The sum of the least and greatest of 3
consecutive integers is 60. What are the
values of the 3 integers?

Answer: [tex]25.5 m^{3}[/tex]

Step-by-step explanation:

If the volume of a sphere is

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

Where [tex]r=2.3 m[/tex] is the radius

The volume of a hemisphere is half the volume of the total sphere:

[tex]V_{hemisphere}=\frac{V}{2}=\frac{\frac{4}{3} \pi r^{3}}{2}[/tex]

[tex]V_{hemisphere}=\frac{2}{3} \pi r^{3}[/tex]

Solving this equation:

[tex]V_{hemisphere}=\frac{2}{3} \pi (2.3 m)^{3}[/tex]

Finally:

[tex]V_{hemisphere}=25.48m^{3} \approx 25.5 m^{3}[/tex]

The volume is approximately 12.8 cubic meters.

To find the volume of a hemisphere, we can use the formula for the volume of a sphere and then take half of that volume.

The formula for the volume of a sphere is:

V = (4/3)πr³

Since we only need the volume of a hemisphere, we'll divide by 2:

V = (1/2) * (4/3)πr³

Given the radius (r) is 2.3 meters, we substitute the value into the formula:

V = (1/2) * (4/3)π (2.3)³

First, calculate the cube of the radius:

2.33 = 2.3 * 2.3 * 2.3 = 12.167

Next, plug this back into the formula:

V = (1/2) * (4/3)π * 12.167

Then, calculate the constant part of this equation:

(4/3)π ≈ 4.18879

So:

V = (1/2) * 4.18879 * 12.167 = 25.5288

Finally, divide by 2:

V ≈ 12.7644

Rounding to the nearest tenth, the volume of the hemisphere is 12.8 cubic meters.

Answer:

1. A   2.A

Step-by-step explanation:

A for number 1 shows how the level of the pot slowly increases as things are added, while cooking the level stays consistent then as one dish is served it decreases a level then stays a bit and keeps repeating that.

A for number 2 shows how the bus speeds up then stays a consistent 25 mph and slows down for two stops then speeds up and stays 25 mph.

Answer: $1935.56

Step-by-step explanation:

T.P=R.P-(12% of R.P)

R.P=$77.30 per 1m²

When m =5.35, m²=5.35²=28.6225

R.P= $(77.30×28.6225)

R.P=$2212.52

12.5% of R.P=0.125×$2212.52=$276.565

Therefore,

T.P = $2212.52-$276.565 = $1935.96

Note: T.P is Trade Price and R.P is Retail Price.

Hope this helps?

Answer:

M=8

Step-by-step explanation:

We have that every score in a sample is multiplied by 5, and the mean is found to be M = 40.

We want to find the original mean.

Since each of the data value is multiplied by 5, the new mean will be 5 times the original mean.

To get the original mean, we need to divide by 5;

Therefore the original mean is [tex]\frac{40}{5}=8[/tex]

To find the original mean, divide the new mean by the multiplying factor.

To find the original mean, we need to undo the multiplication by dividing the new mean by the multiplying factor. Since every score was multiplied by 5, we divide the new mean by 5 to get the original mean.

Original Mean = New Mean / Multiplying factor

Original Mean = 40 / 5

Original Mean = 8

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Perimeter of the triangle is 30.75 inches.

Step-by-step explanation:

Perimeter = 11.25 + 9.25 + 10.25

= 30.75 inches

Step-by-step explanation:

We have:

The unit fraction = [tex]\dfrac{1}{2}[/tex]

To find, the next four multiples of the unit fraction [tex]\dfrac{1}{2}[/tex] = ?

∴ The next four multiples of the unit fraction [tex]\dfrac{1}{2}[/tex]

The first multiple = [tex]\dfrac{1}{2}\times 2= \dfrac{2}{2} =1[/tex]

The second multiple = [tex]\dfrac{1}{2}\times 3= \dfrac{3}{2}[/tex]

The third multiple = [tex]\dfrac{1}{2}\times 4= \dfrac{4}{2} =2[/tex]

The fourth multiple = [tex]\dfrac{1}{2}\times 5= \dfrac{5}{2}[/tex]

∴ The next four multiples of the unit fraction [tex]\dfrac{1}{2}[/tex] are

[tex]\dfrac{2}{2}[/tex] ( 1), [tex]\dfrac{3}{2}[/tex], [tex]\dfrac{4}{2}[/tex] (2) and [tex]\dfrac{5}{2}[/tex].

The first four multiples: [tex]\frac{1}{2}, 1, \frac{3}{2}, 2[/tex]. A multiple of a fraction is found by multiplying that fraction by whole numbers.

To find the next four multiples of the unit fraction [tex]\frac{1}{2}[/tex], we can begin by understanding what a multiple of a fraction means.

Let's calculate the first four multiples of [tex]\frac{1}{2}[/tex]:

First multiple:  [tex]1 \times \frac{1}{2} = \frac{1}{2}[/tex]

Second multiple:  [tex]2 \times \frac{1}{2} = \frac{2}{2} = 1[/tex]

Third multiple:  [tex]3 \times \frac{1}{2} = \frac{3}{2}[/tex]

Fourth multiple:  [tex]4 \times \frac{1}{2} = \frac{4}{2} = 2[/tex]

Answer:

x< 2

Step-by-step explanation:

We are given the inequality;

5(x+3)−8<17

First we take 8 to the other side;

5(x+3)<17 + 8, notice the sign changes like with an equation

Opening the brackets;

5x + 15 < 25

We then take 15 to the other side;

5x < 25 -15

5x < 10

  x < 2

Thus, the solution of the inequality is x< 2

Answer:

Option A

Step-by-step explanation:

The complete question is shown in the attachment.

Note that: [tex](f\cdot g)(x)=f(x)\cdot g(x)[/tex]

We need to multiply all the functions to see which of them satisfy the given criteria.

Option A

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

Option B

[tex]\frac{2}{x} \cdot \frac{2}{c} =\frac{4}{cx}[/tex]

Option C

[tex]\frac{x-2}{3} \cdot 2-3x =\frac{-3x^2+8x-4}{3}[/tex]

Option D

[tex]\frac{1}{2x-2} \cdot \frac{1}{2x+2} =\frac{1}{4(x^2-1)}[/tex]

The correct choice is A

Answer:

y = 6.44

Step-by-step explanation:

"nine times number y" : 9y

"subtracted from 95" : (95 - 9y)

"equals 37" : (95 - 9y) = 37

solving for y

95 - 9y = 37   (subtract 95 from both sides)

-9y = 37 - 95

-9y = -58  (divide both sides by -9)

y = -58/ -9

y = 6.44

The required algebraic expression that is nine times a number y subtracted from 95 equals 37. is 95 - 9y = 37.

Given that,
To determine the algebraic expression for nine times a number y subtracted from 95 equals 37.

The algebraic expression consists of constant and variable. eg x, y, z etc.

In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication and division,

Here,

The number be y
Nine-time of y = 9y
Subtraction of 9y from 95 is equal to 37,
95 - 9y = 37

Thus, the required algebraic expression that is nine times a number y subtracted from 95 equals 37. is 95 - 9y = 37.

Learn more about algebraic expression here:

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Answer: b.14

Step-by-step explanation:

We have two shelves, the top shelf [tex]s_{t}[/tex] and the bottom shelf [tex]s_{b}[/tex].

Now, firstly we are told the top shelf has 10 more than 1/3 the number of books on the bottom shelf. This can be expressed as:

[tex]s_{t}=10+\frac{1}{3}s_{b}[/tex] (1)

Then, we are told there are 12 books on the bottom shelf:

[tex]s_{b}=12[/tex] (2)

Substituting (2) in (1):

[tex]s_{t}=10+\frac{1}{3}(12)[/tex] (3)

[tex]s_{t}=10+\frac{12}{3}[/tex] (4)

[tex]s_{t}=14[/tex] (5) This is the number of books on the top shelf

Hence, the correct option is b.

Answer:

PQ = 16

Step-by-step explanation:

Using the cosine ratio in the right triangle and the exact value

cos60° = [tex]\frac{1}{2}[/tex], then

cos60° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{RQ}{PQ}[/tex] = [tex]\frac{8}{PQ}[/tex] = [tex]\frac{1}{2}[/tex] ( cross- multiply )

PQ = 8 × 2 = 16

Answer:

2x((3x-2)x(3x+2))²

Final answer:

The correct equivalent expressions for 162x⁴-144x²+32 are 2(81x⁴ - 72x² + 16) and 2(9x² - 4)², which correspond to options A and C.

Explanation:

The expression 162x⁴-144x²+32 can be factored by first taking out the greatest common factor (GCF), which is 2, resulting in 2(81x⁴ - 72x² + 16). If we look at the inside expression, we can recognize that it is a perfect square trinomial because 81x⁴ is the square of 9x² and 16 is the square of 4, and the middle term (-72x²) is twice the product of 9x² and 4. Consequently, the expression inside the parentheses can be written as the square of a binomial, resulting in 2(9x² - 4)². Therefore, the equivalent expressions for 162x⁴ - 144x² + 32 are:

Thus, the answers are A and C from the options provided.

Answer:

144

Step-by-step explanation:

If 12 horses eat 96 bales of hay per week

Than one horse eats 96÷12 bales of hay per week

One horse eats 8 bales of hay per week

Than 18 horses will eat 8 × 18 bales of hay per week

18 horses will eat 144 bales of hay per week

Answer:

x = 115°

Step-by-step explanation:

Answer:

3353

Step-by-step explanation:

1. Simplify 960 + 2 to 962.

4 · (962 − 125) + 5

2. Simplify 962 − 125 to 837.

4 · 837 + 5

3. Simplify 4 · 837 to 3348.

3348 + 5

4. Simplify

3353

Answer: 3353

Step-by-step explanation:

4 × 960 = 3840

4 × 2 = 8

4 × -125 = -500

-500 + 8 + 3840 = 3348

3348 + 5 = 3353

Answer:

[tex]6\pi[/tex]

Step-by-step explanation:

use the formula [tex]C=2\pi r[/tex]

r = radius

plug in numbers into the equation to get

[tex]2\pi (3)[/tex] which equals [tex]6\pi[/tex]

Answer:

The answer was 9.42 units

Step-by-step explanation:

Answer:

x=1

Step-by-step explanation:

14=12x+2

subtract 2 from both sides

12=12x

divide both sides by 12 and you get x=1

Answer:

x=5

Step-by-step explanation:

The given equation is [tex]\frac{2}{x-3}=\frac{5}{x}[/tex]

The denominator is never equal to zero.

Therefore [tex]x-3\ne0[/tex] or [tex]x\ne 0[/tex]

[tex]x\ne3[/tex] or [tex]x\ne 0[/tex]

Let us now cross multiply to get:

[tex]2x=5(x-3)[/tex]

Expand to get:

[tex]2x=5x-15[/tex]

Group similar terms to get:

[tex]5x-2x=15[/tex]

[tex]3x=15[/tex]

[tex]x=5[/tex]

Answer:infinitely many solutions

Step-by-step explanation: 4*2x= 8x and (7*4)+3 = 31. 8x+31 is equal to itself, therefore any value of x makes the equation true.

Yo sup??

Dude chill....u will pass for sure :)

SA of composite figure=sum of SA of individual faces

=SA of 2 triangles+SA of rectangle 1+SA of lower cuboid

=2*1/2*8*10+2*9*14+3*10*14+2*10*10

=80+252+420+200

=952 ft^2

Hope this helps.

To save time, you dont need to write "> or ="

You can simply write ">=" without the quotes.

So 3x >= 10 means "3x is greater than or equal to 10"

-----------------------------------

we start with 3x >= 2x+5

we want 3x-10 on the left hand side. We already have a 3x. So if we stick a -10 on the left side, we need to do the same thing to the right side to balance things out. We can subtract 10 from both sides to do this

3x >= 2x+5

3x-10 >= 2x+5-10 ... subtract 10 from both sides

3x-10 >= 2x-5

So it looks like a 5 will go in the blank because the negative portion is already taken care of.

Answer:

The answer is 10

Step-by-step explanation:

Answer:

Therefore 70 year Marc's grandmother be 5 times of as Marc will be after (70-56) = 14 year.

Step-by-step explanation:

Given, Marc was born on his grandmother's 56th birthday.

Let , x year will Marc's grandmother be 5 times as Marc will be then.

At that time the age of Marc will be = (x-56) year

According to the problem,

x= 5(x-56)

⇔x = 5x - 280

⇔x-5x= -280

⇔-4x=-280

⇔x=70

Therefore 70 year Marc's grandmother be 5 times of as Marc will be after (70-56) = 14 year.

Answer:

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3. Find the area of the triangle.

A. 21.2 in

B. 10.5 in

C. 21 in

D. 42 in

The functions whose graphs include the point (16, 4) is y = x−12.

Option: D.

Step-by-step explanation:

To find the function that passes through the point (16,4).

Substitute the point in all the equations and equate the final values to find the correct equation.

A. y=2x.

Substitute (16,4).

4=2(16).

4≠32.

Thus the equation doesn't contains the point (16,4).

B. y=[tex]x^2[/tex].

Substitute (16,4).

4=[tex]16^2[/tex].

4≠ 256.

Thus the equation doesn't contains the point (16,4)

C. y=x+12.

4=16+12.

4≠28.

Thus the equation doesn't contains the point (16,4)

D. y=x−12.

4=16-12.

4=4.

Thus the equation contains the point (16,4)

E. y=14x.

4=14(16).

4≠224.

Thus the equation doesn't contains the point (16,4)

∴The functions whose graphs include the point (16, 4) is y = x−12.

Answer:

Step-by-step explanation:

There are 2 answers to this question. I know one of them wich is D but the other one I think it;s A

Answer:

draw an 8 x 7 rectangle

Step-by-step explanation:

note that

area of rectangle = length x width.

we also know that 56 = 8 x 7

hence you simply need to draw a rectangle and label the long side "8 cm" and the short side "7 cm"

Answer:

[tex]y=-\frac{3}{5}x+\frac{7}{5}[/tex]

Step-by-step explanation:

The correct question is

Write an equation for the line passing through (-6,5) and (4,-1)

step 1

Find the slope

we know that

The formula to calculate the slope between two points is equal to

[tex]m=\frac{y2-y1}{x2-x1}[/tex]

we have

(-6,5) and (4,-1)

substitute

[tex]m=\frac{-1-5}{4+6}[/tex]

[tex]m=\frac{-6}{10}[/tex]

[tex]m=-\frac{3}{5}[/tex]

step 2

Find the equation of the line in point slope form

[tex]y-y1=m(x-x1)[/tex]

we have

[tex]m=-\frac{3}{5}[/tex]

[tex]point\ (-6,5)[/tex]

substitute

[tex]y-5=-\frac{3}{5}(x+6)[/tex]

step 3

Convert to slope intercept form

[tex]y=mx+b[/tex]

Isolate the variable y

[tex]y-5=-\frac{3}{5}x-\frac{18}{5}[/tex]

[tex]y=-\frac{3}{5}x-\frac{18}{5}+5[/tex]

[tex]y=-\frac{3}{5}x+\frac{7}{5}[/tex]

Answer:

(-5,4) (6,-2)

(-2-4)/(6+5)= -6/11

Answer:

-3/5

Step-by-step explanation:

Answer:

-20 and 6

Step-by-step explanation:

-20 x 6 = -120

and if you add -20 and 6, you get -14.

Answer:

(y + 5) = -7(x + 3)

Step-by-step explanation:

Point Slope Form:  (y - y1) = m(x - x1)

Step 1:  Find Slope

m = [tex]\frac{y2 - y1}{x2 - x1}[/tex]

m = [tex]\frac{-19 - (-5)}{-1 - (-3)}[/tex]

m = [tex]\frac{-19 + 5}{-1 + 3}[/tex]

m = [tex]\frac{-14}{2}[/tex]

m = -7

Step 2:  Put into point slope form

Point Slope Form:  (y - y1) = m(x - x1)

(y - (-5)) = -7(x - (-3))

(y + 5) = -7(x + 3)