A cylindrical container with a radius of 5 cm and a height of 14 cm is completely filled with liquid. Some of the liquid from the cylindrical container is poured into a cone–shaped container with a radius of 6 cm and a height of 20 cm until the cone–shaped container is completely full. How much liquid remains in the cylindrical container? (1 cm3 = 1 ml)

Answer: [tex]2.25\sqrt{3}[/tex]

Not sure what you mean by terms of pi, unless you want us to find the area of the sector, not the triangle.

Step-by-step explanation:

Assuming you mean the area of the triangle...

First draw an altitude from the 120 degree angle to the opposite base.  You will find that the altitude will also be a median.  This forms 2 30-60-90 right triangles.  Thus, the height of the altitude is 1.5 and the base of the triangle is 1.5*root3.  Thus, the base of the triangle is [tex]3\sqrt{3}[/tex] and the height is 1.5.  Thus, the area of the triangle is [tex]2.25\sqrt{3}[/tex]

Answer:

x+y

Step-by-step explanation:

#boys+#girls=#children

Answer

X=117°

Step-by-step explanation:

Angle on a straight line =180°

101+y=180

y=180-101

y=79°

then: 38+79+z=180

z=180-38-79

z=63°

angle on a straight line=180°

63+X=180

X=180-63

X=117°

Answer:

B is a trinomial.

Step-by-step explanation: A trinomial is a math equation with 3 terms connected by plus or minus notations. In these 4 answer choices, choice B is the only one with 3 terms.

Answer

13x^3 i think its the right answer but am not sure :(

Answer:

B

Step-by-step explanation:

In an isosceles triangle, the altitude is the median so the altitude splits the base into two segments with lengths of 5. We notice that x is part of a right triangle with legs of 5 and 12, therefore, using the 5 - 12 - 13 Pythagorean Triple, x = 13.

Answer:

(B) 13

Step-by-step explanation:

This isosceles triangle is broken up into two parts, both are right triangles.

To find the length of a missing side in a right triangle, we use the Pythagorean Theorem - [tex]a^2+b^2=c^2[/tex]. where one of the legs is a, the other leg is b, and the hypotenuse is c.

We know that one of the legs is 12, and since the base of the triangle is 10, the leg of one of the right triangles is 5.

Let's solve.

[tex]5^2+12^2=c^2\\25+144=c^2\\169=c^2\\\\\sqrt{169} =c\\13=c[/tex]

So, c is 13, therefore the hypotenuse is 13, therefore x is 13.

Hope this helped!

Answer:

Candice wants one number to summarize all of the values in the data set, so she should find a measure of center. She can calculate the mean or the median of the data set.

Step-by-step explanation:

Measures of Central tendency is a distinct value that describe a data set by recognizing the central location within that data set. The measures of central tendency are every so often are known as measures of central location. They are also known as summary statistics.  

The three measures of central tendency are:

Mean

Median

Mode

The mean is the average value of the data set.

The median is the middle value of the data, when arranged in ascending or descending order.

The mode of the data set is the value with the highest frequency.

The data collected by Candice is continuous and is measured on an interval scale.

The interval level of measurement classifies and arranges the data set. It also defines a specific difference between each interval of scale.

The measure of central tendency for an interval level of measurement are mean and median.

Thus, the complete sentence is:

"Candice wants one number to summarize all of the values in the data set, so she should find a measure of center. She can calculate the mean or the median of the data set."

