Answer: [tex]2,160\ ft^3[/tex]
Step-by-step explanation:
The first step is to find the ratio of the lengths.
According to the information given in the exercise, one the solids has edges of 12 feet and the other solid has edges of 24 feet.
Therefore, the ratio of the length of the smaller solid to the length of the is the following:
[tex]k=\frac{24\ ft}{12\ ft}\\\\k=2[/tex]
Now, the ratio to the volumes of the smaller solid to the other one is the following:
[tex]k^3=2^3=8[/tex]
Then, knowing that the volume of the smaller solid is:
[tex]V_s=270\ ft^3[/tex]
You get that the volime of the larger solid is:
[tex]V_l=270\ ft^3*8\\\\V_l=2,160\ ft^3[/tex]
To find the volume of the larger solid, we cube the ratio of the edge lengths, which in this case is 2. Then, we multiply the volume of the smaller solid by this cubed ratio to get the volume of the larger solid, which is 2160 cubic feet.
The student's question involves finding the volume of a solid similar to another solid, given the edge lengths and the volume of the smaller solid. Since the solids are similar, the ratio of their edges will be the same as the ratio of the sides, the squares of the ratio of the surfaces, and the cubes of the ratio of their volumes. For the solids in the question, the ratio of their edges is 24/12=2. Therefore, the ratio of their volumes will be 23=8.
Given the volume of the smaller solid is 270 cubic feet, the volume of the larger solid will be 270 multiplied by the volume ratio, which is 8. So the volume of the larger solid V is calculated by V = 270 x 8 = 2160 cubic feet.
Find the inverse of the function. State any restrictions on the domain.
f(x) = x^2 + 9
The function is not invertible if you think of it as
[tex]f:\mathbb{R}\to\mathbb{R}[/tex]
because it is not injective: [tex]f(x)=f(-x)[/tex]
So, if we restrict the domain to the positive numbers only:
[tex]f:\mathbb{R^+}\to\mathbb{R}[/tex]
Note that the range is actually [tex][9,\infty)[/tex], so we can be more precise and write
[tex]f:\mathbb{R^+}\to[9,\infty)[/tex]
To find the inverse, we solve the expression for x:
[tex]y=x^2+9 \iff y-9=x^2 \iff x=\pm\sqrt{y-9}[/tex]
But since we restricted to positive values of x, the inverse is
[tex]x=\sqrt{y-9}[/tex]
To find the inverse of the function f(x) = x² + 9, swap x and y and solve for y. The inverse function is f^(-1)(x) = ± √(x-9), with a domain restricted to x ≥ 9.
To find the inverse of the function f(x) = x^²+ 9, we need to switch the roles of x and y and solve for y. The given function is y = x² + 9. Swap x and y to get x = y² + 9. Rearrange this equation to solve for y in terms of x: y² = x - 9. Taking the square root of both sides gives us y = ± √(x-9). Therefore, the inverse function is f^(-1)(x) = ± √(x-9), and the domain is restricted to x ≥ 9.
Learn more about Inverse function here:https://brainly.com/question/35509335
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The state narcotics bureau must form a 5-member investigative team. If it has 25 agents from which
to choose, how many different possible teams can be formed?
Answer:25/5=5
Step-by-step explanation: so the answer will be 5 plz mark brainly
Which of the following is the equation for the graph shown?
x squared over 20 plus y squared over 36 equals 1
x squared over 36 plus y squared over 20 equals 1
x squared over 20 minus y squared over 36 equals 1
x squared over 36 minus y squared over 20 equals 1
What is the area? Of this circle please help meeeee!!
Answer:
I'm pretty sure the answer is 1.0956.
Answer:
I think the answer is 7.065 in
Since the formula to find the area of a circle is A =
πr2
What expression is equivalent to 5(2y + 8) - 12?
Which expression represents the volume of the prism?
Answer:
Step-by-step explanation:
Lorena's home is 125 meters away from the school.how many meter does she walks every day if she takes the same distance back home? How many meters does she walks in a week?
