A survey of 15 students revealed that 9 students brought their lunch from home, and 6 students bought their lunch in the cafeteria. Based on this information, If there are 500 students in the school, how many students could be expected to bring their lunch?​

Answer:

n = 12

Step-by-step explanation:

Given equation:

[tex]\dfrac{9}{n}=\dfrac{75}{100}[/tex]

We can solve the equation for the unknown quantity, n, by cross-multiplying, which means multiplying both sides of the equation by the product of the denominators.

The denominator of a fraction is the part below the division bar.

The denominators of the given equation are n and 100, so their product is 100n.

Multiply both sides by 100n:

[tex]\implies \dfrac{9}{n} \cdot 100n=\dfrac{75}{100}\cdot 100n[/tex]

Simplify and cancel the common factors:

[tex]\implies \dfrac{9\cdot 100n}{n} =\dfrac{75\cdot 100n}{100}[/tex]

[tex]\implies 9\cdot 100 =75\cdot n[/tex]

[tex]\implies 900 =75n[/tex]

To solve for n, divide both sides of the equation by 75:

[tex]\implies \dfrac{900}{75} =\dfrac{75n}{75}[/tex]

[tex]\implies 12=n[/tex]

Therefore, the unknown quantity, n, is 12.

Answer:

Step-by-step explanation:

To find:-

Answer:-

The given equation to us is ,

[tex]\longrightarrow \dfrac{9}{n}=\dfrac{75}{100} \\[/tex]

Simplify the RHS of the equation. This can be done by dividing the numerator and denominator by 25 as it is the HCF of 75 and 100 . So we have;

[tex]\longrightarrow \dfrac{9}{n}=\dfrac{75\div 25}{100\div 25} \\[/tex]

Simplify,

[tex]\longrightarrow \dfrac{9}{n} = \dfrac{3}{4} \\[/tex]

Flip the numerator and denominator on both the sides , as ;

[tex]\longrightarrow \dfrac{n}{9} =\dfrac{4}{3} \\[/tex]

Multiply both the sides by 9 as ,

[tex]\longrightarrow \dfrac{n}{9}\times 9 =\dfrac{4}{3}\times 9\\[/tex]

Simplify,

[tex]\longrightarrow \boxed{\boldsymbol{ n = 12}} \\[/tex]

Henceforth the value of n is 12 .

Answer:

-8 - 1 - 2 = -9 - 3 is not an equal expression because when both sides are simplified you get -12 from -9-3 and -11 from -8-1-2.    (-11)≠(-12)

Step-by-step explanation:

If you are confused with subtracting negatives from negatives there is an equal trick which can make it seem a lot more easier. Basically instead of viewing it as -9-3, you can look at it was -9+(-3). Both of these problems are the same thing, but by just adding the + in the middle makes it seem a lot more easier to interpret. Hope this helps.

If the total is 153, then the percentage would be of 107 be simply calculated by using the formula as 69.935.

The denominator of a percentage (also known as a ratio or fraction) is always 100. Sam, for instance, would have received 30 out of a possible 100 points if he had received 30% on his maths test. In ratio form, it is expressed as 30:100 and in fraction form as 30/100. In this case, the percentage symbol "%" is interpreted as "percent" or "percentage."

This percent sign may always be changed to a fraction or decimal equivalent by using "divided by 100."

We already have our first value 153 and the second value 107. Let's assume the unknown value is Y which answer we will find out.

As we have all the required values we need, Now we can put them in a simple mathematical formula as below:

STEP 1

Y = 107 / 153

By multiplying both numerator and denominator by 100 we will get:

STEP 2

Y =  107 /153 × 100

= 69.935

STEP 3

Y = 69.935

Finally, we have found the value of Y which is 69.935 and that is our answer.

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Complete question;

If the total is 153, what would be the percentage of 107?

The simplified expression is (7/4)a - 11.

What is simplification?

Exam scores are improved by simplifying mathematical problems, which is also used in everyday life to get discounts in malls of up to 35%, flat discounts, or 20% for purchases up to Rs. 100. In this section, you only need to use the basic simplification principles to solve equations.

Therefore, simplifying an expression entails using various techniques to transform it into a simpler variant. The actions needed to reduce things are carried out in a predetermined sequence known as BODMAS.

To simplify the expression, we can start by distributing the coefficients to the terms inside the parentheses:

3/4(5a - 16) - 1/3(6a - 3)

= (3/4 * 5a) - (3/4 * 16) - (1/3 * 6a) + (1/3 * 3)

= (15/4)a - 12 - 2a + 1

= (15/4)a - 2a - 11

= (7/4)a - 11

Therefore, the simplified expression is (7/4)a - 11.

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Answer:

any value of x that satisfies the given conditions (i.e., makes the mean of the marks equal to the given value) is a possible score for Esi in the test. For example, if we want the mean to be 80, we can substitute 80 for Mean in the expression above and solve for x.

Step-by-step explanation:

   Expression for the mean of the marks:

   The mean of the marks is the sum of all the marks divided by the number of students. So, for this problem, the expression for the mean is:

Mean = (92 + 85 + 65 + x) / 4

   Linear inequality for the mean being less than 80:

   We can find the mean of the marks using the expression above:

Mean = (92 + 85 + 65 + x) / 4

To write a linear inequality for the mean being less than 80, we can set up the inequality:

(92 + 85 + 65 + x) / 4 < 80

We can then solve for x:

92 + 85 + 65 + x < 320

x < 320 - 92 - 85 - 65

x < 78

Therefore, if Esi scored less than 78 in the test, the mean of the marks would be less than 80.

   Possible marks Esi scored in the test:

   We can use the expression for the mean of the marks to solve for Esi's score. We know that the mean of the marks is:

Mean = (92 + 85 + 65 + x) / 4

And we know that Esi's score is x. So, we can substitute x with Esi's score and solve for it:

(92 + 85 + 65 + Esi) / 4 = Mean

Multiplying both sides by 4:

92 + 85 + 65 + Esi = 4 x Mean

Simplifying:

242 + Esi = 4 x Mean

Substituting Mean with its value:

242 + Esi = 4 x ((92 + 85 + 65 + x) / 4)

Simplifying:

242 + Esi = 92 + 85 + 65 + x

242 + Esi = 242 + x

Subtracting 242 from both sides:

Esi = x

Answer:

438

Step-by-step explanation:

the rate of decay is 438 the decay factor is 999

we know that

[tex]\text{[volume of a prism]}=\text{length}\times\text{width}\times\text{height}[/tex]

[tex]\text{length}=1 \dfrac{1}{4} \ \text{cm}\longrightarrow \dfrac{(1\times4+1)}{4} \longrightarrow \dfrac{5}{4} \ \text{cm}[/tex]

[tex]\text{width}=1 \dfrac{1}{2} \ \text{cm}\longrightarrow \dfrac{(1\times2+1)}{2} \longrightarrow \dfrac{3}{2} \ \text{cm}[/tex]

[tex]\text{height}=\dfrac{1}{6} \ \text{cm}[/tex]

[tex]\text{[volume of a prism]}=\huge \text(\dfrac{5}{4}\huge \text{)}\times\dfrac{3}{2} \times\dfrac{1}{6} \implies\dfrac{5}{16} \implies 0.3125 \ cm^3[/tex]

the answer is:

the volume is 0.3125 cm³ (5/16 cm³)

1. The data show's a symmetric distribution

The second diagram is left skewed

2. The second shape would have a greater standard deviation because its skewness is more

3. √(2 + 5 + 0 + 3 + 4)²/17

= √(0.8235)²

= √0.6781

= 0.8234

using the same calculation the standard deviation is 1.1418

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The purpose of the study was to determine whether the stress management program had any effects on various health outcomes.

Researchers tested a stress program with 3 groups; treatment groups had fewer illnesses, strokes, lower blood pressure, and emotional outbursts. The researchers conducted an evaluation of a stress management program, in which they randomly assigned subjects to one of three groups: two treatment groups and a control group. The purpose of the study was to determine whether the stress management program had any effects on various health outcomes.

The results of the study indicated that both treatment groups experienced a number of positive health outcomes compared to the control group. Specifically, the treatment groups had fewer illnesses like colds and flu, fewer strokes, a reduction in blood pressure, and reported fewer emotional outbursts.

The findings of this study suggest that a stress management program may have multiple benefits for individuals' health, including reducing the risk of certain illnesses and improving emotional well-being. However, further research is needed to confirm these findings and to determine whether these effects are sustained over time.

