The volume of the cone in terms of π is 12π in³.
Given,The radius of the cone = 3 inThe value of the height is h = xThe value of the slant height is y = 5 In Volume of the cone in terms of π can be calculated using the formula:
V = (1/3)πr²h where r is the radius of the base of the cone and h is the height of the cone.
A right triangle is formed by dimensions of a cone. Let's find the height of the cone using Pythagoras theorem.
For the right triangle, we have:height² + radius² = slant height²x² + 3² = 5²x² + 9 = 25x² = 25 - 9x²
= 16x = 4 In Volume of the cone V = (1/3)πr²h
= (1/3)π(3)²(4)
= 12π in³
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Last season the girls' volleyball team had 5 seventh-grade students and 4 sixth-grade students. What is the ratio of sixth-grade students to seventh-grade students on the volleyball team? A 4:5 B 4:9 C 5:4 D5:9
Answer:
A) 4:5
Step-by-step explanation:
A) 4:5
B) 4:9
C) 5:4
D) 5:9
If there are 4 sixth grade students, you can already cross off D because there is no 4 as an option. There are 5 seventh grade students, you can cross off B because there's no 5. So now it's down to 4:5 or 5:4. Since it wants the ration of sixth to seventh, it's 4 to 5.
Hence, the ratio is 4:5, answer A
Hope this helps :)
Stay Cold,
Brook
answer these 3 questions please :) the table is shown above for these 3 questions
Answer:
Answer
Step-by-step explanation:
for 4. I think sports?
for 5. I think sports also.
Not sure though.. sorry if it's wrong.
Save Homework: Sanchez HW 4 Question , 4.5.39 Pat 34 HW Score: 0.005, 333 points O Points of 1 Complete and card deviation of doctor in the computer and concerts and round and your resu michewa Cost of Living Adjustments Data Obwodoma ) Comparative Stary Mean Standard 52175510 Deviation ed the compartimothes for wema) City Comparative - Say Om NY $16.00 Coors for the land setting percentage and women and CITY Housing Los - 20 Cost of living we City Comparative Housing Sutary OC 587 2105 saepe 187 Love Bone 0.00 229 SEL $50.04 - Nupo 38.000 eden 348.904 1411 Los 3807 New 567.50 245 Portu New Y 47 154570 17 37 15457 NY 49 0 Print Done?
The mean housing cost for the given cities is $20.42.
The standard deviation of housing costs for the given cities is 1.91.
The mean is calculated by summing up all the values in the dataset and dividing the sum by the total number of values. In this case, we have the following data for housing costs in different cities:
Comparative City Housing Cost
NY $16.00
Coors $20.00
Los Angeles $22.05
Santa Barbara $18.70
Oceanside $22.90
Porterville $20.50
New York $21.40
To calculate the mean, we add up all the values:
Sum = $16.00 + $20.00 + $22.05 + $18.70 + $22.90 + $20.50 + $21.40 = $141.55
Next, we divide the sum by the total number of values, which is 7 in this case:
Mean = $141.55 / 7 = $20.42
Therefore, the mean housing cost for the given cities is $20.42.
The standard deviation is a measure of the spread or variability in the dataset. It tells us how much the individual values deviate from the mean.
The formula for calculating the standard deviation is:
σ = sqrt[(Σ(x - μ)^2) / N]
Where:
σ is the standard deviation
Σ represents the sum of
x represents each individual value
μ is the mean
N is the total number of values
Using the given data, we substitute the values into the formula:
σ = sqrt[((16 - 20.42)^2 + (20 - 20.42)^2 + (22.05 - 20.42)^2 + (18.70 - 20.42)^2 + (22.90 - 20.42)^2 + (20.50 - 20.42)^2 + (21.40 - 20.42)^2) / 7]
Simplifying the expression within the square root:
σ = sqrt[(5.2364 + 0.0016 + 0.0264 + 2.7164 + 0.0524 + 0.0064 + 0.0064) / 7]
σ = sqrt[8.0456 / 7]
σ = sqrt(1.1494)
σ ≈ 1.07
Therefore, the standard deviation of housing costs for the given cities is approximately 1.07.
These calculations provide a measure of the average and spread of the housing costs across the different cities.
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(a) Bob wants to open a new fastfood shop. He estimates he needs to spend at least $100,000 on renovation and buying commercial kitchen appliances. The average running cost per customer (for food, staff salary, etc.) is $7. Each customer spends $15 on average.
(i) If the number of customers is n, write down the cost function and revenue function as functions of n.
(ii) Determine the minimum number of customers for the business to breakeven.
(iii) Bob has to borrow $100,000 from a bank with interest rate of 3% p.a. with interest payable monthly. If Bob does not repay a single cent, how much does Bob owe the bank after 3 years?
i) The cost function is x = 100,000 + 7n while the revenue function is y = 15n.
ii) The minimum number of customers for the business to break even is 12,500.
iii) The amount that Bob owes the bank after 3 years at 3% p.a. interest payable monthly, but without any repayment, is $109,272.70.
What is a function?A function is a mathematical equation showing the equality of two or more algebraic expressions.
a) Renovation and appliances costs = $100,000
Average running cost per customer = $7
Selling price per customer = $15
i) Let the number of customers = n
Cost function, x = 100,000 + 7n
Revenue function, y = 15n
ii) For the business to break even, y must be equal to x:
15n = 100,000 + 7n
8n = 100,000
n = 12,500
iii) Bank loan = $100,000
Interest rate = 3% p.a.
Interest payment = monthly
Amount after 3 years without any repayment = $100,000 x 1.03^3
= $109,272.70 ($100,000 x 1.092727)
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Ma Bernier has 52 cats and dogs in her house the number of cats is three times the number of dogs how many cats and dogs are in the house
Answer:
dogs - 13
cats - 39
Step-by-step explanation:
Let the number of dogs Ma Bernier have be represented with d
She has 3 times as many cats as dogs, the number of cats she has :
cats = 3d
The sum of the cats and dogs is 52
d + 3d = 52
4d = 52
divide both sides of the equation by 4
d = 13
She has 13 dogs
Cats = 3d
= 3 x 13 = 39
Five students took a quiz. The lowest score was 4, the highest score was 6, the average (mean) was 5.2, and the mode was 6. A possible set of scores for the students is:
A possible set of scores for the students is: 4, 4, 6, 6, 6
How to solve the measures of Central Tendencies?We are given that five students took the quiz. If the lowest score is 4 and the highest score is 6, we can say that the set of values can be expressed as:
4, x, y, z, 6
Here we can see that the mode is 6 and the mean is 5.2. Therefore, at least one other student of hers has scored her 6, which could result in:
4, x, y, 6, 6
Therefore:
(4 + x + y + 6 + 6)/5 = 5.2
16+x+y=26
x + y = 10
So the other two numbers are probably 6 and 4, because 6 is the mode, so they can't both be 5.
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Simplify: 6a - 2(5a - 6)
Answer:
[tex]-4a + 12[/tex]
Step-by-step explanation:
convert from vertex form to standard form... y= -(x-3)^2-8
Answer:
-x² + 6x - 17
Step-by-step explanation:
First, expand (x-3)² using FOIL
(x - 3)(x - 3)
= x² - 6x + 9
Distribute the negative sign to the expression:
-(x² - 6x + 9)
-x² + 6x - 9
Now, subtract 8 from this
-x² + 6x - 9
= -x² + 6x - 17
So, the equation in standard form is -x² + 6x - 17
The answer is.. x^2+6x-17
Write the equation of the line if the slope is 6 and the y-intercept is -2.
Answer:
y=6x-2
Step-by-step explanation:
slope=6
y-intercept=-2
y=6x-2
I need help I don’t really get it
Answer:
A. 72 cm
Step-by-step explanation:
72 x 2/3 = 48
Answer:
72 cm
Step-by-step explanation:
if the smaller figure is 48 cm and its a 2/3 ratio
lets just say 2x:3x
2x=48 so x would =24
then the larger perimeter would be 3*24 which is 72
8 z
6
OD
UN
4 3
N
1 2 3 4 5 6 7 8 9
x
Which two equations represent the situation?
o y=jx and y=x-4
o =
O y=3+ and y = X+4
O y = 3x and y = x+4
O y = 3x and y = x-4
Answer:
Step-by-step explanation:
Find the area of the composite figure. Please help me
Answer:
51.5 ft^2
Step-by-step explanation:
Question 2 of 10
If f(x) = 3x - 1 and g(x) = x + 2, find (f+ g)(x).
A. 4x + 1
B. 2x - 3
с. 3х – 3
D. 2x - 1
Solve the linear system X 1 X1 + 2x2 3.21 + 4.02 IL || -1 -1 = via Cramer's rule if possible.
The linear system X₁ + 2X₂ = 3.21 and 4.02X₁ + IL || -1 = -1 using Cramer's rule, we need to find the values of X₁ and X₂.
To apply Cramer's rule, we first need to calculate the determinant of the coefficient matrix and the determinants of the matrices obtained by replacing each column of the coefficient matrix with the constant terms.
The coefficient matrix is:
| 1 2 |
| 4.02 IL || |
The determinant of the coefficient matrix, denoted as D, is given by:
D = (1 * IL ||) - (2 * 4.02)
= IL || - 8.04
The matrix obtained by replacing the first column with the constant terms is:
| 3.21 2 |
| -1 IL || |
The determinant of this matrix, denoted as D₁, is given by:
D₁ = (3.21 * IL ||) - (-1 * 2)
= 3.21IL || + 2
The matrix obtained by replacing the second column with the constant terms is:
| 1 3.21 |
| 4.02 -1 |
The determinant of this matrix, denoted as D₂, is given by:
D₂ = (1 * -1) - (4.02 * 3.21)
= -1 - 12.9042
= -13.9042
Now, we can find the values of X₁ and X₂ using the formulas:
X₁ = D₁ / D
X₂ = D₂ / D
Substituting the values we calculated earlier, we have:
X₁ = (3.21IL || + 2) / (IL || - 8.04)
X₂ = (-13.9042) / (IL || - 8.04)
This gives us the solution to the linear system.
Solve the linear system X 1 X1 + 2x2 3.21 + 4.02 IL || -1 -1 = via Cramer's rule if possible.
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Yesterday, the temperature change for a 5-hour period of time was – -degree per
hour. Which statement describes this change?
A
The temperature rose 5 degrees.
B
The temperature rose 4 1/4 degrees.
с
The temperature fell 4 degrees.
D
The temperature fell 5 4/5
degrees
Answer:
D
Step-by-step explanation:
Sophia invest $12,350 in a account that earns 4.5% annual simple interest. Assuming she makes no additional deposits or withdrawals, how much interest will Sophia earn after 36 months?
Answer:
I DO NOT KNOW
Step-by-step explanation:
I am here for the answers
I am hungry
Pizza
Find the difference. Write your answer in simplest form.
9/10 - 5/10
Answer:
2/5 is the simplest form.
Step-by-step explanation:
9/10 - 5/10 = 4/10 (9 - 5 = 4) 4/10 simplified is 2/5 (divide both 4 and 10 by 2 and you get 2/5).
Hope that helps!
what number adds up to three and multiples 22 to
Answer:
Factors of 22: 1, 2, 11, and 22.
Prime Factorization of 22: 22 = 2 × 11.Step-by-step explanation:
26.2 miles in 4 hours. Find the unit rate
Answer:
Step-by-step explanation:
Unit rate = 26.2 ÷ 4 = 6.55
the measure of the vertex angle of an isoceles triangle is 120 degrees and the length of a leg is 8 cm. find the length of the diameter circumcised about this triangle
The length of the diameter circumcised about this isosceles triangle is 32 cm.
To find the length of the circumcircle's diameter, we can use the properties of an isosceles triangle.
In an isosceles triangle, the vertex angle is the angle formed by the two congruent sides. In this case, the vertex angle is given as 120 degrees.
We know that the vertex angle of an isosceles triangle is located opposite the base. Let's denote the base as side a, and the congruent sides as side b.
In an isosceles triangle, the base angles are congruent. Since the sum of the angles in a triangle is 180 degrees, each base angle in this triangle measures (180 - 120) / 2 = 30 degrees.
Now, we can apply the Law of Sines to find the length of the base, side a. The Law of Sines states:
a/sin(A) = b/sin(B) = c/sin(C)
In our case, since angle A is the vertex angle and side a is the base, we have:
a/sin(120) = b/sin(30)
Using the given length of the leg (side b) as 8 cm, we can solve for side a:
a/sin(120) = 8/sin(30)
a = (8 × sin(120)) / sin(30)
Using the values of sin(120) and sin(30) from a trigonometric table or calculator:
a ≈ (8 × √3) / (1/2) = 16√3 cm
Now, let's find the length of the diameter of the circumcircle. The circumcircle of a triangle passes through the vertices of the triangle and has its center at the intersection of the triangle's perpendicular bisectors.
Since the triangle is isosceles, the perpendicular bisector of the base will pass through the vertex angle and bisect it, resulting in two 60-degree angles.
In an equilateral triangle, the perpendicular bisector of a side passes through the triangle's center, which coincides with the center of the circumcircle. Since our isosceles triangle has two congruent sides, we can treat it as half of an equilateral triangle.
The length of the diameter of the circumcircle of an equilateral triangle is given by the formula:
Diameter = 2 × (side length) / √3
In our case, since we have half of an equilateral triangle, the diameter of the circumcircle will be:
Diameter = 2 × (16√3) / √3 = 32 cm
Therefore, the length of the diameter circumcised about this isosceles triangle is 32 cm.
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What is angle BXC and why?? Please help
Answer:
BXC=70 degrees
Step-by-step explanation:
XBC = 55
corresponding angles are equal
XCB=55
isosceles base angles are equal
BXC=70
angles in a triangle add up to 180 degrees
Pls helpppp and thank you
using cramer’s rule, what are the values of x and y in the solution to the system of linear equations below?
The value of x =-3 and y=1 in the system of linear equation.
Given equations
-2x+3y+z=7
-4x-y-2z=15
x+2y+3z=-7
Using cramer's rule to find x and y
First we make matrix of coefficient of x,y and z and then find the determinant
[tex]A = \left[\begin{array}{ccc}-2&3&1\\-4&-1&-2\\1&2&3\end{array}\right][/tex]
Now we find determinant of A
|A|=-2(-3+4)-3(-12+2)+1(-8+1)
|A|=21
[tex]A_x=\left[\begin{array}{ccc}7&15&-7\\-4&-1&-2\\1&2&3\end{array}\right][/tex]
Determinant of Ax
|Ax|=7(-3+4)-3(45-14)+1(30-7)
|Ax|=-63
[tex]A_y=\left[\begin{array}{ccc}7&15&-7\\-4&-1&-2\\1&2&3\end{array}\right][/tex]
Determinant of Ay
|Ay|=-2(45-14)-7(-12+2)+1(28-15)
|Ay|=21
[tex]A_z=\left[\begin{array}{ccc}-2&3&1\\-4&-1&-2\\7&15&-7\end{array}\right][/tex]
Determinant of Az
|Az|=-2(7-30)-3(28-15)+7(-8+1)
|Az|=-42
Now we find for x, y and z
[tex]x=\frac{|A_x|}{|A|}[/tex]
= -63/21 = -3
[tex]y = \frac{|A_y|}{|A|}[/tex]
= 21/21 = 1
[tex]z = \frac{|A_z|}{|A|}[/tex]
= -42/21
= 2
Thus, the value of x =-3 and y=1 in the system of linear equation.
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Given question is incomplete, the complete question is below
using cramer’s rule, what are the values of x and y in the solution to the system of linear equations below?
determine the volume of the rectangular prism.
height:12ft
width:6ft
length:3ft
Answer:
216 ft³
Step-by-step explanation:
h*w*l=v
[tex]12 \times 6 \times 3 = 216[/tex]
10/y=2/9, find the solution of y. stat.
Answer:
y=45
Step-by-step explanation:
Let's solve your equation step-by-step.
10 y = 2 /9
Step 1: Cross-multiply.
10 y = 2 /9
(10)*(9)=2*y
90=2y
Step 2: Flip the equation.
2y=90
Step 3: Divide both sides by 2.
2y /2 = 90 /2
y=45
brainliest please?
Answer:
y = 45
Step-by-step explanation:
10/y=2/9
10 = y * 2/9
10 = 2/9y
10 * 9 = 2/9y * 9
90 = 2y
90/2 = 2y/2
y = 45
ps: * means multiply
Im new here :) but hey you got these qs try your best okie
I hope and im glad to help
A gift box has the shape of a rectangular prism. How much wrapping paper do you need to cover the box?
Thanks in advance!
Answer:
852 inches square
Step-by-step explanation:
2×(16×15 + 16×6 + 15×6)
Answer:
652 in²
Step-by-step explanation:
The formula is 2(wl+hl+hw)
h is height
w is width
l is length
Use PEMDAS/BIDMAS/BODMAS (do the parentheses then multiply it)
326*2 = 652
add your units
652 in^2
You eat 11 grams of cereal each day. If you eat the same amount of cereal each day, how many grams of cereal will you eat in 5 days?
Answer:
55 grams
Step-by-step explanation:
11×5=55 grams
if its the same amount everyday then 55
(it made me type more)
Answer:55
Step-by-step explanation: 11x5
A gardener made a scale drawing of a lawn with a scale factor of 1:4 The dimensions of her drawing are 15 inches long by 10 inches wide. Her partner plans to make another scale drawing of the lawn, but with a scale factor of 1:20. What are the dimensions of her scale drawing? O A. The length is 50 inches and the width is 75 inches, OB. The length is 3 inches and the width is 2 inches. O Q. The length is 75 inches and the width is 50 inches. O D. The length is 2 inches and the width is 3 inches.
Answer:
B is the correct answer
Step-by-step explanation:
A roast beef sandwich costs $6.75. A customer buys multiple roast beef sandwiches. Write an equation that represents the situation. Use $x$ to represent the number of roast beef sandwiches. Then determine how many sandwiches the customer buys.
Amount Used for Payment $80
Change Received $19.25
An equation that represents this situation is
.
The customer buys
sandwiches.
Answer:
[tex]\frac{80-19.25}{6.75} = x[/tex]
Step-by-step explanation:
Subtract $19.25 from the Amount Used for Payment ($80) to get the amount spent, then divide the amount of each sandwich to get the amount of sandwiches bought.
ver imagen para la pregunta
Answer: C
Step-by-step explanation: