EXERCISE 12.1 There are 20 girls and 15 boys in a class. (a) What is the ratio of number of girls to the number of boys? (b) What is the ratio of number of girls to the total number of students in the class?

The level of the first circle's region is the region of the new circle will be 60%. Then, at that point, the right choice is A.

The quantity area demonstrates the amount of a sector on a planar or hemispherical cup. Surface area refers to the area of an open surface or the border of a multi-object, whereas the area of a plane region or plane field refers to the area of a form or planar material.

A circle with a sweep of 5 is changed into the accompanying capability:

(x/3)² + (5y)² = 25

The major and minor axes are given as,

(a/3)² = 25

a = 15

(5b)² = 25

b = 1

The percentage of area is given as,

P = [(Area of ellipse) / (Area of the circle)] x 100

P = [(πab) / (πr²)] x 100

P = [(15 x 1) / (5²)] x 100

P = (15/25) x 100

P = 0.6 x 100

P = 60%

The percentage of the original circle's area in the area of the new circle will be 60%. Then the correct option is A.

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120 people out 500 people would play baseball.

What is fraction ?

The number of parts that make up a whole is all that a fraction informs us. With a slash between the two numbers, you can see if the numbers are fractions. The denominator is the lowest number, and the numerator is the highest. 1/2 is a fraction, for instance.

According to question

People who like baseball = 48/120

= 2/5

People who play baseball = 3/5 * 2/5

= 6/25

so, if there are 500 people,

then

500 * 6/25 = 120

hence, 120 People will play baseball.

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five couples have reserved seats in a row for a concert, 3840 different ways can they be seated. So, using the concept of combination formula we get -

The number of possible ways to choose items from a collection when the order of choice is irrelevant is determined using the combination formula. Combination, to put it simply, is the process of choosing items or things from a bigger group where order is irrelevant.

The formula becomes: [tex]^nC_r[/tex]

Where n = total number of objects in the set.

r = number of choosing objects from the set

Given that,

there are five couples

These couples have reserved seats in a row for a concert.

So, arrangements of 5 couples can be done in 5! × 2⁵= 3840 ways.

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The equation of the perpendicular line is y = -1/7(x + 4) + 6

From the question, we have the following parameters that can be used in our computation:

y = 7x - 2

Also, from the question;

We have the following points

The point is given as

Point = (-4, 6) i.e.  (x, y) = (-4, 6)

The equation of a line can be represented as

y = mx + c

Where

Slope = m

By comparing the equations, we have the following

m = 7

This means that the slope is 7

The slopes of perpendicular lines are opposite reciprocals

This means that the slope of the other line is -1/7

The equation of the line is then calculated as

y = m(x - x₁) +y₁

Where

m = -1/7

(x₁, y₁) = (-4, 6)

So, we have

y = -1/7(x + 4) + 6

Hence, the line has an equation of y = -10/3x + 1

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Answer:

58π or about 182.12

Step-by-step explanation:

In order to find circumference with diameter, you need to use the formula:

C = πd

Multiply the diameter (58) by pi, and since pi is an irrational number, let's use 3.14.

3.14(58) = 182.12

58π would be the answer as well if you don't multiply pi.

Answer:

10,5 should be changed

Step-by-step explanation:

hope this helps

The y-intercept of (f − g)(x) is 8. Therefore, option C is the correct answer.

Given various values of the linear functions f (x) and g(x) in the table.

An intercept is a point on the y-axis, through which the slope of the line passes. It is the y-coordinate of a point where a straight line or a curve intersects the y-axis. This is represented when we write the equation for a line, y = mx+c, where m is slope and c is the y-intercept.

For the function f(x)

Here, (-6, 20) and (-4, 14)

Slope =(14-20)/(-4+6)

= -3

Substitute, m=-3 and (x, y)=(-6, 20) in y=mx+c, we get

20=-3(-6)+c

c=2

Substitute, m=-3 and c=2 in y=mx+c, we get

f(x)=-3x+2 --------(I)

For the function g(x)

Here, (-6, -36) and (-4, -26)

Slope =(-26+36)/(-4+6)

= 10/2 =5

Substitute, m=5 and (x, y)=(-6, -36) in y=mx+c, we get

-36=5(-6)+c

c=-6

Substitute, m=5 and c=-6 in y=mx+c, we get

g(x)=5x-6 --------(II)

Now, (f − g)(x)=-3x+2-(5x-6)

= -3x+2-5x+6

= -8x+8

Here, y-intercept is 8

The y-intercept of (f − g)(x) is 8. Therefore, option C is the correct answer.

