The smith family bought a new tent for a camping trip with a base of 9 by 15 and a height of 7. What is the volume of their new tent?
The volume of the tent is 472.5 cubic units.
What is a triangular prism?'A triangular prism is a three-dimensional shape with two identical faces in the shape of a triangle connected by three rectangular faces.'
According to to the given problem,
Length = 15 units
Base = 9 units
Height = 7
Volume of the tent =( [tex]\frac{1}{2}*9*15*7[/tex] ) cubic units
= 472.5 cubic units.
Hence, we can conclude, the volume of the tent is 472.5 cubic units.
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a rectangular prism is completely packed with 84 cubes of edge length 1 over 3 inch without any gap or overlap
The question involves finding the dimensions of a rectangular prism packed with 84 smaller cubes of a certain size. The answer requires understanding of volume and consideration of the physical characteristics of a rectangular prism.
Explanation:The problem presents a rectangular prism completely packed with 84 cubes of edge length 1 over 3 inch. To find the dimensions of the prism, we must first understand the volume. Given the volumes of the small cubes (edge length cubed), we can multiply this by the number of cubes (84) to find the total volume of the prism.
Next, we use this total volume to derive the possible dimensions of the rectangular prism. The dimensions should be factors of the total volume, keeping in mind the shape of a physical rectangular prism (which usually has length longer than width and height).
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In December, 2003, the average price for a gallon of regular gas in the United States was $1.50. (A) Gerald paid $12.60 for a tank of gas. How much did he pay?
Answer: He paid for 8.4 gallons.
Step-by-step explanation:
Since we have given that
Average price for a gallon of regular gas = $1.50
Amount paid for a tank of gas = $12.60
So, Number of gallons would be
[tex]\dfrac{\text{Total cost}}{\text{Average price}}\\\\\\=\dfrac{12.60}{1.50}\\\\\\=8.4\ gallons[/tex]
Hence, He paid for 8.4 gallons.
An item on sale costs 45% of the original price. The original price was $15.
The selling price of the item in the sale after the discount of 45% will be $8.25.
What is the percentage?The amount of any product is given as though it was a proportion of a hundred. The ratio can be expressed as a quarter of 100. The phrase % translates for one hundred percent. It is symbolized by the character '%'.
The percentage is given as,
Percentage (P) = [Final value - Initial value] / Initial value x 100
A thing on special expenses 45% of the first cost. The first cost was $15.
Let the selling price of the item in the sale be 'x'.
The amount of discount is given as,
⇒ 0.45 × $15
⇒ $6.75
The selling price of the item in the sale is calculated as,
x = $15 - $6.75
x = $8.25
The selling cost of the thing in the deal after the rebate of 45% will be $8.25.
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Which table represents the same linear relationship as the equation y = 3x +5?
A scale on a map shows that 2 inches = 25 miles.
Part A
How many inches on the map represent 60 miles?
Enter your answer in the box.
Part B
How many miles are represented by 1/4inch on the map?
Enter your answer in the box.
60/25 = 2.4
2.4 x 2 = 4.8 inches = 60 miles
25/2 = 12.5 for 1 inch
12.5/4 = 3.125 miles for 1/4 inch
How to factor quadratic expressions in General
Final answer:
To factor quadratic expressions in general, we can use the AC Method, which involves breaking down the middle term and finding two numbers that multiply to give a certain product and add up to the coefficient of the middle term.
Explanation:
To factor quadratic expressions in general, we can use the method known as the AC Method. This method involves breaking down the middle term of the quadratic expression and finding two numbers that multiply to give a certain product (the product of the coefficient of the leading term and the constant term) and add up to the coefficient of the middle term. Once we find these two numbers, we can rewrite the quadratic expression as a product of two binomials.
For example, let's say we have the quadratic expression [tex]2x^2[/tex] + 5x + 3. The product of the leading coefficient (2) and the constant term (3) is 6. We need to find two numbers that multiply to 6 and add up to the coefficient of the middle term (5). The numbers 3 and 2 fit this criteria. Therefore, we can rewrite the quadratic expression as (2x + 3)(x + 1).
Note that if the quadratic expression cannot be factored using this method, it is considered a prime polynomial and cannot be factored further.
