Imagine you are about to run two laps of an athletics track. You can go at any speed for the first lap. On the second lap, you will have to run faster such that your average speed is twice the speed of the first lap. How fast do you have to run the second lap to make this happen?

There are 37 pupils in the class.

The ratio can be defined as the number that can be used to represent one quantity as a percentage of another. Only when the two numbers in a ratio have the same unit can they be compared. Ratios are used to compare two objects.

Given, the ratio of girls to boys is 4:3, this means that for every 4 girls, there are 3 boys.

We can use this ratio to find the number of boys in the class. Let's set up a proportion:

4 girls : 3 boys = 21 girls : x boys

where x is the number of boys in the class.

To solve for x, we can cross-multiply:

4 girls * x boys = 3 boys * 21 girls

4x = 63

x = 15.75

We can't have a fractional number of students, so we need to round up to the nearest whole number. This means there are 16 boys in the class.

Total number of pupils = 21 girls + 16 boys = 37 pupils

Therefore, there are 37 pupils in the class.

Learn more about ratios here:

https://brainly.com/question/13419413

#SPJ1

Complete question:

the ratio of girls to boys is 4:3. Calculate how many pupils there are in the class if there are 21 girls.​

Answer:

[tex](r \;\circ\;q)(4) = \boxed{5}\\\\(q \;\circ\;r)(4) = \boxed{13}\\[/tex]

Step-by-step explanation:

We have the following functions

[tex]q(x) = x^2+4\\\\and\\\\r(x) = \sqrt{x+5}\\\\[/tex]

1. To find
[tex](r \;\circ \;q)(4) = r(\;q(4)\;)[/tex]

First find
[tex]q(4) = 4^2 + 4 = 16 + 4 = 20[/tex]

Substitute this value for x in r(x)

[tex]r(20) = \sqrt{20 + 5} = \sqrt{25} = 5[/tex]

So
[tex]\bold{(r \;\circ \;q)(4) = 5}[/tex]

2. To find
[tex](q \;\circ\;r)(4) = q(\;r(4)\;)[/tex]

First find
[tex]r(4) = \sqrt{4 + 5} = \sqrt{9} = 3\\\\[/tex]

Substitute this value for x in q(x)

[tex]q(3) = 3^2 + 4 = 9 + 4 = 13\\\\\bold{(q \;\circ\;r)(4) = 13}[/tex]

The compositions of functions are:

Here we have the two functions:

q(x) = x² + 4

r(x)=  √(x + 5)

We want to find the two compositions:

(r o q)(4) = r(q(4))

First let's find:

q(4) = 4² + 4 = 16 + 4 = 20

Then:

r(q(4)) = r(20) =  √(20 + 5) = 5

And the other composition is:

(q o r)(4) = q(r(4))

First, r(4) = √(4 + 5) = 3

Then:

q(r(4)) = q(3) = 3² + 4 = 9 + 4 = 13

Learn more about compositions at:

https://brainly.com/question/10687170

#SPJ1

The solutions to the quadratic equation [tex]X^2 + 7X = 0[/tex] are X = 0 and X = -7.

What is quadratic equation?

A quadratic equation is a polynomial equation of the second degree, which means it contains one or more terms that are raised to the power of two. The standard form of a quadratic equation is:

[tex]ax^2 + bx + c = 0[/tex]

where a, b, and c are constants, and x is the variable. The value of x that satisfies the equation is called the root or solution of the quadratic equation.

Quadratic equations can have one, two, or no real solutions, depending on the value of the discriminant [tex]b^2 - 4ac[/tex]. If the discriminant is positive, the equation has two real solutions; if it is zero, the equation has one real solution; and if it is negative, the equation has no real solutions but two complex solutions.

To solve the quadratic equation [tex]X^2 + 7X = 0[/tex] by factoring, we first write it in the standard form:

[tex]X^2 + 7X = 0[/tex]

Next, we factor out the common factor X:

X(X + 7) = 0

Now, we can apply the zero product property, which states that if the product of two factors is zero, then at least one of the factors must be zero. In this case, we have:

X = 0 or X + 7 = 0

Solving for X in each equation, we get:

X = 0 or X = -7

Therefore, the solutions to the quadratic equation X^2 + 7X = 0 are X = 0 and X = -7.

To know more about quadratic equation visit:

brainly.com/question/1214333

#SPJ1

Question:

[tex]X^2 + 7X = 0[/tex]

Solving Quadratics by Factoring

Answer:

area = 16

Step by step

Answer:

8

Step-by-step explanation:

Number of Riders on the Train

Week 1

Day

Monday

Tuesday

Wednesday

Thursd

Answer:

The answer you're looking for is 40%

Step-by-step explanation:

If you divide 12(numerator) by 30(denominator), you get 0.4.
After that, if you want to convert the decimal to a percent you always have to multiply by 100.

[tex]\frac{12}{30} =0.4=0.4 x 100=40%[/tex]

I hope this was helpful!

The value of x in the chord is 2.8 units

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

The circle and the chords

Represent the radius of the circle with r

Next, we calculate the radius using each chord using the Pythagoras theorem

Using the above as a guide, we have the following:

r² = x² + (38/2)²

r² = 12² + (30/2)²

By substitution, we have

x² + (38/2)² = 12² + (30/2)²

So, we have

x² = -(38/2)² + 12² + (30/2)²

Evaluate

x² = 8

Take the square root of both sides

x = 2.8

Hence, the value of x is 2.8 units

Read more about chords at

brainly.com/question/13950364

#SPJ1

Answer:

72 of the students are right handed.

Step-by-step explanation:

Answer:

72

Step-by-step explanation:

90 x 80

100

= 72

Answer:

Step-by-step explanation:

To convert a degree of likelihood to a probability value, we use the formula:

probability = number of favorable outcomes / total number of possible outcomes

In this case, the chances of encountering a car crash on the road are stated as "5 in 17", which means there are 5 favorable outcomes (encountering a car crash) out of 17 possible outcomes (driving on the road).

So, the probability of encountering a car crash can be calculated as:

probability = 5/17

This fraction can be simplified by dividing both the numerator and denominator by their greatest common factor, which is 1 in this case. Therefore, the probability of encountering a car crash on the road is:

probability = 5/17 ≈ 0.2941

Since the probability value is between 0 and 1 inclusive, we can express the indicated degree of likelihood as a probability value of approximately 0.2941.

Answer:

Approximately 13%

Step-by-step explanation:

Troy meant to make 15, but only made 13, meaning that he was off by 2. To find the percent error here, we will divide how off Troy was by the amount Troy meant to make:

2/15=0.133333333, or approximately 13% (multiply the decimal by 100 to find the percent, then round to the nearest integer.)

By using all steps below we can regroup the 89.600 - 47.131 = 42.469.

The first digit after the decimal represents the tenths place. The next digit after the decimal represents the hundredth place. The remaining digits continue to fill in the place values until there are no digits left.

To regroup and show your work for the subtraction problem 89.600 - 47.131, you can line up the numbers vertically with the decimal points aligned, like this:

 89.600 - 47.131 =

Start by subtracting the one's place (0 - 1). Since 0 is less than 1, you need to borrow 1 from the tens place, which becomes 8 - 1 = 7.

The one place becomes 10 + 0 - 1 = 9.

  89.600 - 47.131 = 2.469

Next, subtract the tenth place (0 - 3). Since 0 is less than 3, you need to borrow 1 from the one place, which becomes 9 - 1 = 8.

The tenth place becomes 10 + 0 - 3 = 7.

89.600 - 47.131 = 42.469

Finally, subtract the hundredth place (9 - 1), which gives 8.

 89.600 - 47.131 = 42.469

Therefore, By using all the above steps we can regroup the 89.600 - 47.131 = 42.469.

To learn more about the tenth place visit:

https://brainly.com/question/12091779

#SPJ1

The solution is,

Total capacity: 12 gallons

Equation: G = 12 - R*t

A mathematical expression is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

here, we have,

Let R be rate of gas consumption by car = 2 gallons/hr

Let G be the gallons in the car left

let g be the gallons used by the car while driving

Driven time, t = 4 hrs

Remaining gas =4 gallons

according to the question,

consumption rate, R = g/t

After driving for 4 hours

2 = g/4

g = 2*4 = 8 gallons

remaining gas = 4 gallons

therefore, total capacity of the car = 8 + 4 = 12 gallons

equation in terms of gas left,

G = 12 - R*t

Read more about mathematical expression here :

https://brainly.in/question/26994041

#SPJ1

Using the concept of rotational symmetry, the angle of rotation about the center that results in an image that matches the original figure is; Option A:  90

Rotational symmetry is defined as a process that requires the rotation of a given object about a reference point to produce its image which has the same characteristics. This tells us that its dimensions, measure of internal angles and size do not change except its orientation. The orientation depicts the way in which the object is positioned.

here, we have,

The sum of an angle formed at a point is 360 degrees.

Thus turning a given object about a point implies its rotation with respect to a measured  angle.

Thus in the diagram given in the question, the pattern shown divides the angle at the centered point into four equal parts.

Thus;

Angle of rotation = 360/4 = 90 degrees

Read more about rotational symmetry at; brainly.com/question/29977243

#SPJ1

Answer:

0

Step-by-step explanation:

X^2(x+3)(x-b)=0x2 = 0x =√0x= 0

(hope this helps you <:)

Answer:

Elsa's income tax for last year was 2,660 dollars.

Step-by-step explanation:

The triangle has a surface area of 12 square centimetres.

We can apply the following formula to determine the triangle's area:

Area = base x height x half

The triangle's height in this instance is 4 cm, while its base is 6 cm. We can therefore determine the area by substituting these values into the formula as follows:

Area: 0.5 by 6.4 by 4.4 cm

Amount = 12 cm2

Hence, the triangle has a surface area of 12 square centimetres.

To know more about Area of Triangle visit:

https://brainly.com/question/19305981

#SPJ1

Therefore , the solution of the given problem of  expressions comes out to be option C. 69x is the right response.

Calculations like multiplying, dividing, joining, and presently removing are required. If they were put together, it would say: An equation, some statistics, and a mathematical formula A statement of truth is composed of values, components, and mathematical processes like additions, subtractions, errors, subdivisions, and arithmetic formulas. Words and phrases can be evaluated and analysed.

Here,

The formula 21x + 19(2x) + 2(5x) can be made simpler as follows:

=> 21x + 38x + 10x = 69x

Maliq's total scores can therefore be written as 69x.

To determine which decision is equivalent to 69x, we can also look through the answer options.

A.

=> (21+19)2x + 10x = 40(2x) + 10x = 80x + 10x = 90x,

which is not equivalent to 69x..

B. 42x and 69x are not equal.

C. 69x is the same as 69x.

D. The sum of

=> (21+19+2)(x+2x+5x) = 42(8x) = 336x does not equal 69x.

Therefore, C. 69x is the right response.

To know more about expressions visit :-

brainly.com/question/14083225

#SPJ1

Given:-

[tex] \: [/tex]

[tex] \: [/tex]

Solution:-

now , put the given values of x = -2 nd y = 5 in equation :

[tex] \: [/tex]

[tex] \: [/tex]

[tex] \: [/tex]

[tex] \: [/tex]

[tex] \: [/tex]

━━━━━━━━━━━━━━━━━━━━━━━━━━━

hope it helps! :)

Answer:-45

Step-by-step explanation:

first plug in the x and the y values

4(-2)(5)-(-2+7)

The start using pemdas to simplify

*or bodmas depends on what you learned

Then you should arrive to this

4(-2)(5)+ -(5)

-8(5)+ -5

-40-5= -45

Hope that helps

To solve for x in the equation:

11.6% = x × 17.8% + (1 - x) × 8.4%

We can first convert the percentages to decimal form:

11.6% = 0.116

17.8% = 0.178

8.4% = 0.084

Substituting these values into the equation, we get:

0.116 = x  0.178 + (1 - x) × 0.084

Next, we can simplify the equation by distributing the (1 - x) term:

0.116 = x × 0.178 + 0.084 - x × 0.084

Simplifying further by combining like terms, we get:

