Find the volume of a sphere

Answer:

65

Step-by-step explanation:

let the son's age be x then the man's age is 5x

In 13 years

son's age = x + 13 and man's age = 5x + 13 and he is 3 times as old as son

5x + 13 = 3(x + 13)

5x + 13 = 3x + 39 ( subtract 3x from both sides )

2x + 13 = 39 ( subtract 13 from both sides )

2x = 26 ( divide both sides by 2 )

x = 13 ← son's present age

5x = 5 × 13 = 65 ← man's present age

Answer:

The man's present age is 65.  

Step-by-step explanation:

Let x = the man's age and y = his son's age.

In 13 yr, their ages will be x + 13 and y + 13, respectively.

We have two conditions:

(1)          x = 5y

(2) x + 13 = 3(y + 13)     Remove parentheses

    x + 13 = 3y + 39      Subtract 13 from each side

(3)        x = 3y + 26      Substitute (1) into (3)

         5y = 3y + 26      Subtract 2y from each side

         2y = 26              Divide each side by 2

(4)        y = 13                Substitute (4) into (1)

           x = 5 × 13

           x = 65

The man's present age is 65.

Answer:

B

Step-by-step explanation:

solving the inequality

9 - y > 12 ( subtract 9 from both sides )

- y > 3 ( multiply both sides by - 1 )

Remembering to reverse the inequality symbol when multiplying/ dividing by a negative quantity

y < - 3 ← reverse symbol

Thus y is less than or equal to - 3

The only value from the list which makes this true is - 6 → B

To find a solution to the inequality 9 – y > 12, one must first simplify the inequality to y < -3. After comparing all the options, the correct answer is Option B (– 6), as it is the only value that is less than -3.

The question asks to find a value of y that satisfies the inequality 9 – y > 12.

To find the solution, we need to isolate y on one side of the inequality:

Now that we have the solution to the inequality, we can evaluate the given options.

Therefore, the correct answer is Option B: – 6, because – 6 < – 3.

Answer:

62.8 in

Step-by-step explanation:

Circumfrence=pi x diameter

3.14 x 20=62.8

Final answer:

Given π as approximately 3.14159, the circumference is found to be about 62.8318 inches.

Explanation:

The question asks for the circumference of a circle with a diameter of 20 inches. To find the circumference (C), we use the formula C = πd, where π (Pi) is approximately 3.14159, and d is the diameter of the circle. Given the diameter (d) of 20 inches, the circumference is calculated as follows: C = 3.14159 × 20.

Substituting the values into the equation provides: C = 62.8318 inches. Hence, the circumference of the circle with a diameter of 20 inches is approximately 62.8318 inches.

Answer:

70 feet per minute.

21 minutes

1890 feet

Step-by-step explanation:

(350 ft) / (5 min) = 70 ft/min

(1470 ft) / (70 ft/min) = 21 min

(70 ft/min) * (27 min) = 1890 ft

To solve triangle ABC, we use the Law of Cosines to find angle C and the Law of Sines to find angles A and B. Plugging in the given values, we find that angle C is approximately 103.39 degrees, angle A is approximately 25.70 degrees, and angle B is approximately 50.91 degrees.

Given that c = 82, b = 2, and a = 12, we can use the Law of Cosines to solve for the missing angles.

Using the Law of Cosines, we have:

c^2 = a^2 + b^2 - 2ab*cos(C)

Plugging in the values, we get:

82^2 = 12^2 + 2^2 - 2(12)(2)*cos(C)

6724 = 144 + 4 - 48cos(C)

660 = -48cos(C)

cos(C) = -660/48

C = acos(-660/48)

Using a calculator, we find that C ≈ 103.39 degrees.

To find angle A, we can use the Law of Sines:

a/sin(A) = c/sin(C)

Plugging in the values, we get:

12/sin(A) = 82/sin(103.39)

Solving for sin(A), we get:

sin(A) = (12*sin(103.39))/82

A = asin((12*sin(103.39))/82)

Using a calculator, we find that A ≈ 25.70 degrees.

Finally, we can find angle B using the fact that the sum of the angles in a triangle is 180 degrees:

B = 180 - A - C

Plugging in the values, we get:

B = 180 - 25.70 - 103.39

Using a calculator, we find that B ≈ 50.91 degrees.

A ≈ 25.70 degrees

B ≈ 50.91 degrees

C ≈ 103.39 degrees

To solve the triangle ABC, we can use the Law of Sines. The Law of Sines states. the correct answer is:option b. A≈9.59°, B≈88.41°, c≈12.17°

To solve the triangle ABC, we can use the Law of Sines. The Law of Sines states:

sinA/a = sinB/b=sinC/c

Given that C=82°, b=2, and a=12, we want to find angles A and B and side

Let's find angle A using the Law of Sines:

sinA/12=sin82°/2

Now, solve for angle A:

sinA=12⋅ sin82°/2

A=sin −1(12⋅ sin82°/2)

A≈9.59°

Now that we have angle A, we can find angle B using the fact that the sum of angles in a triangle is 180°:

B=180°−A−C

B=180°−9.59°−82°

B≈88.41°

Now, we can find side c using the Law of Sines:

sinA/a= sinC/c

sin9.59°/12= sin82°/c

Now, solve for c:

c=12⋅sin82°/ sin9.59°

c≈12.17

So, the correct answer is:

A≈9.59°,

B≈88.41°,

c≈12.17°

completed question

Given that C=82°, b=2 , and a=12 , solve triangle ABC. Round the answer to the nearest hundredth.

A. A=9.59°, B=88.41°, c=11.89

B. A=9.59°, B=88.41°, c=12.17

C. A=88.41°, B=9.59°, c=11.89

D. A=88.41°, B=9.59°, c=12.17

Answer:

The answer would be D.

Step-by-step explanation:

You can use an online graphing calculator to see the lines for each equation.

Answer: D

Step-by-step explanation: The slope of a line is rise/run or change in y values/change in x values. We will use the two points (-4, 1) and (0,0) for this problem. 0-1/0-(-4) = -1/4

Answer:

a. p(n) is a function of n

b. p(2)=12.50

c. {0, 1, 2, 3, 4}

Step-by-step explanation:

A function is a rule or equation the p(n) depends on the variable n. We write it as p(n) is a function of n. It can also be written in symbols using p(input)=output for (input,output). We write p(2)=12.50. Lastly, every function has a domain which consists of input values or n values used. Here it is 0, 1, 2, 3, 4.

Answer:

y=2x

Step-by-step explanation:

The equation for slop-intercept form is y=mx+b where m is the slope and b is the y-intercept.

2 represents the rise/over since you rise 2 units (up) and run 1 unit (to the right). So the slope is 2/1 or just 2, and then you multiply it by x to get 2x.

The line starts at the origin (0,0), so the y-intercept would be 0. They didn't say y=2x+0 because the + 0 wouldn't change the line.

The equation that represents a line on a graph can be determined using the slope-intercept form, y = mx + b. To find the equation, you need to determine the slope and the y-intercept.

The equation that represents a line on a graph can be determined using the slope-intercept form, y = mx + b. In this form, m represents the slope of the line and b represents the y-intercept (the point where the line intersects the y-axis).

To find the equation of the line shown on the graph, you need to determine the slope and the y-intercept. You can do this by selecting any two points on the line and using their coordinates to calculate the slope, and then substituting one of the points into the equation to solve for the y-intercept.

Once you have the slope and y-intercept values, you can substitute them into the slope-intercept form to write the equation of the line.

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Answer:

y = 2(x - 3)² + 5

Step-by-step explanation:

the equation of a parabola in vertex form is

y = a(x - h)² + k

where (h, k) are the coordinates of the vertex and a is a multiplier

here (h, k) = (3, 5) and a = 2, hence

y = 2(x - 3)² + 5 ← in vertex form

The equation of the quadratic function in vertex form with given vertex and leading coefficient is y=2(x-3)²+5.

The vertex form of a quadratic function is f(x) = a(x - h)² + k, where (h, k) is the vertex of the parabola. The coefficient a determines whether the graph of a quadratic function will open upwards or downwards.

Given that, the vertex is at (3,5) and has a leading coefficient of 2

Here, (h, k) = (3, 5) and a = 2

Substitute (h, k) = (3, 5) and a = 2 in f(x) = a(x - h)² + k, we get

y=2(x-3)²+5

Therefore, the equation of the quadratic function in vertex form is y=2(x-3)²+5.

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Answer:

13 miles

Step-by-step explanation:

The fare for the Uber

Cost= 5+ .5 m  

where m is the number of miles

We spent 11.50

11.50 = 5 + .5 m

Subtract 5 from each side

11.5 -5 = 5+.5m -5

6.50 = .5 m

Divide by .5 on each side

6.5/.5 = .5m/.5

13 = m

We went 13 miles

Answer:

The answer would round to 55%

Step-by-step explanation:

Answer:

55%

Step-by-step explanation:

We can write an equation! So 23234008 = 41892128*x. Let x be a percent. So x=23234008/41892128 or x is about .5546151. So x is about 55%

Answer:

30 devided by half    so out here we have 30 and now half, we will take our half as 1/2 (which we all know what half is 1/2)

