it took Jill two hours to drive 100 miles. what was her average speed?
Evaluate the integral (e^x)/((e^2x)+3) from 0 to infinity
which of the following is equivalent to 14x2+35x when it is completely factored?
A. 7x(2x+5)
B. 7(2x2+5x)
C. 14x(x+3)
D. x(14x+35)
The equivalent factored form is A. 7x(2x + 5).
How to determine the equivalent to 14x2+35x when it is completely factoredTo factorize the expression 14x^2 + 35x completely, we look for the greatest common factor (GCF) of the terms and apply the distributive property.
In this case, the GCF of 14x^2 and 35x is 7x.
So, we can factor out 7x from the expression:
14x^2 + 35x = 7x(2x + 5)
Therefore, the equivalent factored form is A. 7x(2x + 5).
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How many fifths are the in 60/100
A cylinder has a volume of 320 pi cu. in. and a height of 5". Find the radius of the cylinder. ...?
Answer:
radius of the cylinder is, 8 inches
Step-by-step explanation:
Volume of cylinder(V) is given by:
[tex]V = \pi r^2h[/tex] .....[1]
where,
r is the radius of the cylinder and
h is the height of the cylinder.
As per the statement:
A cylinder has a volume of 320 pi cu. in. and a height of 5"
⇒[tex]V = 320 \pi[/tex] cubic inches and h = 5 inches
Substitute these values in [1] we have
[tex]320 \pi = \pi r^2 \cdot 5[/tex]
Simplify:
[tex]320 = r^2 \cdot 5[/tex]
Divide both sides by 5 we have;
[tex]64=r^2[/tex]
or
[tex]r^2 = 64[/tex]
⇒[tex]r = \sqrt{64} = 8 in[/tex]
Therefore, the radius of the cylinder is, 8 inches
Final answer:
To find the radius of the cylinder, use the formula for the volume of a cylinder, V = πr²h. Rearrange the formula to solve for the radius, and solve the equation to find the value of r.So,radius of cylinder r=8inches.
Explanation:
To find the radius of the cylinder, we can use the formula for the volume of a cylinder, which is V = πr²h. In this case, we need to solve for the radius, so we rearrange the formula as follows:
320π = πr²(5)
We can cancel out the π's on both sides of the equation:
320 = r²(5)
Divide both sides of the equation by 5:
64 = r²
Take the square root of both sides to solve for r:
r = √64
r = 8
Therefore, the radius of the cylinder is 8 inches.
A _____ is a point that helps to define an ellipse.
...?
when translating English sentences into math equations, the word is usually translates to which math symbol?
Jackie deposited $315 into a bank account that earned 1.5% simple interest each year.
If no money was deposited into or withdrawn from the account, how much money was in the account after 3 years?
Round your answer to the nearest cent.
Enter your answer in the box.
Answer:
Step-by-step explanation:
7
Ahmed is taking orders for lunch. A slice of pizza cost $2.9 and a chicken sandwich costs $3.9. He collects $25.3 for the group of 7 people.
Let x=number of pizza orders.Let y=number of chicken orders
Annette rode her bike 6.8 miles at a constant rate for 90 minutes. To find how fast she traveled, she solved the equation 6.8= x⋅90. What does x represent?
a)The total distance after x minutes
b)Her speed in miles per minute
c)The amount of time it takes to travel 6.8 miles
d)The number of miles she has traveled so far
Answer:
x represents Annette speed in miles per minute. Hence, option b) is correct.
Step-by-step explanation:
Given that Annette rode her bike 6.8 miles at a constant rate for 90 minutes. Also to find how fast she traveled, she solved the equation [tex]6.8=x\times 90[/tex]. Now, we have to tell here what x represents.
As, [tex]Speed=\frac{Distance}{Time}[/tex]
Let speed of bike is x miles/min and given distance is 6.8 miles and at a constant rate for 90 minutes.
∴ [tex]x=\frac{6.8}{90}[/tex]
⇒ [tex]6.8=x\times 90[/tex]
which is the same equation as given.
Here x represents Annette speed in miles per minute. Hence, option b) is correct.
Evaluate 5x3 + 2 for x = -1.
-7
-3
4
6
Answer:
The correct option is B) -3
Step-by-step explanation:
Consider the provided expression.
[tex]5x^3 + 2[/tex]
We need to solve the expression when x=-1.
Substitute the values of x in the provided expression.
[tex]5(-1)^3 + 2[/tex]
Simplify the expression.
[tex]5\times -1+ 2[/tex]
[tex]-5+ 2[/tex]
[tex]-3[/tex]
Hence, the value of the provided expression when x=-1 is -3.
Therefore, the correct option is B) -3
The sum of 8 and diane's savings is 56
Two angles in a triangle are 30° and 35°. What type of angle is the other?
what is a mathematical statement that two expressions are equal
Round 89,891 to the nearest ten-thousands place.
A line segment has endpoints at (–1, 4) and (4, 1). Which reflection will produce an image with endpoints at (–4, 1) and (–1, –4)?
a reflection of the line segment across the x-axis
a reflection of the line segment across the y-axis
a reflection of the line segment across the line y = x
a reflection of the line segment across the line y = –x
Answer:- A reflection of the line segment across the line y = –x .
Explanation:-
A reflection over the line y = -x, the x-coordinate and y-coordinate interchange their places and they are negated (the signs are changed).
Given :- A line segment has endpoints at (–1, 4) and (4, 1) such that it reflects produce an image with endpoints at (–4, 1) and (–1, –4).
(-1, 4)→(-4, 1) and
(4, 1)→(-1, -4)
Thus this shows a reflection of the line segment across the line y = –x.
Answer:
A reflection of the line segment across the line y = –x.
Step-by-step explanation:
Given : A line segment has endpoints at (–1, 4) and (4, 1).
To find : Which reflection will produce an image with endpoints at (–4, 1) and (–1, –4).
Solution : We have given that endpoints at (–1, 4) and (4, 1).
After reflection endpoints become (–4, 1) and (–1, –4).
Reflection: (–1, 4) →→ (–4, 1)
(4, 1)→→→ (–1, –4).
We can see x coordinate become -y coordinate and y coordinate become -x coordinate.
(x ,y) →→ (–y, -x)
This is the a reflection of the line segment across the line y = –x rule of reflection .
Therefore, a reflection of the line segment across the line y = –x.
A spruce tree is approximately the shape of a cone with a slant height of 20 ft. The angle formed by the tree with the ground measures 72 degrees. Estimate the height of the tree. Round to the nearest foot.
(picture below)
It’s C on Ed It is C It is C
Sasha has some pennies, nickels, and dimes in her pocket. The number of coins is 16. The expression 0.01p+0.05n+0.10d represents the value of the coins, which is $1.22. She has twice as many nickles as pennies. How many of each coin does Sasha have?
Can you use PEMDAS without parenthesis, exponents, division, or subtraction? Example: 5+1x10=?
Did I do this correctly and if any errors just tell me in the comments
U.s. air has a net income before tax 60,000. it is expected 45% of net income will go to federal and state taxes. how much will u.s. air have left
The graph of a proportional relationship contains the point (20, 4).
What is the corresponding equation?
Enter your answer as a fraction in simplest form
Please help
The corresponding equation is y = 1/5(x).
A graph of the equation is shown below.
In Mathematics and Geometry, a proportional relationship is a type of relationship that passes through the origin (0, 0) and produces equivalent ratios as represented by the following mathematical equation:
y = kx
Where:
y represents the y-variable.
x represents the x-variable.
k is the constant of proportionality.
Next, we would determine the constant of proportionality (k) by using the various data points in table B as follows:
Constant of proportionality, k = y/x
Constant of proportionality, k = 4/20
Constant of proportionality, k = 1/5.
In this context, the corresponding equation is given by;
y = 1/5(x)
Brianna went to Los Angeles for a vacation. She spent 5 nights at a hotel and rented a car for 6 days. Justin stayed at the same hotel, but spent 7 nights and rented a car for 8 days from the same company. If Brianna paid $1170 and Justin paid $1610, how much did one night at the hotel cost?
$150 per night
Use a system of equations using x (cost of hotel) and y (cost of car):
5x + 6y = 1170
7x + 8y = 1610
Solve for y in one of the equations and then use substitution to solve for x in the other:
6y = 1170 - 5x
y = (-5/6)x + 195
7x + 8((-5/6)x + 195) = 1610
7x + (-20/3)x + 1560 = 1610
(1/3)x +1560 = 1610
(1/3)x = 50
x = $150 a night
Find the interest rate needed for an investment of $9,000 to quadruple in 15 years if interest is compounded quarterly. (round your answer to the nearest hundredth of a percentage point.)
What is the slopes for (8,2) and (11,3) (8,0) and (8, 6)
The marginal cost function of producing q mountain bikes is 600/0.3q+5.
If the fixed cost in producing the bicycles is 2200 , find the total cost to produce 30 bicycles.
If the bikes are sold for 205 each, what is the profit (or loss) on the first 30 bicycles?
Find the marginal profit on the 31st bicycle. ...?
The total cost to produce 30 bicycles is $5599.89. The profit from first 30 bikes is $550.11. The marginal profit on the 31st bike is $126.57.
Explanation:The marginal cost function given is 600/(0.3q+5). To find the total cost to produce 30 bicycles, we need to integrate the marginal cost from 0 to 30 and add the fixed cost of 2200.
The result of the integration is 2000*(ln|1+0.3q|). Calculating from 0 to 30 gives us 3599.89. Thus, the total cost to produce 30 bicycles considering the fixed cost is 5599.89.
The revenue of each bike sold is $205. So, the total revenue generated from selling 30 bikes is 30*$205 = $6150. The profit is then the difference between the revenue and the total cost, giving us $6150-$5599.89 = $550.11.
To find the marginal profit on the 31st bike, subtract the marginal cost at 31 bikes from the selling price. The marginal cost at 31 bikes is the marginal cost function evaluated at q=31, which is approximately $78.43, and hence, the marginal profit on the 31st bike is $205 - $78.43 = $126.57.
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To find the total cost, multiply the quantity by the marginal cost function and add the fixed cost. To find the profit or loss, subtract the total cost from the revenue. The marginal profit can be found by subtracting the marginal cost from the selling price.
Explanation:To find the total cost to produce 30 bicycles, you need to calculate the variable cost and add it to the fixed cost. The variable cost can be found by multiplying the marginal cost function by the quantity of bikes. So, the variable cost is (600/0.3*30 + 5) = 6105. Adding the fixed cost of 2200 gives us a total cost of 8305.
To find the profit or loss on the first 30 bicycles, we need to subtract the total cost from the revenue, which is the selling price multiplied by the quantity. So, the revenue is 205 * 30 = 6150. The profit or loss is then 6150 - 8305 = -2155, indicating a loss of $2155.
The marginal profit on the 31st bicycle can be found by subtracting the marginal cost from the selling price. So, the marginal profit is 205 - (600/0.3*31 + 5) = -55, indicating a loss on the 31st bicycle.
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Name the property of real numbers illustrated by the equation.
-3(x+4)=-3x-12
Answer:
distributive property (a)
Step-by-step explanation:
I got 100/100 so this should be correct for you too.
A bunch of 6 bananas costs $3.54. What is the unit rate?
in uniform circular motion, the speed v of point on the edge of a spinning disk is v=2π/T times r. where r is the radius of the disk and T is the time it takes the point to travel once around the circle. Solve the formula for r.
in a chess match, a win counts 1 point, a draw counts 1/2 point, and a loss counts 0 points. After 15 games, the winner was 4 points ahead of the loser. How many points did the loser have? ...?
The loser had 5.5 points in the chess match.
Explanation:To find out how many points the loser had in the chess match, we can set up an equation. Let's say the loser had x points. The winner was 4 points ahead, so the winner had x + 4 points. Since there were 15 games in total, we can set up the equation:
x + (x + 4) = 15
Combining like terms, we get:
2x + 4 = 15
Subtracting 4 from both sides, we get:
2x = 11
Dividing both sides by 2, we get:
x = 5.5
Therefore, the loser had 5.5 points in the chess match.
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