1)A cylindrical container has a diameter has diameter of 14cm and height of 20cm and is full of water. A student pours the water into another cylinder of diameter 20cm. How deep is the water in the second cylinder?

2)A cylindrical water tank is70cm in diameter. To begin with, it is full of water. A leak starts at the bottom so that it loses 10l of water every hour. How long will it take for the water level to fall by 20cm?

3) A cylindrical storage vessel is 4m in diameter and 31/2m deep. How many kilolitres will it hold?​

Hello!

Answer:

[tex]\huge\boxed{x = 4.5}[/tex]

Starting with:

5x + 4(-x - 2) = -5x + 2(x - 1) + 12

Distribute terms outside of the parenthesis:

5x + 4(-x) + 4(-2) = -5x + 2(x) + 2(-1) + 12

5x - 4x - 8 = -5x + 2x - 2 + 12

Combine like terms:

x - 8 = -3x + 10

Isolate for the "x" variable by adding 3x for both sides:

4x - 8 = 10

Add 8 to both sides:

4x = 18

Divide both sides by 4:

x = 18/4

x = 4.5

Hope this helped! :)

Answer:

[tex] \boxed{x = 4.5}[/tex]

Step-by-step explanation:

[tex] \mathrm{5x + 4( - x - 2) = - 5x + 2(x - 1) + 12}[/tex]

Distribute 4 through the parentheses

Similarly, Distribute 2 through the parentheses

[tex] \mathsf{ 5x - 4x - 8 = - 5x + 2x - 2 + 12}[/tex]

Collect like terms

[tex] \mathsf{ x - 8 = - 3x - 2 + 12}[/tex]

Calculate the sum

[tex] \mathsf{x - 8 = - 3x + 10}[/tex]

Move variable to L.H.S and change its sign

Similarly, Move constant to R.H.S and change its sign

[tex] \mathsf{ x + 3x = 10 + 8}[/tex]

Collect like terms

[tex] \mathsf{4x = 10 + 8}[/tex]

Calculate the sum

[tex] \mathsf{4x = 18}[/tex]

Divide both sides of the equation by 4

[tex] \mathsf{ \frac{4x}{4} = \frac{18}{4}} [/tex]

Calculate

[tex] \mathsf{x = 4.5}[/tex]

Hope I helped!

Best regards!

The number of 3060 teams of 4 can be formed for competition.

The correct answer is A.

A combination is a selection of all or a portion of a group of items, regardless of the sequence in which the items are chosen.

Given:

The chess club has 18 students.

To find the number of combination of teams of 4 can be formed for competition:

¹⁸C₄

Solving the combination,

¹⁸C₄

= 18! / 4! x (18-4)!

= 18! / 4! x 14!

= 18 x 17 x 16 x 15 / 4 x 3 x 2 x 1

= 3060

Therefore, the number of teams are, 3060

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Answer:

-2, 6

Step-by-step explanation:

(x - 6)(x + 2) = 0

x - 6 = 0     x+ 2 = 0

  x = 6           x = -2  

The values of x that would result in the given expression being equal to 0, in order from least to greatest, are -2 and 6.

Answer:

7800 brownies will be produced in an 8 hour shift

Step-by-step explanation:

Given : The production rate is 975 brownies per hour at a bakery

To Find :  how many brownies will be produced in an 8 hour shift?

Solution:

No. of brownies produced in 1 hour = 975

We are supposed to find No. of brownies produced in 8 hour

No. of brownies produced in 8 hour =  975 x 8=7800

Hence 7800 brownies will be produced in an 8 hour shift

Hope this helps ФωФ

Answer:

x = 9/4

y = 3/5

z = 2/3

w = -9/5

Step-by-step explanation:

Technically, the matrix is in reduced row echelon form. If there are zeros above and below the ones, it is RREF. If there are zeros only below the ones, then it's REF.

Since it is in RREF, the augmented numbers to the right of the bar are already your solutions. Simply label the variables.

Answer:

y = 3x + 3

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Calculate the slope using the slope formula

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

with (x₁, y₁ ) = (0, 3) and (x₂, y₂ ) = (- 1, 0) ← 2 points on the line

m = [tex]\frac{0-3}{-1-0}[/tex] = [tex]\frac{-3}{-1}[/tex] = 3

The line crosses the y- axis at (0, 3) ⇒ c = 3

y = 3x + 3 ← equation of line

Answer: 1

Step-by-step explanation:

so i put the amount of flour to servings into ratios (fractions)

28:14

9:12

10:13

then I put them into the same denominators

2184:1092

819/1092

840/1092

the first one is the greatest

Answer:

2/5

Step-by-step explanation:

First for the sum:

3/5 + 1/5 i + 4/5 - 2/5 i = 7/5 - 1/5 i

Now for the difference

9/5 - 1/5 i - (7/5 - 1/5 i)

= 9/5 - 1/5 i - 7/5 + 1/5 i

= 2/5 , which is the answer :)

The answer is  2/5.

To find the fraction bar in the box.

A fraction is a part of a whole. In arithmetic, the number is expressed as a quotient, in which the numerator is divided by the denominator. In a simple fraction, both are integers. A complex fraction has a fraction in the numerator or denominator. In a proper fraction, the numerator is less than the denominator.

Given that:

First for the sum:

3/5 + 1/5 i + 4/5 - 2/5 i = 7/5 - 1/5 i

Now substract the sum,

9/5 - 1/5 i - (7/5 - 1/5 i)

= 9/5 - 1/5 i - 7/5 + 1/5 i

= 2/5

So, the answer is  2/5.

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Answer: Because of PEMDAS, the way Morgan rewrote the expression would change the the order of the steps to simplify it.

Step-by-step explanation: PEMDAS is the order of operations and it stands for Parenthesis, Exponents, Multiply, Divide, Addition, and Subtraction. If we simplify Morgan's version of the expression, we would add 90+10 first, which makes 100, then add 4.8 which makes 104.8. We come to the same conclusion when simplifying the original expression, 104.8. The difference is that we add 10+4.8 first and then add it to 90. While in this situation, the outcome was not different, the order of operations was changed.

Answer:

x=1

i hope this helps!

Step-by-step explanation:

x+2/-1 =3

x+2 (1) =3

x+2 = 3

x=1

Answer:

A Yes

Step-by-step explanation:

the ratio is 2:1

Answer:

A. yes

Step-by-step explanation:

Function 1 = negative y intercept

Function 2 = positive y intercept

====================================================

Explanation:

A. This is false because function 2 has a positive y intercept. Each time x goes up, y goes down. Reverse this and decreasing x leads to increasing y.

B. False. Function 1 has a negative y intercept. The y intercept occurs where the diagonal line crosses the y axis.

C. True. The graph shows a negative y intercept. The y intercept of function 2 is (0,2).

D. False. This contradicts choice C.

Answer:

C

Step-by-step explanation:

[tex](2^7 \cdot 3^{-5}\cdot 9)^4[/tex]

Use the Power of a Product Property, where:

[tex](ab)^n=a^nb^n[/tex]

Therefore:

[tex](2^7 \cdot 3^{-5}\cdot 9)^4\\=(2^7)^4\cdot(3^{-5})^4\cdot(9)^4\\=2^{28}\cdot3^{-20}\cdot9^4[/tex]

Answer:

7 * 4 / 2 = 28/2 = 14

Step-by-step explanation:

You are timed. I will just give you the formula where its multiplying the Diagonals and dividing by 2.

x= -4 w= 1 z= -3 y= 5

This is the answer!

Answer:

s = 15 in (positive square root of 225)

Step-by-step explanation:

A = 225 in²

side of square mosaic is sq. root of 225 = 15 in

therefore the side (s) = 15 in

Answer:

Step-by-step explanation:

[tex]3\left(x+1\right)=5\left(x-2\right)+7\\Expand\\3x+3 =5x -10+7\\Collect \:like\: terms\\3x-5x = -10+7-3\\-2x = -6\\Divide \:both\:sides\:of\:the\:equation\:by\:-2\\\frac{-2x}{-2} = \frac{-6}{-2}\\ \\x = 3[/tex]

Answer:

 x = 3

Step-by-step explanation:

3(x+1)=5(x−2)+7

Use the distributive property to multiply 3 by x+1.

3x+3=5(x−2)+7

Use the distributive property to multiply 5 by x−2.

3x+3=5x−10+7

Add −10 and 7 to get −3.

3x+3=5x−3

Subtract 5x from both sides.

3x+3−5x=−3

Combine 3x and −5x to get −2x

−2x+3=−3

Subtract 3 from both sides.

−2x=−3−3

Subtract 3 from −3 to get −6.

−2x=−6

Divide both sides by −2.

x = -6/2

Divide −6 by −2

x = 3

Answer:

69

Step-by-step explanation:

-y/3 = -23

=> -y = -23 x 3

=> -y = -69

=> y = 69

Answer:

69

Step-by-step explanation:

We multiply both sides of the equation by 3 to cancel out the denominator. That gives us -y=-69. Since we cannot have a negative variable, we change the values on both sides, giving us y=69

Answer:

(1, 2)

Step-by-step explanation:

'Undo' the rule on the image to get the pre-image.

[tex](4,3)\rightarrow(4-3,3-1)\rightarrow\boxed{(1,2)}[/tex]

(1,2) would be the pre-image to (4,3).

To see if it's correct:

[tex](1,2)\rightarrow(1+3,2+1)\rightarrow(4,3)[/tex]

(1,2) should be correct.

Answer:

the correct answer is (1,2)

Step-by-step explanation:

Answer:

A. A student who prefers to be healthy is more likely to feel very little pressure from homework than a student who prefers to be rich.

Step-by-step explanation:

Answer:

A THE RIGHT ANSWER

Step-by-step explanation:

Answer:

The number of minutes Nikki needs to listen to the radio to hear 20 commercials is 63.275 minutes

Step-by-step explanation:

The given dependent and independent variables are;

The number of minutes spent by Nikki listening = x

The number of commercials aired = y

The relationship between the independent variable, x ans the dependent variable, y, was given by the Nikki's graphing tool line of best fit as follows;

y = 0.338·x - 1.387

Therefore, the number of minutes, x, Nikki needs to listen to the radio to hear 20 commercials, y is given as follows;

20 = 0.338·x - 1.387

20 + 1.387 = 0.338·x

0.338·x  =20 + 1.387 = 21.387

x =  21.387/0.338 = 63.275 minutes

The number of minutes, x, Nikki needs to listen to the radio to hear 20 commercials, y = 63.275 minutes.

Answer:

C. 63 minutes

Step-by-step explanation:

Answer:

c

Step-by-step explanation:

The expression (9⁶ x 7⁻⁹)⁻⁴ is equivalent to expression 7³⁶ / 9²⁴. Then the correct option is D.

The equivalent is the expressions that are in different forms but are equal to the same value.

The expression is given below.

⇒ (9⁶ x 7⁻⁹)⁻⁴

Simplify the expression, we have

⇒ (9⁻⁶ x 7⁹)⁴

⇒ 9⁻²⁴ x 7³⁶

⇒ 7³⁶ / 9²⁴

Then the correct option is D.

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Answer:

A) No because the theater did not survey everyone in the theater.

Answer:

Yes, because the theater surveyed a random sample.

Step-by-step explanation:

The survey is valid because there was a random sample. They surveyed every fifth person, so there was a variety of age groups, genders, and preferences included in the sample. Therefore, the correct answer is yes, because the theater surveyed a random sample.

Answer:

Option (D)

Step-by-step explanation:

Option (A).

3x⁵ - 2x³

There are two terms with the variable 'x' in the given expression. therefore, it's a binomial with no constant term.

Option (B).

x⁵ - 3x² + 5x

This expression has three terms with variable 'x'.

Therefore, it's a trinomial without no constant term.

Option (C).

7x⁶ + 2x⁴ - x³ + 7

It's a quadrinomial having 4 terms. '7' is the constant term in the given expression.

Option (D).

4x² + x³ - 3 ≈ x³ + 4x² - 3

It's a trinomial with a constant term 3.

Therefore, Option (D) is the answer.

Answer:

Manuel made his first mistake in step 2 leading to the continuous mistakes

Final answer=185

Step-by-step explanation:

Manuel made at least one error as she found the value of this expression. 2(-20) + 3[5/4(-20)] + 5[2/5(50)] + 4(50) Step 1: 2(-20) + 3(-25) + 5(20) + 4(50) Step 2: (3 + 2)(-20 + -25) + (5 + 4)(20 + 50) Step 3: 5(-45) + 9(70) Step 4: -225 + 630 Step 5: 405 Identify the step in which Chris made her first error. After identifying the step with the first error, write the corrected steps and find the final answer.

2(-20) + 3[5/4(-20)] + 5[2/5(50)] + 4(50)

Step 1: 2(-20) + 3(-25) + 5(20) + 4(50)

Step 2: -40 - 75 + 100 +

200

Step 3: -115 + 300

Step 4: 185

Manuel made his first error in step 2 by combining two different terms into one as he has done

(3 + 2)(-20 + -25) and also (5 + 4)(20 + 50)

Step 2: (3 + 2)(-20 + -25) + (5 + 4)(20 + 50)

Step 3: 5(-45) + 9(70) Step 4: -225 + 630 Step 5: 405

He should have evaluated the terms separately as I have done above, giving us 185 as the final answer in contrast to his 405 final answer.

Answer: [tex]y=\dfrac12 x[/tex] .

Step-by-step explanation:

We know that [tex]a f (x)[/tex]  compresses f(x) vertically such that

If we vertically compress the linear parent function, F(x) = x, by multiplying by [tex]\dfrac12[/tex].

Then, the equation of the new function is [tex]y=\dfrac12 F(x)=\dfrac12 x[/tex] .

i.e. [tex]y=\dfrac12 x[/tex] .

Answer:

C

Step-by-step explanation:

1 2/3*3 = about 5

5+1 2/3= 6 2/3<7 1/5

6 2/3+1 2/3 =8 1/3> 7 1/5

C is the best answer because it is the closest to the total amount of paint

Answer:

3,781

Step-by-step explanation:

To solve this problem, we will find the area of the whole circle and use that to find teh area of the 60º section.

First, recognize the formula for the area of a circle:

A = 3.14[tex]r^{2}[/tex]

In this scenario, the radius (r) is 85 feet:

A = 3.14(85[tex])^{2}[/tex]

A circle is 360º and we only require the area of 60º. 360º / 60º = 6 so we will divide by 6:

A = [tex]\frac{3.14(85)^{2} }{6}[/tex]

Finally, we will simplify and round:

A = 3,781

Answer:

The answer is rotation.

Answer:

B

Step-by-step explanation:

(To save time, I'm going to use x instead of θ)

So we have the expression:

[tex](\sin(x)-\cos(x))^2+(\sin(x)+\cos(x))^2[/tex]

First, expand these binomials:

[tex]=(\sin^2(x)-2\sin(x)\cos(x)+\cos^2(x))+(\sin^2(x)+2\sin(x)\cos(x)+\cos^2(x))[/tex]

Combine like terms:

[tex]=\sin^2(x)+\sin^2(x)+\cos^2(x)+\cos^2(x)-2\sin(x)\cos(x)+2\sin(x)\cos(x)\\=2\sin^2(x)+2\cos^2(x)[/tex]

Factor out a 2:

[tex]=2(\sin^2(x)+\cos^2(x))[/tex]

The expression inside the parentheses is the Pythagorean Identity:

[tex]\sin^2(x)+\cos^2(x)=1[/tex]

Substitute:

[tex]=2(1)\\=2[/tex]

The answer is B.