There were 28 students in the RSM Math Challenge class. Over the year, eight students were late to class 12 times, 9 students were late 10 times, and the rest of the students were late

heeeeeeeelp

The solution of the system of equations is

A system of equations are a pair of equations.

Given the system of equations

4/x - 2/y = 12 (1) and

5/x + 1/y = 8 (2)

We proceed to solve as follows.

Since we have

4/x - 2/y = 12 (1) and

5/x + 1/y = 8 (2)

Multiplying equation (1) by 1 and equation (2) by 2, we have that

4/x - 2/y = 12 (1) × 1 and

5/x + 1/y = 8 (2) × 2

4/x - 2/y = 12 (4)  and

10/x + 2/y = 16 (5)

Now, adding equations (4) and (5), we have that

4/x - 2/y = 12 (4)  

+

10/x + 2/y = 16 (5)

14/x = 28

14 = 28x

x = 14/28

x = 1/2

Substituting x = 1/2 into equation (1), we have that

4/x - 2/y = 12 (1)

4/(1/2) - 2/y = 12 (1)

4 × 2 - 2y = 12

8 - 2y = 12

-2y = 12 - 8

-2y = 4

y = 4/-2

y = -2

So,

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The number can be said to be a multiple of 4 if the last two digits of the number is a multiple of 4

Numbers that divide an original number evenly or precisely are known as its factors. A factor is a whole number that can divide a larger number in two equal parts. A factor is a number that divides another number, leaving no remainder

Given data ,

Let the number be represented as n

Now , the number can be said to be a multiple of 4 if the last two digits of the number is a multiple of 4

Let the value of the number n be n = 3240

Now , the last two digits of the number is 40

And , the number 40 is a multiple of 4 , so the number 3240 is also a multiple of 4

where n / 4 = 810

Hence , the factors of the number 4 is a multiple of 4

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The answer is 4 times the cube of the first number minus the sum of the second number and two times the third number. That is the result of the calculation is -6.

To calculate this, first, we multiply the first number by itself twice to get the cube of the first number. Then, we subtract the sum of the second and third numbers multiplied by two from the cube of the first number. This result is our answer.

For example, let's say we have the numbers 2, 3, and 4. We first calculate the cube of 2, which is 8. Then, we subtract the sum of 3 and 4 multiplied by two, which is 14. So, the final answer is 8 - 14 = -6.

We can also show the stepwise calculation as follows:

= 2³ - (3 + 2 × 4)

= 8 - 14

= -6

Therefore, the result of the calculation is -6.

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Option D:

32 ÷ (–16) is equivalent to –18 ÷ (9).

Given expression:

–18 ÷ (9)

Let us first solve this expression.

                = -2  (negative by positive is negative)

To find which expression has the same value for the given expression:

Option A: –18 ÷ 2

            = –9 (negative by positive is negative)

This is not equivalent expression.

Option B: –12 ÷ (–3)

                = 4  (negative by negative is positive)

This is not equivalent expression.

Option C: –10 ÷ 5

            = –2 (negative by positive is negative)

This is not equivalent expression.

Option D: 32 ÷ (–16)

                = -2  (positive by negative is negative)

This is the equivalent expression to the given expression.

Hence ,32 ÷ (–16) is equivalent to –18 ÷ (9).

Option D is the correct answer.

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the equation of the line perpendicular to 5x - 4y = 10 and passing through the point (5,12) is y = -(4/5)x + 16.

How to determine?

To find the equation of the line perpendicular to the line 5x - 4y = 10 and passing through the point (5,12), we need to first find the slope of the given line.

Rewriting the equation of the given line in slope-intercept form (y = mx + b), we get:

5x - 4y = 10

-4y = -5x + 10

y = (5/4)x - 5/2

The slope of this line is (5/4), so the slope of any line perpendicular to it is the negative reciprocal of (5/4), which is -(4/5).

Now we can use the point-slope form of a linear equation to find the equation of the perpendicular line. The point-slope form is:

y - y1 = m(x - x1)

where (x1, y1) is a point on the line and m is the slope.

Plugging in the values we have, we get:

y - 12 = -(4/5)(x - 5)

Expanding and simplifying, we get:

y - 12 = -(4/5)x + 4

y = -(4/5)x + 16

Therefore, the equation of the line perpendicular to 5x - 4y = 10 and passing through the point (5,12) is y = -(4/5)x + 16.

