The sum of three consecutive even numbers is one hundred sixty - two.
What is the smallest of the three numbers ?

Answer:56 students

Step-by-step explanation:

So look 6th grade total 42 and 8th is 72 and the total is 170 but he want 7th grade total so what I did is 42+72=114

Then I did 170-114=56 so the total of 7th grade is 56.

The value of the variables x, y, and z will be 45, 24, and 56.

Algebra is the study of graphic formulas, while logic is the interpretation among those signs.

The students at spring field school can join either the orchestra or the marching band.

Let the missing value x, y, and z are given in the table.

The table is given below.

                           Orchestra         Band           Total

6th Grade                24                  18                 42

7th Grade                32                   x                   y

8th Grade                 z                   27                 72

Total                        101                 69                 170

Then the value of x, y, and z are calculated below.

For value of z, the equation will be

72 = z + 27

 z = 72 – 27

 z = 45

For value of x, the equation will be

18 + x + 27 = 69

      x + 45 = 69

              x = 69 – 45

              x = 24

For value of y, the equation will be

y = 32 + 24

y = 56

Then the value of the variables x, y, and z will be 45, 24, and 56.

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Answer:

V=2x4x5

Step-by-step explanation:

Volume of a solid can be obtained by multiplying lengths of all the three dimensions i.e. Length, width and height.

[tex]V = l \times b \times h \\ \therefore V = 2 \times 4 \times 5[/tex]

The Volume of Solid is, V=2x4x5.

'Volume' is a mathematical quantity that shows the amount of three-dimensional space occupied by an object or a closed surface.

We know few formulas for Volume as

Volume of cuboid = l × w × h

Volume of cube = a³

Volume of Cylinder = πr²h

Volume of Prism= B × h

Volume of sphere = (4⁄3)πr³

Volume of Cone = (1⁄3)πr²h

From all the options given we have to find the relation with multiplication.

So, the volume of this solid is V=2x4x5 which is same as Volume of cuboid = l × w × h

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The number 31 was increased to 44 by approximately 41.9%.

To calculate the percentage increase, you can use the formula:

[tex]\[ \text{Percentage Increase} = \left( \frac{\text{New Value} - \text{Original Value}}{\text{Original Value}} \right) \times 100 \][/tex]

In this case, the original value is 31, and the new value is 44. Plug these values into the formula:

[tex]\[ \text{Percentage Increase} = \left( \frac{44 - 31}{31} \right) \times 100 \][/tex]

[tex]\[ \text{Percentage Increase} = \left( \frac{13}{31} \right) \times 100 \][/tex]

Now, calculate the percentage increase:

[tex]\[ \text{Percentage Increase} \approx 41.9\% \][/tex]

So, the number 31 was increased to 44 by approximately 41.9%.

The number 31 was increased by approximately [tex]\( \boed{41.9\%} \)[/tex] to become 44.

Step 1

To find the percentage increase from 31 to 44, we can use the formula for percentage increase:

[tex]\[ \text{Percentage Increase} = \left( \frac{\text{New Value} - \text{Old Value}}{\text{Old Value}} \right) \times 100\% \][/tex]

Step 2

Given:

- Old value (31)

- New value (44)

[tex]\[ \text{Percentage Increase} = \left( \frac{44 - 31}{31} \right) \times 100\% \]\[ \text{Percentage Increase} = \left( \frac{13}{31} \right) \times 100\% \]\[ \text{Percentage Increase} \approx 0.419 \times 100\% \]\[ \text{Percentage Increase} \approx 41.9\% \][/tex]

So, the number 31 was increased by approximately [tex]\( \boed{41.9\%} \)[/tex] to become 44.

Answer:

c=28.2857142857 inches

Step-by-step explanation:

The circumference of a circle can be found using:

[tex]c=\pi d[/tex]

We know the diameter is 9, and we are using 22/7 for [tex]\pi[/tex], so we can substitute them in

c=22/7*9

Multiply

c=28.2857142857

The circumference is 28.2857142857 inches

The divisors of 240 which are multiples of tens are 10, 20, 30, and 60.

To identify divisors of 240 that are multiples of tens, we must first understand what a divisor is. A divisor is a number that divides another number evenly. For example, in the case of 240, some notable divisors are 1, 2, 3, 4, 5, and so on. However, we are specifically looking for divisors that are themselves multiples of 10. These are numbers that end in zero and could be multiplied by some integer to get 240. In this instance, four such divisors are 10, 20, 30, and 60. For each of these examples, one can multiply these by a whole number to produce 240. For instance, 10*24 is 240, so is 20*12, 30*8, and 60*4.

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Answer:

Yes  because  it fits the Pythagorean Theorem

Step-by-step explanation:

see:   5 ^2 = 25

and   3^2 + 4^2 =  9 + 16 = 25

25 = 25

so it is

Answer:

2/3

Step-by-step explanation:

Answer: the answer is d.2/3 just took the test!!

Step-by-step explanation:

To apply two coats of paint on all the walls, you will need to buy 4 quarts of paint.

To find out how many quarts of paint you need to buy to apply two coats of paint on all the walls, we need to calculate the total area that needs to be painted.

If 2 quarts cover 175 square feet, then 1 quart covers 175/2 = 87.5 square feet.

Since you need to apply two coats of paint, the total area that needs to be painted is 175 square feet x 2 = 350 square feet.

To find out how many quarts you need, divide the total area by the area covered by 1 quart: 350 square feet / 87.5 square feet/quart = 4 quarts.

You will need to buy 4 quarts of paint to complete the job.

Answer:

The parent graph of (x-2)^4+1               shifts 2   units to the right and one unit up.

The parent graph of 3x^4-6            is stretched vertically by a factor of 3   and then shifted 6   units down.

The parent graph of 2(x+3)^4+10                 is shifted 3   units to the left, stretched vertically by a factor of 2   and shifted 10    units up.

The parent graph of 1/4(6x-1)^4                 is shifted one unit to the right, compressed horizontally by a factor of 1/6     , and compressed vertically by a factor of  1/4.

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

r= -6

Step-by-step explanation:

Here's why:

6 r = 6 + 7r

Subtract 7r from each side:

-r = 6

Divide by each side -1 to get the answer of:

r=-6

Answer:

V= 9202.77 in³

Step-by-step explanation:

Answer:

a.The expected value of the game to the player is -$0.2105

b. The player should expect to lose $210.50¢ if he/she places the bet or plays the game 1,000 times

Step-by-step explanation:

Please kindly check the attached files for explanation.

Answer:

Each person will wash all cars for 0.1875 hours

Step-by-step explanation:

One student takes time to wash all cars = 12

8 students take time to wash all cars = [tex]\frac{12}{8}= 1.5 hours[/tex]

So, 8 students together takes 1.5 hours to wash the car

Each person spent hours on washing all cars =[tex]\frac{1.5}{8}[/tex]

Each person spent hours on washing all cars =0.1875 hours

So, Each person will wash all cars for 0.1875 hours

Answer:

1/10 or 10%

Step-by-step explanation:

Step 1:  Find the probability of selecting a card with an A

Picked amount / Total Times

3 / 30

1/10 or 0.1 or 10%

Answer: 1/10 or 10%

Answer:

[tex]\frac{13}{60}[/tex]

Step-by-step explanation:

18 people preferred MILK

29 preferred COFFEE

13 preferred JUICE

We want probability that a person preferred JUICE. For that, we need number of people who preferred juice and total number of people.

Lets find total:

18 + 29 + 13 = 60 total people

Total people who preferred JUICE is:

13

Probability (preferred JUICE) = 13/60

The answer is  [tex]\frac{13}{60}[/tex]

Answer:

Use the 45-45-90 rule.

Step-by-step explanation:

Based on angle A being 45 and angle B looking like its 90 degrees, angle C will be 45 degrees and so you'd use the 45-45-90 rule, which is a special right triangle. The 45 degrees sides are x and the hypotenuse is x[tex]\sqrt{2}[/tex]. It will be easier if you look it up to see a graphic of it, but I'm pretty sure that both sides CB and AB are 6 based on this rule.

Answer:

-4x + 10x - 12 = -3x - 39

6x - 12 = -3x - 39

9x - 12 = -39

9x = -27

x = -3

Step-by-step explanation:

Answer:

(a) The mean is 24

The Absolute deviation is 8.367

(b) Mean is the number of score per game

(b)  The standard  deviation is the normal expected score difference from the mean

(c) Mean reduce

Standard deviation reduce

Step-by-step explanation:

The data is as follows;

21, 45, 21, 14, 21, 28, 24, 14, 24, 28

The  data with n = 10 is presented as follows

x             (x - μ)       (x - μ)²

21      -3         9

45         21         441

21            -3         9

14        -10        100

21         -3            9

28           4        16

24         0       0

14        -10        100

24         0            0

28     4       16

∑x/n =240  ∑(x - μ)²  =  700

24     ∑(x - μ)²/n = σ² = 70

The mean = 24

The Absolute deviation √70 = 8.367

(b) The mean indicates that within the football season, the average game score per game was 24 and the normal variation from the average was 8.367

