The volume of a sphere with a diameter of 9 inches, using 3.14 for pi, is calculated using the formula V = (4/3)πr³. The radius is 4.5 inches, leading to a volume of 381.675 cubic inches, which rounded to the nearest tenth is 381.7 cubic inches.
Explanation:The question is asking for the volume of a sphere with a diameter of 9 inches, using 3.14 for pi. To find the volume, we first need to calculate the sphere's radius. Since the diameter is 9 inches, the radius (which is half the diameter) is 4.5 inches. The formula for the volume of a sphere is V = (4/3)πr³. Substituting the radius into the formula, we get:
V = (4/3)(3.14)(4.5³) = (4/3)(3.14)(91.125) = 381.675 cubic inches. When rounded to the nearest tenth, the volume is 381.7 cubic inches.
which equation represents the parabola shown on the graph? y^2=-2x y^2=-8 y^2=-2y y^2=-8y
Answer:
Choice B is correct
Step-by-step explanation:
The graph of the parabola opens towards the left. This implies that the general form of the equation of the parabola will be;
[tex]y^{2}=f(x)[/tex]
Nevertheless, the points (-2, -4) and (-2, 4) lie on the graph of the parabola. We substitute x = -2 in the equations having the form above.
In the second equation, we have;
[tex]y^{2}=-8(-2)\\\\y^{2}=16\\\\y=\sqrt{16}=+4, -4[/tex]
This is thus the equation of the parabola graphed.
Answer: D x^2=6y
Step-by-step explanation:
Jason ate 1/2 of a whole pizza. The next day, he shared the remaining pizza between himself and 2 friends. What fraction of the original pizza did each of them get?
Answer:
1/6
Step-by-step explanation:
jason ate 1/2, so only 1/2 of the pizza is left.
1 ÷ 2 = 1/2
he split it equally between himself and 2 friends (3 people)
1/2 ÷ 3
= 1/2 × 1/3
=1/6
Use the listing method to represent the following set. { x | x I, 2 ≤ x ≤ 5}
{2, 3, 4}
{2, 3, 4, 5}
{4, 5, 6, 7}
The correct representation of the given set using the listing method is {2, 3, 4, 5}. The second option is correct.
The set {x | x I, 2 ≤ x ≤ 5} can be represented using the listing method.
Here, the set consists of all values of x that satisfy the condition 2 ≤ x ≤ 5. The values of x within this range are 2, 3, 4, and 5.
Therefore, the set can be represented as:
{2, 3, 4, 5}
This set includes all the values of x that are greater than or equal to 2 and less than or equal to 5, as indicated by the condition 2 ≤ x ≤ 5.
The elements listed in the set are 2, 3, 4, and 5, and no other values are included.
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How do i do mean and median
To find median your numbers have to be in numerical order from smallest to largest and the value that occurs more often and if no number is repeated then there is not median aka (mode)
To find mean you need to add all the number and divide the numbers that you add.
To find median you put the numbers least to greatest. Then, cross the numbers until you find an one number and that's it. If they are two numbers that left, you can add together and divide by two.
I hope this help you. :)
Marco is carrying two cylinder-shaped cans. Each can has the same height
and cross-sectional area as the other. Which of the following best describes
the relationship between the cans according to Cavalieri's principle?
Answer:
Choice D
Step-by-step explanation:
The Cavalieri's principle states that if two or more solids have identical cross-sectional area as well as height, then the solids will have equal volume.
Therefore, the volumes of the cylinders are the same
Answer:
The volumes of the cylinders are the same.
Step-by-step explanation:
David is five times older than his son,after 2 years sum of ages will be 40 calculate their present age
5x+2+x+2=40
5x+x=40-2-2
6x=36
x=36/6
x=6
Son=6
David=5*6=30
The question involves solving two linear equations. By solving these equations, we find that the son is currently 6 years old and David is 30 years old.
Explanation:This question is based on linear equations in mathematics. Let's use the given conditions to form two equations and solve them accordingly.
Let's assume that the son's age is 'x'. According to the information provided, David is five times older than his son, so David's age is '5x'.
In two years, David will be 5x + 2 years old and his son will be x + 2 years old. The sum of their ages in two years is given as 40, which leads us to the equation 5x + 2 + x + 2 = 40. After simplifying, we get '6x + 4 = 40', or '6x = 36', and then 'x = 6'.
Hence, currently the son is 6 years old and David is 30 years old.
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If a football team has a 90% chance of making a field goal for 3 points and a 35% chance of making a touchdown for 7 points, find the expected value of a touchdown.
PLEASE HELP!!!
2.7 points (my guess)
Answer: The expected value of touchdown is 2.45.
Step-by-step explanation:
Since we have given that
Probability of making a field goal for 3 points = 90%
Probability of making a touchdown for 7 points = 35%
So, Expected value of a touchdown would be
[tex]\sum xp(x)=7\times \dfrac{35}{100}=\dfrac{245}{100}=2.45[/tex]
Hence, the expected value of touchdown is 2.45.
CAN SOMEONE HELP ME ANSWER THIS
Answer:
It is 1/6
Step-by-step explanation:
This is because there are 6 sides to a dice and the number 3 is only on one of those sides. So, it is 1 in 6 or 1/6
Answer:
1/6
Step-by-step explanation:
The question is asking for the probability of rolling a 3 on a fair-sided die.
Dice have 6 faces.
The number "3" is only on 1 those faces
So, the probability of rolling a 3 on a dice is 1/6
I hope this helps! :)
What is the radius of a sphere with a volume of 1/6 pie
Answer:
[tex]\large\boxed{the\ radius\ R=\dfrac{1}{2}}[/tex]
Step-by-step explanation:
The formula of a volume of a sphere:
[tex]V=\dfrac{4}{3}\pi R^3[/tex]
We have
[tex]V=\dfrac{1}{6}\pi[/tex]
Substitute:
[tex]\dfrac{4}{3}\pi R^3=\dfrac{1}{6}\pi[/tex] divide both sides by π
[tex]\dfrac{4}{3}R^3=\dfrac{1}{6}[/tex] multiply both sides by 3
[tex]3\!\!\!\!\diagup^1\cdot\dfrac{4}{3\!\!\!\!\diagup_1}R^3=3\!\!\!\!\diagup^1\cdot\dfrac{1}{6\!\!\!\!\diagup_2}[/tex]
[tex]4R^3=\dfrac{1}{2}[/tex] divide both sides by 4
[tex]R^3=\dfrac{1}{2}:4\\\\R^3=\dfrac{1}{2}\cdot\dfrac{1}{4}\\\\R^3=\dfrac{1}{8}\to R=\sqrt[3]{\dfrac{1}{8}}\\\\R=\dfrac{\sqrt1}{\sqrt8}\\\\R=\dfrac{1}{2}[/tex]
Given a variance of 1992.8, what is the standard deviation?
about 43.13
about 43.76
about 45.20
about 44.64
ANSWER
about 44.64
EXPLANATION
The standard deviation is the square root of the variance.
So we can write the equation or formula;
[tex]standard \: \: deviation = \sqrt{variance} [/tex]
From the question, it was given that, the variance is 1992.8
To find the standard deviation, we plug in the given value of the variance.
[tex]standard \: \: deviation = \sqrt{1992.8} [/tex]
Take your scientific calculator and the given square root.
You should obtain:
[tex]standard \: \: deviation = 44.64078852[/tex]
We round to the nearest hundredth to obtain; 44.64
Please help I don’t know how to do this!
Answer:c
Step-by-step explanation:
The answer is the top one.
Hope this helps!
If cosX = -0.2, and x is in quadrant II, then what it the value of sinX
[tex]\sin x>0[/tex] when [tex]x[/tex] is in quadrant II, so
[tex]\cos^2x+\sin^2x=1\implies\sin x=\sqrt{1-\cos^2x}=\sqrt{1-(-0.2)^2}\approx1.02[/tex]
Answer:
Step-by-step explanation:
note : cos²x + sin²x = 1
(- 0.2)² + sin²x =1
0.04 + sin²x = 1
sin²x = 1 - 0.04
sin²x = 0.96
sinx = √0.96 or sinx = - √0.96
in quadrant II : sinx > 0 ...so : sinx = √0.96
Select two choices: one for the center and one for the spread.