What is the range of function y=√(-2cos^2x+3cosx-1)
round 345276 to the nearest thousand
A bed & bath company intends to ship out 28,457 blue blankets, and three times as many white blankets. If each box contains 55 blankets of either color, how many full boxes of blankets can be packed, and how many blankets are left over for the last box?
28457 x 3 = 85371 white blankets
85371 + 28457 = 113,828 total blankets
113828/55 = 2069.6 total boxes
so 2069 full boxes
and 55*.6 = 33 left over blankets
Convert 0.79 tons to pounds?
Sasha and Mona practiced swimming every day. They increased the number of minutes of swimming every week as described below: Sasha: Practiced swimming for 10 minutes every day in the first week, 20 minutes in the second week, 40 minutes in the third week, and 80 minutes in the fourth week. Mona: Practiced swimming for 10 minutes every day in the first week, 20 minutes in the second week, 30 minutes in the third week, and 40 minutes in the fourth week. Which statement best describes the methods used by Sasha and Mona to increase the time they practiced swimming?
Mona's method is linear because the number of minutes increased by an equal factor every week.
Sasha's method is exponential because it increases by an equal number every week.
Mona's method is exponential because it increases by a fixed factor, and Sasha's method is linear because it increases by a fixed number.
Sasha's method is exponential because it increases by a fixed factor, and Mona's method is linear because it increases by a fixed number.
Answer:
Option D.
Step-by-step explanation:
As per given statements we see the time of Sasha practice it increases by a fixed factor of '2' or we can say Sasha's time is multiplied by '2' every week.
When we see the time of Mona's practice, it increases by 10 mins every week. hence there is a addition of a fixed number '10'.
so option D is correct which says Sasha's method is exponential because it increases by a fixed factor, and Mona's method is linear because it increases by a fixed number.
1. 7.2 aliens =1 monster. 1 monster= 15.5 oranges. Using the conversion above, about how many oranges are equal to 1 alien?
2. In a scaled drawing, 1 millimeter represents 150 meters. How many square millimeters on the drawing represents 1 square meters?
3. While driving with his father, Amit holds his breath whenever they pass through a particular tunnel. Amit counts the number of seconds he holds his breath, from the beginning of the tunnel to the end of the tunnel, and finds that he holds his breath, on average for about 8 seconds. If his father drives the car at 60 mph through the tunnel, according to the average time, Amit holds his breath, about how long is the tunnel.
4. Lea's car travels on average of 30 miles per gallon of gas. If she spent $20.70 on gas for a 172.5 mile trip, what was the approximate cost of gas in dollars per gallon?
The base of a rectangular pyramid has sides 3 feet long and 7 feet long. The pyramid is 4 feet tall. A second, larger pyramid has dimensions that are 3 times the dimensions of the smaller pyramid. What is the difference between the volumes of the two pyramids?
Answer:
The difference between the volumes is 728 ft³.
Step-by-step explanation:
Our first step will be to find the volume of the smaller pyramid. Notice that we have all the necessary dimensions. The formula for the volume of a pyramid is
[tex]V = \frac{A_bh}{3},[/tex]
where [tex]h[/tex] stands for the height and [tex]A_b[/tex] for the area of the basis. In this case [tex]h=4 ft[/tex], and the area of the basis, which is a rectangle, is [tex]A_b = 3 ft * 7 ft = 21 ft².[/tex] Then,
[tex]V = \frac{(21 ft²)(4 ft)}{3} = 28 ft³.[/tex]
Now, two calculate the volume of the second pyramid, recall that it has dimensions three times larger. This means, [tex]h=3*4 ft=12 ft[/tex] and [tex]A_b = (3*3 ft) *(3* 7 ft) = 9*21 ft² = 189 ft².[/tex] Then,
[tex]V = \frac{(189 ft²)(12 ft)}{3} = 756 ft³.[/tex]
Finally, we only need to substract the values of the volumes:
756 ft³-28 ft³= 728 ft³.
Write the linear equation 5x-15y=-8 in slope-intercept form?
write a story problem that can be solved using the equation: 18.50÷0.5=x
2. Give an example of how you use positive and negative numbers in the real world. Be sure to explain the meaning of 0 in your example.
HELP
Cynthia is finding the measures of the labeled angles in this image.
