There are 32 students in the school day. the ratio of girls to all the students in the play is 5:8.

1. Let's call the first number "x" and the second number "y". We know that:

x = 4 + 2y (equation 1)

x - y = 27 (equation 2)

We can use equation 1 to substitute x in equation 2:

(4 + 2y) - y = 27

Simplifying the equation:

3y = 23

So the second number is:

y = 23/3

Using equation 1, we can find the first number:

x = 4 + 2(23/3) = 50/3

Therefore, the numbers are 50/3 and 23/3.

2. Let's call the length of the equal sides of the triangle "x" and the length of the third side "y". We know that:

y = x + 10 (equation 1)

2x + y = 100 (equation 2)

We can use equation 1 to substitute y in equation 2:

2x + (x + 10) = 100

Simplifying the equation:

3x = 90

So the length of the equal sides is:

x = 30

Using equation 1, we can find the length of the third side:

y = 30 + 10 = 40

Therefore, the lengths of the sides are 30, 30, and 40.

The y-intercept of a linear equation represents the value of the dependent variable when the independent variable is equal to zero.

What is linear equation?

A linear equation is a mathematical equation of the form y = mx + b, where x and y are variables, m is the slope of the line, and b is the y-intercept.

What is y-intercept?

In a linear equation of the form y = mx + b, the y-intercept (b) is the point where the line intersects the y-axis.

The y-intercept of a linear equation represents the value of the dependent variable when the independent variable is equal to zero. In the context of Justine's race, the y-intercept would represent her starting distance from the finish line.

It would be the distance from the finish line when she began the race, or the distance she would have to run to reach the finish line if she started at the beginning. The slope of the line would tell you how much the distance decreases as she runs.

Together, the y-intercept and slope of the line can provide useful information for understanding and analyzing Justine's race.

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The answer of the given question based on the linear relationship is , the y-intercept gives information about Justine's initial position or starting point before she started running the race.

A linear relationship is a type of relationship between two variables where their relationship can be described by a straight line. In other words, the change in one variable is directly proportional to the change in the other variable. This means that as one variable increases or decreases, the other variable also changes in a consistent and predictable way. Linear relationships are commonly studied in mathematics, statistics, and other fields as they provide a useful framework for understanding the relationship between two variables and making predictions based on that relationship.

In the context of this linear relationship, the y-intercept represents the starting point of Justine's race. It is the point where her distance from the finish line is zero, which is the beginning of the race. Therefore, the y-intercept gives information about Justine's initial position or starting point before she started running the race.

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Answer:

1:A

2:B

3:A

that's the answer I think

In conclusion the discount amount is Rs. 1250.

Why it is?

Let's start by using algebra to represent the problem:

Let's assume the market price of the article is "M".

The shopkeeper offers a 20% discount, so the selling price (SP) would be:

SP = M - 0.20M

SP = 0.80M

Then, a 10% VAT is levied on the selling price, so the final price (FP) would be:

FP = SP + 0.10SP

FP = 1.10SP

FP = 1.10(0.80M)

FP = 0.88M

We know that the customer paid Rs. 500 for VAT, so:

0.10SP = 500

Substituting SP = 0.80M, we get:

0.10(0.80M) = 500

Solving for M, we get:

M = 6250

So, the market price of the article is Rs. 6250.

Now, to find the discount amount, we can subtract the selling price from the market price:

Discount amount = Market price - Selling price

Discount amount = Rs. 6250 - 0.80 x Rs. 6250

Discount amount = Rs. 1250

Therefore, the discount amount is Rs. 1250.

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The sample space when 2 lollipops are randomly selected with replacement is S_with_replacement = {(Grape, Grape), (Grape, Cherry), (Grape, Lemon), (Cherry, Grape), (Cherry, Cherry), (Cherry, Lemon), (Lemon, Grape), (Lemon, Cherry), (Lemon, Lemon)}

The sample space when lollipops are selected without replacement is S_without_replacement = {(Grape, Grape), (Grape, Cherry), (Grape, Lemon), (Cherry, Grape), (Cherry, Cherry), (Cherry, Lemon), (Lemon, Grape), (Lemon, Cherry), (Lemon, Lemon)}.

