Jack wants to fill a rectangular box with sand. The length of the sand box is 3 feet, width is 6 inches, and height is 2.4 inches. Each bag of sand contains 0.15 cubic foot of sand. How many bags of sand will Jack need to fill the box completely?
[1 foot = 12 inches]
Numerical Answers Expected!
The number of bags of sand that Jack need to fill the box completely are:
2
Step-by-step explanation:The length(l) of the sand box is 3 feet, width(w) is 6 inches, and height(h) is 2.4 inches.
Also,
1 foot=12 inches
This means that:
1 inch=1/12 foot
i.e.
6 inches=0.5 feet
i.e.
w=0.5 feet
and
h=2.4 inches
i.e. h=0.2 feet
Now, we find the volume of the rectangular box.
The volume of the rectangular box is given by:
Volume=lwh
Hence,
Volume=3×0.5×0.2
i.e.
Volume=0.3 cubic feet.
Also, the volume of one bag of sand= 0.15 cubic feet
This means that the number of bags of sand that will fill the box completely is:
(Volume of rectangular box) / (Volume of one bag of sand)
= 0.3/0.15
=2
Hence, number of bags =2
Line segment YZ was used to translate ABCDE. YZ is 5.5 inches long.what is the length of AA + BB + CC + DD +EE?
Answer:
AA' + BB' + CC' + DD' +EE' = 27.5 inches
Step-by-step explanation:
A translation moves all points of a figure the same distance in the same direction. If line segment YZ is 5.5 inches long, then the distance between original point A and translated point A' would be 5.5 inches. That is also valid to the other points. So, length of AA' = BB' = CC' = DD' = EE' = 5.5 inches. In consequence, AA' + BB' + CC' + DD' +EE' = 5*5.5 inches = 27.5 inches
Many food products are packaged in a variety of sizes. The list below gives the sizes and costs of fruit juice drinks at one store. $1.92 single-serving multi-pack (serves 6) $1.12 one quart (serves 4) $2.16 two quarts (serves 8) $3.52 one gallon (serves 16) Type your responses here: 1. Choose two different sizes and give an advantage for buying each.
which graph represents a circle with equation x2 + y2 = 9
Answer: The correct option is (B). Its image is attached below.
Step-by-step explanation: We are given to select the graph that represents the circle with equation as follows:
[tex]x^2+y^2=9~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]
We know that the standard equation of a circle with center at the point (h, k) and radius r units is given by
[tex](x-h)^2+(y-k)^2=r^2.[/tex]
From equation (i), we have
[tex]x^2+y^2=9\\\\\Rightarrow(x-0)^2+(y-0)^2=3^2.[/tex]
Comparing the above equation with the standard equation of a circle, we get
Center, (h, k) = (0, 0) and radius, r = 3 units.
We draw the graph of the circle with center at the origin (0, 0) and radius 3 units in the attached figure below.
We see that the graph of the circle is same as the one provided in option (B).
Thus, option (B) is CORRECT.
After 2 months of living at his new apartment, Henry had 2 cats. Six months later, Henry still had 2 cats. Which of the graphs below models Henry's cat population?
I know it is just a straight line but I need to know if its horizontal or vertical..
Answer:
The graph with the horizontal line.
Which is the more reasonable measurement of the diameter of a blood cell: 7.4 ⋅ 10−3 mm or 7.4 ⋅ 103 mm? Justify your answer.
Answer:
[tex]7.4\times 10^{-3}\ mm[/tex]
Step-by-step explanation:
Actual measurement of diameter of a blood cell is 6 to 8 μm
Let diameter be d
[tex]1\mu m=10^{-6}\ m[/tex]
[tex]6\times 10^{-6}\ m\leq d\leq 8\times 10^{-6}\ m[/tex]
Now we check the given measurement between the range.
[tex]7.4\times 10^{-3}\ mm[/tex]Change into meter. As we know 1000 mm = 1 m or 1 mm = 10⁻³ m
[tex]7.4\times 10^{-3}\times 10^{-3}\ m[/tex]
[tex]7.4\times 10^{-6}\ m[/tex]
[tex]7.4\times 10^{3}\ mm[/tex][tex]7.4\times 10^{3}\times 10^{-3}\ m[/tex]
[tex]7.4\ m[/tex]
So, [tex]7.4\times 10^{-6}\ m[/tex] lie between [tex]6\times 10^{-6}\ m\leq d\leq 8\times 10^{-6}\ m[/tex]
Hence, [tex]7.4\times 10^{-6}\ m[/tex] more reasonable measurement of diameter of blood cell because it lies between range of diameter of blood cell.
The equation for the cost in dollars of producing computer chips is y =.000015x^2-.03x+35. Where x is the number of chips produced . Find the number of chips that minimizes the cost. What is the cost for that number of chips?
1000 chips minimize the production cost in the given equation, and the minimum cost for producing these chips is $20.
Explanation:To find the number of chips that minimizes the cost in the given quadratic equation, y = 0.000015x^2 - 0.03x + 35, we can use the vertex formula for a parabola, which is derived from the general quadratic equation.
The general form of a quadratic equation is y = ax^2 + bx + c, and the x-coordinate of the vertex, which gives us the number of chips that minimizes the cost, can be found using x = -b/(2a). For our equation, a = 0.000015 and b = -0.03.
Substituting the values of a and b into the vertex formula:
x = -(-0.03)/(2 * 0.000015)x = 0.03/0.00003x = 1000 (number of chips)Now, we plug this value back into the original equation to find the minimum cost:
y = 0.000015(1000)^2 - 0.03(1000) + 35y = 15 - 30 + 35y = $20 (cost for producing 1000 chips)This gives us the minimum cost and the number of chips that lead to this cost. Therefore, 1000 chips minimize the cost, and the minimum cost for producing these chips is $20.
Maria started with $10. She has been saving $3 dollars each week to buy a softball bat. The amount of money Maria has depends on how many weeks she has been saving. Which expression represents Maria after x weeks?
A) f(x) = 10x + 3
B) f(x) = 3x + 10
C) f(x) = 10x - 3
D) f(x) = 3x - 10
Which gas is plotted using the y-axis on the right?
?/48=7/8 what is the numerator
Tracey paid $170 for an item that was originally priced at $580. What percent of the original price did Tracey pay? Round your answer to two decimal places.
Assume that you own a ruby. Apply the law of detachment to the following conditional statement:
If you have a ruby, then it you have at least $1000.
Which of these statements is true, according to the law of detachment?
You have a ruby.
Someone buys the ruby for $1000.
You sell the ruby.
You have at least $1000.
The statement fourth "You have at least $1000" is correct if you have a ruby, then it you have at least $1000.
What is the law of syllogism?Legal syllogism is a legitimate concept that deals with the law and how it is applied, specifically a type of argument that uses deductive reasoning to determine whether a given act is legal.
We have:
Assume that you own a ruby. Apply the law of detachment to the following conditional statement:
The statement is:
If you have a ruby, then it you have at least $1000.
As we know, the law of detachment, we must let go of attachment to both the desired end and all possible routes to get there in order to actualize our wants.
Thus, the statement fourth "You have at least $1000" is correct if you have a ruby, then it you have at least $1000.
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Given the statement 'If you have a ruby, then you have at least $1000.' and the fact that you have a ruby, the Law of Detachment leads to the conclusion 'You have at least $1000.'
Explanation:The Law of Detachment (also known as Modus Ponens) in logic says that if a conditional statement ('if p then q') is true and the first part of the statement (p) is true, then the second part of the statement (q) is true. Let's apply it to your statement.
The original statement is 'If you have a ruby, then you have at least $1000.' You confirmed the first part 'You have a ruby.' So, according to the Law of Detachment, the resulting correct statement would be 'You have at least $1000.' The other statements about selling or someone buying the ruby are irrelevant to the Law of Detachment.
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Two cars leave the same location traveling in opposite directions. One car leaves at 3:00 p.m. traveling at an average rate of 55 miles per hour. The other car leaves at 4:00 p.m. traveling at an average rate of 75 miles per hour. Let x represent the number of hours after the first car leaves. How many hours after the first car leaves will the two cars be 380 miles apart?
Enter an equation that can be used to solve this problem in the first box. Solve for x and enter the number of hours in the second box.
Equation:
x =
x = hours
car 1 left an hour before car 2 so you have 55(x+1)
car 2 = 75x
add them together to equal miles driven:
55(x+1) + 75x = 380
55x+55 + 75x = 380
combine like terms:
130x+55 = 380
subtract 55 from each side:
130x = 325
divide both sides by 130
x = 325 /130 = 2.5
x = 2.5 hours
so 2.5 hours
What key would you use is 10 students chose cartoons
what times what equals 108
12 times 9 = 108, 18 times 6 = 108, 27 times 4 = 108 and 36 times 3 = 108.
What is multiplication?Multiplication is an operation that represents the basic idea of repeated addition of the same number.
Given that, what times what equals 108,
Below is a list of all the different ways that what times what equals 108.
12 times 9 equals 108
18 times 6 equals 108
27 times 4 equals 108
36 times 3 equals 108
54 times 2 equals 108
108 times 1 equal 108
Hence, 12 x 9 = 108. 18 x 6 = 108. 27 x 4 = 108. 36 x 3 = 108.
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There are multiple pairs of numbers that multiply to 108, such as 1 × 108, 2 × 54, 3 × 36, 4 × 27, 6 × 18, and 9 × 12. Therefore, any pair of these factors will correctly answer the question.
To determine what times what equals 108, we need to identify the factors of 108.
1 × 108 = 108
2 × 54 = 108
3 × 36 = 108
4 × 27 = 108
6 × 18 = 108
9 × 12 = 108
There are multiple pairs of numbers that, when multiplied together, equal 108. Therefore, any of these factor pairs are valid answers to the question.
For example, 9 times 12 or 6 times 18 are pairs that satisfy this condition.
How is 2 and 7 tenths written as a decimal?
Karli's shadow is 60 inches long. A nearby fire hydrant casts a shadow 40 inches long. If Karli is 48 inches tall, what is the height of the fire hydrant?