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Answer:6

Step-by-step explanation: because the 2 feet already has four pieces and if you add two more pieces to it there will be six in total.

For given coordinates of a linear equation, the slope will be 3/4 i.e. B.

What is a linear equation, exactly?

When the greatest power of a variable is 1, the equation is said to be linear. Other term used for it is a one-degree equation. The standard form of a linear equation with one variable is Ax + B = 0. There are three variables in this equation: x, A, and B. A denotes a coefficient. A linear equation with only two variables is commonly written as Ax + By = C. There is three more constants added to the constant C: the variables x and y, the coefficients A and B, and the variables.

and general equation of line is y=mx+c

where m=slope=y2-y1/x2-x1

Now,

Here given coordinates are , (-3,4) and (1/7)

then (x1,y1) and (x2,y2) are  (-3,4) and (1/7) respectively

so slope=m=7-4/1-(-3)=3/4

Hence,

          For given coordinates of a linear equation, the slope will be 3/4.

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Answer:

x = 2

Step-by-step explanation:

1) Based on the given conditions, formulate: 4 × x = 8

2) Divide both sides of the equation by the coefficient of variable: x = 8 ÷ 4

3) Calculate the product or quotient: x = 2

4) You then get the result x = 2

The product of 4 and a number w is 8.

[tex]4\times w=8[/tex]

This can also be written as:

[tex]4w=8[/tex]

Divide both sides by 4:

[tex]\dfrac{4w}{4}=\dfrac{8}{4}[/tex]

[tex]\boxed{w=2}[/tex]

Answer:

Step-by-step explanation:

Since the probability of rain on any given day is 0.5, and the weather on each day is independent of the others, we can calculate the probability of it raining all three days by multiplying the probabilities of rain on each individual day:

P(rain on day 1) x P(rain on day 2) x P(rain on day 3) = 0.5 x 0.5 x 0.5 = 0.125

Therefore, the probability of it raining all three days of your trip to Seattle in October is 0.125, or 12.5%.

Answer:

the probability assignments for the x distribution can be computed using the binomial probability formula, with p = 0.26 and n = 5, and the results are shown in the table above.

Step-by-step explanation:

If approximately 26% of adults in the United States live with a disability, then the probability of a randomly selected US adult living with a disability is 0.26. We can use this probability to determine the probability of getting a certain number of adults out of five that live with a disability.

To do this, we can use the binomial probability formula:

P(x) = (n choose x) * p^x * (1-p)^(n-x)

where n is the sample size (in this case, 5), x is the number of adults with a disability, p is the probability of an adult having a disability (0.26), and (n choose x) is the binomial coefficient, which can be calculated as:

(n choose x) = n! / (x! * (n-x)!)

where ! denotes the factorial function.

 = 10 * 0.0676 * 0.4052

 = 0.211

The solution is, 0.211 is the probability assignments for the x distribution.

Here, we have,

the probability assignments for the x distribution can be computed using the binomial probability formula, with p = 0.26 and n = 5, and the results are shown in the table above.

now, we have,

If approximately 26% of adults in the United States live with a disability, then the probability of a randomly selected US adult living with a disability is 0.26. We can use this probability to determine the probability of getting a certain number of adults out of five that live with a disability.

To do this, we can use the binomial probability formula:

P(x) = (n choose x) * p^x * (1-p)^(n-x)

where n is the sample size (in this case, 5), x is the number of adults with a disability, p is the probability of an adult having a disability (0.26), and (n choose x) is the binomial coefficient, which can be calculated as:

(n choose x) = n! / (x! * (n-x)!)

where ! denotes the factorial function.

= 10 * 0.0676 * 0.4052

= 0.211

So, 0.211 is the probability assignments for the x distribution.

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The pitch of the roof with one foot horizontal run and 4 inches elevation is 4 in per foot

An equation is an expression that shows the relationship between two numbers and variables using mathematical operations like addition, subtraction, multiplication, exponents

The roof pitch (steepness) is given as a ratio of inch rise per horizontal foot, It is given by:

Pitch = rise / run

For every 1-foot horizontal run, the roof was elevated by 4 inches, hence:

Pitch = rise / run = 4 in / 1 ft = 4 in per foot

The pitch is 4 in per foot

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The direct distance between the White House and the Pentagon is approximately 3.067 miles.

