The volume of the figure created is 98 cubic units.
Given that:
A triangle with coordinates (0,0), (0, 7), and (6,0) is rotated 360 degrees about the x-axis.
A cone is formed when a triangle rotates. Then the volume created is calculated as,
V = 1/3 x 7² x 6
V = 49 x 2
V = 98 cubic units
The volume is 98 cubic units.
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The vertices of a triangle are at (0,0), (8,8) and (4,12). What is the volume, in cubic units, of the figure created by rotating the triangle about y = x ?
The volume of the figure that was created by the triangle being rotated, would be 94. 83 units ³
How to find the volume ?When a triangle is rotated about y = x, a right circular cone is created. The formula is:
= π r² h / 3
We need to find the height and radius. The coordinates for the right circular cone are:
(0,0) - (0,0)
(8,8) - (8,8)
(4,12) - (12,4)
Using this, we find that the radius is 4 units. The height can be found by using any point such as ( 12, 4).
= √ ( ( 12 - 8) ² + ( 4 - 8 ) ²)
= 5. 66 units
The volume would therefore be:
= π x 4² x 5. 66 / 3
= 94. 83 units ³
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A rectangle has an area of 54 square inches and a length of 6 inches. What is the width, in inches, of the rectangle?
Answer:
width = 9 in
Step-by-step explanation:
Area = A = length x width = w x l
w = A/l = 54 in²/6 in = 9 in
Can someone help me with this maths questions
The solution is, the value of the angle & x is:
x = 43
43°, 51°, 86°
We have,
The sum of the angles is ...
x° + (x +8)° + 2x° = 180°
4x +8 = 180 . . . . . . . . . . . collect terms, divide by °
x +2 = 45 . . . . . . . . . . divide by 4
x = 43 . . . . . . . . . . subtract 2
x +8 = 51
2x = 86
The angles are 43°, 51°, 86°.
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complete question:
The sum of the angle measures of a triangle is 180°. Find the value of x. Then find the angle measures of the triangle.
This question here. Thank you in advance
Answer:
Step-by-step explanation:
211
welcome hun
Find the difference between 6c² +3c+9 and 3c-5.
To find the total number of people sitting in the full rows, Mandy multiplied 142 by 10 and 142 by 2 and then added the products. Does Mandy’s method make sense? Use what you know about multiplication to explain why or why not.
Mandy's solution makes sense since it entails multiplying the total number of persons in those entire rows (142) by the number of people in each row (ten).
How does multiplication apply?Similarly, multiplying the total number of people in the remaining seats (142) by the number of people in each row (2) yields the total number of people in the remaining seats. The total number of persons in the theater is calculated by adding these two components.
This is a viable use of multiplication's distributive property, in which we break down a multiplication issue into simpler products and then add them up. As a result, Mandy's approach is a viable method for determining the total number of people in the theater.
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A bag contains 3 black balls, 2 blue balls, and 3 green balls. A
random sample of 4 balls is selected. Given that x is the number of
black balls. y is the number of blue balls.
a) Find the joint probability function f(x, y)
b) Find the joint probability distribution of f(x, y)
The requreid, the joint probability function f(x, y) is:
f(0,0) = 3/14
f(0,1) = 9/28
f(0,2) = 3/28
f(1,0) = 9/28
f(1,1) = 9/28
f(2,0) = 3/14
f(2,1) = 3/14
f(3,0) = 1/14
To evaluate the joint probability function f(x, y), we need to determine the probability of selecting x black balls and y blue balls out of a sample of 4 balls. We can do this using the hypergeometric probability distribution formula:
f(x,y) = P(X = x, Y = y) = (C(3, x) * C(2, y) * C(3, 4-x-y)) / C(8, 4)
where C(n, k) represents the number of combinations of k items chosen from a set of n items.
Plugging in the values, we get:
f(0,0) = (C(3,0) * C(2,0) * C(3,4-0-0)) / C(8,4) = 3/14
f(0,1) = (C(3,0) * C(2,1) * C(3,4-0-1)) / C(8,4) = 9/28
f(0,2) = (C(3,0) * C(2,2) * C(3,4-0-2)) / C(8,4) = 3/28
f(1,0) = (C(3,1) * C(2,0) * C(3,4-1-0)) / C(8,4) = 9/28
f(1,1) = (C(3,1) * C(2,1) * C(3,4-1-1)) / C(8,4) = 9/28
f(2,0) = (C(3,2) * C(2,0) * C(3,4-2-0)) / C(8,4) = 3/14
f(2,1) = (C(3,2) * C(2,1) * C(3,4-2-1)) / C(8,4) = 3/14
f(3,0) = (C(3,3) * C(2,0) * C(3,4-3-0)) / C(8,4) = 1/14
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Claude Monet's Impression: Sunrise (1872) is considered a(n) _____painting because it was completed out-of-doors.