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The correct answers are:

C. The probability of being included in the sample is the same for all members of the population of interest.

D. Sampling must be done without replacement.

The correct answer is, "The probability of being included in the sample is the same for all members of the population of interest" and "sampling must be done without replacement."

An independent random sample is a subset of a population that is selected in such a way that each member of the population has an equal and independent chance of being included in the sample. This means that the probability of being included in the sample is the same for all members of the population, which is why the statement "the probability of being included in the sample is the same for all members of the population of interest" is correct.

In addition, sampling must be done without replacement, which means that once an individual has been selected for the sample, they cannot be selected again. This ensures that each member of the population has an equal chance of being selected and that the sample is not biased towards certain individuals.

The statement "sampling must be done with replacement" is incorrect because it implies that individuals can be selected multiple times, which would not result in an independent random sample. The statement "every time an individual is selected for the sample, each of the remaining individuals has a higher chance of being included" is also incorrect because it suggests that the sampling process is not independent, which would also result in a biased sample.

Therefore, The probability of being included in the sample is the same for all members of the population of interest and sampling must be done without replacement.

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Answer:

the scale factor used to create the image is 3

Answer:

The answer is 3

Step-by-step explanation:

I took the test and got it right :)

the answer's translation.

The equations [tex]y=2x-3 [/tex]and [tex]y=x+6[/tex],

we can use them to find the point of intersection between the two lines. This point of intersection represents the solution to the system of equations.

Setting the two equations equal to each other, we get:

[tex]2x - 3 = x + 6[/tex]

Simplifying this equation, we can see that x = 9.

Now we can substitute x = 9 into either of the original equations to find the corresponding value of y.

Let's use the equation [tex]y=2x-3[/tex]

[tex]y = 2(9) - 3 = 15[/tex]

Therefore, the solution to the system of equations y=2x-3 and y=x+6 is the point (9, 15).

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Answer: D3 friends equally share 7 peaches​

Step-by-step explanation:
there are 3 1/3 pieces meaning there are 3 friends. Each friend gets 2 so 2x3 = 6 and 1/3 times 3/1 = 1 so 6+1=7

the first five terms of the sequence t(1)=4 and t(n+1)=t(n)-3 are: 4, 1, -2, -5, -8.

To find the first five terms of the sequence defined by the formula t(1) = 4 and t(n+1) = t(n) - 3, we can use the recursive formula to find each term in the sequence:

t(1) = 4

t(2) = t(1) - 3 = 4 - 3 = 1

t(3) = t(2) - 3 = 1 - 3 = -2

t(4) = t(3) - 3 = -2 - 3 = -5

t(5) = t(4) - 3 = -5 - 3 = -8

Therefore, the first five terms of the sequence are: 4, 1, -2, -5, -8.

A recursive formula is a formula used to define a sequence, where each term of the sequence is defined in terms of the previous terms. In other words, to find a particular term in the sequence, you need to know the value of the previous term. This can be useful for generating sequences with complex patterns, such as the Fibonacci sequence. However, recursive formulas can also be more difficult to work with than explicit formulas, which give a direct formula for calculating any term in the sequence without relying on previous terms.

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Answer:

Step-by-step explanation:

√4 - 3.14 ; -2/3 ;  √25 + √6 ; Зx3.14

Hence the value for MN midsegment is triangle is  x = MN = 12 units.

M and N are, respectively, the midpoints of JK and JL in the triangle JKL.

MN is a midsegment of the triangle JKL because it is parallel to KL.

What exactly is  midsegment?

A triangle's midsegment is a line segment that joins the midpoints of its two sides. A triangle's midsegment is always half as long as its third side and runs parallel to it at all times.

Triangles have the following characteristics:

Three sides, three vertices, and three angles make up the polygonal shape known as a triangle.

- The total of a triangle's three angles is 180 degrees.

- Any two triangle sides added together will always be longer than the third side.

- Less than the third side's length separates the two sides of a triangle from one another.

- A triangle's perimeter is the product of its three sides.

KL is 12 units in length. MN is therefore 12 units long as well.

Hence, x = MN = 12 units.

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Drawing a 10 from the bag      unlikely

Rolling a number less than 5   Likely

Drawing a red marble             equally likely and unlikely

Here is the completed frequency table:

Number       frequency

1                       9

2                    12

3                    10

4                    8

5                    5

6                     6

Hiro's prediction is likely.

