The volume of the solid will be 32/7 √3.
How to calculate the volumeSince base of a solid whose cross-sections is perpendicular to the w-axis are equilateral triangles
Now base of triangle. is f(x) = x³ and the Area of Equilateral Triangle is ✓3/4 base²
The volume of the solid will be:
= ✓3/4 (x^7/7)²
= ✓3/4 (128/7)
= 32/7 √3
Therefore, the volume of the solid will be 32/7 √3.
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A student at a local high school claimed that three-
quarters of 17-year-old students in her high school had
their driver's licenses. To test this claim, a friend of hers
sent an email survey to 45 of the 17-year-olds in her
school, and 34 of those students had their driver's
license. The computer output shows the significance test
and a 95% confidence interval based on the survey data.
Test and Cl for One Proportion
Test of p = 0. 75 vs p +0. 75
Sample X N Sample p 95% CI Z-Value P-Value
1
34 45 0. 755556 (0. 6300, 0. 086 0. 9315
0. 8811)
Based on the computer output, is there convincing
evidence that p, the true proportion of 17-year olds at this
high school with driver's licenses, is not 0. 75?
O No, the P-value of 0. 9315 is very large.
Yes, the P-value of 0. 9315 is very large.
O Yes, the 95% confidence interval contains 0. 75.
No, the incorrect significance test was performed.
The alternative hypothesis should be p > 0. 75.
No, the incorrect significance test was performed.
The alternative hypothesis should be p<0. 75.
The results of the survey suggest that the student's claim of three-quarters of 17-year-olds having their driver's licenses may be accurate, but further research would be necessary to confirm this with a larger and more representative sample.
Based on the computer output, there is no convincing evidence that the true proportion of 17-year-olds at this high school with driver's licenses is not 0.75. This is because the P-value of 0.9315 is very large, indicating that the results of the survey are not statistically significant. Additionally, the 95% confidence interval for the sample proportion of 0.755556 includes 0.75, further supporting the claim that the true proportion may be close to 0.75.
It is important to note that the correct significance test was performed, testing the null hypothesis that p = 0.75 against the alternative hypothesis that p ≠ 0.75. This is the appropriate test when the claim being tested is about a specific value of the proportion, as in this case. The alternative hypothesis being p > 0.75 or p < 0.75 would be incorrect, as it assumes a one-sided test rather than a two-sided test.
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Latoya has a bag with 8 balls numbered 1 through 8. She is playing a game of chance. This game is this: Latoya chooses one ball from the bag at random. She wins $1 if the number 1 is selected, $2 if the number 2 is selected, $3 if the number 3 is selected, $4 if the number 4 is selected, and $5 if the number 5 is selected. She loses $1 if 6, 7, or 8 is selected.
(a) Find the expected value of playing the game. Dollars
(b) What can Latoya expect in the long run, after playing the game many times? (She replaces the ball in the bag each time. ) Latoya can expect to gain money. She can expect to win dollars per selection. Latoya can expect to lose money. She can expect to lose dollars per selection. Latoya can expect to break even (neither gain nor lose money)
Latoya may experience some fluctuations in her winnings and losses in the short run, in the long run, her average winnings will approach $0.50 per selection.
What is the expected value of playing the game and what Latoya can expect after playing the game many times?
(a) To find the expected value of playing the game, we need to multiply the amount that Latoya can win or lose by the probability of each outcome, and then add up the results. Let p(i) be the probability of selecting the ball with the number i. Since there are 8 balls in total and each ball is equally likely to be selected, we have:
p(i) = 1/8 for i = 1, 2, ..., 8
Now we can calculate the expected value:
E(X) = ∑[i=1 to 5] (i * p(i)) + ∑[i=6 to 8] (-1 * p(i))
= (1/8)(1) + (1/8)(2) + (1/8)(3) + (1/8)(4) + (1/8)(5)
- (1/8)(1) - (1/8)(1) - (1/8)(1)
= 0.5
Therefore, the expected value of playing the game is $0.50.
(b) In the long run, after playing the game many times, Latoya can expect to break even (neither gain nor lose money) on average per selection. This means that over a large number of selections, she can expect to win some money on some selections and lose some money on others, but on average, her total winnings and losses will balance out to zero.
To see why this is the case, consider that the expected value of a single selection is $0.50. If Latoya plays the game many times, the law of large numbers tells us that the average winnings per selection will converge to the expected value of $0.50. So even though Latoya may experience some fluctuations in her winnings and losses in the short run, in the long run, her average winnings will approach $0.50 per selection.
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When you get home from school, there is 7/8 of a pizza left. You eat 1/2 of it. How much pizza is left over?
Answer: 3/8
Step-by-step explanation:
7/8-1/2
Find common denominator which is 8 and you get that from 1/2 by multiplying 4 on the top and bottom and so you wind up with 4/8 and 7/8-4/8 is 3/8
70°
is the same as
radians. Round your answer to the nearest thousandth.
70 degrees to radian is 1.22 radian.
How to convert from degree to radian?In mathematics,, both degree and radian represent the measure of an angle. One complete anticlockwise revolution can be represented by 2π (in radians) or 360° (in degrees).
Therefore,
360 degrees = 2π radian
where
π = 3.14Therefore, let's find 70 degrees in radian.
Hence,
360 degrees = 2π radian
70 degrees = ?
cross multiply
angle in radian = 70 × 2π / 360
angle in radian = 140π / 360
angle in radian = 0.38888888888 × 3.14
angle in radian = 1.22 radian
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What is the domain and range of g(x)=-|x|
Answer:
Step-by-step explanation
Domain :
x
>
4
, in interval notation :
(
4
,
∞
)
Range:
g
(
x
)
∈
R
, in interval notation :
(
−
∞
,
∞
)
Explanation:
g
(
x
)
=
ln
(
x
−
4
)
;
(
x
−
4
)
>
0
or
x
>
4
Domain :
x
>
4
, in interval notation :
(
4
,
∞
)
Range: Output may be any real number.
Range:
g
(
x
)
∈
R
, in interval notation :
(
−
∞
,
∞
)
graph{ln(x-4) [-20, 20, -10, 10]} [Ans] x>4
Answer:
Step-by-step explanation:
The Domain of g(x) = -|x| is all real numbers (no restrictions on what values x can take).
The Range of g(x) = -|x| is all real numbers less than or equal to zero. Absolute value of any real number is always greater than or equal to zero, and multiplying by a negative sign, that flips the sign of the result. So, g(x) will always be less than or equal to zero.
Domain: (-∞, ∞), {x|x ∈ R}
Range: (-∞, 0), {y ≤ 0}
at the three points 1. Sketch the vector field 7 (x,y) = xî + xyî (1,3), (-1,2), (3,-2)
The vector field for 7 (x,y) = xî + xyî (1,3), (-1,2), (3,-2) can be plotted with arrows with magnitude 4 at point (1,3), magnitude 3 at point (-1,2), and magnitude 3 at point (3,-2).
The given vector field 7 (x,y) = xî + xyî (1,3), (-1,2), (3,-2) can be drawn by plotting arrows at each point (x,y) in the plane with the direction and magnitude of each arrow presented by the vector
7 (x,y) = xî + xyî.
over point (1,3),
the vector is 7(1,3) = 1î + 3î = 4î.
over point (-1,2),
the vector is 7(-1,2) = -1î - 2î = -3î.
Over point (3,-2),
the vector is 7(3,-2) = 3î - 6î = -3î.
The vector field for 7 (x,y) = xî + xyî (1,3), (-1,2), (3,-2) can be plotted with arrows with magnitude 4 at point (1,3), magnitude 3 at point (-1,2), and magnitude 3 at point (3,-2).
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DON'T GIVE FAKE ANSWERS OR I'LL REPORT!
What is the area of a sector with a central angle of 45° and a diameter of 5. 6 in. ? Use 3. 14 for π and round your final answer to the nearest hundredth. Enter your answer as a decimal in the box. What is the area of a sector with a central angle of 120° and a radius of 18. 4 m? Use 3. 14 for π and round your final answer to the nearest hundredth. Enter your answer as a decimal in the box
The area of a sector with a central angle of 45° and a diameter of 5.6 in. is 1.23 square inches.
To see why, you can use the formula for the area of a sector, which is:
A = (θ/360) x π x r^2
where θ is the central angle in degrees, r is the radius, and π is approximately 3.14.
First, you need to find the radius of the sector, which is half of the diameter:
r = d/2 = 5.6/2 = 2.8 in.
Next, you can plug in the values for θ and r into the formula:
A = (45/360) x 3.14 x 2.8^2 = 1.23 square inches
Therefore, the area of the sector is 1.23 square inches.
