Complex mathematical

The given graph's shaded region shows the possible combinations of raw materials the company can buy.

A relation by which we can compare two or more mathematical expression is called an inequality.

Given that;

An electronics company can spend no more than $4,000 on raw materials for circuit boards.

And, The raw materials cost $10 per ounce for copper and $20 per ounce for silver.

Here, The inequality for the given condition is,

⇒ 10c + 20s ≤ 4,000

Where, c is the number of ounces of copper material and s is the number of ounces of silver material.

So, The given graph's shaded region shows the possible combinations of raw materials the company can buy.

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20% of 80 is 16 and 15% of 30 is 4.5, so the sum is 16 + 4.5 = 20.5.

Answer:

Side BC: y = -2x + 10

Side AC: y = 2x + 4

Yes, these three points could form a right triangle. This is because the slopes of the two lines, Side BC and Side AC, are opposite reciprocals of each other. This means that when the two lines intersect, they will form a right angle.

Answer:

Step-by-step explanation:

To solve this system of equations, you can use the substitution method.

In this method, you solve one of the equations for one of the variables in terms of the other variable. Then you substitute this expression into the other equation. This will give you a single equation in one variable, which you can solve to find the value of that variable. Finally, you can substitute this value back into one of the original equations to find the value of the other variable.

To solve this system using substitution, we can solve the second equation for y:

y = x - 4

Then, we substitute this expression for y in the first equation:

x + (x - 4) = 8

Combining like terms, we get:

2x - 4 = 8

Adding 4 to both sides, we get:

2x = 12

Dividing both sides by 2, we find that:

x = 6

Now we can substitute this value back into one of the original equations to find the value of y. Let's substitute it into the second equation:

x - y = 4

Substituting 6 for x, we get:

6 - y = 4

Subtracting 6 from both sides, we find that:

y = 2

So the solution to the system of equations is x = 6 and y = 2.

Answer:

x=6, y = 2

Step-by-step explanation:

If you add 2 expressions, 2x = 12, so x = 6.

So the other one y = 2.

On solving the provided question we can say that  expression which is equivalent form to 3/2 is (5/2-1).

Expressions that are equivalent do the same thing even when they have distinct appearances. When we enter the same value(s) for the variable, two algebraic expressions that are equivalent have the same value (s).

Equivalent systems refer to sets of equations with the same solution. We can create an analogous system from a system of two equations by replacing one equation with the total of the two equations or by replacing an equation with a multiple of itself.

When two expressions can be reduced to a single third expression or when one of the expressions can be expressed in the same way as the other, they are said to be equivalent. When values are replaced for the variable and both expressions yield the same result, you may also tell if two expressions are equal.

The number is 3/2

The expression which is equivalent to 3/2 is (5/2-1)

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Answer:

the k is 7

Step-by-step explanation:

12×2=24

12×3=36

12×4=48

12×5=60

12×6=72

12×7=84

Answer:

k = 7

Step-by-step explanation:

The product of 12 and k is 84 [tex]\rightarrow 12k=84[/tex].

[tex]12k = 84 \\ k = \dfrac{84}{12} \\ \boxed{k = 7}[/tex]

Answer:

Step-by-step explanation:

You want the amount of money each receives if Laura, Tom, and Alex share £95 in the ratio 8:7:4.

The total number of ratio units is 8+7+4 = 19, corresponding to a total amount of £95. That makes each ratio unit represent £95/19 = £5.

Multiplying the ratio units by £5, we find the distribution to be ...

  Laura : Tom : Alex = £40 : £35 : £20

Answer:

Money received by Laura = 8x = 8x5 =  £40

Money received by Tom = 7x = 7x5 =  £35

Money received by Alex = 4x = 4x5 =  £20

Step-by-step explanation:

Given ,

To Find : How much money will each of them receive

Let us take the variable as 'x' to find the money received by them

When we convert it to a equation

8x+7x+4x = 95

19x = 95

x = [tex]\frac{95}{19}[/tex]

x = 5

Money received by Laura = 8x = 8x5 =  £40

Money received by Tom = 7x = 7x5 =  £35

Money received by Alex = 4x = 4x5 =  £20

Hence, the money received by each of them is  £40, £35 and  £20

Answer: It's closer to 1/2

Step-by-step explanation: It's closer to 1/2 and here's why:

So, 1/2 (exact) is 8/16

0 = 0

1 = 16/16

Since 9/16 is the closest to 8/16 or around 1/2 in this case, it'd be about 1/2. I hope this helps!

The length of time to build the fence is 8 hours

From the question, we have the following parameters that can be used in our computation:

Length of the fence = 1 1/3 miles

Rate of building = 1/6 miles per hour

The length of time to build the fence is then calculated as

Length of time = Length of the fence/Rate of building

Substitute the known values in the above equation, so, we have the following representation

Length of time = (1 1/3 miles)/(1/6 miles per hour)

Evaluate the quotient

This gives

Length of time = 8 hours

Hence, the time taken is 8 hours

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Check the picture below.

Answer:

About 47% of books were nonfiction.

The actual percentage includes decimals and it would be this:

%47.0588235294

[tex]~~~~~~ \textit{Simple Interest Earned Amount} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \$ 678400\\ P=\textit{original amount deposited}\dotfill & \$320000\\ r=rate\to 7\%\to \frac{7}{100}\dotfill &0.07\\ t=years \end{cases} \\\\\\ 678400 = 320000[1+(0.07)(t)] \implies \cfrac{678400}{320000}=1+0.07t\implies \cfrac{53}{25}=1+0.07t \\\\\\ \cfrac{53}{25}-1=0.07t\implies \cfrac{28}{25}=0.07t\implies \cfrac{\frac{23}{25}}{0.07}=t\implies \boxed{16=t}[/tex]

Answer:

Step-by-step explanation:

This is a right triangle that has two equal sides - so it is also isosceles.

It can be solved using Pythagoren Theorem.

a²  +  b²  =  c²

In this case a = b

so:  

6²  +  6²  = c²

36 +  36 =  c²

72  =  c²

[tex]\sqrt{72[/tex]  =  [tex]\sqrt{c^{2} }[/tex]

8.49 = c

round to 8.5

This is the length of the flap.

Answer:

-----------------------------------

Given lines:

Plot both of the lines using the graphing calculator by adding the equations, then find the graphical solution as the intersection of the lines.

See attached.

The solution is (-1, 0).

Using the law of sines, it cannot be affirmed whether the conditional is true or false, as we have no information about the measure of angle B.

We suppose a general triangle, for which:

The lengths and the sine of the angles are proportionally related as follows:

[tex]\frac{\sin{A}}{a} = \frac{\sin{B}}{b} = \frac{\sin{C}}{c}[/tex]

The segments in this problem are given as follows:

Hence it can be affirmed that:

BC > AB.

As the measure of angle A is greater than the measure of angle C, hence sin(A) > sin(C) and BC > AB, using the proportional relationship.

As for segment AC, we need the measure of angle B, hence nothing can be affirmed.

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if functions  f(x) = 2x²-4x-6 and g(x)= 2x+7 then f(g(x)) is 8(x+2)(x+4)

A relation is a function if it has only One y-value for each x-value.

Given functions are f(x)= 2x²-4x-6

g(x)=2x+7

We need to find expression of f(g(x))

f(g(x))=f(2x+7)

Now replace x with 2x+7 in f(x)

f(2x+7)=2(2x+7)²-4(2x+7)-6

=2(4x²+49+28x)-8x-28-6

Apply distributive property

=8x²+98+56x-8x-28-6

Add the like terms

=8x²+48x+64

f(g(x))=8(x+2)(x+4)

Hence, if functions f(x) = 2x²-4x-6 and g(x)= 2x+7 then f(g(x)) is 8(x+2)(x+4)

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Answer:

8.5

Step-by-step explanation:

there's a rule to get the distance between 2 points

√((1st x- 2nd x)²+(1st y- 2nd y)²)

√((-6-(-6))²+(5-(-3.5))²)

=√((-6+6))²+(5+3.5))²)

you can just type that on your calculator and you'll get the result

√((-6+6))²+(5+3.5))²)

=√((5+3.5))²)

= √((8.5))²)

the root goes away with the power (exponent)

so it equals 8.5

Answer:

35.84

Step-by-step explanation:

In the geometric series 2, 4, 6, 8, 10, 12,..., 24 is the 12th term. Each number in this series is separated by a factor of two.

the total of a geometric sequence's terms. Sn=a1(1rn)1r, r1 denotes the sum of the first n terms in a geometric series. an infinite geometric series whose total is provided by the expression S=a11r and where |r|1.

A geometric sequence is a set of numbers that follows a pattern in which the next term is determined by multiplying the previous one by a factor known as the common ratio, r.

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Answer:

343.2

Step-by-step explanation:

156 × 2.2

= (156 × 22)/10

= 3432/10

= 343.2

The equation of the line is y = 4x + 1 , where the slope of the line is m = 4

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given data ,

Let the equation of line be represented as A

Now , the value of A is

Let the number of blocks be y

Let the stage number be x

Let the first point be represented as P = P ( 1 , 5 )

Let the second point be represented as Q = Q ( 2 , 9 )

Now , the slope of the line between the points be

Slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Substituting the values in the equation , we get

Slope m = ( 9 - 5 ) / ( 2 - 1 )

Slope m = 4

Now , the equation of line is y - y₁ = m ( x - x₁ )

Substituting the values in the equation , we get

y - 5 = 4 ( x - 1 )

On simplifying the equation , we get

y - 5 = 4x - 4

Adding 5 on both sides of the equation , we get

y = 4x + 1

Therefore , the value of A is y = 4x + 1

Hence , the equation of line is y = 4x + 1

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Tim worked for a total of 7 and half hours on Monday and earned $56.25 gross pay.

