2) An exam worth 145 points
contains 50 questions. Some of
the questions are worth two
points and some are worth five
points. How many two point
questions are on the test? How
many five point questions?

The 3 device trackers and wireless charger purchased at $45.22 using a 15% discount coupon gives the price of one device tracker as $12.52

Number of device trackers = 3

The discount given by the coupon = 15% off the total purchase

Amount paid after using the coupon.= $45.22

Original price of the charger = $15.64

Let x represent the price of one device tracker, we have the following equation;

(1 - 0.15)×(3•x + 15.64) = 45.23

Which gives;

x = ((45.22/(1 - 0.15)) - 15.64)/3 = 12.52

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Step-by-step explanation:

f(g(x)) simply means that g(x) is embedded in f(x) as the input value for f(x).

f(g(x)) = 3(7x + 6) - 1 = 21x + 18 - 1 = 21x + 17

c. is the right answer

g(f(x)) is the other way around. f(x) is now the input value for g(x).

g(f(x)) = 7(3x - 1) + 6 = 21x - 7 + 6 = 21x - 1

a. is the right answer

Answer:

53.13

Step-by-step explanation:

[tex]\tan \alpha=\frac{8}{6} \\ \\ \alpha=\arctan(8/6) \\ \\ \approx 53.13^{\circ}[/tex]

Answer:

53.13

Step-by-step explanation:

correct

The volume of a cuboid or box is the multiplication of length, width, and height by that expression the width of the given cuboid box is 10 inches.

Volume is the scalar quantity of any object that specified occupied space in 3D.

For example, the space in our room is referred to as volume.

The volume of cuboid = length × height × width.

Given that,

Height (H) = 9 inches.

The length is three inches more than the width.

So,

L = 3 + W

Now,

Volume of box = 1170 inches³

Now,

The volume of the cuboid is given as

V = L×W×H

1170 = (3 + W) × W×9

W² + 3W - 130 = 0

W² + 13W - 10W - 130 = 0

W(W + 13) - 10(W + 13) = 0

(W + 13)(W - 10) = 0

W = 10,-13 since the length can never be negative so 10 inches will be right.

Hence "The width of the given cuboid box is 10 inches".

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Answer:

[tex]y=-\frac{5}{3}x +\frac{8}{3}.[/tex]

Step-by-step explanation:

[tex]1. \ formula:\\ \frac{x-x_1}{x_2-x_1} =\frac{y-y_1}{y_2-y_1};[/tex]

2. according to the formula above:

[tex]\frac{x+2}{1+2} =\frac{y-6}{1-6}; \ = > \ \frac{x+2}{3} =\frac{y-6}{-5};[/tex]

3. finally, 5x+3y=8 ⇔

[tex]y=-\frac{5}{3}x +\frac{8}{3}.[/tex]

Answer: The answer for 9 is 50 miles per hour and the one who drove farthest is is ben because at 5 hours he drove already 250 miles. And for number 9 according to the table she is driving 15 miles per hour because on the bottom it always adds up by 15 miles.

Step-by-step explanation: So first to figure out 9 I used y2-y1/x2-x1 to figure out the rate of change and got 50 miles per hour and the point I used were (5,100) and (5,250). Then According to Ben's graph it shows that he drove 250 miles at 5 hours while sally was at 100 miles for 5 hours. So Ben drove the farthest. Then finally for number 9 I concluded that sally is driving 15 miles per hour because distance always adds up by 15 miles.

Hope this Helps :D

The Three solutions for the linear equation are: (0, -0.333), (1,1) and (3, 3.667).

According to the statement

We have to find that the solution of the linear equation.

So, For this purpose, we know that the

A linear equation is defined as an equation that is written in the form of Ax+By=C.

From the given information:

The three solutions for the linear equation 4x-3y = 1.

Then

The given equation is :

4x-3y = 1

Slope intercept form is

y = 4/3x - 1/3.

Then

For x = 0, we have that

y = 4/3x - 1/3.

y = 4/3(0) - 1/3.

y =  - 1/3.

y = -0.334

Then

For x = 1, we have that

y = 4/3x - 1/3.

y = 4/3(1) - 1/3.

y =  3/3.

y = 1.

Then

For x = 3, we have that

y = 4/3x - 1/3.

y = 4/3(3) - 1/3.

y =  11/3.

y = 3.67.

So, The Three solutions for the linear equation are: (0, -0.333), (1,1) and (3, 3.667).

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Answer:

Rectangular Cross Section Surface

The value of g(4) is 7 when given function is g(x)= 4x-9 .

By considering the given function

g(x)= 4x-9

g(4)=4(4)-9

g(4)=16-9

g(4)=7

A function in mathematics that goes from a set X to a set Y assigns exactly one element of Y to each element of X. The sets X and Y are referred to as the function's domain and codomain, respectively.

a mathematical expression, rule, or law that establishes the relationship between an independent variable and a dependent variable (the dependent variable). Functions are everywhere in mathematics, and they are essential for constructing physical relationships in the sciences.

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The scale factor of the graph image shown is 1.5, using the letters with prime as the original image

Scale factors are used to increase or decrease image. The situation of increment is usually called magnifying.

For the given graph the values with prime is assumed to be the the original shape while the the values without prime represent the factored image.

Taking a point of reference say s' and s. The coordinates of s' and the coordinates of s are ( 2, 4 ) ( 3, 6 ) respectively.

solving for the factor, assuming the factor is k

x axis

2k = 3

k = 3/2 = 1.5

y axis

4k = 6

k = 6/4 = 1.5

This factor works for other coordinates hence we say that the scale factor is 1.5

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Answer:

y = 3x + b

Step-by-step explanation:

slope intercept form is y = mx + b

y - y-coordinate   m - slope    b - y-intercept

Answer:

No, for a graph to be proportional it needs to go through the point (0.0)

Step-by-step explanation:

Strategy 2 will generate higher expected profit and the company should invest k 8000 for market research to determine with certainty whether demand will be strong or weak.

                                       →Strong demand (P= 0.6) k12000 outflow

                                   →|

                                       →Weak demand (P=0.4) k30000 outflow

New product launch   ║

                                       →Strong demand (P= 0.6) k80000 outflow

                                    →|

                                       →Weak demand (P=0.4) k20000 outflow

Expected market value in strategy 1 is

= - 120000 x 0.6 + (-30000) x 0.4

= -k 84000

Expected market value in strategy 2 is

= - 80000 x 0.6 + 20000) x 0.4

= k 56000

Therefore strategy 2 will generate higher expected profit

In strategy 2

Expected value in strong demand is 80000 x 0.6 = k 48000

Expected value of weak demand is 20000 x 0.4 = k 8000

Thus the company should invest k 8000 for market research to determine with certainty whether demand will be strong or weak

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The interest earned in next 90 days is  $390.6.

The amount of money earned, in compound interest, after t years, is given by:

A= P[tex]( 1+ r/n)^{(nt)}[/tex]

Given:

A = Amount

P = Principal = $28,214.35

r = rate = 0.055

n = number of periods=365

t = time in years=3/12= 1/4

Using compound interest formula

A= P[tex]( 1+ r/n)^{(nt)}[/tex]

A(90)=  28,604.95[tex]( 1 + 0.055/365)^{(365 * 1/4)}[/tex]

A(90)=28241.35 [tex](1.00015)^{(91.25)}[/tex]

A(90)=  $28,604.95

So, the interest earned in next 90 days is

=28,604.95 - 28,604.95

= $390.6

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The measures of the angles are <1 = 85, <2 = 105, <3 = 85 and <4 = 105

The diagram that completes the question is added as an attachment

From the diagram, we have

<1 + <2 = 180 degrees --- supplementary angles

Given that

<2 - <1 = 30 degrees

Add the above equations

So, we have

2<2 = 210

Divide both sides by 2

<2 = 105

Substitute <2 = 105 in <2 - <1 = 30

So, we have

105 - <1 = 30

Evaluate

<1 = 85

Also, we have

<3 = <1

<4 = <2

This means that

<3 = 85

<4 = 105

Hence, the measures of the angles are <1 = 85, <2 = 105, <3 = 85 and <4 = 105

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The net pay of the individual after having deducted total deductions is $166.54

How do we determine the amount of each deduction?

The amount of each deduction is based on the gross pay of $351.00, as a result, we simply multiply the percentage of deduction by the gross pay to determine the dollar amount of each deduction.

the gross pay=$351

federal tax (assuming 20% of gross earnings)=$351*20%=$70.20

state tax (assuming 6% of gross earnings)=$351*6%=$21.06

social security deductions (assuming 7.05% of gross earnings)=$351*7.05%=$24.75

group health insurance (assuming 13% of gross earnings)=$351*13%=$45.63

pension deduction (assuming 6.5% of gross earnings)=$351*6.5%=$22.82

total deductions=$70.20+$21.06+$24.75+$45.63+$22.82

total deductions=$184.46

net pay=$351-$184.46

net pay=$166.54

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Two or more expressions with an equal sign is Equation.-76(x-61)=x-89 is the equation for −76 times the difference between a number and 61 is equal to the number plus −89.

Two or more expressions with an equal sign is called as Equation.

The sentence −76 times the difference between a number and 61 is equal to the number plus −89. We have to express in the form of equation.

−76 times the difference between a number

Let the number be 'x', times means multiplication and difference is subtraction.

-76(x-61)

the number plus −89

x+(-89)

−76 times the difference between a number and 61 is equal to the number plus −89.

-76(x-61)=x+(-89)

-76(x-61)=x-89

Therefore -76(x-61)=x-89 is the required equation.

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Answer:

11.58 years

6.82 years

Step-by-step explanation:

Compound interest can be represented as: [tex]A=P(1+\frac{r}{n})^{nt}[/tex] where P = initial amount, r=interest rate, n=compounds in each time unit, t = time (usually years)

If you think about it the: [tex](1+\frac{r}{n}})^{nt}[/tex] represents the overall interest being applied to the principal amount.

This would have to be equal to 2, for it to be doubled, so let's set that equal to 2

[tex]2=(1+\frac{r}{n})^{nt}[/tex]

Now let's solve for "t", first let's take the log of both sides

[tex]log(2)=log([1+\frac{r}{n}]^{nt})[/tex]

Now let's use log properties, specifically the exponent one to rewrite

[tex]log(2)=nt *log(1+\frac{r}{n})[/tex]

Now divide both sides by the log(1 + r/n) and n

[tex]t=\frac{log(2)}{n*log(1+\frac{r}{n})}[/tex]

Our "n" is going to be the same for both equations, 12 since it's compounded monthly

The interest will be a bit different, but in the first case it will be 6% which is 0.06

[tex]t=\frac{log(2)}{12*log(1+\frac{0.06}{12})}[/tex]

simplifying this we get

[tex]t\approx11.581[/tex]

Rounding this we get: [tex]t=11.58[/tex]

Now let's do this to the other equation:

[tex]t=\frac{log(2)}{12*log(1+\frac{0.102}{12})}[/tex]

simplifying this we get:

[tex]t\approx 6.824[/tex]

approximately 6.82

Answer:

12, 24, 36, 48, 60, 72, 84, 96

Step-by-step explanation:

The smallest natural number that is a common multiple of 3 and 4 is 12. The answer is all multiples of 12 less than 100.

Answer: 12, 24, 36, 48, 60, 72, 84, 96

The Coordinates of the point D will be (-3, 3) and point E will be (0, 5) and point F will be (2, -2).

According to the statement

We have to find that the points of the coordinates.

So, For this purpose, we know that the

Coordinates are a set of values which helps to show the exact position of a point in the coordinate plane.

From the given information:

the coordinates of D, E, and F after a reflection over the y axis? Plot these points on the grid, and label them D′, E′ and F′.

Then

Coordinates of a point is given by (x,y)

And

Here, x represents the horizontal distance of the point from origin (0,0) and y represents the vertical distance of the point from origin.

Let's take an example of point D,

Horizontal distance of point D from origin x =-3 and vertical distance from origin y =3.

Then

Coordinates of the point D will be (-3, 3).

Coordinates of the point F will be (2, -2).

Coordinates of the point E will be (0, 5).

For more details please see the image below.

So, The Coordinates of the point D will be (-3, 3) and point E will be (0, 5) and point F will be (2, -2).

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Answer:

Step-by-step explanation:

beep boop beep bap bap slat twan
answer it yo self

The charges which sum up to 0 are +7 charge and −7 charge.

An integer is the number zero, a positive natural number or a negative integer with a minus sign. The negative numbers are the additive inverses of the corresponding positive numbers.

Given:

two charges have a sum of 0

So, taking one by one the pairs of option are

+7 charge and +7 charge

=+ 14 charge

−7 charge and −7 charge

=-14 charge

−7 charge d +7 charge

=0 charge

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The expression y3¹⁰ - 10y³ is a binomial polynomial.

In the given situation y3¹⁰ - 10y³ is a binomial polynomial as there are two terms in the expression.

Therefore, the expression y3¹⁰ - 10y³ is a binomial polynomial.

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According to this formula, the time when the world population reach 8 billion is D. 2026.

From the information given, the capita growth rate of the world population continues to be what it was in the year 2016, the world population t years after July 1, 2016, will be 7.4 ✕ 1.011t billion.

Therefore, the year when the world population reach 8 billion will be:

80 billion = 7.4 × 1.011t billion

1.011t = 80/7.4

1.011t = 10.8

t = 10.8/1.011

t = 10

Therefore, the number of years will be added. This will be:

= 2016 + 10

= 2026

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Step-by-step explanation:

0.25(x+10) = 2+0.5(x-1)

0.25 * x + 0.25 * 10 = 2.05 * x - 2.05 * 1

0.25x + 2.5 = 2.05x - 2.05

0.25x - 2.05x = -2.05 - 2.5

-1.8x = - 4.55

x = -4.55/-1.8

x = 2.53777777778

Answer:

11.  17.7 units

12.  24.7 units

Step-by-step explanation:

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

To find the perimeter of a polygon, sum the lengths of its sides.

Use the distance formula to find the length of each side.

[tex]\boxed{\begin{minipage}{4.7 cm}\underline{Distance Formula}\\\\$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$\\\\where $(x_1,y_1)$ and $(x_2,y_2)$ are the two endpoints.\end{minipage}}[/tex]

Given points:

Use the distance formula to find the length of each side of ABC:

[tex]\begin{aligned}AB & = \sqrt{(x_B-x_A)^2+(y_B-y_A)^2}\\& = \sqrt{(2-(-2))^2+(5-1)^2}\\& = \sqrt{4^2+4^2}\\& = \sqrt{16+16}\\& = \sqrt{32}\end{aligned}[/tex]

[tex]\begin{aligned}BC & = \sqrt{(x_C-x_B)^2+(y_C-y_B)^2}\\& = \sqrt{(5-2)^2+(1-5)^2}\\& = \sqrt{3^2+(-4)^2}\\& = \sqrt{9+16}\\& = \sqrt{25}\\& = 5\end{aligned}[/tex]

[tex]\begin{aligned}AC & = \sqrt{(x_C-x_A)^2+(y_C-y_A)^2}\\& = \sqrt{(5-(-2))^2+(1-1)^2}\\ & = \sqrt{7^2+0^2}\\ & = \sqrt{49}\\ & = 7\end{aligned}[/tex]

To find the perimeter, sum the sides:

[tex]\begin{aligned}\sf Perimeter & = AB+BC+AC\\& = \sqrt{32}+5+7\\& = 4\sqrt{2}+12\\& = 17.7\;\sf units\;(nearest\:tenth)\end{aligned}[/tex]

Given points:

After plotting the given points, it is clear that the polygon is a parallelogram. As the opposite sides of a parallelogram are equal in length:

Therefore, we only need to find the length of two sides to calculate the perimeter.

Use the distance formula to find AB and BC:

[tex]\begin{aligned}AB & = \sqrt{(1-(-3))^2+(6-5)^2}\\& = \sqrt{4^2+1^2}\\& = \sqrt{16+1}\\& = \sqrt{17}\end{aligned}[/tex]

[tex]\begin{aligned}BC & = \sqrt{(3-1)^2+(-2-6)^2}\\& = \sqrt{2^2+(-8)^2}\\& = \sqrt{4+64}\\& = \sqrt{68}\end{aligned}[/tex]

Therefore, the perimeter of ABCD is:

[tex]\begin{aligned}\sf Perimeter & = 2(AB+BC)\\& = 2(\sqrt{17}+\sqrt{68})\\& = 6\sqrt{17}\\& =24.7\;\sf units\;(nearest\:tenth)\end{aligned}[/tex]

Answer:

x= 8

Step-by-step explanation:

Sum of the two angles = 90

12x - 30 + 3x = 90

15x -30 = 90

15x = 90 + 30

15x = 120

x = 120/15 = 8

Answer: 1/6

Step-by-step explanation:

The relation can be written as a set of ordered pairs as: a. {(–3, 3), (0, 0), (2, –2)}.

A relation, in maths, is defined as a relationship between two variables, x and y, which are linked to each other.

The x-value and the y-value of each set of points in a relation is written as (x, y).

Thus, in the given relation that is represented by the graph below, we have the following set of ordered pairs representing each point on the graph: (–3, 3), (0, 0), and (2, –2).

Therefore, the relation can be written as a set of ordered pairs as: a. {(–3, 3), (0, 0), (2, –2)}.

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