The experiment with replacement (Part A) shows independent events because the probability of each lollipop being chosen is the same for both selections.

When selecting 2 lollipops with replacement, we put the first lollipop back into the bag before choosing the second one.  When selecting 2 lollipops without replacement, we do not put the first lollipop back into the bag before choosing the second one.

The outcome of the first event does not affect the probability of the second event.

The experiment without replacement (Part B) shows dependent events because the probability of the second lollipop being chosen is affected by the outcome of the first event. When one lollipop is removed from the bag, there are fewer options available for the second selection, and the probabilities of the remaining lollipops change.

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Step-by-step explanation: The answer is D. The quality a design has if it maintains all of its characteristics when it is reflected over an axis lying in its plane. This is the definition of reflectional symmetry. A and B are examples of reflectional symmetry over a vertical or horizontal axis, but not the general case. C is the definition of rotational symmetry.

If there is a statistically significant interaction effect, we would not expect to see a pattern of parallel lines on a graph that plots the means of the dependent variable for each level of the two factors anova.

If there is a statistically significant interaction effect in a two-factor ANOVA, it means that the effect of one independent variable (factor) on the dependent variable depends on the level of the other independent variable. In other words, the effect of one factor on the dependent variable varies across the levels of the other factor.  

If there is no interaction effect, the lines would be parallel and have the same slope. But if there is an interaction effect, the lines would cross or have different slopes, indicating that the effect of one factor on the dependent variable depends on the level of the other factor.

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For a sample of 72 batteries, the probability that the average battery life of the sample exceeds 1173.8 minutes is 0.9918.

It states a battery life variance of 8100 minutes and a median battery life of 1192 minutes.

In a sample of 72 batteries, find the probability that the average battery life (x) of the sample exceeds 1173.8 minutes.

Due to the large sample size (n = 72), we can use the central limit theorem to assume that the sample mean follows a normal distribution with mean μ = 1192 and standard deviation σ = sqrt(8100/72) = 30.

So the z-score for x= 1173.8 is

z = (x - μ) / (σ / sqrt(n))

= (1173.8 - 1192) / (30 / square(72))

= -2.4

You can use a standard normal distribution table or calculator to find the probability that a  standard normal random variable is greater than -2.4. This is 0.9918 (rounded to four decimal places).

Therefore, for a sample of 72 batteries, the probability that the average battery life of the sample exceeds 1173.8 minutes is 0.9918 (rounded to four decimal places) if the claim is correct. 

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Answer:c

Step-by-step explanation:

The answer for B is: 5÷4 cups of fruit drink are made with 1 cup of apple juice.

What is Algebraic expression ?

An algebraic expression is a mathematical phrase that can contain variables, constants, and mathematical operations such as addition, subtraction, multiplication, division, and exponentiation. Algebraic expressions are used to represent and solve problems in many areas of mathematics, science, engineering, and finance.

For A:

We want to find the ratio of carrot juice to apple juice when 1 cup of apple juice is used. Let's represent the amount of carrot juice with "x".

So, we have the ratio:

x : 1 cup

which is equivalent to:

1÷5 cup : 3÷5 cup

To solve for x, we can set up a proportion:

1÷5 cup ÷ 3÷5 cup = x ÷ 1 cup

Simplifying the left side:

(1÷5 cup) ÷ (3÷5 cup) = (1÷5 cup) x (5÷3) = 1÷3 cup

So, the ratio of carrot juice to apple juice when 1 cup of apple juice is used is:

1÷3 cup : 1 cup

Therefore, the answer for A is: 1/3 cup of carrot juice is used for 1 cup of apple juice.

For B:

We want to find how many cups of fruit drink are made with 1 cup of apple juice. Let's represent the amount of fruit drink with "y".

