The graph depicts the growth in costs using a line segment. Use the midpoint formula to approximate the cost during the year 1987.The approximate cost during the year 1987 was $ ____.

Given:

To write it in scientific notation:

It can be written as,

Hence, the scientific notation is,

Let's begin by listing out the information given to us:

Amount spent = $240

discount = 25%

Therefore, the customer paid $180 for his purchase

You can only subtract or divide?

Answer: x = 17

Step-by-step explanation:

         We can tell that these two angles are supplementary angles because we can use corresponding angles. See attached.

(x + 14)° + (9x - 4)° = 180°

x° + 14° + 9x° - 4° = 180°

14°- 4° + x° + 9x° = 180°

10° + 10x° = 180°

10x° = 170°

x = 17

(a) Plan B, 8

(b) 250, Plan A

Given data:

The given mean is m=24.

The given standard devaition is s=0.62.

The given vallue is x=22.9.

The expression for the value of z is,

Refer the standard z-table.

The number of box required are,

Thus, the number of boxes are 288.

The set-builder form is { x | x is a calculus book}.

A set is a collection of quantities based  on a specific criteria. A set can be expressed in two forms.

We usually use the form {a, b, c,....} in which we include each element of the set separated with a comma in between. This form of set notation is called the roster form.

Another set notation is the set-builder form. This form is more concise and precise and easily understandable also. In this form, all the elements are included in the set which has a same property. That is, here we don't write each and every element separately in the set but just emphasize the property of the elements which are included in the set.

We are asked to write the set of all calculus books in set-builder form.

The set-builder form for 'The set of all calculus books' is { x | x is a calculus book}.

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Answer: 16

Step-by-step explanation:

The perimeter of the triangle is [tex]2x+2x+x-8=5x-8[/tex].

The perimeter of the square is [tex]4(x+2)=4x+8[/tex].

Setting the perimeters equal to each other,

[tex]5x-8=4x+8\\\\x-8=8\\\\x=16[/tex]

The constant of proportionality that lies in all of the pairs of values that we have here is given as 17.5

This is the term that is used to refer to the ratio that is known for the fact that it helps to relate two values that are given in a proportional way.

For instance we are to find the constant proportionality of (9, 148.50)

This is given as 9 + 148.5 / 9

= 157.5 / 9

= 17.5

Then the second pair is (15 ,247.50)

In the same way 15 + 247.50 / 15 = 17.5

Hence we can see that the constant of proportionality in all of the pairs is 17.5

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Answer:

its 16.50 i literally just took the test trust me.

Step-by-step explanation:

9 x 16.50 = 148.50

15 x 16.50= 247.50

21  x 16.50 = 346.50!

hope this helps! =)

Given any line, to find the slope of the line, follow the procedure below:

First, pick any two points (x1,y1) and (x2,y2) on the line.

Then, substitute the points into the formula for slope below:

You can use this method to find the slope of any given line.

Answer:

600

Step-by-step explanation:

the total is 626 but round it to the nearest hundred is 600 because the rule 5 or more go up one more 4 or less stay at rest

Since the two cylinders are congruent, it means that their dimensions are exactly the same thing.

In other words, the radius of cylinder 1 is the same as that of cylinder 2, and the height of cylinder 2 is the same as that of cylinder 1. This is what it means for two solid shapes to be congruent.

Now, to find the volume of cylinder 2, we apply the frmula for the volume of a tyical cylnder:

Now,

radius of cylinder 2 = radius of cylinder 1 = 3

height of cylinder 2 = 8

Thus: r = 3, h= 8

Therefore:

Therefore the volume of cylinder 2 is 72pi cubic units (Option D)

The exact solution of log 3(2x - 1) + log 3(2x + 1) = log 3(x + 2) While x = 1 is 0.954.

Given:

log 3(2x - 1) + log 3(2x + 1) = log 3(x + 2)

= log 3(x + 2)

putting x = 1

= log 3( 1 + 2 )

= log 3 . 3

= log 3 + log 3

= 0.477 + 0.477

=0.954

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The sum of all interior angles of a triangle is 180° thus the measure of the exterior angle to ∠K is 168° so option (A) is correct.

A triangle is a 3-sided shape that is occasionally referred to as a triangle. There are 3 sides and three angles in every triangle, some of which may be the same.

It is known that the sum of all three angles inside a triangle will be 180°.

So,   m∠J +  m∠L +  m∠K = 180°

m∠K = 180° - 78° -  90°

m∠K = 12°.

The exterior angle of k = 180- 12 = 168°.

Hence "The sum of all interior angles of a triangle is 180° thus the measure of the exterior angle to ∠K is 168°".

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Answer: We have to calculate the (i) volume and (ii) the surface area of the cone:

The formula (1) is for the lateral surface of the cone and the formula (2) is for the volume of the cone, the unknowns are determined as follows:

Therefore the volume and the lateral surface area is calculated as follows:

Therefore x and y are the answers.

Answer:

Step-by-step explanation:

First you want to make the denominator the first multiple of both numbers so: 2/3 -3 5/6 = 2/6 - 3 5/6

Next you want to multiply the numerator by the amount of times you had to multiply the denominator so: 4/6 - 3 5/6

Then subtract the answer: 3 1/6

The equation of the line passing through points  (0,1) and (2,2) will be y = ( 1 / 2) x + 1

What is an equation of the line?

An equation of the line is defined as a linear equation having a degree of one. The equation of the line contains two variables x and y. And the third parameter is the slope of the line which represents the elevation of the line.

The general form of the equation of the line:-

y = mx + c

m = slope

c = y-intercept

Slope = ( y₂ - y₁ ) / ( x₂ - x₁ )

Slope= 2-1   /   2-0  =  1 /2

Now pick one of the points and put in for y and x use (2,2).

2= 1/2(2) +b

2=1 + b

2-1 =1-1 +b   subtract 1 from each side

1 = b   This is your y-intercept

The equation will be written as:-

y = ( 1 / 2) x + 1

First determine the common ratio between consecutive terms.

4.5/3 = 9/6 = 3/2

6.75/4.5 = 27/18 = 3/2

and so on. The [tex]n[/tex]-th term in the sequence is given by

[tex]a_n = 3 \cdot \left(\dfrac32\right)^{n-1}[/tex]

Solve for [tex]n[/tex] that gives the last term to find how many terms are in the sum.

[tex]n = 1 + \log_{3/2}\left(\dfrac{a_n}3\right)[/tex]

Plug in the last term.

[tex]n = 1 + \log_{3/2} \left(\dfrac{34.171875}3\right) = 1 + 6 = 7[/tex]

Then the sum of the first 7 terms of this sequence is

[tex]\displaystyle \sum_{n=1}^7 3 \cdot \left(\frac32\right)^{n-1} = 3\cdot\frac{1 - \left(\frac32\right)^7}{1-\frac32} = \boxed{\frac{6177}{44}} = 96.515625[/tex]

where we use the formula

[tex]\displaystyle \sum_{n=1}^k r^{n-1} = \frac{1-r^n}{1-r}[/tex]

x = 36° (option C)

The adjacent angles in a parallelogram are supplementary. This means the sum of the angles is equal to 180 degrees

The adjacent angles in this paralllelogram are (4x + 2)° and 34°

(4x + 2)° + 34° = 180°

4x + 2 + 34 = 180

4x + 36 = 180

4x = 180 - 36

4x = 144

Divide both sides by 4:

4x/4 = 144/4

x = 36° (option C)

Lionel should be the correct answer.

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;

Dotty and Lionel are making a graph comparing a car's age with its gas mileage.

Dotty says the graph should show discrete points because the car sage is started in whole numbers of years.

Lionel says they should make a continuous line because age increases gradually, like time.

Now,

Clearly, The Lionel is correct because when we talk about the age, that means time and Time is continuous , never stopping or slowing down for anyone.

Thus, Lionel should be the correct answer.

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The value of x is 15

Here, we want to get value of x

From the question, we have that AC = AD

This means that what we have is an isosceles triangle

Mathematically, the bases of an isosceles triangle have same angle

For triangle ACD; the measure of angle D and the measure of angle C is same

That means the value of x is 15 too

To write the equation of the line that passes through (10,80) (5,65)

we will use the formula;

x₁ = 10 y₁ = 80 x₂ = 5 y₂ = 65

substituting the above into the formula;

we will go ahead and simplify

y- 80 = 3(x - 10)

y- 80 = 3x - 30

y -3x -80 + 30 = 0

y - 3x - 50 = 0

The above is the equation of the line.

To write in a slope-intercept form simply means to write it in the form;

y = mx + b

where m is the slope and b is the intercept

Hence;

y = 3x + 50

The above is the equation of the line in a slope-intercept form

we have that

3 years=3(12)=36 months

so

$2,400+$167(36)=$8,412

and

39,087-36,000=3,087 miles

so

$0.12*(3,087)=$370.44

therefore

The total cost is

$8,412+$370.44=$8,782.44

Answer:

Equation: 2x +2x +x -8= 4(x +2)

x= 16

Step-by-step explanation:

The perimeter is the total length of the sides of a particular shape or figure.

Given that the triangle and square have an equal perimeter,

Perimeter of triangle= perimeter of square

Since a square has 4 equal sides,

2x +2x +x -8= 4(x +2)

Let's solve the above equation.

Simplify and expand:

5x -8= 4x +8

Move x terms to the left of the equation, constants to the right.

5x -4x= 8 +8

x= 16

Thus, the value of x is 16.

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Answer:

x = 16

Step-by-step explanation:

The perimeter of a two-dimensional shape is the distance all the way around the outside.

As the sides of a square are equal in length, the perimeter of a square is four times the length of one side.

[tex]\begin{aligned}\implies \textsf{Perimeter of the square}&=4(x+2)\\& = 4x+8\end{aligned}[/tex]

[tex]\begin{aligned}\implies \textsf{Perimeter of the triangle}&=2x+2x+(x-8)\\&=4x+x-8\\&=5x-8\end{aligned}[/tex]

If the perimeter of the triangle and the perimeter of the square are equal then:

[tex]\begin{aligned}\implies\textsf{Perimeter of the triangle}&=\textsf{Perimeter of the square}\\5x-8&=4x+8\\5x-8-4x&=4x+8-4x\\x-8&=8\\x-8+8&=8+8\\x&=16\end{aligned}[/tex]

Therefore, the value of x is 16.

Answer:

a) The curved surface area is;

b) The volume of the cylindrical tank is;

Explanation:

Given that the cylindrical tank has height 15m and radius 7m.

The curved surface area of a cylinder can be calculated using the formula;

substituting the given values;

Therefore, the curved surface area is;

The volume of the cylindrical tank can be calculated using the formula;

Substituting the given values;

Therefore, the volume of the cylindrical tank is;

Answer:

Each bottle cost $0.20.  That is the unit rate

Step-by-step explanation:

[tex]\frac{5.00}{25}[/tex]

In order to solve the system, we can compare both y values from each equation:

So the solution for this system is the pair (0, -4), that is, x = 0 and y = -4.

Answer:

15

Step-by-step explanation:

Speed= 230 per hour

Distance=3,647

Formula

Time=Distance upon speed

divide 230 into 3,647=15 time