A hot water heater measures 20" in diameter. What is the area of a metal base for the water heater, assuming a 2 inch overhang around the base of the water heater? (Round to the nearest tenth.) square inches.

Since, a bicyclist was traveling from the village to the railroad station with a speed of 15 mph and he was coming back to the village with a speed of 10 mph.

Let the time taken in traveling from village to the railroad station be 't' hours

Distance is calculated by the formula:

[tex] d= s \times t [/tex]

So, the distance traveled from village to the railroad station is:

[tex] d=15 \times t [/tex]

Since, the time taken in traveling from railroad station to the village is 1 hour more = 't+1' hours

So, the distance traveled from railroad station to the village is:

[tex] d=10 \times (t+1) [/tex]

Therefore, distance traveled from village to railroad station is equals to the distance traveled from railroad station to the village.

So, [tex] 15 \times t=10(t+1) [/tex]

[tex] 15t=10t+10 [/tex]

[tex] 5t=10 [/tex]

So, t=2

Therefore, distance from village to railroad station = [tex] 15 \times t [/tex]

= [tex] 15 \times 2 [/tex]

= 30 miles.

Therefore, the distance from village to railroad station is 30 miles.

The distance from the village to the railroad station is 30 miles

Speed is the ratio of distance to time taken. It is given by:

Speed = distance/time

Let d represent the distance from the village to the rail station.

When Going at a speed of 15mph, let us assume he spent a hour, hence:

15 = d/a

d = 15a

When coming at a speed of 10mph, let us assume he spent b hour, hence:

10 = d/b

d = 10b

Therefore:

15a = 10b

But it took 1 more hour for the bicyclist to get back to the village, hence b = a + 1, hence:

15a = 10(a + 1)

15a = 10a + 10

5a = 10

a = 2 hours

d = 15a = 15(2) = 30 miles

Therefore, the distance from the village to the railroad station is 30 miles

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Answer:

the y coordinate of vertex is 9. It represents the maximum height .

Step-by-step explanation:

A baseball player hits a ball. The table represents a quadratic function that shows how the height of the ball changes over time.

Time (s) Height (ft)

0 5

0.25 8

0.50 9

0.75 8

1.00 5

1.25 0

To find the y coordinate of vertex, first we find the vertex point from the given table

after and before x=0.50 the value of y is 8 and it starts decreasing so the vertex point is (0.50,9)

the y coordinate of vertex is 9. It represents the maximum height .

Answer: [tex]24\pi\text{ units}^2[/tex]

Step-by-step explanation:

We know that the total surface area of a cylinder is given by :-

[tex]TSA= 2\pi r(r+h)[/tex] , where r = radius  and h= height of cylinder.

Given : Height : h= 4 units

Radius = 2 units

Then, the total surface area of the cylinder is given by :-

[tex]TSA= 2\pi 2(2+4)[/tex]

[tex]\Rightarrow\ TSA= 2\pi (12)=24\pi\text{ units}^2[/tex]

Hence, the total area for the cylinder = [tex]24\pi\text{ units}^2[/tex]

Answer:

Combine like terms

Addition property of equality

Division property of equality

Step-by-step explanation:

13x+5x=18x

18x-4=5 negative 4 would become positive and you will as it to 5 to get 9

18x=9 simply divide

The reasons required to complete this question are;

This is an equation in which we just need to write the accurate steps on each required side.

We are asked to prove x = 1/2 from 5x - 4 + 13x = 5

On the statement side, we are given an equation

[tex]5x -4 + 13x = 5[/tex]

On the reason side, we already have our answer as Given

On the statement side, we have an equation

[tex]18x-4=5[/tex]

On the reason side, we should write down addition property of equality

we have an equation

[tex]18x = 9[/tex]

On the reason side, we should write Combine like terms

On the statement side, we have an equation

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

On the reason side, we should write down Division property of equality.

Within the four steps above, we were able to justify and prove how x = 1/2.

The key operations performed are

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Answer: The probability of Stephanie being on a top bunk is 50%

The probability of Stephanie being in Spruce Cabin is 3333.3%

The probability of Stephanie being in Pine cabin on bottom bunk is 80%

Step-by-step explanation:

The probability of Stephanie being assigned to the Pine Cabin and a bottom bunk bed is 1/6.

We have,

To find the probability of Stephanie being assigned to a specific cabin and a specific bunk, we need to know the total number of possible outcomes.

