Marian and Robin, by combining their efforts, can weed a garden together in approximately 1 hour and 43 minutes by adding their individual work rates and calculating the time taken to complete one whole task at this combined rate.
Explanation:The question involves discovering the collective work rate of Marian and Robin when weeding a garden. To solve, we first identify the individual rates: Marian can weed a garden in 3 hours, which means her rate is 1/3 of the garden per hour. Robin's rate is 1/4 of the garden per hour, as he can complete it in 4 hours. To find the rate at which they can weed the garden together, we add their individual rates: (1/3) + (1/4) = 4/12 + 3/12 = 7/12.
Thus, their combined rate is 7/12 of the garden per hour. To find the total time taken, we divide the whole task (1 garden) by their collective rate (7/12). Hence, the time taken for them to complete the weeding together is 12/7 hours, which can be simplified to approximately 1 hour and 43 minutes.
The shoes still have a marginal cost of $25. You want to earn a profit, so you charge a price of _
525
$10
$50
Answer:
$50
Step-by-step explanation:
Let's write an equation to solve:
We can represent the profit as "p"
In that case, we have:
(p - 25) = 35
Adding 25:
p = 25.
If you charge 50, you will get 25 dollars back.
If you charge 10, you will get no profit.
Thus, the answer is $50.
a bag of pretzels contains approximately 17 1/2 ounces. one serving of pretzels is 1 1/4 ounces. how many servings of pretzels are in the bag?
Answer:
14
Step-by-step explanation:
Answer: The answer is: 14
Step-by-step explanation: I just took that test!
Have a great day!
-Sunny
To find the surface area of the figure shown Mia found the surface area and the rectangular prism and the rectangular prism from this Mia subtracted 6ft did mia make an error
Answer:
The answer is b
Step-by-step explanation:
Because i just did it and got it right
Answer:
B
Step-by-step explanation:
just got it right
There are three children in the McComb family. Which sample space represents the gender order, M (Male) or F(Female), in which the children could have been born?
Answer:
d
Step-by-step explanation:
{MMM, MMF, MFM, MFF, FMM, FMF, FFM, FFF}
Use a tree diagram to list the possibilities.
Answer:
The answer is D
Step-by-step explanation:
30 percent of 120 is the same as 80 percent of what number?
Answer:
45
Step-by-step explanation:
Taking into account the definition of equation and percentage, 30 percent of 120 is the same as 80 percent of 45.
An equation is defined as an established equality between two expressions, in which there may be one or more unknowns or variables.
So solving an equation consists of finding the value or values of the variables so that they fulfill the equality represented in the equation. That is, when changing the variable for the solution found, the equality must be true.
On the other side, the percentage is a value that represents the proportionality between two established quantities. That is, the percentage tells what part of a total represents a quantity.
Mathematically, the percentage is the division between an initial quantity and the total quantity, all multiplied by one hundred.
And to calculate the percentage of a quantity, the quantity is multiplied by the percentage and divided by 100. Then, 30 percent of 120 can be expressed as: (30×120)÷100
On the other hand, 80 percent of a number can be expressed as: (80×number)÷100
Since 30 percent of 120 must be the same as 80 percent of an unknown number, the following equation can be expressed:
(30×120)÷100= (80×number)÷100
Solving:
3600 ÷100= (80×number)÷100
36= (80×number)÷100
36×100= 80×number
3600= 80× number
3600÷ 80= number
45= number
The, 30 percent of 120 is the same as 80 percent of 45.
Learn more about percentage with this examples:
https://brainly.com/question/19295956?referrer=searchResultshttps://brainly.com/question/1301322?referrer=searchResults In her class of 10 girls and 8 boys, the teacher has to select 1 girl AND 1 boy. In how many ways can she make her selection? PLZ CORRECT ANSWER FOR TEST!
A.3060
B.5040
C.1260
D.73
Answer:
The answer is A
Step-by-step explanation:
whats the nameof people that steal kids called
Answer:
Kidnappers
Step-by-step explanation:
Answer:
kidnappers
Step-by-step explanation:
Please Help!!!!! 17 Points!!!!!!! I don't know if I have the right answer.
Answer:
SAS
Step-by-step explanation:
The sides have the same ratio and the angle between them is congruent, so it's SAS
Josh's grandparents put $3,000 into a college savings account when he was born. The account earns 6% interest per year. How long will it take before he has $15,000?
Answer:
Therefore it will take 28 years.
Step-by-step explanation:
To find the years, we use the following formula,
[tex]A=P(1+r)^n[/tex]
A= Total balance after n years
P= Initial amount.
r= Rate of interest per year.
n = Time in years.
Given that, Josh's grandparents put $3,000 into a college saving account when he was born. The account earn 6% interest per years.
Here A=$15,000,P=$3,000, r=6%=0.06 ,n=?
[tex]\therefore 15,000=3,000(1+0.06)^n[/tex]
[tex]\Rightarrow (1.06)^n=\frac{15,000}{3,000}[/tex]
[tex]\Rightarrow (1.06)^n=5[/tex]
Taking ln both sides
[tex]\Rightarrow ln(1.06)^n=ln(5)[/tex]
[tex]\Rightarrow n=\frac{ln(5)}{ln(1.06)}[/tex]
[tex]\Rightarrow n\approx 28[/tex]
Therefore it will take 28 years.
Marge and Kimo equally Shared 1/4 of a pie that was left over. What fraction of the original pie did each friend get? Use the picture to help you find the solution
Answer:
1/8
Step-by-step explanation:
1/4 divided by 2
Final answer:
Each friend received 1/8 of the original pie after equally sharing 1/4 that was left over.
Explanation:
Marge and Kimo equally shared 1/4 of a pie that was left over. To determine the fraction of the original pie that each friend got, we divide that 1/4 by two, since there are two people sharing it. So, each friend received 1/8 of the original pie.
Step-by-step explanation:
The leftover pie is 1/4 of the whole pie.Divide that 1/4 portion by 2 to share equally between Marge and Kimo.Dividing 1/4 by 2 gives us 1/8.Therefore, each friend gets 1/8 of the original pie.Find the area of the shaded sector in circle P. Please!
Answer:
the answer is c
Step-by-step explanation:
Answer: C. 25π/3 cm²
Step-by-step explanation:
The sector is an area of a circle bounded by two radii. The formula for determining the area of a sector is expressed as
Area of sector = θ/360 × πr²
Where
θ represents the central angle.
r represents the radius of the circle.
π is a constant whose value is 3.14
From the information given,
Radius, r = 10 cm
θ = 30 degrees
Therefore,
Area of sector = 30/360 × π × 10²
= 3000π/360 = 25π/3 cm²
John invests 18000 at a rate of 4.5% compounded annually. What will his new balance be after 6 years
Final answer:
John's new balance after 6 years with an original investment of $18,000 at a 4.5% annual compound interest rate will be approximately $23,362.65.
Explanation:
To calculate John's new balance after 6 years with a principal investment of $18,000 at an annual compound interest rate of 4.5%, we use the formula for compound interest:
A = P[tex](1+r/n)^{(nt)}[/tex]
Where:
A is the amount of money accumulated after n years, including interest.
P is the principal amount (the initial amount of money).
r is the annual interest rate (decimal).
n is the number of times that interest is compounded per year.
t is the time the money is invested for, in years.
In this case, P = $18,000, r = 0.045 (4.5%), n = 1 (since it's compounded annually), and t = 6 years.
Now we plug the values into the formula:
A = 18000(1 + 0.045/1)⁶
A = 18000(1 + 0.045)⁶
A = 18000(1.045)⁶
Calculating this, we get:
A ≈ 18000(1.297925)
A ≈ $23,362.65
Therefore, after 6 years, John will have approximately $23,362.65 in his account.
Which ordered pair is a solution of the equation ? y + 1 = 3(x - 4) Choose 1 answer: Only * (4, - 1) ) Only (5, 2) Both (4, - 1) ) and (5, 2) ) Neither
Replacing the ordered pairs into the equation, we find that the correct option is:
Both (4, - 1) and (5, 2)
The equation is:
[tex]y + 1 = 3(x - 4)[/tex]
Ordered pair:An ordered pair (x,y) is a solution to the equation if we replace (x,y) in the equation and get an identity.
Test if (4,-1) is a solution:
[tex]-1 + 1 = 3(4 - 4)[/tex]
[tex]0 = 0[/tex]
Identity, so it is.
Test if (5,2) is a solution:
[tex]2 + 1 = 3(5 - 4)[/tex]
[tex]3 = 3[/tex]
Identity, so it is.
Hence, both is the correct option.
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She Elle has 100 meters of fencing to build a rectangular garden. The garden's area (in square meters) as a function of the garden's width "w" (in meters) is modeled by: A(w) = -(w-25)^2+625 What is the maximum area possible in square meters?
Answer:
[tex]625 m^2[/tex]
Step-by-step explanation:
In this problem, we are told that the area of the garden is given by the expression
[tex]A(w)=-(w-25)^2+625[/tex]
where
w is the width of the garden (in meters)
Here we want to find the maximum possible area.
The maximum of a function f(x) can be found by requiring that its first derivative is zero:
[tex]f'(x)=0[/tex]
Therefore, here we have to calculate the derivative of [tex]A(w)=0[/tex] and find the value of w for which it is equal to zero.
Let's start by rewriting the area function as
[tex]A(w)=-(w^2-50w+625)+625=-w^2+50w[/tex]
Now we calculate the derivative with respect to w:
[tex]A'(w)=-2w+50[/tex]
Now we require this derivative to be zero, so
[tex]-2w+50=0\\w=-\frac{50}{-2}=25 m[/tex]
So now we can substitute this value of w into the expression of A(w) to find the maximum possible area:
[tex]A(25)=-(25-25)^2+625 = 625 m^2[/tex]
This value is allowed because we know that the maximum length of the perimeter of the fence is 100 meters; If the garden has a square shape, the length of each side is [tex]L=\frac{100}{4}=25 m[/tex], and the area of the squared garden is
[tex]A=L^2=(25)^2=625 m^2[/tex]
Which is equal to what we found earlier: this means that the maximum area is achieved if the garden has a squared shape.
Answer:
Step-by-step explanation:
Sketch the solid and set up the triple integral in Cartesian coordinates that gives the volume of the solid bounded below by the cone z = √x 2 + y 2 and bounded above by the sphere x 2 + y 2 + z 2 = 8. Evaluate the integral to find the volume.
Answer:
Evaluate The Integral To Find The Volume. This problem has been solved! See the answer. Sketch the solid and set up the triple integral in Cartesian coordinates that gives the volume of the solid bounded below by the cone z = \sqrt{x^2+y^2} and bounded above by the sphere x2 + y2 + z2 = 8. Evaluate the integral to find .
Step-by-step explanation:
took it
Urgent!!! What is the volume of this rectangular prism? Picture provided.
A: 15/2x
B: 3x+12/2x+8
C: 15/2x+2
D: 15/8
Answer:
V = [tex]\frac{15}{2x}[/tex]
Step-by-step explanation:
Using the volume formula
V = [tex]\frac{12}{x}[/tex] × [tex]\frac{x+4}{4}[/tex] × [tex]\frac{5}{2x+8}[/tex] ← cancel 12 and 4 by 4 and factor 2x + 8
= [tex]\frac{3}{x}[/tex] × [tex]\frac{x+4}{1}[/tex] × [tex]\frac{5}{2(x+4)}[/tex] ← cancel (x + 4) on numerator/denominator
= [tex]\frac{3}{x}[/tex] × 1 × [tex]\frac{5}{2}[/tex]
= [tex]\frac{15}{2x}[/tex]
A child who is 58 inches tall is standing next to the woman who is 5 feet and 4 inches tall casts a shadow that is 40 inches long. How long is the child’s shadow?
Final answer:
To find the length of the child's shadow, set up a proportion comparing the woman's height and shadow length to the child's height and unknown shadow length. Solving the proportion 64/40 = 58/Child's shadow, we find that the child's shadow is approximately 36.25 inches long.
Explanation:
The question involves using proportions to calculate the length of the child’s shadow. Since the child is shorter than the woman, we can expect that the child’s shadow will also be shorter in proportion to her height. The woman is 5 feet and 4 inches tall, which converts to 64 inches. The shadow to height ratio is the same for both individuals because they are standing under the same lighting conditions.
We can set up a proportion using the woman’s height and shadow length to find the child’s shadow length:
Woman’s height / Woman’s shadow = Child’s height / Child’s shadow
64 inches / 40 inches = 58 inches / Child’s shadow
To solve for the child’s shadow, we cross-multiply:
64 * Child’s shadow = 58 * 40
Child’s shadow = (58 * 40) / 64
Child’s shadow = 2320 / 64
Child’s shadow = 36.25 inches
Therefore, the child’s shadow is roughly 36.25 inches long.
A wedding cake has two layers, as shown. Each layer is in the shape of a cube. The bottom of the cake and the area where the two cakes meet is not frosted. What is the area of the cake that is frosted? Show and explain your work.
The area of the cake that is frosted is 464 in²
What is the area of the cake that is frosted?
Bottom cake = 10 inches
Top cake = 6 inches
The lateral area of the bottom cube is 4 faces, each of which is a 10-inch square.
Lateral area = 4 × s²
= 4 × (10 in)²
= 400 in²
Top cube
The top area is the difference in area between a 10-inch square and a 6-inch square;
= (10 in)² - (6 in)²
= (100 -36) in²
= 64 in²
Therefore,
Area of the cake frosted = the sum of the lateral area and the top frosted area.
Area of the cake frosted = 400 in² +64 in²
= 464 in²
If the point ( x , √3/2) is on the unit circle, what is x?
A. √3/2
B. 1/2
C. - √3/2
D. 2/√3
Answer:
B. 1/2
Step-by-step explanation:
This problem involves the use of the Pythagorean theorem. In the unit circle, the hypotenuse of any right triangle formed is 1 while the coordinates of the point are then the two legs that make up the triangle.
a = 1 (given)
b = √3/2 (given)
a² = b² + c² (Pythagorean Theorem)
1² = (√3/2)² + c² (Substitute information)
Now, we need to solve for c
1 = (3/4) + c² (square the hypotenuse and one of the legs)
1 - (3/4) = (3/4) + c² - (3/4) (subtract 3/4 on both sides)
1/4 = c² (combine like terms)
√(1/4) = √(c²) (square root both sides)
√1 / √4 = c (square root both sides)
1/2 = c (final answer)
Therefore the other leg of the right triangle is 1/2, this also means that the other coordinate, or x, is 1/2, so the answer is B. 1/2.
Final answer:
The x-coordinate for the point (x, √3/2) on the unit circle is determined using the Pythagorean theorem for a unit circle. After substituting √3/2 for y and solving for x, the x-coordinate can be ±1/2. The correct option from the given choices is B. 1/2.
Explanation:
If the point (x, √3/2) is on the unit circle, we must use the Pythagorean theorem that applies to the unit circle, which states that x² + y² = 1, where x and y are the coordinates of a point on the circle. For a unit circle, the radius is 1. Since the y-coordinate is given as √3/2, we can substitute this value into the equation and solve for x:
x² + (√3/2)² = 1
x² + (3/4) = 1
x² = 1 - 3/4
x² = 1/4
x = ±√(1/4)
x = ±(1/2)
Therefore, x could be either 1/2 or -1/2. Since the question doesn't specify which quadrant the point is in, both answers are correct. However, within the given options, the correct answer is B. 1/2.
Which of the following graphs are identical?
y= square root of x
y= ^3 square root of x
y= square root of negative x
y= ^3 square root of negative x
y= negative square root of x
y= negative ^3 square root of x
Answer:
1. D & F
2. A, C, D
Step-by-step explanation:
DID ON EDGE
None of the given graphs are identical. Their differences arise from the distinct characteristics of their specific square root or cube root functions, as well as the range of x-values they apply to.
Explanation:None of the aforementioned graphs are identical. The syntax y=√x corresponds to the graph of the square root function, which is always positive and only defined for x≥0. On the other hand, the syntax y=-√x describes the graph that's a reflection of y=√x in the x-axis. However, y=∛x and y=-∛x both entail the cube root function, which is distinguishable from the square root function by its shape and the fact it includes values for negative x. Lastly, y=√-x and y=∛-x are not properly defined real functions, since taking square or cube roots of negative x values leads to complex numbers.
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if A=(3,9] and B= [6,9) then find A u B
U means "Union" or all the numbers from one set and all the numbers from the other set combined. So your answer is any of the numbers included in one set or the other or both.
Which is the solution set for (z+4)>15
Answer:
Sol set = {12, 13, 14, 15, 16, 17,....... ".}
Step-by-step explanation:
[tex](z + 4) > 15 \\ z + 4 > 15 \\ z > 15 - 4 \\ z > 11 \\ z = \{12, \: 13, \: 14, \: 15, \: 16, \: 17, ........... \}[/tex]
What is the sum of -20 and 4?
Answer:
-16
Step-by-step explanation:
-20 + 4 Equals -16. Try it on a number line.
Answer:-16
Step-by-step explanation:
-20+4=-16
Which of the following statements is NOT true about the graph of a system of
equations with infinitely many solutions?
The lines will have the same slope.
The lines will have one positive y-intercept and one negative
y-intercept.
The lines will have the same y-intercept.
The lines will share all of the same points.
Answer:
The lines will have one positive y-intercept and one negative y-intercept is NOT true.
Step-by-step explanation:
If a graphed system has infinitely many solutions, that means that the two equations are the exact same. This means that they'll have the same slope, y-intercept, and will share all of the same points. Answer b is the only choice left.
The lines will have one positive y-intercept and one negative y-intercept that is not true.
What is the graph?The graph is a diagram showing the relation between variable quantities, typically of two variables, each measured along with one of a pair of axes at right angles.
Determining:The lines will have one positive y-intercept and one negative y-intercept is NOT true.
If a graphed system has infinitely many solutions, that means that the two equations are the exact same. This means that they'll have the same slope, and y-intercept, and will share all of the same points. Answer b is the only choice left.
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A circle with area 36 pi has a sector with a central angle of
48°
What is the area of the sector?
Either enter an exact answer in terms of # or use 3.14 for
a and enter your answer as a decimal rounded to the
nearest hundredth.
Answer: 36 pi over 7.5
Step-by-step explanation:
UN NADADOR 50 METROS POR MINUTO EN LA COPETENCIA DE NADO LIBRE CUANTO ES POR 33.3 MINUTOS POR FAVOR AYUDENME
Answer:
99000 meters.
Step-by-step explanation:
We have the swimmer going at 50 m / s, and we want to know where he is going in 33.3 minutes.
The first thing is to pass the time from minutes to seconds, we know that 1 minutes is 60 seconds, therefore:
33.3 min * 60 s / 1 min = 1998 seconds
Now to know the distance is to multiply this time by the speed they give us, like this:
1998s * 50m / s = 99900 m
Which means that in that time and at the speed of the swimmer, he has traveled 99000 meters.
Can someone help me answer this question please.
Answer:
55 and 7.5 for number 3
Step-by-step explanation:
Dwayne buys ingredients to make a cake. He buys 1/1/2 pounds of flour, 12 ounces of coconut, and 1/1/4 pounds of sugar. What is the total weight of the ingredients Dwayne bought?
Answer:
3 1/2 pounds or 3.5 pounds
Step-by-step explanation:
Two ingredients are measured in pounds while one is measured in ounces. Recall that 1 pound = 16 ounces. Thus, 12 ounces of cocoanut comes out to
(12/16) pound. Next, we sum up 1 1/2 pounds of flour, 12/16 pound of cocoanut and 1 1/4 pounds of sugar, after rewriting these mixed numbers with the same denominator (4):
1 1/2 pounds stays 1 2/4 pounds;
12 ounces becomes 3/4 pound; and
1 1/4 pounds stays 1 1/4 pounds
Summing up the fractions results in 6/4 pounds, or 1 1/2 pounds; and summing up the integers results in 2 pounds.
The final sum is 1 1/2 pounds + 2 pounds, or 3 1/2 pounds.
Dwayne buys 3 1/2 pounds of ingredients.
Alternatively, we could convert all of these measurements to decimal fractions and then add up those fractions:
1.5 pounds + 0.75 pounds + 1.25 pounds = 3.5 pounds (same as before).
Your college fund has $56,000. It is currently in an account which pays 3.4% compounded quarterly. How much money will you have in 11 years
Answer:
$81,269.53
Step-by-step explanation:
Lets use the compound interest formula provided to solve this:
[tex]A=P(1+\frac{r}{n} )^{nt}[/tex]
P = initial balance
r = interest rate (decimal)
n = number of times compounded annually
t = time
First, change 3.4% into a decimal:
3.4% -> [tex]\frac{3.4}{100}[/tex] -> 0.034
Since the interest is compounded quarterly, we will use 4 for n. Lets plug in the values now:
[tex]A=56,000(1+\frac{0.034}{4})^{4(11)}[/tex]
[tex]A=81,269.53[/tex]
After 11 years, you will have $81,269.53
What is the volume of the smallest square-based prism that would hold this cylinder?
Answer:
The answer to your question is Volume = 80000 cm³
Step-by-step explanation:
Data
height = 50 cm
radius = 20 cm
Process
1.- The smallest dimensions of the prism must have the same dimensions that the cylinder.
Radius = 20 cm then the length of a side = 2 x radius = 40 cm
2.- Calculate the area of the base
Area = 40 x 40
= 1600 cm²
3.- Calculate the volume of the prism
Volume = Area x height
= 1600 x 50
= 80000 cm²