plein-air
alfresco
alla prima
sfumato
Answer:
the answer
Step-by-step explanation:
plein-air painting
-x^2(x-4)
simplify the equation
Answer:
-x³ + 4x²
Step-by-step explanation:
-x^2(x-4)
Distribute
-x³ + 4x²
So, the answer is -x³ + 4x²
If y= 2x +3, What is Y=(-5) + 3=
The value of the expression is -4
What is a function?
A function can simply be explained as an equation, law, rule or expression that tends to show the relationship between two distinct variables.
These variables are called the independent variables and dependent variables.
From the information given, we have the function as;
y= 2x +3
First, let's determine the function y(-5)
Substitute the values of x as -5 in the function;
y(-5) = 2(-5) + 3
expand the bracket
y(-5) = -10 + 3
Add the values
y(-5) = -7
Then, we get;
y(-5)+ 3
-7 + 3
-4
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Help me please! if a conditional statement is written in the form “If p then q”, how is the converse of the conditional statement is written?
A) If not q then p
B) If q then p
C) If not p then q
D) If not p then not q
The converse statement is of the conditional “If p then q” is the one in option B.
if q then p.
How can we identify the converse statement?For two given propositions p and q, a conditional statement is written as:
"if p, then q"
So, if the proposition p is true, also is the proposition q.
The converse statement just changes the order of the two propositions ( if the proposition q is true, also is the proposition p), then here start with q and end with p, so the converse statement is:
if q then p.
The correct option is B.
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5 ft:25 ft to fraction in its simplest form
Answer:
The answer is 1/5
Step-by-step explanation:
5ft:25ft=5ft/25ft=1/5
Answer:
1/2
Step-by-step explanation:
14. Sarah makes and sells candles. She spends $80 on supplies, and she sells
each candle for $6. Write an expression that represents her profit for
selling c candles.
Answer: hmm this question is based on 6-80 and if you calulate the sum and difference it is -74
The rim of a basketball hoop is 10 feet high. When Chase stretches his hand, it is 88 inches high. How many feet does Chase have to jump to be able to touch the rim?
Chase has to jump 2.67 feet to touch the rim.
The rim of the basketball hoop is 10 feet high, which is equal to 120 inches .
Chase's hand can reach 88 inches high.
To find out how many feet Chase has to jump to touch the rim, we need to subtract his reach from the height of the rim:
120 inches (height of rim) - 88 inches (Chase's reach) = 32 inches
So Chase has to jump 32 inches to touch the rim. To convert this to feet, we can divide by the number of inches in a foot:
32 inches ÷ 12 inches/foot = 2.67 feet
Therefore, Chase has to jump 2.67 feet to touch the rim.
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A container built for transatlantic shipping is constructed in the shape of a right rectangular prism. Its dimensions are 2 ft by 2 ft by 12.5 ft. If the container is entirely full and, on average, its contents weigh 0.22 pounds per cubic foot, find the total weight of the contents. Round your answer to the nearest pound if necessary.
Answer:
38.81 pounds
Step-by-step explanation:
Considering the definition of right rectangular prism and its volume, the total weight of the contents is 38.81 pounds.
Right rectangular prism
A right rectangular prism (or cuboid) is a polyhedron whose surface is formed by two equal and parallel rectangles called bases and by four lateral faces that are also parallel rectangles and equal two to two.
Volume of right rectangular prism
To calculate the volume of the rectangular prism, it is necessary to find the product of its dimensions, or of the three edges that converge at a certain vertex.
That is, to calculate the volume of a rectangular prism, multiply its 3 dimensions: length×width×height.
Volume of the container
In this case, you know that:
the dimensions of the container built are 7.5 ft by 11.5 ft by 3 ft.
the container is entirely full and, on average, its contents weigh 0.15 pounds per cubic foot.
So, the volume of the container is calculated as:
7.5 ft× 11.5 ft× 3 ft= 258.75 ft³
Then, the total weight of the contents is calculated as:
258.75 ft³× 0.15 pounds per cubic foot= 38.8125 pounds≅ 38.81 pounds
Finally, the total weight of the contents is 38.81 pounds.
help see photo on simple interest
The principal amount was £1260, and the annual interest rate is 5.5%.
Given that, Olivia gets £1606.50 and £1675.80 after 5 years and 6 years of investment in simple interest respectively.
SI = principal × rate × time / 100
So,
P + 5pr = £1606.50
P = £1606.50 - 5pr............(i)
P + 6pr = £1675.80
P = £1675.80 - 6pr.........(ii)
Therefore,
£1606.50 - 5pr = £1675.80 - 6pr
Pr = 69.3
Put the value of pr in eq(i)
P + 5(69.3) = 1606.50
P = 1606.5 - 346.5
P = 1260
Now,
(1260)r = 69.3
r = 0.055
The annual interest is 5.5%
Hence, the principal amount was £1260, and the annual interest rate is 5.5%.
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I just need the answer for the blank space, thank you.
At a drug research testing facility:
The population mean is 240 minutes.The population standard deviation is 40 minutes.The sample size is 10 people.Yes, it is given that the population distribution is normally distributed.The mean of the sample means will also be 240 minutes, which is the same as the population mean.The standard deviation of the sample means is (population standard deviation)/(sqrt(sample size)) = 40/(√(10)) = 12.65 minutes.What are the probabilities?To find the probability that the drug will wear off in less than 200 minutes:
The z-score is (200-240)/40 = -1.
Using a standard normal distribution table or calculator, P(z < -1) = 0.1587. Therefore, the requested probability is P(x < 200) = 0.1587.
To find the probability that the drug will wear off after 220 minutes:
The z-score is (220-240)/40 = -0.5.
Using a standard normal distribution table or calculator, P(z < -0.5) = 0.3085. Therefore, the requested probability is P(x > 220) = 0.3085.
To find the probability that the drug will wear off between 200 and 220 minutes:
Using the z-scores calculated above, find the area between them on the standard normal distribution. P(-1 < z < -0.5) = 0.1867.
Therefore, the requested probability is P(200 < x < 220) = 0.1867.
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find f(g(4)) and g(f(4)) given f(x)=2x-3 and g(x)=5x^2-4x+1
Answer:
g(f(4)) = 106.
Step-by-step explanation:
To find f(g(4)), we first need to find
g(4):g(4) = 5(4)^2 - 4(4) + 1 = 80 - 16 + 1 = 65
Now that we know g(4) is 65, we can find
f(g(4)):f(g(4)) = f(65) = 2(65) - 3 = 127
Therefore,
f(g(4)) = 127.
To find g(f(4)), we first need to find f(4):f(4) = 2(4) - 3 = 5
Now that we know f(4) is 5, we can find g(f(4)):
g(f(4)) = g(5) = 5(5)^2 - 4(5) + 1 = 125 - 20 + 1 = 106
Therefore, g(f(4)) = 106.
Gary has 24 quarters, 16 dimes, and 32 pennies. Write a ratio that compares the combined number of dimes and pennies to the number of quarters
suppose sin(A)=2/5 use the trig identity sin^2(A)+cos^2(A)=1 to find sin (A) in quadrant IV
The trigonometry identity value of sin(A) is -2/5
Solving the trigonometry identityFrom the question, we have the following parameters that can be used in our computation:
sin(A) = 2/5 sin^2(A) + cos^2(A) = 1 The angle A is in Quadrant IVThe value of sin(A) has already been given
However, because the angle A is in Quadrant IV, the value of the trigonometry identity would be negative (sine are negative in the 4th quadrants)
So, we have
sin(A) = -2/5
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You decide to make an investment in bonds. After much deliberation, you decide to purchase 10 State Farm bonds at a price of 99.40. These bonds have a 5% interest paid annually.
• How much did you pay for the 10 bonds (excluding commission)?
• How much interest will you receive each year from the bonds?
• What is your bond yield (to the nearest tenth percent)?
The bond yield is approximately 5.0% to the nearest tenth of a percent.
We have,
To find the total cost of the 10 State Farm bonds, we can multiply the price per bond by the number of bonds:
10 bonds x $99.40 per bond = $994.00
So, we paid $994.00 for the 10 State Farm bonds.
To calculate the amount of interest we will receive each year from the bonds, we can use the following formula:
Interest = Principal x Rate
where:
The principal is the amount invested in the bonds
Rate is the interest rate
In this case, our principal is $994.00 and our rate is 5%, or 0.05 as a decimal.
So, the annual interest we will receive from the bonds is:
Interest = $994.00 x 0.05 = $49.70
So,
We will receive $49.70 in interest each year from the bonds.