In this case, there are 6 possible outcomes because there are 3 cabins and 2 bunk bed options for each cabin:

Pine Cabin, top bunk

Pine Cabin, bottom bunk

Maple Cabin, top bunk

Maple Cabin, bottom bunk

Spruce Cabin, top bunk

Spruce Cabin, bottom bunk

Let's say we want to find the probability of Stephanie being assigned to the Pine Cabin and a bottom bunk bed.

There is only one outcome that satisfies this condition (Pine Cabin, bottom bunk),

So the probability is:

1 outcome / 6 possible outcomes = 1/6

Therefore, the probability of Stephanie being assigned to the Pine Cabin and a bottom bunk bed is 1/6.

We can similarly calculate the probability for any other combination of cabin and bunk bed by counting the number of outcomes that satisfy the condition and dividing by the total number of possible outcomes.

Thus,

The probability of Stephanie being assigned to the Pine Cabin and a bottom bunk bed is 1/6.

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The complete questions:

Stephanie is going to summer camp. There are three cabins to which she could be assigned: Pine Cabin, Maple Cabin, or Spruce Cabin. She can be assigned either a top bunk bed or bottom bunk bed.

Find the probability of Stephanie being assigned to the Pine Cabin and a bottom bunk bed.

4(x - 2) + 6 = 2(5x - 6)     use distributive property

(4)(x) + (4)(-2) + 6 = (2)(5x) + (2)(-6)

4x - 8 + 6 = 10x - 12

4x - 2 = 10x - 12       add 2 to both sides

4x = 10x - 10       subtract 10 from both sides

-6x = -10      divide both sides by (-6)

x = 10/6

The Answer to the problem  is B. 920 ft 2

Answer:d

Step-by-step explanation:

If there are 5 boys and 10 girls in the glee club then the ratio which represents the number of boys to the total number of students in the club will be 1/3 which is option a.

Ratio is basically a relationship between two quantities which are expressed in times of another.

Number of boys in the glee club=5

Number of girls in the glee club=10

Total number of students=10+5=15

Ratio=number of boys/total number of students

=5/15

=1/3

Hence the ratio between the boys to total number of students is 1/3.

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You can use the given circumference of 132 feet to find the radius using the formula C=2πr. Once the radius is found to be approximately 21 feet, use the formula for the area of a circle, being A=πr², to calculate an area of approximately 1386 square feet.

To find the area of a circle when you know the circumference, you can use the formula for the circumference of a circle, which is C = 2πr (C is the circumference and r is the radius). From the circumference, we can find the radius.

Let's rearrange the formula for r: r = C / 2π .  Plugging in the given value, r = 132 / 2π approximately equals 21 feet.

Next, we use the area of a circle formula A = πr² and plug in the radius to calculate the area. Here, A = π * (21)^2 that gives us an area of approximately 1386 square feet.

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Yared takes 15 minutes to wrap 3 presents, and Luke takes 20 minutes to wrap 5 presents.

I divided 15 by 3 to get 5, and did the same with Luke, and I got 4. Both boys have a total amount of 20 presents to wrap, so I multiplied 5 by 20, to get 100, and I multiplied 4 by 20, and got 80.

I subtracted 100 by 80, and got a 20.  Since I am finding information for Yared, I’m going to use 5, I divided 20 by 5, and got 4.

(b) Yared still needs to wrap 20% of his presents when Luke has finished wrapping presents.

Since the total amount of presents to wrap is 20, I divided that by the total amount of presents that Yared still needs to finish wrapping, which is 4. 4 divided by 20 is 0.2, and I multiplied 0.2 by 100, 100 is the whole, and I got 20.

2. (a) 50 people said their favorite color was red.

(b) The number of strikes and the total number of pitches he threw in this game is 80 total pitches.

 
Hoped I helped! 

Answer:

so have I

1. (a)Yared will still need to finish wrapping 4 presents when Luke finished wrapping all of his own presents.

Yared takes 15 minutes to wrap 3

presents, and Luke takes 20 minutes to wrap 5 presents.

I divided 15 by 3 to get 5, and

did the same with Luke, and I got 4. Both boys have a total amount of 20

presents to wrap, so I multiplied 5 by

20, to get 100, and I multiplied 4 by 20, and got 80.

