Answer:
A
Step-by-step explanation:
Final answer:
To find the amount of snow needed to build the snowman, we need to calculate the volume of each ball and then add them together. The total volume is 18.84 cubic feet, rounded to 19 cubic feet.So,Option A.19 cubic feet of snow is correct.
Explanation:
To find how much snow is needed to build the whole snowman, we need to calculate the volume of each ball and then add them together. The volume of a sphere can be found using the formula V = (4/3) * pi * r³, where r is the radius of the sphere.
The bottom ball has a diameter of 3 feet, so the radius is 3/2 = 1.5 feet. The volume of the bottom ball is (4/3) * 3.14 * (1.5³) = 14.13 cubic feet.
The middle ball has a diameter of 2 feet, so the radius is 2/2 = 1 foot. The volume of the middle ball is (4/3) * 3.14 * (1³) = 4.19 cubic feet.
The top ball has a diameter of 1 foot, so the radius is 1/2 = 0.5 feet. The volume of the top ball is (4/3) * 3.14 * (0.5³) = 0.52 cubic feet.
The total volume of the snowman is 14.13 + 4.19 + 0.52 = 18.84 cubic feet. Therefore, the answer is 19 cubic feet of snow.
A class of 18 students took a math test. Seven students had an average of 90. The other students had an average of 82.
What is the average for the whole class? Round to the nearest whole percent.
A) 80
B) 83
C) 85
D) 87
Answer: C- 85%
Step-by-step explanation:
7x11=630
Remaining Students: 18-7=11
11x82=902
Aveage:
630+902=1532
1532/18=85.1111
9x-3y=3; 3x+8y=-17
I want to know the steps and answers
What is the length of the altitude of the equilateral triangle below
Answer
Find out the altitude of the equilateral triangle .
To proof
By using the trignometric identity.
[tex]tan\theta = \frac{Perpendicular}{base}[/tex]
As shown in the diagram
and putting the values of the angles , base and perpendicular
[tex]tan 60^{\circ} = \frac{a}{4\sqrt{3}}[/tex]
[tex]tan 60^{\circ} = \sqrt{3}[/tex]
solving
[tex]\sqrt{3} = \frac{a}{4\sqrt{3}}[/tex]
[tex]a = \sqrt{3}\times 4 \sqrt{3}[/tex]
As
[tex]\sqrt{3}\times \sqrt{3} = 3[/tex]
put in the above
a = 4 × 3
a = 12 units
The length of the altitude of the equilateral triangle is 12 units .
Option (F) is correct .
Hence proved
Answer:
F. 12
Step-by-step explanation:
We have been given an image of a triangle and we are asked to find the length of the altitude of our given triangle.
Since we know that altitude of an equilateral triangle splits it into two 30-60-90 triangle.
We will use Pythagoras theorem to solve for the altitude of our given triangle.
[tex]\text{Leg}^2+\text{Leg}^2=\text{Hypotenuse}^2[/tex]
Upon substituting our given values in above formula we will get,
[tex](4\sqrt{3})^2+a^2=(8\sqrt{3})^2[/tex]
[tex]16*3+a^2=64*3[/tex]
[tex]48+a^2=192[/tex]
[tex]48-48+a^2=192-48[/tex]
[tex]a^2=144[/tex]
Upon taking square root of both sides we will get,
[tex]a=\sqrt{144}[/tex]
[tex]a=12[/tex]
Therefore, the length of the altitude of our given equilateral triangle is 12 units and option F is the correct choice.
A student is running a 10-kilometer race. He runs 1 kilometer every 4 minutes. Select the function that describes his distance from the finish line.
f(x) = - 1 over 4x + 4
f(x) = - 1 over 10x + 4
f(x) = - 1 over 10x + 10
f(x) = - 1 over 4x + 10
Answer:
Option D is correct
[tex]y =-\frac{1}{4}x+10[/tex]
Step-by-step explanation:
Slope intercept form:
The equation of line is given by:
[tex]y=mx+c[/tex] .....[1]
where, m is the rate or slope and c is the y-intercept or initial value.
As per the statement:
Here, y represents the distance in kilometer and x represents the time in minutes.
A student is running a 10-kilometer race
⇒y(0) = b = 10 km
It is also given that he runs 1 kilometer every 4 minutes.
Now, with each passing minute the student is getting closer and closer to the finish line which was 10 kilometers away when the race started. Thus, as the race progresses, the distance between the student and the finish line will decrease.
[tex]m =-\frac{1}{4}[/tex]
Substitute these in [1] we have;
[tex]y = -\frac{1}{4}x+10[/tex]
Therefore, the function that describes his distance from the finish line is, [tex]y = -\frac{1}{4}x+10[/tex]
Write the trigonometric expression in terms of sine and cosine, and then simplify.
csc2 x − cot2 x
Which number belongs to the solution set of the equation below? x - 7 = 35
A) 22
B) 28
C) 42
D) 41
A company introduces a new product for which the number of units sold S is
S(t)= 200 ( 5- 9/(2+t))
where t is the time in months
(a) Find the avg. value of S(t) during the first year.
(b) During what month does S'(t) equal the avg value during the first year? ...?
There are five seniors in a class. For each situation, write how the binomial formula is used to calculate the probability.
a) In how many ways can I choose one senior to represent the group?
b) In how many ways can I choose two seniors to represent the group?
c) In how many ways can I choose three seniors to represent the group?
d) In how many ways can I choose four seniors to represent the group?
e) In how many ways can I choose five seniors to represent the group?
After 3 years, what is the total amount of a compound interest investment of $5,000 at 4% interest, compounded quarterly?
$5,203.71
$5,360.68
$20,480,000
$5,634.13
How to find the product of rational expressions
Find the number of years it would take for $1,200 to earn simple interest of $324 at an annual interest rate of 6% per year.
Please help me
All of the following are equivalent except _____.
2%
0.2
1/50
0.02
A rectangle's length is 4 feet more than its width. If the area of the rectangle is 396 square feet, what is its width, in feet?
which is greater 14 ounces or 0.4 kilograms
After converting 0.4 kilograms to ounces using the appropriate conversion factors, it is determined that 0.4 kilograms is slightly greater than 14 ounces.
Explanation:To determine which is greater, 14 ounces or 0.4 kilograms, we first need to use the appropriate conversion factors to compare the two measurements in the same unit. Since 1 pound is equivalent to 0.4536 kilograms, and 1 pound is also equal to 16 ounces, we need to convert one of the measures so that both are in either ounces or kilograms for a direct comparison.
Converting 0.4 kilograms to ounces:
1 kilogram is approximately 2.20462 pounds (since 1 pound is 0.4536 kg).So, 0.4 kilograms is 0.4 * 2.20462 pounds, which is approximately 0.882 pounds.Next, we convert 0.882 pounds to ounces by multiplying by the conversion factor of 16 ounces per pound: 0.882 * 16 = 14.11 ounces (approximately).Now we have both weights in ounces, and we can see that 14.11 ounces is slightly more than 14 ounces. Therefore, 0.4 kilograms is greater than 14 ounces.
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Jared wrote an equation for the perimeter of an equilateral triangle as 3x = 20. What does x represent in his equation?
Answer:
The length of a side of the triangle.
Step-by-step explanation:
An equilateral triangle has 3 equal sides so the x would be equal to one side of the triangle.
Given that f(x) = 6x 2 and g(x) =2x=4/5 , solve for g(f(1))
Answer:
The answer would be 4.
Step-by-step explanation:
What you have to do here is you have to substitute
So the problem told you the f(x) = 1. So what you want to do is plug that into the function f(x).
So:
f(x) = 6(1)2
= 8
Now we know that f(x) = 8, so what we going to do now is plug f(x) into g(x).
So:
g(f(8)) = 2(8) + 4/5
= 4
The value of g(f(1)) is 4.
Composite function -Composition of functions is the process of plugging one function into another, and simplifying or evaluating the result at a given x-value. Another way to read it is "f circle g of x." It is a process that joins two functions to create a third, unique function.Given ,
f(x) = 6x + 2
g (x) = 2x + 4 /5
To get value of g(f(1)) first we have to solve f(x).
f(x) = 6x + 2 .......................(1)
We simply put x = 1 in equation 1 .
Then, F(1) = 6 × 1 + 2 ⇒ 8
Now , we put value of f(1) in g(f(1)) ,
So, g(f(1)) = [tex]\frac{2x + 4}{5}[/tex]
= [tex]\frac{2 * 8 + 4}{5}[/tex]
= [tex]\frac{16 + 4}{5}[/tex]
= 20/5 ⇒ 4
Therefore, the value of g(f(1)) is 4 .
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5,893,402 + 19,392,009 =
your new cell phone plan charges $50 per month for 400 minutes of talk time. the plan charges $0.10 for each additional minute you talk. you use 50 additional minutes this month. what is your bill for the month?
Answer:
$55
Step-by-step explanation:
21. The Johnsons framed a family picture to hang on the wall. The perimeter of the frame is 72 inches. Use the formula P = 2 l + 2 w to find the length of the frame if the width is 14 inches. 21. The Johnsons framed a family picture to hang on the wall. The perimeter of the frame is 72 inches. Use the formula P = 2 l + 2 w to find the length of the frame if the width is 14 inches.
The perimeter of the rectangle below is 128 units. Find the length of side VW .
Write your answer without variables.
Karina uses the system of equations below to compare the monthly utility costs in July and December for electricity, x, and natural gas, y.
750x + 17y = 141.61
300x + 30y = 75.90
Karina solves the system using linear combination and arrives at the equation 116y = 96.28. She then solves this equation for y. Which statement explains Karina’s solution?
a. The cost of electricity is $0.17 per unit.
b. The cost of natural gas is $0.20 per unit.
c. The cost of electricity is $0.72 per unit.
d. The cost of natural gas is $0.83 per unit.
D: The cost of natural gas is $0.83 per unit.
Answer:
Option d is correct
The cost of natural gas (y) = $0.83 per unit
Step-by-step explanation:
Given the system of equation:
750x + 17y = 141.61 ......[1]
300x + 30y =75.90 ......[2]
where x is the cost of electricity and y is the costs of natural gas.
Multiply equation [1] by 30 and equation [2] by 75 we get;
[tex]30 \cdot (750x + 17y) = 30 \cdot 141.61[/tex]
Simplify:
22500x + 510y = 4248.3 ......[3]
[tex]75 \cdot (300x + 30y) = 75 \cdot 75.90[/tex]
Simplify:
22500x + 2250y = 5692.5 .......[4]
Subtract equation [3] from [4] we get;
1740 y = 1444.2
Divide by 15 both sides, we get
116 y = 96.28
Since, Katrina solves the above system using linear equation and arrives at the equation :
116 y = 96.28
Division property of equality states that divide the same number to both sides of an equation:
Divide by 116 to both sides of an equation, to solve for y;
[tex]\frac{116 y}{116} =\frac{96.28}{116}[/tex]
Simplify:
y = 0.83 where y represents the cost of natural gas
Therefore, the cost of natural gas y ,is, $ 0.83 per unit.
How many times does 59 go into 295?
Which equation is satisfied by all of the plotted points?
A. y = 2x
B. y = x + 3
C. y = 2x + 1
D. y = -2x
E. y = x
F. y = 3x -3
The answer is y= -2x
A piece of furniture has a retail price of $3,200 and is on sale at a 30% discount. how much money will be saved if the piece of furniture is purchased at the sale price?
simplify please I need help don't get it
7.What are the steps that you would follow to recreate a triangle using a protractor, a string, and the AAS Congruence Theorem?
ANSWER:
To construct a triangle given one side and the angle at each end of it with compass and straightedge or ruler. It works by first copying the line segment to form one side of the triangle, then copy the two angles on to each end of it to complete the triangle. Follow these steps to draw the recreate a triangle using a protector, a string and angle, angle side congruence theorem.
STEP-BY-STEP EXPLANATION:
Step 1: You will need to choose two angle and one length for both triangle. Noted that the two angle and one length must be the same for both triangle.
Step 2: Draw a long line on a paper
Step 3: Use a ruler to measure the length ,and then make a mark on the string.
Step 4: Use the string to mark on the long line.
Step 5: Use a protractor to measure
Step 6: Use AAS Congruence Theorem to prove that both triangle are congruent.
What is 4/5 4/5 as a mixed number fraction?
how do u right this Seven less than the quotient of x and 9
Answer:
(x÷9)−7 is your answer.
How many regions would a net for a three-dimensional solid like the one shown have?
Answer:
A
Step-by-step explanation:
What is the unit rate of 50.4 feet in 14 years?