The area of a sector with a central angle of 120° and a radius of 18.4 m is 1908.57 square meters.
To see why, you can use the same formula for the area of a sector:
A = (θ/360) x π x r^2
First, you need to convert the radius from meters to centimeters, since π is in terms of centimeters:
r = 18.4 m x 100 cm/m = 1840 cm
Next, you can plug in the values for θ and r into the formula:
A = (120/360) x 3.14 x 1840^2 = 1908.57 square meters
Therefore, the area of the sector is 1908.57 square meters.
April’s grandmother bought her a set of Russian dolls from St. Petersburg. The dolls stack inside of each other and are similar to each other. The diameters of the two smallest dolls are 1. 9 cm and 2. 85 cm. The scale factor is the same from one doll to the next. April estimates that the volume of the smallest doll is 7 cm^ 3. Determine the volume of the 4th doll
The volume of the 4th doll is approximately [tex]130.1 cm^3.[/tex]
The diameter of the smallest doll is 1.9 cm, so its radius is 0.95 cm (half of the diameter).
Similarly, the radius of the second smallest doll is (2.85/2) = 1.425 cm.
Since the scale factor is the same from one doll to the next, the ratio of the radius of the second smallest doll to the radius of the smallest doll is:
1.425 cm / 0.95 cm = 1.5
Similarly, the ratio of the radius of the third smallest doll to the radius of the second smallest doll is also 1.5.
Using this pattern, we can find the radius of the 4th doll as:
Radius of 4th doll = 1.5 × (Radius of 3rd doll) = 1.5 × 2.1375 cm = 3.2063 cm (rounded to 4 decimal places)
The volume of the 4th doll can then be calculated as:
Volume of 4th doll = (4/3) × π ×[tex](Radius of 4th doll)^3[/tex]
= (4/3) × π × [tex](3.2063 cm)^3[/tex]
≈ [tex]130.1 cm^3[/tex]
Therefore, the volume of the 4th doll is approximately [tex]130.1 cm^3.[/tex]
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Write an equation to show the total length of the bandages if they are placed end-to-end
There is an image attached btw
We can see here that an equation to show the total length of the bandages if they are placed end-to-end is:
([tex]1\frac{1}{4}[/tex] × [tex]2) + (1\frac{2}{4}[/tex] × 1) + ([tex]1\frac{3}{4}[/tex] × 3) + (2 × 4) + (3 × 6) = [tex]35\frac{1}{4}[/tex]
What is an equation?An equation in mathematics is a claim made regarding the equality of two expressions. Normally, it has two sides that are separated by an equal sign (=).
Variables, constants, and mathematical operations including addition, subtraction, multiplication, division, exponentiation, and more can be used on each side of the equation.
We can see here that the above answer is correct because on the number line:
[tex]1\frac{1}{4}[/tex] has 2 Xs on it.
[tex]1\frac{2}{4}[/tex] has 1 X on it.
[tex]1\frac{3}{4}[/tex] has 3 Xs on it.
2 has 4 Xs on it.
3 has 6 Xs on it.
And multiplying and adding the variables, we arrived at: [tex]35\frac{1}{4}[/tex]
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300 high school students were asked how many hours of tv they watch per day. the mean was 2 hours, with a standard deviation of 0. 5. using a 90% confidence level, calculate the maximum error of estimate.
0. 27%
5. 66%
7. 43%
4. 75%
The maximum error of estimate is 4.75%.
To calculate the maximum error of estimate for the given problem, we will use the formula for margin of error:
Margin of Error = Z-score * (Standard Deviation / √n)
Where:
- Z-score corresponds to the 90% confidence level, which is 1.645
- Standard Deviation is 0.5 hours
- n is the sample size, which is 300 students
Margin of Error = 1.645 * (0.5 / √300) ≈ 0.0475
To express this as a percentage, multiply by 100:
0.0475 * 100 ≈ 4.75%
Thus, the maximum error of estimate with a 90% confidence level is 4.75%.
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Jim is building a deck for his family to enjoy. Because of a big bay window that juts out next to the deck, he has to build an angled section for the steps going down to the yard. The section will be a parallelogram. Assuming that he cannot accurately prove that any two sides are parallel, how can he be assured that he has an actual parallelogram? Identify the theorem that he will use and how he will use it
By applying the Consecutive Angles Theorem, Jim can confirm that the angled section for the steps is indeed a parallelogram, even without accurately proving that any two sides are parallel.
Jim building a deck with an angled section in the shape of a parallelogram. To be assured that he has an actual parallelogram, Jim can use the Consecutive Angles Theorem.
This theorem states that if the consecutive angles of a quadrilateral are supplementary (add up to 180 degrees), then the quadrilateral is a parallelogram.
To use the Consecutive Angles Theorem, Jim should follow these steps:
1. Measure the four angles of the quadrilateral he has created for the angled section of the deck.
2. Check if the consecutive angles are supplementary (i.e., the sum of each pair of consecutive angles is equal to 180 degrees).
3. If all consecutive angles are supplementary, he can be assured that the quadrilateral is a parallelogram.
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Jerry has the following assets a house with equity of $15. 0. A car with equity of $2. 500, and household goods worth $6,000 (no single item over $400). He also has tools worth $5. 800 that he needs for his business. Using the federal list, the total amount of exemptions that Jerry would be allowed is $____. 0. Using the state list, the total amount of exemptions that jerry would be allowed is $____. 0.
00. Using the state list the total amount of exemptions that Jerry would be allowed is s
. 0. The state
list will be more favorable for him
tially Connect
Using the federal list, the total amount of exemptions that Jerry would be allowed is $25,150.
Jerry's assets include a house with equity of $15,000, a car with equity of $2,500, household goods worth $6,000 (no single item over $400), and tools worth $5,800 that he needs for his business.
Using the state list, the total amount of exemptions that Jerry would be allowed varies depending on the state in which he resides. Without knowing the state, it is impossible to provide an accurate answer. However, it is worth noting that the state list is often more favorable for individuals than the federal list.
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Mathetmatics
Class - 6 question
Topic - Roman Numerals :-
Question:-
The number VCX is incorrect. Explain why?
Answer as fast as you can. I'l mark you as brainliest
In Roman Numerals, smaller numbers can be subtracted from larger numbers, but only to a certain extent.
The number VCX is incorrect in Roman Numerals because V (5) cannot be subtracted from X (10) to make 5, and C (100) cannot be subtracted from X (10) to make 90.
In Roman Numerals, smaller numbers can be subtracted from larger numbers, but only to a certain extent.
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Ben makes orange paint by mixing red, yellow and white paint in the ratio 20 : 16 : 1. 5. How much of each colour does he need to make 1. 5 litres of orange paint?
Using the ratio, we solve and get, Ben needs 0.8 litres of red paint, 0.64 litres of yellow paint, and 0.06 litres of white paint to make 1.5 litres of orange paint.
To make 1.5 litres of orange paint, Ben needs to mix the red, yellow, and white paint in the ratio of 20 : 16 : 1.5.
To calculate the amount of each color needed, you first need to find the total number of parts in the ratio.
The total number of parts is 20 + 16 + 1.5 = 37.5.
Next, you can calculate the amount of each color needed by dividing 1.5 litres by the total number of parts in the ratio, and then multiplying by the respective parts for each color.
So, the amount of red paint needed is:
(1.5/37.5) x 20 = 0.8 litres
The amount of yellow paint needed is:
(1.5/37.5) x 16 = 0.64 litres
And the amount of white paint needed is:
(1.5/37.5) x 1.5 = 0.06 litres
Therefore, Ben needs 0.8 litres of red paint, 0.64 litres of yellow paint, and 0.06 litres of white paint to make 1.5 litres of orange paint.
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2 Liam bought too much fencing and had 26 feet of it left over. He and his brother
decided to make a rectangle-shaped garden patch for their little sister. They wanted
to use all the extra fencing to outline her garden patch. What could be the dimen-
sions of the patch they make for their sister? (Use only whole numbers of feet. )
Show all your work.
The perimeter is indeed 26 feet, which means they have used all the extra fencing.
Let's start by assuming that the length and width of the garden patch are whole numbers of feet, since we are asked to use only whole numbers.
Let's call the length of the garden patch "L" and the width "W".
We know that Liam has 26 feet of fencing left over. This fencing will be used to make the perimeter of the garden patch, which is given by:
Perimeter = 2L + 2W
We can substitute the value of the perimeter with the amount of fencing that Liam has:
26 = 2L + 2W
Simplifying this equation, we get:
13 = L + W
Since we want to use all the extra fencing, we know that the perimeter of the garden patch must be 26 feet. We can use this information to write another equation:
Perimeter = 2L + 2W = 26
We can substitute the value of 13 for L + W in this equation:
2L + 2W = 26
2L + 2(13-L) = 26
2L + 26 - 2L = 26
26 = 26
This equation is true, which means that our assumption that L and W are whole numbers is correct.