Answer:
The best measure of location or center is the median.
The best measure of spread or dispersion is the interquartile range (I.Q.R).
Step-by-step explanation:
The data set is skewed to the left since most of the data values fall in the upper end of the distribution. In other words the data set is negatively skewed since it is tailed to the left.
For any skewed data set;
The best measure of location or center is always the median. This is because the median is robust to outliers unlike the mean.
On the other hand, the best measure of spread or dispersion is the interquartile range (I.Q.R).
Answer:
B and D
Step-by-step explanation:
Water is being pumped into a 12-foot-tall cylindrical tank at a constant rate.
• The depth of the water is increasing linearly.
• At 2:30 p.m., the water depth was 2.6 feet.
• It is now 5:00 p.m., and the depth of the water is 3.6 feet.
What will the depth (in feet) of the water be at 6:00 p.m.?
Answer:
4 feet
Step-by-step explanation:
It is given that:
• At 2:30 p.m., the water depth was 2.6 feet.
• It is now 5:00 p.m., and the depth of the water is 3.6 feet.
So in 2.5 hours ( 5pm - 2:30pm) the water rose 1 feet (3.6 - 2.6).
Now we can find how much water rises in 1 hour by setting up a ratio (let x be the depth increase of water in 1 hr):
[tex]\frac{2.5}{1}=\frac{1}{x}\\2.5x=1*1\\2.5x=1\\x=\frac{1}{2.5}\\x=0.4[/tex]
So, in 1 hour, the water level will rise 0.4 feet
So, at 6pm (1 hour from 5 pm) it will rise to 3.6 + 0.4 = 4 feet
The depth of the water is increasing at a rate of 0.4 feet per hour, so by 6:00 p.m., the depth will be 4 feet.
Explanation:We are given the information that water is being pumped into a cylindrical tank and the height of the water increases linearly over time. At 2:30 p.m. the depth was 2.6 feet, and at 5:00 p.m. it was 3.6 feet. To find the rate of change in height, we need to first calculate the time difference and the change in height of the water:
Time difference between 2:30 p.m. and 5:00 p.m. is 2.5 hours.The change in height of the water is 3.6 feet - 2.6 feet = 1 foot.Dividing the change in height by the time gives us the rate of change, which is 0.4 feet per hour (1 foot / 2.5 hours). Now we use this rate to predict the height at 6:00 p.m., which is one hour after 5:00 p.m.:
Depth at 5:00 p.m. = 3.6 feet + (0.4 feet per hour * 1 hour) = 4 feet.
Therefore, the expected depth of the water at 6:00 p.m. is 4 feet.
which inequality matches the graph?
Answer:
2x - 3y < 7
Step-by-step explanation:
The coordinate is on 0 and this number is LESS THAN 0.
PLEASE MARK ME AS BRAINLIEST BECAUSE I REALLY NEED IT :(
5=w/2.2
W=__
Halpppp I am confusion!!1111!+
Answer:
[tex]w=11[/tex]
Step-by-step explanation:
we have
[tex]5=w/2.2[/tex]
Solve for w
That means----> isolate the variable w
Multiply by 2.2 both sides
[tex](2.2)*5=(2.2)*w/2.2[/tex]
Simplify
[tex]11=w[/tex]
Rewrite
[tex]w=11[/tex]
The solution to the equation 5 = w/2.2 is 11
How to calculate the value of wFrom the question, we have the following parameters that can be used in our computation:
5 = w/2.2
Rewrite the equation as follows
w/2.2 = 5
So, we have
w = 5 * 2.2
Evaluate the product of 5 and 2.5
So, we have
w = 11
Hence, the solution to the equation is 11
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Josh invested $12,000 in mutual funds and received a sum of $20,000 at the end of the investment period. Calculate the ROI.
Answer:
ROI = 66.67%
Step-by-step explanation:
Given:
josh investment= $12,000
Received sum= $20,000
ROI=?
