Find the volume of this sphere.Use 3 for TT..V ?20 ftV ==Tr3Hint: The radius (r) is1/2 of the diameter.

step 1

Find out the measure of angle P

Remember that the sum of the interior angles in any triangle must be equal to 180 degrees

so

P+Q+R=180 degrees

substitute given values

P+70+60=180

P=180-130

P=50 degrees

step 2

Applying the law of sines

QR/sin P=PR/sin 70

substitute given values

QR/ sin 50=5/sin 70

QR=(5/sin 70)*sin 50

Answer:

Q is greater than P by 291

Step-by-step explanation:

The terms of these Arithmetic Sequences are odd natural numbers, because their common difference is 2

And, sum of 'n' odd natural numbers starting from 1 = n²

P = 99² - (1) = 9800

Q = 101² - (1 + 3 + 5) = 10192

Q - P = 291

Answer:

C - 3/4

Step-by-step explanation:

The value of m∠Y in triangle XYZ is 99°

An equation is used to show the relationship between two or more numbers and variables.

In triangle XYZ, the angles are angle x, y and z. Hence:

∠X + ∠Y + ∠Z = 180° (sum of angles in a triangle)

Substituting:

38 + (5x -11) + (4x -45) = 180

Collecting like terms:

9x - 18 = 180

9x = 198

x = 22

m∠Y = 5(22) - 11 = 99°

m∠Y is 99°

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Answer:

See below

Step-by-step explanation:

Period = 1/2 year    total 4years = 8 periods

i = interest per period in decimal form = .12/2 = .06

initial deposit = ?

Final value = 60 000

60 000 = ? ( 1 + .06)^8

? = 37644.74

Answers:

[tex]\cos(\theta) = \frac{-3\sqrt{5}}{7}\\\\\tan(\theta) = -\frac{2}{3\sqrt{5}} = -\frac{2\sqrt{5}}{15}\\\\\csc(\theta) = \frac{7}{2}\\\\\sec(\theta) = -\frac{7}{3\sqrt{5}} = -\frac{7\sqrt{5}}{15}\\\\\cot(\theta) = \frac{-3\sqrt{5}}{2}\\\\[/tex]

=================================================

Explanation:

We're given that [tex]\sin(\theta) = \frac{2}{7}\\\\[/tex]

Plug that into the pythagorean trig identity [tex]\sin^2(\theta)+\cos^2(\theta) = 1\\\\[/tex] and solve for cosine to find that [tex]\cos(\theta) = \frac{-3\sqrt{5}}{7}\\\\[/tex]

I skipped steps in solving so let me know if you need to see them.

Keep in mind that cosine is negative in quadrant 2

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Once you've determined cosine, divide sine over cosine to get tangent

[tex]\tan(\theta) = \sin(\theta) \div \cos(\theta)\\\\\tan(\theta) = \frac{2}{7} \div \frac{-3\sqrt{5}}{7}\\\\\tan(\theta) = \frac{2}{7} \times -\frac{7}{3\sqrt{5}}\\\\\tan(\theta) = -\frac{2*7}{7*3\sqrt{5}}\\\\\tan(\theta) = -\frac{2}{3\sqrt{5}}\\\\\tan(\theta) = -\frac{2\sqrt{5}}{3\sqrt{5}*\sqrt{5}}\\\\\tan(\theta) = -\frac{2\sqrt{5}}{3*5}\\\\\tan(\theta) = -\frac{2\sqrt{5}}{15}\\\\[/tex]

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To determine cosecant, we apply the reciprocal to sine.

[tex]\sin(\theta) = \frac{2}{7} \to \csc(\theta) = \frac{1}{\sin(\theta)} = \frac{7}{2}\\\\[/tex]

Similarly, secant is the reciprocal of cosine

[tex]\cos(\theta) = \frac{-3\sqrt{5}}{7} \to \sec(\theta) = \frac{1}{\cos(\theta)} = -\frac{7}{3\sqrt{5}} = -\frac{7\sqrt{5}}{15}\\\\[/tex]

Depending on your teacher, rationalizing the denominator may be optional.

Lastly, cotangent is the reciprocal of tangent

[tex]\tan(\theta) = -\frac{2}{3\sqrt{5}}\to \cot(\theta) = \frac{1}{\tan(\theta)} = \frac{-3\sqrt{5}}{2}[/tex]

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Side notes:

Sine and cosecant are the only things positive in Q2

Everything else (cosine, tangent, secant, cotangent) are negative in Q2.

Answer:

644

Step-by-step explanation:

-4x23=-92

-92x-7=644

i hope this helped :)

The expresion is:

to find the intercepts with the x axis we have to rplace in the equation y = 0, so:

and we solve for x

the intersection with the x axis is -2

And for the itercepts with the y axis we replace x = 0

and we solve for y

This means that the intersepts with the y axis is -8

Answer:

A. 1 over z raised to the twelfth power

Step-by-step explanation:

Hope this helps! :))
Please tell me if this is incorrect

Answer:

1 over z raised to the twelfth power

Step-by-step explanation:

Two parallel lines has the same slope.

The given line:

Is written in the form y=mx+b where m is the slope.