I subtracted 100 by 80, and got a

20.  Since I am finding information for

Yared, I’m going to use 5, I divided 20 by 5, and got 4.

(b) Yared still needs to wrap 20%

of his presents when Luke has finished wrapping presents.

Since the total amount of

presents to wrap is 20, I divided that by the total amount of presents that

Yared still needs to finish wrapping, which is 4. 4 divided by 20 is 0.2, and I

multiplied 0.2 by 100, 100 is the whole, and I got 20.

2. (a) 50 people said

their favorite color was red.

Since there is 250 people in total, I used the percentage of the color red, which is 20%, and multiply it by 250.  20 divided by 100 is 0.2, and I multiply 0.2 by 250, which got me 50.  

(b) 20 more people said their favorite vehicle color was blue compared to those who said white.I used the same formula as (a). The percentage of blue is 32%, so I divided 32% by 100, and I got 0.32. I multiplied the total amount of people, which is 250, by 0.32, and I got 80. The total amount of people who said they liked blue is 80.       The percentage of people who said they like white is 24%, so I divided 24% by 100, and I got 0.24. I multiplied that to 250, and got 60. The total amount of people who said they liked white is 60.   I subtracted 80 to 20, to get 20.  

(c) 45 people said their favorite vehicle color was black.   I divided 18 by 100, and got 0.18. I multiplied 0.18 by 250. I got 45.

3. (a) The total number of pitches Haruto threw in this game is 90 pitches.

(b) The number of strikes and the total

number of pitches he threw in this game is 80 total pitches.

Hoped I helped! 

For the solution of this question we will use a technique called the Unitary Method. In this method we find the value of a single unit, which is 1, and then finding the necessary value by multiplying the single unit value.

In our case we are already given the value of the single unit which is 1 inch. And it is also given in the question that 1 inch = 50 miles. Thus, to find the value in miles 2.6 inches, all that we have to do multiply the single unit value, which is 50 miles, with the value given which is 2.6 inches.

Thus, we have:

If 1 inch represents 50 miles,

then 2.6 inches represents [tex] 2.6\times 50 [/tex] miles=130 miles

Thus, 130 miles is the correct answer.

Final answer:

The area of the semicircle shaped window is approximately 307.7 square inches when rounded to the nearest tenth.

Explanation:

The student has asked to find the area of a window in the shape of a semicircle with a diameter of 28 inches. To calculate the area of a semicircle, we first find the radius of the full circle, which is half the diameter, and then apply the formula for the area of a circle, A = πr², before halving it since we want the area of a semicircle.

Find the radius (r) of the semicircle: r = diameter/2 = 28 inches / 2 = 14 inches.

Calculate the area of the full circle: A = πr² = π * (14 inches)².

Halve the area to get the semicircle's area: Semicircle area = A/2.

Using the value of π as 3.14 and rounding to the nearest tenth: Semicircle area ≈ (3.14 * [tex](14)^2[/tex])/2 = (3.14 * 196)/2 = 307.72 inches².

Hence, the area of the semicircle shaped window is approximately 307.7 square inches when rounded to the nearest tenth.

A dinner plate having a diameter of 7 in approximately is given.

The distance around a circle is called the circumference.It is the perimeter of the circle.

The circumference of a circle can be found by multiplying pi ( π = 3.14 ) by the diameter of the circle.

Circumference is a special case of perimeter.

Circumference =[tex] \pi .d [/tex]

Given dinner plate has a diameter of 7 in.

Substituting d=7in we have:

Circumference = [tex] \pi (7)=3.14 (7)=21.98 in [/tex]

The pair of angles that must be congruent for the given pair of congruent triangles are ∠CAB and ∠GEF.

The ASA criterion states that two triangles are congruent if two angles and the included side of one triangle are equal to the two angles and the included side of the other triangle.

In the figure, we have:

∠ABC = ∠GEF (given)

∠ACB = ∠EGF (included angles)

AC = EG (included side)

Therefore, by the ASA criterion, triangles ABC and GEF are congruent.

The other possible pairs of congruent angles are:

∠ACB and ∠FEG

∠CAB and ∠EGF

∠ABC and ∠GFE

However, none of these pairs of angles are included angles.

Therefore, the only pair of congruent angles that must be congruent is ∠CAB and ∠GEF.

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The above question is incomplete, the complete question is:

if ABC and GEF are congruent by the ASA criterion, which pair of angles must be congruent

Attached figure.