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3 years ago

How do you do number 14?

Mathematics

1 answer:

Dimas [21]3 years ago

4 0

Answer: 3/8

Step-by-step explanation:

When three coins are flipped, we get 8 total outcomes: (HHH,HHT,HTH,HTT,THH,THT,TTH,TTT)

Two tails and one head is (HTT, TTH, THT)

Probability = number of favorable outcomes/ number of total outcomes

Number of Favorable outcomes = 3

Number of Total outcomes= 8

Therefore, probability of getting 2 tails and one head

= 3/8

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Angles α and β are the two acute angles in a right triangle. Use the relationship between sine and cosine to find the value of β

Dimas [21]

Answer:

From given relation the value of β is 37.5°

Step-by-step explanation:

Given as :

α and β are two acute angles of right triangle

Acute angle have measure less than 90°

Now given as :

$sin(\frac{x}{2} + 2x)$ = $cos(2x +\frac{3x}{2})$

Or, $cos(90° - (\frac{x}{2}+2x))$ = $cos(2x +\frac{3x}{2})$

SO, $(90° - (\frac{x}{2}+2x))$ = $2x+\frac{3x}{2}$

Or, 90° = $2x+\frac{3x}{2}$ + $\frac{x}{2}+2x$

or, 90° = $\frac{4x}{2}$ + 4x

Or, 90° = $\frac{12x}{2}$

So, x = $\frac{90}{6}$ = 15°

∴ $sin(\frac{x}{2} + 2x)$ = $sin(\frac{15}{2} + 30)$

So, $sin(\frac{x}{2} + 2x)$ = sin $\frac{75}{2}$

∴ The value of Ф_1 = $\frac{75}{2}$ = 37.5°

Similarly $cos(2x +\frac{3x}{2})$ = $cos(30 +\frac{45}{2})$

So ,The value of Ф_2 = $\frac{105}{2}$ = 52.5°

∵ β α

So, As 37.5°52.5°

∴ β = 37.5°

Hence From given relation the value of β is 37.5° Answer

7 0

3 years ago

If John pays $144 for 9 pounds of pears, how much is each pound

Artist 52 [7]

Answer:

$16 per pound

Step-by-step explanation:

We want to find the price per pound.

Therefore, we must divide the cost by the pounds.

$\frac{cost}{pounds}$

We know it costs $144 for 9 pounds of pears. Therefore, $144 is the cost and there are 9 pounds.

$\frac{\$144}{9 pounds}$

Divide.

$\$16 /pound$

It costs $16 for each pound of pears.

5 0

3 years ago

Read 2 more answers

What is the point called where the perpendicular bisectors of the sides of a triangle intersect

Vikki [24]

Answer: Circumcenter

This is the center of the circle that goes through the three vertices of the triangle. This circle is known as the circumcircle. It is the smallest circle possible in which the circle encompasses the triangle and none of the triangle spills outside the circle.

6 0

3 years ago

HELPPPP DUE SOON!!! WILL MARK BRAINLYIST AND 10 POINTS

larisa86 [58]

Answer:

688.7

Step-by-step explanation:

Top and Bottom

Area = 3/4 * pi * r^2

r = 6

Area = 3/4 * 3.14 * 6^2

Area = 84.78

Don't round yet.

Vertical surface

Vertical surface = 3/4 * pi * d * h

d = 12 inches (the diameter)

Vertical surface = 3/4 * 3.14 * 12 * 15

Vertical surface = 423.9

Two inner faces

They are both rectangles

Area = 2 * L * W

L = 15

w=6

Area = 2 * 15 * 6 <u> 180</u>

Total 688.68

Total = 688.7

7 0

2 years ago

A private and a public university are located in the same city. For the private university, 1038 alumni were surveyed and 647 sa

Snezhnost [94]

Answer:

The difference in the sample proportions is not statistically significant at 0.05 significance level.

Step-by-step explanation:

Significance level is missing, it is α=0.05

Let p(public) be the proportion of alumni of the public university who attended at least one class reunion

p(private) be the proportion of alumni of the private university who attended at least one class reunion

Hypotheses are:

$H_{0}$ : p(public) = p(private)

$H_{a}$ : p(public) ≠ p(private)

The formula for the test statistic is given as:

z= $\frac{p1-p2}{\sqrt{{p*(1-p)*(\frac{1}{n1} +\frac{1}{n2}) }}}$ where

p1 is the sample proportion of public university students who attended at least one class reunion ( $\frac{808}{1311}=0.616$ )

p2 is the sample proportion of private university students who attended at least one class reunion ( $\frac{647}{1038}=0.623$ )

p is the pool proportion of p1 and p2 ( $\frac{808+647}{1311+1038}=0.619$ )

n1 is the sample size of the alumni from public university (1311)

n2 is the sample size of the students from private university (1038)

Then z= $\frac{0.616-0.623}{\sqrt{{0.619*0.381*(\frac{1}{1311} +\frac{1}{1038}) }}}$ =-0.207

Since p-value of the test statistic is 0.836>0.05 we fail to reject the null hypothesis.

6 0

3 years ago