Answers
Related Questions
The function (x) = 0.42x + 50 represents the cost (in dollars) of a one-day truck rental when the truck is
driven x miles.
a. What is the truck rental cost when you drive 85 miles?
b. How many miles did you drive when your cost is $65.96?
Answers
a. The truck rental cost when you drive 85 miles is $85.7.
b. The number of miles driven when the cost is $65.96 is 0.42x.
a. To find the truck rental cost when driving 85 miles, we can substitute the value of x into the given function.
f(x) = 0.42x + 50
Substituting x = 85:
f(85) = 0.42(85) + 50
= 35.7 + 50
= 85.7
Therefore, the truck rental cost when driving 85 miles is $85.70.
b. To determine the number of miles driven when the cost is $65.96, we can set up an equation using the given function.
f(x) = 0.42x + 50
Substituting f(x) = 65.96:
65.96 = 0.42x + 50
Subtracting 50 from both sides:
65.96 - 50 = 0.42x
15.96 = 0.42x
To isolate x, we divide both sides by 0.42:
15.96 / 0.42 = x
38 = x
Therefore, the number of miles driven when the cost is $65.96 is 38 miles.
In summary, when driving 85 miles, the truck rental cost is $85.70, and when the cost is $65.96, the number of miles driven is 38 miles.
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Ray has tea. He has 2.671 liters of tea he pours 0.47 liters in a glass. how many liters did he pour? Solve.
Answers
On solving the given problem by help of mathematical operations, we got - After Ray poured 0.47L, he was left with 2.201L.
What does the term "mathematical operations" mean?The term "operation" in mathematics refers to the process of calculating a value using operands and a math operator. For the given operands or numbers, the math operator's symbol has predetermined rules that must be followed.
What are the five operations in mathematics?In mathematics, there are five basic operations: addition, subtraction, multiplication, division, and modular forms.
Total amount of tea Ray has - 2.671L
Amount of tea Ray poured - 0.47
Therefore,
amount he was left with was = 2.671- 0.47 = 2.201L
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The Thompson family uses up a 1/2-gallon jug of milk every 3 days. At what rate do they drink milk?
Answers
Answer:
The Thompson family uses up a 1/2
gallon jug of milk every 3 days.
rate drink milk per day
Solution =1/2÷3
= 1/6
So the answer is 1/6
Step-by-step explanation:
Hope you have a great/Amazing day.
An art teacher is making packages
Answers
a. The greatest number of packages the teacher can make using all the paintbrushes and paint is 8
b. The number of paintbrushes in each package would be 3 and the number of tubes of paints would be 5
How do we determine the number of packages?In order to determine the greatest number of packages the teacher can make using all the paintbrushes and paint, we have to determine the highest common factor of the number of brushes and the number of tubes of paint
Highest common factor is the highest factor that is common to two or more numbers:
Factors of 24 = 1,2,3,4,6,8,12 and 24
Factors of 40 = 1, 2, 4, 5, 8, 10, 20 and 40.
Common factors of 24 and 40 = 1, 2, 4, 8
Therefore, the highest common factor is 8.
The number of paintbrushes in each package:
= Number of brushes / number of package
= 24/8
= 3 brushes
The number of tubes of paint:
= number of tubes of paints / number of package
= 40 / 8
= 5 tubes of paints
Full question "An art teacher is making packages of paint brushes and paint for his. He has 24 brushes and 40 tubes of paint. Each package will have the same number An art teacher is making packages of paintbrushes and paint for his students. of brushes and the same number of tubes of paint. Part a. What is the greatest number of packages that the art teacher can make using all the paintbrushes and paint? Show your work Part b. How many paintbrushes and tubes of paint are in each package?".
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The following pattern is repeated. What is the color of square 61?
Answers
Answer: Black
Step-by-step explanation: There are 12 squares, so just think of a multiple of 12 that is close to 64.
12*5 = 60
So the same pattern can be repeated 5 times, the 60th square would be the last one, so the new pattern starts with 61, which is black.
62 and 63 would be white, so 64 is the 4th square, which is black.
If the pattern is repeated than the color of square 61 is black.
What is Sequence?Sequence is an enumerated collection of objects in which repetitions are allowed and order matters.
The given patterns has 12 square which has 4 black shades.
We have to find the color of the square which is at 61.
Let us find the number which is near to 61 and a multiple of 12.
Which is 64.
We know that 12×5 = 60
So the same pattern can be repeated 5 times, the 60th square would be the last one, so the new pattern starts with 61, which is black.
62 and 63 would be white, so 64 is the 4th square, which is black.