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Answer:

D

Step-by-step explanation:

He has max $55, so the total cost must be minor or equal to this value

6.25 + 7.50p ≤ 55

7.50p ≤ 55 - 6.25

7.50p ≤ 48.75

p ≤ 48.75 / 7.50

p ≤ 6.5

p = 6

The number of boys in the class = 48 boys

The number of girls in the class = 12 girls

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the number of boys in the class be = x

Let the number of girls in the class be = y

Now , the total number of students in the class = 60

So , the equation , will be

x + y = 60   be equation (1)

Now , the number of boys = 4 times the number of girls

So , the equation will be

x = 4y   be equation (2)

Substitute the value of equation (2) in equation (1) , we get

4y + y = 60

On simplifying the equation , we get

5y = 60

Divide by 5 on both sides of the equation , we get

y = 12

So , the value of y is 12

Substitute , the value of y in equation (2) , we get

x = 4y

x = 4 x 12

x = 48

Therefore , the number of boys is 48 and the number of girls is 12

Hence , The number of boys in the class = 48 boys

The number of girls in the class = 12 girls

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Answer:

it's so simple like very simple

Step-by-step explanation:

you just have to do

5x-3=2

x=2

The percentage of large  buttons  Tessa  bought   is 38%

You should know that percentage deals with the proportion of the large buttons when divided by 100

The given parameters are

Recall that she bought mixed buttons on the shop

19 large buttons

31 small buttons

Then total number of buttons is 19+31=50 mixed buttons

Then percentage of large buttons is

(19/50)*100

Simplify the fractions to have

=38%

In conclusion, Tessa bought 38% of large buttons

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The probability that it will NOT snow is 0.42

From the question, we have the following parameters that can be used in our computation:

Probability of snow = 0.58

The probability that it will NOT snow is the complement of the probability that it will snow

This is represented as

Probability that it will NOT snow = 1 - probability that it will snow

Substitute the known values in the above equation, so, we have the following representation

Probability that it will NOT snow = 1 - 0.58

Evaluate

Probability that it will NOT snow = 0.42

Hence, the value is 0.42

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Answer:y=124

x=67

Step-by-step explanation:

y=180-56

y=124

x=67

The amount of time the tennis ball will be in the air after launch is √2 seconds.

A function can be defined as the outputs for a given set of inputs.

The inputs of a function are known as the independent variable and the outputs of a function are known as the dependent variable.

The height of the tennis ball is given by the function h = - 16t² + 36, where t represents time in seconds.

Now, The amount of time the tennis ball will be in the air can be determined by the time when it hits the ground and at that time height of the ball should be zero.

Therefore, The time in the air is,

0 = - 16t² + 36.

16t² = 36.

t² = 2.

t = + √2 seconds, as time can not be negative.

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Answer:

Step-by-step explanation:

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Answer:

y = 6x

Explanation:

This question is asking you to write a linear equation in slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept.

The y-intercept (where the line crosses the y-axis) is visibly 0. As for the slope, you can take two points, I'll use (0,0) and (0.1,0.6) to calculate it.

Slope = y - y/x- x

Slope = (0.6 - 0)/(0.1 - 0) = 0.6/0.1 = 6

Plug in 0 for b and 6 for m and you have an equation.

y = 6x + 0

y = 6x

Answer: y = 6x

Step-by-step explanation: To find the equation you use the form y=mx+b, m is the slope meaning the rise of the function over the run of the function. This function rises 0.6 in terms of y in the time it takes to move or “run” over 0.1 in terms of x. so it would be 6/10 divided by 1/10. which leaves you with 6. b stands for the y-intercept which in this case it crosses the y-axis at zero so it would be zero. so putting it together you would have y=6x

Answer:

A:  y = -0.4x -5

B:  y = -1x +7

C:  y = 1.25x +7

D:  y = 3x -5

Step-by-step explanation:

See the attached worksheet.  Finding the equations for the graph lines is reasonabvly straightforward, but the number of lines quadruples the space required.  We'll find equations of the form y=mx+b, where m is the slope and b is the y-intercept (the value of y when x = 0).  The worksheet notes the 4 steps needed:

1.  mark any two points on the graph for each line.