Probability determines the odds that a random event would happen. If the probability value is 0.5, it is equally likely and unlikely that the event would happen. If it is less than 0.5, it is unlikely that the event would happen. If it is greater than 0.5, it is likely that the event would happen.

Probability of drawing a 10 = number of 10s in the bag / total number in the bag = 1/100 = 0.01

It is unlikely that you would draw a 10.

Probability of rolling a number less than 5 = numbers that are less than 5 / total number of sides =  4/6 = 0.67

It is likely that a number less than 5 would be rolled.

Probability of drawing a red marble = total number of red marbles / total number of marbles = 8 / 16 = 0.5

It is equally likely and unlikely that a red marble would be picked

In order to determine the frequency, if the denominator of the relative frequency of the number is equal to 50, then the numerator is equal to the frequency. In the case where the denominator is less than 50, divide 50 by the number, multiply the quotient by the numerator in order to determine the frequency.

The frequency of 2 = (50 / 25) x 6 = 12

Number       frequency

1                       9

2                    (6 x 2) 12

3                    (1 x 10) 10

4                    (4 x 2) = 8

5                    (1 x 5) 5

6                     (3 x 2) 6

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A square-based box with an open top and volume of 4,000 cm³ has minimum surface area when its dimensions are 10√2 cm by 10√2 cm by 20√2 cm.

Let's assume that the box has a square base with side length x and height h. Then, its volume is given by:

V = x^2 * h

We are given that the volume is 4,000 cm³, so we can write:

x^2 * h = 4,000

Solving for h, we get:

h = 4000 / x^2

The amount of material used to construct the box is the sum of the areas of its five faces (four sides and the base). Since the box has an open top, we don't need to consider its area. The area of the base is x^2, and the area of each side is x times the height h. Thus, the total surface area A of the box is given by:

A = x^2 + 4xh

Substituting the expression we found for h, we get:

A = x^2 + 4x(4000 / x^2)

Simplifying and factoring out 4, we get:

A = 4(x^2 + 1000/x)

To find the dimensions of the box that minimize the amount of material used, we need to find the value of x that minimizes A. We can do this by taking the derivative of A with respect to x and setting it equal to zero:

dA/dx = 8x - 4000/x^2 = 0

Solving for x, we get:

x = 10√2

Substituting this value back into the expression we found for h, we get:

h = 20√2

Therefore, the dimensions of the box (in cm) that minimize the amount of material used are:

side length of the base: 10√2 cm

height: 20√2 cm

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Answer:

x = 3

Step-by-step explanation:        

Check attachment. I did this lesson in class so I know.        

The correct statement is:

B. The gummy bear is more likely to be strawberry than orange or raspberry.

What are likely events?

In probability theory, an event is a set of outcomes of an experiment or a random phenomenon. A likely event is an event that has a high probability of occurring

To determine the probability of selecting a gummy bear of a particular flavor, we need to divide the number of gummy bears of that flavor by the total number of gummy bears in the package.

The total number of gummy bears is:

4 + 3 + 8 + 9 + 12 = 36

So the probabilities of selecting a gummy bear of each flavor are:

Pineapple: 4/36 = 1/9

Lemon: 3/36 = 1/12

Raspberry: 8/36 = 2/9

Orange: 9/36 = 1/4

Strawberry: 12/36 = 1/3

Therefore, the correct statement is:

B. The gummy bear is more likely to be strawberry than orange or raspberry.

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The strengthening of National Ambient Air Quality Standards for maximum daily concentration of PM2.5 from 65 micrograms to 35 micrograms is expected to have a positive impact on public health.

The PM2.5 is defined as a fine particulate matter which penetrate deep into the lungs and cause a range of health problems, including asthma attacks, heart disease, and lung cancer.

By lowering the maximum daily concentration of PM2.5, the EPA is aiming to reduce the amount of air-pollution that people are exposed to, which should lead to improvements in public health.

Therefore, the strengthening of the National Ambient Air Quality Standards for PM2.5 is a positive step towards protecting public health and reducing the burden on medical facilities.

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The value of [tex]\frac{XZ}{YZ}[/tex] include the following: C. [tex]\frac{180}{181}[/tex]

In Mathematics and Geometry, Pythagorean's theorem is represented by the following mathematical equation:

a² + b² = c²

Where:

a, b, and c represent the side lengths of a right-angled triangle.

