- Calculate how many pupils there are in the class if there are 21 girls.​

The answer is C) 18/48 and 21/56.

Two ratios are proportional if they have the same ratio when simplified to lowest terms.

A) 7/10 and 10/10 cannot be proportional because 7/10 cannot be simplified further, while 10/10 simplifies to 1/1.

B) To simplify the first ratio, we can divide both the numerator and denominator by 4, giving us 5/7. To simplify the second ratio, we can divide both the numerator and denominator by 3, giving us 5/6. Since these simplified ratios are not equal, the two ratios are not proportional.

C) To simplify the first ratio, we can divide both the numerator and denominator by 6, giving us 3/8. To simplify the second ratio, we can divide both the numerator and denominator by 7, giving us 3/8. Since these simplified ratios are equal, the two ratios are proportional.

D) To simplify the first ratio, we can multiply both the numerator and denominator by 2, giving us 6/10, which simplifies to 3/5. The second ratio is already in simplified form. Since these simplified ratios are not equal, the two ratios are not proportional.

Answer:

Step-by-step explanation:

This problem involves a binomial distribution where the probability of success (passing on the first attempt) is 0.65, and the probability of failure (not passing on the first attempt) is 0.35. We want to find the probability that less than 3 out of 5 people pass on their first attempt.

We can use the binomial probability formula to calculate this:

P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2)

Where X is the number of people who pass on their first attempt.

P(X = 0) = (5 choose 0) * 0.65^0 * 0.35^5 = 0.0024

P(X = 1) = (5 choose 1) * 0.65^1 * 0.35^4 = 0.0289

P(X = 2) = (5 choose 2) * 0.65^2 * 0.35^3 = 0.1323

So,

P(X < 3) = 0.0024 + 0.0289 + 0.1323 = 0.1636

Therefore, the probability that less than 3 out of 5 people pass their driver's tests on the first attempt is approximately 0.164, rounded to three decimal places.

Check the picture below.

Answer:

6,000 Video Games

Step-by-step explanation:

To find out how many video games Cloey sold on Sunday, we need to add the number of video games she sold on Friday and Saturday and then subtract that total from the total number of video games she sold over the three days:

Total number of video games sold on Friday and Saturday = 3,878 + 8,999 = 12,877

Total number of video games sold over the three days = (number sold on Friday) + (number sold on Saturday) + (number sold on Sunday)

We know that the total number of video games sold over the three days is the sum of the number sold on Friday and Saturday plus the number sold on Sunday. We can rearrange this equation to solve for the number sold on Sunday:

Number sold on Sunday = Total number sold over three days - Number sold on Friday and Saturday

Substituting in the values we know, we get:

Number sold on Sunday = (number sold on Friday) + (number sold on Saturday) + (number sold on Sunday) - (number sold on Friday) - (number sold on Saturday)

Number sold on Sunday = Total number sold over three days - Number sold on Friday and Saturday

Number sold on Sunday = (3,878 + 8,999 + X) - 12,877

Number sold on Sunday = X - 0

Simplifying this expression, we get:

Number sold on Sunday = 6,000

Therefore, Cloey sold 6,000 video games on Sunday.

The prove that triangle ABE is congruent to triangle CDE is given below

Generally, To prove that triangle ABE is congruent to triangle CDE, we need to show that they have the same size and shape.

First, we can see that angle AED and angle CEB are opposite angles and therefore congruent, since AB || DC.

Also, since line AB = line DC, we know that segment AE is congruent to segment CE and segment BE is congruent to segment DE.

Using these congruent sides and the congruent angle, we can apply the Side-Angle-Side (SAS) congruence criterion to conclude that triangle ABE is congruent to triangle CDE.

Therefore, we have proven that triangle ABE is congruent to triangle CDE.

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Therefore, the percentage increase in the price of petrol is approximately 5.57%.

One tenth of any amount is represented by the relative number 10% in the image. Since one percent (1%) represents the one tenth of something, 100 percent (100%) denotes the entire thing, and 200 percent (200%) denotes twice the amount indicated. percentage. Mathematical percentile is a similar subject.

