in the problem 10-4=6, whats the correct term for the number 4
the slope of a line is -2 and the line contains the points (7,4) and (x,12). what is the value of x?
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 value of x to the nearest tenth?
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?
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?
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.
How do you work out a percentile rank of a score of 57
A photograph has a length that is 6 inches longer than its width, x. So its area is given by the expression x(x+6) square inches. If the area of the photograph is 112 square inches, what is the width of the photograph?
The width of the photograph is 8 inches
let
width of the photograph = x
length of the photograph = 6 + x
Area = x(6 + x)
112 = x(6 + x)
112 = 6x + x²
x² + 6x - 112 = 0
x² - 8x + 14x - 112 = 0
x(x - 8) + 14(x - 8) = 0
(x + 14)(x - 8)
x = -14 or 8
x = 8
x cannot be negative so we use only 8.
width of the photograph = 8 inches
learn more: https://brainly.com/question/25171592?referrer=searchResults
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.
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
To learn more about net working capital click :
https://brainly.com/question/13126692
#SPJ5
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.
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.
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:
A new car dealer offered to sell her demonstrator model for 90% of the retail price. If the sale price was $9,750, what was the retail price?
90% = 9,750
9750/90 = 1%
1% = 108.3
100% = 10,833.3
original retail price = $10,833.30
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]
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
How many times greater is 700 than 70
Answer:
10 times greater
Step-by-step explanation:
700÷70=10
Let x and y represent two real numbers. Write an algebraic expression to denote the quotient obtained when the product of the two numbers is divided by their sum.
An algebraic expression to denote the quotient obtained when the product of the two numbers is divided by their sum is (xy)/(x+y).
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that let x and y represent two real numbers. The expression to denote the quotient obtained when the product of the two numbers is divided by their sum is written as,
E = (xy)/(x+y).
To know more about an expression follow
https://brainly.com/question/15408774
#SPJ2
What is the slope of a line that is perpendicular to the line whose equation is 0.5x−5y=9
To find the slope of a line perpendicular to the line defined by the equation 0.5x−5y=9, first convert the equation into slope-intercept form to determine the slope of the original line. The slope of the line perpendicular to this is its negative reciprocal. For this specific problem, the slope of the line perpendicular to the given line is -10.
Explanation:Firstly, rearrange the given equation, 0.5x−5y=9, into the slope-intercept format, i.e. y=mx+b. Here, 'm' is the slope of the line. To illustrate this rearrangement: 5y = 0.5x - 9, then divide through by 5 to get y = 0.1x - 1.8. Thus, the slope of the given line is 0.1.
Lines that are perpendicular to each other have slopes that are negative reciprocals of each other. In this case, the slope of the given line is 0.1, so the negative reciprocal (which represents the slope of the line perpendicular to this line) is -1/0.1, which equals -10. This is the slope of the line perpendicular to the given line.
Learn more about Perpendicular Line Slope here:https://brainly.com/question/9379960
#SPJ2
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]
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.
Learn more about least common multiple here:
https://brainly.com/question/30060162
#SPJ6
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.
Harry rolls a number cube what is the probability that he will roll an even number or a number greater than four
Solve the following system of equations.
7x -8y= -19
-2x +5y =0
x=
y=
simplify 10a + 3b + 7a+ 6b
March 21, the 80th day of the year, is the spring equinox. find the number of hours of daylight in fairbanks on this day
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.
Learn more about Probability Distribution here:https://brainly.com/question/32733554
#SPJ11
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.
Learn more about Volume of Solid here:https://brainly.com/question/32439212
#SPJ3
The quotient of 8.4x10^9 and a number n results in 5.6 x 10^27 What is the value of n?
Answer:
[tex]1.5\times 10^{-18}[/tex]
Step-by-step explanation:
We have been given that the quotient of [tex]8.4\times 10^9[/tex] and a number n results in [tex]5.6\times 10^{27}[/tex]
To find the value of n we will write our given information in an equation as:
[tex]\frac{8.4\times 10^9}{n}=5.6\times 10^{27}[/tex]
[tex]\frac{8.4\times 10^9}{5.6\times 10^{27}}=n[/tex]
Using quotient rule of exponents [tex]\frac{a^m}{a^n}=a^{m-n}[/tex] we will get,
[tex]\frac{8.4\times 10^{9-27}}{5.6}=n[/tex]
[tex]\frac{8.4\times 10^{-18}}{5.6}=n[/tex]
[tex]1.5\times 10^{-18}=n[/tex]
Therefore, the value of n is [tex]1.5\times 10^{-18}[/tex].