In order to determine the length of XZ in right-angled triangle XYZ, we would have to apply Pythagorean's theorem.

YZ² = XY² + XZ²

181² = 19² + XZ²

XZ² = 32,761 - 361

XZ = √32,400

XZ = 180 units

For the ratio, we have:

Ratio = XZ/YZ

Ratio = 180/181

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

The grocer's gain percentage is 5% after he sells 40 liter of oil for the cost price of 42 liter.

In business and finance, profit is the amount of money earned by a company or an individual after deducting all the expenses and costs associated with producing and selling goods or services. It is essentially the difference between the revenue earned from selling goods or services and the costs incurred in producing and selling those goods or services.

Let's assume that the cost price of 1 liter of oil is $1 for simplicity.

According to the problem, the grocer is selling 40 liters of oil for the cost price of 42 liters. So, his total cost price for 40 liters of oil is 40 * $1 = $40.

However, he is selling 42 liters worth of oil, which means his selling price is 42 * $1 = $42.

Therefore, his profit in this case is $2 (selling price - cost price).

To find his gain percentage, we can use the following formula:

Gain percentage = (Profit / Cost price) x 100

Substituting the values, we get:

Gain percentage = ($2 / $40) x 100 = 5%

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The answer of the given question based on equation is the complete equation is: 746 x 34 = 2,984 + 1,023 + 22,462.

A variable is a symbol or letter that represents a value that can change or vary. It is often used to express relationships between quantities or to represent unknown values. Variables are commonly used in algebra, where they are used to represent unknown quantities in equations. Variables can also be used in calculus to represent functions and their derivatives. In statistics, variables are used to represent different types of data, like numerical values or categorical groups.

To solve for the blanks, we can simplify the left side of the equation first:

746 x 34 = 25,444

Then, we can write:

25,444 = 2,984 + 22x + 8

where x represents the first blank and (22x + 8) represents the second blank.

To solve for x, we can subtract 2,984 from both sides of the equation:

25,444 - 2,984 = 22x + 8

22,460 = 22x + 8

Subtracting 8 from both sides of the equation, we get:

22,452 = 22x

Dividing both sides of the equation by 22, we get:

x = 1,023

Therefore, the missing values are 1,023 and 22,462.

So, the complete equation is:

746 x 34 = 2,984 + 1,023 + 22,462.

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The overall shape of the distribution is normal.

If the overall shape of the combined distribution for both the class samples and the simulation samples was normal, then it suggests that the individual distributions of the samples were either normally distributed or approximately normally distributed.

A normal distribution, also known as a Gaussian distribution or a bell curve, is a probability distribution that is symmetric and bell-shaped. The normal distribution is commonly used in statistical analysis and modeling because it is often observed in real-world data and has some desirable properties.

When the individual distributions of the samples are combined, their values are added up or averaged, resulting in a larger sample size and a more representative estimate of the underlying distribution. If the individual distributions are normally distributed, then the central limit theorem states that the combined distribution will tend towards normality as the sample size increases. This can explain why the overall shape of the combined distribution for both the class samples and the simulation samples was normal.

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Here are the solutions for each situation, listed from least to greatest:

In mathematics, probability refers to the measure of the likelihood or chance of an event occurring. It is a numerical value between 0 and 1, where 0 represents an impossible event, and 1 represents a certain event.

The probability of an event A is denoted by P(A) and is calculated by dividing the number of favorable outcomes by the total number of possible outcomes in a given situation.

For example, if we roll a fair six-sided die, the probability of rolling a 4 is 1/6 because there is only one favorable outcome (rolling a 4) out of six possible outcomes (rolling any number from 1 to 6).

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Answer: 10 children

Step-by-step explanation:

Given:

First, let's find the cost "per child"

Notebook: 1 × 1.15

+

Pencils: 2 × 0.34

Equation for cost per child:

1(1.15) + 2(0.34)

Solve:

1.15 + 0.68

= 1.83$

We have $20. So, to find how many children can be provided with supplies, we divide 20 by 1.83 (which is the cost per child)

20 ÷ 1.83 = 10.928

(Gives us a terminating decimal)

Since we can't just give a child .928 of a set of supplies, we round down to 10.

Therefore,

10 children can be provided with supplies with $20.