30 ÷ 1/2   (now here we will reciprocate the fraction on the right side as well as chnge division sign to multiplication one)

=30/1  x  2/1   (now look carefully here we have to multply 2 and 30 which will then give us our answer )

=60/1 ( as 60/1 means whole we will just write 60 as we dont need 1 out here)

=60 ANSWER

 Step-by-step explanation:

hOPE THIS HELPS MERRY CHRISTMAS

Answer:

70

Step-by-step explanation:

The first step said to take 30 and divide it by 1/2

30 ÷ 1/2

We can copy dot flip

30 * 2/1

60

Then we need to add 10

60 + 10

70

Answer:

6/16

Step-by-step explanation:

12/16-3/8

12/16-6/16

6/16=3/8

6/16

12/16-3/8

12/16-6/16

6/16=3/8

Answer:  Circumference of cake board is 35π cm.

Step-by-step explanation:

Since we have given that

Diameter of a round cake = 30 cm

Diameter of a cake board is 5 cm longer than the diameter of a round cake.

So, Diameter of a cake board = 30+5=35 cm

So, radius of a cake board will be

[tex]r=\frac{35}{2}[/tex]

As we know the formula for " Circumference of Circle ":

So, According to question, we get,

[tex]C=2\pi r\\\\C=2\pi\times \frac{35}{2}\\\\C=35\pi[/tex]

Hence, Circumference of cake board is 35π cm.

Answer:

35pi

Step-by-step explanation:

Answer:

3

√

−

216

x

9

Rewrite  

−

216

x

9

as  

(

−

6

x

3

)

3

.

3

√

(

−

6

x

3

)

3

Pull terms out from under the radical, assuming positive real numbers.

−

6

x

3

Step-by-step explanation:

Hope This Helped

Answer:

The correct option is 1.

Step-by-step explanation:

From the given table is notices that the function f(x) is a downward parabola.

The maximum value of f(x) is 5 at x=1.

The function g(x) is

[tex]g(x)=-x^2+4x[/tex]

vertex of the parabola is

[tex](\frac{-b}{2a}, g(\frac{-b}{2a}))[/tex]

[tex](\frac{-4}{2\times 1}, g(\frac{-4}{2\times 1})[/tex]

[tex](2, g(2))[/tex]

Put x=2.

[tex]g(x)=-2^2+4(2)=4[/tex]

Therefore the vertex of g(x) is (2,4). The vertex of a downward parabola is the maximum point of the function.

Therefore ƒ(x) has the greater maximum. Option 1 is correct.

Answer:

ƒ( x) has the greater maximum.

Step-by-step explanation:

Answer:

There will be 18 3/4 Inches on each side of the frame!

Hope this helped:)

Step-by-step explanation:

4*12=48

48-10.5=37.5

37.7/2=18.75

Answer:

Step-by-step explanation:

We know that, the picture is 10.5 inches wide, and the wall is 4 feet wide.

First we have to transform feet to inches and subtract. So, we know that 1 feet is 12 inches, how much inches would be 4 feet?

[tex]4 \ ft\frac{12 \ in}{1 \ ft}=48 \ in[/tex]

So, the wall is 48 inches wide.

Now,

[tex](48 - 10.5)in=37.5in[/tex]

There's 37.5 inches of space. If the picture is in the middle, then each side would be have:

[tex]\frac{37.5}{2}=18.75 \ in[/tex]

Therefore, there's 18.75 inches of space at each side of the picture.

Answer:

The theoretical probability of obtaining exactly four heads when flipping six coins is also 23.4%.

Step-by-step explanation:

Getting x successes out of n trials is a binomial distribution and is given by:

p(x) = [tex]nC_{x} p^{n-x} q^{x}[/tex]

Here, n = 6

x = 2

p = probability of one head = [tex]\frac{1}{2}[/tex]

q = 1 - p

= [tex]1-\frac{1}{2}[/tex]

= [tex]\frac{1}{2}[/tex]

Substitute these values, we get,

p(2) = [tex]6C_{2} (\frac{1}{2} )^{6-2} (\frac{1}{2} )^{2}[/tex]

= [tex]15(\frac{1}{2} )^{6}[/tex]

= [tex]\frac{15}{64}[/tex]

= 0.234

= 23.4%

We know that [tex]6C_{2} =6C_{6-2}[/tex]

[tex]6C_{2} =6C_{4}[/tex]

Now,

p(4) = [tex]6C_{4} (\frac{1}{2} )^{6-4} (\frac{1}{2} )^{4}[/tex]

= [tex]15(\frac{1}{2} )^{6}[/tex]

= p(2)

Hence, the theoretical probability of obtaining exactly four heads when flipping six coins is also 23.4%.

Answer:

c = 5 and t = 20

Step-by-step explanation:

t = 2c + 10, t = 4c

so

2c + 10 = 4c

-2c = -10

c = 5

t = 4(5)

t = 20

Answer:

c=5 t=20

Step-by-step explanation:

Answer: 1.4286 gallons

Step-by-step explanation: the equation would be:

0.9*5+0x=0.7(5+x)

then you can shorten it down to:

4.5=3.5+0.7x

subtract both sides by 3.5 and you end up with:

1=0.7x

divide both sides by 0.7 and you get 1.4286 gallons

The chemist needs to add approximately 1.43 gallons of distilled water to 5 gallons of acid to obtain a 70% pure tannic acid solution.

Here, we have,

To solve this problem, we can use a mixture equation that equates the amount of pure tannic acid in the initial solution to the amount of pure tannic acid in the final solution.

Let's denote the amount of distilled water to be added as "x" gallons.

The initial solution contains 5 gallons of acid at 90% purity. This means it contains 0.90 * 5 = 4.5 gallons of pure tannic acid.

When the distilled water is added, the total volume of the solution becomes 5 + x gallons.

The goal is to obtain a 70% pure solution, which means it should contain 0.70 * (5 + x) gallons of pure tannic acid.

According to the mixture equation, we can set up the following equation:

4.5 = 0.70 * (5 + x)

Now, let's solve for x:

4.5 = 0.70 * 5 + 0.70 * x

4.5 = 3.5 + 0.70x

0.70x = 4.5 - 3.5

0.70x = 1

x = 1 / 0.70

x ≈ 1.43

Therefore, the chemist needs to add approximately 1.43 gallons of distilled water to 5 gallons of acid to obtain a 70% pure tannic acid solution.

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Answer: there are 40 marbles in the bag.

Answer:

x=11

Step-by-step explanation:

M is the midpoint this means that we can set AM and BM equal to eachother, once this is done we can solve for x

9x-6=6x+27 (set equal to eachother)

9x=6x+33 (add 6)

3x=33 (subtract 6x)

x=11 (divide by 3)

Midpoint M of AB splits AB into two equal segments. By solving given equation, we find that x = 11, AM = 93 and BM = 93.

The question pertains to the concept of midpoints in geometry. In this problem, we are given that M is the midpoint of AB. Since M is the midpoint, AM equals BM. So, we can set up the equation 9x - 6 = 6x + 27. Solving this equation we get x = 11. Substituting x = 11 into AM = 9x - 6, we get AM = 9(11) - 6 = 93. Similarly, substituting x = 11 into BM = 6x + 27, we get BM = 6(11) + 27 = 93. Therefore, both AM and BM equal 93.

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a) 0.92v or 23v/25 or 92%v

b)Oringaly, there was 100%. 8% was token away, so 100%-8%=92%

Answer:

Step-by-step explanation:

175 divided by 7 is 25

There are 25 rows

Answer:

25

Step-by-step explanation:

175 divided by 7 =25

Answer:

The answer is C.  ASA

Step-by-step explanation:

The SAS doesn't work here, and there are not two angles right next to each other to use.

Answer: D) not possible

SAS won't work because the angles marked are not between the side lengths with the tickmarks

AAS won't work because we only have one pair of angles, not two. ASA is a similar story.

So that leaves "not possible" as the only answer. We simply don't have enough info. The triangles could be congruent, or they may not be. We simply don't know.

Answer:

Alright well the Answers to your question is

- 2 Hope this helps have a nice day :)

Step-by-step explanation:

Since the equation can be written in the form y = kx, y varies directly with x and. The constant of variation, k, is - 2

Hope this help's as well Hope u have a nice day :)

Answer:

This is direct variation with the constant of variation being -2.

Step-by-step explanation:

The equation for direct variation is y = kx

We have the equation y = -2x

This is direct variation with the constant of variation being -2.

Answer: x = 7 (choice C)

"sum of 1 and 3 times a number" means we have the expression 1+3*x for some unknown number x. This is set equal to 22, and we isolate x. The idea is to follow the order of operations PEMDAS in reverse. So start with subtraction and try to undo it. If it's not present, then undo addition, and so on, until x is all by itself on one side.

1+3x = 22

3x+1 = 22

3x+1-1 = 22-1 ... see note 1 below

3x = 21

3x/3 = 21/3 .... see note 2 below

x = 7

note1: Undoing addition. We undo the "+1" by subtracting 1 from both sides

note2: Undoing multiplication. 3x means "3 times x". The inverse of this is division which means we divide both sides by 3