So, we have the ratio:

1 cup : y

which is equivalent to:

3÷5 cup : (1÷5 cup + 3÷5 cup) = 4÷5 cup

To solve for y, we can set up a proportion:

1 cup ÷ 4÷5 cup = y ÷ 1

Simplifying the left side:

(1 cup) ÷ (4÷5 cup) = (1 cup) x (5÷4) = 5÷4 cup

So, 5/4 cups of fruit drink are made with 1 cup of apple juice.

Therefore, the answer for B is: 5÷4 cups of fruit drink are made with 1 cup of apple juice.

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Step-by-step explanation:

The GCF of 24 and 18 is '6'...factor that out to get

6 ( 4a-3b)   that is all you can do....

Answer:

The first step is to calculate the total cost of energy used in two months. To do that, we need to multiply the amount of energy used by the cost per kilowatt-hour:

3550 kW•h x $0.10/kW•h = $355.00

So the total cost of energy used in two months is $355.00. This is the amount of the bill that the business will receive for its electricity usage.

Step-by-step explanation:

Answer:

To calculate the bill, we need to multiply the amount of energy used (3550 kW•h) by the cost per kW•h (10 cents).

3550 kW•h x 10 cents/kW•h = $355.00

Therefore, the bill for the business is $355.00.

Step-by-step explanation:

please pa brainliest po thanks.

If 25% of customers come in after 5:00 pm, then we can expect that 0.25 times the total number of customers come in after 5:00 pm.

Let's use this to find how many customers we expect to come in after 5:00 pm on last Tuesday:

Number of customers who came in after 5:00 pm = 0.25 * 84 = 21

Therefore, we would expect that 21 customers came in after 5:00 pm on last Tuesday.

The answer of the given question based on the Similarity of triangles is the correct answer is (c) not similar.

Congruent triangles are two or more triangles that have exactly the same size and shape. In other words, their corresponding sides and angles are equal in measure. When two triangles are congruent, we can superimpose one on top of the other so that they coincide exactly.

To determine whether two triangles APT and DPE are the similar, we need to check if their corresponding angles are the congruent and if their corresponding sides are the proportional.

Looking at the diagram, we can see that angle APT and angle DPE are both right angles, so they are congruent.

To check if the sides are proportional, we can compare the ratios of corresponding side lengths:

AP/DP = 39/26

PT/PE = 40/16

We can simplify these ratios:

AP/DP = 3/2

PT/PE = 5/2

The ratios are not equal, so the corresponding sides are not proportional.

Therefore, the triangles APT and DPE are not similar.

The correct answer is (c) not similar.

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Answer:

  6050 square meters

Step-by-step explanation:

You want to know the largest rectangular area that can be enclosed using 220 meters of fencing for 3 sides.

For enclosure length x, the width of the enclosure is half the remaining fence: (220 -x)/2. The area is the product of length and width.

  A = (x)(220 -x)/2

This is the equation of a parabola that opens downward. Its vertex (maximum) is halfway between the zeros, which are x=0 and x=220. This means the area is maximized when x=110 and the width is (220-110)/2 = 55.

The maximum area is (110 m)(55 m) = 6050 m².

__

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The answer is 2025 sq. meter.

If you have 220 meters of fencing and want to enclose a rectangular area up against a long, straight wall, the largest area you can enclose is 4840 square meters. Explanation: To determine the largest possible area, we have to find out how to divide the 220 meters of fencing so that we can maximize the space enclosed by it. If one side of the rectangle is x meters long, the other side is (110 - x) meters long (because we have one straight wall to use as a side).The perimeter of the rectangle can be calculated by adding up all four sides of the rectangle. Hence:2x + (110 - x) + (110 - x) = 220We simplify the equation to solve for x:2x + 220 - 2x = 220-x = 55Therefore, one side of the rectangle is 55 meters long, and the other side is (110 - 55) = 55 meters long as well. The area of a rectangle is given by its length multiplied by its width. In this case, the area is:55 x 55 = 3025.

