A ball of radius 14 has a round hole of radius 4 drilled through its center.
Find the volume of the resulting solid.

The phrases which describe the graph are;

The absolute function in the task conten is;

f(x) = |x|, Hence, the domain and range of the graph are as described above.

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The polynomial function with real coefficients of a least possible degree having zero 2 of multiplicity 2, and zero i of single multiplicity is                   x⁴ - 4x³ + 5x²- 4x + 4 = 0. This can be obtained by finding factors and multiplying them.  

Given that zeroes, 2 of multiplicity 2, and i of single multiplicity, that is,       (x - 2), (x - i) and (x + i) are the factors of the polynomial.

Thus the polynomial can be written as  

(x - 2)²(x - i)(x + i) = 0 ((x - 2) is squared as multiplicity is 2)

(x² - 4x + 4)(x²-i²) = 0

(x² - 4x + 4)(x²+1) = 0

x⁴ - 4x³ + 4x² + x² - 4x + 4 = 0

⇒ x⁴ - 4x³ + 5x²- 4x + 4 = 0

Hence the polynomial function with real coefficients of a least possible degree having zero 2 of multiplicity 2, and zero i of single multiplicity is                   x⁴ - 4x³ + 5x²- 4x + 4 = 0.

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Answer:

x = 65

Step-by-step explanation:

using the Altitude- on- Hypotenuse theorem

(leg of big Δ )² = (part of hypotenuse below it ) × (whole hypotenuse)

x² = 25 × 169 = 4225 ( take square root of both sides )

x = [tex]\sqrt{4225}[/tex] = 65

Answer:

1/27

Step-by-step explanation:

To find the probability of a defective jelly bean

P(defective) = number defective/ total

                     =2/54

                      = 1/27

The constant of variation based on the information is one half.

From the information given, when x is 2, y is 1, when x is 4, y is 2, etc. It should be noted that this is a direct variation.

This will be illustrated as:

y = kx

when y = 1, x = 2.

1 = 2k

Divide both side by 2.

k = 1/2

Therefore, the constant of variation is 1/2.

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The required probability is
a) both are cups is 0.05

b) At least one cup is 0.19

c) One is a cup and the other is a sword is   0.06

Probability can be defined as the ratio of favorable outcomes to the total number of events.

a) for both are cups

P= 12*11/48*47
p = 0.05

b) for  At least one cup
p = 12*36/48*47
p = 0.19

c) for One is a cup and the other is a sword
p = 12*12/48*47
p = 0.06

Thus, the required probability is 0.05, 0.19, 0.06

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Answer:

[tex]x=14[/tex]

Step-by-step explanation:

1) Since we know two of the sides of that right-angled triangle, we can use the Pythagorean Theorem to find x. His theorem is: [tex]c^2 = a^2 + b^2[/tex].

Substitute the values into the formula above.

Let x = c

[tex]c^2 = 8^2 + 11.5^2\\c^2 = 196.25\\c= \sqrt{196.25}\\c=14[/tex]

Answer:

Step-by-step explanation:

A squared garden has area 1764m2. Find its length and perimeter?​

Area = l²

l = √Area

√1764 = 42 m

42 * 4 = 168 m

Answer:

length=42m

perimeter=168m

Step-by-step explanation:

Area=L^2

L^2=1764

L=√1764

L=42m

Perimeter=42+42+42+42 which equals to 168m

The approximate solution to the given system of equations, considering the graph, is given as follows:

D. [tex]\left(-\frac{13}{4}, \frac{5}{2}\right)[/tex].

A system of equations is when two or more variables are related, and equations are built to find the values of each variable.

