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A student is checking the shading on her graph of the solution of an inequality. The graph is shown. She chooses the value x = -17 to substitute. Will substituting this value back into the original inequality result in a true or a false statement? Explain your answer.

The measure of angle B is 40 degrees.

In this question, we have been given angle A and angle B are supplementary angles.

m∠A=(4x−16)°

and m∠B=(x+1)°

since angle A and angle B are supplementary angles,

angle A + angle B = 180°

So we get an equation,

(4x − 16)° + (x + 1)° = 180°

5x - 16 + 1 = 180

5x = 180 + 15

5x = 195

x = 39

So, x + 1 = 39 + 1

              = 40°

Therefore, the measure of angle B is 40 degrees.

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James has $37.67 now after all his expenses

James had $x, his brother had $y, and his sister had $z when the morning began.

By using algebra,

James's sibling had twice as much money as James.

Now, x =y/2..... (i)

James had $27 fewer dollars than his sister did.

So, x = z - 27 ........ (ii)

⇒  {From equation (1)}

⇒ y/2 = z -27

⇒ y = 2z - 54

⇒ 2z - y =54 ..........(3)

Now, James and his sister each received $12 from his brother.

James now has $(x + 12), his brother now has $(y -24), and his sister now has $(z + 12).

Given that James' sister has twice as much money as James' brother after payoff,

So, z+12/2 = y-24

⇒ z + 12 = 2y - 48

⇒ 2y - z = 50 ......... (4)

The result of resolving equations (3) and (4) is

3y = 54 + 100 = 154

⇒ y =  51.33.

The result of equation (3) is now z = 52.67.

And from equation (1), x = 51.3/2= 25.67

So, now, James has (25.67 + 12) = $37.67

Hence, James has $37.67 now after all his expenses

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The solution to the compound inequality is x > -3. The correct option is the third option x > -3

From the question, we are to solve the given compound inequality

2x - 2 > -8 or -4x ≤ -36

Solving the first inequality

2x - 2 > -8

Add 2 to both sides of the inequality

2x -2 + 2 > -8 + 2

2x > -6

Divide both sides by 2

2x/2 > -6/2

x > -3

Solving the second inequality

-4x ≤ -36

Divide both sides of the inequality

-4x/-4 ≤ -36/-4

x ≥ 9

From the two solutions, we can conclude that x > -3

Hence, the solution is x > -3

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Using the z table, the probability that a standard normal random variable will be between 0.3 and 3.2 is 0.3814.

In the given question,

We have to find that the probability that a standard normal random variable will be between 0.3 and 3.2 .

We firstly learn about a standard normal random variable which is expressed with a mean and standard deviation.

Since we have to find the probability that a standard normal random variable will be between 0.3 and 3.2 .

So The probability should be

P(0.3<z<3.2)=P(z<3.2)−P(z<0.3)

From the standard value of z

P(0.3<z<3.2)=0.9993−0.6179

Simplifying

P(0.3<z<3.2)=0.3814

Hence, the probability that a standard normal random variable will be between 0.3 and 3.2 is 0.3814.

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The slopes of both lines that passes through the given points are different, therefore: d. No, they are not perpendicular because their slopes are not reciprocals.

For any two lines that passes through two set of points to be perpendicular to each other, their slopes must have a product that is equal to -1, or be negative reciprocals.

Find the slope of the line that passes through P(0, –9) and Q(2, –8):

Slope of PQ (m) = (-8 -(-9)) / (2 - 0)

m = 1/2

Find the slope of the line that passes through R(1, 4) and S(3, 3):

Slope of RS (m) = (3 - 4) / (3 - 1)

m = -1/2

The slope of both lines are not equal neither are they negative reciprocals of each other. Therefore: d. No, their slopes are not reciprocals.

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The answer of the inequality is [tex]-3 < k < -\frac{1}{3}[/tex]

What does algebraic inequality mean?

An inequality in maths shows the relationship between the two values in an uneven algebraic expression. A sign of inequality can be employed to indicate that one of the two variables is less than, greater than or equal to, less than, or equal to another value.

Given That:
-16<6k+2<0
Now to solve this equation we will subtract 2 from all the side
-16-2<6k<-2
now we will divide by 6 on all the side
-18/6<k<-2/6
[tex]-3 < k < -\frac{1}{3}[/tex]
Hence this the answer to the question

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8,16,24

Given:

the relation between number of sandwiches and time is :

y = 8x

where, y is number of sandwiches

x is time

For 1 hour,

y = 8*1

y = 8.

For 2 hour,

y = 8*2

y = 16.

For 3 hour,

y = 8*3

y = 24.

#123

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sandwiches eaten by Jimmy in consecutive hours are 8, 16, and 24.

Given info;

Jimmy consistently consumes sandwiches. The linear equation y = 8x represents the number of sandwiches(y) that he can consume in an hour(x).

To know how many sandwiches he ate in consecutive hours;

Case(1):

y = 8x

x = 1 hour

y = 8*1

  = 8

Case(2):

y = 8x

x = 2 hours

y = 8*2

  = 16

Case(3):

y = 8x

x = 3 hours

y = 8*3

  = 24

Therefore, sandwiches eaten by Jimmy in consecutive hours are 8, 16, and 24.

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Charlie needs to sell 1000 packages per month in order to pay himself a monthly salary of $5000. By using the Equation concept we solved this problem.

A mathematical statement known as an equation is made up of two expressions joined together by the equal sign.

Let the number of packages that Charlie needs to sell is ‘x’

So, According to the question , the below equation has been formed,

10x – (1500 + 3.50x) = 5000

10x – 1500 – 3.50x = 5000

6.50x = 5000+1500

6.50x = 6500

x = 6500/6.50

x = 1000 packages.

So that is how we calculated the number of packages that Charlie needs to sell per month.

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The property used in expression 3 x 5 = 5 x 3 will be ''Commutative property''.

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The expression is,

⇒ 3 x 5 = 5 x 3

Now,

We know that;

The commutative property is defined as;

⇒ a x b = b x a

Hence, In the expression,

⇒ 3 x 5 = 5 x 3

The commutative property is used.

Thus, The property used in expression 3 x 5 = 5 x 3 will be ''Commutative property''.

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If y is exactly proportional to x, then the value of y at x=16 is 40 if y=5 when x=2.

[tex]&y \propto x \\[/tex]

[tex]&y=k x[/tex]

When x = 2, y = 5

[tex]&5=k(2) \\[/tex]

therefore

[tex]k=\frac{5}{2}[/tex]

When x = 16,

[tex]&y=\left(\frac{5}{2}\right) \\[/tex]

y = 40

Hence, If y is exactly proportional to x, then the value of y at x=16 is 40 if y=5 when x=2.

The complete question is:

If y is directly proportional to x and y=5 when x=2, what is the value of y when x=16?

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The domain of the function in the graph is {yl1≤y≤9}.  Option b is the correct answer.

Graph:

The domain of a function is the collection of all conceivable values that can be used as inputs, or alternatively, it is the full range of potential values for independent variables.

A graph is an organized visual representation of any data in mathematics. The relationship between the variable quantities is depicted on the graph. In a graph theory, the set of items that are somehow connected to one another is represented by a graph. The vertices or nodes of the objects are essentially mathematical notions, and the edges between the nodes represent the relationships between the nodes. In mathematics and statistics, there are various types of graphs that are used to visually display data. The study of points and lines is known as graph theory. It is a branch of mathematics that focuses on the investigation of graphs. The mathematical truth is shown visually in this picture. Relationships are studied using graph theory.

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The average of first 50 numbers is 25.5 because average is computed by adding a set of numbers and then dividing by the total number of those numbers.

The average of a list of data is a mathematical expression for the central value of a set of data. The ratio of all the data points to all the units in the list is how it is mathematically defined. The average of a specific set of numerical data is also referred to as the "mean" in statistics.

The four sorts of average that we recognize are mean, mode, median, and range. Although the others are our most popular "measures of central tendency," range is actually a measure of spread or distribution.

The first 50 natural numbers are 1,2,3,...,50

The sum of first n natural numbers = n(n+1)/2

Sum of first 50 natural numbers is  50(51)/2

=25(51)/2=1275

Hence, average of first 50 natural numbers is  

1275/50

=25.5

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Answer: Mean :286.6 Median:294 Mode:169, 294, 188, 295, 487

Multiplying vector v we get 2.5v =  (-10, 10).

What is the vector?

A vector is a quantity or phenomenon with two distinct properties: magnitude and direction. The term can also refer to a quantity's mathematical or geometrical representation. In nature, vectors include velocity, momentum, force, electromagnetic fields, and weight.

The magnitude of a vector indicates the vector's length. It is typically represented by an arrow pointing in the vector's direction. A vector a is defined as a1 ^ii^ + b1 ^jj^ + c1 ^kk^, where a1, b1, and c1 are its constituents.

We have,

v = (-4,4)

2.5v = ?

Multiplying vector v by 2.5 we get,

2.5v =  (-10, 10)

Hence, by Multiplying vector v we get 2.5v =  (-10, 10).

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Answer:

56

Step-by-step explanation:

Answer:

The answer is the screenshot shown.

Step-by-step explanation:

How to graph it in that is to check the given first.

y= -5x

x = 0

y = -5

-

So you will have to plot the line at 0 for x and for y, you should put it at -5

The equation of the line (-4,3) and (2,-4) is y = -7/6x -5/3.

What is equation of line?

The equation of a line is the algebraic representation of a line using cartesian coordinates. The general form of the equation of a straight line is written as y = mx + c. Where m is the gradient of the straight line and c  is the y y-intercept of the straight line.

Given, the points are (-4,3) and (2,-4)

m = -4-3/2+4

m = -7/6

The equation we get

y = -7/6x +b

the point (-4,3), we get

3 = -7/6(-4) +b

3 = 14/3 +b

3-14/3 = b

b = -5/3

Hence, the equation of line is y = -7/6x -5/3.

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If the mill starts out with 490 tons of grain , then the amount of grain that remains to be sold after milling is 450.8 ton.

In the question ,

it is given that ,

the percent of grain that is lost due to spillage = 3%

the percent of grain that is lost due to mildew = 5%

the total percent of grain lost = grain lost due to spillage + grain lost due to mildew

= 3% + 5%

= 8% of total grain  

given that amount of grain =  490 tons .

amount of grain lost = 8% of 490

= 0.08 * 490

= 39.2 ton ,

So , 39.2 ton of grains is lost .

the amount of grain remain to be sold = 490 - 39.2 = 450.8 ton

Therefore , If the mill starts out with 490 tons of grain , then the amount of grain that remains to be sold after milling is 450.8 ton   .

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Answer:

3

Step-by-step explanation:

1 foot = 12 inches

Jana can jump 36 inches!

Divide this by 12 to get the feet:

36 / 12 = 3

Check: 12 + 12 = 24 + 12 = 36

so, Jana can jump 3 feet above the ground

By using the formula for area of triangle using coordinates, the following results are obtained

13) Area of triangle = [tex]\frac{15}{2} \ sq. units[/tex]

14) Area of triangle = [tex]\frac{49}{2} \ sq. units[/tex]

What is area of triangle?

Area of a triangle is the total space taken by the triangle. If the coordinates of triangle are [tex](x_1, y_1), (x_2, _2) \ and \ (x_3, y_3)[/tex], then area of triangle is calculated by the formula

Area of triangle = [tex]\frac{1}{2}|x_1(y_2 - y_3) + x_2(y_3 - y_1) + x_3(y_1 - y_2)|[/tex]

13) The given coordinates are E (3, 1), F(3, -2) and G(-2, 2)

Area of triangle =

[tex]\frac{1}{2}|3(-2-2) + 3(2-1) + (-2)(1 -(-2))|\\\\\frac{1}{2}|3(-4) + 3(1) -2(3)|\\\\\frac{1}{2}|-12 + 3 - 6|\\\\\frac{1}{2}|-15|\\\\\frac{15}{2} \ sq. units[/tex]

14) The given coordinates are E (-3, 4), F(4, 4) and G(3, -3)

Area of triangle =

[tex]\frac{1}{2}|(-3)(4-(-3)) + 4(-3-4) + 3(4-4)|\\\\\frac{1}{2}|(-3)(7)+4(-7)+3(0)]\\\\\frac{1}{2}|-21-28+0|\\\\\frac{1}{2}|-49|\\\\\frac{49}{2} \ sq. units[/tex]

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According to question, project managers can assess the outcomes to identify any hazards the project might encounter after it is completely executed.

These risks are frequently examined by project managers and stakeholders to decide whether they are controllable and whether it is worthwhile to move on with the entire project. An organization can control the risk of a novel concept and spot any flaws through a pilot project before significant resources are spent.

On the other hand, a trial is a limited implementation before you launch the pilot project broadly. All the advantages of a pilot project are present, but they are more thorough, and the team is frequently able to test out more features and observe the results on a wider scale.

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The equation to represent the area of the desk is A=3.5 x 12.  The length of the large office desk is 12.

The area a rectangle occupies on a two-dimensional plane is known as the area of the rectangle. A quadrilateral, a type of two-dimensional shape with four sides and four vertices, is what a rectangle is.

A large office desk is given, with area 42 ft^2. The shape of the desk is rectangle. The area of the rectangle is given by A=l*w.

Given, the area is 42 ft^2.

w=3.5 feet.

A= 42

42=3.5*l

l=42/3.5

l=12 feet.

The length of the rectangular desk is 12 feet. The equation to represent the area of the large office desk is A=12*3.5.

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Answer:

-1

Step-by-step explanation:

Thus, Bao age is 27.

acc to our question-

hence,Thus, Bao age is 27.

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The crew will take 6 hours to mulch 12 flower gardens.

Given, that

A landscaping crew can mulch 3 flower gardens in 1(1/2) hours i.e. 3/2 hours.

so, 3 flower gardens mulch = 3/2 hours

Now, we are asked that how long will it take the crew to mulch 12 flower gardens.

As, 3 flower gardens mulch = 3/2 hours

1 flower garden mulch = (3/2)×(1/3) hours

1 flower garden mulch = 1/2 hour

12 flower gardens mulch = (1/2)×12 hours

12 flower gardens mulch = 6 hours

So, it will take 6 hours by the crew to mulch 12 flower gardens.

Hence, the crew will take 6 hours to mulch 12 flower gardens.

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Using the standard form of the equation of line, the slope of the line represented by the equation 3x-4y=7 is 3/4.

In the given question,

We have to find the slope of the line represented by the equation 3x-4y=7.

The given equation is 3x-4y=7.

To find the slope we first express the given equation in the form of standard equation of line.

The standard form of equation is y=mx+c where m is slope of the equation.

Now expressing the equation in standard form.

3x-4y=7

Subtract 3x on both side

3x-4y-3x=7-3x

-4y=7-3x

Divide by -4 on both side

-4/-4 y=7/-4 - (-3)/(-4) x

Simplifying

y=3/4x-7/4

Now comparing from the standard equation to find the slope(m).

m = 3/4

Hence, the slope of the line represented by the equation 3x-4y=7 is 3/4.

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Answer:75 ft

Step-by-step explanation:sea level is represented as 0. going from 0 to -75 is 75 ft

Answer: 8%

Step-by-step explanation: Rate = Interest 484 ÷ Principle (550) x Time (11), with this formula the answer is 8%.

If a decision maker wishes to reduce the margin of error associated with a confidence interval estimate for a population mean, she can increase the sample size.

The margin of error refers to the statistic measurement that expresses the level of random sampling error in the outcomes of a survey. If the margin of error of the result is high, the confidence level would be low that a result reflects the census of the entire population. It indicated the difference between the actual and estimated results in a random survey sample. The margin of error is generally used in non-survey contexts to show observational error in reporting measured quantities. In order to minimize the margin of error associated with a confidence interval estimate for a population mean, the researchers can increase the sample size to capture the actual trend of the population more accurately.

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Hence the complete table is ,

=>  laps        Miles

       3             3.75

       7              8.75

       8              10

      13              16.25

What is miles ?

   A mile is a unit of length that is exactly equal to 5280 feet, or 1760 yards, and was standardised as exactly 1609.344 metres by an International agreement in 1959. It is the largest unit commonly used to measure the distance between distant locations.

Here the distance 2 laps = 2.5 miles. Then ,

=> 1 laps = 2.5/2 = 1.25 miles.

Now 3 laps = 3*1.25 = 3.75 miles

Here n laps = 8.75 miles .

=> n* 1.25 = 8.75

=> n = 7 laps .

Now 8 laps = 8*1.25 = 10 miles.

And n laps = 16.25

=> n = 16.25/1.25 = 13 laps. miles

Hence the complete table is ,

=>   laps        Miles

       3             3.75

       7              8.75

       8              10

      13              16.25

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