Therefore, the largest area that can be enclosed is 3025 square meters.

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The total number of ways in which the group of seven people can be seated together in a row are 1440.

The group of seven people are attending the movie together and two of them are insisting that they will sit side by side to each other.

Now if all the people were to be seated in any random order then the number of positions would have been seven but now as two people are sitting side by side so we will consider only six positions in which we have to make the combinations.

And as we know that the seven people will be unique and there will be no repetition total number of ways in which the seven can be fitted together in a row is,

= 6 x 5 x 4 x 3 x 2 x 1 x 2

= 1440

It is to be noted that we have multiplied by the number of positions with to because the two people who are sitting together can be seated in two possible ways.

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Hence, value of variable y in the triangle is 7.5

Triangle proportionality is a relationship that exists between the sides of a triangle when a line is drawn parallel to one side of the triangle, intersecting the other two sides. Specifically, the line divides the two sides in proportion to the length of the third side.

We know that,  if a line is drawn parallel to one side of a triangle, then the line divides the other two sides in proportion.

AB/AC=2y+5/2y+25

We know that

AB=BC=1/2AC

½=2y+5/2y+25

2y+25=4y+10

2y=15

y=7.5

value of variable y in the triangle is 7.5.

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Answer: y-3= 5/4(x-1) is the point slope form answer, y = 1.25x + 1.75 is the slope intercept form answer.

Step-by-step explanation:

Answer:

quadratic

Step-by-step explanation:

see image above for explanation.

Answer:

alternate exterior angles

Step-by-step explanation:

Both x and 100° are alternate exterior angles. Therefore, by definition, x = 100°.

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Answer:  9 square feet

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Given: [tex]\textsf{Keisaun needs to cover a square. One side is 3 feet}[/tex]

Find:  [tex]\textsf{We need to find how much paper he needs}[/tex]

Solution:  Using the information that was given to us we know that we need to determine the area of the square that Keisaun needs to cover.  We know that the area formula for a square is side * side.  We are also given the information that a single side of the board is measured to be 3 feet.  Therefore, using that information we can plug the value into the square area formula and solve.

Therefore, the answer to the question would be that Keisaun would need 9 square feet of paper to cover the square bulletin board.

Answer: Given that MNOP is a trapezium with MN parallel to OP and A is the midpoint of NO.

To prove that the area of triangle MAP is half the area of trapezium MNOP, we need to use the following theorem:

Theorem: If a line segment joins the midpoint of one side of a triangle to a vertex opposite to that side, then the segment divides the triangle into two equal areas.

Proof:

Since A is the midpoint of NO, we can draw a line segment AP from vertex P to point A on NO as shown in the figure below:

      M _______N

       |\      |

       |  \    |

       |    \  |

       |      \|

      O--------P

            A

We can see that triangle MAP is formed by the line segment AP and side MP of the trapezium.

Also, we can see that triangle MAN is congruent to triangle NOP because they are both right triangles with corresponding sides parallel. Therefore, they have the same area.

Since MNOP is a trapezium, the area of trapezium is given by:

Area of trapezium MNOP = (1/2)(MN+OP) × height

Since MN is parallel to OP, the height of the trapezium is the same as the height of triangle MAN and NOP.

Therefore, the area of trapezium MNOP can be written as:

Area of trapezium MNOP = (1/2)(MN+OP) × height

= (1/2)(MA+AP+OP) × height

= (1/2)(MA+MP) × height (Since AP = NO/2 = height)

So, we have proved that:

Area of trapezium MNOP = (1/2)(MA+MP) × height

Using the theorem, we know that AP divides triangle MAP into two equal areas. Therefore,

Area of triangle MAP = (1/2) × Area of triangle MAP

Substituting the above in the expression for the area of trapezium, we get:

Area of trapezium MNOP = Area of triangle MAP + (1/2) × Area of triangle MAP

= (3/2) × Area of triangle MAP

Therefore, we have:

Area of triangle MAP = (1/2) × Area of trapezium MNOP

Thus, we have proved that the area of triangle MAP is half the area of trapezium MNOP.

The volume of the give cone is 4.0913 π m³.

What is volume ?

Volume is the measure of the amount of three-dimensional space enclosed by a closed surface or shape. It is usually expressed in cubic units, such as cubic meters (m³), cubic centimeters (cm³), or cubic inches (in³). The volume of an object can be calculated by multiplying its length, width, and height, or by using a formula specific to the shape of the object, such as the formula for the volume of a sphere or a cylinder. Volume is an important concept in geometry, physics, and engineering, and is used to measure the capacity of containers, the displacement of liquids, and the size of solid objects.

We know that, volume of cone = 1/3 πr²h

here, h = 3.4 cm

         r = 1.9 cm

so, volume of given cone = 1/3 πr²h

                                           =  1/3 π × 1.9² × 3.4

                                           = 4.0913 π m³

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The perimeter of ΔJKL = KJ + JL + KL = 35 + 43.986 + 37.5 = 116.5

What is perimeter?

To find the perimeter of ΔJKL, we first need to find the length of JL. We can use the law of cosines to do this:

cos(J) = (KJ² + JL² - KL²) / (2KJJL)

cos(57) = ((35)² + x² - (37.5)²) / (235x)

x² - 23537.5*cos(57)*x + ((35)² - (37.5)²) = 0

Using the quadratic formula, we get:

x = [23537.5cos(57) ± √((23537.5cos(57))² - 4*((35)²-(37.5)²))]/2

x = [23537.5cos(57) ± √((435)²(37.5)²cos(57)² + 4*(37.5)²)]/2

x = 43.986 or x = 10.402

Since x represents the length of a side of a triangle, we know that the value of x we're looking for is the larger one, so x = 43.986.

Now we can find the perimeter of ΔJKL:

Perimeter = KJ + JL + KL = 35 + 43.986 + 37.5 = 116.486

Rounding to the nearest tenth, we get a final answer of 116.5.

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Complete question is: The perimeter of ΔJKL = KJ + JL + KL = 35 + 43.986 + 37.5 = 116.5

It will cost $1200 to cover both sides of the green roof with plants at a cost of $0.75 per square foot.

To calculate the cost of covering both sides of the green roof, we first need to find the area of the roof. We can use the formula for the area of a rectangle:

area = length x width

Since the roof is 40 feet long, we need to find the width to calculate the area. We can estimate the width from the picture, but it's not given explicitly. So, we can make a reasonable assumption that the width is the same as the length of the shorter side of the roof, which appears to be about 20 feet.

Using this assumption, we can calculate the area of one side of the roof:

area = length x width = 40 ft x 20 ft = 800 sq ft

Since there are two sides to the roof, the total area is twice this amount:

total area = 2 x 800 sq ft = 1600 sq ft

To find the total cost of covering both sides of the roof, we can multiply the area by the cost per square foot of plants:

total cost = area x cost per sq ft

= 1600 sq ft x $0.75/sq ft

= $1200

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The probability that the class length is more than 51.7 min is 0.3 or 30%.

To solve the problem, we first need to find the total possible outcomes, which is the range of class lengths between 50.0 min and 52.0 min, which is 2.0 min. Since the distribution is uniform, each possible class length within this range is equally likely.

Next, we need to find the favorable outcomes, which is the range of class lengths that are more than 51.7 min. This range is 52.0 min minus 51.7 min, which equals 0.3 min.

To find the probability, we divide the number of favorable outcomes by the total number of possible outcomes:

Probability = (favorable outcomes) / (total outcomes) = 0.3 min / 2.0 min = 0.15 or 15%.

Therefore, the probability of a randomly selected class length being more than 51.7 min is 0.3 or 30%.

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Answer: [tex]\angle F = 44\°\\angle D= 46\°[/tex]

Step-by-step explanation: