For questions 1 and two find the volume of the given prism. Round to the nearest tenth if necessary.
Answers
The volume of the rectangular and triangular prisms are 269.3 cubic centimeters and 1756.3 cubic yards respectively
How to calculate the volume of the prism?The formula for calculating the volume of a prism is given as;
V = lwh
l is the length
w is the width
h is the height
1) The volume of the prism is expressed as;
V = 12.1 * 5.3 * 4.2
V = 269.3 cubic centimeters
2) Volume of the triangular based prism = BH
Base area = 1/2(13)(13)sin60
Base area = 84.5(0.8660)
Base area = 73.177 square yard
Height H = 24 yards
Volume of the prism = 24 * 73.177
Volume of the prism = 1756.3 cubic yards
Hence the volume of the rectangular and triangular prisms are 269.3 cubic centimeters and 1756.3 cubic yards respectively
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Related Questions
to the nearest whole number, how many times larger is the volume of Earth compared to the volume of our moon? use a radius of 1079 miles for the moon and 3,959 miles for the Earth.
Answers
The volume of Earth is about 49 times larger than the volume of the Moon, based on their provided radii.
To the nearest whole number, the volume of Earth is approximately 49 times larger than the volume of the Moon.
Given that the volumes of spheres are proportional to the cubes of their diameters, and using the radii provided (1079 miles for the Moon and 3959 miles for Earth), we can calculate the volume ratio:
Volume of Earth: [tex](3959)^3[/tex]
Volume of Moon: [tex](1079)^3[/tex]
Volume of Earth compared to the Moon, = [tex](3959^3) / (1079^3)[/tex] ≈ 49.
There volume of the earth is 49 times larger.
The function f(x) is given by the set of ordered pairs.
{(1,0), (-10,2), (0,6), (3,17), (-2,-1)}
which equation is true?
f(-10)=1
f(2)=-10
f(0)=6
f(1)=-10
Answers
Explanation:
Ther ordered pairs are: (x,y) or (x, f(x) )
So, (1,0) means that f(1) = 0 which denies the fourth choice.
(-10,2) means that f(-10) = 2 which denies the first choice
(0,6) means that f(0) = 6, which is the third choice. So, that is the true equation.
Answer: the correct option is (C) f(0) = 6.
Step-by-step explanation: We are given the function f(x) by the following set of ordered pairs :
{(1,0), (-10,2), (0,6), (3,17), (-2,-1)} .
We are to select the TRUE equation.
We know that
in the ordered pairs, the first element stands for the independent variable x and the second element stands for the dependent variable f(x).
So, the equations that comes from the given ordered pairs are
[tex]f(1)=0,~~f(-10)=2,~~f(0)=6,~~f(3)=17,~~f(-2)=-1.[/tex]
Thus, the only true equation is f(0) = 6.
Option (C) is CORRECT.
What is 4x-2x answer asap
Answers
[tex]4x-2x = 4(x) - 2(x) = (4-2)(x) = 2(x) = 2x. [/tex]
You could also think of this as:
( x + x + x + x ) - ( x + x ) = x + x + x + x - x - x
Help please........................
Answers
You have the right answer. 2.5 * 2.5 = 6.25 Can't beat being right.
1. You have 60 in. of molding to use as a frame around a picture you are painting. The area of the painting is giving by the function y = 30x - x^2 where x is the width in inches. What width gives the maximum area for the painting? What is the maximum area?
2. You are trying to dunk a basketball. You need to jump 2.5 ft in the air in order to dunk the ball. The height that your feet are above the ground is given by the function h = -16t^2 + 12t. What is the maximum height your feet will be above the ground? Will you be able to dunk the basketball?
I need a lot of help with these problems. Please answer them to the best of your capabilities. I'M GOING INSANE!!! Thanks so much!
Answers
[tex]x = -b/2a = -30/2(-1) = 15[/tex]
[tex]y = -(15)^2+20(15) y = -225+450 y = 225[/tex]
So, 15 as the width would give us the maximum area for the painting.
---------------------------------------------------------------------------------------------------------
2) The maximum height your feet will be above the ground is 2.25 ft.
No, you wouldn't be able to dunk the ball because the maximum height you can jump is 2.25, but you need to jump 2.5 ft to dunk.
what number does point A represent?
a.0.1
b.0.2
c.1.02
d.1.2
Answers
Point A= 1.0 + 0.1 + 0.1 = 1.2
answer
d.1.2
Without additional context or an image, we can't definitively determine which number the point A represents in your question.
Explanation:The point A represents the number 0.1.
Points on a number line represent numbers. The numbers between 0 and 1 can be represented as decimals. The point A is located between 0 and 1, closer to 0, so it represents the number 0.1.
Therefore, the correct answer is option a. 0.1.
Unfortunately, without further context such as a diagram or graph, it's not possible to definitively identify which number Point A would represent. In a standard coordinate system, points are typically represented as pairs of numbers (x, y) which indicate their position on the grid. In a number line, each point corresponds to a specific number. Please provide additional details or an image to get a more accurate answer.
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What is the weight ( in grams) of a liquid that exactly fills a 163.5 millimeter container if the density of the liquid is 0.492 grams/millimeter?
Answers
The formula for density is [tex] \text{density} = \frac{m}{V} [/tex]
Givens
V = 163.5 mL
d = 0.492 grams / mL
Solution
m = d * V The formula has been rearranged.
m = 0.492 * 163.5
m = 80.442 grams. <<<<< Answer
graph
[tex]y = |x| - 1[/tex]
Answers
(0; 0); (2; 2)
Symmetry about the x-axis (green)
Translation down 1 unit (red)
The athlete’s salary, in thousands, for the first two years is $400 and $400(1.05). Explain how to find her salary for each of the next three years. Do these values form a geometric sequence? Explain.
Answers
where
[tex]a_{n}[/tex] is the nth term of the sequence
[tex]a_{1}[/tex] is the first term in the sequence
[tex]r[/tex] is the common ratio
[tex]n[/tex] is the position of the term in the sequence
To check if the values $400 and 400(1.05) for a geometric sequence, we are going to find their common ratio. To find the common ratio, we are going to use the formula [tex]r= \frac{a_{n} }{a_{n-1}} [/tex]
where
[tex]a_{n}[/tex] is the current term in the sequence
[tex]a_{n-1}[/tex] is the previous term in the sequence
We can infer from our values, that the current term of the sequence is 400(1.5), so [tex]a_{n-1}=400(1.5)[/tex]. That leaves 400 as the previous term, so [tex]a_{n-1}=400[/tex]. Lets replace those values in our formula to find [tex]r[/tex]:
[tex]r= \frac{a_{n} }{a_{n-1}} [/tex]
[tex]r= \frac{400(1.05)}{400} [/tex]
[tex]r=1.05[/tex]
Now that we have our common ratio, we can replace it in our formula for the nth term to find the athlete's salary for each of the next three years. Notice that the first term of our sequence is $400, so [tex]a_{1}=400[/tex]
[tex]a_{n}=a_{1}r^{n-1}[/tex]
[tex]a_{n}=400(1.05)^{n-1}[/tex]
[tex]a_{3}=400(1.05)^{3-1}[/tex]
[tex]a_{3}=400(1.05)^{2}[/tex]
[tex]a_{3}=441[/tex]
[tex]a_{4}=400(1.05)^{4-1}[/tex]
[tex]a_{4}=400(1.05)^{3}[/tex]
[tex]a_{4}=463.05[/tex]
[tex]a_{5}=400(1.05)^{5-4}[/tex]
[tex]a_{5}=400(1.05)^4[/tex]
[tex]a_{5}=486.2025[/tex]
We can conclude that the athlete's salary for each of the next three years is: $441,$463.05,486.2025 respectively. Also, those vales for a geometric sequence because they share a common ratio, (1.05).
Answer:
Edge Checklist:
Find the third year’s salary by multiplying the second year’s salary by 1.05
Find the fourth year’s salary by multiplying the third year’s salary by 1.05.
Find the fifth year’s salary by multiplying the fourth year’s salary by 1.05.
The salaries form a geometric sequence because the athlete’s salary changes by a common ratio of 1.05 each year.
Dakota built a wall with bricks like this one:
Look at Dakota’s wall:
What is the length of the side of the brick labeled a? ____________
What is the length of the side of the brick labeled b? _____________
What is the total height of the wall? ____________
What is the total length of the wall? __________
Answers
A computer screen has a diagonal length of 17 in. and a height of 9 in. To the nearest tenth of an inch, what is the area of the screen?
Answers
Classify each number as rational or irrational.
Drag the choices into the boxes to correctly complete the table.
Answers
-1/10 → rational
0 → rational
√2 → irrational
Answer: √3 and √2 are irrational numbers;
[tex]-\dfracP{1}{16}[/tex] and 0 are rational numbers.
Step-by-step explanation: We are given to classify the following numbers as rational or irrational:
[tex]\sqrt{3},~~-\dfrac{1}{16},~~0,~~\sqrt{2}.[/tex]
Rational number: The digits after the decimal are either repeating or terminating.
Irrational number: The digits after the decimal are non-terminating and non-terminating.
(a) We have
[tex]\sqrt{3}=1.732050807568877~.~.~.[/tex]
Since the digits after the decimal are non-terminating and non-repeating, so √3 is an IRRATIONAL number.
(b) We have
[tex]-\dfrac{1}{16}=-0.0625.[/tex]
Since the digits after the decimal are terminating, so [tex]-\dfrac{1}{16}[/tex] is a RATIONAL number.
(c) We have
[tex]0=0.000.[/tex]
Since the digits after the decimal are terminating, so [tex]0[/tex] is a RATIONAL number.
(d) We have
[tex]\sqrt{2}=1.414213562373095~.~.~.[/tex]
Since the digits after the decimal are non-terminating and non-repeating, so √2 is an IRRATIONAL number.
a local parts shop buys a machine that costs $500,000. its value depreciates exponentially each year by 10%. what is the machines value after 5 years? round to nearest integer
Answers
Answer:
$295.295
Explanation:
Of the statement, we have that the price of the machine decreased 10% every year exponentially, so in the first year it real value drops to 90% of the costs. For 5 years, It can be expressed and simplified by the following equation:
We can't use that the percent drop as a percent itself, so we are going to divide 90% by 100%, and it will give us an entire number.
[tex]\frac{90}{100}=0,9 \\ \\ Value=Costs.(0.9)^{years}[/tex]
By substituting we have:
[tex]Value=500000.(0.9)^{5}[/tex]
Value: $295.245
Have a nice day!
which of the following mesurments are greater than 130 fluid ounces. 5 quarts, 16 cups, 9 pints, 2 gallons or 1 gallon
Answers
130 fluid ounces to cups is 16.25, so 16 cups is smaller.
130 fluid ounces to pints is 8.13, so 9 pints is larger.
130 fluid ounces to gallons is 1.02, so 2 gallons is larger and 1 gallon is smaller.
Could someone please help me on this
Answers
b = 12n.
In Mr. Diaz's classroom, the desks are arranged in 4 rows with 7 desks in each row. Each desk has 2 pencils on it. How many total pencils are there on all the desks?
Answers
What is the equivalent decimal?
Drag the answer into the box to match the fraction.
5/45
Answers
1/9 into a decimal is 0.1111111.
The image contains the answer.
Answer: (c)
Write 5.62 as a mixed number in simplest form
Answers
281/50
...........
Decimal form 5.62
Exact form 281/50
hope this helps
Classify the angles in questions 1-3 below. PLEASE HELP
Answers
2. This is obtuse because it’s more than 90 degrees.
3. This is right because it’s exactly 90 degrees, indicated by the square in the angle measure’s place.
Name the point with the given coordinates (4 -2)
Answers
The point with the given coordinates (4 -2) is h.
What are the coordinates of midpoint of the line segment AB?Suppose we've two endpoints of a line segment as:
A(p,q), and B(m,n)
Then let the midpoint be M(x,y) on that line segment. Then, its coordinates are:
[tex]x = \dfrac{p+m}{2}[/tex]
and
[tex]y = \dfrac{q+n}{2}[/tex]
We are given that;
The graph of four points
Now,
One point is k with (-4,2)
One point is g with (2,4)
One point is h with (4,-2)
One point is j with (-2,-4)
Therefore, by the midpoint the answer will be h(4,-2).
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Jack or three protein bars for a total of $4.26. Which equation could be used to find the cost c in dollars of each protein bar?
Answers
(total cost / quantity bought) = c
$4.26 / 3 = $1.42
The cost of an individual protein bar is $1.42.
First, set up your equation. I'll let "b" represent the value of each individual bar:
3b = 4.26
Now, divide the total value by the number of bars for the answer:
b = $1.42
A set of weights includes a 4 lb barbell and 6 pairs of weight plates. Each pair of plates weighs 20 lb. If x pairs of plates are added to the barbell, the total weight of the barbell and plates in pounds can be represented by f x( ) = 20x + 4. What is the range of the function for this situation? Please explain.