(c) Removing the outlier, 45 which ls most equal to two means will reduce the mean or average score per game of the team  to as follows

21 ,  21 , 14,  21,  28,  24,  14,  24,  28

∑x = 195 and μ = (∑x)/n = 195/9 = 21.67

The standard deviation = 4.83

Therefore, removing the outlier 45 which is almost double the mean will reduce the mean by almost μ/n and the standard deviation is also reduced.

Answer:

z=3.8196

Step-by-step explanation:

-We notice that this is a normal distribution problem.

-Given the mean is $8500, standard deviation is $1200 , and n=350, the critical z-value using alpha=0.05 is calculated as:

[tex]z=\frac{x-\mu_o}{\sigma/\sqrt{n}}\\\\=\frac{8745-8500}{1200\sqrt{350}}\\\\\\=3.8196[/tex]

Hence, the test statitic is z=3.8196

Answer:

210xy

Step-by-step explanation:

15x * 14y can be written as 15 * x * 14 * y. Due to the commutative property of multiplication, we can change around the order of these numbers to make this expression easier to understand.

We're going to move the expression around so it is now 15 * 14 * x * y. Now, you can see clearly that you can multiply 15 and 14 together, which will get you 210.

And naturally what you have left is 210 * x * y, which simply appears as 210xy.

I hope this helped!

Answer:

x = 3.75 inches

Step-by-step explanation:

We have,

Perimeter of a rectangle, P = 21 inches

Its length is 3 inches greater than its width. Let width is x. So, length of rectangle is l = 3+x

The perimeter of a rectangle is :

[tex]P=2(l+b)[/tex]

l is length and b is breadth

Here, l = 3+x, b = x

Perimeter :

[tex]P=2(3+x+x)\\\\21=2(3+2x)[/tex]

[tex]21=6+4x\\\\15=4x\\\\x=3.75\ \text{inches}[/tex]

So, the width is 3.75 inches.

Final answer:

To find the width of the rectangle, create an equation using the perimeter formula P = 2l + 2w. By substituting the known perimeter and the relationship between length and width, solve for w, resulting in a width of 3.75 inches.

Explanation:

The student is tasked with finding the width of a rectangle when the perimeter is known to be 21 inches and the length is 3 inches greater than the width. To solve this, we set up an equation representing the perimeter of a rectangle: P = 2l + 2w, where P is the perimeter, l is the length, and w is the width.

Let w represent the width of the rectangle. The length is then w + 3 inches. Substituting these values into the perimeter formula, we get: 21 = 2(w + 3) + 2w. Simplifying this, we get 21 = 2w + 6 + 2w or 21 = 4w + 6. Solving for w, we subtract 6 from both sides to get 15 = 4w, and then divide both sides by 4 to get w = 3.75 inches. This means the width of the rectangle is 3.75 inches.

Answer:

No

Step-by-step explanation:

If GH is tangent to circle F, then it forms a right angle with FG.  Therefore, triangle FGH would be a right triangle and would satisfy Pythagorean theorem.

34² + 256² = 288²

66692 = 82944

The sides are not a Pythagorean triple, so GH is not tangent to the circle.

Answer:

y= 1/5 (fraction)

x=−3

Step-by-step explanation:

Let's solve for x.

x−5y=15

Step 1: Add 5y to both sides.

x−5y+5y=15+5y

x=5y+15

Let's solve for y.

x−5y=15

Step 1: Add -x to both sides.

x−5y+−x=15+−x

−5y=−x+15

Step 2: Divide both sides by -5.

−5y

−5

=

−x+15

−5

Answer:

Area of the square base: 144 in²

Area of each triangular face: 66 in²

Amount of paint needed: 408 in²

Step-by-step explanation:

We basically want to find the surface area of this square pyramid.

First, find the areas of the 4 triangular sides. The area of a triangle is denoted by: [tex]A=\frac{1}{2} bh[/tex], where b is the base and h is the height.

Here, the base coincides with the side length of the square, so b = 12. The height is 11, so h = 11. Plug these in:

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

[tex]A=\frac{1}{2}[/tex] * 12 * 11 = 66 inches squared

Each triangular face is thus 66 inches squared.