Answer:

a) 3/1 that is 3

b) 8/7

c) the mixed fraction is converted into simple fraction: 3*2+2/3 = 8/3

therefore the reciprocal is 3/8

d) 1/5

e) the mixed fraction is converted into simple fraction: 6*6+1/6 = 37/6

therefore the reciprocal is 6/37.

plz mark my ans as branlliest and like it upvote it

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Answer:

a. [tex]3[/tex]

b. [tex] \frac{8}{7} [/tex]

c. [tex] \frac{3}{8} [/tex]

d. [tex] \frac{1}{5} [/tex]

e. [tex] \frac{6}{37} [/tex]

Step-by-step explanation:

a. [tex] \frac{1}{3} [/tex]

Just flip the fraction , you will get:

[tex] = \frac{3}{1} [/tex]

[tex] = 3[/tex]

b. [tex] \frac{7}{8} [/tex]

flip the fraction

[tex] = \frac{8}{7} [/tex]

c. [tex]2 \frac{2}{3} [/tex]

The first thing you have to do is that convert mixed fraction into improper fraction

[tex] \frac{8}{3} [/tex]

Flip the fraction

[tex] = \frac{3}{8} [/tex]

d. [tex]5[/tex]

flip the fraction

[tex] = \frac{1}{5} [/tex]

e. [tex]6 \frac{1}{6} [/tex]

Convert mixed fraction into improper fraction

[tex] = \frac{37}{6} [/tex]

Flip the fraction in order to get reciprocal

[tex] = \frac{6}{37} [/tex]

Hope this helps...

Best regards!!

Answer:

740 m^2

Step-by-step explanation:

Answer:

The answer to your question is 18

Step-by-step explanation:

Process

1.- Write the fraction given

              [tex]\frac{-108}{-6}[/tex]

2.- Divide the numbers as usual

               18

         6  108

               48

                 0

3.- Divide the signs

      negative / negative = positive

4.- Write the answer

        [tex]\frac{-108}{-6}= 18[/tex]

5.- Check the result

Multiply 18 by -6 and the result must be -108

       -6 x 18 = 108

We know a negative times a negative is equal to a positive.

- 108 / - 6      is the same as 108 / 6     because the larger number is on top.

Therefore she can drop the negative signs and solve 108/6 to verify her answer.

Step-by-step explanation:

Shape A is flipped horizontally onto the x-axis

The new shape is mirroring Shape A

Hey there! I'm happy to help!

The domain is any possible number you can input into the function to get a real output. The domain of h just means the domain of this entire function, which is called h.

Let's look at the answer options.

OPTION A

All real values of x such that x≠0.

The only way to make it so that we do not have a real output is if we get a negative square root. You cannot multiply any number by itself to get a negative number unless you use imaginary numbers, but using imaginary numbers makes our output not real.

Anyways, plugging in 0 would give us √-10, which is not a real number. That part is correct, but this option says ALL REAL NUMBERS except for 0. The problem is is that we can take any number less than ten and plug it in and we would get a negative square root, a fake number. So, this option is incorrect.

OPTION B

All real values of x such that x≥10.

Let's say we use 10 for our x and plug it in. This gives us √0, which is 0, a real output. Anything bigger than this 10 will give us a real output as well, so this option is correct.

We don't even need to check the other options because we have already found the correct answer. C,D, and E are all incorrect though because they include values less ten, which would give us a negative square root, a fake number.

I hope that this helps! Have a wonderful day!

Answer:

cost of one drink: $1.70

Step-by-step explanation:

P = price of pizza

L = Price of each large drink

Gift certificate discount =$ 7

Net paid= $12.10

P +3L -7 = 12.10

14 +3L -7 =12.10

7+3L =12.10

3L = 12.10 -7 = 5.10

 L = $1.70 for each large drink

hopefully this helped :3

Answer: The equation to model this situation is  3d + $14.00 – $7.00 =     $12.10 and the cost of one large drink is $1.7 .

Step-by-step explanation:

As given

John and 2 friends are going out for pizza for lunch.

They split one pizza and 3 large drinks. The pizza cost $14.00. After using a $7.00 gift certificate, they spend a total of $12.10.

let us assume that the numbers of large drinks are represented by d .

Than the equation becomes

Total money spend = Number of drinks × d + Pizza cost  - Gift certificate amount .

Putting all the values in the above

12.10 = 3d + 14.00 - 7.00

Simplify the aboves

12.10 = 3d + 14 - 7

12.10 = 3d + 7

12.10 - 7 = 3d

5.1 = 3d

d = $ 1.7

Therefore the equation to model this situation is  3d + $14.00 – $7.00 = $12.10 and the cost of one large drink is $1.7 .

Step-by-step explanation: A term can be a number, a variable, or a number times one or more variables.

So in this expression, the terms are +2n, +5, -3p, and +4q.

This means that there are 4 terms.

The answer is D - 4 :)

Answer:

[tex] y = 9.1 [/tex]

Step-by-step explanation:

y can be found using the Law of sines as explained below:

m < Y = 106°

m < X = 58°

WY = x = 8

WX = y = ?

Thus,

[tex] \frac{x}{sin(X)} = \frac{y}{sin(Y)} [/tex]

[tex] \frac{8}{sin(58)} = \frac{y}{sin(106)} [/tex]

[tex] \frac{8}{0.848} = \frac{y}{0.961} [/tex]

Multiply both sides by 0.961 to solve for y

[tex] \frac{8}{0.848}*0.961 = \frac{y}{0.961}*0.961 [/tex]

[tex] \frac{8*0.961}{0.848} = y [/tex]

[tex] \frac{8*0.961}{0.848}*0.961 = y [/tex]

[tex] 9.07 = y [/tex]

[tex] y = 9.1 [/tex] (to the nearest tenth)

Answer: Option C, 1 unit bellow.

Step-by-step explanation:

The residual of a data point is equal to the vertical distance between the point and the regression line

If the data point is above the line, the residual is positive

if the data point is below the line, the residual is negative.

So here we have a negative residual equal to -1

This would mean that our point is 1 unit below the regression line.

Then the correct option is C.

Answer:

The answer is 1 unit below.

Step-by-step explanation:

This is because the residual is the difference between the actual value of a dependent variable & the value predicted by a regression equation. So if the data point has a residual of -1, that means that the data point lies 1 unit below the regression line.

Answer:

Step-by-step explanation:

To find angle B we use tan

tan ∅ = opposite / adjacent

From the question

AC is the opposite

BC is the side adjacent to angle B

So we have

tan B = AC / BC

tan B = 6/9

tan B = 1/3

B = tan-¹ 1/3

B = 18.43°

B = 18° to the nearest hundredth

Hope this helps you

Step-by-step explanation:

Hi there!!

Here, your equation is y= -2/3 x +1

so, let's find coordinate.

To find coordinate you must put the value of x.

so, when you keep value of x you will get,

x 0 3 6

y 1 -1 -3

Therefore, the coordinates are (0,1), (3,-1), (6,-3).

let me make you clear on using the value of x.

we generally put the value of variable (which is in right side) from a smaller digit like 0,1,2... or you may use 0,-1,-2... but they must be in eqaul interval such like i used the values in equal interval of 3 in above question.

I hope you got it...

if not you can ask me help..

now plot those points on graph, alright.

best of luck...

Answer:

Option D. 6√5.

Step-by-step explanation:

Please see attached photo for details.

The value of x can be obtained by using pythagoras theory as illustrated below:

In triangle ΔABC:

x² = z² + 12².... (1)

In triangle ΔABD:

15² = x² + y²...... (2)

In triangle ΔACD:

y² = z² + 3²....(3)

Substitute the value of y² in equation 3 into equation 2. We have:

15² = x² + y²

15² = x² + z² + 3²... (4)

From equation:

x² = z² + 12²

Make z² the subject

z² = x² – 12²

Substitute the value of z² into equation 4. We have:

15² = x² + z² + 3²

15² = x² + x² – 12² + 3²

15² = 2x² – 12² + 3²

225 = 2x² – 144 + 9

Collect like terms

225 + 144 – 9 = 2x²

360 = 2x²

Divide both side by 2

360/2 = x²

180 = x²

Take the square root of both side

x = √180

Expressing in surd form, we have:

x = √(36 x 5)

x = √36 x √5

x = 6√5

Answer:

5.65%

Step-by-step explanation:

Principal=$600

Time=20 years

FV=600*3=$1800

n=1

r=?

r= n[(A/P)^1/nt - 1]

=1{(1800/600)^ 1/1*20 - 1}

={(3)^1/20-1}

=3^0.05-1

=1.0565-1

=0.0565

rate=0.0565*100

=5.65% to the nearest hundredth percent

Answer:

If the scale on a map is 5in : 3 miles, it means every 3 inches is 5 miles. 6 inches is 10 miles and so on.

Answer:

  $198,859.03

Step-by-step explanation:

The amortization formula is good for this. Fill in the given numbers and solve for the unknown.

 A = P(r/n)/(1 -(1 +r/n)^(-nt))

where A is the monthly payment, P is the principal amount of the loan, r is the annual interest rate, n is the number of times per year interest is compounded, and t is the number of years.

  1340.00 = P(0.0525/12)/(1 -(1 +0.0525/12)^(-12·20)) ≈ 0.00673844·P

  P ≈ 1340/0.00673844 ≈ $198,859.03

The family can afford a loan for $198,859.

Answer:

363.741 feet

Step-by-step explanation:

Let the height of the cliff be represented by x. Applying the appropriate trigonometric function, we have;

Tan θ = [tex]\frac{opposite side}{adjacent side}[/tex]

Tan [tex]60^{0}[/tex] = [tex]\frac{x}{210}[/tex]

cross multiply to have;

   x = 210 × Tan [tex]60^{0}[/tex]

      = 210 × 1.7321

      = 363.741

The cliff is 363.741 feet high.

Answer: 1:5

Step-by-step explanation:

Given: The cost of every mirror is proportional to the cube of the mirror's radius.

i.e. [tex]\dfrac{\text{Cost of smallest mirror}}{\text{Cost of largest mirror}}=\dfrac{(\text{radii of smallest mirror}^3)}{\text{(radii of largest mirror)}^3}[/tex]

Their largest mirrors have radii of 5 meters and their smallest mirrors have radii of 1 meter.

Then,

[tex]\dfrac{\text{Cost of smallest mirror}}{\text{Cost of largest mirror}}=\dfrac{1^3}{(5)^3}=\dfrac{1}{125}[/tex]

The ratio of the total cost of 25 of the company's smallest mirrors to the cost of one of the company's largest mirrors will be:

[tex]\dfrac{\text{Cost of 25 smallest mirror}}{\text{Cost of largest mirror}}=\dfrac{25\times 1}{125}=\dfrac{1}{5}[/tex]

Hence, the ratio of the total cost of 25 of the company's smallest mirrors to the cost of one of the company's largest mirrors = 1:5 .

Answer: Choice C

x/w and z/(y+v)

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

Explanation:

All answer choices have that first fraction with a denominator of w. This implies that AB = w is the hypotenuse. This only applies to triangle ABD.

Focus on triangle ABD. It has an opposite leg of AD = x, when the reference angle is ABD (or angle B for short).

So we can say sin(ABD) = opposite/hypotenuse = AD/AB = x/w

x/w is one of the answers

-----------

Also note how y+v is the same for each denominator in the second fraction. y+v is the hypotenuse of triangle ABC. When the reference angle is ABD (aka angle ABC), the opposite side of this same triangle is AX = z

Therefore,

sin(ABD) = sin(ABC) = opp/hyp = AC/BC = z/(y+v)

z/(y+v) is the other answer

Side note: triangle ACD is not used at all.

Answer:

[tex]\frac{x}{w}, \: \frac{z}{y+v}[/tex]

Step-by-step explanation:

sin θ = [tex]\frac{opposite}{hypotenuse}[/tex]

Let’s take triangle ABD, where w is the hypotenuse.

sin ∠ABD = [tex]\frac{x}{w}[/tex]

Let’s take triangle ABC (whole triangle), where y + v is the hypotenuse.

sin ∠ABD = [tex]\frac{z}{y+v}[/tex]

Answer:

Step-by-step explanation:

(2, -1) & (-1, -2)

(-2+1)/(-1-2)= -1/-3= 1/3 is the slope of the line

Answer:

3.47 and 3.21

Step-by-step explanation:

Let us assume the nails length be X

[tex]X \sim N(3.34,0.07^2)[/tex]

Value let separated the top 3% is T and for bottom it would be B

[tex]P(X < T)= 0.97[/tex]

Now converting, we get

[tex]P(Z < \frac{T-3.34}{0.07})= 0.97[/tex]

Based on the normal standard tables, we get

[tex]P(Z < 1.881)= 0.97[/tex]

Now compare these two above equations

[tex]\frac{T-3.34}{0.07} = 1.881 \\\\ T = 1.881 \times 0.07 + 3.34 \\\\ = 3.47[/tex]

So for top 3% it is 3.47

Now for bottom we applied the same method as shown above

[tex]P(Z < \frac{B-3.34}{0.07})= 0.03[/tex]

Based on the normal standard tables, we get

[tex]P(Z < -1.881)= 0.03[/tex]

Now compare these two above equations

[tex]\frac{B-3.34}{0.07} = -1.881[/tex]

[tex]= -1.881 \times 0.07 + 3.34 \\\\ = 3.21[/tex]

hence, for bottom it would be 3.21

Answer:

Step-by-step explanation:

Independent Variable

The independent variable is the condition that you change in an experiment. It is the variable you control. It is called independent because its value does not depend on and is not affected by the state of any other variable in the experiment. Sometimes you may hear this variable called the "controlled variable" because it is the one that is changed. Do not confuse it with a "control variable," which is a variable that is purposely held constant so that it can't affect the outcome of the experiment.

Dependent Variable

The dependent variable is the condition that you measure in an experiment. You are assessing how it responds to a change in the independent variable, so you can think of it as depending on the independent variable. Sometimes the dependent variable is called the "responding variable."

9.77 in

Step-by-step explanation:

arc length is 80/360 × 2 × pi × radius

2/9 × 2 × 22/7 × 7

88/9

9.77in

Answer:

arc length = 9,76(8) inches

Step-by-step explanation:

Formula

2π·r(x°/360°)

= 2·3,14·7in·80°/360°

= 3516,8in/360

= 9,76(8) inches

Answer:

The answer is

Step-by-step explanation:

To find the volume of the sphere we must first find the radius

Surface area of a sphere = 4πr²

where r is the radius

From the question surface area = 3000m²

3000 = 4πr²

Divide both sides by 4π

750/π = r²

Find the square root of both sides

r = 15.45 cm

Volume of a sphere is 4/3πr³

So we have

4/3π(15.45)³

= 15448.06

= 15448m³ to the nearest hundredth

Hope this helps you

Answer:

The value of x is 30.

We have to find the value of x in the given equation.  

Using distributive property  

We have,

[tex]1/2(x+6)=18\\a.(b+c)=a.b+a.c\\1/2(x+3)=18\\1/2x=15\\x=3[/tex]

other are also solve by this methode;)

The required solution of the expression [tex]1/2(x+6) = 18[/tex] is 30.

To solve the equation using the distributive property and properties of equality. One-half (x + 6) = 18 and value of x to be determined.

The equation is the well-organized link of the variables of two expressions that contain equal between them.

distributive properties are used to evaluate the math problem easily by distributing numbers to the numbers present in parenthesis. eg, if we apply the distributive property of multiplication to solve the expression
a( b + c ) = a.b + a.c

[tex]1/2(x+6) = 18[/tex]
Using distributive property a( b + c ) = a.b + a.c

[tex]1/2.x+1/2*6 = 18\\1/2x+3=18\\1/2x=18-3\\1/2x=15\\x=2*15\\x=30\\[/tex]

Thus, The required solution of the expression [tex]1/2(x+6) = 18[/tex] is 30.

Learn more about the equation here:
https://brainly.com/question/10413253

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