There are 88 students in 4 classes. If there are equal number of students in each class, how many students per class?

An equation that depicts a straight line on a graph is said to be linear line.

Linear refers to a straight line. Straight-line graphs called linear graphs are used to show the relationship between two values. The single straight lines on this graph assist to represent a result. The phrase "linear" refers to a straight line and excludes the usage of curves, dots, bars, etc.

A linear line can include more than one variable. Linear lines with two variables, for example, are those that have two variables in them. 2x - 3 = 0 and 2y = 8 are few examples of linear lines.

Steps to draw a linear graph are described below:

Examine the line to see if it is straight or curved. A straight line indicates a linear equation. A nonlinear equation is one that is curved.

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The class width can be calculated by subtracting the lower-class limit from the upper-class limit.  By subtracting the lower-class limits from the upper-class limits gives us 10, 10, and 10so the class width is 10.

The class width can be calculated by subtracting the lower-class limit from the upper-class limit.

In this case, the lower-class limits are 40, 50, and 60, and the upper-class limits are 50, 60, and 70.

Subtracting the lower-class limits from the upper-class limits gives us 10, 10, and 10.

Therefore, the class width is 10.

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The class-width for this frequency distribution is 10. Each class interval spans 10 units.

The class-width refers to the size or width of each class interval in a frequency distribution. To find the class-width, you need to determine the range of the data and divide it by the number of classes.

In this case, the given frequency distribution includes three class intervals: 40 up to 50, 50 up to 60, and 60 up to 70. The range of the data can be found by subtracting the lower limit of the first class from the upper limit of the last class. So, the range is 70 - 40 = 30.

To find the class-width, divide the range by the number of classes. Since there are three classes, divide 30 by 3:

30 ÷ 3 = 10

In summary, the class-width for the given frequency distribution is 10. This means that each class interval covers a range of 10 units.

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Answer:

(-2 , -2)

Step-by-step explanation:

Here,

(-6,-4)=(x1,y1)

(2,0)=(x2,y2)

Mid point formula,

(x,y)=(x1+x2/2 , y1+y2/2)

=(-6+2/2 , -4+0/2)

=(-2 , -2)

The total number of rounds in the tournament is approximately log2(n).

In this tournament, participants stand in a circle and flip a fair coin. If they flip tails, they look to their left, and if they flip heads, they look to their right. If two people are facing each other, they play a game. The winner stays in the circle, while the loser exits. This process continues until only two people are left, and they play a final game to determine the winner of the tournament.

To analyze the tournament, let's consider the number of people initially in the circle. Suppose there are n people. In the first round, each person has a 50% chance of looking towards their left and a 50% chance of looking towards their right. This means that on average, n/2 people will be facing each other and play a game.

In each subsequent round, the number of people in the circle decreases by half. This continues until only two people are left, who play the final game. Therefore, the total number of rounds in the tournament is approximately log2(n).

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We know that coefficient of an equation is the number multiplied by variable.

-8 and 1.5 are the constants for our given equation.

The variable of our given equation is x. We can also see that x is being multiplied by 0.5, therefore, 0.5 would be the decimal coefficient of our given equation.

Answer:

Below in bold.

Step-by-step explanation:

When x = -3, y = -(-3) - 2 = 3-2 = 1.

When x = 0,  y = -0 - 2 = -2.

When x = 4,  y = -4 - 2 = -6.

To draw the graph plot the 3 points and you should be able to draw a straight line through them.

Answer:

The first y value with -3, is 1.

The second y value with 0, is -2.

The third y value with 4, is -6.

A graph is shown below.

Step-by-step explanation:

It states that the rule is y = -x-2. So all we do is plug in the values shown in the table.

y = -(-3)-2

y = 1

The first point of intersection is at (-3,1)

y = -(0)-2

y = -2

The second point of intersection is at (0,-2)

y = -(4)-2

y = -6

The third point of intersection is at (4,-6)

So now, we plot the points, and draw a line connecting them all.

Answer: A.

Step-by-step explanation: if you look close enough, you can see exactly how long it is, and see that it does also have the two arrows along with it, but it’s the exact same just tilted a little bit but trust me I believe he correct answer is A.

When constructing a histogram, the horizontal (x) axis represents the range of values of the variable being measured or observed, while the vertical (y) axis represents the frequency or count of observations falling within each interval or bin.

More specifically, the x-axis usually represents the range of possible values of the variable being measured or observed, divided into a series of intervals or bins. Each bin represents a range of values that fall within a certain interval or category. The width of the bins should be chosen carefully to ensure that the data is displayed clearly and accurately.

The y-axis represents the frequency or count of observations that fall within each bin. This can be represented as either the number of observations that fall within each bin or as a percentage of the total number of observations. The y-axis should also be chosen carefully to ensure that the data is displayed clearly and accurately.