ROI is the return on investment that gives the loss or gain in any investment and is calculated by the following formula:
ROI= (interest/investment) x 100
Finding interest:
interests= received sum- investment
= 20,000-12,000
=8000
Putting values in ROI formula we get:
ROI= (8000/12000) x 100
= 66.67%
Hence the return on investment is 66.67%!
1. Graph the function . f(x)= sin (x) -2
The graph of f(x) = sin(x) - 2 is a sinusoidal wave shifted down 2 units with period 2π and amplitude 1.
To graph the function, we can start by plotting the points where the graph intersects the x-axis. These points occur when sin(x) = 0, which is when x = 0, ±π, ±2π, and so on. Since the graph is shifted downwards by 2 units, these points will all be 2 units below the x-axis.
Next, we can plot the points where the graph reaches its maximum and minimum values. These points occur when sin(x) = ±1, which is when x = ±π/2 + 2πn, where n is any integer.
Since the graph is shifted downwards by 2 units, the maximum points will be 1 unit above the x-axis, and the minimum points will be 3 units below the x-axis.
Once we have plotted a few points, we can sketch the rest of the graph by connecting the points with a smooth curve. The graph should oscillate between -2 and 0, with a period of 2π.
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A recipe for sabayon calls for 2 egg yolks, 3 tablespoons of sugar, and 1⁄4 cup of white wine. After cracking the eggs, you start measuring the sugar, but accidentally put in 4 tablespoons of sugar. How can you compensate?
Answer:
Step-by-step explanation:
A recipe for sabayon calls for 2 egg yolks, 3 tablespoons of sugar, and ¼ cup of white wine. After cracking the eggs, you start measuring the sugar, but accidentally put in 4 tablespoons of sugar. How can you compensate?
Note that we put in 4/3 more sugar than we wanted, because 3(4/3) = 4
So we need to increase eveything else by 4/3
So 2(4/3) = 8/3 = 2 +2/3 egg yolk and (1/4)(4/3) =4/12 = 1/3 cup of wine
To counterbalance the additional tablespoon of sugar in the recipe, you could increase the other ingredients by a third as well. Hence, you'd require roughly 3 egg yolks and 1/3 cup of white wine.
Explanation:In this recipe situation, since you accidentally put in 4 tablespoons of sugar instead of the required 3 tablespoons, you've essentially increased the sugar quantity by a third. To compensate for this, your best option would be to increase the quantities of the other ingredients by a third as well. Therefore, you would need:
Using these measurements, you should retain the balance of ingredients in your recipe. Nevertheless, remember that cooking often involves personal taste. You might want to adjust the recipe according to your taste preferences afterwards.
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gema has 4
FT of wire how much wire does she need to wrap one meter of her garden?
Answer:
3.28 feet
Step-by-step explanation:
One meter equals to 3.28 feet.
The question isn't exactly clear what Gema wants to use her wire for, because "wrap one meter" isn't correct.
You wrap something around something else... and you can't wrap something around a meter. You can wrap around a square meter by doing the perimeter... but then you'd need more than meter to do the perimeter of a square meter (the perimeter can be around 4 meters).
So, assuming she has a length of 1 meter to cover, she would need 3.28 feet.
3g+5+3g+5+3g+5 Simplify!!!!!! PLZZ
Answer:
9q + 15
Step-by-step explanation:
3g+5+3g+5+3g+5
Combine like terms
= 9q + 15
Answer:
15+9g
Step-by-step explanation:
5 4/5 b+6 3/4 −(2 11/15 +7 7/12 )
The value of the given expression is equal to the [tex]\frac{29b}{5}-3\frac{17}{30}[/tex].
We have given that,
[tex]5\frac{4}{5}b+6\frac{3}{4}-\left(2\frac{11}{15}+7\frac{7}{12}\right)[/tex]
We have to determine the,
[tex]=\frac{29}{5}b+6\frac{3}{4}-\left(2\frac{11}{15}+7\frac{7}{12}\right)[/tex]
What is the expression?The expression consists of numbers and arithmetic operators. It does not contain equality or inequality symbols. The expression consists of unknown variables.
