Twice a number t decreased by eight equals seventy.

∠FED and ∠DEW are complementary because it is a sum of 90 degrees.

By the law of addition of complementary angles,m∠FED + m∠DEW = 90°

m∠FED + m∠DEW = m∠FEW by the Angle addition postulate.

By the substitution property of equality, m∠FEW = 90°.

The ∠FEW is a right angle by the definition of right angles.

Complementary Angles defined as angles that sum up to 90 degrees.

Now, we are given that;

∠FED and ∠DEW are complementary.

We want to prove that ∠FEW is a right angle. Thus;

∠FED and ∠DEW are complementary because it is a sum of 90 degrees.

By the law of addition of complementary angles, we can say that;

m∠FED + m∠DEW = 90°

Also,

m∠FED + m∠DEW = m∠FEW by the Angle addition postulate.

By the substitution property of equality, m∠FEW = 90°.

The ∠FEW is a right angle by the definition of right angles.

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Initial temperature T₀ = 13°c

second Temperature T₁= 10°c

Change in Temperature  T₂ =  T₀ - T₁   = 13°c - 10°c   = 3°c

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The probability that the amount dispensed per box will have to be increased is 0.0062.

Consider the provided information.

Sample of 16 boxes is selected at random.

If the mean for 1 hour is 1 pound and the standard deviation is 0.1

1 Pound = 16 ounces , then 0.1 Pound = 16/10 = 1.6 ounces

Thus: μ = 16 ounces and σ = 1.6 ounces.

Compute the test probability

z= x−μ/σ/[tex]\sqrt{n}[/tex]

z= 15-16/ 1.6/4

z= -1/ 0.4

z= -2.5

By using the table.

Probability p value = P(Z<-2.50) = 0.0062

Thus, the probability that the amount dispensed per box will have to be increased is 0.0062.

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Answer:

Step-by-step explanation:

5(y + 1) = 5

Divide both sides by 5

=> 5(y + 1)/5 = 5/5

=> y + 1 = 1   [ 5 in numerator and 5 in denominator cancel]

Subtract 1 from both sides

y + 1 -1 = 1 - 1

y + 0 = 0

=> y = 0

Answer:

k = - 5

Step-by-step explanation:

calculate the slope between the 2 points using the slope formula and equate to 9

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (0, k ) and (x₂, y₂ ) = (1, 4 )

m = [tex]\frac{4-k}{1-0}[/tex] = [tex]\frac{4-k}{1}[/tex] = 4 - k

then equating to 9

4 - k = 9 ( subtract 4 from both sides )

- k = 5 ( multiply both sides by - 1 )

k = - 5

Answer: 310

Step-by-step explanation:

(190/38) x 100 = 500 total students

500-190 = 310 students

Answer:

Hamid's original weight was 80 kgs

Answer:

4

Step-by-step explanation:

[tex]\frac{(-6) - (-3)}{s - 5} = -3\\-3(s-5)=-3\\s-5=-1\\\\s=4[/tex]

The daily rate charged to the client for each associate is $800 and the daily rate for each partner is $1800.  The equations that could be used to determine the number of associates assigned to the case and the number of partners assigned to the case is: 800 x + 1800 y = 17600.

Let variable x = number of associates, assigned to the case

Let variable y = number of partners assigned to the case.

The system of equations to describe this are:

800 x + 1800 y = 17600

y = x + 2

Plugging equation 2 in equation 1, we get,

800 x + 1800(x+ 2) = 17600

2600 x + 3600 = 17,600

Collect like terms

2400 x = 14,000

Divide both side by 2400x

x = 14,000 / 2400

x = 5.8

x = 6 (Approximately)

So,

y = x + 2

y = 5.8 +3

y = 7.8

y = 8 (Approximately)

Therefore the number of associates assigned to the case were 6, and the number of partners associated to the case were 8.

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The maximum profit which this company can expect to earn is $11,650.

The maximum value of a function can be defined as a point on the graph where the function reaches its highest point. This ultimately implies that, the maximum value of a function simply refers to its vertex on a graph.