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Here, we want to calculate the assessed value of the home

From the question, we are told that the rate of assessment is 40%

Hence, the value on the tax statemet is 40% of the assessed value

Let us have the assessed value as$x

Answer:

Step-by-step explanation:

AAS and SAS

The congruence theorems or postulates could be given as reasons why ABC= ADEF are SAS, AAS the correct options are A and F.

Suppose it is given that two triangles ΔABC ≅ ΔDEF

Then that means ΔABC and ΔDEF are congruent. Congruent triangles are exact same triangles, but they might be placed at different positions.

The order in which the congruency is written matters.

For ΔABC ≅ ΔDEF, we have all of their corresponding elements like angle and sides congruent.

Thus, we get:

\(\rm m\angle A = m\angle D \: or \: \: \angle A \cong \angle D \angle B = \angle E\\\\\rm m\angle B = m\angle E \: or \: \: \angle B \cong \angle E \\\\\rm m\angle C = m\angle F \: or \: \: \angle C \cong \angle F \\\\\rm |AB| = |DE| \: \: or \: \: AB \cong DE\\\\\rm |AC| = |DF| \: \: or \: \: AC \cong DF\\\\\rm |BC| = |EF| \: \: or \: \: BC \cong EF\)

(|AB| denotes length of line segment AB, and so on for others).

We are given that;

The diagram

Now,

Based on the information given in the diagram, we can use the following congruence theorems or postulates as reasons why ABC= ADEF:

SAS (Side-Angle-Side): If two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the triangles are congruent.

We can use SAS to show that ABC and ADEF are congruent, since AB = AD, BC = DE, and the included angle BAC = the included angle EDF.

AAS (Angle-Angle-Side): If two angles and a non-included side of one triangle are congruent to two angles and the corresponding non-included side of another triangle, then the triangles are congruent.

We can use AAS to show that ABC and ADEF are congruent, since the included angles BAC and EDF are congruent, angle ABC is congruent to angle ADE (since they are vertical angles), and side BC is congruent to side EF.

Therefore, by congruent triangles the answer will be SAS, AAS.

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Answer:

y = 4x hope this Helps!

Step-by-step explanation:

y = kx

k = y/x = 60/15 = 4

y = 4x

Answer:

x = 14, BC = 27, CD = 61, BD = 88

Step-by-step explanation:

Answer:

the y-intercept is positive 1

Step-by-step explanation:

Answer:

-1/7x

Step-by-step explanation:

y increases by 7 everytime x increases by 1,

Thus, you just need to divide x by 7 and subtract one which y would be 0 and being the y intercept.

Answer:

A and E

Step-by-step explanation:

at the end of the 10 weeks, annie's dads plan gives her 511 dollars, which is more than her mothers. it is a geometric sequence.

Answer:

Supplementary angles means the sum will be 180 degrees. So since Zx = 142 degrees, allow: 180 = 142 + Zy. So, 180 - 142 = 38 degrees = Zy.

Step-by-step explanation:

The present value can be calculated using the formula P = F / (1 + rt), where P is the present value, F is the future amount, r is the interest rate, and t is the time period. Plugging in the values, the present value of $73,000 for 6 months at 8% simple interest is approximately $68,037.

Explanation: To find the present value, we use the formula P = F / (1 + rt), where P is the present value, F is the future amount, r is the interest rate, and t is the time period. In this case, the future amount is $73,000, the interest rate is 8% (0.08 as a decimal), and the time period is 6 months (0.5 as a decimal).

Substituting these values into the formula, we have P = 73,000 / (1 + 0.08 * 0.5). Simplifying the expression, we get P = 73,000 / 1.04, which is approximately $68,037.

Therefore, the present value of the given future amount of $73,000 for 6 months at 8% simple interest is approximately $68,037.

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The cost of direct labor per unit is $5.628 per apple.

To calculate the cost of direct labor per unit, we need to determine the total labor hours required to produce one unit of output and then multiply it by the wage rate.

Let's denote the labor hours required for the first resource as "L₁" and the labor hours required for the second resource as "L₂".

