An exercise machine with an original price of $565 is on sale at 6% off.
a. What is the discount amount?
b. What is the exercise machine's sale price?
a. The discount amount of the exercise machine is $3.39.
b. The exercise machine's sale price will be $561.61
What is a percentage?A percentage is a value or ratio that may be stated as a fraction of 100. If we need to calculate a percentage of a number, we should divide it's entirety and then multiply it by 100.
Since the exercise machine with an original price of $565 is on sale at 6% off. The discount will be:
= Discount percentage × Price
= 6% × $565
= $3.39
The exercise machine's sale price will be:
= Original price - Discount
= $565 - $3.39
= $561.61
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If 4x is one factor of 4x^2 - 12x, what is the other factor?
Answer:
(x - 3)
Step-by-step explanation:
4x² - 12x ← factor out 4x from each term
= 4x(x - 3)
the factors are 4x and (x - 3)
How many pounds of chamomile tea that cost $9 per pound must be mixed with 8 pounds of orange tea that cost $6 per pound to make a mixture that costs $7.80?
The number of pounds of chamomile tea that cost $9 per pound that must be mixed with 8 pounds of orange tea that cost $6 per pound to make a mixture that costs $7.80 from the algebraic equation is; 12 pounds
How to solve algebraic equations?Let x represent the number of pounds of Chamomile tea needed.
We are told to find the number of pounds of chamomile tea that cost $9 per pound that must be mixed with 8 pounds of orange tea that cost $6 per pound to make a mixture that costs $7.80.
Therefore,
9x + 6(8) = 7.8(8 + x)
9x + 48 = 62.4 + 7.8x
9x - 7.8x = 62.4 - 48
1.2x = 14.4
x = 14.4/1.2
x = 12
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Please help ASAPPPP!!!!!!!!!!!!! It’s due in 3 mins
The ball hits the ground after x = 6 seconds.
What is an equation?Two or more expressions with an equal sign are defined as an equation.
The given equation is h(x) = -2x² + 8x + 24.
(a) when the ball is thrown, the time is t = 0 sec.
Therefore, the height of the ball when it is thrown is,
h(0) = -2(0)² +8(0) +24
h(0) = 24
(b) The derivative of the function is,
h'(x) = -4x + 8
Substitute h'(x) = 0 into the above equation,
0 = -4x +8
4x = 8
x = 2
The second derivative of the function is,
h''(x) = -4
Since the second derivative of the function is negative, the function is maximum at x = 2.
(c) The maximum height of the ball is,
h(2) = -2(2)² + 8(2) +24
h(2) = -8 +16 +24
h(2) = 32
(d) The ball hits the ground when h(x)= 0, therefore,
0 = -2x² +8x +24
0 = -2x² +12x - 4x + 24
0 = -2x(x - 6) - 4(x - 6)
0 = (x - 6)(-2x - 4)
(x - 6) = 0 or (-2x-4) = 0
x = 6 or x = -2
Since time cannot be negative, it follows, x = 6 seconds.
Hence, the ball hits the ground after x = 6 seconds.
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How many natural numbers less than 200 are divisible by 4 but not divisible by 12.
There are 33 numbers that are less than 200 and divisible 4 but not divisible 12. this can be solved with the help of simplification.
What is simplification?
The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Main body:
Given that,
To determine how many natural numbers less than 200 are divisible by 4, but not divisible by 12.
Here,
Let the largest number divisible by 4 less than 200 is 198
The total numbers divisible by 4 and less than 200 is,
= 198 / 4 = 49
Similarly
The total number divisible by 12 and less than 200 is,
= 192/ 12 = 16
So the numbers that are less than 200 but divisible 4 not by 12 is,
= 49 - 16
= 33
Hence, there are 33 numbers that are less than 200 and divisible 4 but not divisible 12.
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Help my with this problem please 50 points
Answer:
[tex]-4x^2-4x+20[/tex]
Step-by-step explanation:
Since we're subtracting the entire quadratic, we can place the second equation in parentheses and distribute the subtraction sign.
[tex]2x^2-9x+8-(6x^2-5x-12)\\2x^2-9x+8-6x^2+5x+12\\2x^2-6x^2-9x+5x+8+12\\-4x^2-4x+20[/tex]
Answer:
[tex]-4x^2-4x+20[/tex]
Step-by-step explanation:
To find the difference of the two quadratic expressions, subtract the second expression from the first expression:
[tex]\implies (2x^2-9x+8)-(6x^2-5x-12)[/tex]
Remove the parentheses and apply the distributive law
[tex]-\left(a-b\right)=-a+b[/tex]
[tex]\implies 2x^2-9x+8-6x^2+5x+12[/tex]
Collect like terms:
[tex]\implies 2x^2-6x^2+5x-9x+8+12[/tex]
Combine like terms:
[tex]\implies -4x^2-4x+20[/tex]
Therefore, the difference of the two quadratic expressions is:
[tex]\large \boxed{-4x^2-4x+20}[/tex]
a cylindrical can that has a capacity of 20 m 3 will be made. the metal used to build the top costs $10 per square meter while the bottom costs $20 per square meter. the material used for the side costs $15 per square meter. what are the dimensions that will minimize the cost?
The dimensions that will minimize the cost is
h= 2.82876 and r = 1.06078
Given That, C₁ = $10 and C₂= $10 and C₃ = $15
lets multiply the top and bottom, we get,
C₁ × C₂ = $10 ×$ 20 = $ 30
The total cost is,
C = (2πr²) C₁ + (2πrh)C₂
Here, r is base radius and h is the side length.
The volume is given by and the volume to 20 m³
∴ V = πrh² ⇒ πr²h = 20
So, h = 20/πr²
Now, the problem can be stated as
minimum h, r C(h, r) restricted to V(h, r) = V₀
Using language multiplier it reads,
L(h ,r,λ) = C(h, r) + λ [ V(h ,r) - V₀]
Solving for h, r, λ, we get,
h = ∛(2 C₁/C₂)² V₀ /π , r = ∛ (C₂/C₁) (v₀/2π)
λ = -2 ∛2πC₁C₂² /V₀
or, h= 2.82876 , r= 1.06078 with associated cost C= 424.214
We know that is a minimum because,
(C₀ V) = 2 ( C₁πr³ + C₂V₀) /r
d²/dr² (C₀V) (r) = 4 (C₁πr³+ C₂V₀)/ r³
and for the found solution has the value
d²/dr² (C₀V) (r) = 240 π > 0
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How many solutions are there to the system of equations shown?
Answer:
There are two solutions. The parabola and the line intersect at two different points.
Answer:
Two
Step-by-step explanation:
there are two slope lines, so you need two equations for each lines.
Hey! I don’t understand this proof. Can anyone help me thank you!
Proved that the length of AB ≅ the length of CD
The conditions are given that
The line BC and the line AD are parallel lines
The parallel lines are two coplanar straight lines are at equal distance from each other and never intersect each other
Similarly
The measure of angle BAD is equal to the measure of angle DCB
If angle BAD = angle DCB, then we can say that the given shape is a parallelogram
In the parallelogram the opposite sides will be equal
Then the length of the length of AB equal to the length of CD
Hence, proved that the length of AB ≅ the length of CD
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-2(9x-1)=-(x-9) - 7x
Answer:
Step-by-step explanation: 34
Answer:
x = [tex]\frac{11}{26}[/tex]
Step-by-step explanation
Expand 2(9x - 1): 18x - 2
Expand - ( x - 9 - 7x: -8 + 9
Add 2 to both sides 18x - 2 +2 = -8x + 9 + 2
Simplify
18x = -8x + 11
Add 8x to both sides
18x + 8x = -8x + 11 + 8x
Simplify
26x = 11
Divide both sides by 26
[tex]\frac{26x}{26}[/tex] = [tex]\frac{11}{26}[/tex]
Simplify
x = [tex]\frac{11}{26}[/tex]
w+5r use s=2 and b=3
Answer:
Assuming w=2 and r=3, we plug in these values
2+5*3 = 2+15 = 17
Step-by-step explanation:
Write an equation of the line passing through the point A (8, 2) that is perpendicular to the line y = 4x - 7.
The equation of line perpendicular to line y = 4x – 7 and passing through point A (8, 2) is y + (1/4)x = 4.
What does the point slope form of a line equation look like?A line's point slope form equation is y - y₁ = m(x - x₁). Consequently, y - 0 = m(x = 0), or y = mx, is the equation of a line passing through the origin with a slope of m.How do you figure out the slope of a line that is perpendicular to another line?The slope of a line that is perpendicular to another line is equal to the negative reciprocal of that line's slope.
Given: A line is perpendicular to line y = 4x – 7 and passes through point A (8, 2).
We know that,
Slope of line perpendicular to another line is negative reciprocal of its slope.
So, m(slope) = -1/4
Equation of line is given as follows:
y - y₁ = m(x - x₁)
y - 2 = -1/4(x - 8)
y + (1/4)x = 4
Therefore, the equation of line perpendicular to line y = 4x – 7 and passing through point A (8, 2) is y + (1/4)x = 4.
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Choose the correct numbers from the
box below to complete the subtraction
sentence that follows.
The correct numbers from the box below are 5/6 - 1/3 = 1/2.
What is a fraction?A fraction is written in the form of p/q, where q ≠ 0.
Fractions are of two types they are proper fractions in which the numerator is smaller than the denominator and improper fractions where the numerator is greater than the denominator.
Given, A table with five different fractions.
Now, 5/6 - 1/3 we will check and the result must fall in the fractions given in the table.
5/6 - 1/3.
= (5 - 2)/6.
= 3/6.
= 1/2.
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Using the table, give the percentage associated with each unit of standard deviation in the standard normal curve to the nearest hundredth.
Standard Deviation Percentage Area
-2 to -1 ____________%
0 to +1 ____________ %
0 to +2 _____________%
+1 to +3 _____________%
-1 to +2 _____________%
The corresponding standard deviation percentage area for -2 to -1, 0 to +1, 0 to +2, +1 to +3 and -1 to +2 are 13.59%, 34.13%, 47.72%, 15.74% and 81.85%
How to find the percentage associated with standard deviation?To find the Standard Deviation Percentage Area, you have to consider the lower and upper points:
-2 to -1
The gap between -2 and -1 is 1 step, you will subtract -1 from -2:
-2 to -1 => 0.4772 - 0.3413 = 0.1359 = 13.59%
Note: the values for -2 and +2 are the same. The same also applies to -1 and +1 and others
0 to +1
Check the value under 1. That is 0.3413 = 34.13%
0 to +2
Check the value under 2. That is 0.4772 = 47.72%
+1 to +3
The gap between +1 and +3 is 2 steps, you will subtract 1 from 3:
+1 to +3 => 0.4987-0.3413 = 0.1574 = 15.74%
-1 to +2
-1 to +2 is the same as moving -1 to 0 and then moving from 0 to +2, you will add the values for -1 and +2:
-1 to +2 => 0.3413 + 0.4772 = 0.8185 = 81.85%
Therefore, the Standard Deviation Percentage Area for -2 to -1, 0 to +1, 0 to +2, +1 to +3 and -1 to +2 are 13.59%, 34.13%, 47.72%, 15.74% and 81.85% respectively
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what is the answer to 3 2/13 + 7/8
Answer:
the exact form is 419/104
decimal for:4.02884615...
mixed number form: 4 3/104
Step-by-step explanation:
calculator
Emma is going to invest $720 and leave it in an account for 18 years. Assuming the interest is compounded monthly, what interest rate, to the nearest hundredth of a percent, would be required in order for Emma to end up with $2,440?
The interest rate that would be required for Emma to end up with $2440 in her bank account is 6.8%
Given,
P = $720
A = $2440
t = 18 years.
r = n[(A/P)^1/nt - 1]
r = 12 × [(2440/720)¹/⁽¹²⁾¹⁸ - 1]
r = 0.06799764
Then convert r to R as a percentage.
R = r × 100
R = 0.06799764 × 100
R = 6.8%/year
Hence the rate of interest is 6.8%
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the weight of football players is normally distributed with a mean of 210 pounds and a standard deviation of 10 pounds. the probability of a player weighing less than 220 pounds is . a. 0.1587 b. .5000 c. 0.3413 d. 0.8413
what does a linear graph with a negative slope indicate? responses as the independent variable decreases, the dependent variable increases. as the independent variable decreases, the dependent variable increases. there is no relationship between the independent and dependent variables. there is no relationship between the independent and dependent variables. as the independent variable increases, so does the dependent variable. as the independent variable increases, so does the dependent variable. as the independent variable increases, the value of the dependent variable remains the same. as the independent variable increases, the value of the dependent variable remains the same.
A linear graph with a negative slope indicates that as the independent variable decreases, the dependent variable increases.The line with a negative slope is sloping down to the right.
This relationship is represented by a line sloping down to the right. A line with a negative slope indicates that there is a negative correlation between the two variables. This means that as one variable decreases, the other variable increases.
This is because the line is going down from left to right, which means that the y-value is increasing as the x-value decreases. This relationship is known as a negative correlation.It is also known as an inverse relationship. In an inverse relationship, the two variables move in opposite directions. As one variable decreases, the other variable increases.
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Write an equation of the line that passes through (4,-1) and is parallel to the line y = 3x +7
An equation of the parallel line is
Answer:
[tex]y=3x-13[/tex]
Step-by-step explanation:
Parallel lines have the same slope. So, the equation is:
[tex]y+1=3(x-4) \\ \\ y+1=3x-12 \\ \\ y=3x-13[/tex]
3(5a+4b)-3a+b I need help with this problem. I just am really confused
Answer:
12a + 13b
Step-by-step explanation:
3(5a + 4b) - 3a + b
multiply 3 by 5a and 4b
15a + 12b - 3a + b
Now add the a terms together and b terms together
15a - 3a + 12b + b
12a + 13b
Answer:
12a + 13b
Step-by-step explanation:
3(5a+4b)-3a+b
To simplify the expression, we need to distribute the 3 to all terms inside the parentheses
3*5a+3*4b-3a+b
15a+12b-3a+b
Combine like terms
12a + 13b
Help!! Question Solve. 2 1/3−1/2x=−2/3 Enter your answer in the box. x =
Answer:
x = 6
Step-by-step explanation:
2 [tex]\frac{1}{3}[/tex] - [tex]\frac{1}{2}[/tex] x = - [tex]\frac{2}{3}[/tex] ( subtract 2 [tex]\frac{1}{3}[/tex] from both sides )
- [tex]\frac{1}{2}[/tex] x = - [tex]\frac{2}{3}[/tex] - 2 [tex]\frac{1}{3}[/tex] = - 3 ( multiply both sides by - 2 to clear the fraction )
x = - 3 × - 2 = 6
x = 6
Aldo purchased a prepaid phone card for $45.75. Calls cost 7 cents a minute using this card. The credit, C (in dollars), left on the card after it is used for x
minutes of calls is given by the following function.
C(x)=45.75-0.07x
How much credit is left on the card after Aldo uses it for 20 minutes of calls?
Answer: 44.35
Step-by-step explanation:
0.07x20=1.4
45.75-1.4
a theater sells adult and child tickets to its plays. 2 adult tickets and 3 child tickets cost $30.75. 3 adult tickets and 2 child tickets cost $33.00. let represent the cost of 1 adult ticket, and represent the cost of 1 child ticket. which system of equations can be used to determine the cost of each type of ticket? a. b. c. d.
The system of equations that can be used to represent the cost of each type of ticket is 2a + 3c = 30.75 and 3a + 2c = 33 .
In the question ,
it is given that ,
a theater sells adult and child tickets for its play .
the cost for 2 adult ticket and 3 child ticket is = $30.75
and the cost for 3 adult tickets and 2 child tickets = $33.00
let the cost of 1 adult ticket = "a" and
let the cost of 1 child ticket = "c"
So, According to the question ,
the equation to represent both the situation is
2a + 3c = 30.75 and
3a + 2c = 33
Therefore , The system of equations that can be used to represent the cost of each type of ticket is 2a + 3c = 30.75 and 3a + 2c = 33 .
The given question is incomplete , the complete question is
A theater sells adult and child tickets to its plays. 2 adult tickets and 3 child tickets cost $30.75. 3 adult tickets and 2 child tickets cost $33.00. let "a' represent the cost of 1 adult ticket, and "c" represent the cost of 1 child ticket . Write a system of equations can be used to determine the cost of each type of ticket ?
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1 3/5+(-2 7/10)= what is this
Answer:
-1.1
Step-by-step explanation:
:)
PLEASE HELP FAST
A cylindrical jar has a radius of 6 inches and a height of 10inches. The jar is filled with marbles that have a volume of 20 in3. Use 3.14 for pi. Show work. Complete sentences.
a. What is the volume of the jar?
b. How many whole marbles can fit in the jar? *Each marble has the volume of 20 cubic inches
The volume of the cylindrical jar be 1130.97 in³.
Also, 56 whole marbles can fit in the jar.
Given, a cylindrical jar has a radius of 6 inches and a height of 10 inches.
The jar is filled with marbles that have a volume of 20 in³.
(a) The volume of the cylindrical jar be,
Volume = πr²h
Volume = (3.14)(6)²(10)
Volume = 1130.97 in³
(b) Now, if each marble has the volume of 20 in³
then, the number of marbles that can be fit in the jar be,
The number of marbles = 1130.97/20
The number of marbles = 56.
Hence, the volume of the cylindrical jar be 1130.97 in³.
Also, 56 whole marbles can fit in the jar.
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The value of "y" varies directly with "x" and
y = -8 when x = 20.
Find "y" if x = -4.
Now use the value you found for k, in y=kx to
solve for y when x is -4.
k=-²/
y =
Reduce to simplest form.
Answer:
y = 8/5
Step-by-step explanation:
Formula we use,
→ y = kx
Then the value of y will be,
→ y = kx
→ y = (-2/5) × (-4)
→ y = (-2 × -4)/5
→ [ y = 8/5 ]
Hence, the value of y is 8/5.
Harold solved a division problem in the following way. Check his work. Is the solution valid. Why or why not?
Harold's solution for the given division problem is not valid because it is not accurate.
We are given two numbers. The numbers are given in scientific notation. The first number is 8.4×10^(-7). The second number is 3.6×10^(-2). We need to find the result of the division of the first number by the second number. Let the result of division be denoted by the variable "Q".
Q = [8.4×10^(-7)] ÷ [3.6×10^(-2)]
Q = [(8.4/3.6)×10^(-7 - (-2))]
Q = [(8.4/3.6)×10^(-7 + 2)]
Q = 2.33×10^(-5)
Harold solved this division problem by first rounding the numbers. His result is 2×10^(-5).
Harold's result differs a lot from the actual result. So, his result is not accurate. Hence, his solution is not valid.
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examples of a unit rate
A unit rate means a rate for one of something. We write this as a ratio with a denominator of one. For example, if you ran 70 yards in 10 seconds, you ran on average 7 yards in 1 second. Both of the ratios, 70 yards in 10 seconds and 7 yards in 1 second, are rates, but the 7 yards in 1 second is a unit rate.
3. Candice eats six egg whites a day with a protein
content of 21.6 grams. Calculate her protein intake, if
he consumes 9 egg whites a day.
Protein intake, if he consumes 9 egg whites a day is 32.4 grams.
Given:
Candice eats six egg whites a day with a protein content of 21.6 grams.
6 egg white = 21.6 grams.
1 egg white = 21.6/6
= 216/10/6
= 216/10*6
= 216/60
= 3.6 grams.
9 eggs white = 9 * 3.6
= 9 * 36/10
= 324/10
= 32.4 grams.
Therefore protein intake, if he consumes 9 egg whites a day is 32.4 grams.
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The Watkins family is trying to decide which kind of in-ground pool to install. They are determining whether to put in a saltwater pool or a basic chlorine pool. The graphs below model the average annual cost of owning each type of pool after t years.
If the family plans to move to their retirement home in 10 years, which pool would be more cost effective to install? How do you know?
The chlorine pool is more cost effective because the y-value at 10 years is less on graph B than it is on graph A.
The saltwater pool is more cost effective because the y-value at 10 years is less on graph A than it is on graph B.
They would be equally cost effective because the vertical asymptotes for each graph are the same.
They would be equally cost effective because the horizontal asymptotes for each graph are the same.
Watkins family should install a chlorine pool because it is more cost effective because the y-value at 10 years is less on graph B than it is on graph A.
What is Graph?Graph is a mathematical representation of a network and it describes the relationship between lines and points.
If the family plans to move to their retirement home in 10 years, We need to find which pool would be more cost effective to install.
As in the given graph, the x-axis denotes the year while the y-axis denotes the cost of maintaining the pool in that year.
When we compare the two of the given graph we will find the cost of maintaining a chlorine pool is less as compared to a salt water pool at x=10, therefore, after 10 years.
Hence, the Watkins family should install a chlorine pool because it is more cost effective because the y-value at 10 years is less on graph B than it is on graph A.
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Answer:
a
Step-by-step explanation:edge