[tex]=\frac{29}{5}b+\frac{27}{4}-\left(2\frac{11}{15}+7\frac{7}{12}\right)[/tex]
[tex]=\frac{29}{5}b+\frac{27}{4}-\left(\frac{41}{15}+7\frac{7}{12}\right)[/tex]
[tex]=\frac{29}{5}b+\frac{27}{4}-\left(\frac{41}{15}+\frac{91}{12}\right)[/tex]
[tex]=\frac{29b}{5}+\frac{27}{4}-\frac{619}{60}[/tex]
[tex]=\frac{29b}{5}-\frac{107}{30}[/tex]
[tex]=\frac{29b}{5}-3\frac{17}{30}[/tex]
The value of the given expression is equal to the [tex]\frac{29b}{5}-3\frac{17}{30}[/tex].
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Please help me with this question.
Step-by-step explanation:
First, reflect over the y-axis:
(1, -2) → (-1, -2)
Then, rotate 180° around the origin:
(-1, -2) → (1, 2)
What is the effect on the volume of a sphere if the radius is divided by 3?
For this case we have by definition, that the volume of a sphere is given by:
[tex]V = \frac {4} {3} \pi * r ^ 3[/tex]
Where:
r: It is the radius of the sphere
If the radius is divided by 3 we have:
[tex]\frac {r} {3}:[/tex]
[tex]V = \frac {4} {3} \pi * (\frac {r} {3}) ^ 3\\V = \frac {4} {3} \pi * \frac {r ^ 3} {27}\\V = \frac {4} {81} \pi * r ^ 3[/tex]
ANswer:
the volume decreases considerably because the denominator increases
Which number line represents this expression?
-8 + 5
PLEASE HELP ME!!!
I NEED THIS FINISHED NOW, PLEASE HELP ME!!!
I believe it’s the third one
Lines C and D are represented by the equations given below:
Line C: y=x+8
Line D: y=3x+2
Which statement shows the solution to the system of equations given below:
(3, 11) because the point does not lie on any axis
(3, 11) because both lines pass through this point
(4, 14) because one of the lines passes through this point
(4, 14) because the point lies between the two axes
The answer is (3,11) because both lines pass through this point.
If you plug these coordinates into the equations in place of x and y :
3+8= 11
3(3)+2= 11
So we know that the coordinates (3,11) are correct, however the answer is C. because solutions to systems of equations are represented by a point of intersection.
The answer is:
The correct option is the second option:
(3, 11) because both lines pass through this point
Why?To find which statement shows the solution to the system of equations, we need to find which of the given points are solutions to the system of equations. We must remember that if a point is a solution to a system of equations, it will satisfy both equations.
So, we are given the lines:
Line C
[tex]y=x+8[/tex]
Line D
[tex]y=3x+2[/tex]
Now, evaluating the first point to see if satisfies the line equations:
Evaluating (3,11)
Line C
[tex]11=3+8[/tex]
[tex]11=11[/tex]
We have that the point (3,11) satisfy the equation of the Line C, so, the linea pass through this point.
Line D
[tex]y=3x+2[/tex]
[tex]11=3*3+2[/tex]
[tex]11=11[/tex]
We have that the point (3,11) satisfies the equation of the Line C, so, the linea pass through this point.
Hence, we have that the points satisfies both lines, so it's a solution to the system of equation.
So, the correct option is the second option:
(3, 11) because both lines pass through this point
Have a nice day!
Translate the sentence into an equation.
Four less than a number is 17.
Which equation is correct?
x – 17 = 4
x – 4 = 17
x + 4 = 17
x + 17 = 4
Let the number = X
Then to get four less you need to subtract 4 from x so you have X-4.