Therefore, the dimensions of the garden patch that Liam and his brother can make for their sister are 6 feet by 7 feet.
To check, we can calculate the perimeter:
Perimeter = 2L + 2W = 2(6) + 2(7) = 12 + 14 = 26
So the perimeter is indeed 26 feet, which means they have used all the extra fencing.
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PLS HELP ME FAST!!!
Write an expression for the sequence of operations described below. Subtract 5 from 7, then divide 3 by the result.Type x if you want to use a multiplication sign. Type / if you want to use a division sign. Do not simplify any part of the expression.
Answer:
3 / (7-5)
Step-by-step explanation:
"Subtract 5 from 7"
When you're subtracting from something, the reverse the order of the numbers. So, the expression here would be "7 - 5"
"Then, divide 3 by the result."
Here, you're dividing 3 by the result, so the 3 must be in the numerator (on top of the fraction), and the "result from the previous step must be in the denominator (on the bottom of the fraction). So, the expression here would be "3 / result"
Since order of operations forces division to happen before subtraction, we'll need parentheses around the first result to force the subtraction to happen first, as instructed.
So, the final expression would be "3 / (7-5)"
Solve the following Exact Inexact Differential Equation. If it is inexact, then
solve it by finding the Integrating Factor.
(3xy + y^2) dx + (x^2 + xy) dy = 0
The general solution to the differential equation is, |3x^4/(y(x+y))|x + |x^3| ln|y| + |x^3| ln|x+y| + h(x) = C.
The partial derivative of (3xy + y^2) with respect to y is 6xy + 2y, and the partial derivative of (x^2 + xy) with respect to x is 2x + y. Since these are not equal, the differential equation is not exact.
To make it exact, we need to find an integrating factor μ(x, y) such that μ(x, y)(3xy + y^2) dx + μ(x, y)(x^2 + xy) dy = 0 is exact. We can find μ(x, y) by using the formula:
μ(x, y) = e^(∫(∂M/∂y - ∂N/∂x)/N dx)
where M = 3xy + y^2 and N = x^2 + xy. We have:
(∂M/∂y - ∂N/∂x)/N = (6xy + 2y - 2x - y)/(x^2 + xy) = (6xy - x - y)/(x^2 + xy)
We can now find the integrating factor μ(x, y) by integrating this expression with respect to x:
μ(x, y) = e^(∫(6xy - x - y)/(x^2 + xy) dx) = e^(3ln|x| - ln|y| - ln|x+y| + C) = e^(ln|x^3/(y(x+y))| + C) = |x^3/(y(x+y))|e^C
where C is the constant of integration.
Now we multiply the original differential equation by the integrating factor μ(x, y) to obtain:
|3x^4/(y(x+y))| dx + |x^3/(y(x+y))| dy = 0
This is now an exact differential equation, and we can find its solution by integrating with respect to x or y. Integrating with respect to x, we get:
|3x^4/(y(x+y))|x + g(y) = C
where g(y) is the constant of integration. To find g(y), we integrate the coefficient of dy:
g(y) = ∫|x^3/(y(x+y))| dy = |x^3| ln|y| + |x^3| ln|x+y| + h(x)
where h(x) is another constant of integration. Substituting g(y) back into the solution, we have:
|3x^4/(y(x+y))|x + |x^3| ln|y| + |x^3| ln|x+y| + h(x) = C
This is the general solution to the differential equation.
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Unit 8: right triangles & trigonometry homework 4 trigonometry finding sides and angles
To find the length of the opposite side and the adjacent side, we can use the ratios of the sides in a 30-60-90 degree triangle.
In a right triangle with a hypotenuse and acute angle given what is the length of the opposite side and the adjacent side?The ratio of the opposite side to the hypotenuse is 1:2, and the ratio of the adjacent side to the hypotenuse is √3:2.
Using these ratios, we can find the length of the opposite side and the adjacent side as follows:
Opposite side = 1/2 x hypotenuse = 1/2 x 10 = 5 units
Adjacent side = √3/2 x hypotenuse = √3/2 x 10 = 5√3 units
Given a right triangle with an acute angle of 60 degrees and an adjacent side of 5 units, find the length of the hypotenuse and the opposite side.
To find the length of the hypotenuse and the opposite side, we can use the ratios of the sides in a 30-60-90 degree triangle.
The ratio of the hypotenuse to the adjacent side is 2:1, and the ratio of the opposite side to the adjacent side is √3:1.
Using these ratios, we can find the length of the hypotenuse and the opposite side as follows:
Hypotenuse = 2 x adjacent side = 2 x 5 = 10 units
Opposite side = √3 x adjacent side = √3 x 5 = 5√3 units
Given a right triangle with an acute angle of 45 degrees and an opposite side of 7 units, find the length of the hypotenuse and the adjacent side.
To find the length of the hypotenuse and the adjacent side, we can use the ratios of the sides in a 45-45-90 degree triangle.
In this type of triangle, the opposite side and the adjacent side are equal, and the hypotenuse is √2 times the length of the legs.
Using these ratios, we can find the length of the hypotenuse and the adjacent side as follows:
Opposite side = Adjacent side = 7 units
Hypotenuse = √2 x opposite side = √2 x 7 = 7√2 units
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3. James has a box shaped as a rectangular prism. The container is 8 inches long, 4 inches wide, and 5 inches high. (a) Here is a model of the box. It is filled with unit cubes. Find the volume of the box using the unit cubes. Explain your answer. Answer: 160 cubic inches (b) Find the volume of the box using the formula. Answer: (c) Find the volume of the box using the formula. Answer: (d) How does using the volume formulas to find the volume of a rectangular prism compare to counting unit cubes? Compare your answers in parts (b) and (c) your answer in part (a) to answer the question. Answer:
The volume of the box is 160 cubic inches. Using the volume of a rectangular prism formula the volume of the box is 160 cubic inches. Using another formula base area times height, the area is the same.
The volume of James' rectangular prism box can be calculated using both unit cubes and a formula. Part (a) involves counting the unit cubes in the model and multiplying the number of cubes by their volume, which is 1 cubic inch. In this case, there are 160 unit cubes, so the volume of the box is 160 cubic inches.
Part (b) involves using the formula for volume of a rectangular prism, which is length times width times height. Plugging in the given dimensions, we get 8 x 4 x 5 = 160 cubic inches, which is the same as the answer in part (a) using unit cubes.
Part (c) involves using a different formula for volume, which is base area times height. In this case, the base of the rectangular prism is a rectangle with length 8 inches and width 4 inches, so the base area is 8 x 4 = 32 square inches. Multiplying by the height of 5 inches, we get 160 cubic inches, which is again the same as the answers in parts (a) and (b).
Using the volume formulas is much quicker and more efficient than counting unit cubes, especially for larger boxes. However, counting unit cubes can provide a more concrete visual representation of the volume and can be helpful for students who are just learning about volume. In this case, the answers obtained using the formulas were the same as the answer obtained by counting unit cubes, which reinforces the accuracy of the formulas.
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Find the solution to the linear system using Gaussian elimination x+2y=5 2x+3y=6
The solution to the system of linear equations is (x, y) = (13, -4).
Find the solution using Gaussian elimination x+2y=5 2x+3y=6To solve the system of linear equations using Gaussian elimination, we need to eliminate one variable from one of the equations. Here, we can eliminate x from the second equation by subtracting twice the first equation from the second equation:
x + 2y = 5 (equation 1)
2x + 3y = 6 (equation 2)
--------------
-2x - 4y = -10 (2 * equation 1)
y = -4
Now, we can substitute the value of y into the first equation to solve for x:
x + 2(-4) = 5
x - 8 = 5
x = 13
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Which statement could be made based on the diagram below?
A) m∠3 + m∠6 = 90
B) ∠3 = ∠6
C) ∠3 = ∠5
D) m∠4 + m∠5 = 180
Two similar cylinders have heights 6cm and 30cm. The volume of the smaller cylinder is 90cm3. What is the volume of the larger cylinder?
Answer:
Step-by-step explanation:
Since the two cylinders are similar, their corresponding dimensions (radius and height) are proportional. Let the radius of the smaller cylinder be r.
Then, we can write:
r / 6 = R / 30
where R is the radius of the larger cylinder.
Simplifying this equation, we get:
R = 5r
Now, we can use the formula for the volume of a cylinder to find the volume of the larger cylinder:
Volume of smaller cylinder = πr^2h = 90 cm^3
Volume of larger cylinder = πR^2H = π(5r)^2(30) = 750πr^2 cm^3
Substituting R = 5r, we get:
Volume of larger cylinder = 750πr^2 cm^3
Therefore, the volume of the larger cylinder is 750π times the volume of the smaller cylinder:
Volume of larger cylinder = 750π(90 cm^3) = 67,500π/ cm^3 (approx. 211,239.74 cm^3 rounded to five decimal places).
Find the equation of the axis of
symmetry for this function.
f(x) = -4x² + 8x - 28
Hint: To find the axis of symmetry, use the equation: x =
FR
2a
Simplify your answer completely. Enter
the number that belongs in the green box.
x = [?]
Enter
The equation of the axis of symmetry for the given function is x = 1.
To find the equation of the axis of symmetry for the function f(x) = -4x² + 8x - 28, we can use the formula:
x = -b / (2a)
where "a" and "b" are coefficients in the quadratic equation ax² + bx + c.
In this case, a = -4 and b = 8. Plugging these values into the formula, we get:
x = -8 / (2*(-4))
x = -8 / (-8)
x = 1.
The axis of symmetry for a quadratic function in the form of [tex]f(x) = ax^2 + bx + c[/tex] can be found using the formula x = -b / (2a).
In the case of the given quadratic function f(x) = -4x² + 8x - 28, the coefficient of [tex]x^2[/tex] is a = -4 and the coefficient of x is b = 8.
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A factory makes light fixtures with right regular hexagonal prisms where the edge of a hexagonal base measures 4 centimeters and the lengths of the prisms vary. It costs $0. 04 per square centimeter to fabricate the prisms and the factory owner has set a limit of $11 per prism. What is the maximum length of each prism?
The maximum surface area for a prism is.
So, the maximum length for a prism is cm
The maximum length of each prism is equal to 7.99 centimeter.
Maximum surface area = 275 square centimeter (cm²).
Given, Light fixtures of regular hexagonal prism .
Determine the maximum surface area of this regular hexagonal prism by using this mathematical expression:
Maximum surface area (quantity) = Cost/unit price
Maximum surface area (quantity) = $11/$0.04
Maximum surface area (quantity) = 275 square centimeter (cm²).
Mathematically, the surface area of a regular hexagonal prism can be calculated by using this formula:
[tex]A = 6al + 3\sqrt{3} a^2[/tex]
Where:
A represents the surface area of a regular hexagonal prism.
a represents the edge length (apothem) of a regular hexagonal prism.
l represents the length of a regular hexagonal prism.
Substituting the given parameters into the formula, we have;
[tex]275 = 6 \times 4l + (3\sqrt{3} \times 4^2)[/tex]
[tex]275 = 24l + 48\sqrt{3} \\24l = 275 - 48\sqrt{3}\\ 24l = 191.8616\\l = 191.8616/24[/tex]
Length, l = 7.99 centimeter.
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URGENT !Tricia has 10 quarters, 17 dimes, 40 nickels, and 15 pennies.
How much money does Tricia have in all?
O A. $5. 15
B. $5. 85
OC. $6. 20
D. $6. 35
Tricia has a total of $6.35. The answer is D.
Tricia has 10 quarters, which is equivalent to $2.50 (since 1 quarter is $0.25).
She also has 17 dimes, which is equivalent to $1.70 (since 1 dime is $0.10).
Tricia has 40 nickels, which is equivalent to $2.00 (since 1 nickel is $0.05).
Finally, she has 15 pennies, which is equivalent to $0.15 (since 1 penny is $0.01).
To find the total amount of money Tricia has, we can add up the values of each coin:
$2.50 + $1.70 + $2.00 + $0.15 = $6.35
Therefore, Tricia has a total of $6.35. The answer is option D.
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is root 9 /25 a rational number?
Answer:
Yes
Step-by-step explanation:
9/25
√9/√25 = 3/5 = 0.6
so it is a rational number because it has an integer as a denominator also because the decimal is not reoccurring
Answer: Yes
Step-by-step explanation:
Yes.
9/25 = .36
Because the decimal stop it is rational
Only decimals that have no pattern and go on infinitely then it is irrational like [tex]\pi[/tex] or √7 if you plug those into a calculator they go on forever and have no pattern
What is the volume of a rectangle when the length is 3 1/3 the width is 4 2/3 and the height is 25
To find the volume of a rectangle APR prism, you need to multiply its length, width, and height. In this case, the length is 3 1/3 (or 10/3) units, the width is 4 2/3 (or 14/3) units, and the height is 25 units.
So, the volume of the rectangle can be calculated as:
Volume = length x width x height
Volume = (10/3) x (14/3) x 25
Volume = 1166.67 cubic units (rounded to two decimal places)
Therefore, the volume of the rectangle with a length of 3 1/3, a width of 4 2/3, and a height of 25 is approximately 1166.67 cubic units.
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A shipping company must design a closed rectangular shipping crate with a square base. The volume is 12288ft3. The material for the top and sides costs $2 per square foot and the material for the bottom costs $10 per square foot. Find the dimensions of the crate that will minimize the total cost of material.
Optimize crate cost by expressing material cost in terms of x and y, calculating cost of all four sides, and finding minimum cost. Optimal dimensions: x = 16 ft, y = 48 ft. Minimum cost: $8704.
To find the dimensions of the crate that will minimize the total cost of material, we need to use optimization techniques, we need to express the cost of materials in terms of x and y then calculate the cost of all four sides, then find the minimum cost.
Let's start by defining the variables we need to work with:
Let x be the length of one side of the square base (in feet), Let y be the height of the crate (in feet).
From the given volume, we know that:
V = x^2 * y = 12288 ft^3
We can use this equation to solve for one of the variables in terms of the other:
y = 12288 / (x^2)
Now we need to express the cost of materials in terms of x and y.
The area of the bottom is x^2, so the cost of the bottom is:
[tex]C_b = 10 * x^2[/tex]
The area of each side is x * y, and there are four sides, so the cost of the sides is:
[tex]C_s = 4 * 2 * x * y = 8xy[/tex]
The area of the top is also x^2, so the cost of the top is:
[tex]C_t = 2 * x^2[/tex]
The total cost of materials is the sum of these three costs:
[tex]C = C_b + C_s + C_t = 10x^2 + 8xy + 2x^2[/tex]
Now we can substitute y = 12288 / (x^2) into this equation:
[tex]C = 10x^2 + 8x * (12288 / x^2) + 2x^2[/tex]
Simplifying this expression, we get:
[tex]C = 12x^2 + 98304 / x[/tex]
To find the minimum cost, we need to find the value of x that minimizes this expression. We can do this by taking the derivative of C with respect to x and setting it equal to zero:
C' = 24x - 98304 / x^2 = 0
Solving for x, we get:
x = 16 ft
Now we can use this value of x to find y:
y = 12288 / (16^2) = 48 ft
Therefore, the dimensions of the crate that will minimize the total cost of material are:
- Length of one side of the square base = x = 16 ft
- Height of the crate = y = 48 ft
To check that this is indeed the minimum cost, we can plug these values back into the expression for C and calculate the cost:
C = 10 * 16^2 + 8 * 16 * 48 + 2 * 16^2 = 8704
Therefore, the minimum cost of material for the crate is $8704.
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what is the volume of a cylinder with a radius of 2.5 and a height of 4 answer in terms of pi
options:
-20 5/6π
-25π
-8 1/3π
-15 5/8π
Step-by-step explanation:
volume of a cylinder is pi × r² × height
r = 2.5
height= 4
volume = pi × 2.5² × 4
volume = 25 pi
Roy made a pizza that is 12 inches in diameter. He knows he can eat about 84. 8 in, at what angle should Roy cut the pizza in radians? Round your answer to the tenths place
Roy should cut the pizza at an angle of 4.7 radians if the total diameter of the pizza is 12 inches.
Diameter of the pizza = 12 inches
The area he can eat = 84. 8 inches
The area of the pizza for 12 inches diameter can be calculated by using the formula:
Area = π*[tex]r^2[/tex]
Area = π* ([tex]6^2[/tex])
Area = 36π
The angle of the slice of pizza he can eat about 84.8 square inches can be calculated as:
Area of sector = (θ/2) ×[tex]r^2[/tex]
84.8 = (θ/2) × [tex]6^2[/tex]
84.8 = 18*θ
θ = 84.8 / 18
θ = 4.71 radians
Therefore, we can conclude that Roy should cut the pizza at an angle of 4.7 radians.
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