Using function notation on the table, we can say that:
f(3) = -2
When f(x) = -5, x = 4
How to write function notation?Function notation is defined as a way of expressing a relationship between two variables.
From the given table, we see that:
when x = -6, f(x) = 8
when x = 7, f(x) = 3
when x = 4, f(x) = -5
when x = 3, f(x) = -2
when x = -5, f(x) = 12
Thus, we can say that:
f(3) = -2
When f(x) = -5, x = 4
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Wooden blocks in the shape of
cubes are painted with different
colors. How many square
centimeters will be painted?
4 cm
The total area of all six sides that will be painted on the wooden cube is 96 square centimeters.
First, we need to understand that each cube has six faces or sides, which are all squares of the same size. When we paint the cube, we will be painting all six sides of it. Therefore, we need to find the total area of all six sides that will be painted.
To calculate the area of each side, we need to know the length of the side. You mentioned that the wooden blocks are cubes, so each side will have the same length. Let's say the length of each side is 4 cm.
Now, we can calculate the area of one side of the cube by squaring the length of the side. In this case, the area of one side will be:
Area of one side = (length of side)²
= (4 cm)²
= 16 cm²
Since there are six sides to each cube, we can find the total area of all six sides by multiplying the area of one side by six:
Total painted area = 6 x Area of one side
= 6 x 16 cm²
= 96 cm²
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I need help with this question
A contractor can by two types of wood. she got 45 expensive wood and 60 cheap wood for the same total price. if the 45 expensive wood cost $3.00 more than the 60 cheap wood, then which equation below shows the correct relationship between the 2 types of wood that she purchased. Also (x =price of the 60 cheap wood)
A.45(x+3)=60x
B.45(x-3)=60x
C.60(x-3)=45x
D.60(x+3)=45x
The correct answer is,
C. 60(x - 3) = 45x.
This equation is based on the information that the 45 expensive wood costs $3.00 more than the 60 cheap wood. In other words, if the price of the 60 cheap wood is x, the price of the 45 expensive wood is x + 3.
Since, Algebra involves working with numbers, equations, and variables to solve real-world problems and understand abstract relationships.
Now, To solve this equation, we must use algebra and solve for x.
First, we multiply both sides of the equation by 4/5. This gives us:
48x + 36 = 45x
-36 = 3x
Finally, we divide left side of the equation by 3, giving us the final solution:
x = -12
Therefore, the price of the 60 cheap wood is $12, and the price of the 45 expensive wood is $15.
that is, 60 (x - 3) = 45x
This equation shows the correct relationship between the two types of wood that the contractor purchased.
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The same honey is sold in 2 different size jars. Large jar=540 for £4.10 small jar= 360 for £2.81 which jar is the best value for money?
The large jar has better value for money than the smaller one.
Which jar is the best value for money?To see which jar is the best value for the money, we need to take the quotient between the cost of each jar and the size. The smaller that value gets, the best value we have.
For the first jar we have:
q = £4.10/540 = 0.0075
For the second jar we have:
q' = £2.81/360 = 0.0078
Then we can see that the large jar has the best value for money.
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Suppose there are four shelves of books in a library with 12 books, 18 books, 25 books, and 30 books respectively. In how many ways can a person choose three books, one from each shelf? Explain the rule used to solve the problem.
Answer:
Step-by-step explanation:
To solve this problem, we can use the multiplication principle of counting, which states that if there are k choices for one task and m choices for a second task, then there are k x m choices for both tasks combined.
In this case, we can apply this principle to each shelf of books, as there are different numbers of books on each shelf. For the first shelf, there are 12 choices, for the second shelf there are 18 choices, for the third shelf there are 25 choices, and for the fourth shelf there are 30 choices.
To choose one book from each shelf, we need to multiply the number of choices for each shelf together, which gives us:
12 x 18 x 25 x 30 = 16,200,000
Therefore, there are 16,200,000 ways to choose three books, one from each shelf, in the library.
The total number of ways of choosing three books , one from each shelf is given by A = 162,000 ways
What are Combinations?The number of ways of selecting r objects from n unlike objects is given by combinations
ⁿCₓ = n! / ( ( n - x )! x! )
where
n = total number of objects
x = number of choosing objects from the set
Given data ,
There are 12 ways to choose a book from the first shelf, 18 ways to choose a book from the second shelf, 25 ways to choose a book from the third shelf, and 30 ways to choose a book from the fourth shelf
So , the total number of ways = 12 x 18 x 25 x 30
A = 162,000 ways
Hence , the combination is solved and there are 162,000 ways
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The function d = 45t gives the distance d in miles a car travels in t hours. Graph this function
A graph of this function d = 45t is shown in the image below.
What is a proportional relationship?In Mathematics and Geometry, a proportional relationship refers to a type of relationship that produces equivalent ratios and it can be modeled or represented by the following mathematical equation:
d = kt
Where:
d represents the distance in miles.t represents the time in hours.k is the constant of proportionality.Next, we would determine the constant of proportionality (k) by using various data points as follows:
Constant of proportionality, k = y/x
Constant of proportionality, k = 45/1 = 90/45
Constant of proportionality, k = 45.
Therefore, the required linear equation or function is given by;
d = kt
d = 45t
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Which of the following is not a money market mutual fund?(1 point)
Responses
a pension fund that tracks growth stocks
a fund with a minimum investment that tracks the value of cash
a fund that tracks the S&P 500
a fund that tracks commodities such as gold and silver
Answer:
Step-by-step explanation:
1. $4,076.92
2. Assets = Liabilities + Equity
3. They can be used to make online purchases.
4. by using an emergency fund for this unplanned expense
5. a fund with a minimum investment that tracks the value of cash (This question)
6. 1930s
7. Banks because they are highly regulated by the government, so the loan terms will not be predatory.
8. their vacation cabin
9. You should shop around for the best overall deal.
10. If you use a credit card, it is easy to run up huge debts.
11. They are tied directly to your bank account.
12. preventative care
13. $100,000 per person bodily injury, $300,000 per incident for bodily injury, $50,000 for property damage
14. how long the coverage lasts, how much the premium costs, and the cash value
15. 1-year renewable group term life
16. Identity thieves can intercept unencrypted data being sent to Wi-Fi hot spots.
17. Wells Fargo employees were opening unauthorized deposit and credit accounts for its customers.
18. 2 year in state community college degree
19. tuition assistance
20. -a sundae, -movie tickets
Explanation: All of these answers are correct!
Personal Finance Semester Exam
5/11/2023
which choice represents the fraction below as a single exponential expression?
Answer:
C
Step-by-step explanation:
Find the slope of a line perpendicular to the line whose equation is 6x + 5y = -30.
Fully simplify your answer.
Answer:
[tex]6x + 5y = - 30[/tex]
[tex]5y = - 6x - 30[/tex]
[tex]y = - \frac{6}{5} x - 6[/tex]
Since the slope of this line is -6/5, the slope of a perpendicular line is 5/6. The slopes of perpendicular lines are negative reciprocals.
Please help me I have no idea how to do it
The length QT of the given chords is determined as 14.5.
What is the length QT?The length QT is calculated by applying the following formula for intersecting chord theorem.
QS x QT = OR x TR
Substitute the given values;
10.5QT = 10(OR)
We don't know the length of the radius, so we are going to form another equation.
Since O is the center, angle QRT is a right angle, and we will apply Pythagoras theorem do determine the length QT.
Also, QS = QR
QT² = TR² + QR²
QT² = 10² + 10.5²
QT = √ (10² + 10.5²)
QT = 14.5
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The difference in length of a spring on a pogo stick from its non-compressed length when a teenager is jumping on it after θ seconds can be described by the function f of theta equals 2 times sine theta plus radical 2 period
Part A: Determine all values where the pogo stick's spring will be equal to its non-compressed length. (5 points)
Part B: If the angle was doubled, that is θ became 2θ, what are the solutions in the interval [0, 2π)? How do these compare to the original function? (5 points)
Part C: A toddler is jumping on another pogo stick whose length of its spring can be represented by the function g of theta equals 1 minus cosine squared theta plus radical 2 period At what times are the springs from the original pogo stick and the toddler's pogo stick lengths equal? (5 points)
The values of θ for different conditions were calculated with the help of trigonometric functions.
Given that;
The difference in length of a spring on a pogo stick from its non-compressed length when a teenager is jumping on it after θ seconds can be described by the function,
f (θ) = 2 sin θ + √ 2
Hence, We can simplify as;
A) Function is,
f (θ) = 2 sin θ + √ 2
f (θ) = 2 sin θ + √ 2 = 0
2 sin θ + √ 2 = 0
2 sin θ = - √ 2
sin θ = - 1/√2
θ = nπ ± π/4
Where, n = 1, 3, 5, 7, ...
So, At θ = nπ ± π/4 pogo stick's spring will be equal to its non compressed length.
2) If the angle was doubled, the function will look like this,
f (θ) = 2 sin 2θ + √ 2
f (θ) = 2 sin 2θ + √ 2 = 0
2 sin 2θ + √ 2 = 0
2 sin 2θ = - √ 2
sin 2θ = - 1/√2
θ = nπ/2 + π/8
Where, n = 1, 3, 5, 7, ...
n = 1;
θ = π/2 + π/8
θ = 5π/8
n = 2;
θ = π + π//8
θ = 9π/8
Hence, Solutions are, 5π/8, 9π/8, ...
3) g (θ) = 1 - cos²θ + √2
g (θ) = sin²θ + √2
sin²θ + √2 = 2 sinθ + √2
sin²θ - 2 sinθ= 0
sinθ (sinθ - 2) = 0
sinθ = 0
θ = nπ
Where, n = 1, 3, 5, 7, ..
So, θ = nπ , the lengths of springs from the original pogo stick and the toddler's pogo stick are equal.
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(Score for Question 2: ____ of 7 points) 2. Aisha and Jordan do some research to find out the prices and sizes of carpet tiles and rugs for the floor of the treehouse. Carpet Tiles Rugs • Each square tile has a side length of 1.5 feet. • They can only use whole tiles. • Each tile costs $5.75. • Each 3 feet by 5 feet rug costs $35.99. • Each 4 feet by 6 feet rug costs $55.99. (a) How many carpet tiles do they need to cover as much of the floor as possible? You can use the grid to help you. Each square on the grid has a side length of 1 foot. What is the area of the greatest amount of floor they can cover with carpet tiles?
Aisha and Jordan need 63 carpet tiles to cover the maximum amount of floor with the whole tiles.
To find the area of the greatest amount of floor that can be covered with carpet tiles, we need to figure out how many tiles can fit in that area. Since each tile has a side length of 1.5 feet, we can divide the grid into squares with side lengths of 1.5 feet to see how many tiles can fit.
Dividing the grid in this way, we can see that the area of each square is 2.25 square feet (1.5 ft x 1.5 ft). To find the maximum area that can be covered with whole tiles, we need to find the dimensions of the largest rectangle that can be formed using these squares.
In the grid, the longest side that can be formed using whole tiles is 9 squares long (13.5 feet), and the shortest side that can be formed using whole tiles is 7 squares long (10.5 feet). Therefore, the maximum area that can be covered with whole tiles is:
Area = Length x Width = 13.5 ft x 10.5 ft = 141.75 square feet
To find out how many tiles are needed to cover this area, we need to divide the area by the area of each tile:
Number of tiles = Area / Area of each tile = 141.75 sq ft / 2.25 sq ft per tile = 63 tiles
Therefore, Aisha and Jordan need 63 carpet tiles to cover the maximum amount of floor with the whole tiles.
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Let f(g(x)) = 3sin (pi/4(x − 1)) and g(f(x)) = pi/4(3 sin(x) − 1). Find a single formula for f and a single formula for g so that both compositions hold true.
Assume that g(x) does not equal x and f(x) does not equal x.
The single formulas for f and g so that both compositions hold true are f(x) = 3sin(x) and g(x) = π/4(x − 1)
Calculating the functions f(x) and g(x)From the question, we have the following parameters that can be used in our computation:
f(g(x)) = 3sin (pi/4(x − 1))
g(f(x)) = pi/4(3 sin(x) − 1)
Express pi as π
So, we have
f(g(x)) = 3sin (π/4(x − 1))
g(f(x)) = π/4(3 sin(x) − 1)
In f(g(x)) = 3sin (π/4(x − 1)), replace the expression in bracket with g(x)
So, we have
f(g(x)) = 3sin (g(x))
This means that
f(x) = 3sin(x) and also, it means
g(x) = π/4(x − 1)
Hence, the single formulas that both compositions hold true are f(x) = 3sin(x) and g(x) = π/4(x − 1)
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Two more then a product of 11 and a number
Step-by-step explanation:
( 11 * x ) + 2 where 'x' is a number
Graph the following features: Slope = − 2 −2 Y-intercept = 3 3
Answer: graphed and attached
Step-by-step explanation:
to graph a y intercept and slope, first find the y intercept on the graph and place your point. here the y intercept is 3, so (0, 3) because x=0 at a y intercept.
next use slope to find your next point. slope of -2 is the same as -2/1 or down -2 and right +1. so from your y intercept of 3, go down -2 and right 1 and place your point (1, 1). do this again for a 3rd point at (2, -1).
graph is attached.
solve for x ( needed quickly)
What is the product of the rational expressions below?
6-X 6+** 2-X Zt
The value of the product of the rational expressions is,
⇒ (4x - 32) (x² - 36)
We have to given that;
The rational expressions is,
⇒ 4x/(x+6) times (x-8) / (x-6)
Now, We can multiply as;
⇒ 4x/(x+6) times (x-8) / (x-6)
⇒ 4x/(x+6) × (x-8) / (x-6)
⇒ 4 (x - 8) / (x + 6) (x - 6)
⇒ (4x -32) / (x² - 6²)
⇒ (4x - 32) (x² - 36)
Thus, The value of the product of the rational expressions is,
⇒ (4x - 32) (x² - 36)
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The volume of a cylinder is 180π cubic meters. The height of the cylinder is 11.25 meters. What is the radius of the cylinder?
Answer :
Radius = 4 meters.Step-by-step explanation :
It's given that :
The volume of a cylinder is 180π cubic meters. The height of the cylinder is 11.25 meters.
Formula of volume of cylinder = πr²h
where,
r denotes radius of the cylinderh denotes height of the cylinder.By substituting the values of values of height and volume in the above formula we'll get the required value of the radius.
[tex]:\implies [/tex] 180π = πr² 11.25
[tex]:\implies [/tex] 180π = r² × 11.25 π
[tex]:\implies [/tex] 180π/11.25 π = r²
[tex]:\implies [/tex] 16 = r²
[tex]:\implies [/tex] r² = √16
[tex]:\implies [/tex] r = 4
Hence, Radius of the cylinder is 4 meters.
―――――――――――――――――――――――-5|x-8|+2=2 pls help me pls
Answer:
x = 8
Step-by-step explanation:
[tex]5|x-8|+2=2 \\ −5∣x−8∣=0 \\ ∣x−8∣=0 \\ x = 8[/tex]
First, you need to cancel out the 2 by subtracting 2 from both sides. Then, we divide both sides by -5. And finally, we remove the absolute value.
Joshua and Amahle are selling boxes of fruit for a Habitat for Humanity fundraiser. Customers can buy small
boxes of fruit and large boxes of fruit. Joshua sold 15 small boxes of fruit and 15 large boxes of fruit for a
total of $390.00. Amahle sold 20 small boxes of fruit and 25 large boxes of fruit for a total of $592.50. Find the cost of one small box of fruit and the cost of one large box of fruit.
Cost of small box: $
Cost of large box: $
The cost of one small box of fruit and the cost of one large box of fruit is $11.5 and $14.5 respectively.
What is the cost of small and large box?Let
cost of one small box of fruit = x
cost of one large box of fruit = y
15x + 15y = 390
20x + 25y = 592.50
From (1)
x + y = 26
x = 26 - y
Substitute x = 26 - y into (2)
20x + 25y = 592.50
20(26 - y) + 25y = 592.50
520 - 20y + 25y = 592.50
- 20y + 25y = 592.50 - 520
5y = 72.50
divide both sides by 5
y = 72.50/5
y = 14.5
Substitute y = 14.5 into
15x + 15y = 390
15x + 15(14.5) = 390
15x + 217.5 = 390
15x = 390 - 217.5
15x = 172.5
divide both sides by 15
x = 172.5/15
x = 11.5
Therefore, small box cost $11.5 and large box cost $14.5
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what kind of number is -15/3?
A) whole number
B) integer
C) rational
D) irrational
Answer:
Rational
Step-by-step explanation:
Improper fractions are always rational.
Need help finding the area..
The area of the region in this problem is given as follows:
A = 1 square unit.
How to obtain the area of the region?The curve represented in this problem is given as follows:
y = sin(x).
The bounds of the region are given as follows:
x = 0.x = π/2.Hence the area of the region is represented by the definite integral presented as follows:
[tex]\int_{0}^{\frac{\pi}{2}} \sin{x} dx[/tex]
The integral of the sine is the negative cosine, hence the area is:
A = -cos(x), from x = 0 to x = π/2.
Applying the Fundamental Theorem of Calculus, we have that the area is given as follows:
A = -cos(π/2) + cos(0)
A = -0 + 1
A = 1 square unit.
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Find the length of the indicated line segment of VX and SU
Questions 17-18
The length of the indicated segments are determined as:
17. VX = 6 18. SU = 15
How to Find the Length of the Indicated Line Segment?Based on the side-splitter theorem, the sides that are intercepted are divided proportionally. Using this theorem, we will find the length of the indicated segments below:
17. 8/20 = VX/15
Cross multiply:
VX * 20 = 8 * 15
VX * 20 = 120
VX = 120/20
VX = 6
18. SU/10 = 12/8
Cross multiply:
SU = 120/8
SU = 15
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Let z = 3( cos pi/2 + i sin pi/2). Find the exact value of z^7 where 0 (less than equal to) theta (less than equal to) 2pi.
From the given value of z = 3(cos pi/2 + isin pi/2), the exact value of z⁷ is -2187i.
Given z = 3(cos pi/2 + isin pi/2)
which can be represented as 3sin(pi/2) in polar form.
Now, by applying De-Moivre's theorem,
z⁷ = (3cis(pi/2))⁷
= 3⁷cis(7pi/2)
= 3⁷cis(3pi/2) [7pi/2 --- 3pi/2 ]
To write it in complex form,
z⁷ = 3⁷(cos(3pi/2) + isin(3pi/2))
z⁷ = 3⁷(0-i) [cos(3pi/2) = 0 and sin(3pi/2) = -1]
z⁷ = 3⁷(-i)
z⁷ = -2187i
From the above explanation, we can conclude that the value of z⁷ is -2187i.
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12. Select all the pairs that are equivalent.
A 5.80; 5+0.08
B (2x1)+(3x):2.3
6.050; six and five thousandths
D eight and seventy-one hundredths; (8X1) + (7 x 100) + (1 x 1,000)
E nine and nine tenths; 9.9
Results:
The equivalent pairs are:
A. 5.80; 5+0.08,
C. 6.050; six and five thousandths, and
E. nine and nine-tenths; 9.9
How do we determine the equivalent expressions?A. 5.80; 5+0.08
The two are equivalent expressions because they both represent the same decimal number. 5.80 can be interpreted as 5 units and 0.80 units, which is the same as 5 units and 0.08 units. So 5.80 is equal to 5+0.08.
C. 6.050; six and five thousandths
The two expressions describe the same decimal number. 6.050 means 6 whole units, 5 hundredths, and 0.005 thousandths, while "six and five thousandths" means the same thing - 6 whole units, 5 hundredths, and 0.005 thousandths.
E. nine and nine tenths; 9.9
They are also equivalent. Nine and nine-tenths mean 9 whole units and 9 tenths, while 9.9 means the same thing - 9 whole units and 9 tenths.
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What is the length of the unknown leg of the triangle?5 ft 8 ft
Set up an equation for x and solve to the nearest degree
In the right triangle, the value of x is approximately 64°
Trigonometry: Solving for the value of xFrom the question, we are to set up an equation for x and then solve for the value of x.
To determine the value of x, we will use SOH CAH TOA
sin (angle) = Opposite / Hypotenuse
cos (angle) = Adjacent / Hypotenuse
tan (angle) = Opposite / Adjacent
In the given diagram,
x is the included angle
Adjacent = 12
Opposite = 25
Thus,
We can write that
tan (x) = 25/12
tan (x) = 2.0833
x = tan⁻¹ (2.0833)
x = 64.3586
x ≈ 64° (to the nearest degree)
Hence,
The value of x is approximately 64°
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pls help due today, select the correct option
Answer: 2b.[tex]\frac{1}{a^{18} }[/tex]
A(t)=600e^-0.05t
Find the half life of the material to the nearest 10th of a day
The half life of the decaying material is found to be 13.9 days to the nearest 10th of a day.
Using the radioactivity formula given to find out the concertation and the half life of the material. In this case, we are given the function A(t) = 600e^(-0.05t), which represents the quantity of the material at time t.
Let A(0) be the initial amount of the material, then we have,
[tex]A(0) = 600e^{-0.05(0)} = 600[/tex]
To find the half-life, we need to solve for t when A(t) = A(0)/2:
A(t) = A(0)/2
[tex]600(e^{-0.05t}) =\frac{600}{2}[/tex]
Taking natural logarithm,
[tex]ln(e^{-0.05t}) = ln(\frac{1}{2})[/tex]
-0.05t = ln(1/2)
t = -ln(1/2)/0.05
t ≈ 13.9
Hence, the half life is found to be about 13.9 to the nearest tenth of the day.
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l want the solution
The equation of tangent line related to the parametric equations is equal to y = 3 · x - 22.
How to find the equation of a tangent line
In this question we find the case of two parametric equations evaluated at t = - 1, whose tangent line equation must be found. Equation of the tangent line is introduced below:
y = m · x + b
Where:
x - Independent variable.y - Dependent variable.m - Slopeb - Intercept.First, determine the slope of the tangent line:
dx / dt = 1 + 2 · t
dx / dt = 1 - 2
dx / dt = - 1
dy / dt = 2 · t - 1
dy / dt = - 2 - 1
dy / dt = - 3
m = (dy / dt) / (dx / dt)
m = (- 3) / (- 1)
m = 3
Second, evaluate the parametric functions at t = - 1:
x = - 1 + (- 1)² + 8
x = 8
y = (- 1)² - (- 1)
y = 2
Third, determine the intercept of the tangent line:
b = y - m · x
(m = 3, x = 8, y = 2)
b = 2 - 3 · 8
b = 2 - 24
b = - 22
Fourth, write the equation of the tangent line:
y = 3 · x - 22
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