Since there are 4 triangles, multiply 66 by 4: 66 * 4 = 264 inches squared

Now, find the area of the square base. The area of a square is: A = s * s, where s is the side length. Here, the side length is 12, so s = 12. Plug this into the equation:

A = s * s

A = 12 * 12 = 144

So, the square base is 144 inches squared.

Finally, add 144 to 264 to get the total area Gabriel needs to paint:

144 + 264 = 408 inches squared

Answer:

The area of the square base is 144 in²

The area of each triangular face is 66 in²

Gabriel will need 408 in² of paint.

Step-by-step explanation:

The area of the square base is:

12² = 144 in²

The area of each triangular face:

½(12×11) = 66 in²

Gabriel will need:

4(66) + 144 = 408 in²

Answer: 7.32 inches

Step-by-step explanation: We can set up an equation to solve: y = 0.61x where y is the total amount of rain in inches and x is how many days it rained.

Multiply 0.61 by 12 to get how many inches total it rained: y = 0.61(12)

y = 7.32 inches

Answer:

A) base = 6 units

B) height = 4 units

C) Area = 24 square units

Step-by-step explanation:

Base on the gragh given,

The base = |-5| + |1| = 6 unit

The height = |2| + |-2| = 4 unit

The area = base × height

The area = 6 × 4 = 24 square units.

Answer:

The parallelogram has vertices at (–2, 2), (4, 2), (1, –2), and (–5, –2).

Complete each sentence.

The base of the parallelogram is

✔ 6

units.

The height of the parallelogram is

✔ 4

units.

The area of the parallelogram is

✔ 24

square units.

Step-by-step explanation:

Answer:

(1,4), (2,2) (3,0)

Step-by-step explanation:

adjust the equation so that the y is isolated so subtract 4 x

2y=4x +12

Every number is divisible by 2 so you can further isolate the y

y=-2x+6

Plug your x coordinates into the equation so get the y coordinates

Answer:

y=-2x+6

Step-by-step explanation:

You want to to turn the given equation 4x+2y=12 into y=mx+b

** m is the slope and b is the y-intercept

The first step is to isolate y. First subtract 4x from both sides:

4x+2y=12

2y=-4x+12

Now you have y mostly isolated, all you have to do is divide both sides by 2:

2y=-4x+12

y=-4/2x +12/2

y=-2x +6

Now you have your equation, plug in values for x to find y to fill in the table:

ex: y=-2(2)+6

y= -4+6

y= 2

** an order pair ex.: (2,2)

Answer: 10:55

Step-by-step explanation:

Taking statement at face value and the simplest scenario that commencing from 08:00am the buses take a route from depot that returns bus A to depot at 25min intervals while Bus B returns at 35min intervals.

The time the buses will be back at the depot simultaneously will be when:

N(a) * 25mins = N(b) * 35mins

Therefore, when N(b) * 35 is divisible by 25 where N(a) and N(b) are integers.

Multiples of 25 (Bus A) = 25, 50, 75, 100, 125, 150, 175, 200 etc

Multiples of 35 (Bus B) = 35, 70, 105, 140, 175, 210, 245 etc

This shows that after 7 circuits by BUS A and 5 circuits by Bus B, there will be an equal number which is 175 minutes.

So both buses are next at Depot together after 175minutes (2hr 55min) on the clock that is

at 08:00 + 2:55 = 10:55

Answer: 4 Tons

Step-by-step explanation:

Simply just add and subtract

companies often win in a credit transaction, due to their clients continually pay them for their usage.

Final answer:

The 'winner' in a credit transaction varies; it could be the lender earning interest or the borrower who benefits from immediate funds. Credit transactions do not create new money but reallocate it, and for personal debt management, debts with higher interest should be paid first.

Explanation:

In credit transactions, the winner is not easily defined as it depends on the perspective and the outcome of the transaction. If we consider a credit card transaction where a customer makes a purchase, the credit card issuer initially appears to win by providing funds to the customer and earning interest on the borrowed amount. The customer benefits by receiving the goods or services they need immediately, with the expectation of repaying the funds.

In a typical credit transaction, one party relinquishes money today while the other party promises to return a specified sum, possibly with interest, at a future date. This does not create new money but shifts existing money from one party to another. The perceived 'winner' could be the lender, who will receive the original amount plus interest, or the borrower, who gets immediate use of the funds.

When managing personal finances, it's advisable to pay off debts with the highest interest rates first, as suggested by the adage, "A penny saved is a penny earned".