What is the exact volume of the cone?
80π ft³
4003π ft³
400π ft³
418710π ft³
What is the area of this circle if the diameter is 4ft
Answer:
The answer is 12.56636
Step-by-step explanation:
A = πr²
A = area
r = radius
radius is half diameter, so the radius is 2. Plug π (2)² into your calculator and you get 12.56636
If I were you, I would round it to the second decimal place, so 12.57, but it depends on what your teacher wants
Rectangle ABCD has vertices A(8, 5) , B(8, 10) , C(14, 10) , and D(14, 5) . A dilation with a scale factor of 1.2 and centered at the origin is applied to the rectangle. Which vertex in the dilated image has coordinates of (9.6, 6) ?
A′
B′
C′
D′
The vertex A' corresponds to the coordinates (9.6, 6).
To find the vertex in the dilated image with coordinates (9.6, 6), we can apply the formula for dilation.
In a dilation centered at the origin with a scale factor of 1.2, the coordinates of a point (x, y) are transformed to (1.2x, 1.2y).
Let's calculate the coordinates of the vertices after dilation:
Vertex A' = (1.2 * x-coordinate of A, 1.2 * y-coordinate of A)
= (1.2 * 8, 1.2 * 5)
= (9.6, 6)
Vertex B' = (1.2 * x-coordinate of B, 1.2 * y-coordinate of B)
= (1.2 * 8, 1.2 * 10)
= (9.6, 12)
Vertex C' = (1.2 * x-coordinate of C, 1.2 * y-coordinate of C)
= (1.2 * 14, 1.2 * 10)
= (16.8, 12)
Vertex D' = (1.2 * x-coordinate of D, 1.2 * y-coordinate of D)
= (1.2 * 14, 1.2 * 5)
= (16.8, 6)
Comparing the coordinates of the dilated vertices to the given coordinates (9.6, 6), we can conclude that the vertex with coordinates (9.6, 6) is Vertex A' of the dilated image.
The vertex A' corresponds to the coordinates (9.6, 6).
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1/2m-4=5
What is the variable 'M' equal to.
Carissa leaves a 20% tip at her favorite restaurant. Her bill is $32.18. What tip should she leave?
Carissa should leave a tip amounting to $6.43 at her favorite restaurant. This is calculated by converting the 20% tip rate to a decimal and multiplying that by the bill total of $32.18.
Explanation:To calculate the tip that Carissa would leave based on a 20% rate, you would use the formula for percentage calculations which is (Percentage / 100) × Total. In this case, the percentage is 20 and the total is $32.18, her restaurant bill.
Step-by-step calculation:
Convert the percentage to a decimal by dividing by 100: 20/100 = 0.2.Multiply the result by the total bill: 0.2 × $32.18 = $6.43.So, Carissa should leave a $6.43 tip at her favorite restaurant.
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it cost $35 for one adult and two children to attend a show. It cost $60 for two adults and three children to attend the same show. How much does it cost one adult to attend the show?
You plan on financing a home theater system for $1,752. The audio shop offers a 15% APR for a 25 month loan. Use this information, and the table above, to determine the monthly payments. Round your answer to the nearest cent.
a.
$29.89
c.
$82.04
b.
$70.08
d.
$85.32
Final answer:
To calculate the monthly payments for a $1,752 home theater system at 15% APR over 25 months, convert APR to a monthly rate and apply the loan payment formula, yielding an estimated payment not precisely matching the provided options. This suggests a potential discrepancy in calculation or provided options.
Explanation:
To determine the monthly payments for financing a home theater system at a 15% APR for a 25-month loan costing $1,752, we use the formula for calculating the monthly payment on an amortizing loan. First, convert the annual interest rate to a monthly rate by dividing by 12. In this case, 15% annually becomes 1.25% per month. Then, apply the formula: Monthly Payment = P * (r(1+r)^n) / ((1+r)^n - 1), where P=principal amount ($1,752), r=monthly interest rate (0.0125), and n=number of payments (25).
Plugging into the formula gives us: Monthly Payment = 1,752 * (0.0125(1+0.0125)^25) / ((1+0.0125)^25 - 1), which calculates to approximately $76.55.
However, since the provided options do not include this exact figure, it's essential to note that either there's been a miscalculation or a misunderstanding in the method or given options. The closest provided option is $70.08.
During a research experiment, it was found that the number of bacteria in a culture grew at a rate proportional to its size. At 7:00 AM there were 6,000 bacteria present in the culture. At noon, the number of bacteria grew to 6,500. How many bacteria will there be at midnight?
To determine the number of bacteria at midnight, we can use the concept of exponential growth in bacteria. We set up an equation and solve for the growth rate constant, then use the formula to calculate the number of bacteria at midnight.
Explanation:To solve this problem, we can use the concept of exponential growth in bacteria. In this case, the number of bacteria is growing at a rate proportional to its size. We can set up an equation to represent the growth: dN/dt = kN, where N represents the number of bacteria and t represents time. Since the rate of growth is proportional to the current population, we can use the formula N(t) = N0ekt to calculate the number of bacteria at any given time.
In this case, we have the initial number of bacteria N0 = 6000 at 7:00 AM and N(t) = 6500 at noon, so we can plug these values into the formula and solve for k. Then we can use the formula again to calculate the number of bacteria at midnight.
By using this approach, we can determine the number of bacteria that will be present at midnight based on the given growth rate and initial population.
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Help me please
This is the choices for the first one
A)-x^2
B)2x^2
C)(x/2)^2
D)x^2
Second
A)10+x
B)10-x
C)10x
D)7-x
Third
A)3x-10
B)(3x-)/2
C)(3x-10)/2
D)3x/2
Stacey worked 12 hours and Amy worked 6 hours. They made the same amount of money per hour. If they made a total of $90 how much did they make per hour
Choose the equation that models the graph below
A computer was on sale for 2/3 of the original price. If the original price was $900 what was the sale price? show work please.
The length of rectangle ABCD is 4 in. The length of similar rectangle DEFG is 6 in. How many times greater than the area of ABCD is the area of DEFG?
The area of rectangle DEFG is 9/4 times greater than that of rectangle ABCD. This is determined by squaring the scale factor that relates their lengths, since the rectangles are similar.
The area of rectangle DEFG is how many times greater than the area of rectangle ABCD can be found by comparing the squares of their corresponding lengths, since they are similar rectangles. The length of rectangle ABCD is 4 inches, while the length of rectangle DEFG is 6 inches. To determine the area comparison, we square the scale factor, which is the ratio of the lengths of the two rectangles. This means the scale factor is 6/4, which simplifies to 3/2. Squaring this gives us (3/2)² = 9/4. Therefore, the area of DEFG is 9/4 times greater than the area of ABCD.
In the case of the squares Marta has, if one square has side lengths twice that of the other, the larger square will have an area that is 2² = 4 times larger than the smaller square. Applying this concept of squaring the scale factor to rectangles, as in the original question, gives us our ratio of areas between similar figures.
Compare the dimensions of the prisims. How many time greather is the surface area of the red prism than the surface area of the blue prism
Answer:
The dimensions of the red prism are 1.5
times the dimensions of the blue prism.
The surface area of the red prism is 2.25
times the surface area of the blue prism.
Step-by-step explanation:
Final answer:
To compare the surface areas of the red and blue prisms, divide the surface area of the red prism by the surface area of the blue prism. In this case, the surface area of the red prism is 2 times greater than the surface area of the blue prism.
Explanation:
To compare the surface areas of the red and blue prisms, we need to find the surface area of each prism. The surface area of a prism is found by adding the areas of all of its faces.
Let's say the surface area of the red prism is 100 square units and the surface area of the blue prism is 50 square units. To find out how many times greater the surface area of the red prism is than the blue prism, we can divide the surface area of the red prism by the surface area of the blue prism: 100/50 = 2.
Therefore, the surface area of the red prism is 2 times greater than the surface area of the blue prism.
ellie brought 60 cookies to class today. 30% of them have mint filing. how many cookies have the mint filling
What binomial must be subtracted from 7t-5) so that the difference of the 2 polynomials is (5r+8)?
.............................................. Nvm
Answer:
35. Monthly payment = ((total cost) -(initiation fee))/(number of payments)
36. ((sum of given scores) +(missing score))/5 = 98
37. 3 dozen is 1 dozen less than half a dozen times the number of marbles in the bag. How many marbles are in the bag?
38. (Rebecca's earnings last month) + $366 +$2895 = $5278
Step-by-step explanation:
How does energy travel in a mechanical wave?
A. In a medium
B. In Space
C. In Time
D. In a vacuum
Answer:
The answer is In a medium
Step-by-step explanation:
Mechanical waves are waves that require a medium in which to travel, this involves a transfer of kinetic energy from one place to another in the material.
A factory employs skilled laborers at$25 per hour and unskilled laborers at $12 per hour. The total hourly cost of the factory’s 24 workers is $405. How many of each type of laborer works at the factory.
Please help me I don’t know which one goes in order
the function f(x)=40x-80 models the number of visitors a website received x days after it was created. Which is the most appropriate domain for function?
The most appropriate domain for the given function is x ≥ 0.
Explanation:The domain of a function represents the set of all possible input values, or x-values, for which the function is defined. In this case, the function f(x) = 40x - 80 represents the number of visitors a website received x days after it was created. Since time cannot be negative and the website exists only after it was created, the most appropriate domain for the function would be x ≥ 0. This ensures that the function is defined for all non-negative values of x, which aligns with the context of the problem.
**PLEASE HELP** Suppose your class is raising money for the Red Cross. You make $5 on each basket of fruit and $3 in each box of cheese that you sell. How many items of each type must you sell to raise more than $150?
a. Write a linear inequality that describes the situation.
b. write two possible solutions to the problem
7) David bought a computer that was 20% off the regular price of $1080. If an 8% sales tax was added to the cost of the computer, what was the total price David paid?
8) Suzanne bought a sweater at the sale price of $25. The original cost of the sweater was $40. What percent represents the discount that Suzanne received when buying the sweater?
9) Leo bought a used car for x dollars. One year later the value of the car was 0.88 x. Which expression is another way to describe the change in the value of the car?
find the solutions to the system; y=x^2-3x-1 and y=8x-1
a) (0,-1) and (11,388)
b) (0,-1) and (11,87)
c) (-1,0) and (87,11)
d) no solution
I know the first step is to make them equal to each other, x^2-3x-1=8x-1
Just by looking at y = −x 2 + 1, how do you know that it does not represent a line?
A) x is squared.
B) There is no constant term.
C) There is an increase of 1.
D) The coefficient is − 1.
Answer:
x is squared. is correct.
y = mx + b represents a line. The x term is to the first power. In y = −x2 + 1, the x is squared.
The graph shows the quadratic function f(x) . What is the average rate of change for the quadratic function from x = 10 to x = 12? Enter your answer in the box.
Answer:
3
Step-by-step explanation:
Which pair shows equivalent expressions?
A.2(2/5x + 2)=2 2/5x + 1
B.2(2/5x + 2)=4/5x + 4
C.2(2/5x + 4)=4/5x + 2
D.2(2/5x + 4)=2 2/5x + 8
Which pair shows equivalent expressions?
A.2(2/5x + 2)=2 2/5x + 1
B.2(2/5x + 2)=4/5x + 4
C.2(2/5x + 4)=4/5x + 2
D.2(2/5x + 4)=2 2/5x + 8
Solution:
[tex] 2(\frac{2}{5}x + 2) [/tex]
Let us distribute 2 inside the parenthesis.
That is, we use distributive property:
a(b+c)=ab+ac
[tex] 2(\frac{2}{5}x + 2) =\frac{2*2}{5}x+2*2 [/tex]
So, [tex] 2(\frac{2}{5}x + 2) =\frac{4}{5}x+4 [/tex]
Answer:Option (b)
[tex] 2(\frac{2}{5}x+4) [/tex]
Applying distributive property, a(b+c)=ab+ac
[tex] 2(\frac{2}{5}x+4) =2*\frac{2}{5} x+2*4 [/tex]
[tex] 2(\frac{2}{5}x+4) =\frac{2*2}{5} x+2*4 [/tex]
[tex] 2(\frac{2}{5}x+4) =\frac{4}{5} x+8 [/tex]
So, Option (B) is correct.
Answer:
B.
Step-by-step explanation:
Find an ordered pair (x,y) that satisfies both of the equations below:
2x - 3y = -5
5x - 2y = 4
Answer:
(2,3)
Step-by-step explanation:
Multiplying the first equation by 5 and the second equation by $-2$ gives
\begin{align*}
10x-15y&=-25,\\
-10x + 4y &=-8.\\
\end{align*}Adding the two equations gives $-11y = -33$, so $y=3$. Substituting $y=3$ in the first original equation gives $2x - 9 = -5$, so $2x = 4$ and $x = 2$. Therefore, the solution is $(x,y) = \boxed{(2,3)}$
Help me please I can’t do this
please help i will mark brainliest