Answer:31
Step-by-step explanation: Since you are trying to find a percentage of a number all you have to do is multiply 242 by 12.9% and because you have to round to the nearest tenth it will be 31
Felipe rented a truck for one day. There was a base fee of $17.95, and there was an additional charge of 86 cents for each mile driven. Felipe had to pay $270.79 when he returned the truck. For how many miles did he drive the truck?
Answer:
421.4 miles
Step-by-step explanation:
Numner of miles= ($270.79-$17.95)/86 cents
= $252.84/$0.60
=421.4 miles
Simplifying assumptions identified for the use of cost behavior pattern data include:a) linearity and relevant range.b) fixed range and variability.c) fixed activity and linearity.d) relevant range and liquidity.
linearity and relevant range include the use of cost behavior pattern data.
what is linearity?the existence of a chain of thoughts or actions wherein one directly follows another: True autobiographies rarely have a linear structure. We don't have a linear existence. Constantly thrown off balance is the narrative's traditional linearity.
what is relevant range?The accounting phrase "relevant range" refers to the production or activity parameters that a company must adhere to in order to keep its fixed costs constant. Fixed costs in accounting are constant and unaffected by particular production rates.
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John shared 3 cookies with 4 friends. What fraction of a cookie did each friend recieve?
Answer:
0.75 .................
1. Use the Pythagorean theorem to find AD.
HELP FAST
Answer:
9
Step-by-step explanation:
3-4-5 is a famous Pythagorean triple
12 = 4 x 3
15 = 5 x 3
9 = 3 x 3
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Please help me I am so bad at math
(f ◦ g)(x) is the composition of f(x) with g(x), equivalently
(f ◦ g)(x) = f(g(x))
To get f(g(x)), replace every instance of x in the definition of f(x) with g(x):
f(x) = -x + 7 ⇒ f(g(x)) = f(√(x - 3)) = -√(x - 3) + 7
Jill was shopping for cars. She noticed the price of a mercedes c class is 8,000 higher than a year ago. If it cost 32,500 last year, what is the % increase in the price of the car?
If Jill was shopping for cars. She noticed the price of a mercedes c class is 8,000 higher than a year ago. If it cost 32,500 last year, Then 24.6 is the % increase in the price of the car
What is Percentage?Percentage, a relative value indicating hundredth parts of any quantity.
Given,
In last year the cost of the car is thirty two thousand five hundred. 32500
The price of a mercedes c class is 8,000 higher than a year ago
We need to find the percentage of increase in the price of the car.
32500×x=8000
Divide both sides by 32500
x=8000/32500
x=0.246
As we know percent is hundredths part of a quantity.
So multiply x value with hundred
0.246×100
24.6%
Hence 24.6 is the % increase in the price of the car.
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2. (7 points) If f(x) = -5 cosx+xtanx, find df and evaluate if x = pi/4 and dx = 1/24
The value of df, when x = π/4 and dx = 1/24, is (-5π - 5√2)/(96√2).
To find the derivative of the function f(x) = -5cos(x) + xtan(x), we'll use the sum and product rules of differentiation. Let's start by finding df/dx.
Apply the product rule:
Let u(x) = -5cos(x) and v(x) = xtan(x).
Then, the product rule states that (uv)' = u'v + uv'.
Derivative of u(x):
u'(x) = d/dx[-5cos(x)] = -5 * d/dx[cos(x)] = 5sin(x) [Using the chain rule]
Derivative of v(x):
v'(x) = d/dx[xtan(x)] = x * d/dx[tan(x)] + tan(x) * d/dx[x] [Using the product rule]
= x * sec^2(x) + tan(x) [Using the derivative of tan(x) = sec^2(x)]
Applying the product rule:
(uv)' = (5sin(x))(xtan(x)) + (-5cos(x))(x * sec^2(x) + tan(x))
= 5xsin(x)tan(x) - 5xcos(x)sec^2(x) - 5cos(x)tan(x)
Simplify the expression:
df/dx = 5xsin(x)tan(x) - 5xcos(x)sec^2(x) - 5cos(x)tan(x)
Now, we need to evaluate df/dx at x = π/4 and dx = 1/24.