2.  Find the slope for each line by calculating the Rise/Run

3.  Find the y-intercepts from the graph.

4.  Assemoble the slopes and intercepts into the four equations.

Use a spreasheet to keep organized, and nbe patient.  Check the equations using a free online graphing utility (e.g., DESMOS).

The value of x is 135°

What is Exterior Angle Theorem?

The exterior angle theorem states that the measure of an exterior angle is equal to the sum of the measures of the two opposite(remote) interior angles of the triangle.

An exterior angle is supplementary to its adjacent interior angle as they form a linear pair of angles.

Linear pair of angles are,

∠1 + ∠2 = 180°

where, ∠1 is exterior angle

and, ∠2 is interior angle

Given ,

One angle is = 90°

Then other two angle will be = 45° and 45°

Now, According to Exterior angle property,

x + 45 = 180

x = 180 - 45

x = 135°

Hence, the value of x is 135°

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Answer: 2, 4

Step-by-step explanation:

Assuming this is a linear relationship, [tex]y[/tex] increases by 2 whenever [tex]x[/tex] increases by 1.

So, the blanks in the table are [tex]0+2=2[/tex] and [tex]2+2=4[/tex], respectively.

Answer:

yes congruent means identical of the same

Step-by-step explanation:

hope this helps

Answer: The answer is here

Step-by-step explanation:

If the two sides of a triangle are in the same proportion of the two sides of another triangle, and the angle inscribed by the two sides in both the triangle are equal, then two triangles are said to be similar. Thus, if ∠A = ∠X and AB/XY = AC/XZ then ΔABC ~ΔXYZ.

If the measures of the corresponding sides of two triangles are proportional then the triangles are similar. Likewise if the measures of two sides in one triangle are proportional to the corresponding sides in another triangle and the including angles are congruent then the triangles are similar.

m=10d is the equation of line of the given graph.

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

In the given graph,

the line shows the Arias savings account.

Arias savings account over time.

As the line is passing through the origin it forms a linear equation.

From the graph we can see for 1 month it is 10 dollars

2 months has 20 dollars

m=10d

Hence, m=10d is the equation of line of the given graph.

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Answer:

Estimate: 3

Sum: 2.73

Step-by-step explanation:

To find the estimate, we can round our numbers to the nearest tenth (1.52 would become 1.5, and 1.21 would become 1.2). When we add these two numbers together, we get 2.7, which can be rounded up to 3.

To find the sum, we simply add 1.52 + 1.21, which equals 2.73.

The value of x for the given equation is 8.

Logarithm function is defined as the inverse of the exponential function.

If a^(b) = c, then b = log(c) at the base of a.

For negative numbers, the logarithm are complex numbers.

The given equation is as below,

x^(-1/3) = 32x^(-2)

It can be solved as follows,

x^(-1/3) = 32x^(-2)

Take logarithm on both sides to obtain,

log (x^(-1/3)) = log (32x^(-2))

=> -1/3 log(x) = log(32) - 2log(x)

=> 2log(x) - 1/3 log(x) = log(32)

=> 5/3log(x) = log(32)

=> log (x^(5/3)) = log(32)

Remove log from both sides to get,

x^(5/3) = 32

=> x = 32^(3/5)

=> x = 8

Hence, the solution of the given equation is x = 8.

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Answer:

this is easy get a protractor

Step-by-step explanation:

The equation that can be used to determine the number of hours, h, that Jayden worked the week his paycheck was the same is 65.25 = 5.22h and total amount of money that Jayden made when both paychecks were the same is $202.85.

Given :

Jayden has two jobs. One week his paycheck was the same for both jobs. As a server he eared $9. 64 per hour plus $82. 35 in tips Working at a jewelry store he earned $14. 86 per hour plus $17. 10 in sales

A )

Let h be the number of hours

9.64 * h + 82.35 = 14.86 * h + 17.10

82.35 - 17.10 = 14.86h - 9.64h

65.25 = 5.22h

B )

The total amount of money :

= 9.64 * 12.5 + 82.35

= 120.5 + 82.35

= $202.85

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Answer: false

Step-by-step explanation: