If all three dimensions of a pyramid are multiplied by a factor of 2, the volume of the pyramid increases by a factor of 8, meaning the new volume is eight times the original volume.
If all three dimensions of a pyramid are multiplied by a factor of 2, the new pyramid will be twice as long, twice as wide, and twice as tall as the original pyramid. Therefore, the volume of the new pyramid will be 2 x 2 x 2 = 8 times the volume of the original pyramid.
In other words, if V1 is the volume of the original pyramid, and V2 is the volume of the new pyramid, we can write:
V2 = 8 x V1
So the volume of the pyramid increases by a factor of 8.
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The graph shows the range of amounts of carbon dioxide (CO2) given off to produce one kilowatt/hour for different methods
of electricity production.
How does the amount of carbon dioxide given off by nuclear power compare with the amount of carbon dioxide produced by other
sources of energy?
A)
B)
C)
D)
Nuclear power produces the second lowest amount of carbon dioxide in
the graph.
Nuclear power produces the second highest amount of carbon dioxide in
the graph.
G
Nuclear power produces less carbon dioxide than all other sources of
power in the graph.
Nuclear power produces more carbon dioxide than all other sources of
power in the graph.
What would the final bill after applying the discount be?
Answer:
80.925
Step-by-step explanation:
124.5 x 0.35 = 43.575
124.5 - 43.575 = 80.925
in xyz, m∠x = (32x)° and m∠z = (6.5x)°. Write and solve an equation to find the measure of each angle
Finally, use the sum of interior angles equation again to find the measure of angle Y:
m∠Y = 180° - m∠X - m∠Z
Hello! To find the measure of each angle in triangle XYZ, we need to use the fact that the sum of the interior angles of a triangle is 180°. We are given that m∠X = (32x)° and m∠Z = (6.5x)°. Let's represent the measure of angle Y as m∠Y.
Now we can write an equation:
m∠X + m∠Y + m∠Z = 180°
(32x)° + m∠Y + (6.5x)° = 180°
We need to find the value of x and m∠Y. First, combine the x terms:
38.5x° + m∠Y = 180°
Now, we'll solve for x and then find m∠Y using the equation above. To find x, subtract m∠Y from both sides:
38.5x° = 180° - m∠Y
After finding the value of x, substitute it back into the expressions for m∠X and m∠Z to find the measures of angles X and Z.
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the altitude of a triangle is increasing at a rate of 3 centimeters/minute while the area of the triangle is increasing at a rate of 1 square centimeters/minute. at what rate is the base of the triangle changing when the altitude is 10 centimeters and the area is 94 square centimeters?
If the altitude of a triangle is increasing at a rate of 3 centimeters/minute while the area of the triangle is increasing at a rate of 1 square centimeter/minute. then the Base of the triangle is changing at a rate of 28.2 cm/min when the altitude is 10 cm and the area is 94 sq cm.
The given data is the altitude of a triangle is increasing at a rate of 3 centimeters/minute while the area of the triangle is increasing at a rate of 1 square centimeter/minute. then the rate of the base of the triangle changing when the altitude is 10 centimeters and the area is 94 square centimeters is calculated as,
Area of a triangle = 1/2 * base * height
The given area of the triangle is 94 square centimeters.
Area of the triangle = 1/2 * base * altitude
94 = 1/2 * b * 10b
= 18.8 centimeters
Differentiate w.r.t t 94 = 1/2 * b * hdb/dt
= -94 / 5 dA/dt
= 1 square centimeter/minute
= dh/dt * b / 2dh/dt
= (2 / b) * dA/dt
Substitute the values in the above equation,
3 = (2 / 18.8) * dA/dtdA/dt
= (3 * 18.8) / 2
= 28.2
square centimeters/minute Base of the triangle is changing at a rate of 28.2 cm/min when the altitude is 10 cm and the area is 94 sq cm.
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Find the y -intercept
of the parabola y = x2 + 2x + 10
Step-by-step explanation:
The y-axis is where x = 0 ....so the y-axis intercept occurs at x = o
put in '0' for 'x'
y = 0^2 + 2(0) + 10 <===== 10 is the y-axis intercept
I NEED HELP ON THIS ASAP!!
Therefore, the area of triangle XYZ is 2 square units.
What is area?Area is a measure of the size of a two-dimensional shape or surface. It is defined as the amount of space inside the boundary of a flat or planar figure, such as a triangle, square, rectangle, or circle. The unit of area is typically square units, such as square meters (m²), square feet (ft²), or square centimeters (cm²).
Here,
To determine the area of triangle XYZ with coordinates (6,1), (2,5), and (10,9), we can use the formula for the area of a triangle:
Area = (1/2) * base * height
where the base is any side of the triangle and the height is the perpendicular distance from the base to the opposite vertex.
Distance between (6,1) and (2,5):
= √((6 - 2)² + (1 - 5)²)
= √(20)
So, the base of the triangle is √(20).
We can use the formula for the distance between a point and a line to do this:
Distance from (10,9) to line passing through (6,1) and (2,5):
= |(10 - 6)(5 - 1) - (2 - 6)(9 - 1)| / √((5 - 1)² + (6 - 2)²)
= 4 / √(20)
So, the height of the triangle is 4 / √(20).
Now, we can plug in the values for the base and height into the formula for the area of a triangle:
Area = (1/2) * base * height
= (1/2) * √(20) * (4 / √(20))
= 2
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4 hundreds+6 hundreds=10 hundreds=
Answer: 2,000
Step-by-step explanation:
4 x 100 = 400
6 x 100= 600
400 + 600= 1,000
10 x 100= 1,000
1,000 + 1,000= 2,000
Can someone please help me ASAP it’s due today!! I will give brainliest if it’s done correctly
Answer:
HHH, HHT, HTH, HTT, THH, THT, TTH, TTT
Step-by-step explanation:
You have to construct a probability tree diagram.
Write an equation that the hanger diagram models. How can you use hanger diagram to find the value of X?
Answer: x=6
Step-by-step explanation:
Step 1: Add all the 4's together (20) and then you get 20+(5*x)=50
5x6=30+20=50.
2. (07.03)
What is the value of y in the equation 2(4y - 1) = 6? (4 points)
O
00
01
06
08
Answer:
The answer to your problem is, y = 1
Step-by-step explanation:
2(4y - 1) = 6, use distributive property: a(b - c) = ab - ac
8y - 2 = 6, add 2 to both sides
8y = 8, divide both sides by 8
Y = 1
Thus the answer to your problem is, y = 1
Answer:
1 is the answer
I took the test
What is the volume of the prisms below?
10 m
8 m
11 in.
12 in.
11 in.
11 cm
16 cm
8 cm
Answer:
Step-by-step explanation:129412515968569028414 m
one fourth of 120 is equal to 10% of what number
Answer:
3
Step-by-step explanation:
Please help my solve this
Answer:
The answer is Sin B
Step-by-step explanation:
I remember in 8th grade doing this
Help me pls fast!!!!!!!!
Answer:
Select the one at the lowest point on the right of the y-axis. This point has an x value (horizontal) of 1 and 1/2, with a y value (vertical) of -5.
Hoped this helped.
Please help due soon!
Answer:
Step-by-step explanation:
[tex]x^2=17^2-15^2[/tex] (Pythagoras Theorem)
[tex]x^2=64[/tex]
[tex]x=8[/tex]
15.1 central angles and inscribed angles an equilateral triangle is inscribed in a circle. how does the relationship between the measures of the inscribed angles and intercepted arcs help determine the measure of each angle of the triangle? what is the relationship between inscribed angles and central angles in a circle?
The intercepted arcs of the inscribed angle are in proportion to the inscribed angle itself. In other words, the larger the inscribed angle, the more significant the intercepted arc it cuts, and vice versa. So, in an equilateral triangle, each of the inscribed angles of the circle measures 60°, which is half of the central angle of 120° that intercepts the same arc.
The angle measure and intercepted arcs of inscribed angles in an equilateral triangle inscribed in a circle are related, and the relationship between inscribed angles and central angles in a circle is that the inscribed angles are half of the central angle. Let us have a more in-depth understanding of these two angles.An inscribed angle is an angle that has its vertex on the circle and is formed by two chords that intersect at that point. It is half of the central angle that intercepts the same arc.A central angle is an angle whose vertex is at the center of the circle, and the sides of the angle pass through any two points on the circumference of the circle.
For an equilateral triangle inscribed in a circle, each angle measures 60°, and the central angle measures 120°. So, each of the two inscribed angles measures half of the central angle, i.e., 60°.The relationship between inscribed angles and intercepted arcs.
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a rectangle storage container with an open top is to have a volume of 10 cubic meter. the length of its base is twice the width. material for the base cots $10 per square meter. material for the sides cost $6 per square meter. find the cost of materials for the cheapest such rectangular container.
The cost of materials for the cheapest container is 69.6 dollars.
Let's first express the dimensions of the rectangular container in terms of a single variable. Let the width of the base be x meters, then the length of the base is 2x meters, and the height of the container is 10/(2x^2) = 5/x^2 meters, since the volume of the container is 10 cubic meters.
The area of the base is x * 2x = 2x^2 square meters, so the cost of the base is 10 * 2x^2 = 20x^2 dollars.
The area of each side of the container is (2x)(5/x^2) = 10/x square meters, so the cost of the four sides is 4 * (10/x) * 6 = 240/x dollars.
The total cost C of the materials is the sum of the cost of the base and the cost of the sides:
C = 20x^2 + 240/x
To find the value of x that minimizes this expression, we can take its derivative with respect to x and set it equal to zero:
dC/dx = 40x - 240/x^2 = 0
Solving for x, we get:
x^3 = 6
x = (6)^(1/3)
Substituting this value of x back into the expression for C, we get:
C = 20(6)^(2/3) + 240/(6)^(1/3) ≈ 69.6 dollars
Therefore, the cost of materials for the cheapest rectangular container is approximately 69.6 dollars.
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an auto dealer has 5 different cars and 6 different trucks. how many ways are there to select two vehicles?
The number of possible ways to select two vehicles = 55
Let m represents the number of cars and n represents the number of trucks.
An auto dealer has 5 different cars and 6 different trucks.
This means that m = 5 and n = 6
so, the total number of vehicles (t) would be,
t = m + n
t = 5 + 6
t = 11
Let us assume that p represents the number of possible ways to select two vehicles.
We use the combination formula.
[tex]^{n}C_r=\frac{n!}{r!(n-r)!}[/tex]
here, n = 11 and r = 2
Using combination formula,
p = [tex]^{11}C_2[/tex]
p = [tex]\frac{11!}{2!\times (11-2)!}[/tex]
p = 55
Therefore, the number of possible ways = 55
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A bag contains 7 marbles: one each of red, orange, yellow, green, blue, violet, and white. A child randomly pulls 4 marbles from the bag. What is the probability that the marbles chosen are green, blue, red, and yellow? round
The probability of selecting green, blue, red, and yellow marbles from the bag is 1/35.
To find the probability of choosing specific marbles from the bag, we first need to find out the total number of ways in which four marbles can be selected from seven marbles.
The total number of ways in order to select 4 marbles from 7 marbles is given by the combination formula:
C(7,4) = 7!/(4!3!) = 35
There are 35 ways in which four marbles which will be selected from the bag. We need to find out the number of ways in which we can select green, blue, red, and yellow marbles.
We have only one way to select these specific four marbles from the bag. Number of ways to select green, blue, red, and yellow marbles is 1.
Probability of selecting green, blue, red, and yellow marbles:
P = (Number of ways to select green, blue, red, and yellow marbles) / (Total number of ways to select 4 marbles)
P = 1/35
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3 times a number is 28 less than the square of that number. Find the negative solution
Answer:
-b = √(3a+28)
Step-by-step explanation:
3a = -28 + b²
3a + 28 = b²
√(3a + 28) = √b²
negative solution:
-b = √(3a+28)
A boat is heading towards a lighthouse, where Jaxson is watching from a vertical distance of 103 feet above the water. Jaxson measures an angle of depression to the boat at point A to be 12 degrees.At some later time, Jaxson takes another measurement and finds the angle of depression to the boat (now at point B) to be 64 degrees. Find the distance from point A to point B. Round your answer to the nearest foot if necessary.
Answer:
We can use trigonometry to solve this problem. Let's call the distance from point A to the boat "x" and the distance from point B to the boat "y". Then we have:
In triangle AOC, tan(12) = OC / x
In triangle BOC, tan(64) = OC / y
We want to find the distance from point A to point B, which is the difference between x and y:
Distance AB = y - x
To solve for x and y, we need to eliminate OC. We can do this by setting the two expressions for OC equal to each other and solving for OC:
tan(12) = OC / x
OC = x tan(12)
tan(64) = OC / y
OC = y tan(64)
x tan(12) = y tan(64)
y = x tan(12) / tan(64)
Now we can substitute this expression for y into the equation for Distance AB:
Distance AB = y - x
Distance AB = x tan(12) / tan(64) - x
We can simplify this expression by factoring out an x:
Distance AB = x (tan(12) / tan(64) - 1)
Now we just need to plug in the values and calculate:
Distance AB = x (0.2174 - 1)
Distance AB = -0.7826 x
Since distance cannot be negative, we know that x > 0. Therefore, the boat is between point A and point B, and the distance from point A to point B is:
Distance AB = x (0.2174 - 1)
Distance AB = -0.7826 x
Distance AB ≈ 1.28 x
We don't know the actual value of x, but we can see that the distance from point A to point B is approximately 1.28 times the distance from point A to the boat when Jaxson measured the angle of depression to be 12 degrees.
Step-by-step explanation:
Answer:434
Step-by-step explanation:It’s correct
of the 75 entries in a costume contest, 31 entrants were dressed as heroes and 31 entrants were wearing a mask. if 15 entrants were dressed as heroes wearing a mask, how many entrants were neither dressed as heroes nor wearing a mask?
The 75 entries in a costume contest, 31 entrants were dressed as heroes and 31 entrants were wearing a mask. 8: No masks or costumes were worn by contestants .
What is Probability?The possibility of an event occurring is described by the concept of probability. In real life, we frequently have to make predictions about the future. We might know about the result of an occasion.
We declare that there is a possibility that the event will take place when this occurs.
In conclusion, probability can be used in a lot of great ways in business, entertainment, and this new area of artificial intelligence.
By simply dividing the total number of possible outcomes by the favorable number, the probability of an event can be calculated using the probability formula.
n(A)=31 and n(B) = 20 and n(AB) =9
50-42 = 8
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What is the surface area?
8 ft
8 ft
2 ft
square feet
The calculated surface area of the cuboid has a value of 192 square feet.
Calculating the surface area of the cuboidThe surface area of a cuboid is the sum of the areas of all six faces.
In this case, the dimensions of the cuboid are 8 ft by 8 ft by 2 ft. So we can calculate the surface area as follows:
The top and bottom faces each have an area of 8 ft x 8 ft = 64 sq ft.The front and back faces each have an area of 8 ft x 2 ft = 16 sq ft.The left and right faces each have an area of 8 ft x 2 ft = 16 sq ft.Therefore, the total surface area of the cuboid is:
= 2(64 sq ft) + 2(16 sq ft) + 2(16 sq ft)
= 128 sq ft + 32 sq ft + 32 sq ft
= 192 sq ft.
So the surface area of the given cuboid is 192 square feet.
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What is the result when the number 59 is increased by 6.7%?
Answer:
The value of the percentage increase = 6.7% × 59
The new value = 59 + The value of the percentage increase
Step-by-step explanation:
The new value =
59 + The value of the percentage increase =
59 + (6.7% × 59) =
59 + 6.7% × 59 =
(1 + 6.7%) × 59 =
(100% + 6.7%) × 59 =
106.7% × 59 =
106.7 ÷ 100 × 59 =
106.7 × 59 ÷ 100 =
6,295.3 ÷ 100 =
62.953 ≈
62.95
One day the farm stand sold 5/6 of the watermelons for $5.75 each. They still have 8 watermelons left. They took in how much money selling watermelons that day?
Therefore, they took in $43.10 selling watermelons that day.
Describe the dollar sign($)?
The dollar sign, also referred to as the peso sign, is a symbol that looks like a capital "S" crossed with one or two vertical strokes ($ or Cifro symbol depending on typeface), and it's used to denote the unit of many different currencies around the world, including the majority of currencies denominated in "pesos" and "dollars." The Portuguese word for the specifically double-barred Cifro symbol is cifro.
The sign is also present in a number of compound currency symbols, including those for the Nicaraguan córdoba (C$) and the Brazilian real (R$).
If they sold 5/6 of the watermelons, then they sold 8/6 of the watermelons. So, they sold 4/3 of the watermelons.
If they sold 4/3 of the watermelons for $5.75 each, then they sold each watermelon for $4.31.
They sold 5/6 of the watermelons for $5.75 each,
so they sold
5/6 × 4/3
= 20/18 = 10/9 of the watermelons for $4.31 each.
$4.31 * 10 = $43.10 That day.
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What is the decimal multiplier to increase by 6. 1%?
Answer: 1.061
Step-by-step explanation:
1). Based on conditions, formulate: 1+6.1%
2). Then convert to a decimal: 1.061
HELPPP ITS ABT ESTIMATION ILL MARK U BRAINLIST
Answer: the answer is A
reason: 224294 * 43 / 100 = around 96320
N On the return journey, the lorry leaves at 14 55 and arrives at the factory at 18 15. Calculate the time taken and the average speed of the lorry on the return journey.
After calculation, we know that the time taken by the lorry is 3 hours and 20 minutes.
What is time?Time is the ongoing progression of existence and things that happen in what seems to be an irrevocable order from the past, present, and forward into the future.
Military time starts with 0000, also known as "zero hundred hours" or just "zero hundred," at the stroke of midnight.
Then, multiply each hour by one hundred, such that 1 a.m. is equal to 0100 (zero one hundred) hours, 2 a.m. is equal to 0200 (zero two hundred) hours, and so on.
So, we need to calculate the time as follows:
Leaving time = 14:55
Arriving time = 18:15
Then,
14:55 to 15:15 = 20 minutes
Then, 15:15 to 18:15 = 3 hours
Then, the total time taken would be:
3 hours and 20 minutes
Therefore, after calculation, we know that the time taken by the lorry is 3 hours and 20 minutes.
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Complete question:
On the return journey, the lorry leaves at 14 55 and arrives at the factory at 18 15. Calculate the time taken.
A bank offers two different types of savings
account which pay interest as shown
below. Lewis wants to invest £3100 in one
of these accounts for 15 years.
a) Which account will pay Lewis more
interest after 15 years?
b) How much more interest will that
account pay?
Give your answer in pounds (£) to the
nearest 1p.
Account 1
Simple interest at a
rate of 7% per year
Account 2
Compound interest at a
rate of 5% per year
Answer:
a) Account 2 will pay Lewis more interest after 15 years because it pays compound interest, which means that the interest is calculated on both the initial deposit and the accumulated interest from previous years. On the other hand, Account 1 pays simple interest, which means that the interest is calculated only on the initial deposit.
b) To calculate the amount of interest paid by each account, we can use the following formulas:
For Account 1: I = P × r × t, where I is the interest earned, P is the principal (initial deposit), r is the annual interest rate as a decimal, and t is the time in years.
I = 3100 × 0.07 × 15 = £3255
For Account 2: A = P × (1 + r/n)^(n × t), where A is the amount of money at the end of the investment period, P is the principal, r is the annual interest rate as a decimal, n is the number of times the interest is compounded per year, and t is the time in years.
In this case, n = 1 (compounded annually), so the formula simplifies to:
A = 3100 × (1 + 0.05)^15 = £5569.62
The interest earned by Account 2 is the difference between the final amount and the initial deposit:
I = A - P = £5569.62 - £3100 = £2469.62
Therefore, Account 2 will pay £2469.62 - £3255 = -£785.38 less in interest than Account 1 after 15 years.
Step-by-step explanation:
cody was 165 cm 165cm165, start text, c, m, end text tall on the first day of school this year, which was 10 % 10, percent taller than he was on the first day of school last year. how tall was cody on the first day of school last year? cm cm
If Cody was 10 %, percent taller than he was on the first day of school last year then he was 150 cm tall on the first day of school last year.
To find out the height of Cody on the first day of school last year, we need to perform a calculation as follows:
Let's say their height of Cody on the first day of school last year is 'x'.
His height of Cody on the first day of school this year is 165 cm.
Cody is 10% taller than he was on the first day of school last year, so:
165 = x + (10% of x)
Simplifying this equation will give
165 = x + 0.1 x 165
= 1.1xx
= 150
Therefore, Cody was 150 cm tall on the first day of school last year.
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