Substitute x = π/4 into the derivative expression:
df/dx = 5(π/4)sin(π/4)tan(π/4) - 5(π/4)cos(π/4)sec^2(π/4) - 5cos(π/4)tan(π/4)
Simplify the trigonometric values:
sin(π/4) = cos(π/4) = 1/√2
tan(π/4) = 1
sec(π/4) = √2
Substituting these values:
df/dx = 5(π/4)(1/√2)(1)(1) - 5(π/4)(1/√2)(√2)^2 - 5(1/√2)(1)
Simplifying further:
df/dx = 5(π/4)(1/√2) - 5(π/4)(1/√2)(2) - 5(1/√2)
= (5π/4√2) - (10π/4√2) - (5/√2)
= (5π - 10π - 5√2)/(4√2)
= (-5π - 5√2)/(4√2)
= (-5π - 5√2)/(4√2)
Now, to evaluate df/dx when dx = 1/24, we'll multiply the derivative by the given value:
df = (-5π - 5√2)/(4√2) * (1/24)
= (-5π - 5√2)/(96√2)
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Gina puts $5500 into an account earning 5.25% interest compounded continuously how long will it take for the amount in the account to go to $7450
Using the formula of compound interest, the number of years is 7.6 years
What is compound interest?Compound interest is the interest calculated on the principal and the interest accumulated over the previous period. It is different from simple interest, where interest is not added to the principal while calculating the interest during the next period.
The formula of compound interest is given as;
\(A = P(1 + \frac{r}{n} )^n^t\)
A = Compounded InterestP = Principalr = raten = number of times compoundedt = number of years.But in this case, the interest was compounded continuously
\(A = Pe^r^t\)
Substituting the values into the formula;
\(7450 = 5500e^(^0^.^0^5^2^5 ^* ^t^)\)
Solving for t;
t = 7.6 years
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9. A has some amount of money with him. He gave one half of one third from that amount One half of the amount received by B is 20. What is the amount that A originally had?
Using the expression 5x/12 = 20, the amount that A originally had was $48.
We have,
Let x be the amount of money that A originally had.
Then, A gave away 1/2 x 1/3 = 1/6 of the amount, which is equal to x/6.
The amount received by B is 1/2 of the remaining amount,
which is (x - x/6)/2 = 5x/12.
We know that 5x/12 = 20,
Solving for x.
5x/12 = 20
5x = 240
x = 48
Therefore,
The amount that A originally had was $48.
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A test to determine whether a certain antibody is present is 99.3% effective. This means that the test will accurately come back negative if the antibody is not present (in the test subject) 99.3% of the time. The probability of a test coming back positive when the antibody is not present (a false positive) is 0.007 . Suppose the test is given to six randomly selected people who do not have the antibody.
(a) What is the probability that the test comes back negative for all six people?
(b) What is the probability that the test comes back positive for at least one of the six people?
a) The probability that the test comes back negative for all six people is 95.8%,
b) The probability that the test comes back positive for at least one of the six people is 4.2%.
(a) To find the probability that the test comes back negative for all six people, we can use the fact that the test is 99.3% effective in accurately detecting the absence of the antibody.
Since the test is 99.3% effective, the probability of it coming back negative for each individual who does not have the antibody is 0.993. Therefore, the probability that the test comes back negative for all six people is calculated as follows:
P(negative for all 6) = (0.993)^6 ≈ 0.958
Therefore, the probability that the test comes back negative for all six people is approximately 0.958, or 95.8%.
(b) To find the probability that the test comes back positive for at least one of the six people, we need to consider the probability of a false positive.
The probability of a false positive, which is the probability of the test coming back positive when the antibody is not present, is given as 0.007. Therefore, the probability of the test correctly identifying the absence of the antibody is 1 - 0.007 = 0.993.
The probability that the test comes back positive for at least one person is the complement of the probability that the test comes back negative for all six people. So we can calculate it as follows:
P(positive for at least one person) = 1 - P(negative for all 6) ≈ 1 - 0.958 = 0.042
Therefore, the probability that the test comes back positive for at least one of the six people is approximately 0.042, or 4.2%.
In summary, the probability that the test comes back negative for all six people is approximately 95.8%, while the probability that the test comes back positive for at least one of the six people is approximately 4.2%.
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3. What is the value of x
Answer:
10
Step-by-step explanation:
using HYPOTHENUS theorem
8^2 + 6^2 = x^2
64 + 36= 100
√100=10
Answer:
10
Step-by-step explanation:
pythagros theorem
8 time 8 is 64
and
6 time 6 is 36
add them up we have
100
square root of 100 is 10
so the answer is 10
ur. welcome
A square pyramid has a base edge of 1 meter. The height of each triangular face is 1 meter. What is the pyramid's surface area?
Answer:
A square pyramid has 5 faces: 1 square base and 4 triangular faces.
The area of the base is:
A = s^2
where s is the length of the base edge.
In this case, s = 1 m, so:
A = 1^2 = 1 m^2
The area of each triangular face is:
A = 1/2 * b * h
where b is the base of the triangle (which is equal to the length of one side of the square base) and h is the height of the triangle (which is given as 1 m).
In this case, b = 1 m and h = 1 m, so:
A = 1/2 * 1 * 1 = 0.5 m^2
The total surface area of the pyramid is the sum of the area of the base and the area of the four triangular faces:
SA = A_base + 4 * A_triangles
SA = 1 + 4(0.5)
SA = 1 + 2
SA = 3 m^2
Therefore, the surface area of the pyramid is 3 square meters.
Pyramids height us 16in and the base is 4 ft and the width is 4 ft what is the volume
After answering the given query, we can state that The pyramid's pyramid capacity is 8.89 cubic feet as a result.
what is pyramid?A pyramid is a shape in mathematics, formed by connecting locations referred to as bases and polygonal edges. For each hace and vertex, a triangular called a face is formed. a cone with a hexagonal form. A pyramid with a base and n pyramids has 2n edges, n+1 vertices, and n+1 vertices. Each pyramid is dual in itself. Pyramids can be seen in three dimensions. The apex, the intersection of a pyramid's smooth tri face and polygonal base, is where they come together. The base and apex are connected to form a pyramid. Triangle faces that link to the top are formed by the corners of the base.
We apply the following method to determine a pyramid's volume:
Volume equals (1/3) of base surface times height.
Given that the basic area in this instance is a rectangle with four-foot sides, its area is:
16 square feet (4 feet x 4 feet)
The height of the pyramid is listed as 16 inches, but in order to apply the algorithm, we must change this measurement to feet. Twelve centimeters make up one foot, so
1 foot is equal to 16 inches divided by 12 inches. (rounded to two decimal places)
The numbers can now be entered into the algorithm to obtain:
Volume is equal to 16 x 1.33 x (1/3) cubic feet.
equals 8.89 cubic feet of volume
The pyramid's capacity is 8.89 cubic feet as a result.
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Use the image to determine the direction and angle of rotation.
graph of triangle ABC in quadrant 4 and a second polygon A prime B prime C prime in quadrant 2
90° clockwise rotation
90° counterclockwise rotation
180° clockwise rotation
270° counterclockwise rotation
The angle of rotation for the described transformation is
180° clockwise rotationHow to know the angle of rotationThe movement or transformation described is form quadrant 4 to quadrant 2.
The transformation will require 180 degrees transformation.
In this type of transformation, both clockwise and the counter clockwise have similar effects
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A certain strain of bacteria is growing at a rate of 44% per hour, and with 2,000 bacteria initially, this event can be modeled by the equation B(t) = 2,000(1.44)t. With this fast growth rate, scientists want to know what the equivalent growth rate is per minute. Using rational exponents, what is an equivalent expression for this bacterial growth, expressed as a growth rate per minute?
The given equation for the growth rate per hour is:
\(B(t)=2,000(1.44)^t\)Where t is the time in hours.
The equivalent growth rate per minute would be the equivalent in minutes for hours, then:
\(1\min \cdot\frac{t\text{ hours}}{60\min }=\frac{t}{60}\)Where t is the time in minutes, then the answer is:
\(B(t)=2,000(1.44)^{\frac{t}{60}}\)Scale factor: 2:1
10 in
5 in
13 in
Scale drawing
Object
A. Side a is 26 inches long, side bis 20 inches long, and side cis 10
inches long
B. Side a is 15 inches long, side bis 12 inches long, and side cis 7
inches long
C. Side a is 11 inches long, side bis 8 inches long, and side cis 3
inches long
D. Side ais 2.5 inches long, side bis 5 inches long, and side cis 6.5
inches long
Answer: A. Side a is 26 inches long, side b is 20 inches long, and side c is 10.
Step-by-step explanation:
Scale factor for drawing = 2:1
Dimensions of drawing : 10 in, 5 in, 13 in
Dimension of object = Scale factor x Dimension of drawing
Sides of object:
2 x 10 in =20 in [b]
2 x 5 in = 10 in [c]
2 x 13 in = 26 in. [a]
Hence, the correct option is
A. Side a is 26 inches long, side b is 20 inches long, and side c is 10.
Answer:
Side a is 2.5 inches long, side b is 5 inches long and side c is 6.5 inches long.
Step-by-step explanation:
Solve the inequalities 2(x-9)>-2
Answer:
x>8
Step-by-step explanation:
2(x-9)>-2
(x-9)>-2/2 = (x-9)>-1
x>-1+9 = x>8
f(x) = (x + 2)2 and g(x) = x2 − (x + 2)2. Find f(x) − g(x).
The solution of the function f(x) − g(x) is x² + 8x + 8.
How to solve function?A function relates input and output values. In a simpler term, a function relates an independent variable and a dependent variable.
Let's solve the functions as follows;
f(x) = (x + 2)²
g(x) = x² − (x + 2)²
Let's find f(x) − g(x)
f(x) = (x + 2)² = (x + 2)(x + 2) = x² + 2x + 2x + 4 = x² + 4x + 4
g(x) = x² − (x + 2)² = x² - ( x² + 4x + 4) = x² - x² - 4x - 4 = -4x - 4
Hence,
f(x) − g(x) = x² + 4x + 4 - (-4x - 4)
f(x) − g(x) = x² + 4x + 4 + 4x + 4
f(x) − g(x) = x² + 8x + 8
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7,165.482 rounded nearest hundredth
7,165.48 is the answer
I hope this helps
The water usage at a car wash is modeled by the equation W(x) = 5x3 + 9x2 − 14x + 9, where W is the amount of water in cubic feet and x is the number of hours the car wash is open. The owners of the car wash want to cut back their water usage during a drought and decide to close the car wash early two days a week. The amount of decrease in water used is modeled by D(x) = x3 + 2x2 + 15, where D is the amount of water in cubic feet and x is time in hours. Write a function, C(x), to model the water used by the car wash on a shorter day. C(x) = 5x3 + 7x2 − 14x − 6 C(x) = 4x3 + 7x2 − 14x + 6 C(x) = 4x3 + 7x2 − 14x − 6 C(x) = 5x3 + 7x2 − 14x + 6
Joe, Kent, Bryan and Julie scored an average of 63 mark in Mathematics test. If we know that Julie's score qas 25% of Joe's score. Bryan scored 10 more marks thsn Joe and Kent scored 18 fewer marks than Joe. What is the total score of kent and bryan?
Perform the following metric-metric conversion.
1.68 g/L_____ g/mL
Answer: 1680ml
Step-by-step explanation:
1000 mL are in 1 L, so with that logic
1=1000
.68=680
1000+680=1680
2³(3÷4+x)+12=2 iuybki[ojiouhnkluibkjb
Answer:
what?
Step-by-step explanation:
hansnskekkwkwnw
Answer:
X=-2
Step-by-step explanation:
1. Open up the brackets
You then get
6+8x+12=2
2. Send the whole numbers to the other sides
8x= 2-6-12
8x = - 16
3. Divide both sides by 8 to leave x alone
X=-2
Find the measure of angle A
Pls help
Step-by-step explanation:
x+85+x+44+63=180(sum of angles of a triangle)
or,2x+192=180
or,2x=180-192
or,x=-12
Angle A=x+44
=-12+44
=32°
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How do I Write this ratio in simplest form?
10 inches to 1 yard
Answer:
10 over 1
Step-by-step explanation:
Answer:
10 to 1
Step-by-step explanation:
its common sense
Which expression shows the result of applying the distributive property to 3 (1/5x - 1/7)
A. -3/5x + 3/7
B. 3/5x - 3/7
C. -3/5x - 3/7
D. 3/5x + 3/7
Hi,
3(1/5x - 1/7)
= 3/5x - 3/7
B
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PLEASE HELP AS SOON AS POSSIBLE
A) The Slope is: 2
B) The interpretation of the slope is that there are two races for each number of track meet.
C) The y-intercept from the graph is at: y = 4
D) Equation of the line is: y = 2x + 4
How to find the slope of the linear graph?The general form of equation of a line in slope intercept form is:
y = mx + c
where:
m is slope
c is y-intercept
From the given graph, we can see that the slope is gotten from the formula:
A) Slope = (y₂ - y₁)/(x₂ - x₁)
Thus:
Slope = (10 - 4)/(3 - 0)
Slope = 6/3
Slope = 2
B) The interpretation of the slope is that there are two races for each number of track meet.
C) The y-intercept from the graph is at: y = 4
D) Equation of the line is:
y = 2x + 4
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If G&M Foods issues a $1,000 bond with an interest rate of 3.5 percent and a maturity date of January 1, 2025, G&M is agreeing to pay the bondholder __________ interest each year until January 1, 2025, when it must repay the full $1,000.
G&M is agreeing to pay the bondholder the interest amount of $35 each year until January 1, 2025.
Using this formula
Interest=Bond amount× Interest rate
Where:
Bond amount=$1,000
Interest rate=3.5% or 0.035
Let plug in the formula
Interest=$1,000×0.035
Interest=$35 each year
Inconclusion G&M is agreeing to pay the bondholder the interest amount of $35 each year until January 1, 2025.
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Find the values of x, y, and z
Brooklyn is going to invest in an account paying an interest rate of 3.5% compounded continuously. How much would Brooklyn need to invest, to the nearest ten dollars, for the value of the account to reach $64o in 9 years?
Brooklyn needs to invest $432.43, rounded to the nearest ten dollars.
To determine how much Brooklyn needs to invest in an account that pays a continuously compounded interest rate, we can use the formula:
A = \(Pe^(^r^t^)\)
where A is the future value of the account, P is the principal investment, e is the mathematical constant approximately equal to 2.71828, r is the interest rate, and t is the time in years.
In this case, we want the future value of the account to be $640, the interest rate is 3.5% (or 0.035 as a decimal), and the time is 9 years. We can substitute these values into the formula and solve for P:
640 = \(Pe^(^0^.^0^3^5^*^9^)\)
640 = Pe^0.315
P =\(640/e^0^.^3^1^5\)
P = 432.43
Therefore, to have a future value of $640 in 9 years with a continuously compounded interest rate of 3.5%.
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