Then that equals 17, so the equation would be:
x - 4 = 17
The equation of the sentence 'four less than a number is 17' is x – 4 = 17
How to convert a sentence into an equation?Let the number be x
Four less than the number means x - 4
Therefore,
Four less than a number is 17 means x – 4 = 17
Therefore, option x – 4 = 17 is the correct answer
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Find the value of each trigonometric ratio
:) Hope this answers your question :)
Solve the Equation
12x-14y=-8
-8x-14y=-52
Answer:
[tex]\large\boxed{x=\dfrac{11}{2},\ y=\dfrac{86}{35}}[/tex]
Step-by-step explanation:
[tex]\left\{\begin{array}{ccc}12x-14y=-8\\-8x-14y=-52&\text{change the signs}\end{array}\right\\\underline{+\left\{\begin{array}{ccc}12x-14y=-8\\8x+14y=52\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad20x=44\qquad\text{divide both sides by 20}\\.\qquad x=\dfrac{44:4}{20:4}\\\\.\qquad x=\dfrac{11}{5}\\\\.\qquad\boxed{x=2.2}\\\\\text{Put the value of x to the second equation}\ 8x+14y=52:[/tex]
[tex]8(2.2)+14y=52\\17.6+14y=52\qquad\text{subtract 17.6 from both sides}\\14y=34.4\qquad\text{divide both sides by 14}\\y=\dfrac{34.4:2}{14:2}\\\\y=\dfrac{17.2\cdot10}{7\cdot10}\\\\y=\dfrac{172:2}{70:2}\\\boxed{y=\dfrac{86}{35}}[/tex]
The solution to the system of equations is: [tex]\[x = 2.2, \quad y = 2.457\][/tex]
To solve the system of linear equations:
[tex]\[12x - 14y = -8\]\[-8x - 14y = -52\][/tex]
We can use the method of elimination to find the values of x and y.
First, let's eliminate y by subtracting the second equation from the first equation. Before that, we should multiply the equations to have the same coefficients for y with opposite signs:
Multiply the first equation by 1:
12x - 14y = -8
Multiply the second equation by -1:
8x + 14y = 52
Now, add the two equations:
[tex]\[(12x - 14y) + (8x + 14y) = -8 + 52\][/tex]
Simplifying this, we get:
[tex]\[20x = 44\]Solve for \(x\):\[x = \frac{44}{20}\]\[x = \frac{22}{10}\]\[x = 2.2\][/tex]
Now that we have x, we can substitute this value back into one of the original equations to find y. Using the first equation:
12x - 14y = -8
Substitute x = 2.2:
[tex]\[12(2.2) - 14y = -8\]\[26.4 - 14y = -8\][/tex]
Subtract 26.4 from both sides:
[tex]\[-14y = -8 - 26.4\]\[-14y = -34.4\][/tex]
Divide both sides by -14:
[tex]\[y = \frac{-34.4}{-14}\]\[y = 2.4571 \approx 2.457\][/tex]
Thus, the solution to the system of equations is:
[tex]\[x = 2.2, \quad y = 2.457\][/tex]
To ensure accuracy, let's substitute x and y back into the original equations and verify that they hold true.
Check the first equation:
[tex]\[12(2.2) - 14(2.457) = -8\]\[26.4 - 34.398 = -8\]\[-7.998 \approx -8 \quad \text{(approximately correct)}\][/tex]
Check the second equation:
[tex]\[-8(2.2) - 14(2.457) = -52\]\[-17.6 - 34.398 = -52\]\[-51.998 \approx -52 \quad \text{(approximately correct)}\][/tex]
Alena is packing a box that has a height of one inch more than the width and a length of three inches more than the width, as shown in the diagram below. Write a polynomial expression, In simplified form, that represents the volume of the box.
(I need help...)
Answer:
The polynomial that represent the volume of the box is [tex]V=(x^{3}+4x^{2}+3x)\ in^{3}[/tex]
Step-by-step explanation:
we know that
The volume of the box is equal to
[tex]V=LWH[/tex]
we have
[tex]L=(x+3)\ in[/tex]
[tex]W=x\ in[/tex]
[tex]H=(x+1)\ in[/tex]
substitute in the formula
[tex]V=(x+3)(x)(x+1)\\V=(x^{2} +3x)(x+1)\\V=x^{3}+x^{2} +3x^{2} +3x\\ V=(x^{3}+4x^{2}+3x)\ in^{3}[/tex]