To find the percentage increase in the price of petrol, we can use the formula:

percentage increase = (new value - old value) / old value x 100%

Here, the old value is R12.58 per litre, and the new value is R13.28 per litre. Substituting these values into the formula, we get:

percentage increase = (13.28 - 12.58) / 12.58 x 100%

percentage increase = 0.70 / 12.58 x 100%

percentage increase = 0.0557 x 100%

percentage increase = 5.57%

Therefore, the percentage increase in the price of petrol is approximately 5.57%.

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Student 1's answer is the correct answer: (x+2)(x+12).

An expression in math is a sentence with a minimum of two numbers or variables and at least one math operation. This math operation can be addition, subtraction, multiplication, or division.

Expression is a mathematical phrase which combines, numbers, variables and operators to show the value of something. An equation is a mathematical statement wherein two expressions are set equal to each other.

Student 2's answer, 3(x+2)(x+12), is incorrect because they multiplied the factors by 3, which is not necessary and changes the value of the expression.

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Answer:

The answer is no. It ought to be X-(16*10) given that she has made 10 necklaces out of 16 shells each using 160 total shells. To determine how many shells she still has, you would need to subtract those 160 from the initial number of shells she purchased, which was X.

In response to the supplied query, we may state that Draw a dot to coordinates  indicate the position (4.5, -2.25) where the two lines cross after finding the points on the x-axis and the y-axis.

A coordinate system is a technique used in geometry to precisely locate points or other geometrical objects on a manifold, such as Euclidean space, using one or more numbers or coordinates. A point or item on a two-dimensional plane is located using a pair of numbers known as coordinates. The x and y coordinates are two numbers that describe a point's location on a 2D plane. a collection of integers that indicate exact locations. Typically, the figure has two numbers. The first number represents the front-to-back distance, while the second number represents the top-to-bottom distance. When there are 12 units below and 5 above, as in (12.5), this is an example.

Plotting the coordinates of the point (4.5, -2.25) requires the following actions:

Create the x- and y-axes.

Identify the intersection of the x and y axes. The coordinates of this place, which is known as the origin (0, 0).

Find the coordinates (4.5, -2.25) on the x- and y-axes.

Move 4.5 units to the right of the origin to find the point on the x-axis.

Go 2.25 units down from the origin to find the point on the y-axis.

Draw a dot to indicate the position (4.5, -2.25) where the two lines cross after finding the points on the x-axis and the y-axis.

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The total cost of the driver to fill the fuel is given by A = $ 251.72

Equations are statements in mathematics that have two algebraic expressions on either side of the equals (=) sign.

It displays the similarity of the connections between the phrases on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are examples of the parts of an equation. When creating an equation, the "=" symbol and terms on both sides are necessary.

Given data ,

Let the total cost of the driver to fill the fuel be A

Now , the value of A is

Let the total capacity of the fuel tank be = 28 Liters

Now , the driver fills half the tank

So , the amount of fuel to be filled = 28 / 2 = 14 Liters

Now , the cost of fuel per Liter = $ 17.98

And , the total cost of the driver to fill the fuel A = amount of fuel to be filled x cost of fuel per Liter

On simplifying the equation , we get

The total cost of the driver to fill the fuel A = 14 x $ 17.98

The total cost of the driver to fill the fuel A = $ 251.72

Hence , the equation is A = $ 251.72

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The length of the side z is equal to 16.94 to the nearest hundredth using the sine rule.

The sine rule is a relationship between the size of an angle in a triangle and the opposing side.

We shall first evaluate for the angle m∠Z as follows:

9/sin32° = 15/sinY

sinY = (15 × sin32)/9 {cross multiplication}

Y = sin⁻¹(0.8832)

Y = 62.0308

m∠Z = 180 - (32° + 62.0308)

m∠Z = 180 - 94.0308

m∠Z = 85.9692

z/sin85.9692 = 9/sin32

z = (9 × sin85.9692)/sin32 {cross multiplication}

z = 16.9357

Therefore, the length of the side z is equal to 16.94 to the nearest hundredth using the sine rule.

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Answer:

The speed is: 186000 Miles/Sec

Step-by-step explanation:

The explanation is given in the picture.

Thank you!

Answer:

7b + 29 ≤ -26

Step-by-step explanation:

Given information:

The sum of a number times 7 and 29 is at most -26.

Sum- is referring to Addition ( + )

Times- is referring to Multiplication ( × )

At most - is referring to maximum. The maximum amount that it can get. Which ≤ means less than or equal to which refers to "At Most"

Hence, the inequality is

7b + 29 ≤ -26

RevyBreeze

The total amount of water in buckets that contain more than one quart is 39 gallons.

Amount is a noun that refers to a quantity or number of something. It can also be used to refer to a sum of money. Amount is commonly used in mathematics, banking, and accounting to represent a specific quantity or monetary figure. Amounts are often expressed as a whole number, fraction, or decimal. Amounts can be expressed in various ways, such as in dollars, euros, pounds, or other forms of currency. Amount is also used to describe the size or extent of something, such as an amount of time or effort.

According to the line plot, buckets with numbers 1, 2, 3, 4, 6, 8, 12, 14, 15, and 17 all contain more than one quart of water, for a total of 39 gallons. Bucket 5 has one quart exactly, and the other buckets contain less than one quart.

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The total amount of water in buckets that contain more than one quart is 39 gallons.

Amount is a noun that refers to a quantity or number of something. It can also be used to refer to a sum of money. Amount is commonly used in mathematics, banking, and accounting to represent a specific quantity or monetary figure. Amounts are often expressed as a whole number, fraction, or decimal. Amounts can be expressed in various ways, such as in dollars, euros, pounds, or other forms of currency. Amount is also used to describe the size or extent of something, such as an amount of time or effort.

According to the line plot, buckets with numbers 1, 2, 3, 4, 6, 8, 12, 14, 15, and 17 all contain more than one quart of water, for a total of 39 gallons. Bucket 5 has one quart exactly, and the other buckets contain less than one quart.

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The equation deduced by Malik is the correct equation.

An equation is a mathematical statement that shows that two mathematical expressions are equal.

For example, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an 'equal' sign.

Given that, the Boy Scout troop raised money in a fundraiser. they donated $400 to the food bank and half of the remaining amount to the animal shelter, they both represented the amount donated for the animal shelter :-

Malik: y = (x-400) / 2

Jacob: y = x/2 - 400

So, if we consider y as the money donated for the animal shelter and x is the total-raised money,

Therefore, according to the question,

$400 donated to food bank, then the left amount = x-400

Half of the money donated to the animal shelter based = (x-400) / 2

Therefore, the equation will be:-

y = (x-400) / 2

Hence, the equation deduced by Malik is the correct equation.

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Let the 7 letters A through G represent the ages of the 7 person family.

7/2 = 3.5 which rounds to 4 represents the slot number of the median, aka the middle-most position. The 4th letter is D. Because the median is 16, we know that D = 16.

We go from this

A,B,C,  D,  E,F,G

to this

A,B,C,  16,  E,F,G

I put a bit of spacing to help show why D is the middle.

-------------------

The modes are 12 and 45, which means those values show up more than once. Let's assume they show up 3 times each.

That tells us A,B, and C are all equal to 12. Furthermore, that assumption indicates E,F,G are all equal to 45.

We go from this

A,B,C,  16,  E,F,G

to this

12,12,12,  16,  45,45,45

But we run into a problem. The range is max-min = 45-12 = 33 and not 35 like we want.

We have no choice but to remove one copy of "12" and remove one copy of "45". We need to remove both because removing only one of those would result in the mode being just one value (rather than two).

-------------------

So we have this now

A,12,12,  16,  45,45,G

where A < 12 and G > 45

range = max - min = G-A = 35

G-A = 35 solves to G = 35+A

We can update the set to

A,12,12,  16,  45,45,35+A

-------------------

Now to figure out what "A" is.

The bit of info we haven't used yet is the mean.

Recall the mean has us add up the numbers and then divide by the number of values.

mean = (sum of the values)/(number of values)

mean = (A+B+C+D+E+F+G)/7

mean = (A+12+12+16+45+45+35+A)/7

mean = (2A+165)/7

Set that equal to the stated mean of 23 so we can solve for "A".

mean = (2A+165)/7

(2A+165)/7 = 23

2A+165 = 7*23

2A+165 = 161

2A = 161-165

2A = -4

A = -4/2

A = -2

That's not good. We should have gotten a positive whole number for "A". Since "A" is negative, it means there is a typo somewhere in the given instructions.

It's impossible to have a family of 7 people where the mean age is 23, the median is 16,  the modes are 12 and 45, and the range is 35. At least one of those starting values needs to change. If for instance the "45"s were changed to "41", then the equation above would solve to A = 2.

I would ask your teacher for clarification.

Answer:

The first step is to calculate the daily interest rate. We can do this by dividing the annual percentage rate (APR) by 365 (the number of days in a year):

Daily interest rate = 15% / 365 = 0.00041096

Next, we need to calculate the interest that accrues on the outstanding balance for the first month. Since there are 30 days in a typical month, we can multiply the daily interest rate by the outstanding balance and the number of days in the month:

Interest for first month = 0.00041096 × $400 × 30 = $4.93

This means that the outstanding balance after the first payment will be:

$400 + $4.93 - $75 = $329.93

So the balance after the first payment will be $329.93.

Answer:

I assume around 700 people vist the zoo

Hi

im pretty sure 88m2 is the answer

here is the workong out

hope it helps

good luck:)

Answer:

112m squared

Step-by-step explanation:

1/2 * b * h is the formula for a triangles so 1/2 * 6 * 8 is 24 * 2 because the other triangle is symmetrical and the formula for a square is b * h so 8 * 8 is 64 and adding 24 + 24 + 64 = 112 m squared

3. The solutions are (3, 8) and (–1, 0).

4. The solutions are (5, 7) and (-2, 0).

5. Data is most appropriate for a linear model.

6. The graph of y = -2x² + 2 is a downward-facing parabola

7. The graph of y = -x² is a downward-facing parabola

8. The graph of y = 2x² is an upward-facing parabola

9. The graph of y = 3x² - 4 is an upward-facing parabola

What is  solutions to the system?

A collection of values for a variable that simultaneously fulfill each equation is the solution to a system of equations.

A system of equations must be solved by identifying all possible sets of variable values that make up the system's solutions.

3. The solutions to the system are (3, 8) and (–1, 0).

To solve the system, we can substitute y = x + 5 from the first equation into the second equation:

x + 5 = x² – x + 2

Rearranging and simplifying, we get:

x² - 2x - 3 = 0

Factoring, we get:

(x - 3)(x + 1) = 0

Therefore, x = 3 or x = -1.

Substituting each value of x into y = x + 5, we get the corresponding y-value:

When x = 3, y = 3 + 5 = 8

When x = -1, y = -1 + 5 = 4

Therefore, the solutions are (3, 8) and (–1, 0).

4. The solutions to the system are (3, 7) and (-4, -2).

To solve the system, we can substitute y = x + 2 from the second equation into the first equation:

x² - 2x - 8 = x + 2

Rearranging and simplifying, we get:

x² - 3x - 10 = 0

Factoring, we get:

(x - 5)(x + 2) = 0

Therefore, x = 5 or x = -2.

Substituting each value of x into y = x + 2, we get the corresponding y-value:

When x = 5, y = 5 + 2 = 7

When x = -2, y = -2 + 2 = 0

Therefore, the solutions are (5, 7) and (-2, 0).

5. The data shown in the graph is most appropriate for a linear model.

6. The graph of y = -2x² + 2 is a downward-facing parabola that opens up and has a y-intercept of (0, 2).

7. The graph of y = -x² is a downward-facing parabola that opens up and passes through the origin (0, 0).

8. The graph of y = 2x² is an upward-facing parabola that opens up and has a y-intercept of (0, 0).

9. The graph of y = 3x² - 4 is an upward-facing parabola that opens up and has a y-intercept of (0, -4).

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Answer:

Step-by-step explanation:

45

Answer: The atmospheric pressure decreases with altitude. This is because as we move higher above the earth's surface, there is less air above us and therefore less weight pushing down on us. Therefore, the correct answer is:

C. An altitude of 7 km above sea level

At an altitude of 7 km above sea level, a person would experience the least atmospheric pressure because they would be furthest from the earth's surface and there would be very little air above them. This is why the air pressure in the Earth's upper atmosphere is much lower than at the surface of the Earth.

Step-by-step explanation:

The zeros ( roots ) of the function y = (x + 2)^2 - 25 are x = 3 and x = -7.

Given the function in the question;

y = ( x + 2 )² - 25

To find the zeros of the function, simply means find the values of  x in the function y = ( x + 2 )² - 25, when y equals zero.

Equat the function to 0

(x + 2)^2 - 25 = 0

Adding 25 to both sides, we get:

(x + 2)^2 - 25 + 25  = 0 + 25

(x + 2)^2  = 25

Taking the square root of both sides, we get:

x + 2 = ±√25

x + 2 = +5

Solving for x, we get:

x = -2 + 5 = 3

or x = -2 - 5 = -7

Therefore, the zeros of the function are 3 and -7.

Option 4) -7 and 3 is the correct answer.

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Answer:

Step-by-step explanation:

We can use the rule of 72 to estimate the time it takes for Arthur's investment to double. The rule of 72 states that the time it takes for an investment to double is approximately 72 divided by the annual rate of return.

To apply this rule, we need to calculate the annual rate of return that Arthur is earning on his investment. We can do this by calculating the percentage increase in his account balance from year to year.

From year 1 to year 2, his account balance increased by (118.81 - 109)/109 = 9.81/109 = 0.09 = 9%.

From year 2 to year 3, his account balance increased by (129.5 - 118.81)/118.81 = 10.69/118.81 = 0.09 = 9%.

So the average annual rate of return over this period is approximately 9%. Using the rule of 72, we can estimate that it will take approximately 72/9 = 8 years for Arthur's investment to double.

Therefore, the closest option among the given responses is option D. It will take about 8.04 years for Arthur's investment to double.

The simplified form is  [tex]-(sina + 1)[/tex].

One of the most significant areas of mathematics, trigonometry has a wide range of applications. Trigonometry is a discipline of mathematics that primarily focuses on the analysis of how a right-angle triangle's sides and angles relate to one another.

Given the function:

[tex]\frac{cos^2a}{sina - 1}[/tex]

Simplifying by using conjugate multiplication:

[tex]\frac{cos^2a \times (sina + 1)}{sina - 1 \times (sina + 1)}[/tex]

[tex]= \frac{cos^2a \times (sina + 1)}{sin^2a - 1^2}[/tex]

using [tex]sin^2a + cos^2a = 1[/tex]

[tex]= \frac{cos^2a \times (sina + 1)}{-cos^2a}[/tex]

[tex]= -(sina + 1)[/tex]

Hence, the simplified form is  [tex]-(sina + 1)[/tex].

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Answer:

I would solve for x with the first equation, then use that to solve for y in the second, then check by inputting values.

3x+y=-2

x-y=6

x=6+y

then...

3(6+y)+y=-2

18+3y+y=-2

18+4y=-2

4y=-20

y=-5

So..

3x+-5=-2

3x=3

x=1

3(1) + -5 = -2

Step-by-step explanation:

this might be correct.

Answer:

d) 360

Step-by-step explanation:

To solve this problem, we can use a Venn diagram. Let R, C, and J represent the sets of students who like rock, country, and jazz, respectively. We can fill in the diagram with the given information:

       J

      / \

     /   \

    /     \

 RC-----C

    \     /

     \   /

      \ /

       R

We know that:

The total number of students surveyed is 500.

9 students like all three types of music, so we can put 9 in the intersection of all three sets (RCJ).

24 like rock and country, so we can put 24 in the intersection of R and C (RC).

29 like rock and jazz, so we can put 29 in the intersection of R and J (RJ).

29 like country and jazz, so we can put 29 in the intersection of C and J (CJ).

We can calculate the number of students who like only one type of music by subtracting the number of students who like two or three types of music from the total number of students surveyed:

Total = R + C + J - RCJ

500 = 204 + 164 + 129 - 9

We can use this equation to solve for R, C, and J:

R = 204 - 24 - 29 - 9 = 142

C = 164 - 24 - 29 - 9 = 102

J = 129 - 29 - 29 - 9 = 62

So there are 142 students who like rock only, 102 students who like country only, and 62 students who like jazz only. Therefore, the total number of students who like exactly one type of music is:

142 + 102 + 62 = 306

Therefore, the answer is (d) 360.

Answer:

x = 12

Step-by-step explanation:

96 / 24 = 4, 28/ 7 = 4, assuming that it dilated by 4, so use 4 to multiply 25, 4 x 25 = 100 so 6x+28 = 100 then plug it in 6(12) + 28 = 100., 100 = 100

To check use a^2 + b^2 = c^2

28^2 + 96^2 = (6(12)+28)^2

784 + 9216 = (72+28)^2

784 + 9216 = 100^2

784 + 9216 = 10000

10000 = 10000