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Answer:

[tex]d = 1.2973\pi r^3[/tex]

Step-by-step explanation:

Given

[tex]R_1 = r[/tex]

[tex]R_2 = 0.3[/tex]

Required

The difference in their volumes

The volume of a sphere is:

[tex]V = \frac{4}{3}\pi r^3[/tex]

So, the difference d is:

[tex]d = \frac{4}{3}\pi [R_1^3 - R_2^3][/tex]

[tex]d = \frac{4}{3}\pi [r^3 - (0.3r)^3][/tex]

[tex]d = \frac{4}{3}\pi [r^3 - 0.027r^3][/tex]

[tex]d = \frac{4}{3}\pi *0.973r^3[/tex]

[tex]d = \frac{3.892}{3}\pi r^3[/tex]

[tex]d = 1.2973\pi r^3[/tex]

Volume is a three-dimensional scalar quantity. The difference in the volume between a sphere with radius r and a sphere with radius 0.3r is 4.0757r³ unit³.

A volume is a scalar number that expresses the amount of three-dimensional space enclosed by a closed surface.

The volume of the sphere with radius(r) is,

Volume = (4/3)×π×r³

The volume of the sphere with radius (0.3r) is,

Volume = (4/3)×π×(0.3r)³

The difference in the volume between a sphere with radius r and a sphere with radius 0.3r is,

Difference = [(4/3)×π×r³] - [(4/3)×π×(0.3r)³]

                  = (4/3)πr³[1-0.027]

                  = (4/3)πr³(0.973)

                  = 4.0757r³ unit³

Hence, The difference in the volume between a sphere with radius r and a sphere with radius 0.3r is 4.0757r³ unit³.

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5÷18

answer D 40 quotient

Answer:

325 boys

Step-by-step explanation:

The ratio 5:7 represents 5+7=12 students. If we were to proportionalize this ratio to 780 students, we would multiply the ratio by 65/65 since 780/12=65.

Therefore, you have (5*65)/(7*65)=325/455 as your ratio. This means that there are 325 boys in the school

it is 5.

but wth is x intercept

Answer:

42in²

Step-by-step explanation:

So, it's area time, the formula for the area of a trapezoid is (base + base) ÷ 2 x height, so:

5 + 9 = 14

14 ÷ 2 = 7

7 x 6 = 42

So the area of the trapezoid is 42in²

hope this helps:)

Answer:

36.87

Step-by-step explanation:

We can use SOH CAH TOA (sine, cosine, and tangent) to solve this problem.

SOH- means Opposite over Hypotenuse

CAH- means Adjacent over Hypotenuse

TOA- mean Opposite over Adjacent

U can use either one of these to solve this problem, I will be using sine SOH (sine).

sine C = 3/5

sine ^-1 3 divided by 5 =36.8698

So, angle C = 36.8698 and rounded to the nearest hundred is 36.87

Answer:

x=5.8

Step-by-step explanation:

I kinda guessed on this due to the fact you didn't provide a photo. I used the pythagorean equation to solve this.

Start by identifying you a, b, and c sides.

Answer:

the third one

Step-by-step explanation:

Answer:

An ion with a -2 charge, atomic number 17, an atomic mass of 25 has how many electrons?

Step-by-step explanation:

Help me

Answer:

4x + 64

Step-by-step explanation:

(X + 14) + (X + 14) + (2x + 36) = 4x + 64

Ms. Jaffey put approximately 85.7 ounces of pretzels into each bowl.

To find out how many ounces of pretzels Ms. Jaffey put into each bowl, we need to divide the total number of ounces by the number of bowls.

Ms. Jaffey had a total of 428.5 ounces of pretzels, and she distributed them equally among 5 bowls. Therefore, we can divide the total number of ounces by 5 to determine the amount in each bowl.

428.5 ounces ÷ 5 bowls = 85.7 ounces.

So, Ms. Jaffey put approximately 85.7 ounces of pretzels into each bowl.

Since it's unlikely to have exact measurements when dividing a total quantity into equal parts, we round the result to one decimal place, giving us 85.7 ounces. This means that each bowl contains approximately 85.7 ounces of pretzels.

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Answer:

30 - 4z

Step-by-step explanation:

6(5 – z) + 2z

(Multiply 6 by each term in the brackets)

6(5) - 6(z) + 2z

30 - 6z + 2z

(add 'like' terms)

30 -4z

Answer:

The answer is option C..........

To prove that AB is parallel to CD, we need to show that the slope of AB is equal to the slope of CD.

A line segment is a section of a line with two endpoints. A line segment, unlike a line, has a fixed length.

To demonstrate that AB is parallel to CD, we must show that the slope of AB equals the slope of CD.

The slope of AB can be calculated using the formula:

mAB = (y2 - y1) / (x2 - x1)

Similarly, the slope of CD can be calculated using the formula:

mCD = (ya - Y3) / (xx - X3)

If mAB = mCD, then AB is parallel to CD.

Therefore, the condition that needs to be met to prove AB is parallel to CD is: (y2 - y1) / (x2 - x1) = (ya - Y3) / (xx - X3)

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Answer:

It will take 17 years to get a population of 42,800.  (Specifically 17.3)

Step-by-step explanation:

We will use the equation

y = population

x = amount of years

y = 20000(1 + 0.045)^x

20000 is the original population.

(1 + 0.045) is the increase of 4.5% every year

Answer:

24,0

Step-by-step explanation:

Answer:A) 20,500

Step-by-step explanation: because 27,000+48,00=75,00  so you divdie that by 30 and you will get your answer of 20,500

To find how many times it will land on 3 in 10,00 spins you need to find 25% of 10,000 so 10,000 times .25 is the equation which is 2,500 so if I'm not mistaken the spinner should land on the third section 2,500/ times in 10,000 spins theoretically speaking, but if you have to find something close to it, its 2538 due to it being the closest.

Answer:

third one 2538

Step-by-step explanation:

Answer: 54 cm^2

Step-by-step explanation:

Area of a triangle= 1/2 * b * h

A= 1/2 * 9 * 12

A= (9*12)/2

A= 108/2

A- 54 cm^2

Answer:

The correct answer is:

(a) 0.0784

(b) 0.0588

(c) 0.1493

Step-by-step explanation:

According to the question,

Number or ace or king,

n (ace or king) = 8

Number of red,

n (red) = 26

Number of club,

n (club) = 13

Number or jack,

n (jack) = 4

(a)

Probability of 1st ace or king and 2nd in red will be:

⇒ [tex]P(ist \ ace \ or \ king \ and \ 2nd \ red) = \frac{8}{52}\times\frac{26}{51}[/tex]

⇒                                                    [tex]=0.0784[/tex]

(b)

Probability of both clubs will be:

⇒ [tex]P(clubs) =\frac{13C_2}{52C_2}[/tex]

⇒                [tex]=0.0588[/tex]

(c)

Probability of at least one is jack will be:

⇒ [tex]P(at \ least \ one \ is \ jack)=1-P(none \ jack)[/tex]

⇒                                       [tex]=1-\frac{48C_2}{52C_2}[/tex]

⇒                                       [tex]=0.1493[/tex]

Answer:

5.6 miles

Step-by-step explanation:

[tex]\frac{7}{80} =\frac{x}{64}[/tex]   Set up the proportion

[tex]7(64)=x(80)[/tex]  Cross multiply

[tex]448=80x[/tex]     Simplify

[tex]\frac{448}{80}=\frac{80x}{80}[/tex]    Divide both sides by 80

[tex]5.6=x[/tex]

Answer:

11 and -4

Step-by-step explanation:

Let the required two numbers be x and y

If the sum of two numbers is 7, then

x + y = 7 .. 1

If the difference of their squares is 105, then;

x² - y² = 105 ...2

From 1;

x = 7 -  y... 3

Substitute 3 into 2;

(7-y)² - y² = 105

Expand

49-14y+y² -y² = 105

49-14y = 105

-14y = 105 - 49

-14y = 56

y = -56/14

y = -4

Substitute y = -4 into 3

x = 7 -  y... 3

x = 7 - (-4)

x = 7+4

x = 11

Hence the numbers are 11 and -4

Answer:

C

Step-by-step explanation:

Answer: its c.

Step-by-step explanation: :)

Answer:

a) 0.3921 = 39.21% probability that fewer than 14 of them have had a physical examination in the past two years.

b) 0.107 = 10.7% probability that at least 17 of them have had a physical examination in the past two years.

Step-by-step explanation:

For each women, there are only two possible outcomes. Either they visit their doctors for a physical examination at least once in two years, or they do not. The probability of a woman visiting their doctor at least once in this period is independent of any other women. This means that we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

And p is the probability of X happening.

70% of adult women visit their doctors for a physical examination at least once in two years.

This means that [tex]p = 0.7[/tex]

20 adult women

This means that [tex]n = 20[/tex]

(a) Fewer than 14 of them have had a physical examination in the past two years.

This is:

[tex]P(X < 14) = 1 - P(X \geq 14)[/tex]

In which

[tex]P(X \geq 14) = P(X = 14) + P(X = 15) + P(X = 16) + P(X = 17) + P(X = 18) + P(X = 19) + P(X = 20)[/tex]

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 14) = C_{20,14}.(0.7)^{14}.(0.3)^{6} = 0.1916[/tex]

[tex]P(X = 15) = C_{20,15}.(0.7)^{15}.(0.3)^{5} = 0.1789[/tex]

[tex]P(X = 16) = C_{20,16}.(0.7)^{16}.(0.3)^{4} = 0.1304[/tex]

[tex]P(X = 17) = C_{20,14}.(0.7)^{17}.(0.3)^{3} = 0.0716[/tex]

[tex]P(X = 18) = C_{20,18}.(0.7)^{18}.(0.3)^{2} = 0.0278[/tex]

[tex]P(X = 19) = C_{20,19}.(0.7)^{19}.(0.3)^{1} = 0.0068[/tex]

[tex]P(X = 20) = C_{20,20}.(0.7)^{20}.(0.3)^{0} = 0.0008[/tex]

So

[tex]P(X \geq 14) = P(X = 14) + P(X = 15) + P(X = 16) + P(X = 17) + P(X = 18) + P(X = 19) + P(X = 20) = 0.1916 + 0.1789 + 0.1304 + 0.0716 + 0.0278 + 0.0068 + 0.0008 = 0.6079[/tex]

[tex]P(X < 14) = 1 - P(X \geq 14) = 1 - 0.6079 = 0.3921[/tex]

0.3921 = 39.21% probability that fewer than 14 of them have had a physical examination in the past two years.

(b) At least 17 of them have had a physical examination in the past two years

[tex]P(X \geq 17) = P(X = 17) + P(X = 18) + P(X = 19) + P(X = 20)[/tex]

From the values found in item (a).

[tex]P(X \geq 17) = P(X = 17) + P(X = 18) + P(X = 19) + P(X = 20) = 0.0716 + 0.0278 + 0.0068 + 0.0008 = 0.107[/tex]

0.107 = 10.7% probability that at least 17 of them have had a physical examination in the past two years.

Trig identity are written in term of cosine, sine and tangent, he value of cosθ if the value of sinθ is 9/41 is 40/41

Given the following parameters

sinθ = 9/41

According to the SOH CAH TOA identity

sinθ = opposite/hypotenuse

Determine the adjacent sides

a= √41² - 9²

a = √ 1600

a = 40

Determine the value of cosθ

cosθ = adjacent/hypotenuse

cosθ = 40/41

Hence the value of cosθ if the value of sinθ is 9/41 is 40/41

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Answer:

-40/41

Step-by-step explanation: