20 children were asked to name their favourite colour.


All the results are shown in the bar chart below.


Number of children


Red


Blue Green


Yellow


Pink


Put the correct numbers on the vertical axis of the bar chart.

Answer:

B. 30 in

Step-by-step explanation:

The circumference is pi d.

30 pi = pi d

30 pi / pi = d

30 = d

Explanation:

Focus on one point, such as A = (1,2). Note how it moves to point A ' = (-1, -2). Both x and y coordinates have been flipped from positive to negative. The rule therefore is [tex](x,y) \to (-x,-y)[/tex]. This describes a 180 degree rotation (either clockwise or counterclockwise, it doesn't matter). Points B and C follow the same idea.

Side note: Lines AA', BB' and CC' all go through the origin (0,0).

Answer:

A

Step-by-step explanation:

Let me know If you want me to explain it.

Answer:

A. h = V/(pi * r^2)

Step-by-step explanation:

V = pi r^2 h

Divide both sides by pi r^2.

V/(pi r^2) = h

The h variable is isolated now.

Graph of function is attached below.

Option D is correct.

To understand more, check below explanation.

We have to draw the graph of function,

                    [tex]f(x)=\left \{ {x, {x < 1} \atop {1, x\geq 1}} \right.[/tex]

The graph of above function is attached below,

For domain [tex]x > 1, f(x)=x[/tex]

For domain, [tex]x\geq 1, f(x)=1[/tex]

After observing attached graph, option D is correct.

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The function is plotted and is attached , Option D is the correct graph similar to one in the image.

It is an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (dependent).

It is given in the question that

f(x) =

x if x <1

1 if x>_ 1

The graph of above function is attached below,

For domain x > 1, f(x)=x

For domain, x≥ 1, f(x)=1

When we see the graph that have been plotted on the basis of domain, Option D is the correct graph similar to one in the image attached.

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Answer:

Step-by-step explanation:

One solution would be (1, -4), and the other would be (4, -7).

The ordered pairs which are the solutions of the system of equations shown in the graph below are (1,-4) and (4,-7).

The ordered pair is the pair of two numbers which represented in a manner that it provides a particular order.

In a order pair the first term indicates the x-coordinate, while the second term indicate the y-coordinates. The ordered pair are written in close bracket in the following way.

[tex](x,y)[/tex]

System of equation-

In the given graph, one linear line and one parabola is shown. In this graph the parabola intersect with the line at point (1,-4) and (4,-7).

Thus, the ordered pairs which are the solutions of the system of equations shown in the graph below are (1,-4) and (4,-7).

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Answer:

The answer is D.

Step-by-step explanation:

Answer:

x= 14.1

y= 19.4

(to the nearest tenth)

Step-by-step explanation:

Please see attached picture for full solution.

Answer:

40°

Step-by-step explanation:

The triangle is a right triangle, so one measure of one of the angles is 90 degrees.

One acute angle measures 50 degrees.

Angles in a triangle add up to 180 degrees.

180 - 90 - 50

⇒ 40

The measure of the other acute angle is 40 degrees.

Acute angles measure less than 90 degrees. 40 degrees is less than 90 degrees, so it is an acute angle.

The measure of the other acute angle is 40°.

Given that, in a right triangle, one acute angle measures 50°.

A right angled triangle is a triangle with one of the angles as 90 degrees. A 90-degree angle is called a right angle, and hence the triangle with a right angle is called a right triangle.

Let the measure of other acute angle be x.

Using angle sum property of a triangle, we get

90°+50°+x=180°

⇒ x=180-140

⇒ x=40°

Therefore, the measure of the other acute angle is 40°.

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Answer: The graph shown in picture is correct answer.

Step-by-step explanation: An equation for this is 11x=$ he makes where x represent hours.

In graph some points would be (0,0) (1,11) (2,22)....    .

Answer:

Answer is given below with explanations.

Step-by-step explanation:

[tex]a \: bag \: has \: 5\: apples \: , \:10 \: oranges \: and \: 5 \: peaches \\ n(S) = 5 + 10 + 5 \\ n(S) = 20 \\ let \: A \: be \: an \: event \: of \: pulling \: out \: an \: apple \\ P(A) = \frac{n(A)}{n(S)} \\ n(A) = 5 \\ P(A) = \frac{5}{20} \\ (reduced \: fraction) = \frac{1}{4} \\ (decimal) = 0.25 \: percent \\ this \: is \: an \: example \: of \\ \: theoritical \: probability \\ sample \: space \: is \: given \: in \: image\\ in \: this \: case \: this \: event \: is \: compound \: event. \\ let \: O \: be \: an \: event \: of \: pulling \: an \: orange \: ball \\ n(O) = 10 \\ P(O) = \frac{n(O)}{n(S)} \\ P(O) = \frac{10}{20} \\ (reduced \: fraction \: ) = \frac{1}{2} \\ decimal = 0.50 \: percent \\ the \: pulling \: of \: orange \: is \: more \: likely \: to \: occur. \\ because \: it \: has \: highest \: probability \: percentage.[/tex]

Answer:

mRP = 125°

mQS = 125°

mPQR = 235°

mRPQ = 305°

Step-by-step explanation:

Given that

Then:

Given that

Then:

Given that

Then:

Given that

Then:

mQOS + mROP + mQOR + mSOP = 360°

250° + 2mQOR = 360°

mQOR = (360°- 250°)/2

mQOR = mSOP = 55°

And (QOR and SOP are central angles):

Finally:

measure of arc PQR, mPQR = mQOR + mSOP + mQOS = 55° + 55° + 125° = 235°

measure of arc RPQ, mRPQ = mROP + mSOP + mQOS = 125° + 55° + 125° = 305°

Answer:

[tex] \boxed{ \sf Rose's \ height = 1.5 \ m \ \ \ OR \ \ \ 150 \ cm} [/tex]

Given:

Cole's height = 1.7 m

Rose's height = 20 centimetres shorter than Cole

To Find:

Rose's height

Step-by-step explanation:

[tex]\sf 1 \ m = 100 \ cm \\ \\ \sf So, \\ \sf 1.7 \ m = 1.7 \times 100 \ cm \\ \sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 170 \ cm[/tex]

[tex]\therefore \ \sf Cole's \ height = 170 \ cm \\ \\ \sf \implies Rose's \ height = Cole's \ height - 20 \\ \\ \sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 170 - 20 \\ \\ \sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 150 \: cm[/tex]

[tex]\sf 1 \ cm = \frac{1}{100} \ m \\ \\ \sf So, \\ \sf 150 \ cm = 150 \times \frac{1}{100} \ m \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf = \frac{150}{100} \:m \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf = 1.5 \: m[/tex]

[tex]\therefore \ \sf Rose's \ height = 1.5 \ m[/tex]

Using algebra, Rose's height in centimeters is calculated as: 150 centimeters.

Let's use algebra to find Rose's height in centimeters based on the given information.

Let's assume Rose's height in centimeters is represented by "R".

We know that Cole is 1.7 meters tall, which is equivalent to 170 centimeters.

According to the given information, Rose is 20 centimeters shorter than Cole. So, we can set up the equation:

R = 170 - 20

Simplifying the equation:

R = 150

Therefore, Rose's height in centimeters is 150 centimeters.

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Hope this helps!

Stay safe and have a great day :D

The properties of exponents, which mathematical operation changes 2 1/3 to 2 is 2^(1/3) * 2^(2/3) = 2

The steps are as follow:

a^m * a^n = a^(m + n)

2^1 = 2^(1/3) * 2^n

2^1 = 2^(1/3)+n

1 = (1/3) + n

n = 2/3

So the properties of exponents, which mathematical operation changes 2 1/3 to 2 is 2^(1/3) * 2^(2/3) = 2

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Answer:

- Inverse Variation

- Equation: [tex]XY = 12[/tex]

Step-by-step explanation:

Given

X-> 2 | 4 | 8 | 12

Y-> 6 | 3 | 3/2 | 1

Required

- State the type of variation the table represents

- Determine the equation to model the data

To check for type of variation; we'll make use of trial by error method.

To start with; We'll check for direct variation.

This is done using the following expression;

[tex]Y = kX[/tex]where k is the constant of variation

Make k the subject of formula

[tex]k = \frac{Y}{X}[/tex]

When Y = 6, X= 2

[tex]K = \frac{6}{2} = 3[/tex]

When Y = 3, X = 4

[tex]K = \frac{3}{4}[/tex]

There's no need to check further as both values of k are not equal

To check for inverse variation;

[tex]Y = \frac{k}{X}[/tex]

Make k the subject of formula

[tex]k = YX[/tex]

When Y = 6, X= 2

[tex]K = 6 * 2 = 12[/tex]

When Y = 3, X = 4

[tex]K = 3 * 4 = 12[/tex]

When Y = 3/2; X = 8

[tex]K = \frac{3}{2} * 8 = \frac{24}{2} = 12[/tex]

When Y = 1, X = 12

[tex]K = !2 * 1 = 12[/tex]

Note that for all values of X and Y, K remains constant;

Hence, the table represents an inverse direction

To determine the equation;

We make use of  [tex]k = YX[/tex]

Substitute 12 for k

So, the equation becomes

[tex]12 = XY[/tex]

Reorder

[tex]XY = 12[/tex]

Hence, the equation is [tex]XY = 12[/tex]

Answer:

16:1

Step-by-step explanation:

The ratio of the surface areas of the similar solids is the square of the lengths.

(4:1)²

4²:1²

⇒ 16:1

Answer: A

Slope = -6

Step-by-step explanation:

Given that the column of the table are:

Column X (-2,-1,0,1,2) and

Column Y (8,2,-4,-10,-16) 

Since the table represent a linear function, the equation of the function will obey the general linear equation

Y = MX + C

Where M = slope

M = ( Y2 - Y1 ) / ( X2 - X1 )

Let Y1 = 8, Y2 = 2 and X1 = -2 and X2 = -1

Substitutes all the parameters into the formula

M = ( 2 - 8 )/( -1 - - 2 )

M = ( 2 - 8 ) / ( -1 + 2 )

M = -6/1

M = -6

Therefore, the slope of the function is -6

Answer:

x< 2 2/3

Step-by-step explanation:

5/8 X -1/3 < 1 1/3

Add 1/3 to each side

5/8 X -1/3+1/3 < 1 1/3+1/3

5/8x < 1 2/3

Change to an improper fraction

5/8 x < 5/3

Multiply each side by 8/5 to isolate x

8/5 * 5/8x  < 5/3 * 8/5

x < 8/3

Changing back to a mixed number

x< 2 2/3

Answer: Yes.

Step-by-step explanation:

Step-by-step explanation:

f(x) = 5x – 1

To find the inverse equate f(x) to y

That's

f(x) = y

y = 5x - 1

Interchange the terms

x = 5y - 1

Make y the subject

we have

5y = x + 1

Divide both sides by 5

y = x+1/5

Therefore f^-1(x)= x + 1/5

Hope this helps you

Answer:

25

Step-by-step explanation:

u stink

Answer:

C - It decreased by about 1%

Step-by-step explanation:

We can immediately eliminate two of the potential answers - A and B. Both answers suggest the unemployment rate increased, but the question states it actually decreased from 3.2 million to 2.5 million, so we know both of those answers are incorrect.

So we're left with options C and D.

The first thing we're going to do is figure out 1% of 74 million using this equation;

74,000,000 ÷ 100 = 740,000.

This tells us that 1% of the country's population is 740,000, and since the population didn't change during the decrease of unemployment, this is the number that will decide the percentage in our answer.

Next we're going to subtract 2.5 million from 3.2 million to find the difference between the two, and thus, the amount the unemployment rate decreased by.

3,200,000 - 2,500,000 = 700,000.

The result of that equation (700,000) already gives us our answer. If 1% of the population is 740,000, and the number the unemployment rate dropped by is 700,000, then the answer to the question is C.

The numbers can't get any closer, therefore the answer to the question is option C - It decreased by about 1%

Extra:

Just for confirmation, I'll show you what we'd have done to figure out 9%, and why it couldn't have been the answer.

To find 9% we would've either divided 74 million by 10 to get 10%, and then subtracted 1%, or we could've multiplied 1% by 9. Since we already know the value of 1%, let's go with the latter method;

740,000 (1%) × 9 = 6,660,000.

9% of 74 million is 6,660,000.

Obviously, this number is no where near to the number the unemployment rate decreased by, and therefore, could not have been the answer. Since we have eliminated options A, B and D, we know for sure the answer is C.

The country's unemployment rate decreased by about 1%, so option C. is the right choice.

Rates are always defined in percentages, determining what percent of the total quantity it is.

Rate = Given quantity/Total quantity * 100%

We are informed that the number of a country's unemployed workers decreased from 3.2 million to 2.5 million last year, which has the total population at a constant equal to 74 million.

We are asked to find the change in the unemployment rate in the last year.

First, we find the initial rate of unemployment, R1:

R1 = 3.2/74 * 100% = 0.0432432*100% =  4.32432%

Then, we find the final rate of unemployment, R2:

R2 = 2.5/74 * 100% = 0.03378*100% = 3.378%

To find the change in the unemployment rate, we need to find the difference between the final rate and the initial rate.

Change in rate = Final Rate - Initial Rate

or, Change in rate = R2 - R1

or, Change in rate = 3.378% - 4.32432% = -0.9459% ≈ -1%, the negative sign shows that the rate of unemployment has decreased.

∴ The rate of unemployment decreased by about 1% last year. So, option C. is the correct answer.

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Answer:

x=1

x=-5

Step-by-step explanation:

we know that

The solution of the system of equations is the intersection point both graphs

In this problem there are two intersection points

so

The system has two solutions

we have

one solution is the point (-4.9, 5.4) and the other (0.92, -0.42)

see the attached figure

therefore

x=1

x=-5

Step-by-step explanation:

This system has three solutions (D).

Explanation for each of these problems are in the images below.

Answer & Step-by-step explanation:

For this problem, we will be using the tangent trig ratio because we are dealing with the opposite side and the adjacent side of the triangle. Although cosine may be a good ratio to use as well, it is not the best ratio to use because if you were to use the cosine ratio, you will have more steps to complete in order to solve the problem. Plus, we are not dealing with the hypotenuse side of the triangle. Therefore, it is best to use the tangent ratio because it is more efficient and it corresponds to the side lengths we are using.

On the next page, we are given a Venn Diagram. We are asked to tell the difference between finding the angle and finding the side. Then, we are asked to find the similarity between them.

When solving for the unknown side, you have to flip the equation because one of the sides will be known as a variable.

When solving for the unknown angle, you have to use the inverse of the trig ratio that you are using for that problem.

The similarity between the two is that they will always use one of the trig ratios.

Answer:

25

Step-by-step explanation:

80% times twenty gives you twenty-five

The answer is c

heh hope you have a good day ;^

Answer:

second option

Step-by-step explanation:

Under a rotation about the origin of 90°

a point (x, y ) → (- y, x )

The solution is, :A triangle is rotated 90° about the origin, then, (x, y) - (y, -x), this rule describes the transformation.

A transformation is a dramatic change in form or appearance. An important event like getting your driver's license, going to college, or getting married can cause a transformation in your life. A transformation is an extreme, radical change.

here, we have,

Rotation is a process in which the orientation of a given figure is changed by turning it about a point called origin.  The rotation can be done either clock-wisely or counterclockwise about the origin.

If the given triangle is rotated 90° clockwise, the rule that describe the transformation is; (x, y) - (y, -x)

If the given triangle is rotated 90° counterclockwise, the rule that describe the transformation is; (x, y) - (-y, x)

In the given question, the required rule is; (x, y) - (y, -x). This shows a clockwise rotation of 90° about the origin.

Hence, The solution is, :A triangle is rotated 90° about the origin, then, (x, y) - (y, -x), this rule describes the transformation.

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Answer:

Step-by-step explanation:

Given,

Radius ( r ) = 1 m

Height (h) = 10 m

Surface area of cylinder= ?

Now,

Surface area of cylinder :

[tex]2\pi \: {r}^{2} + 2\pi \: r \: h[/tex]

[tex] = 2\pi \: r \: (r + h)[/tex]

[tex] = 2\pi \: \times 1(1 + 10)[/tex]

[tex] = 2\pi \: \times 1 \: \times 11[/tex]

[tex] = 22\pi[/tex]

[tex] = 22 \: \times 3.14[/tex]

[tex] = 69.08 \: {m}^{2} [/tex]

Hope this helps...

Good luck on your assignment..

Answer:

657680

Step-by-step explanation:

just did the math