0.116 = 0.178x + 0.084 - 0.084x

0.116 = 0.094x + 0.084

Subtracting 0.084 from both sides of the equation, we get:

0.032 = 0.094x

Finally, dividing both sides of the equation by 0.094, we get:

x = 0.3404 or approximately 0.34

Therefore, x is approximately 0.34

To know more about equation:

brainly.com/question/17429689

#SPJ1

Answer: 90%

Step-by-step explanation:

18/2=9

20/2=10

9 out of 10 is 90%

Answer: 81.82%

Step-by-step explanation: A percentage is a number or ratio that can be expressed as a fraction of 100.

here, we have,

given that,

In Mrs. Stone's class, 18 out of 22 students turned in their homework on time.

now,

the  percent of the class turned their homework in on time is,

18/22 * 100

=81.82%

The diagonal length of his current TV is 65 inches.

Pythagoras theorem states that for a right-angled triangle, the square of the hypotenuse is the sum of the squares of base and altitude. It can be used to find the diagonal of a rectangle if we know the length and the width.

As per the given data:

Length of the TV (l) = 56 inches

Width of the TV (b) = 33 inches

To find the diagonal length (d) of the TV:

From Pythagoras theorem:

[tex]d = \sqrt{l^2 +b^2}\\d = \sqrt{(56)^2 +(33)^2}\\d = \sqrt{3136 +1089}\\d = \sqrt{4225}\\d = 65 inches[/tex]

Hence, the diagonal length of his current TV is 65 inches.

Learn more about Pythagoras Theorem here :

brainly.com/question/21926466

#SPJ9

In response to the aforementioned query, we may say that The future interest value of the loan, or the total amount due after three months, is $8140.

By dividing the principal by the interest rate, the passage of time, and other factors, simple interest is determined. Simple return equals principle plus interest plus hours is the formula used in marketing. The easiest way to compute interest is by using this method. The most typical method for calculating interest is as a portion of the principle amount. For example, if he borrows $100 from a buddy and agrees to pay back the loan at 5% interest, he will only pay his share of the 100% interest. $100 (0.05) = $5. When you borrow money, you must pay interest, and you must charge interest when you lend it. Typically, interest is determined as an annual percentage of the loan total. The loan's interest is the name given to this percentage.

The following formula can be used to determine a loan's future value A:

[tex]A = P + Prt[/tex]

When P is the principal borrowed, r denotes the interest rate in decimal form, and t denotes the length of time in years.

P equals $8,000, r equals 0.07 (because the interest rate is specified as 7%), and t equals 3/12 to 0.25 years in this example (since the time period is given in months and we need to convert it to years).

With these values entered into the formula, we obtain:

[tex]A = $8000 + $80000.070.25\\A = $8000 + $140 \sA = $8140[/tex]

The future value of the loan, or the total amount due after three months, is $8140.

To know more about interest visit:

https://brainly.com/question/28792777

#SPJ1

[tex]~~~~~~ \textit{Simple Interest Earned Amount} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill & \$900\\ r=rate\to 10\%\to \frac{10}{100}\dotfill &0.10\\ t=years\dotfill &1 \end{cases} \\\\\\ A = 900[1+(0.10)(1)] \implies A = 990[/tex]

Since the sum of a triangle's internal angles is always 180 degrees, x has a value of 40 degrees.

The polygonal shape of a triangle has three edges and three angles. It is one of the most fundamental and significant geometric shapes and is utilised in a wide range of mathematical, scientific, and engineering fields. The edges and angles of a triangle can be used to classify it in various ways. Triangles can be categorised in one way by their sides: Three equal sides make up an equilateral triangle. Two of the edges of an isosceles triangle are equal. Three of the edges of a scalene triangle are unequal.

given

The property of angles in a triangle, which says that the sum of a triangle's interior angles is always 180 degrees, can be used to determine the value of x in the given figure.

Triangle ABC consists of:

∠A + ∠B + ∠C = 180

Since we know that A = 50 degrees and B = 90 degrees, we can use these numbers as a substitute:

50 + 90 + ∠C = 180

When we simplify the solution, we obtain:

140 + ∠C = 180

140 from both sides is subtracted, giving us:

∠C = 40

Since the sum of a triangle's internal angles is always 180 degrees, x has a value of 40 degrees.