Using the formula for volume of a cone, express r in terms of V, h and pi
The volume of the cone is one-third of the volume of the cylinder which is equal to the product of area of the base and the height. The equation is,
V = (1/3)(pi)(r^2)h
Dividing both sides of the equation by (1/3)(pi)(h) will give us,
3V/(pi)(h) = r^2
Taking the square-root of both sides,
r = sqrt(3V/(pi)(h))
Answer:
[tex]r = \sqrt{\displaystyle\frac{3V}{h\pi}}[/tex]
Step-by-step explanation:
We are given the following information in the question.
Using the formula for volume of cone, we have to express r in terms of V, h and pi.
Formula:
[tex]\text{Volume of cone, V} = \displaystyle\frac{1}{3}\pi r^2 h\\\\\text{where r is the radius of cone, h is the height of radius}[/tex]
Now, we have to evaluate r, the radius of cone.
Rearranging the terms, we have,
Working:
[tex]V = \displaystyle\frac{1}{3}\pi r^2 h\\\\r^2 = \frac{3\times V}{\pi\times h}\\\\r^2 = \frac{3V}{h\pi}\\\\r = \sqrt{\frac{3V}{h\pi}}[/tex].
Thus, r in form of V, h and pi can be written as:
[tex]r = \sqrt{\displaystyle\frac{3V}{h\pi}}[/tex]
Which is precisely defined using the undifined terms point and plane
Solve each equation for y 2x+3y=18 plus show work
divide using synthetic division (2x^3 + 14x^2 - 58x) / (x + 10) 58 POINTS!!!!
yvonne made 2 3/4 quarts of punch. Write 2 3/4 as a decimal
Which one of the following statements is true of parallel lines?
Find the greatest possible error for the measurement 0.991 g. A. 0.001 g B. 0.1 g C. 0.005 g D. 0.0005 g
If the sum of six consecutive even integers is 390 what is the smallest of the six integers
A box contains 19 large marbles and 11 small marbles. each marble is either green or white. 5 of the large marbles are green, and 6 of the small marbles are white. if a marble is randomly selected from the box, what is the probability that it is large or green? express your answer as a fraction or a decimal number rounded to four decimal places.
The probability that a randomly selected marble is either large or green is approximately 0.6333 or you can express it as a fraction: 19/30.
Consider the total number of marbles that satisfy either of these conditions.
Total large marbles: 19
Total green marbles: 5
However, the large marbles include the green marbles, so we need to subtract the overlap:
Number of large green marbles: 5
Total marbles that are either large or green = Total large marbles + Total green marbles - Number of large green marbles
Total marbles that are either large or green = 19 + 5 - 5
= 19
Now, we'll find the probability by dividing the total marbles that are either large or green by the total number of marbles:
Probability = (Total marbles that are either large or green) / (Total number of marbles)
Probability = 19 / (19 + 11)
Probability ≈ 0.6333 (rounded to four decimal places)
Therefore, the probability that a randomly selected marble is either large or green is approximately 0.6333 or you can express it as a fraction: 19/30.
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The probability that randomly selected marble from the box is large or green is 0.7667.
Explanation:The probability of selecting a large or green marble from a box can be found by analysing the given information. We have 19 large marbles, out of which 5 are green. We also have 11 small marbles, out of which 6 are small and green since small marbles cannot be large. This means there are a total of 30 marbles (19 large and 11 small), and 9 of them are green. To calculate the probability that a marble is large or green, we need to include all large marbles (since they meet one condition) and add the small green marbles (since they meet the other condition, but aren't already counted with the large marbles).
The number of favorable outcomes is therefore 19 (large marbles) plus 4 (small green marbles), since 5 large marbles have already been counted as green, we don't count them again. That makes a total of 23 favorable outcomes. The probability is the number of favorable outcomes divided by the total number of marbles:
Probability = 23 / 30. As a decimal rounded to four places, this is approximately 0.7667.
PLEASE HELP: When two-thirds of an even number is added to one-quarter of the next consecutive even number, the result is 28. What are the numbers?
Approximately 55% of the 750 pupil student body voted for Suresh for student body president. How many students voted for him?
Elizabeth bought 4 drinks and some nachos. The nachos cost $6, and she spent a total of $18. How much did each drink cost? Use d to represent the cost of each drink. A. ; each drink cost $4. B. ; each drink cost $6. C. ; each drink cost $2. D. ; each drink cost $3.
Answer:
D. ; each drink cost $3
Step-by-step explanation:
Given that Elizabeth bought 4 drinks and some nachos.
Total amount spent = [tex]18[/tex]$
She can buy only in integers the drinks i.e.1,2,or 3
Nachos also she can buy 1,2...
If x is the no of nachos and d the cost of drink, we get
[tex]6x+4d=18[/tex]
If x=1, d =3
x=2, d = 1.50
d=3, d=0 (which is not possible)
Hence d can take values either as 3 or 1.50
Out of the options given 3 is only there.
D. ; each drink cost $3
The equation of a line is −6x−2y=−18.
What is the x-intercept of the line?
Enter your answer in the box.