In order to determine the maximum profit which this company can expect to earn, we would differentiate the given function as follows:

f(x) = y = -10x² + 700x - 600

y' = -20x + 700

-20x + 700 = 0

20x = 700

x = 700/20

x = 35.

Substituting the parameter into the formula, we have;

f(x) = -10x² + 700x - 600

f(35) = -10(35)² + 700(35) - 600

f(35) = -12250 + 24,500 - 600

f(35) = $11,650.

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b. Division property of equality justifies going from the first statement: 5x = 20 to the second statement: x = 4.

Division property is a type of property of equality that states that if both sides of an equation are divided by the same number except 0, then that equation will remain true.

This property can be proved for the given statements as follows;

5x = 20

According to the division property of equality, we divide both sides by the same number which in this case is 5. Therefore;

5x = 20

5x/5 = 20/5

x = 4

As x = 4 is the second statement, therefore property of equality that justifies going from the first to the second statement is the division property of equality.

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Answer:

i think n = 7 idrk

Step-by-step explanation:

gl

Answer:

The third side is 4cm

Step-by-step explanation:

[tex] {3}^{2} + {a}^{2} = {5}^{2} [/tex]

a=25-9

a=16

a=4

The x and y intercepts are (7/5, 0) and (0, -7/2) respectively.

Given equation is 5x-2y = 7.

To find the x-intercept substitute y = 0 in the equation and then solve,

5x - 0 = 7

x = 7/5

So the x-intercept is (7/5, 0).

Similarly, to find the y-intercept substitute x = 0 in the equation and then solve,

0 - 2y = 7

y = -7/2

So the y-intercept is (0, -7/2).

Now, graph the intersections of (7/5, 0) and (0, -7/2).

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Answer:

Step-by-step explanation:

x=0.83

[tex] = \sqrt{( {x2 - x1})^{2} + ( {y2 - y1})^{2} } \\ = \sqrt{ (- 1 - 6 )^{2} + ( {14 - 16)}^{2} } \\ = \sqrt{( { - 7)}^{2} + ( { - 2)}^{2} } \\ = \sqrt{49 + 4} \\ = \sqrt{53} [/tex]

ATTACHED IS THE SOLUTION

After solving percent equation ,the number of red pins from the set of red and yellow pins that Pam ordered is 910 red pins out of 1000 pins.

Eventually, we'll run into a problem that requires us to calculate a percentage of something. The percent equation is the formula we'll employ and it goes like this: part = percent x whole.

The symbol for percent (%) denotes a percentage of one hundred.

You'll need to convert between a percent and a decimal to express these numbers, so let's take a moment to go over that. When you see a percentage, it means 40 out of 100, or 40/100, and that is our fraction. When you divide 40 by 100, you get the decimal 0.40. Remember that 0.40 is the same as 40/100, which means 40%, when converting a decimal to a percent.

Pam ordered a set of red and yellow pins. She received 1,000 pins, and 91% of them were red, so the amount of red pins is

red pins = 91/100  ×  1000

red pins = 910

Thus, the number of red pins from the set of red and yellow pins that Pam ordered is 910 red pins out of 1000 pins

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Answer:

-8

Step-by-step explanation:

[tex]\frac{-6-0}{-9-h} = 6\\6(-9-h)=-6\\-9-h=-1\\-h=8\\h=-8[/tex]

The display to represent the data of the number of employees based on job classification is A. Bar chart; because job classification is categorical.

Categorical data refers to the data types that can be grouped instead of calculated numerically.

Some examples of categorical data include sex, age group, educational level, job classification, and racial categories.

Bar charts and histograms are handy for representing categorical data because they use rectangular bars with heights or lengths to represent proportional values.

Thus, the correct display for the categorical data of job classification is Option A.

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Answer:

A

Step-by-step explanation:

Bar Chart

Answer:

3√2

Step-by-step explanation:

We have an isoceles right triangle, so the length of the hypotenuse is √2 the length of each leg.

[tex]y \sqrt{2} = 6[/tex]

[tex]y = \frac{6}{ \sqrt{2} } ( \frac{ \sqrt{2} }{ \sqrt{2} } ) = \frac{6 \sqrt{2} }{2} = 3 \sqrt{2} [/tex]

Answer:

Hii! This is already written in slope intercept form.

For a refresher, slope intercept form is [tex]y=mx+b[/tex]

[tex]y[/tex] = y-coordinate

[tex]m[/tex] = slope

[tex]x[/tex] = x-coordinate

[tex]b[/tex] = y-intercept

In this equation,

[tex]m[/tex] is [tex]-1/2[/tex]

[tex]b[/tex] is [tex]-5[/tex]

Hope this answers your questions.

The interquartile range of the number of jumps of the 10 students during the competition is 38.

The interquartile range is the difference between the third quartile and the first quartile. The interquartile range is used to determine the variation of a data set.

Th first step is to determine the median of the first half of the dataset. The median of the first half is the first quartile.

First half of the data set: 30, 36, 38, 45, 57

Median = first quartile =  38

The next step is to determine the median of the second half of the dataset. The median of the second half is the third quartile.

Second half of the data set: 60, 77, 86, 88, 88

Median : third quartile =  86

Interquartile range = third quartile - first quartile

86 - 38 = 48

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The expression to represent the equation is given by  y = x + 3 .

An algebraic expression is one that was created in mathematics utilizing integer variables, constant, and algebraic procedures (accumulation, deletion, multiplication, separation, and exponentiation by a rational exponent).

The required expressions are :

y₁ = x + 3

y₂ = 3x²

y₃ = 3ˣ

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The description which represents the roots is Four real roots and no non-real roots.

A function is a statement, rule, or law that establishes the connection between two variables. In mathematics, functions are everywhere and are necessary for constructing physical connections.

The graph is given below;

The function can be written as;

f(x) = [tex]x^4[/tex] - 3x² - 4

Then the values of x for which the value of the function is zero will be;

f(x) = 0

f(x) = [tex]x^4[/tex] - 3x² - 4 = 0

Then the function will be f(x) = [tex]x^4[/tex] - 3x² - 4. Then Four real roots and no non-real roots.

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There are 6 customers in the barber shop on an average.

What is average in ?

As per the Little's law, the average number of costumers or individuals in a system (L) can be calculated by multiplying the average arrival rate (λ) and the average time each customer spends in the system (W).

The algebraic expression, is as follows:

L = λW

Here,

L=inventory or average number of customers in the system.

λ=arrival rate = 10

W=flow time average customer spends in the system = 0.6

L = 0.6 * 10 = 6

Thus, there are 6 customers in the barber shop on an average.

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The equation that models the balance y after x months is;

y = 1,700 - 130x

What is Equation of line?

The equation of line with slope m and y intercept at point b is given as;

y = mx + b

Given that;

Zachary purchased a computer for $1,700 on a payment plan.

Seven months after he purchased the computer, his balance was $790.

Eight months after he purchased the computer, his balance was $660.

Now, Let months is represented by x and models the balance is represented by y.

So, We get;

For 0 months, balance is $1,700.

For 7 months, Balance is $790

For 8 months, balance is $660.

So, Slope = (1,700 - 790) / 7

               = 910/7

               = 130

And, Slope = (1,700 - 660) / 8

                = 1,040/8

                = 130

So, The equation with slope 130 and starting balance $1,700 will be;

y = 1,700 - 130x

Thus, The equation that models the balance y after x months is;

y = 1,700 - 130x

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The relation that is a function from the given option is Graph A.

In mathematics, a relation is a group of ordered pairs that expresses the relationship between two sets.

Function contains both domain and codomain which are also known as dependent and independent variables

For the relation to be a function, two or more of the coordinates must not lie on the same line.

From the given graphs, the relation that is a function is Graph A since two points does not lie on the same vertical line.

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