To know more about triangle visit:

https://brainly.com/question/2773823

#SPJ1

The scale factor between the original and resulting points is equal to 4 / 3.

In this problem we find a representation of a quadrilateral and its image depicted in Cartesian plane. According to the statement, the coordinates of the original and resulting points are, respectively:

B(x, y) = (- 3, 6), B'(x, y) = (- 4, 8)

Then, the scale factor can be found by means of the following formula:

B'(x, y) = k · B(x, y)

(- 4, 8) = (- 3 · k, 6 · k)

k = 4 / 3

To learn more on dilations: https://brainly.com/question/13176891

#SPJ1

The bridge needs to be 1.6 miles long. The solution has been obtained by using Pythagoras theorem.

What is Pythagoras theorem?

According to the Pythagorean Theorem, the square of a right-angled triangle's hypotenuse side is equal to the sum of the squares of its other two sides.

We are given a right angled triangle with base 3 miles and the hypotenuse 3.4 miles.

The perpendicular is given to be 'x'.

Using Pythagoras theorem, we know that

⇒Hypotenuse² = Perpendicular² + Base²

⇒(3.4)² = x² + 3²

⇒11.56 = x² + 9

⇒x² = 2.56

⇒x = 1.6 miles

Hence, the bridge needs to be 1.6 miles long.

Learn more about Pythagoras theorem from the given link

https://brainly.com/question/343682

#SPJ1

We can say that approximately 4.29 inches of rain fell in 15 minutes.

We can apply a proportion to determine the amount of rain that fell in 15 minutes.

We can calculate the proportion because we know that 12 inches of rain fell in 42 minutes:

x inches in 15 minutes equals 12 inches in 42 minutes.

where x is how much rain fell in 15 minutes.

We can cross-multiply and simplify to find x's value:

42 minutes equals 12 inches times 15 minutes (x inches)

180 = 42x

x = 180 / 42

x = 4.2857...

We may estimate that 4.29 inches of rain, rounded to the nearest hundredth, fell in 15 minutes.

To know more similar question visit:

https://brainly.com/question/3614551

#SPJ1

The measure of x from the angles of the parallel lines are solved

Straight, equally spaced lines that never cross each other and are on the same plane are called parallel lines. The angles that are created when any two parallel lines are intersected by a line (referred to as the transversal) have a relationship. Corresponding angles, Alternate Interior Angles, Alternate Exterior Angles, and Consecutive Interior Angles are some of the several pairs of angles that are created at this intersection.

Corresponding angles

When two parallel lines are intersected by a transversal, the corresponding angles have the same relative position

Alternate Interior Angles

Alternate interior angles are formed on the inside of two parallel lines which are intersected by a transversal.

Alternate Exterior Angles

The pairs of angles formed on either side of a transversal that divides two parallel lines are known as alternate exterior angles.

Consecutive Interior Angles

When two parallel lines are cut by a transversal, the pairs of angles formed on the inside of one side of the transversal are called consecutive interior angles or co-interior angles.

Given data ,

Let the figure be represented as A

Now , let the missing angle be represented as x

a)

Let the figure be A

Now , the measure of m∠x = 125° ( corresponding angles )

So , the measure of angle x = 125°

b)

Let the figure be A

Now , the measure of m∠x = 57° ( alternate interior angles )

So , the measure of angle x = 57°

c)

Let the figure be A

Now , the measure of m∠x = 70° ( Vertically opposite angles are same )

So , the measure of angle x = 70°

d)

Let the figure be A

Now , the measure of m∠x = 180° - 105°( co interior angles add up to 180° )

So , the measure of angle x = 75°

e)

Let the figure be A

Now , the measure of m∠x = 180° - 53°( co interior angles add up to 180° )

So , the measure of angle x = 127°

f)

Let the figure be A

Now , the measure of m∠x = 180° - 133° ( corresponding angles )

So , the measure of angle x = 47°

Hence , the measures of angles are solved

To learn more about parallel lines cut by transversal click :

https://brainly.com/question/28182928

#SPJ9