Hence, if the pattern is repeated than the color of square 61 is black.
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Write the inequality represented by the graph below.
Answers
Answer:
y > -x + 3
Step-by-step explanation:
find the slope and y-intercept so you can create a linear equation:
y = mx + b ; m = slope and b = y-intercept
slope (m) = (3-0) / (0-3)
m = 3/-3 or -1
we can see the y-intercept by looking at the graph, it is 3
y > -x + 3
Fill in the blank with the correct response.
What is the scale factor?
3
S
R
ARST - AMNO
5.5 T
6
N
M
X
O
Answers
The scale factor of the dilation of the triangles is 2
What is the scale factor of the dilation?From the question, we have the following parameters that can be used in our computation:
The similar triangles
The scale factor of the dilation is the division of the corresponding sides
So, we have
Scale factor = 6/3
When evaluated, we have
scale factor = 2
Hence the scale factor is 2
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onsider the function represented by the table.
The ordered pair given in the bottom row can be written using function notation as
f(9)=5.
f(5)=9.
f(5, 9)=14.
f(9, 5)=14.
Answers
Answer:
Step-by-step explandation:
d
Simplify the expression:
3(3+5g)
Answers
The value of the expression 3(3+5g) is 9 + 15g.
What is an expression?Expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both. Addition, subtraction, multiplication, and division are all possible mathematical operations.
In this case, we want to simplify 3(3 + 5g)
It's important to open the parentheses. This will be:
=3(3 + 5g)
= 9 + 15g
Therefore, the value is 9 + 15g.
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a son is a years old his father is b times older how old was his fathe when his son was born
Answers
Using a system of equations, it is found that the father was (a + b - 1) years old when the son was born.
What is a system of equations?A system of equations is when two or more variables are related, and equations are built to find the values of each variable.
In this problem, the variables are:
Variable a: The son's age.Variable x: The father's age.The son is a years old his father is b times older, hence:
\(x = ab\)
The son was born when the father was \(x - a\) years old, hence, that is, when \(a = 1, x = x - a + 1\).
Then:
\(x = ab\)
\(x - a + 1 = b\)
\(x = a + b - 1\)
The father was (a + b - 1) years old when the son was born.
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Water is exiting a giant cone shaped funnel at a rate of 15 cubic inches per second. The funnel is 75 inches high and has a maximum radius of 40 inches. What is the rate at which the water level of the funnel is changing when the water is 15 inches high? Note that the volume of a cone is V = 1/3phi^2h. O -1/3phi in/sec O -15/64phi in/sec O -12/35phi in/sec O -9/55phi in/sec O -7/36phi in/sec
Answers
The rate at which the water level of the funnel is changing when the water is 15 inches high is C: -12/35 phi in/sec.
To solve this problem, we can use related rates and the formula for the volume of a cone: V = 1/3 πr^2h.
Let's first find an expression for the radius of the cone in terms of its height. Since the maximum radius is 40 inches and the height is 75 inches, we know that the cone has similar triangles. Therefore, we can use the ratio of corresponding sides to find:
r/h = 40/75
r = (40/75)h
Now, we can substitute this expression for r into the formula for the volume of a cone:
V = 1/3 π(40/75)^2h^3
Taking the derivative of both sides with respect to time (t), we get:
dV/dt = 2π(40/75)^2h^2 dh/dt
We know that the rate of change of volume (dV/dt) is -15 cubic inches per second, since water is exiting the cone at a rate of 15 cubic inches per second. We also know that the height of the water level (h) is 15 inches. We need to find the rate at which the water level is changing, or dh/dt, when the height of the water level is 15 inches.
Plugging in the known values and solving for dh/dt, we get:
-15 = 2π(40/75)^2(15)^2 dh/dt
dh/dt = (-15) / [2π(40/75)^2(15)^2]
Simplifying this expression, we get:
dh/dt = -12/35π
Therefore, the rate at which the water level of the funnel is changing when the water is 15 inches high is approximately -12/35π inches per second.
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The flight of a cannonball toward a hill is described by the parabola y=2+0.12x- 0.0004x^2
Answers
The computation shows that the placw on the hill where the cannonball land is 3.75m.
How to illustrate the information?To find where on the hill the cannonball lands
So 0.15x = 2 + 0.12x - 0.002x²
Taking the LHS expression to the right and rearranging we have:
-0.002x² + 0.12x -.0.15x + 2 = 0.
So we have -0.002x²- 0.03x + 2 = 0
I'll multiply through by -1 so we have
0.002x² + 0.03x -2 = 0.
