Answers
Answer:
The volume of the figure is [tex](\frac{l^{3}}{3})[\frac{\pi }{2}-1]\ units^{3}[/tex]
Step-by-step explanation:
we know that
The volume of the figure is equal to the volume of the cone minus the volume of the square pyramid
step 1
Find the volume of the cone
The volume of the cone is equal to
[tex]V=\frac{1}{3}\pi r^{2}h[/tex]
we have
[tex]r=\frac{l\sqrt{2}}{2}\ units[/tex] ----> the diagonal of the square base of pyramid is equal to the diameter of the cone
[tex]h=l\ units[/tex]
substitute
[tex]V=\frac{1}{3}\pi (\frac{l\sqrt{2}}{2})^{2}(l)[/tex]
[tex]V=\frac{1}{6}\pi (l)^{3}\ units^{3}[/tex]
step 2
Find the volume of the square pyramid
The volume of the pyramid is equal to
[tex]V=\frac{1}{3}Bh[/tex]
where
B is the area of the base
h is the height of the pyramid
we have
[tex]h=l\ units[/tex]
[tex]B=l^{2}\ units^{2}[/tex]
substitute
[tex]V=\frac{1}{3}l^{2}(l)[/tex]
[tex]V=\frac{1}{3}l^{3}\ units^{3}[/tex]
step 3
Find the volume of the figure
[tex]\frac{1}{6}\pi (l)^{3}\ units^{3}-\frac{1}{3}l^{3}\ units^{3}=(\frac{l^{3}}{3})[\frac{\pi }{2}-1]\ units^{3}[/tex]
Related Questions
Will bought a package of 24 juice bottles for $7.44. Which equation relates the cost , c of a package of juice bottles to the number of bottles, b, in the package?
Answers
7.44÷24=c because to find the unit price you need divide 7.44 by 24
Answer:
c=0.31b
Step-by-step explanation:
$7.44 divided by 24 = 0.31
helppppp due toarrow very easy simple
Answers
132+396=528 is 100%
132 is ?%
?=132x100/528=25%
Answer is 25% ate CFA
Answer:
25%
Step-by-step explanation:
Although the problem statement doesn't say so, you have to find the total number of people who bought hamburgers. It's 132 + 396, or 528.
132 people out of a total of 528 people ate at Chick-a-Fil. This comes to
132
------- = 0.25, or 25%
528
You must write out your conclusion: "25% of these people ate at Chick-a-Fil.
What is the average rate of change of the function over the interval x = 0 to x = 8?
Answers
Answer:
The average rate of change is:
[tex]\frac{13}{161}[/tex]
Step-by-step explanation:
The rational function given to us is;
[tex]f(x)=\frac{3x+4}{2x+7}[/tex]
[tex]f(0)=\frac{3(0)+4}{2(0)+7}[/tex]
[tex]f(0)=\frac{4}{7}[/tex]
[tex]f(8)=\frac{3(8)+4}{2(8)+7}[/tex]
[tex]f(0)=\frac{28}{23}=1[/tex]
The average rate of change of this function from x=0 to x=8 is the slope of the secant line connecting:
(0,f(0)) and (8,f(8))
Average rate of change =[tex]=\frac{f(8)-f(0)}{8-0}[/tex]
[tex]=\frac{\frac{28}{23}-\frac{4}{7} }{8}[/tex]
[tex]=\frac{13}{161}[/tex]
what is the area of a hexagon with an apothem of 10
Answers
Since the perimeter of said hexagon is 120√3, we simply multiply this number by 10 and divide it by 2.
1200√3/2 = 600√3
Department A had sales of $200,000.00, Department B had sales of $600,000.00, and total overhead expenses were $32,000.00. The allocation of overhead to Department A should be ________.
Answers
Answer:
the allocation of overhead to department A is $8,000.00
Step-by-step explanation:
Given that Department A had sales of $200,000.00 and Department B had sales of $600,000.00, the ratio of department A's sales to that of department B is 200,000.00 / 600,000.00 = 1/3.
The total overhead expenses were $32,000.00, the allocation of overhead to department A is 32,000.00 / (3 + 1) = $32,000.00 / 4 = $8,000.00
How do you Graph y-3=1/3(x+1)
Answers
Answer:
You can find the point of intersection of the line with the y-axis and the the point of intersection of the line with the x-axis. See the graph attached.
Step-by-step explanation:
Find the intersection with the y-axis. Substitute [tex]x=0[/tex] into the equation and solve for y:
[tex]y-3=\frac{1}{3}(x+1)\\\\y-3=\frac{1}{3}(0+1)\\\\y-3=\frac{1}{3}(1)\\y=\frac{1}{3}+3\\\\y=\frac{10}{3}[/tex]
[tex]y[/tex]≈3.33
Find the intersection with the x-axis. Substitute [tex]y=0[/tex] into the equation and solve for x:
[tex]y-3=\frac{1}{3}(x+1)[/tex]
[tex]0-3=\frac{1}{3}(x+1)\\(-3)(3)=x+1\\-9-1=x\\x=-10[/tex]
Now, you know that the line passes through the point (0,3.33) and (-10,0). Now you can graph the function. (Observe the graph attached)
which equation is equivalent to the equation 5x-7y=-70
A.y=-7/5x-14
B.y=7/5x+14
C.y=5/7x-10
D.y=5/7x+10
Answers
Answer:
[tex]\large\boxed{D.\ y=\dfrac{5}{7}x+10}[/tex]
Step-by-step explanation:
[tex]Ax+By=C\qquad\text{it's a standard form of an equation of a line}\\\\\\y=mx+b\qquad\text{it's a slope-intercept form of an equation of a line}\\\\\text{We have the equation in the standard form:}\\\\5x-7y=-70\\\\\text{Convert it to the slope - intercept form:}\\\\5x-7y=-70\qquad\text{subtract 5x from both sides}\\\\-7y=-5x-70\qquad\text{divide both sides by (-7)}\\\\y=\dfrac{5}{7}x+10[/tex]
What is the value of X
Answers
Answer:
120
Step-by-step explanation:
it is an obtuse angle
The answer is:
The missing angle "x" is equal to 130°.
Why?We need to remember that the sum of all of the angles of any polygon will be all equal to 360°.
So, we are given the following exterior angles:
[tex]140\°\\34\°\\56\°\\[/tex]
Now, if the sum of all the exterior angles is equal to 360°, we can use it to calculate "x", so:
[tex]360\°=140\°+34\°+56\°+x\\\\x=360\°-(140\°+34\°+56\°)=360\°-230\°\\\\x=130\°[/tex]
Hence, the missing angle "x" is equal to 130°.
Have a nice day!
What is the estimate for the probability of selecting a red crayon OR a yellow crayon from the bag?
Answers
Answer: It would be both because there is no number to it
Step-by-step explanation:
For example if there were 15 red crayons and 10 yellow ones it would be the red crayons because there is a bigger amount of them in the bag but because there is no number you have the same possibility of picking both.
To estimate the probability of selecting a red crayon OR a yellow crayon from the bag, calculate the individual probabilities of each color and use the OR probability formula to find the estimate.
Estimate for the probability of selecting a red crayon OR a yellow crayon from the bag:
Calculate the individual probabilities of selecting a red crayon and a yellow crayon.Use the formula P(A OR B) = P(A) + P(B) - P(A AND B) to find the estimate for the probability of selecting a red crayon OR a yellow crayon.Substitute the individual probabilities into the formula to get the final estimated probability.Which of the following is a continuous random variable?
a. The number of employees in an office
B. The salaries of employees in an office
C. The numbers of printers in an office
D. The number of phone calls made daily from an office.
Answers
Answer:
B: The salaries
Step-by-step explanation:
B: The salaries. While not strictly continuous, the range of salaries is closest of these four choices to being continuous. In contract, "number of employees," "number of printers," and "number of phone calls" are all discrete random variables.
The statement at D "The number of phone calls made daily from an office" is a continuous random variable.
What is meant by a continuous random variable?A random variable is defined for all the values in an interval or between two values.
Verifying the given statements:A. The number of employees in an office.
It is a constant value. It's not a continuous random variable.
B. The salaries of employees in an office
It is a constant value. It has only one value means represented in a closed interval. So, not a continuous random variable
C. The number of printers in an office
This is also a constant value. So, not a continuous random variable
D. The number of phone calls made daily from an office
The number of phone calls made daily, may not be the same and are continuous. If the interval of a month, there may be a different number of phone calls. So, it is a continuous random variable.
So, option D is correct.
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What number should be added to both sides of the equation to complete the square? X^2-6xx=5
Answers
Answer:
9
Step-by-step explanation:
To complete the square, divide the coefficient of the b term 6x in two. This becomes -6/2=-3. Now square the number -3 and it becomes 9. To complete the square add 9 to both sides.
Answer:
9
Step-by-step explanation:
[tex]x^2-6x = 5\\[/tex]
We know the binomial formula: [tex](a-b)^2 = a^2 -2ab + b^2[/tex]
Let's consider 6x = 2ab, we know a is our first term - x;
6x = 2axb
6 = 2b
b = 3
So to make a perfect square, we need to add [tex]b^2[/tex] to both sides
[tex]x^2 - 6x + 3^2 = 5 + 3^2\\x^2 - 6x + 9 = 5 + 9\\(x-3)^2 = 14[/tex]
Pre Cal | Multiple Choice | Apex
Which conic section does the equation below describe?
