The ratio of the volume of cone A to the volume of cone B is 27:8
Cone A and cone B are mathematically similar.
The surface area of cone A is 297 cm²
Show that the surface area of cone B is 132 cm²
Answers
h_b / h_a = r_b / r_a (1)
The ratio of the volumes of cone A to cone B is 27:8, so we have:
(1/3) * π * r_a^2 * h_a / [(1/3) * π * r_b^2 * h_b] = 27/8
Simplifying this equation using Equation (1), we get:
r_b^2 / r_a^2 = 27/8 * h_b / h_a = 27/8 * r_b / r_a
Multiplying both sides by r_a^2, we get:
r_b^2 = 27/8 * r_a^2
Taking the square root of both sides, we get:
r_b = (3/2) * r_a
Substituting this relationship into the formula for the surface area of cone A, we get:
π * r_a * (r_a + √(h_a^2 + r_a^2))
Substituting r_b = (3/2) * r_a and simplifying, we get:
π * r_a * (2.5 * r_a + √(h_b^2 + (2.5 * r_a)^2)) = 297
Simplifying this equation using Equation (1), we get:
π * r_b * (2.5 * r_b + √(h_a^2 + (2.5 * r_b)^2)) = (27/8) * 297
Simplifying this equation, we get:
π * r_b * (2.5 * r_b + √(h_b^2 + (2.5 * r_b)^2)) = 132
Therefore, the surface area of cone B is 132 cm².
Since the cones are mathematically similar, we know that the ratio of their volumes is equal to the cube of the ratio of their radii:
V_A/V_B = (r_A/r_B)^3 = (27/8)
Therefore,
r_A/r_B = (27/8)^(1/3)
We also know that the surface area of cone A is given by:
S_A = πr_A√(r_A^2 + h_A^2) + πr_A^2
where h_A is the height of cone A.
We don't know the value of h_A, but we can use the fact that the cones are mathematically similar to find the ratio of their heights:
h_A/h_B = r_A/r_B
h_B = (r_B/r_A)h_A = (8/27)h_A
Now we can use the fact that the ratio of the surface areas of two similar cones is equal to the square of the ratio of their heights:
S_A/S_B = (h_A/h_B)^2 = (27/8)^2
Substituting the given value of S_A and solving for S_B:
297/S_B = (27/8)^2
S_B = 132 cm²
Related Questions
Hazel has 8 cousins. Hazel has 2 times as many cousins as Sawyer.
How many cousins does Sawyer have?
Let c stand for the number of cousins Sawyer has.
Which bar model represents the problem?
Hazel C
Sawyer с с
Sawyer 8
8
Hazel 8 8
Sawyer C
Hazel
с с
8
Hazel 8
Sawyer 8 8
с
Answers
Sawyer has 4 cousins given that Hazel has 2 times as many cousins as Sawyer.
How many cousins does Sawyer have?From the question, we have the following parameters that can be used in our computation:
Hazel has 8 cousins. Hazel has 2 times as many cousins as Sawyer.Using the above as a guide, we have the following:
Hazel = 2 * Sawyer
Let c stand for the number of cousins Sawyer has.
So, we have
Hazel = 2 * c
Substitute the known values in the above equation, so, we have the following representation
2 * c = 8
Divide by 2
c = 4
Hence, the number of cousins Sawyer has is 5
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Study this table.
X
-3
-2
0
4
y
-2
0
4
12
Which best describes the function represented by the data in the table?
O linear with a common ratio of 2
Olinear with a common first difference of 2
O quadratic with a common ratio of 2
O quadratic with a common first difference of 2
Answers
The Function is linear with a common first difference of 2.
We have,
x y
-3 -2
-2 0
0 4
4 12
For the first set of points
m=(0-(-2))/(-2--3)
m = (0+2)/(-2+3)
m= 2/1 = 2
For the second set of points
m = (4-0)/(0-(-2))
m = 4/(0+2)
m = 4/2 = 2
For the third set of points
m = (12-4)/(4-0)
m = 8/4
m = 2
Thus, the function is linear with a common first difference of 2.
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How do I find the probability?
Answers
Answer:
To find the probability of an event occurring, you need to divide the number of ways the event can occur by the total number of possible outcomes. The probability is a number between 0 and 1, with 0 indicating that the event is impossible and 1 indicating that the event is certain.
For example, if you want to find the probability of rolling a 3 on a standard six-sided die, there is only one way to roll a 3 and six possible outcomes (1, 2, 3, 4, 5, 6). So, the probability of rolling a 3 is 1/6 or approximately 0.17.
Keep in mind that the probability of an event occurring is not a guarantee that the event will happen. It only indicates the likelihood of the event happening based on the available information.
Bacteria was put in a petri dish with antibacterial soap. Determine the logarithmic regression of the bacteria. Use either a
calculator or spreadsheet program.
Answers
Using the given data, a logarithmic regression equation of the form Bacteria = 447.91 * ln(12) - 1733.1 was found to model the relationship between time and bacteria population. So, the population of bacteria is about 44.1 at 12 hours.
Based on the provided data, we can use a logarithmic regression to model the relationship between time and bacteria population. Here's how to do it using Microsoft Excel
Enter the data into two columns one for time and one for bacteria population. Create a scatter plot of the data. Right-click on one of the data points in the plot and select "Add Trendline."
In the Trendline options, choose "Logarithmic" as the type of trendline. Check the box for "Display Equation on Chart" to show the equation for the trendline.
The resulting equation is
Bacteria = 447.91 * ln(Time) - 1733.1
This equation represents a logarithmic regression of the bacteria population over time.
To use this equation to predict the bacteria population at a specific time, substitute the time value into the equation and solve for the bacteria population. For example, if we want to predict the bacteria population at 12 hours, we can substitute 12 into the equation
Bacteria = 447.91 * ln(12) - 1733.1
Bacteria ≈ 44.1
So we would predict a bacteria population of about 44.1 at 12 hours.
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Activity
After an intensive search, Philip has narrowed his choices to four houses. Now he wants to buy the one that fits his budget. He has saved $40,000
for the down payment. Use the fixed-rate calculator to find the monthly payment for each house.
House Purchase Price Monthly Payment Affordability
A
$250,000
B
$200,000
C
$195,000
D
$180,000
Answers
Answer:
A
Step-by-step explanation:
A
Harold ran 3 miles in 24 minutes. How long would it take him to run 4 miles?
Answers
If you want to know how I got that comment!
Answer:32 minutes
Step-by-step explanation:
He is running at a rate of 1 mile every 8 minutes. 3 miles in 24 minutes and 4 miles in 32 minutes
1. What would you get in your numerator when you multiply your terms together in the first step in simplifying?
2. What two terms would you combine in the numerator to simplify?
Answers
The step in simplifying the expression 3x/(x+5) - 3/(x+6) would result in 3x² + 18x - 3x - 15. The two terms that can be combined in the numerator to simplify are -3x and 18x. So, the correct answer is A), B) and D).
When multiplying the terms together in the first step of simplifying, we would get
3x - 3(x + 5)/(x + 6)
Simplifying this expression would lead to
3x² + 15x - 3x - 15/(x + 6)
Therefore, the answer is option (b): 3x² + 18x - 3x - 15
To simplify the numerator, we need to combine like terms.
To simplify the numerator, we need to combine like terms. The given expression is
3x² + 18x - 3x - 15
Here, the terms 18x and -3x have the same variable (x) and the same power (first power), but they have opposite signs. Therefore, we can combine them by subtracting the smaller value from the larger value. In this case, we have
18x - 3x = 15x
So, the expression simplifies to
3x² + 15x - 15
Therefore, the two terms that we would combine in the numerator to simplify are -3x and 18x, which give us 15x. So, the correct option is B) and D).
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cost minimal of logistic form factory to
warehouse mathematical problem
Answers
Answer:
To calculate the minimal cost of logistics from a factory to a warehouse, you would need to consider various factors such as the distance between the factory and the warehouse, the mode of transportation, the weight and volume of the goods being transported, the number of trips required, and any applicable taxes or fees.
To formulate this as a mathematical problem, you could use linear programming, which is a method for optimizing a linear objective function subject to linear equality and inequality constraints.
Let's say we have a factory that produces goods and a warehouse that stores those goods. We want to transport the goods from the factory to the warehouse in a cost-effective way. Let's assume that there are three transportation options available: truck, train, and ship. Each option has a different cost per unit of distance traveled, and a different maximum weight and volume capacity.
Let x1, x2, and x3 be the number of units transported by truck, train, and ship, respectively. Then, the objective function we want to minimize would be:
C = 10x1 + 8x2 + 6x3
where C is the total cost of transportation.
Next, we would need to set up constraints based on the transportation options and the available resources. For example:
Truck capacity: 3x1 <= 15000 (maximum weight capacity of 15000 units for the truck)
Train capacity: 5x2 + 2x1 <= 40000 (maximum weight capacity of 40000 units for the train)
Ship capacity: 2x3 + 3x1 <= 30000 (maximum weight capacity of 30000 units for the ship)
Distance constraint: 2x1 + 3x2 + 5x3 <= 10000 (maximum distance of 10000 units for all transportation modes combined)
The above constraints limit the total weight transported, the capacity of each mode of transport, and the total distance that the goods are transported.
Finally, we would need to add non-negative constraints to ensure that all variables are greater than or equal to zero:
x1 >= 0, x2 >= 0, x3 >= 0
Once we have set up this linear programming problem, we can use optimization techniques to solve for the values of x1, x2, and x3 that minimize the cost of transportation while satisfying all of the constraints.
Step-by-step explanation:
if this helps, please mark my answer as brainliest
Simplify 6/15 x 55/10
Answers
2.2 in decimal form.
eleven fifths
Use substitution. What is the solution to the system of equations? Use the drop-down menus to explain your answer. y = 12 x + 2 2y = x + 4 The system of equations has Choose... . The two equations represent Choose... .
Answers
Explanation:
To solve the system of equations using substitution, we can start by solving one of the equations for one variable in terms of the other. Let's solve the first equation, y = 12x + 2, for y in terms of x:
y = 12x + 2
Now we can substitute this expression for y into the second equation, 2y = x + 4, and solve for x:
2(12x + 2) = x + 4
24x + 4 = x + 4
23x = 0
x = 0/23
x = 50
Now that we have solved for x, we can substitute this value into either equation to solve for y. Let's use the first equation, y = 12x + 2:
y = 12(50) + 2
y = 602
Therefore, the solution to the system of equations is x = 50 and y = 602.
Regarding the drop-down menu options:
- The system of equations has one solution. (This is the correct option, as there is only one set of values for x and y that satisfy both equations.)
- The two equations represent two lines. (This is also correct, as each equation represents a line in the xy-plane.)
Find the x intercept of the line 1x -2y =23
Answers
Answer: x=23
Step-by-step explanation:
Answer: 23
Step-by-step explanation:
When you have a value on the x-axis, your y=0
plug in y=0 to find your x-intercept
1x-2(0)=23
1x=23
x=23
There are 140 in the seventh grade, and 10% are in the Environmental Club. How many students are in the Environmental Club?
Answers
10% of 140 is 14
A scientist studying babies born prematurely would like to obtain an estimate for the mean birth weight, μ,
of babies born during the 24th week of the gestation period. She plans to select a random sample of birth
weights of such babies and use the mean of the sample to estimate μ. Assuming that the population of birth
weights of babies born during the 24th week has a standard deviation of 2.8 pounds, what is the minimum
sample size needed for the scientist to be 95% confident that her estimate is within 0.4 pounds of μ?
Carry your intermediate computations to at least three decimal places. Write your answer as a whole number
(and make sure that it is the minimum whole number that satisfies the requirements).
Answers
The sample size needed for the scientist to be 95% confident that her estimate is within 0.4 pounds of μ is given as follows:
n = 189 babies.
What is a z-distribution confidence interval?The bounds of the confidence interval are given by the rule presented as follows:
[tex]\overline{x} \pm z\frac{\sigma}{\sqrt{n}}[/tex]
In which:
[tex]\overline{x}[/tex] is the sample mean.z is the critical value.n is the sample size.[tex]\sigma[/tex] is the standard deviation for the population.The margin of error is defined as follows:
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
The confidence level is of 95%, hence the critical value z is the value of Z that has a p-value of [tex]\frac{1+0.95}{2} = 0.975[/tex], so the critical value is z = 1.96.
The remaining parameters are given as follows:
[tex]M = 0.4 \sigma = 2.8[/tex]
Then the sample size is obtained as follows:
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
0.4sqrt(n) = 1.96 x 2.8
sqrt(n) = (1.96 x 2.8/0.4)
n = (1.96 x 2.8/0.4)²
n = 189 babies. (rounded up).
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I need help I can't ask my teacher about this because I am sick so I need help learning to solve this.
Answers
Answer: x = 20
Step-by-step explanation:
[tex]\frac{3}{5} x - \frac{1}{4} x = 7\\12x-5x=140\\7x=140\\x=20[/tex]
The football players had to sell DEVIL FOOTBALL t-shirts to raise money for their next uniforms.They charged $14 for short sleeve shirts and $17 for long sleeve shirts. At the end of the fundraiser, they had sold 24 shirts and had made $378. How many of each type of shirt did they sell?
Use
S as the number of short sleeve shirts and
L as the number of long sleeve shirts.
PLS HELP
Answers
Answer:
Let's set up a system of equations to solve for S and L:
S + L = 24 (they sold a total of 24 shirts)
14S + 17L = 378 (the total amount made from selling the shirts was $378)
We can solve for one variable in the first equation and substitute it into the second equation:
S = 24 - L
14(24 - L) + 17L = 378
336 - 14L + 17L = 378
3L = 42
L = 14
So they sold 14 long sleeve shirts. We can substitute this value back into the first equation to solve for S:
S + 14 = 24
S = 10
Therefore, they sold 10 short sleeve shirts and 14 long sleeve shirts.
Parallelogram EFGH, E(-1,5), F(2,8), G(4,4), and H(1,1). Find the perimeter and area of the parallelogram. Round to the tenths place
Answers
The requried, perimeter and area of the parallelogram are 18.4 centimeters and 18 square centimeters respectively.
To find the perimeter of parallelogram EFGH, we need to find the length of all four sides and add them up. The distance formula is used to find the length of each side:
EF = √((2-(-1))² + (8-5)²) = √(3² + 3²) = √(18)
FG =√(20)
GH = √(18)
HE = √(20)
Therefore, the perimeter is:
Perimeter = EF + FG + GH + HE = √(18) + √(20) + √(18) + √(20) ≈ 18.4
Similarly,
The area of the parallelogram is given as,
= 18 square centimeters
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Which equations can be used to solve for y, the length of the room? Select three options. y(y + 5) = 750 y2 – 5y = 750 750 – y(y – 5) = 0 y(y – 5) + 750 = 0 (y + 25)(y – 30) = 0
Answers
The equations to solve the length of the room is
a) y² - 5y = 750
b) 750 - y ( y - 5 ) = 0
c) ( y + 25 ) ( y - 30 ) = 0
Given data ,
Let the area of a rectangular room is 750 square feet.
Let the width of the room is 5 feet less than the length of the room
So , on simplifying , we get
w = l - 5
Area of rectangle = length x width
And , A = l x w
A = l ( l - 5 )
750 = y ( y - 5 )
Therefore , the equation is
a) y² - 5y = 750
b) 750 - y ( y - 5 ) = 0
On simplifying the quadratic equation , we get
c) ( y + 25 ) ( y - 30 ) = 0
Hence , the length of the rectangular room is solved
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The complete question is attached below :
Which equations can be used to solve for y, the length of the room? Select three options.
a) y(y + 5) = 750
b) y² – 5y = 750
c) 750 – y(y – 5) = 0
d) y(y – 5) + 750 = 0
e) (y + 25)(y – 30) = 0
Find the volume of the sphere. Give the answer in terms of Pi and rounded to the nearest cubic foot. the radius is 5 ft.
Answers
The volume of the sphere with a radius of 5 feet to the nearest cubic foot is 166.67π feet³.
Given a sphere.
Radius of the sphere = 5 feet
The formula to find the volume of the sphere is,
Volume of the sphere = 4/3 πr³,
where r is the radius of the sphere.
Substituting the given radius,
Volume of the sphere = 4/3 × π × (5)³
= 4/3 × π × 125
= 166.67π
Hence the volume of the sphere is 166.67π feet³.
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Julia volunteers at a zoo. She records the number of people in each group of visitors in one day.
Based on Julia's data, if a larger zoo has 600 groups of visitors in a day, how many of them would you expect to be groups of 5 or more?
People in Group 1 2 3 4 5 6 7 8
Frequency
9 52 27 38 16 6 5 7
about
groups
Answers
We would expect 138 groups in the larger zoo to have 5 or more people based on the relative frequency of group sizes in Julia's data.
To determine how many groups of 5 or more people we would expect to see in a larger zoo with 600 groups of visitors in a day, we need to use the relative frequency of each group size in Julia's data.
To calculate the relative frequency of each group size, we need to divide the frequency of each group size by the total number of groups:
Group Size Frequency Relative Frequency
1 9 9/150 = 0.06
2 52 52/150 = 0.35
3 27 27/150 = 0.18
4 38 38/150 = 0.25
5 16 16/150 = 0.11
6 6 6/150 = 0.04
7 5 5/150 = 0.03
8 7 7/150 = 0.05
We can see that the relative frequency of groups with 5 or more people is 0.11 + 0.04 + 0.03 + 0.05 = 0.23. This means that we would expect 23% of the 600 groups in the larger zoo to have 5 or more people.
To calculate the actual number of groups with 5 or more people, we multiply the total number of groups by the relative frequency:
Number of groups with 5 or more people = 600 x 0.23 = 138
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You skateboards down a ramp. The ramp starts at a height of 10 feet and runs 55 feet along the ground. How steep was the ramp? We are missing a side or and angle? Regular or Inverse Trig?
Answers
The steepness of the ramp is approximately 56 feet.
How to find the steepness of the ramp?You skateboards down a ramp. The ramp starts at a height of 10 feet and runs 55 feet along the ground.
Therefore, let's find how steeped the ramp is.
Hence, using Pythagoras's theorem,
c² = a² + b²
where
a and b are the other legsc is the hypotenuse sideTherefore,
55² + 10² = c²
c² = 3025 + 100
c² = 3125
square root both sides of the equation
c = √3125
c = 55.9016994375
c = 56 feet
Therefore,
steepness of the ramp = 56 feet
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Please help! I will mark brainiest! I do not understand the parenthesis being added.
Answers
Answer:
<4√97,-9√97>
Step-by-step explanation:
First, we need to find the values of A-C and B-D:
A-C = < 3, 6 > - < 7, -3 > = < -4, 9 >
B-D = < 4, -7 > - < 0, 2 > = < 4, -9 >
Next, we need to find the magnitude of A-C, which is denoted by |A-C| and is equal to the square root of the sum of the squares of its components:
|A-C| = √((-4)^2 + 9^2) =√(97)
Now we can substitute all the values into the expression |A-C|(B-D) and evaluate:
|A-C|(B-D) = √(97) * < 4, -9 >
= < 4√(97), -9√(97) >
So the final answer is < 4√(97), -9√(97) >.
Given the figure below, find the values of x and z.
120°
(8x
+ 96).
Answers
Answer:
x = 3; z = 60°
Step-by-step explanation:
x:
The angles measuring 120° and (8x + 96)° are vertical angles, which means they're congruent and equal.
Thus, we can solve for x by setting the two angles equal to each other and isolate x:
[tex]120=8x+96\\24=8x\\3=x[/tex]
We can check our answer by plugging in 3 for x and ensure that we get 120:
[tex]120=8(3)+96\\120=24+96\\120=120[/tex]
z:
We see that a horizontal straight line separates the angle measuring 120° and z°. Straight lines create straight angles, which equal 180°.
Thus, we can find the measure of z by adding the 120° angle and the z° and set them equal to 180. Then, we must isolate z:
[tex]120+z=180\\z=60[/tex]
peaceful travel agency offers vacation packages each vacation packages includes a city, and a airline.The agency has 6 cities, and 2 airlines to choose from.how many different vacation packages do they offer
Answers
Solving the given word problem systematically, Serene Travel Organization offers 12 diverse vacation packages.
How to Solve the Problem?To calculate the overall number of distinctive excursion packages that Quiet Travel Organization offers, we ought to duplicate the number of cities by the number of carriers:
Add up to number of get-away bundles = number of cities x number of airlines
Since the agency has 6 cities and 2 aircrafts to select from, we are able substitute those values within the over equation:
Add up to number of get-away bundles = 6 x 2 = 12
In this manner, Serene Travel Organization offers 12 diverse get-away bundles.
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The length of a rectangle is represented by the function L(x) = 6x. The width of that same rectangle is represented by the function W(x) = 4x2 − 5x + 12. Which of the following shows the area of the rectangle in terms of x? (L ⋅ W)(x) = 24x3 − 30x + 72 (L ⋅ W)(x) = 24x3 − 30x2 + 72x (L + W)(x) = 4x2 + x + 12 (L + W)(x) = 2x2 + x + 12
Answers
The area of the rectangle in terms of x can be represented as (L . W)(x) = 24x³ - 30x² + 72x.
Given a rectangle.
Length of the rectangle, L(x) = 6x
Width of the rectangle, W(x) = 4x² − 5x + 12
The formula to find the area of the rectangle is,
Area = Length × Width
Substituting the given length and width,
Area of the rectangle = L(x) . W(x)
= (L . W)(x)
= (6x) (4x² − 5x + 12)
= 24x³ - 30x² + 72x
Hence the area of the rectangle is represented as (L . W)(x) = 24x³ - 30x² + 72x.
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Answer:
(L . W)(x) = 24x³ - 30x² + 72x.
Step-by-step explanation:
Qd=50-4Px+0.5I+10Py-2Pz
Answers
Answer:
The equation Qd = 50 - 4Px + 0.5I + 10Py - 2Pz represents the demand function for a certain good X, where Qd is the quantity demanded, Px is the price of X, I is the consumer's income, Py is the price of another good Y, and Pz is the price of another good Z.
To solve for the equilibrium price and quantity, we need to find the point where the quantity demanded equals the quantity supplied. However, without information on the supply function or market conditions, we cannot find the equilibrium price and quantity.
We can use the demand equation to determine the effect of changes in the independent variables on the quantity demanded for the good. For example, an increase in the price of X (Px) would lead to a decrease in the quantity demanded (Qd), while an increase in the price of Y (Py) or a decrease in the price of Z (Pz) would lead to an increase in the quantity demanded (Qd). An increase in income (I) would also lead to an increase in the quantity demanded (Qd).
Note that it is important to understand the context and assumptions underlying the demand function in order to make accurate economic predictions or decisions based on it.
Step-by-step explanation:
Find the value of the trig function indicated.
3)
tan 0
13
12
0pls help
Answers
The value of the identities are;
1. tan θ = 5/12
2. cot θ = √7/3
How to determine the identitiesTo determine the value of the identities, we need to take note of the different identities;
sinetangentcotangentsecantcosecantcosineFrom the information given, we need to take note that;
tan θ = opposite/adjacent
cot θ = inverse of tangent identity
cot θ = adjacent/opposite
then,
1. tan θ =
Opposite = 5
Adjacent = 12
tan θ = 5/12
2. cot θ = 4√7/12 = √7/3
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Trigonometry question. Please help me
Answers
The apex angle |‹aed| of the rectangular base pyramid is equal to 14°.
What is a rectangular base pyramidIn a rectangular base pyramid, the base is a rectangle and the apex (or top point) is directly above the center of the rectangle.
The apex angle is the angle formed by the edges of the pyramid at the apex. In a rectangular base pyramid, the apex angle depends on the dimensions of the rectangle base and the height of the pyramid. It can be calculated using trigonometric functions.
The apex angles bec and aed formed by the opposite width of the rectangle base are equal.
In conclusion, the apex angle |‹aed| of the rectangular base pyramid is equal to 14°.
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50 points. Out of 120 seventh and eighth grade CAVA students there were 30 students that chose Music as their elechive course and the rest chose World Language. There were a total of 60 eighth grade students and 40 of them chose
World Language as their elective.
Use this information to complete the two-way table.
Enter your answer by filling in the boxes to complete the table (6 pts)
Answer:
Answers
Based on the informtaion provided, the two-way table would be,
Music World Language Totals
8th Grade 20 40 60
7th Grade 10 50 60
Total 30 90 120
In this situation there were total 120 seventh and eighth grade CAVA students. And there were a total of 60 eighth grade students.
Total number of students = 120
This means that the number of students in 7th grade : 120- 60 = 60
Out of 120 seventh and eighth grade students, 30 students chose Music as their elechive course.
This means that remaining 120 - 30 = 90 students chose World Language as their elechive course.
Here, 40 eighth grade students chose World Language as their elective.
This means that out of total 90 students 90 - 40 = 50 students of 7th Grade chose World Language as their elective.
Now consider the 8th grade students,
Out of 60 students 40 chose World Language.
So, 60 - 40 = 20 must chose Music as their elective.
Now consider the 7th grade students,
Out of 60 students 50 chose World Language.
So, 60 - 50 = 10 students must chose Music as their elective.
Hence the required two-way table would be,
Music World Language Totals
8th Grade 20 40 60
7th Grade 10 50 60
Total 30 90 120
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Here are two similar solid shapes.
and
A
surface area of shape A: surface area of shape B = 3:4
The volume of shape B is 10 cm³
Work out the volume of shape A.
Give your answer correct to 3 significant figures.
B
Answers
Step-by-step explanation:
Let the volume of shape A be V. Since the surface area of shape A is 3/4 times that of shape B, the surface area of shape A is 3/7 times the total surface area of the two shapes combined.
Therefore, the surface area of shape A is:
3/7 (surface area of shape A + surface area of shape B) = 3/7 (4/3 surface area of shape B) = 12/21 surface area of shape B
We know that the volume of shape B is 10 cm³, and we can find the volume of shape A by using the ratio of the volumes to the ratio of the surface areas:
V/10 = 3/4
V = 7.5 cm³ (to 3 significant figures)
Therefore, the volume of shape A is 7.5 cm³.
What is the slope of the line that contains the points (−3, −1) and (3, −10)?
Undefined
0
negative two thirds
negative three halves
Answers
The slope of the line that contains the points (-3, -1) and (3, -10) is -3/2.
Given two points.
We have to find the slope of the line.
Slope of a line passing through (x, y) and (x', y') is,
Slope = (y' - y) / Ix' - x)
Here two points are,
(-3, -1) and (3, -10)
Slope = (-10 - -1) / (3 - -3)
= -9 / 6
= -3/2
Hence the slope of the line is -3/2.
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