Answers
The range of the function is the possible output values for the function. In this case, it is from zero to the highest possible weight. Since there are 6 pairs of weight plates, we can input 12 for x to get the maximum.
20(12) + 4 = 244
|1 - 4x| > 7
A. {x|x < -1.5 ∪ x > 1.5}
B. {x|x < -1.5 ∪ x > 2}
C. {x|-1.5 < x < 2}
Answers
Lisa is asked to draw a triangle with the following specifications:
two angles are complementary
the side between the two complementary angles has a length of 12 centimeters
Which of the following statements about this triangle is true?
A.
Exactly one triangle exists with the given conditions, and it must be an isosceles triangle.
B.
More than one triangle exists with the given conditions, and all instances must be right triangles.
C.
More than one triangle exists with the given conditions, and all instances must be isosceles triangles.
D.
Exactly one triangle exists with the given conditions, and it must be a right triangle.
Answers
Since two of the angles are complementary, adding up to 90°, the third angle must be 180-90=90°.
However, this does not mean only one triangle exists. The only information we are given about the two angles is that they are complementary. This could be 30 and 60; 45 and 45; or multiple other combinations. This means there is more than one triangle that fits these criteria.
Final answer:
Triangles with two complementary angles must be right triangles. Since these angles add up to 90 degrees, the side between them is part of a right triangle. There can be many different right triangles that satisfy these conditions, but all must have a 90-degree angle. (Option D)
Explanation:
The question asks about the conditions that define a certain type of triangle. With two angles being complementary, they add up to 90 degrees. In geometry, a complementary pair of angles adds up to 90 degrees, which means that the two angles in question must be acute angles that add up to form a right angle. Therefore, the triangle with two complementary angles must be a right triangle.
Since the triangle can have many different dimensions for the other sides and angles while keeping the side between the complementary angles at 12 centimeters, we can infer that there are infinite variations of this triangle, each with different measures for the remaining side and angle. However, all those triangles must satisfy the condition of being right triangles.
Thus, the correct answer to this question is:
D. Exactly one triangle exists with the given conditions, and it must be a right triangle.
Use unit multipliers to convert 123 pounds per mile to ounces per centimeter. There are 5,280 feet in 1 mile. There are 16 ounces in 1 pound. There are approximately 2.54 cm in 1 inch. Enter your answer as a decimal rounded to the nearest hundredth. Just enter the number.
Answers
We want to convert 123 pounds per mile to ounces per centimeter.
First, we are going to express the quantity to convert as a fraction:
123 pounds per mile=[tex]123 \frac{pounds}{mile} [/tex]
Next, we are going to find our multipliers:
- We know for our problem that there are 5,280 feet in 1 mile, so our first multiplier will be: [tex] \frac{1mile}{5280ft} [/tex]
- We also know that there are 16 ounces in 1 pound, so our second multiplier will be: [tex] \frac{16ounces}{1pound} [/tex]
- We know that there are 12 inches in 1 foot, so our third multiplier will be: [tex] \frac{1ft}{12in} [/tex]
- We know that there are approximately 2.54 cm in 1 inch, so our fourth multiplier will be: [tex] \frac{1in}{2.54cm} [/tex]
Now we can put all our multipliers together:
[tex]123 \frac{pounds}{mile} * \frac{1mile}{5280ft}*\frac{16ounces}{1pound}* \frac{1ft}{12in}*\frac{1in}{2.54cm}=0.01 \frac{ounces}{cm} [/tex]
We can conclude that the answer is 0.01
Find the product of two numbers whose sum is 11 and difference is 3.
Answers
The two numbers are 7 and 4
Let the first number = x
let the second number = y
The sum of the numbers is 11, in algebra form x + y = 11
The difference of the two numbers is 3, in algebra form, x - y = 3
To obtain the two unknown numbers, we solve the two equations;
from the first equation, x = 11 - y
substitute the value of x into the last equation;
(11 - y) - y = 3
11 - y - y = 3
11 - 2y = 3
2y = 11 - 3
2y = 8
y = 4
The value of x = 11 - 4 = 7
Thus, the two numbers are 7 and 4
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To find the product of two numbers with a sum of 11 and a difference of 3, solve the system of equations to find the numbers (7 and 4) and multiply them to get the product, which is 28.
Explanation:To find the product of two numbers whose sum is 11 and whose difference is 3, we can let the two numbers be x and y, with x being the larger number. Therefore, we have two equations from the given information: x + y = 11 and x - y = 3.
Adding these two equations, we get:
2x = 14x = 7Using x = 7 in the first equation, we have:
7 + y = 11y = 4Now that we have both numbers, we can find their product:
Product = x * yProduct = 7 * 4Product = 28The product of the two numbers is 28.
one number is 2 larger than another number. the sum of their squares is 100. find the numbers
Answers
x+2= second number
x^2 + (x + 2)^2= 100
square the parentheses
x^2 + [(x + 2)(x + 2)]= 100
x^2 + x^2 + 2x + 2x + 4= 100
combine like terms
2x^2 + 4x + 4= 100
subtract 100 from both sides
2x^2 + 4x - 96= 0
factor
2(x−6)(x+8)=0
set each parentheses equal to 0
x-6= 0
x= 6
OR
x+8= 0
x= -8
CHECK:
x^2 + (x + 2)^2= 100
(6)^2 + (6 + 2)^2= 100
36 + (8)^2= 100
36 + 64= 100
100= 100
x^2 + (x + 2)^2= 100
(-8)^2 + (-8 + 2)^2= 100
64 + (-6)^2= 100
64 + 36= 100
100= 100
ANSWER: x= 6 or x= -8
Hope this helps! :)
The numbers are 6 and -8
let
the first number = x
One of the number is 2 larger than another number .Therefore, the second number will be as follows;
x + 2Sum of there squares will be as follows:
x² + (x + 2)² = 100Therefore,
x² + x² + 4x + 4 = 100
2x² + 4x + 4 - 100 = 0
2x² + 4x - 96 = 0
x + 2x - 48 = 0
let's find x
x - 6x + 8x - 48 = 0
x(x - 6) + 8(x - 6) = 0
(x - 6)(x + 8) = 0
x -6 = 0 and x + 8 = 0
x = 6 and x = -8
The numbers are 6 and -8.
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divide 660 g in the ratio 4 : 7
Answers
Final answer:
To divide 660 grams in a 4:7 ratio, you first calculate the value of each part by dividing 660 grams by 11 (the sum of the ratio parts), resulting in 60 grams per part. Then multiply 60 grams by 4 to get 240 grams, and by 7 to get 420 grams, giving you two portions that comprise the ratio 4:7.
Explanation:
To divide 660 grams in the ratio 4:7, first add the two parts of the ratio together to find the total number of parts. This is 4 + 7 = 11 parts in total. The ratio indicates that for every 11 parts of the total weight, 4 parts should be in one portion and 7 parts in another. To find the weight of each part, divide the total weight (660 g) by the total number of parts (11).
660 g ÷ 11 = 60 g per part
Now, to get the weights for the two portions:
For the 4 parts: 60 g/part × 4 = 240 grams
For the 7 parts: 60 g/part × 7 = 420 grams
Thus, 660 grams divided in the ratio 4:7 of gives two portions of 240 grams and 420 grams, respectively.
Which number sentences could be used to solve this problem?
Carrie is making 16 goodie bags for her party. She is putting 3 pencils and 2 erasers into each bag. What is the total number of objects she will put into the 16 bags?
Choose exactly two answers that are correct.
A.
2 × 3 × 16 = □
B.
(2 × 16) + (3 × 16) = □
C.
16 × (2 × 3) = □
D.
16 × (2 + 3) = □
Answers
The number sentences that solves the problem are;
B. (2 × 16) + (3 × 16) = 80
D. 16 × (2 + 3) = 80
To determine the number sentence, we have from the information given that;
There are 16 goodies bag3 pencils2 erasersThen, we can say that in each bag, there are;
= 3 + 2
= 5 objects
Now, in 16 of the goodies bag, the number of objects would be;
= 5 ×16
= 80 objects
Therefore, the sentences are in options B and D
Please help me.I need this answered
Answers
2. 0.5(9•11)= 49.5.
3. pi•(17/12)^2= about 289/144pi.
4. 3.75•7.6= 28.5.
5. (42•20)+(10•22)= 840+220= 1,060.
6. 0.5(10.667•3.2)+(10.667•15)= 170.667+160= 330 and two thirds.