the slope of a line is -2 and the line contains the points (7,4) and (x,12). what is the value of x?
How many times greater is 700 than 70
Answer:
10 times greater
Step-by-step explanation:
700÷70=10
Suppose Sn is defined as 2 + 22 + 23 + . . . + 2n . What is the next step in your proof of Sn = 2(2n - 1), after you verify that Sn is valid for n = 1?
A. Show that Sn is valid for n = k + 2.
B. Assume that Sn is valid for n = k .
C. Verify that Sn is valid for n = 1.
D. Show that Sn is valid for n = k.
At the beginning of the year, a firm has current assets of $316 and current liabilities of $220. at the end of the year, the current assets are $469 and the current liabilities are $260. what is the change in net working capital?
The solution is $ 153
The change in the net working capital is $ 153
What is Net Working Capital?
The difference between a company's current assets and current or short-term liabilities is known as net working capital, or working capital.
Cash flow will have an operational origin, when there is a net decrease in working capital
Working Capital = Current Assets - Current Liabilities
Given data ,
Let the change in net working capital be A
Now , the equation will be
Working Capital at the beginning = Current Assets - Current Liabilities
Substituting the values in the equation , we get
Working Capital at the beginning = 316 - 220
Working Capital at the beginning = $ 96
And ,
Working Capital at the end = Current Assets - Current Liabilities
Substituting the values in the equation , we get
Working Capital at the end = 469 - 260
Working Capital at the end = $ 209
So ,
The change in net working capital A = Working Capital at the end - Working Capital at the beginning
Substituting the values in the equation , we get
The change in net working capital A = 209 - 96
The change in net working capital A = $ 153
Therefore , the value of A is $ 153
Hence , change in the net working capital is $ 153
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The sales tax for an item was $22.50 and it cost $450 before tax. Find the sales tax rate. Write your answer as a percentage.
Final answer:
The sales tax rate is found by dividing the amount of sales tax by the cost of the item before tax and then multiplying by 100. In this case, the sales tax rate is 5%.
Explanation:
To find the sales tax rate of an item, you need the amount of sales tax paid and the cost of the item before tax. The formula to calculate the sales tax rate is:
sales tax rate = (amount of sales tax \/ cost of the item before tax) \ 100
Applying the formula, we have:
sales tax rate = ($22.50 \/ $450) \ 100
sales tax rate = 0.05 \ 100
sales tax rate = 5%
Therefore, the sales tax rate for the item is 5%.
What is the value of x to the nearest tenth?
If your monthly net (after-tax) income is $1,500, what should be your maximum amount spent on credit payments? A. $200 B. $300 C. $400 D. $500
According to budgeting guidelines often referred to as the 20/30/50 rule, no more than 20% of your net income should be spent on debt repayments. Therefore, the maximum amount spent on credit payments for a $1,500 monthly income should be $300.
Explanation:The best practice for budgeting recommends that no more than 20% of your net monthly income should be spent on debt repayments, including credit payments. This is commonly referred to as the 20/30/50 rule. Therefore, given a monthly net income of $1,500, the maximum amount spent on credit payments should be 20% of $1,500, which equals to $300.
Here's how you would calculate it:
Convert 20% to decimal form by dividing it by 100. 20/100 = 0.2.Multiply the decimal by your net income to get your maximum spend on credit payments. 0.2 x $1,500 = $300.So, the correct answer is B. $300.
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Harry rolls a number cube what is the probability that he will roll an even number or a number greater than four
Two similar regular hexagons have a common center. If each side of the big hexagon is twice the side of the small one and the area of the small hexagon is 3 sq. in, what is the area of the big hexagon?
The area of the larger square is 4 times larger than the area of the smaller square. The area of the big hexagon is 12 sq. in.
Explanation:The area of the larger square is 4 times larger than the area of the smaller square. This is because the area of a square is proportional to the square of its side length.
In this case, the side length of the larger square is twice the side length of the smaller square, so the area of the larger square is 2² times greater than the area of the smaller square.
Given that the area of the small hexagon is 3 sq. in, the area of the big hexagon can be found by multiplying the area of the small hexagon by the square of the scale factor:
Area of big hexagon = (scale factor)² * Area of small hexagon = 2² * 3 sq. in = 12 sq. in
Use cylindrical coordinates. find the volume of the solid that is enclosed by the cone z = x2 + y2 and the sphere x2 + y2 + z2 = 72.
Step 1: The intersection curve is only at the origin.
Step 2: Set up the volume integral over the sphere region.
Step 3:Evaluate the integral to find the volume: [tex]\(V = 216\pi\sqrt{2}\).[/tex]
To find the volume of the solid enclosed by the cone [tex]\(z = x^2 + y^2\)[/tex] and the sphere[tex]\(x^2 + y^2 + z^2 = 72\),[/tex] we'll first find the intersection curve of the cone and the sphere in cylindrical coordinates, then set up the triple integral to find the volume.