The first resource has a capacity of 2.1 apples per hour, and the demand is 1.6 apples per hour. Therefore, the labor hours required for the first resource per unit of output are:

L₁ = 1 apple / (2.1 apples/hour) = 0.4762 hours/apple (rounded to 4 decimal places)

The second resource has a capacity of 4.4 apples per hour, and the demand is 1.6 apples per hour. Therefore, the labor hours required for the second resource per unit of output are:

L₂ = 1 apple / (4.4 apples/hour) = 0.2273 hours/apple (rounded to 4 decimal places)

Now, let's calculate the total labor hours required per unit:

Total labor hours per unit = L₁ (first resource) + L₂ (second resource)

= 0.4762 hours/apple + 0.2273 hours/apple

= 0.7035 hours/apple (rounded to 4 decimal places)

Finally, to calculate the cost of direct labor per unit, we multiply the total labor hours per unit by the wage rate:

Cost of direct labor per unit = Total labor hours per unit * Wage rate

= 0.7035 hours/apple * $8/hour

= $5.628 per apple (rounded to 3 decimal places)

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Answer:

see explanation

Step-by-step explanation:

Under a reflection in the line y = x

a point (x, y ) → (y, x ) , thus

(- 1, - 2 ) → (- 2, - 1 )

(1, 1 ) → (1, 1 )

(4, - 3 ) → (- 3, 4 )

Answer:

0.475 kg

Step-by-step explanation:

1/2 kg = 0.5 kg

125g = 0.125kg

475g = 0.475kg

grams are lighter than kg and 0.5kg,0.125g, and 0.6kg are all lighter than 0.475kg

hope this helps!

Answer:

0.6 kg

Step-by-step explanation:

The easy way to find out the answer is to bring all into same unit:

Comparing all four we see the greatest number is 600, so the answer is :

The mean of a binomial random variable with n = 10 and p = 0.4 is 4, which represents the average number of successes in the given number of trials. the correct answer is option a. 4.

To find the mean of a binomial random variable, we multiply the number of trials (n) by the probability of success (p). In this case, we have n = 10 and p = 0.4.

The mean (μ) of a binomial random variable is given by the formula:

μ = n * p

Substituting the given values, we have:

μ = 10 * 0.4

Calculating this, we get:

μ = 4

Therefore, the mean of this binomial random variable is 4.

The mean represents the average number of successes in a binomial distribution. In this case, we have 10 trials with a probability of success of 0.4. So, on average, we can expect to have 4 successes.

To understand this intuitively, let's consider an example. Suppose we have 10 fair coins, and we flip each coin independently. The probability of getting a head (success) on each flip is 0.4.

The mean of 4 means that, on average, we would expect to get approximately 4 heads out of the 10 flips. This is because the probability of success (getting a head) is 0.4, and we have 10 trials (coin flips) in total. Therefore, The correct answer is option a. 4.

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1. 2

2. The Y axis

3. 3 rights and 1 down (3, -1)

Answer:

y=4x+2

Step-by-step explanation:

Answer:

y=4x+4

Step-by-step explanation:

move 8x to the left side than divide 2y by 8x and 4 to give u that answer. hope it helps

The probability that a randomly selected car with no 4-wheel drive has third-row seats is given by: Option B: 0.4

Suppose that there are finite elementary events in the sample space of the considered experiment, and all are equally likely.

Then, suppose we want to find the probability of an event E.

Then, its probability is given as

\(P(E) = \dfrac{\text{Number of favorable cases}}{\text{Number of total cases}} = \dfrac{n(E)}{n(S)}\)

where favorable cases are those elementary events who belong to E, and total cases are the size of the sample space.

For two events A and B, by chain rule, we have:

\(P(A \cap B) = P(B)P(A|B) = P(A)P(B|A)\)

where P(A|B) is probability of occurrence of A given that B already occurred.

For this case, the table given is:

Entries                          4-wheel drive        No 4-wheel drive        Total

Third Row Seats                  18                                12                        30

No Third Row Seats             7                                28                        35

Total                                     25                               40                        65

Let we take

A = event that a randomly selected car has no-4 wheel drive

B = event that a randomly selected car has third row seats

The total ways a car can be selected = 65 = n(S)

Total ways A can happen = n(A) = 40 (from the table).

Similarly, n(B) = 30

P(A) = n(A)/n(S) = 40/65

P(B) = n(B)/n(S) = 30/65

P(A∩B) = n(A∩B)/n(S) = 12/65

As by chain rule, we have:

P(A∩B) = P(A)P(B|A) = P(B)P(A|B)

We need P( A randomly selected car has three seats given that the selected car is with no 4-wheel drive)

which is symbolically P( B | A)

Thus, we use: P(A∩B) = P(A)P(B|A)

or

\(12/65 = (30/65)(P(B|A))\\\dfrac{12/65}{30/65} = P(B|A)\\\\P(B|A) = \dfrac{12}{30} = \dfrac{2}{5} = 0.4\)

Thus, the probability that a randomly selected car with no 4-wheel drive has third-row seats is given by: Option B: 0.4

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Answer:

b.  0.4

Step-by-step explanation:

took the test

The value of x is 111°

Arc angle theorem states that If two chords intersect inside a circle, then the measure of each angle is one-half the sum of the measures of the arcs intercepted by the angle and its vertical angle.

Representing the arc angle of x by y

y = 180-137( angle on straight line)

y = 43°

Therefore;

y = 1/2 ( x-25)

43 = 1/2 ( x-25)

86 = x-25

x = 86+25

x = 111

therefore the value of x is 111°

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The entropy of the sum obtained when a pair of fair dice are rolled is 7.6.

This can be calculated by first working out the probability of each possible sum of two dice. There are 36 possible outcomes when two fair dice are rolled (6 x 6 = 36).

Each of the possible sums, from 2 to 12, will occur with a probability of 1/36.

The entropy of a probability distribution is calculated using the formula: Entropy = -(sum of (Probability of each outcome x log2 of probability of that outcome)).

Therefore, the entropy of the sum of two fair dice is:

- (1/36 x log2(1/36)) + (1/36 x log2(1/36)) + (1/36 x log2(1/36)) + (1/36 x log2(1/36)) + (1/36 x log2(1/36)) + (1/36 x log2(1/36)) + (1/36 x log2(1/36)) + (1/36 x log2(1/36)) + (1/36 x log2(1/36)) + (1/36 x log2(1/36)) + (1/36 x log2(1/36)) + (1/36 x log2(1/36)) + (1/36 x log2(1/36))

= - (1/36 x 5.17) - (1/36 x 4.32) - (1/36 x 3.58) - (1/36 x 2.93) - (1/36 x 2.37) - (1/36 x 1.90) - (1/36 x 1.51) - (1/36 x 1.19) - (1/36 x 0.93) - (1/36 x 0.72) - (1/36 x 0.56) - (1/36 x 0.43)

= 7.6

As a result, the sum that results from the roll of two fair dice has an entropy of 7.6.

Complete Question:

Determine the entropy of the sum that is obtained when a pair of fair dice is rolled.

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The tοtal weight οf all the tennis balls in the fully packed bοx is apprοximately 31 pοunds.

Geοmetry is a branch οf mathematics that deals with the study οf pοints, lines, angles, shapes, and their prοperties, as well as space and the relatiοnships between οbjects in space.

1. First, we need tο cοnvert all the dimensiοns οf the bοx tο inches: 1 ft = 12 inches, sο the dimensiοns οf the bοx in inches are 12 in * 13 in * 19 in. The diameter οf a tennis ball is 2.6 inches, sο the radius is 1.3 inches.

Tο find the maximum number οf tennis balls that can be packed in the bοx, we need tο find hοw many can fit in each dimensiοn. In the 13-inch dimensiοn, we can fit 5 tennis balls (since 5 * 2.6 = 13). In the 19-inch dimensiοn, we can fit 7 tennis balls (since 7 * 2.6 = 18.2, which is less than 19).

Fοr the height οf the bοx, we need tο find hοw many layers οf tennis balls can fit. The height οf a tennis ball is 2.6 inches, sο we can fit 7 layers in the 12-inch dimensiοn (since 7 * 2.6 = 18.2, which is less than 12).

Therefοre, the maximum number οf tennis balls that can be packed in the bοx is 5 x 7 x 7 = 245.

2. The vοlume οf each tennis ball is (4/3)π(1.3)^3 cubic inches, which is apprοximately 9.14 cubic inches. Sο the tοtal vοlume οf 245 tennis balls is 245 x 9.14 = 2238.3 cubic inches.

The weight οf οne cubic inch οf tennis balls is 0.014 pοund, sο the weight οf 2238.3 cubic inches is 2238.3 x 0.014 = 31.33 pοunds, rοunded tο the nearest pοund.

Hence, the tοtal weight οf all the tennis balls in the fully packed bοx is apprοximately 31 pοunds.

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Answer:

1(a)1,030,000+0.13x

(b)$1,030,026

2. (a)Base and Index

(b)See Explanation

Ste-by-Step Explanation

(a)Total Amount to be paid to the four actors

=500,000+(300,000+0.02x)+(150,000+0.03x)+(80,000+0.08x)

Collect like terms

=500,000+300,000+150,000+80,000+0.02x+0.03x+0.08x

\(\text{Total Amount Paid= }1,030,000+0.13x\)

(b)When x=200

\(\text{Total Amount Paid= }1,030,000+0.13(200)\\=1,030,000+26\\=$1,030,026\)

Question 2

(a)The two parts of a power are the base and index.

Take, for example, the expression: \(a^b\\\)

\(a$ is the base\\b is the index\)

Another example using numbers is: \(10^3\)

In this case:

\(10$ is the base\\3 is the index\)

(b)Like terms are terms that have the same letter/variable attached to them.

For example, the following pairs are like terms

These, however, are not like terms