Distance is a measure of how far apart two objects or points are from each other. It is a fundamental concept in mathematics, physics, and other scientific disciplines, and plays a crucial role in our everyday lives.

Distance can be measured in various units, such as meters, kilometers, miles, feet, and inches, depending on the context and application. In mathematics, the distance between two points in a plane can be found using the Pythagorean theorem, which states that the distance between two points (x1, y1) and (x2, y2) is given by the formula:

distance = √((x2-x1)² + (y2-y1)²)

In this formula, the square of the difference in the x-coordinates and the y-coordinates of the two points are added and then the square root of the sum is taken to obtain the distance.

Using the distance formula, the direct distance between the two buildings is:

d = sqrt[(x2 - x1)^2 + (y2 - y1)^2]

where (x1, y1) = (-8,-6) and (x2, y2) = (-1,10)

d = sqrt[(-1 - (-8))^2 + (10 - (-6))^2]

d = sqrt[7^2 + 16^2]

d = sqrt(49 + 256)

d = sqrt(305)

Since each unit on the grid represents 0.125 miles, we can convert the answer to miles by multiplying by 0.125:

d = sqrt(305) * 0.125

d = 3.067 miles (rounded to 3 decimal places)

Therefore, the direct distance between the White House and the Pentagon is approximately 3.067 miles.

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Answer:

y=5

Step-by-step explanation:

i think it is ahhhh&hhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhh

Yes, they are statistically different.

Statistical significance is a term used to indicate that a result from a statistical test is likely to be reliable and reproducible. It is the probability that a result is caused by something other than random chance. Statistical significance is usually determined by calculating the probability, or p-value, that the result occurred by chance. A result is deemed to be statistically significant if the p-value is below a certain threshold. This threshold is typically set at 0.05, but can be adjusted depending on the study.

A p-value below 0.05 is generally considered to be statistically significant, indicating that the differences observed between the two groups are unlikely to have occurred by chance. In this case, a p-value of 0.03 is well below the threshold, indicating that the two groups are statistically different

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[tex]\dfrac{x^2-15x+36}{5x-60}[/tex]

[tex]= \dfrac{(x-3)(x-12)}{5x-60}[/tex]

[tex]= \dfrac{(x-3)(x-12)}{5(x-12)}[/tex]

[tex]= \dfrac{(x-3)}{5}\\= \dfrac{x-3}{5}[/tex]

[tex]\dfrac{x-3}{5}[/tex], [tex]x\neq12[/tex]

Answer:

2h

Step-by-step explanation:

You can still divide 6h by 3 even if its not 3h

Imagine there are 6 h's:

H H H H H H

now divide them by 3:

     1                   2

  HHH            HHH

Now you have 2 groups of H so:

2H

Answer:

15.81 units

Step-by-step explanation:

Let the hypotenuse of the triangle be x.

Let us use the Pythagorean theorem to find x.

x² = 9² + 13²

x² = 81 + 169

x² = 250

x = √250

x = 15.81 units

Joanna can assemble her bracelet in 30 ways.

In mathematics, a permutation of a set is, loosely speaking, an arrangement of its members into a sequence or linear order, or if the set is already ordered, a rearrangement of its elements. The word "permutation" also refers to the act or process of changing the linear order of an ordered set.

here, we have,

to find the number of ways in which the bracelet can be assembled:

It is given that Joanna has 6 beads and of those 6 beads, 2 are of the same color.

The rest 4 are of different colors.

Six beads can be arranged in a circle in 6!/6 ways.

This means that the six beads can be arranged in 5! ways.

Since this is a bracelet, it can be flipped around.

Therefore, it can be arranged in 5!/2 ways.

5!/2

= 5*4*3*2*1/2

= 60

Now, we know that two beads are of the same color. Therefore, we must divide this by two again.

Therefore, we get:

60/2 = 30

The six beads can be arranged in 30 ways to make the bracelet.

Therefore, we have found that Joanna can assemble her bracelet in 30 ways.

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Answer:

To simplify the expression −8(1+x)+7x, we can use the distributive property of multiplication over addition, which states that a(b+c) = ab + ac. Applying this property, we get:

−8(1+x) + 7x = −81 − 8x + 7x (distributing the -8)

= -8x - 8 + 7x (simplifying the multiplication)

= -x - 8 (combining like terms)

Therefore, the simplified form of the expression −8(1+x)+7x is −x − 8.

Answer:

7/5, 3/2, 11/4, 15/4, 13/3.

Step-by-step explanation:

Convert all to decimal then arrange from lowest to highest

Answer:

integers . whole number and nutural number

It can't because 15 + 8=23 and the sum of the first 2 sides have to be greater than the third side
So the answer is 18

Answer:

x=5

Step-by-step explanation:

26=4x+6
20=4x

x=5

1. The probability the project will be finished in 62 weeks or less is 0.6915. 2.The probability the project will be finished in longer than 65 days is 0.8944.

The standard score in statistics is the amount of standard deviations that a raw score (i.e., an observed value or data point) deviates from or exceeds the mean of the thing being observed or measured. Standard scores are positive for raw scores above the mean and negative for raw scores below the mean.

It is determined by deducting the population mean from a given raw score, then dividing the result by the population standard deviation. Standardizing or normalising is the process of transforming a raw score into a standard score.

Given that,

mean = 60 weeks

SD = 4 weeks

1. P (p ≤ 62) = P(z ≤ 62)

The z-score is given by:

z-score = x - mean / SD

Substituting the values we have:

z-score = 62 - 60/4 = 2/4 = 0.5

P(z ≤ 0.5) = 0.6915 (Using the z -table)

Hence, the probability the project will be finished in 62 weeks or less is 0.6915.

Similarly,

2. P(z > 65) = P(z > 1.25) = 0.8944

Hence, the probability the project will be finished in longer than 65 days is 0.8944.

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The graph of the piecewise function is attached at the end.

A piecewise function is a function that is defined on a sequence of intervals. For example -

[tex]$|x| =\left \{ {{-x\;\;\;\;x < 0} \atop {x\;\;\;\;x > 0}} \right.[/tex]

Given is the piecewise function as -

[tex]$f(x) =\left \{ {{-x-1\;\;\;\;x < 3} \atop {-x+1\;\;\;\;x \geq 3}} \right.[/tex]

Refer to the graph of the piecewise function. The graph of the function is attached. The line one does not include the point {x = 3}. The second line includes the point {x = 3}

Therefore, the graph of the piecewise function is attached at the end.

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If two parallel lines are crossed by a transversal, the value of x is option (b) x = 70 degrees

When two parallel lines are intersected by a transversal, eight angles are formed. Two of these angles are vertical angles, which are opposite angles that share the same vertex and are formed by the intersection of two lines.

Vertical angles are always congruent, meaning they have the same measure. This is a geometric property that is true regardless of the angle's degree measurement.

In this problem, one of the vertical angles is given to be 70 degrees. Therefore, the other vertical angle must also have a measure of 70 degrees. This means that the value of x, which is the measure of one of the vertical angles, is also 70 degrees.

So, correct option is (b) x = 70 degrees.

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The given question is incomplete, the complete question is:

Two parallel lines are crossed by a transversal. What is the value of x? a) x = 40 b) x = 70 c) x = 110 d) x = 130.

Answer:

28.6 grams

Step-by-step explanation:

Percentage of cocoa in the chocolate bar = 54%

Weight of the chocolate = 53 grams

Weight of the cocoa = 54% of 53 = 28.62 grams

Rounding off to nearest tenth = 30 grams

Answer: 464

Step-by-step explanation: First you multiply by 580 times .20 and subtract the answer of that by 580

Answer:

Step-by-step explanation:

You want the values of g(1) and f(g(1)), given that f(x) = x² +x -6 and g(x) = 7x +3.

To find the value of a function for a particular argument (value of x), put that value where x is and do the arithmetic.

  g(1) = 7·1 +3 = 7 +3 . . . . . use 1 in place of x in 7x+3

  g(1) = 10

For f(g(1)), we first need to find g(1). We already did that, above.

  f(g(1)) = f(10) = 10² +10 -6 - 100 +10 -6 = 110 -6

  f(g(1)) = 104

Answer:

Step-by-step explanation:

I believe its

(-2,-6)