Step 1: Finding the intersection curve:
The cone equation in cylindrical coordinates becomes [tex]\(z = r^2\)[/tex] and the sphere equation remains the same as [tex]\(r^2 + z^2 = 72\).[/tex]
To find the intersection, we set these two equations equal to each other:
[tex]\[r^2 = r^2 + z^2\][/tex]
Substitute [tex]\(z = r^2\)[/tex] from the cone equation:
[tex]\[r^2 = r^2 + (r^2)^2\][/tex]
[tex]\[r^2 = r^2 + r^4\][/tex]
[tex]\[r^4 = 0\][/tex]
From this, we see that the only solution is (r = 0), which corresponds to the point at the origin.
Step 2: Setting up the integral for volume:
We'll integrate over the region where the cone lies within the sphere, which is the entire sphere. In cylindrical coordinates, the limits of integration are [tex]\(0 \leq r \leq 6\)[/tex] (since the sphere has radius [tex]\(\sqrt{72} = 6\)) and \(0 \leq \theta \leq 2\pi\).[/tex]
The limits for \(z\) are from the cone to the sphere, so it's from [tex]\(r^2\) to \(\sqrt{72-r^2}\).[/tex]
Thus, the volume integral is:
[tex]\[V = \iiint_{E} r \, dz \, dr \, d\theta\][/tex]
Where (E) is the region enclosed by the cone and the sphere.
Step 3: Evaluate the integral:
[tex]\[V = \int_{0}^{2\pi} \int_{0}^{6} \int_{r^2}^{\sqrt{72-r^2}} r \, dz \, dr \, d\theta\][/tex]
Let's evaluate this integral step by step:
[tex]\[V = \int_{0}^{2\pi} \int_{0}^{6} (r\sqrt{72-r^2} - r^3) \, dr \, d\theta\][/tex]
[tex]\[V = \int_{0}^{2\pi} \left[-\frac{1}{4}(72-r^2)^{3/2} - \frac{1}{4}r^4\right]_{0}^{6} \, d\theta\][/tex]
[tex]\[V = \int_{0}^{2\pi} \left[-\frac{1}{4}(0)^{3/2} - \frac{1}{4}(6^4) - \left(-\frac{1}{4}(72)^{3/2} - \frac{1}{4}(0)^4\right)\right] \, d\theta\][/tex]
[tex]\[V = \int_{0}^{2\pi} \left[\frac{1}{4}(72)^{3/2}\right] \, d\theta\][/tex]
[tex]\[V = \frac{1}{4}(72)^{3/2} \int_{0}^{2\pi} 1 \, d\theta\][/tex]
[tex]\[V = \frac{1}{4}(72)^{3/2} \cdot 2\pi\][/tex]
[tex]\[V = 36\pi \sqrt{72}\][/tex]
[tex]\[V = 36\pi \times 6\sqrt{2}\][/tex]
[tex]\[V = 216\pi\sqrt{2}\][/tex]
So, the volume of the solid enclosed by the cone and the sphere is [tex]\(216\pi\sqrt{2}\).[/tex]
What is the probability that a randomly selected person will have a birthday in march? assume that this person was not born in a leap year. express your answer as a simplified fraction or a decimal rounded to four decimal places?
there are 31 days in August
365 days in a year
31/365 = 0.0849 probability
Answer:
0.0849
Step-by-step explanation:
Let's consider the event: a birthday takes place in March. The probability (P) of such event is:
[tex]P = \frac{favorable\ cases }{possible\ cases}[/tex]
The favorable cases are 31 because March has 31 days.
The possible cases are 365 because there are 365 days in a year.
The probability of a birthday being in March is:
[tex]P=\frac{31}{365} =0.0849[/tex]
The volume of a box(V) varies directly with its length(l). If a box in the group has a length of 30 inches, and the girth of 20 inches (perimeter of the side formed by the width and height), what is its height? Use k = 24. (Hint: Volume = length • width • height. Solve for length, and substitute into the equation for constant of proportionality.)?
A total of
564
tickets were sold for the school play. They were either adult tickets or student tickets. The number of student tickets sold was three times the number of adult tickets sold. How many adult tickets were sold?
What is the least common multiple of 2, 10 and 6
The least common multiple of 2, 10 and 6 by using the definition of multiple is 30.
The lowest possible number that can be divisible by all the given numbers is called as least common multiple (LCM). It is the smallest multiple which is common in all the numbers.
The least common multiple of 2, 10 and 6 can be calculated as:
The multiples of 2 are: 2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34.........
The multiples of 10 are: 10,20,30,40,50,60,70.............
The multiples of 6 are: 6,12,18,24,39,36,42,48,54,60,66...........
The lowest common multiple among 2,10,6 is 30.
Thus, the least common multiple of 2, 10 and 6 is 30.
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If each dimension of the rectangular prism is doubled, how will its total surface area change?
mc006-1.jpg
[Not drawn to scale]
The surface area doubles.
The surface area triples.
The surface area increases by a factor of four.
The surface area increases by a factor of eight.
Answer:
inceases by factor four
Step-by-step explanation:
Write a research problem that would be best studied using a probability sample.
A regular octagon has side length 10.9 in. The perimeter of the octagon is 87.2 in and the area is 392.4 in2. A second octagon has side lengths equal to 16.35 in. Find the area of the second octagon.
To solve this problem, let us first calculate for the Perimeter of the other octagon. The formula for Perimeter is:
Perimeter = n * l
Where n is the number of sides (8) and l is the length of one side. Let us say that first octagon is 1 and the second octagon is 2 so that:
Perimeter 2 = 8 * 16.35 in = 130.8 inch
We know that Area is directly proportional to the square of Perimeter for a regular polygon:
Area = k * Perimeter^2
Where k is the constant of proportionality. Therefore we can equate 1 and 2 since k is constant:
Area 1 / Perimeter 1^2 = Area 2 / Perimeter 2^2
Substituting the known values:
392.4 inches^2 / (87.2 inch)^2 = Area 2 / (130.8 inch)^2
Area 2 = 882.9 inches^2
Therefore the area of the larger octagon is about 882.9 square inches.
A lawn sprinkler sprays water 8 feet at full pressure as it rotates 360 degrees. If the water pressure is reduced by 50%, what is the difference in the area covered?
Answer:
[tex]150.72 feet^2[/tex] is the difference in the area covered.
Step-by-step explanation:
A lawn sprinkler sprays water 8 feet at full pressure, P.
A lawn sprinkler rotates 360 degree which means area covered by sprinkler is of circular shape. Since the sprinkler is in center and sprays the the water 8 feet away in all the direction while rotating.
Radius of the circle = 8 feet
Maximum pressure = P
As we know that higher the pressure higher will the force by which water will move out of the sprinkler. And with more force, sprinkler will able to spray water farther.
So we this we can say that pressure of the sprinkler is directly proportional to the radius of the circle in which water sprayed
[tex]pressure\propto Radius[/tex]
[tex]P\propto r[/tex]
[tex]\frac{P_1}{r_1}=\frac{P_2}{r_2}=constant[/tex]
[tex]P_1=P.P_2=P-50\%\times P=0.5 P[/tex]
[tex]r_1=8 feet.r_2=?[/tex]
[tex]r_2=\frac{0.5 P\times 8 feet}{P}=4 feet[/tex]
Area when , [tex]r_1= 8 feet[/tex] (Area of circle=[tex]\pi (radius)^2[/tex])
[tex]A=\pi r_1^{2}=\pi (8 feet)^2[/tex]
Area when ,[tex]r_2= 4 feet[/tex]
[tex]A'=\pi r_1^{2}=\pi (4 feet)^2[/tex]
Difference in Area = A- A'
[tex]\pi (8 feet)^2-\pi(4 feet)^2=\pi(48 feet^2)=150.72 feet^2[/tex]
[tex]150.72 feet^2[/tex] is the difference in the area covered.
March 21, the 80th day of the year, is the spring equinox. find the number of hours of daylight in fairbanks on this day
simplify 10a + 3b + 7a+ 6b
A car rents for $180 per week plus $0.75 per mile. Find the rental cost for a two-week trip of 500 miles for a group of three people.
Answer:
$735
Step-by-step explanation:
$180/week * 2 weeks = $360 for 2 weeks
$0.75/mile * 500 miles = $375
$360 + $375 = $735 for 2 week trip of 50 miles
Use cylindrical coordinates. find the volume of the solid that lies between the paraboloid z = x2 + y2 and the sphere x2 + y2 + z2 = 2
To find the volume of the solid that lies between the paraboloid z = x^2 + y^2 and the sphere x^2 + y^2 + z^2 = 2 using cylindrical coordinates, set up the integral for the volume by rewriting the sphere equation in cylindrical coordinates, determining the limits for r and z, and evaluating the integral.
Explanation:To find the volume of the solid that lies between the paraboloid z = x^2 + y^2 and the sphere x^2 + y^2 + z^2 = 2
We can rewrite the sphere equation in cylindrical coordinates as r^2 + z^2 = 2. The limits for r are from 0 to √(2-z^2), and for z, they are from 0 to √(2-r^2).
The volume can be found by integrating the constant 1 over the limits of r and z: V = ∭1 dz dr dθ. Evaluate this integral to find the volume of the solid.
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in the problem 10-4=6, whats the correct term for the number 4
csc(-x)/1+tan^2x) = ?
Juan will rent a car for the weekend. He can choose one of two plans. The first plan has an initial fee of
$55
and costs an additional
$0.30
per mile driven. The second plan has no initial fee but costs
$0.80
per mile driven.
For what amount of driving do the two plans cost the same?
What is the cost when the two plans cost the same?
Let x be a random variable giving the number of aces in a random draw of 4 cards from an ordinary deck of 52 cards. construct a table showing the probability distribution of x
The provided table outlines the probability distribution for drawing varying numbers of aces in a random draw of 4 cards from a standard 52-card deck, using combinatorial probability calculations.
Explanation:To answer your question, we need to consider the different possibilities for pulling aces in a draw of four cards. There are 4 aces in a standard deck of 52 cards, and here's a table showing the probability distribution for each outcome:
x = 0 - this represents no aces drawn. The number of ways to choose no aces from 4 aces and 4 non-aces from 48 non-aces is (4 choose 0)*(48 choose 4). So the probability P(X=0) = (comb(4, 0)*comb(48, 4))/comb(52,4)x = 1 - one ace is drawn. The probability P(X=1) = (comb(4, 1)*comb(48, 3))/comb(52,4).x = 2 - two aces are drawn. The probability P(X=2) = (comb(4, 2)*comb(48, 2))/comb(52,4).x = 3 - three aces are drawn. The probability P(X=3) = (comb(4, 3)*comb(48, 1))/comb(52,4).x = 4 - all four aces are drawn, and the probability P(X=4) = (comb(4, 4)*comb(48, 0))/comb(52,4).Please note that 'comb(a, b)' in this case represents 'a choose b', which is a way to compute combinations in probability.
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you need 2 3/4 wheelbarrows of sand to make 8 wheelbarrows of concrete. how much sand will you need to make 248 cubic feet of concrete
A. 84 cubic feet
B. 85 1/4 cubic feet
C. 682 cubic feet
D. Not enough info
Answer:
Option B.
Step-by-step explanation:
We need [tex]2\frac{3}{4}[/tex] wheelbarrows of sand for 8 wheelbarrows of concrete.
That means ratio between sand and concrete is [tex]2\frac{3}{4}:8[/tex]
Or [tex]\frac{11}{4}:8[/tex]
Now we have to calculate the amount of sand to make 248 cubic feet of concrete.
If the amount of sand required is x cubic feet then the ratio of sand and concrete will be x : 248.
Since both the ratios should be same therefore,
[tex]\frac{x}{248}=\frac{\frac{11}{4} }{8}[/tex]
[tex]\frac{x}{248}=\frac{11}{32}[/tex]
x = [tex]\frac{11\times 248}{32}[/tex]
x = [tex]\frac{2728}{32}[/tex]
x = [tex]\frac{341}{4}[/tex]
= [tex]85\frac{1}{4}[/tex] cubic feet
Option B will be the answer.
An artisan is creating a circular street mural for an art festival. The mural is going to be 50 feet wide. One sector of the mural spans 38 degrees. What is the area of the sector to the nearest square foot?
What is the domain of the function f(x) = x2 + 3x + 5?
A ball of radius 0.200 m rolls with a constant linear speed of 3.00 m/s along a horizontal table. the ball rolls off the edge and falls a vertical distance of 2.08 m before hitting the floor. what is the angular displacement of the ball while the ball is in the air
The angular displacement of the ball while it's in the air is 9.77 radians.
Here's how we can find it:
Time in the air: First, we need to find the time the ball spends in the air. We can use the following kinematic equation for vertical motion:
h = 1/2 * g * t^2
where:
h is the vertical distance (2.08 m)
g is the acceleration due to gravity (9.81 m/s²)
t is the time in the air
Solving for t, we get:
t = sqrt(2 * h / g) = sqrt(2 * 2.08 m / 9.81 m/s²) ≈ 1.43 s
Angular velocity: The angular velocity (ω) of the ball is related to its linear velocity (v) and radius (r) by the following equation:
ω = v / r
where:
v is the linear velocity (3.00 m/s)
r is the radius (0.200 m)
Plugging in the values, we get:
ω = 3.00 m/s / 0.200 m = 15 rad/s
Angular displacement: Finally, the angular displacement (θ) of the ball is the product of its angular velocity (ω) and the time (t) it spends in the air:
θ = ω * t = 15 rad/s * 1.43 s ≈ 21.45 rad ≈ 9.77 rad (rounded to three significant figures)
Therefore, the angular displacement of the ball while in the air is approximately 9.77 radians.