( x-9 )^2/4 + ( y+2 )^2/25=1
A. Circle
B. Ellipse
C. Hyperbola
D. Parabola
Answers
Ellipse is your answer, because if you plug the equation into a graphing calculator and identify the conic, the term ellipse is given-
What is the slope of the line through the points (-2,-1) and (8,-3)?
Answers
Answer:
- 1/5
Step-by-step explanation:
Slope of a line passing through two points can be calculated as:
[tex]\text{slope}=\frac{\text{rise}}{\text{run}} \\\\ \text{slope}=\frac{\text{Difference of y coordinates}}{\text{Difference of x coordinates}}[/tex]
The given points are (-2, -1) and (8, -3). Using the values in above formula, we get:
[tex]\text{slope}=\frac{-3-(-1)}{8-(-2)}\\\\ \text{slope}=\frac{-3+1}{8+2}\\\\ \text{slope}=\frac{-2}{10}\\\\ \text{slope}=\frac{-1}{5}[/tex]
Thus the slope of the line through the given points is -1/5. So 2nd option gives the correct answer
Answer:
The correct answer is second option
-1/5
Step-by-step explanation:
Points to remember
The slope of line passing through (x₁, y₁) and (x₂, y₂) is given by,
Slope = (y₂ - y₁)/(x₂ - x₁)
To find the slope of given line
Here, (x₁, y₁) = (-2, -1) and (x₂, y₂) = (8, -3)
Slope = (y₂ - y₁)/(x₂ - x₁) = ( -3 - - 1)/(8 - -2)
= (-3 + 1)/(8 + 2) = -2/10
= -1/5
Therefore the correct answer is second option -1/5
PLS HELP ME I WILL GIVE BRAINLIEST
Answers
Answer:
78°
Step-by-step explanation:
The angular distance of an arc is twice the angle that forms it if that angle lies of the edge of the circle.
By this, Arc AK has angular distance 158°.
Arc JL = 202°.
Arc KL = 122°.
By subtracting these we get 80° for Arc JK.
Arc KA = 158°.
Arc AJ = KA - JK
AJ = 158-80
AJ = 78°
Which of the following payments is the same amout each time it is paid? A) Property Taxes B) PMI C) Interest D) Principal
Answers
The payment that is the same amount each time that it is paid is given as follows:
B) PMI.
What is the monthly payment formula?The monthly payment formula is defined as follows:
[tex]PMI = P\frac{\frac{r}{12}\left(1 + \frac{r}{12}\right)^n}{\left(1 + \frac{r}{12}\right)^n - 1}[/tex]
In which the parameters are listed and defined as follows:
P is the initial amount, also known as the principal.r is the interest rate.n is the number of payments.The monthly payment is calculated before a purchase is made, meaning that it assumes the same amount each time it is paid, and thus option B is the correct option in this problem.
The principal is a one time payment, while taxes and interest vary over time.
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In a thirty-year fixed-rate mortgage, the principal portion of the payment is the same amount each time it is paid, while the interest decreases over time, thus maintaining a consistent total payment amount.
Explanation:The student is asking which of the following payments is the same amount each time it is paid: Property Taxes, PMI (Private Mortgage Insurance), Interest, or Principal. The answer is Principal in the context of a thirty-year fixed-rate mortgage.
This type of mortgage has a consistent monthly payment that includes both the principal and the interest. Early in the loan, the payment consists of more interest than principal, but as the loan matures, the portion of the payment that goes towards the principal increases while the interest portion decreases.
This ensures that the total payment amount remains the same throughout the life of the loan.
Example of Principal Payment Over Time
If you have a thirty-year fixed-rate mortgage, your monthly payment is calculated at the outset to ensure that each payment is the same, even though the principal paid increases over time as the outstanding balance of the loan decreases.
Find the surface area of the cone. Leave your answer in terms pi
Answers
Answer:
The answer is C. 119cm³
Step-by-step explanation:
SA= [tex]\pi r^{2} +\pi rl[/tex]
= 49[tex]\pi +\pi 7(10)[/tex]
= 49[tex]\pi +20\pi[/tex]
SA= 119[tex]\pi[/tex]
Answer:
The correct answer is option C. 119π cm²
Step-by-step explanation:
Points to remember
Surface area of cone = πrl + πr²
Where r is the base radius and l is the lateral edge
To find the surface area of given cone
Here r = 7 cm and l = 10 cm
Surface area = πrl + π r² =( π * 7 * 10) + (π *7²)
= 70 π + 49π
= 119π cm²
Therefore correct answer is option C. 119π cm²
The number 18.34 has four significant figures
Answers
Answer:
True
Step-by-step explanation:
The number 18.34 has four significant figures. Yes it is true that it has four significant figures.
