adding and subtracting fractions with unlike denominators

The given inequality is:

|-8x+24| \leq 16

This inequality can be divided in two parts as:

a) -16 \leq -8x +24

b) -8x + 24 \leq 16

Solving part a:

-16 \leq -8x+24 \\ \\ 
-40 \leq -8x \\ \\ 
5 \geq x \\ 
or \\ 
x \leq 5

Solving part b:

-8x+24 \leq 16 \\ \\ 
-8x \leq -8 \\ \\ 
x \geq 1

Therefore, the solution to the given inequality is x \leq 5 and x \geq 1. Combining both the ranges we get the solution: 1 \leq x \leq 5.

In interval notation, this solution can be expressed as [1,5

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Answer:

Option C is correct

(1, 5)

Step-by-step explanation:

A system of equations contains two or more than two linear equations that divide two or more unknowns.

To find a solution for the system of equations,

we must find a value from the graph that is true for all equations in the given system.

We know that:

If the graphs of the equations intersect,

then there is one solution that is true for both equations.

Given the graph.

There are two lines

Equation of Blue line : y = -x+6

Equation of Red line = y = 2x+3

Since, the graph of two lines y = -x+6 and  y = 2x+3 intersects which means there is one solution that satisfies the both equation.

Therefore, the solution to the system of equations graphed is, (1, 5)

Answer:

Option C

Step-by-step explanation:

we need to find the solution(s) to the quadratic equation 50 – x^2 = 0

50 – x^2 = 0

Subtract 50 from both sides

– x^2 = -50

Now divide by -1 from both sides

x^2 = 50

To remove square , take square root on both sides

[tex]x=+-\sqrt{50}[/tex]

[tex]x=+-\sqrt{25*2}[/tex]

[tex]x=+-5\sqrt{2}[/tex]

Option C is the answer

Answer:

B

Step-by-step explanation:

The ratio of male clients to female clients for the hairstylist is 21:49, which simplifies to 3:7 after dividing both numbers by the GCD of 7.

The question asks to find the ratio of male clients to female clients for a hairstylist. In this scenario, the hairstylist has had 49 female clients and 21 male clients. To find the ratio of male to female clients, we compare the number of male clients to the number of female clients.

The ratio is expressed as male clients : female clients. Thus, the ratio of male clients to female clients is:

21 male clients : 49 female clients

To simplify the ratio, we find the greatest common divisor (GCD) of 21 and 49, which is 7. Dividing both numbers by 7, we get:

3 male clients : 7 female clients

Answer:

the asnwer is 5

Step-by-step explanation:

i did this question

To find the original weight of a bag of grapes before some were eaten, you divide the current weight of 5/8 lb by 4. The calculation reveals that the bag's original weight was 5 pounds.

The question asks us to calculate the original weight of a bag of grapes before it was partially eaten. After eating some of the grapes, the bag now weighs 5/8 of a pound. To find the original weight, we need to determine what weight, when multiplied by 4, would equal 5/8 of a pound. We do this by dividing the current weight by 4 to reverse the multiplication. Using the formula:

Original Weight = Current Weight / 4

So:

Original Weight = (5/8) lb / 4

When we do the calculation:

Original Weight = (5/8) lb / (4/1)

Original Weight = (5/8) lb \(1/4)

Original Weight = (5/32) lb

Since (5/32) lb is equivalent to 5 pounds (when multiplied by 4, it gives 20/32 lb, which simplifies to 5/8 lb), the original weight of the bag of grapes was 5 pounds.

Final answer:

To determine what Noah will receive or pay after figuring his taxes for the year, we need to calculate his tax liability. According to the 2020 tax brackets, a married couple filing jointly with a taxable income of $27,156 falls into the 12% tax bracket. Since Noah has already paid $3,260 in federal taxes, he has overpaid his taxes and will receive a refund of $1.28.

Explanation:

To determine what Noah will receive or pay after figuring his taxes for the year, we need to calculate his tax liability.

First, we need to determine his taxable income after considering his filing status. As he is filing as married filing jointly, we can check the tax brackets for that status.

According to the 2020 tax brackets, a married couple filing jointly with a taxable income of $27,156 falls into the 12% tax bracket. To calculate the tax liability, we multiply the taxable income by the tax rate, which gives us $27,156 * 0.12 = $3,258.72.

Since Noah has already paid $3,260 in federal taxes, he has paid more than his tax liability for the year. In this case, he will receive a tax refund equal to the difference between his tax liability and the amount he has already paid, so the amount he will receive is $3,258.72 - $3,260 = $-1.28.

Therefore, Noah will receive a tax refund of $1.28 after figuring his taxes for the year.

Answer:

100

Step-by-step explanation:

Solution:

we are given that

Camilla’s class played soccer for 2/3 hour.

She played for 3/5 of the game.

we have been asked to find

How much time did Camilla play?

Here we are given total time of play for the whole class and camilla played part of that time so we will just multiply the total play time with the fraction of time that camilla played. That will give the actual play time of camilla.

So camila played for [tex]=\frac{2}{3}*\frac{3}{5} =\frac{6}{15}Hr[/tex]

Hence camilla played for 6/15 Hr.

Hence the correct option ois B.

To find the probability mass function (pmf) of the number of red M&Ms in a bag, use the binomial distribution formula. The probability a bag has no red M&Ms is calculated by raising (4/5) to the 25th power, as per the binomial distribution with a success probability of 1/5 and 25 trials.

The question involves finding the probability mass function (pmf) of the number of red M&Ms in a bag of 25 M&Ms where each M&M has an equal chance of being one of five colors.

To determine the pmf of the number of red M&Ms, which we'll call r, we can use the binomial distribution, since each M&M is an independent Bernoulli trial with two outcomes (red or not red), and each M&M has the same probability of being red.

The probability of getting a red M&M is 1/5, so the pmf of r for k red M&Ms in a bag of 25 is given by P(r=k) = (25 choose k) × (1/5)^k × (4/5)^(25-k).

To find the probability that a bag has no red M&Ms, we set k to 0 in the pmf formula: P(r=0) = (25 choose 0) × (1/5)⁰ × (4/5)²⁵. This simplifies to (4/5)²⁵, since any number to the zero power is 1 and (25 choose 0) is also 1.

Answer:

a 24

Step-by-step explanation:

For this case we have the following definitions:

Answer:

x ----------------> Variable

3 ----------------> Coefficient

1 ----------------> Constant

[tex]3x ^ 2-4x + 1[/tex] -----------> Algebraic expression

2 ----------------> Degree

Answer:

There are 3 elements in the set.

Step-by-step explanation:

Given set,

{A, B, C}

∵ Set is the collection of defined distinct objects,

These objects are called elements of the set,

We have given a set in which A, B, C are present thus they must be distinct,

So, by the above definition,

The given set has three elements.