H_1 if obs. $T > t_{\alpha /2;n-1}$

here obs.T=1.879

$\therefore obs.T \ngtr 2.447=t_{0.025;6}$

we accept $H_o:\mu _{1}=\mu_{2}$ at 5% level of significance.

i.e there is no sufficient evidence to indicate that the special study program is more effective at 5% level of significance.

1.

this problem is simillar to the previous one except the alternative hypothesis.

Let X_i's denote the bonuses given by female managers and Y_i's denote the bonuses given by male managers.

we assume that $X_i \sim N(\mu _{1},\sigma _{1}^{2}) Y_i \sim N(\mu _{2},\sigma _{2}^{2})$ independently

We want to test $H_0:\mu_{1}=\mu_{2} vs H_1:\mu_{1}\neq \mu_{2}$

define $D_i=X_i-Y_i , i=1(1)8$

now $D_i\sim N(\mu _{1}-\mu _{2}=\mu _{D},\sigma _{1}^{2}+\sigma _{2}^{2}=\sigma _{D}^{2}) , i=1(1)8$

the hypothesis becomes

$H_0:\mu_{D}=0 vs H_1:\mu_{D}\neq 0$

in the third attached image, we use the same test statistic as before

i.e at 5% level of significance there is not enough evidence to indicate a difference in average bonuses .

3 0

2 years ago

If the 7th of an AP is equal to 11 times the 11th term, find the 18th term

Zina [86]

Answer:

-33 or 33

Step-by-step explanation:

The seventh term of an AP is written as:

$a + 6d$

The eleventh term of an AP is written as:

$a + 10d$

If the 7th term is 11 times the 11th term, then;

$a + 6d = 11(a + 10d)$

Expand to get:

$a + 6d = 11a + 110d$

$11a - a = 6d - 110d$

$10a = - 104d$

$\frac{a}{d} = - \frac{104}{10}$

$\frac{a}{d} = - \frac{52}{5}$

We must have a=-52 and d=5

Or

a=52 and d=-5

For the first case, the 18th term is :

$- 52 + 5 \times 17 = 33$

For the second case,

$52 - 5 \times17 = - 33$

3 0

3 years ago

69, 62, 64, 67, 62, 64, 63, 65, 60, 64 1. Find the mean, median, and mode

marta [7]

First order them from the smallest number 60
to the biggest number 69

Mean:582.4

Median:64

Mode:62 and 64

4 0

3 years ago