On a graph, the solution of a system of equations is given by the intersection between the curves. In this graph, the intersection of the two curves happen close to x = -3.25, y = 2.5, hence the solution is approximated by:

D. [tex]\left(-\frac{13}{4}, \frac{5}{2}\right)[/tex]

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Answer:

d

Step-by-step explanation:

Answer:Answer

Step-by-step explanation:

For the first part, divide 46.54 by 5.2

46.54/5.2=8.95

$8.95 per pound

For the second part if he buys half as much, its half of 5.2 plus 5.2. Now use similar steps that I used in the first part to solve for your problem.

I got $97.50, but i am not 100% sure if it is correct, so try give it a try.

From the given condition m ∠LOM = m ∠JKI, m ∠MON = m ∠IKH it is proved that m ∠LON = m ∠HKJ as they are congruent angles.

Congruent angles are defined as angles with equal measure. According to the question,

m ∠LOM = m ∠JKI  (given congruent angles)   _____(1)

m ∠MON = m ∠IKH  (given congruent angles)  _______(2)

Add both the side angle  m ∠MON in (1) we get m ∠LOM + m ∠MON = m ∠JKI + m ∠MON

Replace angle  m ∠MON = m ∠IKH from (2)  on right-hand side we get,

m ∠LOM + m ∠MON = m ∠JKI + m ∠IKH  ____(3)

m ∠LOM + m ∠MON = m ∠LON  ( M is the interior point of ∠LON)  ___(4)

m ∠JKI + m ∠IKH = m ∠HKJ  ( I is the interior point of ∠HKJ)  ___(5)

Form (3), (4), and (5) we get, m ∠LON = m ∠HKJ  (Congruent angles)

Hence, from the given condition it is proved that m ∠LON = m ∠HKJ, are congruent angles.

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Answer: [tex]42.6^{\circ}[/tex]

Step-by-step explanation:

Let the angle of depression be x.

[tex]\sin x=\frac{23}{34}\\\\x=\sin^{-1} \left(\frac{23}{34} \right) \approx 42.6^{\circ}[/tex]

The quadratic model and the linear model of the table of values are the same

To do this, we make use of a graphing calculator.

From the graphing calculator, we have the following summary:

The regression equation is

y = mx + b

Where

m = SP/SSX = 28/10 = 2.8

b = MY - bMX = 22.6 - (2.8*0) = 22.6

So, we have:

y = 2.8x + 22.6

See attachment for graph (1)

To do this, we make use of a graphing calculator.

From the graphing calculator, we have the following summary:

0 X^2 +2.8 X +22.6

The regression equation is

y = ax^2 + bx + c

So, we have:

y = 0x^2 + 2.8x + 22.6

See attachment for graph (1)

The graphs look the same because when the quadratic model is simplified, it gives the linear model.

This in other words mean that:

The quadratic model and the linear model of the table of values are the same

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Answer:

you should download AIR MATH

Only p(x) has an average rate of change of -4 over [-2, 2].

Find the average rate of change of each given function over the interval [-2, 2]]:

The average rate of change of m(x) over [-2, 2]:

The average rate of change = [tex]\frac{m(b)-m(a)}{b-a}[/tex]

Where, a = -2, m(a) = -12

b = 2, m(b) = 4

Plug the values into the equation

The average rate of change

[tex]=\frac{4-(-12)}{2-(-2)} =\frac{16}{4}[/tex]

The average rate of change = 4

The average rate of change of n(x) over [-2, 2]:

The average rate of change = [tex]\frac{n(b)-n(a)}{b-a}[/tex]

Where, a = -2, n(a) = -6

b = 2, n(b) = 6

Plug the values into the equation

The average rate of change

[tex]=\frac{6-(-6)}{2-(-2)} \\=\frac{12}{4}[/tex]

The average rate of change = 3

The average rate of change of q(x) over [-2, 2]:

The average rate of change = [tex]\frac{q(b)-q(a)}{b-a}[/tex]

Where, a = -2, q(a) = -4

b = 2, q(b) = -12

Plug the values into the

The average rate of change = [tex]\frac{-4-12}{2-(-2)}[/tex]

= [tex]\frac{-16}{4}[/tex]

The average rate of change = -2

The average rate of change of p(x) over [-2, 2]:

The average rate of change = [tex]\frac{p(b)-p(a)}{b-a}[/tex]

Where, a = -2, p(a) = 12

b = 2, p(b) = -4

Plug the values into the equation

The average rate of change = [tex]\frac{-4-12}{2-(-2)}[/tex]

[tex]=\frac{-16}{4}[/tex]

The average rate of change = -4

The answer is D.

Only p(x) has an average rate of change of -4 over [-2, 2].

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The 98% confidence interval for the mean gas mileage for this car model is (26.07,30.73).

Confidence intervals are defined as a range of values with a known chance that a parameter's value falls inside them.

The confidence interval of statistical data is computed using the formula:

[tex](\overline{x} - Z\frac{\sigma }{n},\overline{x} + Z\frac{\sigma }{n})[/tex]

where [tex]\overline{x}[/tex] is the mean, Z is the Z-score corresponding to the confidence interval, σ is the standard deviation, and n is the sample size.

In the question, the sample size (n) = 36, the mean of the sample ([tex]\overline{x}[/tex]) = 28.4 mi/gallon, the standard deviation (σ) = 6 mi/gallon.

The confidence interval given to us is 98%.

Z-score corresponding to this (Z) = 2.33.

Thus, the confidence interval can be calculated as:

(28.4 - 2.33{6/√36},28.4 + 2.33{6/√36})

= (28.4 - 2.33,28.4 + 2.33)

= (26.07,30.73).

Thus, the 98% confidence interval for the mean gas mileage for this car model is (26.07,30.73).

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The reason why partitioning and fractioning are different is because; The ratio given is part to part. The total number of parts in the whole is 1 + 3 = 4.

It follows from the task content that a close analysis of the statement of ratios; 1:3 implies that the whole is divided into four parts; 1+3 = 4.

On the contrary, one-third simply means 1 out of 3 equal parts of the line.

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Answer: OPTION C

Step-by-step explanation:

Step-by-step explanation:

k = √(49 - 12√5)

= √(45 + 4 - 2 √180)

= √45 - √4

= 3 √5 - 2.

So, k + 2 = 3 √5 - 2 + 2 = 3 √5.

Answer:

k + 2 = 3√5

Explanation:

[tex]\sf Given: k = \sqrt{49 - 12\sqrt{5} }[/tex]

[tex]\sf \rightarrow k = \sqrt{49 - 12\sqrt{5} }[/tex]

step 1: breakdown

[tex]\sf \rightarrow k = \sqrt{4 + 45- 2 \times 2 \times 3 \sqrt{5} }[/tex]

step 2: rewrite 45 = (3√5)²

[tex]\sf \rightarrow k = \sqrt{4 + (3\sqrt{5})^2 - 2 \times 2 \times 3 \sqrt{5} }[/tex]

step 3: rearrange as per a² -2ab + b² = (a - b)²

[tex]\sf \rightarrow k = \sqrt{ (3\sqrt{5})^2 - 2 \times 3 \sqrt{5} \times 2 +2^2}[/tex]

step 4: comparing, here: a = 3√5, b = 2

[tex]\sf \rightarrow k = \sqrt{ (3\sqrt{5} -2)^2}[/tex]

step 5: simplify √a² = a

[tex]\sf \rightarrow k = 3\sqrt{5} -2[/tex]

Then find k + 2

[tex]\rightarrow \sf k = 3\sqrt{5} -2 + 2[/tex]

[tex]\rightarrow \sf k = 3\sqrt{5}[/tex]

[tex]p(r) = \frac{2}{9} [/tex]

[tex]p(b) = \frac{3}{9} = \frac{1}{3} [/tex]

Answer:

the anwer is x= -3

Step-by-step explanation:

(3+5)=2

The number of rice balls Justin can make with 700 grams of rice is 7.

How many rice balls can Justin make?

In order to determine the rice balls he can make, divide the grams of rice he has by the grams needed to make one rice ball. Division is the process of grouping a number into equal parts using another number.

Rice balls he can make = 700 grams / 100 grams = 7

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Answer:

7 rice balls

Step-by-step explanation:

Here is the completed table:

Hours       Weeks

168              1

1008             6

840               5

The mathematical operation that would be used to determine the missing values are division and multiplication. In order to convert hours to weeks, divide by 168 hours. To convert weeks to hours, multiply by 168.

1008 hours to weeks = 1008 / 168 = 6 weeks

5 weeks to hours = 5 x 168 = 840 hours

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The possible sequences of rolls could there have been Sequence = 120

Given

6 rolls of a die;

Required

Determine the possible sequence of rolls

From the question, we understand that there were three possible outcomes when the die was rolled;

The outcomes are either of the following faces: 1, 2 and 3

Total Number of rolls = 6

Possible number of outcomes = 3

The possible sequence of rolls is then calculated by dividing the factorial of the above parameters as follows;

Sequence = \frac{6!}{3!}

Sequence = \frac{6 * 5 * 4* 3!}{3!}

Sequence = 6 * 5 * 4

Sequence = 120

Hence, there are 120 possible sequence.

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Repeat the following 12 times:

>            Move forward 5 cm

>            Turn clockwise 30°

Want to know how I found this out? Well, let me tell you.

First, they gave us the information that a 12-sided polygon is to be modeled with side lengths 5 cm. So, that basically gives us our first step. That was easy!

Well, now this is a bit harder. How many degrees do we move? There're so many possibilities! Well, not quite.

According to the Polygon Exterior Angle-Sum Property, the exterior angles of any polygon is always 360 degrees. So, we just divide 360 by how many sides there are in the polygon.

There are 12 sides in this polygon, so, [tex]\frac{360}{12}[/tex] is equal to 30 degrees per side. Well, now we have the second step! We're all done. Congratulations!

Answer:

the answer is 8/10

Step-by-step explanation:

The reason is that both of the denominators are the same so that you can add the two numerators and then get the answer.

Answer:

2

Step-by-step explanation:

3 x 2 = 6

1 x 2 = 2

hope it helps

sorry if I'm wrong

Answer: F

Step-by-step explanation:

Bisectors of an angle split the angle in half which you can visually see from the image. So, the answer is F.

Answer:

x + x+1 + x+2 + x+3 + x+4 + x+5 + x+6 =217

7x+21=217

7x=196

x=28

Middle Number will be:

x+3

28+3

=31

Therefore, the middle number is 31.

Step-by-step explanation:

Answer:

31

Step-by-step explanation:

Let's put this into equation form.

n + (n + 1) + (n+2) + (n+3) + (n+4) + (n + 5) + (n+6) = 217

Each number is increasingly getting farther away from n (the first number) by 1.

If we simplify, by adding all of the numbers and the n's. We get:

7n + 21 = 217

Let's subtract 21 from both sides to start the process of isolating x.

7n = 196

Now we can divide both sides by 7, to isolate x.

n = 28.

That looks like the answer, but it is not. Remember n is the first number, we want the middle, which out of 7 is the 4th number.

The 4th number is equal to (n+3) or (28 + 3)

The 4th number is 31.

Let's check if this is correct.

28 + 29 + 30 + 31 + 32 + 33 + 34 = 217.

The problem is complete.

Her grade on a fourth test is 75.

The average of e for the four tests is 84.

By substituting the given data in the equation, we get

Let the fourth test marks be x

83 + 90 + 88 + x / 4 = 84

261 + x / 4 = 84

261 + x = 336

x = 336 - 261

x = 75

An average may be described as the sum of all numbers divided by means of the whole quantity of values.

A mean can be defined as an average of the set of values in a sample of data. In different words, a median is also called the mathematics mean.

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