The slope is 8

To find the parallel line you need to write the given options in the form y=mx+b by solving y, as follow:

Slope is -1/8 (it is not parallel to given line)

_______________

Slope is 1/8 (it is not parallel to given line)

________________

Slope is -8 (it is not parallel to given line)

Differentiate using the product rule:

g. We take out the constant:

So:

Now

Substituting the derivatives found:

Simplify:

Answer:

Answer:

[tex]15xy+6x[/tex]

Given the group of 175 college students who took math last term:

(a) You can identify in the table that the total number of students that passed math is:

Therefore, knowing the total number of students that were interviewed, you can determine that the percentage of the students who passed math is:

(b) Based on the data shown in the table, the total number of students who live on campus is:

Therefore, you can determine that the percentage of the students who live on campus is:

(c) You can identify that 49 students live on campus and passed math. Therefore, the percentage of the students who live on campus and passed math is:

(d) Knowing that 63.6% of the students who live on campus passed math, 40% of the student who live on campus, and 44% of the students interviewed passed math, you can identify that students who live on campus tend to pass math more often than average, because:

Hence, the answers are:

(a)

(b)

(c)

(d) Last option.

Answer:

400

Step-by-step explanation:

4 x 10^, 20^2

Answer:

25 pounds  16 ounces = 6400

Step-by-step explanation:

Hello!

What is a slope-intercept line:

 [tex]y = mx + b[/tex]

            [tex]slope = \dfrac{y_2-y_1}{x_2-x_1} =\frac{-4--2}{3-0} =-\dfrac{2}{3}[/tex]

           ==> value of y-intercept is '-2'

Thus the equation is [tex]y=-\dfrac{2}{3}x-2[/tex]

Hope that helps!

Answer: y=-2/3x-2

Step-by-step explanation:

1) Draw a triangle from one point to the next point.

For this example, I will use (-3,0) and (0,-2).

You can see that the number goes down 2 and right 3. From this, you can conclude that the rate is -2/3 using the equation rise/run.

2) Find the y-intercept

Looking at the graph, you can find that the y-intercept is (0,-2).

3) Fill in the y=mx+b

y=-2/3x-2

Answer:

26

Step-by-step explanation:

PEMDAS

8 + 2 = 10

6 - 4 = 2

10 x 2 = 20

2 x 3 = 6

20 + 6 = 26

The range of the graph is 0 <= M <= 5.5

The range of a function is the set of output values of the graph.

This in other words mean the range of a function is the set of y values of the graph.

The domain

On the graph of the function, we can see that:

The x values start from 0 and it ends at 7.5

This means that the domain is 0 <= x <= 7.5

The range

On the graph of the function, we can see that:

The x values start from 0 and it ends at 5.5

This means that the range is 0 <= M <= 5.5

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Answer:

0 <= M <= 5.5

Step-by-step explanation:

The value of the base is 7 (option A)

Given:

To find:

To complefe the sentence by ill ingthe blanks

In powers and exponents:

The value of the base is 7 (option A)

Simplify the given expression as shown below

we know that

There are: 9 ways to put the first trophy.

8 ways to put the second trophy after putting the first one.

7 ways to put the third trophy after putting the second one.

6 ways .............the third one

5 ways --------> the fourth

4 ways------> 5

3 ways -----> 6

2 ways ----> 7

1 ways-----> 8

therefore

n!

where n=9

9!=9*8*7*6*5*4*4*2*1

9!=362,880

the answer is

The Greatest common factors for each pair of numbers are;

1, ( 9 , 15 ) = 3

2. ( 12 , 18 ) = 6

3. ( 15 , 27 ) = 3

4. (30, 54) = 6

What is Greatest common factors?

The highest number that divides exactly into two more numbers, is called  Greatest common factors.

Given that;

The pairs of numbers are;

1, ( 9 , 15 )

2. ( 12 , 18 )

3. ( 15 , 27 )

4. (30, 54)

Now,

Find the Greatest common factors of the pairs of the numbers as;

1, ( 9 , 15 )

LCM of 9 = 3 x 3

LCM of 15 = 3 x 5

So, GCF of 9 and 15 = 3

2. ( 12 , 18 )

LCM of 12 = 2 x 3 x 2

LCM of 18 = 3 x 3 x 2

So, GCF of 12 and 18 = 3 x 2 = 6

3. ( 15 , 27 )

LCM of 15 = 3 x 5

LCM of 27 = 3 x 3 x 3

So, GCF of 15 and 27 = 3

4. (30, 54)

LCM of 30 = 2 x 3 x 5

LCM of 18 = 3 x 3 x 2

So, GCF of 30 and 54 = 3 x 2 = 6

Thus, The Greatest common factors for each pair of numbers are;

1, ( 9 , 15 ) = 3

2. ( 12 , 18 ) = 6

3. ( 15 , 27 ) = 3

4. (30, 54) = 6

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We are given the following function:

We will take "-6" as a common factor:

Now, we will complete the square in the expression inside the parenthesis by adding and subtracting the following term:

Answer:

264.9 in³

Explanation:

The volume of a cone can be calculated using the following equation:

Where π is approximately 3.14, r is the radius of the cone and h is the height.

So, replacing r by 5 in and h by 10.125 in, we get:

Therefore, the volume of the cone is 264.9 in³

This question has to do with the change in the subject of the formula.

So we will proceed thus:

The correct answer, therefore, is the third option:

Let's draw the figure to better understand the scenario:

Let,

s = the measure of the sides of the square

For us to be able to determine the area, let's first find out the measure of its side.

We will be using the Pythagorean Theorem:

Let's now determine the area of the square:

Therefore, the area of the square is 16.