This is a quadratic equation with two solutions x1 = 25 and x2 = -40 since x cannot be negative x = 25.
The second solution y = 0.15 * 25 = 3.75
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Complete question:
The flight of a cannonball toward a hill is described by the parabola y = 2 + 0.12x - 0.002x 2 . the hill slopes upward along a path given by y = 0.15x. where on the hill does the cannonball land?
pls pls pls pls help me ( show your work ).
Answers
Answer:
14:250 15:2800
Step-by-step explanation:
14: 32%=80 dividing both sides by 8 we get 4% = 10. multiply both sides by 25 and we get 100%=250
15: same strategy, 2%=56 so 1%=28. multiply by 100 to get 100%=2800
James works at a clothing store where he earns a 4% commission on his total sales How much does James earn from commission on a day when he sells $2,540 worth of clothing?
A $101.60 B $635.00 C $2,438.40 D $2,641.60.
Answers
Answer:
101.60
Step-by-step explanation:
The volume of a sphere with a diameter of 6cm, rounded to the nearest tenth
Answers
V = (4/3) * π * (d/2)^3
where d is the diameter of the sphere and π is the mathematical constant pi (approximately equal to 3.14159).
Substituting the given value, we get:
V = (4/3) * π * (6 cm/2)^3
V = (4/3) * π * (3 cm)^3
V = 113.0973355 cubic centimeters
Rounding to the nearest tenth, we get:
V ≈ 113.1 cubic centimeters.
Answer:
113.1 cm³
Step-by-step explanation:
diameter = 2 X radius
Volume of sphere = (4/3) X π X r ³
= (4/3) π (3)³
= 36π
= 113.1 cm³ to nearest tenth
A company has to decide whether to invest money in the development of a microbiological product. The company's research director has that there is a 60% chance that a successful development could be achieved in 2 years. However, if the product had not been successfully developed at the end of this period, the company would abandon the project, which would lead to a loss in present-value terms of $ 3 million. (Present value is designed to take the company's time preference for money into account. The concept is explained in Chapter 8) In the event of a successful development, a decision would have to be made on the scale of production. The returns generated would depend on the level of sales which could be achieved over the period of the product's life. For simplicity, these have been catorized as either high or low. If the company opted for large-volume production and high sales were achieved, then net returns with a present-value of $6 million would be obtained. However, large-scale production followed by low sales would lead to net returns with a present value of only $1 million.In contrast, if the company decided to invest only small-scale production facilities then high sales would generate net returns with a present value if facilities then high sales would generate net returns with a present value of $4 million and low sales would generate net returns with a present value of $2 million. The company's marketing manager estimates that there is a 75% chance that high sales could be achieved.(a) Construct a decision tree to represent the company's decision problem. (b) Assuming that the companys objective is to maximize its expected returns, determine the policy that it should adopt. (c) There is some debate in the company about the probability that was estimated by the research diretor. Assuming that allo other elements if the problem remain the same, determine how low this probility would have ti be before the option of not developing the product should be chosen. (d) before the final decision us nade the company us taken iver by a bew owner, who has the utilities shown below for the sums of money involved in the decision. (The owner has no ointerest in other attributes which may be associated with the decision, such as developing a prestige product or maintaining employment.) What implications does this have for the policy that you iidentified in (b) and why?Present value of net returns New owner's utility-$3m, $0m, $1m, $2m, $4m, $6m 0, 0.6, 0.75, 0.85, 0.95, 1.0
Answers
The optimal policy for the new owner is to invest in large-scale production. This decision branch has the highest expected utility of $4.285m.
The initial node represents the decision whether to invest in the development of the microbiological product.
The two possible outcomes are a successful development or failure after 2 years.
(b) To determine the policy that the company should adopt to maximize its expected returns, we need to calculate the expected value at each decision node.
Starting from the end nodes and working backwards, we have:
For large-scale production with high sales:
Expected value = 0.75 x $6m + 0.25 x $1m = $4.25m
For large-scale production with low sales:
Expected value = 0.75 x $1m + 0.25 x $6m = $1.75m
For small-scale production with high sales:
Expected value = 0.75 x $4m + 0.25 x $2m = $3.5m
For small-scale production with low sales:
Expected value = 0.75 x $2m + 0.25 x $4m = $1.75m
At the 2-year node, the expected value for a successful development is:
For large-scale production:
Expected value = 0.75 x $4.25m + 0.25 x $1.75m = $3.5m
For small-scale production:
Expected value = 0.75 x $3.5m + 0.25 x $1.75m = $2.81m
Finally, at the initial node, the expected value for investing in the development is:
Expected value = 0.6 x $3.5m + 0.4 x (-$3m) = $0.1m
Therefore, the policy that the company should adopt to maximize its expected returns is to invest in the development of the microbiological product, choose large-scale production if the development is successful, and choose small-scale production otherwise.
(c) If the probability of a successful development is lower than a certain threshold, the option of not developing the product should be chosen. Let p be this threshold probability. Then the expected value at the initial node is:
Expected value = p x $0m + (1-p) x (-$3m) = -$3m + $3mp
Setting this equal to zero and solving for p, we get:
p = 1
Therefore, if the probability of a successful development is lower than 100%, the company should not invest in the development of the microbiological product.
(d) The new owner's utilities represent their preferences for the sums of money involved in the decision.
The utilities are increasing and concave, indicating diminishing marginal utility of money.
This means that the new owner is risk-averse.
The policy identified in (b) may not be optimal for the new owner because their utilities are different from the present-value net returns.
To determine the optimal policy for the new owner, we need to use the new owner's utility values to calculate the expected utility of each decision branch in the decision tree.
If the company invests in large-scale production and high sales are achieved, the expected utility is 0.75 * 0.95 * 1.0 * $6m = $4.285m.
If the company invests in large-scale production and low sales are achieved, the expected utility is 0.75 * 0.95 * (1 - 0.0) * $1m = $712,500.
If the company invests in small-scale production and high sales are achieved, the expected utility is 0.75 * 0.05 * 1.0 * $4m = $150,000.
If the company invests in small-scale production and low sales are achieved, the expected utility is 0.75 * 0.05 * (1 - 0.0) * $2m = $75,000.
If the company decides not to invest in the product, the expected utility is 0.25 * (1 - 0.6) * $0m + 0.25 * 0.6 * (1 - 0.0) * -$3m = -$450,000.
Therefore, the optimal policy for the new owner is to invest in large-scale production. This decision branch has the highest expected utility of $4.285m.
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What do you have to do to each side to solve 5x < 20?
Solve 5x < 20. ✏️Show your work
Answers
Answer:
x < 4
Step-by-step explanation:
Step 1: Write inequality
5x < 20
Step 2: Solve for x
Divide both sides by 5: x < 4Here we see that any number less than 4 will work. So numbers like 3, 0, or even -12587235897 would work.
HELP FAST ILL GIVE A DECENT AMOUNT OF POINTS! A cylindrical water tank with an open top has a volume of 3818m3 and a radius of 9 m. Calculate the height of the tank. Round your answer to the nearest whole number.
Answers
Answer:15m
Step-by-step explanation:
The volume of a cylinder= πr^2h
Radius=9m
Volume=3818
Height=?
3818=22/7 x 9^2 x h
26726=22 x 81 xh
26726=1782h
H = 14.9
Height= 15m
If there is something that is not clear, let me know
What is the least common multiple of 3 and7
Answers
Answer: The answer is 21
Step-by-step explanation:
Answer:
21
Step-by-step explanation:
7x3
7. Luke, Evan, Sarah, and Skylar are equally sharing three pies: blueberry, apple, and cherry. What amount of pie will each person get? O 4/3 of a pie 3/4 of a pie O a 2/3 of a pie O 1/2 of a pie
Answers
There are 3 pies: blueberry, apple, and cherry
4 people are to share the pies
To get the amount each person will get, we can represent one person share with y
To obtain y, we will have to cross multiply
so that 4 x y = 3 x 1
4y = 3
Divide both sides by 4
y = 3/4
Answer = 3/4 of a pie
Under the mapping w = z³, Find the image for 0
Answers
the image of 0 under the mapping w = z³ is also 0.
To find the image of 0 under the mapping w = z³, we substitute z = 0 into the equation:
w = (0)³
Simplifying this expression, we have:
w = 0
what is expression?
In mathematics, an expression refers to a combination of numbers, variables, and mathematical operations that are written in a specific format or notation. It can represent a mathematical calculation, a relationship, or a statement.
Expressions can be simple or complex, and they can involve various mathematical operations such as addition, subtraction, multiplication, division, exponentiation, and more. They can also include functions, constants, and variables.
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workout the surface area of this cylinder 12cm and the height 35cm
Answers
(4, -9) is it a solution yes or no ?
Answers
Answer:
Yes
Step-by-step explanation:
We cannot see the full problem
But go with no
Find the product of 6/9 and 3/8 . Express your answer in simplest form.A.6/24 B.1/6 C.18/72 D.1/4
Answers
Answer:
D.) 1/4
Step-by-step explanation:
6/9 x 3/8
6(3) /8(9)
= 18/72
18/18=1
72/18=4
= D.) 1/4
Answer:
D. 1/4
Step-by-step explanation:
First, we will multiply the numerator 6 × 3 = 18. Then, we'll multiply the denominators, 9 × 8 = 72. Then, divide 18 ÷ 18 = 1 and 72 ÷ 18 = 4. So there we go. the numerator is 1 and the denominator is 4. So the answer is 1/4 which is a proper fraction :) (mark this answer brainliest plz )
What is the probability that the spinner will land on either yellow (y) or green (g)?
A: 1/4.
B: 1/3.
C: 1/2.
D: 2/3.
Answers
Answer:
I believe it's 1/3
I haven't done these in a while, but basically since there is 6 places and it's asking the probability of it landing on 2 out of the 6, so the answer would be 2/6. Since the answer isn't there, just simpify. 2/6 simplified is 1/3. I'm so sorry if wrong, I haven't done this in a while!
How many solutions does the equation y = -2x2 - 7x + 5 have?
Answers
The number of solutions which the equation y = -2x² -7x + 5 has as required in the task content is; 2.
What is the number of solutions for the given equation?As evident in the task content; the number of solutions which the given equation has is to be determined.
Since the given equation; y = -2x² -7x + 5 is a quadratic equation.
It follows that the number of solutions which the equation has is two.
PS; Quadratic equations are polynomials with degree 2 and hence, have two solutions.
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Investment increase exponentially by about 26% every 3 years. if you start with $2,000 investment how much money would you have after 45 years
Answers
Using an exponential function, it is found that you would have an amount of $64,060 in 45 years.
What is an exponential function?An increasing exponential function is modeled by:
\(A(t) = A(0)(1 + r)^t\)
In which:
A(0) is the initial value.r is the growth rate, as a decimal.In this problem, considering the initial value of A(0) = 2000, with a growth rate of r = 0.26 each 3 years, the equation is given by:
\(A(t) = 2000(1.26)^{\frac{t}{3}}\)
In 45 years, the amount will be given by:
\(A(45) = 2000(1.26)^{\frac{45}{3}} = 64060\)
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HELP! ASAP! PLEASE!
PLEASE EXPLAIN AND TRY NOT TO GET IT WRONG. I'M AT 79 AND IF I GET 80 = PASS.
Answers
Answer:
negative
Step-by-step explanation:
a posotive times a negative is a negative
Answer:
positive
Step-by-step explanation:
Based on the number line, we can assume u is -1/2 and v is 2Plug the values of u and v in: \(-\frac{-\frac{1}{2} }{2}\) Because there are two negatives, they can cancel out to become a positive: \(\frac{\frac{1}{2} }{2}\) \(\frac{\frac{1}{2} }{2}\) = 1/2 ÷ 2 = 0.25Because 0.25 is positive, the answer is positiveI hope this helps!
which expression is equivalent to (x1/4y^16)^1/2
Answers
Answer:
y8x122
Step-by-step explanation:
Simplify this expression.
what is the volume of the solid generated when the region bounded by the graph of y=x3, the vertical line x=4, and the horizontal line y=8 is revolved about the horizontal line y=8 ?
Answers
The volume of the solid generated is 512π cubic units.
What is the volume of the generated solid?To find the volume of the solid, we can use the method of cylindrical shells. The region bounded by the graph of y = x^3, the vertical line x = 4, and the horizontal line y = 8 forms a shape that, when revolved about the line y = 8, creates a solid with a cylindrical shape. The cylindrical shells method involves calculating the volume of each cylindrical shell and summing them up to find the total volume.
Considering the given region, we can see that the minimum radius of the cylindrical shells is 8 - y, and the maximum radius is 4 - y^(1/3). The height of each shell is dx, as we are integrating with respect to x. Therefore, the volume of each shell is given by 2π(radius)(height) = 2π[(4 - y^(1/3)) - (8 - y)]dx.
To find the total volume, we integrate this expression over the range from x = 0 to x = 4. Since y = x^3, we express the integral in terms of y: ∫[0,8] 2π[(4 - y^(1/3)) - (8 - y)]dy. Evaluating this integral yields the volume of the solid as 512π cubic units.
In conclusion, the volume of the solid generated when the region bounded by the graph of y = x^3, the vertical line x = 4, and the horizontal line y = 8 is revolved about the horizontal line y = 8 is 512π cubic units.
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