For significant figures, we start counting from the first non zero digit.
The first non zero digit in 18.34 is 1.
Count from this number to the last number, we have four numbers.
Therefore, it is true that the number 18.34 has four significant figures.
You and your mom enter a drawing with three different prizes. A total of eight people entered the drawing and prizes are awarded randomly.
There are 336 ways to award the prizes.
What is the probability that you win first prize and your mom won second prize?
Answers
Answer: C. [tex]\dfrac{6}{336}[/tex]
Step-by-step explanation:
Given: The number of different prizes = 3
The number of people entered the drawing = 8
The total number of ways to award the prizes. = 336
Now, The number of ways to select for 3 prizes, such that you win first prize and your mom wins second prize is given by :-
[tex]1\times1\times(8-2)=6[/tex]
Hence, the probability that you win first prize and your mom wins second prize=[tex]\dfrac{6}{336}[/tex]
Calculate the finance charge and new balance using the previous balance method. Previous balance = $199.19 Annual rate = 14%
Answers
Answer:
Finance charge = $2.32
new balance = $201.51
Step-by-step explanation:
Finance charge = Previous balance×Periodic percentage rate
The previous balance is 199.19
The annual percentage rate is 0.14. Therefore, the periodic percentage rate is; (0.14/12)
Finance charge = 199.19 * (0.14/12)
= 2.3239 = $2.32
new balance = previous balance + finance charge
= 199.19 + 2.32
= $201.51
If f(x) and its inverse function, f–1(x), are both plotted on the same coordinate plane, what is their point of intersection?
Answers
Answer:
-3
Step-by-step explanation:
f(-1) = 3(-1)
f(-1) = -3
Answer with explanation:
The given function is:
⇒ y =3 x
And it's inverse function can be Calculated by, replacing , x by y, and , y by x, in the above equation
⇒x=3 y, is the equation of inverse function.
Both the original function , and inverse function passes through origin, As well as Origin is the point of Intersection, which can be shown as follows:
3 x-y=0-----(1)
x-3 y=0
3 x - 9 y =0 ------(2)
EQ.(1) - Eq.(2)
3 x - y - (3 x- 9 y)=0
-y + 9 y=0
8 y=0
y=0
Putting the value of , y in equation (2)
x=3 × 0
x=0
⇒Point of intersection of ,f(x) and it's inverse =(0,0)
If x = 6 cm, what is the surface area of the geometric shape formed by this net?
A. 144 square cm.
B. 432 square cm.
C. 216 square cm
D. 576 square cm
Please explain because these still stump me
Answers
Answer:
the answer is D. 576 square cm
Step-by-step explanation:
Find the area of one of the rectangular faces using the formula, Area = lw.
A = (12 cm) (6 cm)
A = 72 square cm
Since there are 4 rectangular faces, multiply the area of one rectangular face by 4 to get a total of 288 square cm.
The area of one of the congruent squares is 12 cm × 12 cm, or 144 cm2. Multiply 144 cm2 by 2 to get a total of 288 cm2.
To find the surface area of the rectangular prism, add the area of the four rectangular faces to the area of the two square faces.
288 square cm + 288 square cm = 576 square cm
what is the gcf of 18 and 54
Answers
Answer:
18 is the GCF
Step-by-step explanation:
Factors of 18: 1, 2, 3, 6, 9, 18
Factors of 54: 1, 2, 3, 6, 9, 18, 27, 54
Answer is provided in the image attached.
a man can do a job in 4 days working alone and his helper can do the same job in 12 days working alone what part of the job can they do in one day when working together at their respective rates?
Answers
Solution:
Let t = working together in terms of days
(1/4) + (1/12) = 1/t
Solve for t.
Multiply both sides by the LCD.
LCD = 12t
3t + t = 12
4t = 12
t = 12/4
t = 3
Together, they can do the job in 3 days.
Which expressions can be used to find m∠ABC? Check all that apply.
Answers
Answer:
[tex]\cos^{-1}(\frac{6.3}{9.8})[/tex]
[tex]\sin^{-1}(\frac{7.5}{9.8})[/tex]
Step-by-step explanation:
Recall the mnemonics SOH-CAH-TOA
The sine ratio is the length of the opposite side expressed over the hypotenuse.
[tex]\sin m\angle ABC=\frac{7.5}{9.8}[/tex]
Take the sine inverse of both sides to get;
[tex]m\angle ABC=\sin^{-1}(\frac{7.5}{9.8})[/tex]
The cosine ratio is the length of the adjacent side expressed over the hypotenuse.
[tex]\cos m\angle ABC=\frac{6.3}{9.8}[/tex]
Take the cosine inverse of both sides to get;
[tex]m\angle ABC=\cos^{-1}(\frac{6.3}{9.8})[/tex]
identify the correct trigonometry formula to use to solve for x.
Answers
Answer:
sin(62)=18/x
Step-by-step explanation: sine = opp/hyp
Answer: Third option.
Step-by-step explanation:
Given the right triangle in the figure attached, you know that, for the known angle of 62 degrees, the lenght of the opposite side is 18 and the hypotenuse is "x"
Therefore, you need to remember the following identity:
[tex]sin\alpha=\frac{opposite}{hypotenuse}[/tex]
Then, having that:
[tex]\alpha=62\°\\opposite=18\\hypotenuse=x[/tex]
You need to substitute these values into [tex]sin\alpha=\frac{opposite}{hypotenuse}[/tex], then you get that the correct trigonometry formula to use to solve for "x" is:
[tex]sin(62\°)=\frac{18}{x}[/tex]
If ∠3 = 5x - 1, and ∠5 = 3x + 11, then x =
Answers
Answer:
6
Step-by-step explanation:
cause we will add them together
5x -1 = 3x +11
2x=12
x=6
The value of x if ∠3 = 5x - 1, and ∠5 = 3x + 11, is 6.
What is angle?An angle is a figure in Euclidean geometry made up of two rays that share a common terminal and are referred to as the angle's sides and vertices, respectively.
Angles created by two rays are in the plane where the rays are located. The meeting of two planes also creates angles.
Given;
∠3 = 5x - 1, and ∠5 = 3x + 11,
Calculate the value of x as shown below,
∠3 = ∠5 (Alternate interior angles between parallel lines are equal)
5x - 1 = 3x + 11
5x - 3x = 11 + 1
2x = 12
x = 12 / 2
x = 6
Thus, the value of x is 6.
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if you apply the changes below to the absolute value parent function f(x)=lxl, what is the equation of the new function?
Shift 4 units left
Shift 2 units up
Answers
Answer:
[tex]f(x)=|x+4|+2[/tex]
Step-by-step explanation:
The given absolute value function is
[tex]f(x)=|x|[/tex]
This is the base or the parent function.
The transformation [tex]f(x)=|x+b|+c[/tex] will shift the parent function b units to the left and c units up.
From the question, b=4 units and c=2 units.
The new equation is [tex]f(x)=|x+4|+2[/tex]
Answer: The equation of the new function is [tex]f(x)=|x+4|+2.[/tex]
Step-by-step explanation: We are given to find the equation of the new function if we apply the following changes to the absolute value parent function f(x)=lxl :
Shift 4 units left and Shift 2 units up.
We know that
if we shift the absolute value parent function f(x) = |x| to h units left and k units up, then the new equation will be
[tex]f(x)=|x+h|+k.[/tex]
Therefore, if the function is shifted 4 units left and 2 units up, then the equation of the new function will be
[tex]f(x)=|x+4|+2.[/tex]
Thus, the equation of the new function is [tex]f(x)=|x+4|+2.[/tex]
what is the mean between the numbers 3,19,21,6.8,9.3,21.7,2.9
Answers
Answer:
About 11.96
Step-by-step explanation:
The mean of a data set is basically the average.
To find the average, add up all of the data values and then divide by the amount of numbers there are.
First, add the numbers.
3 + 19 + 21 + 6.8 + 9.3 + 21.7 + 2.9 = 83.7
There are 7 numbers in this data set so divide 83.7 by 7
83.7/7 = 11.95714285714286
Round this number to the nearest hundreth, to get 11.96
So, the mean of this data set is 11.96
I hope this helps!
15 over 1000 wrote in scientific notation
Answers
Answer:
1.5*10^-2
Step-by-step explanation:
You mean 15/1000 written in scientific notation?
In this case, it would be- 1.5*10^-2.
What is the area of point ?
Answers
Answer:
314 cm²
Step-by-step explanation:
It's not the point O, but the circle O, a point has no area.
The area of a circle is given by the formula A = π r²
We don't have r (radius), but we have the diameter, which is double the radius. So, r = d / 2 = 20 cm / 2 = 10 cm
Now, we can plug r directly into the equation:
A = π r² = π 10² = 100π = 314 cm²