To calculate the bond yield, we need to use the following formula:
Bond yield = (Annual interest / Total cost) x 100%
In this case, the annual interest is $49.70 and the total cost is $994.00, so we can plug these values into the formula:
Bond yield = ($49.70 / $994.00) x 100% ≈ 5.0%
Therefore,
The bond yield is approximately 5.0% to the nearest tenth of a percent.
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Which expression is NOT equivalent to 24 + 12
Group of answer choices
3(8+4)
2(12+10)
2(12+6)
6(4+2)
The least squares regression line was found. Using technology, it was determined that the total sum of squares (SST) was 11654 and the sum of squares of regression (SSR) was 11405.0.
The value of R² (coefficient of determination) is 0.0214
We know that the formula for the coefficient of determination is,
R² = 1 - (SSR / SST)
where, R² is the coefficient of determination
SST is the total sum of squares
SSR is the sum of squares of regression
Here, the total sum of squares (SST) = 11654
and the sum of squares of regression (SSR) = 11405
Using above formula,
R² = 1 - (SSR / SST)
R² = 1 - (11405 / 11654 )
R² = 1 - 0.9786
R² = 0.0214
This is the required value.
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Find the complete question below.
Complete the ratio table please help will mark the first answer brainliest answer
The proportional relationship is complete as follows:
Input of 57 for an output of 438.Output of 584 for an input of 76.What is a proportional relationship?A proportional relationship is a type of relationship between two quantities in which they maintain a constant ratio to each other.
The equation that defines the proportional relationship is given as follows:
y = kx.
In which k is the constant of proportionality, representing the increase in the output variable y when the constant variable x is increased by one.
The constant for this problem is given as follows:
k = 146/19
k = 7.684.
Hence the equation is:
y = 7.684x.
The input for an output of 438 is given as follows:
7.684x = 438
x = 438/7.684
x = 57.
The output for an input of 76 is obtained as follows:
y = 7.684 x 76
y = 584.
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Determine whether the ordered pair is a solution to the given equation.
(−4, 24); y = −6x
Answer: Yes, (-4, 24) is a solution to the given equation.
Step-by-step explanation:
24 = -6(-4)
24 = 24
Pls help
The shape below contains a rectangle and four semi circles.
The perimeter of the shape is 13π
The area of the shape is 48.125π square units
What are the perimeter and area of the shapes?The perimeter of the shape is calculated as follows:
The perimeter of shape = perimeter of the two semicircles of radius 2 + perimeter of the two semicircles of radius 4.5The perimeter of a semicircle = πr
The perimeter of shape = 2 * π * 2 + 2 * π * 4.5
The perimeter of shape = 13π
The area of the shape = area of the two semicircles of radius 2 + area of the two semicircles of radius 4.5 + area of the rectangle
Area of semicircle = πr²/2
The area of the shape = π * 2²/2 + π(4.5)²/2 + 4 * 9
The area of the shape = 48.125π square units
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Cual es el volumen, en cm cúbicos, de un prisma rectangular con una altura de 3 cm, un ancho de 2 cm y una longitud de 18 cm ?
Answer:
El volumen en cm cúbicos es 108 cm cúbicos (o a la tercera potencia). La fórmula utilizada para encontrar el volumen es largo por ancho por alto.
(1/3)k=-4=7
what's k
The value of the variable k is 33
What are algebraic expressions?Algebraic expressions are simply described as the expressions that consist of variables, terms, coefficients, constants and factors.
These expressions also consist of certain mathematical operations, such as;
AdditionBracketSubtractionParenthesesMultiplicationFrom the information given, we have that;
(1/3)k - 4=7
collect the like terns
1/3k = 7 + 4
Add the values
1/3k = 11
cross multiply the values, we have;
k = 11(3)
Multiply the values
k = 33
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17. The diameter of a cylinder is 7 yards. The height
is 12 yards. What is the volume, in terms of and
to the nearest cubic yard, of the cylinder?.7.GR.2.3
The volume of the cylinder that has a diameter of 7 yards and a height of 12 yards is: 147π cubic yard.
What is the Volume of a Cylinder?The volume of a cylinder can be determined by applying the volume formula which is given as:
Volume (V) = πr²h,
where "r" is the radius of the cylinder
"h" is the height of the cylinder
π is a constant
Given the following:
Diameter of cylinder = 7 yards, thus, radius (r) = 7/2 = 3.5 yards
Height (h) = 12 yards
Plug in the values:
Volume of the cylinder = π * 3.5² * 12 = 147π cubic yard.
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Lesson 7 Practice Problems
(1.A crew has paved of 3/4 a mile of road. If they have completed 50% of the work, how
long is the road they are paving? Where did the 2 come from