What is the least number of angle measures she needs to know to find the measures of all labeled angles in the image?
A.She only needs to know the measure of one angle, angle D.
B.She only needs to know the measure of one angle, angle A.
C.She only needs to know the measures of two angles, angles A and B.
D.She only needs to know the measures of two angles, but one of the angles must be one of the remote interior angles.
A wall in Marcus's bedroom is 8 2/5 feet high and 16 2/3 feet long. If he paints 1/2 of the wall blue, how many square feet will be blue?
Marcus's wall has an area of 140 square feet. If he paints half of it blue, 70 square feet will be blue.
To find the area of the wall, we multiply its height by its length:
[tex]\[ \text{Area of the wall} = \text{Height} \times \text{Length} \][/tex]
First, convert the mixed numbers to improper fractions:
- Height: [tex]\(8 \frac{2}{5} = \frac{42}{5}\) feet[/tex]
- Length: [tex]\(16 \frac{2}{3} = \frac{50}{3}\) feet[/tex]
Now, multiply:
[tex]\[ \text{Area} = \left( \frac{42}{5} \right) \times \left( \frac{50}{3} \right) \][/tex]
[tex]\[ \text{Area} = \frac{42 \times 50}{5 \times 3} = \frac{2100}{15} = 140 \text{ square feet} \][/tex]
If Marcus paints half of the wall blue, the area painted blue is:
[tex]\[ \text{Blue area} = \frac{1}{2} \times 140 = 70 \text{ square feet} \][/tex]
Therefore, 70 square feet of the wall will be blue.
Suppose you are driving to visit a friend in another state. You are driving at an average rate of 50 miles per hour. You must drive a total of 345 miles. If you have already driven 145 miles, how much longer will it take you to reach your destination?
A mule deer can run one over four of a mile in 25 seconds. At this rate, which expression can be used to determine how fast a mule deer runs in miles per hour? A. twenty-five seconds over one-fourth mile = 36 miles per hour B. one-fourth mile over twenty-five seconds = 36 miles per hour C. one-fourth mile over twenty-five seconds = 100 miles per hour D. twenty-five seconds over one-fourth mile = 100 miles per hour
Answer:
At this rate, which expression can be used to determine how fast a mule deer runs in miles per hour. A 25 seconds/ 1/4 mile = 36 miles per hour
Answer:
B) one-fourth mile over twenty-five seconds = 36 miles per hour
Ariana has 2/3 quart of milk. She uses 3/4 of it in a cookie recipe. How much milk did Ariana use In her recipe?
Use pascal's triangle to find (8 4)
I don't get how to do this can some one help me please!!
Oliver earns $9 per hour. Write and solve equation to find how many hours he mustwork to earn in your equation. $315. to define the variable you use
Rectangle ABCD is shown above. Find the midpoint of diagonal AC. (Please Help Me Find The Answer)
Which of the following side lengths can form a triangle?
16 cm, 21 cm, and 47 cm
1 in, 2 in, and 3 in
34 mm, 75 mm, and 100 mm
8 ft, 24 ft, and 33 ft
the smaller of two numbers is 7/8 of the larger. Their sum is 30. Find the two numbers
Which is an equation for the line that passes through (0, 2) and (-2, 0)?
f. y = -x
g.y = x - 2
h.y = x + 2
j.y = -x - 2
the product of 7 and a nimber increased by 3 is equal to twice the number subtracted from 39
A student needs to make a square cardboard piece. The cardboard should have a perimeter equal to at least 92 inches. The function f(s) relates the perimeter of a cardboard piece, in inches, to the length of its side in inches. Which of the following shows a reasonable domain for f(s)?
a 23 < s < 46
b 23 < s < 92
c s ≥ 92
d s ≥ 23
Answer: d. s ≥ 23
Step-by-step explanation:
Let s be the side of the square.
We know that the perimeter of a square =4s
Let f(s)=4s
If the cardboard should have a perimeter equal to at least 92 inches, the inequality would look like
[tex]4s\geq 92[/tex]
Divide both sides by 4, we get
[tex]s\geq\frac{92}{4}\\\Rightarrow\ s\geq23[/tex]
Thus, d. is the right answer. The reasonable domain of f(s) is [tex]s\geq23[/tex]