Prior to payroll deductions, earned wages are referred to as gross pay. Employers utilize this amount—$60,000 per year or $25 per hour—when talking to employees about pay. Additionally, the federal and state income tax brackets sometimes refer to gross salary.

The amount of pay that employees get after payroll deductions varies; some may be optional, while others may be required.

Given, On Monday of his time card Tim clocked in at 8:15 am and clocked out at 4:15 pm.

So, The total number of hours she worked is 8 hours, 8:15 to 12:15 is 4 hours, and another four hours.

Also given the time he took for lunch is half an hour.

Therefore, The total hour he worked is 7:30 hours.

He earns $7.5 per hour so his gross pay for Monday is $(7.5×7.5).

= $56.25.

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Answer:  An equation has two solutions when it has two distinct values that can be assigned to the variable to make the equation true.

In this case

equation A. W=-1 is a single solution

equation B. W=1 is a single solution

equation C. W=-2 is a single solution

equation D. W=0 is a single solution

So none of the given equations have two solutions. they all have only one solution.

It's worth mentioning that, if the equation is a quadratic equation (in the form of ax² + bx + c = 0) and it has a non-zero discriminant (b² - 4ac) then the equation will have two distinct real solutions.

In this case the equations are not in that form, and also doesn't show any signs of having two solutions.

Step-by-step explanation:

The amount of rain required would be 2.5 inches.

What is the addition?

Addition is a mathematical operation that represents the process of combining two or more numbers together. The result of this operation is called the sum. The addition operation is often represented using the symbol "+", and it can be used to add any two or more numbers together.

To beat the record by one-tenth of an inch, an additional 0.1 inches of rain must fall.

Currently, the average amount of rain per day is 12 inches / 5 days = 2.4 inches per day.

So, the amount of rain that must fall on Friday to beat the record by one-tenth of an inch is 2.4 inches + 0.1 inches = 2.5 inches

Hence, the amount of rain required would be 2.5 inches.

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Answer:

(-2,-6)

Step-by-step explanation:

we can solve this system of equations with the substitution method because y is already by itself.

since they are both equal to y, we can set both equations equal to each other.

4x+2=x-4

subtract 2 from both sides

4x=x-6

subtract x from both sides

3x=-6

divide both sides by 3

x = -2

now that we know x, we can plug this value into one of the original equations and solve for y.

y=-2-4

y=-6

so on a graph, these two equations will intersect at the point (-2,-6)

Answer:

No Solutions

Step-by-step explanation:

Hello!

We can solve for a by isolating the variable.

Since -29 cannot be equal to -9, there are no solutions for this equation.

Answer: C correctly rewrites the formula to solve I

Step-by-step explanation:

The equation of the perpendicular line will be x + y - 5 = 0. Then the correct option is B.

Let the equation of the line be ax + by + c = 0. Then the equation of the perpendicular line that is perpendicular to the line ax + by + c = 0 is given as bx - ay + d = 0. If the slope of the line is m, then the slope of the perpendicular line will be negative 1/m.

The equation of the line passing through (-5, 6) and (-6, 5) will be given as,

(y - 6) = [(5 - 6) / (- 6 + 5)](x + 5)

y - 6 = (x + 5)

y = x + 1

The equation of the line that is perpendicular to the above line is given as,

y = - x + c

The equation of the line is passing through (3, 2)

3 = - 2 + c

c = 5

Then the equation of the perpendicular line will be given as,

y = -x + 5

x + y - 5 = 0

The equation of the perpendicular line will be x + y - 5 = 0. Then the correct option is B.

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The complete question is given below.

The probability that on average these students spend more than $425 on books is given as follows:

0.0009 = 0.09%.

The z-score of a measure X of a variable that has mean symbolized by [tex]\mu[/tex] and standard deviation symbolized by [tex]\sigma[/tex] is obtained by the rule presented as follows:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The parameters for this problem are given as follows:

[tex]\mu = 400, \sigma = 80, n = 100, s = \frac{80}{\sqrt{100}} = 8[/tex]

The desired probability is one subtracted by the p-value of Z when X = 425, hence:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem:

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{425 - 400}{8}[/tex]

Z = 3.125.

Z = 3.125 has a p-value of 0.9991.

1 - 0.9991 = 0.0009 = 0.09%.

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The probability of tossing 3 heads in a row is P = 0.125, and after that, because the events are independent, the probability of getting heads (or tails) still is p = 0.5

Assuming that we have a fair coin, we assume that both outcomes have the same probability, so:

P(tails) = 0.5

P(heads) = 0.5

Then the probability of getting heads 3 times in a row, is the product of the probability of getting heads 3 times, this will be:

P(3 heads) = 0.5*0.5*0.5

P(3 heads) = 0.5^3

P(3 heads) =  0.125

Now, after this point, what is the probability of getting heads or tails?

Remember that each toss of the coin is independent of the previous one, so the probability of getting tails still is 0,5, and the same for the probability of getting heads.

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