Hello friend!
Answer: 1750 meters.
Lorenas walks 125 meters to school and back, therefor that's 250 meters. If we take 250 and multiply that by home many days are in a week (which is seven) are answer will be 1750.
125x2=250x7=1750.
Have a amazing day and good luck on your assignment!
-Edge
1750 meters.
Lorenas walks 125 meters to school and back, therefor that's 250 meters. If we take 250 and multiply that by home many days are in a week (which is seven) are answer will be 1750.
125x2=250x7=1750.
HOPE YOU ACE WHATEVER YOUR TAKING!!!
Which is the closest to the height of a giraffe?
Answer:15-20 ft
Step-by-step explanation:
one winter, a group of students measured snowfall totals at their school. This chart shows how many inches of snow the students measured each month. How much snowfall did they receive in January and February combined?
December: 3.6
January: 8.6
February: 2.8
To calculate the total snowfall in January and February, we add the snowfall measurements for both months. The total snowfall for January (8.6 inches) and February (2.8 inches) is 11.4 inches.
Explanation:The question involves adding the amounts of snowfall for two different months, which is a basic arithmetic operation covered in mathematics. To find the total snowfall in January and February combined, we simply add the snowfall totals for each month.
According to the given information, there were 8.6 inches of snow in January and 2.8 inches in February.
Total snowfall for January and February combined is 8.6 + 2.8 = 11.4 inches.
If we consider the additional provided information, we can infer that since the schools closed and more than three inches of snowfall triggers a closure, it's reasonable to assume that in at least one of these months the snowfall was above three inches.
You make $32,000.00 .Using the 20% to 25% range, calculate the least and greatest amount you should spend on housing.
Answer: im am not sure but try your best
Step-by-step explanation:
To determine housing affordability based on a $32,000 annual income, calculate 20% for the least ($6,400 per year or $533.33 per month) and 25% for the greatest amount ($8,000 per year or $666.67 per month) you should allocate to housing costs.
To calculate the least and greatest amount you should spend on housing based on an income of $32,000.00 using the 20% to 25% range, you first need to determine 20% and 25% of your annual income. The formula to calculate a percentage of a number is:
(Percentage / 100) x Total Amount
For the least amount (20%): (20 / 100) x $32,000 = $6,400 per year
For the greatest amount (25%): (25 / 100) x $32,000 = $8,000 per year
To find the monthly housing cost, divide these amounts by 12:
Least amount monthly: $6,400 / 12 = $533.33
Greatest amount monthly: $8,000 / 12 = $666.67
Therefore, you should spend between $533.33 and $666.67 per month on housing, based on the 20% to 25% range of your annual income.
Rank the following in order from most precise to least precise.
5.46 seconds
900 miles
980 meters
8.431 grams
Answer:
8.431 grams>5.46 seconds>980 meters>900 miles
Precision in measurements is indicated by the level of detail or the number of decimal places. The measurements ranked from most precise to least are 8.431 grams, 5.46 seconds, 980 meters, and 900 miles.
To rank the given measurements from most precise to least precise, we need to consider how detailed the measurement is, which is often indicated by the number of decimal places or significant figures. Precision refers to how close multiple measurements are to each other, and in this context, we measure it by the detail level provided in the measurement.
8.431 grams - This measurement is the most precise since it is given to three decimal places.
5.46 seconds - The next most precise measurement, given to two decimal places.
980 meters - This measurement, although a whole number, is more precise than '900 miles' since distances in meters usually imply a more precise measurement scale in common contexts.
900 miles - The least precise measurement, with no decimal places, indicating a broad estimate of distance.
Therefore, from most to least precise, the measurements are: 8.431 grams, 5.46 seconds, 980 meters, and finally 900 miles.
what is the value of b
b+18=-24
i need help
Answer:
the correct answer is
b=-24-18
b=-42
Answer:
-42
Step-by-step explanation:
Just do invers operation
help please please please
Answer:
There are 9 quarters and 3 nickels
Step-by-step explanation:
problems used: 0.5x+0.25y=3.09
x=y+6
so substitute what x is equal to into the problem
0.5(y+6)+0.25y=3.09 <--------- distribute
0.5y+3+0.25y=3.09 <--------- Combine like terms
0.3y+3=3.09 <----------- Subtract 3 on both sided to get y by itself
0.3y=0.9 <------------ Divide by 0.3 on both sides to get what y is equal to
y=3 <-------- now substitute to find what x is equal to
x=3+6
x=9
Answer:
There are 8 nickels and 14 quarters.
Step-by-step explanation:
Let n and q represent the numbers of nickels and quarters present.
Then q = n + 6 states that there are 6 more quarters than there are nickels.
($0.25)(q) + ($0.05)n = $3.90, in which we substitute n + 6 for q:
($0.25)(n + 6) + ($0.05)n = $3.90
Combining the n terms, we get 0.25n + 0.05n = 3.90 - 0.25*6, or:
0.30n = 3.90 - 1.50, or:
$2.40
n = ----------------------- = 8
0.30
There are 8 nickels and 14 quarters.
Check: 14 quarters comes to $3.50 and 8 nickels to $0.40, and $3.50 + $0.40 sums up to $3.90.
The following table represents the number of whales spotted on the Oregon coast during one week. Which line graph best represents the information presented in the table?
Day Number of Whales
Sunday 31
Monday 4
Tuesday 0
Wednesday 12
Thursday 0
Friday 11
Saturday 7
Answer: I am not sure how to help you answer this without the attached graph options.
Step-by-step explanation:
If you could add those in, then I would be more than willing to help you!
Answer:
C. Its the third graph.
3. Sarah's parents give her a $100.00 allowance at the
beginning of each month. Sarah spends her allowance on
comic books. The graph below represents the amount of
money Sarah spent on comic books last month.
What is the rate of change ?
What does the rate of change represent ?
Answer:
See explanation section
Step-by-step explanation:
Requirement A)
According to the graph, whenever Sarah purchased one comic book, she lost $5 from her allowance. Now the allowance remain after purchasing one comic book = ($100 - 5) = $95
Whenever she purchased three comic books, she lost $5 × 3 = $15 from her allowance. Now the allowance remain after purchasing three comic books = ($100 - 15) = $85. In that way, she lost her $50 after purchasing 10 comic books from her allowance. Therefore, the rate of change is $5.
Requirement B)
It represents that she spent $5 on her each comic book. It also represents that her each book decreases her allowance by $5.
Answer:
a) -5
Step-by-step explanation:
a) slope = (90-100)/(2-0) = -5
b) rate of change represents the deduction in amount left when one more book is purchased.. which is the cost of one book
George weeded 1/5 of the garden and Summer weeded some too. When they were done 2/3 was left of the garden. How much did Summer weed.
Answer:
Step-by-step explanation:
Step one) Figure our what peace of information you need to find and write down what information you already know.
•George weeded 1/5 of the garden.
•At the end 2/3 of the garden was left, which means that 1/3 of the garden was weeded.
•Now we need to figure out how much Summer weeded.
Step Two) Find the LCM (Lowest common multiple) of 5 and 3.
The LCM of 5 and 3 is 15.
Step three) Change the denominator of both problems to 15. Now the information you have should be:
•George weeded 3/15 of the garden. (We get the 3 on top because we multiplied 5 x 3 to get 15 so we multiply the numerator by 3 as well.)
•At the end there was 10/15 left. (We get the ten on top because the bottom was multiplied 3 x 5 to get 15, so then we take the numerator which is 2 and multiply that by 5 as well.)
•Now we know that if 10/15 weren’t picked that means that 5/15 were picked.
•We still need to figure out the amount that was picked by Summer.
Step 4)
Now we will use all the previous information to do the final step.
If a total of 5/15 were picked, and 3/15 of those were picked by George, then we do the problem:
5-3=2
Answer: Sally picked 2/15.
A triangle has side lengths of (6.2p + 4.5q) meters, (3.4p – 0.7r) meters, and (2.9r – 4.1q) meters. Which expression represents the perimeter, in meters, of the triangle?
A 9.6p + 0.4q + 2.2r
B 9.6p + 7.4q – 4.8r
C 9.6p – 1.2qr
D 10.7pq + 2.7pr – 1.2qr
Answer:
A
Step-by-step explanation:
THe perimeter is the sum of all the sides.
A triangle has 3 sides and we sum up the expressions to find the expression for perimeter.
Lets do this:
[tex](6.2p + 4.5q)+(3.4p-0.7r)+(2.9r-4.1q)\\=(6.2p+3.4p)+(4.5q-4.1q)+(-0.7r+2.9r)\\=9.6p+0.4q+2.2r[/tex]
We have added "p"s and "q"s and "r"s, together.
THe answer is Option A
Which of the following data could be graphed using a dot plot? Select all that apply.
Answer:
You need to provide more information, images data etc.
Step-by-step explanation:
Answer:cars and siblings
Step-by-step explanation:
Can you please help me on -6(b+3)+6b=-6(-4b+3)
Answer:
3.75=b
Step-by-step explanation:
If you use a cone-shaped container to fill a cylinder-shaped container with the same height and radius, how many times
will you have to empty the cone-shaped container to fill the cylinder-shaped container?
1/3
1
2
3
Answer:
3 times
Step-by-step explanation:
The volume of a cone is 1/3*pie *r^2 * h whereas the volume of a cylinder is pie*h*r^2 which means that if the height and radius are the same the volume of the cone is 1/3 of the cylinder thus you need 3 cones to fill the cylinder.
Please hurry it’s urgent
Answer:
[tex]V=\pi r^2h\\V=\pi(5)^2(10)\\V=\pi(25)(10)\\V=250\pi\\V=785.4[/tex]
Estimated
Step-by-step explanation:
Answer:
150π in^2
Step-by-step explanation:
The surface area of cylinder is calculated by 2πrh+2πr2 (r: radius, h : height)
2π×5×10 + 2π×5^2 = 150π in^2
A table top is in the shape of an equilateral triangle. If the perimeter of the
table top is 255 inches, what is the length of one side of the table?
A. 765 inches
B. 258 inches
C. 252 inches
D. 85 inches
Answer: The correct answer is D: 85 inches
Step-by-step explanation: The figure specified in the question is an equilateral triangle and one of it's properties is that all three sides have equal measurements.
The perimeter simply is a measurement of the lengths that runs around the entire shape. In other words the perimeter of a triangle is given as
Perimeter = 3L
Where L is the length of one side of the triangle.
If the perimeter of the table top is given as 255 inches, then we can now express it more properly as follows
255 = 3L
Divide both sides of the equation by 3
85 = L
Therefore the length of one side of the table measures 85 inches.
Multiply and simplify. Show work to earn full credit. (4 points) (7x-6)(3x^2-4x+5)
Answer:
21x³ - 46x² + 59x - 30
Step-by-step explanation:
21x³ - 28x² + 35x - 18x² + 24x - 30
= 21x³ - 46x² + 59x - 30
Step-by-step explanation:
7x ( 3x^2 - 4x + 5) - 6 ( 3x^2 - 4x +5)
21x^3 - 28x^2 + 35x - 18x^2 + 24x - 30
21x^3 - 46x^2 +59x - 30
Twenty minus the product of 4 and a number is 4
Answer:
20-(4*4)=4
Step-by-step explanation:
Final answer:
The number that satisfies the equation is 4.
Explanation:
To solve the equation, let's assume the number is represented by 'x'.
The product of 4 and the number would be 4*x or 4x.
Twenty minus the product of 4 and the number can be written as
20 - 4x.
According to the problem, this expression is equal to 4.
So, we can write the equation as
20 - 4x = 4.
To solve for 'x', we can isolate the variable by subtracting 20 from both sides:
-4x = 4 - 20 = -16.
Then, we divide both sides by -4:
x = -16 / -4 = 4.
Therefore, the number that satisfies the equation is 4.
Write the equivalent expression for k(1/4+3)
Answer:k1/4+k3
k3 1/4
Step-by-step explanation:
what decimal is equivalent to negative 3 over 8
Answer:
-9 / 24
Step-by-step explanation:
Step 1: Find an equivalent to -3/8
(-3*3) / (8*3)
-9 / 24
Answer: -9 / 24
Answer:
-0.375
Step-by-step explanation:
-3/8 is the same as saying -3 divided by 8
so just divide those puppies and you get -0.375
Simplify the equations:
1.)6x+2(5x-2)
2.)7x+3(8+7)
Answer:
1) 16x -4
2) 7x + 45
Step-by-step explanation:
1 ) 6x + 2(5x -2)
we are going to open the bracket
we have,
6x + 10x - 4
16x -4
4(4x - 1).................................................... simplified
number 2
7x + 3(8+7)
7x +24 + 21
7x + 45........................................................... simplified
so therefore the solution to the first and 2nd question is
1) 16x -4
2) 7x + 45
Alice is having her birthday party at a game center. The center charges $100 plus $20 per guest. The total cost of the party y can be
represented by the equation y = 20x + 100. What does the y-intercept represent?
a. the number of guests
b. the cost to rent the game center
c. the cost per guest
d. Alice's age
Final answer:
The y-intercept represents the fixed cost of the party, while the slope signifies the variable cost per guest.
Explanation:
The y-intercept represents the one-time fee that Alice has to pay for her birthday party at the game center, which is $100.
The slope of $20 per guest indicates the additional cost incurred for each guest that attends the party.
In the equation y = 20x + 100, 'y' represents the total cost of the party, 'x' represents the number of guests, the y-intercept is the fixed cost, and the slope is the variable cost per guest.
from a 200 ft observation tower on the beach, a man sights a whale in difficulty. the angle of depression of the whale is 7 degrees.how far is the whale from the shoreline
The whale is 24.54 feet away from the shoreline.
Step-by-step explanation:
Step 1:
The man is 200 feet from the ground and the angle at which he sees the whale is 7°.
So a right-angled triangle can be formed using these measurements. The angle of the triangle is 7° while the opposite side of the triangle measures x feet while the adjacent side of the triangle measures 200 feet.
We need to find the opposites side's length of the triangle.
Step 2:
Since we have the length of the adjacent side and need to calculate the length of the opposite side we use the tan of the given angle.
The opposite side of the triangle = x feet.
[tex]\tan \theta = \frac{opposite side}{adjacent side} , tan (7) = 0.1227,[/tex]
[tex]tan(7)=\frac{x}{200}, x = 0.1227 (200) = 24.54 feet.[/tex]
So the whale is 24.54 feet away from the shoreline.
To find the distance of the whale from the shoreline, set up a right triangle, use the observation tower height as one side, and apply the tangent function to the 7-degree angle of depression.
Explanation:To determine how far the whale is from the shoreline, we can use trigonometry, specifically the tangent function, since we have the height of the observation tower and the angle of depression. The angle of elevation from the whale to the top of the tower would also be 7 degrees. By setting up a right triangle with the observation tower as one side, the line of sight to the whale as the hypotenuse, and the distance from the whale to the base of the tower (along the shore) as the other side, we can solve for the distance to the whale using the tangent function.
The formula to use is:
Distance to the whale (d) = Height of the tower (h) / tan(angle of depression)Step-by-step solution:
Convert the angle of depression to radians if necessary (for some calculators).Use the tangent of the angle of depression, which is 7 degrees.Calculate the distance by dividing the height of the tower by the tangent of the angle: d = 200 ft / tan(7 degrees).The distance to the whale from the base of the tower is approximately 1,630.49 feet from the shoreline (considering tan(7°) = 0.12278).
Someone help
Plzzz I need an answer