Answer:
Volume of the pit is [tex]31.11[/tex] cubic yards.
Step-by-step explanation:
First lets change all the values to yards.
1 yard = 3 foot
Width in yards = [tex]\frac{4}{3}[/tex] yards
Length in yards = [tex]\frac{280}{3}[/tex] yards
Depth in yards = [tex]\frac{0.75}{3}[/tex] yards
Volume of the pit = Length * Width * Depth
=[tex]\frac{4}{3} *\frac{280}{3} *\frac{0.75}{3}[/tex]
=[tex]\frac{4*280*0.75}{3*3*3}[/tex]
=[tex]\frac{840}{27}[/tex]
=[tex]31.11[/tex] cubic yards.
Volume of the pit is [tex]31.11[/tex] cubic yards.
What is 21/16 simplified
SUSAN NEEDS EXACTLY 4 PLATES ON EACH TABLE FOR THE BANQUET,AND 5 PLATES AT THE MAIN TABLE.IF SHE HAS 417 PLATES,HOW MANY TABLES IS SHE ABLE TO PREPARE?INCLUDE THE MAIN TABLE IN COUNT
In a certain class of students, there are 10 boys from wilmette, 5 girls from kenilworth, 10 girls from wilmette, 7 boys from glencoe, 5 boys from kenilworth and 6 girls from glencoe. if the teacher calls upon a student to answer a question, what is the probability that the student will be from kenilworth?
What is the speed of a plane that travels at a rate of 410 mph with a wind of r mph?
130.8996939 rounded to the nearest hundredth
In a recent semester at a local university, 490 students enrolled in both General Chemistry and Calculus I. Of these students, 61 received an A in general chemistry, 63 received an A in calculus, and 25 received an A in both general chemi: and calculus Find the probability that a randomly chosen student received an A in general chemi stry or calculus or both
Consider the diagram shown where a ladder is leaning against the side of a building. The base of the ladder is 12 ft from the building. How far is the top of the ladder from the ground?(to the nearest ft)
when you divide a whole number by a fraction with a numerator of 1, explain how you can find the quotient
Find the values of x,y, and z. The diagram is not to scale.
A. x = 86, y = 94, z = 75
B. x = 86, y = 75, z = 94
C. x = 75, y = 94, z = 86
D. x = 75, y = 86, z = 94
Answer:
b) x=86,y=75,z=94
Step-by-step explanation:
Write an expression that is equivalent to 3x3x3x3x3x3x3 ?!?!?!
The expression 3x3x3x3x3x3x3 is equivalent to 3⁷.
Given that an expression 3x3x3x3x3x3x3, we need to write an equivalent expression to it,
The expression that is equivalent to 3x3x3x3x3x3x3 can be simplified using the exponentiation operation.
In mathematics, when you have a number or variable multiplied by itself multiple times, you can represent it using exponentiation.
In this case, we have the number 3 multiplied by itself 7 times. Using exponentiation, we can rewrite this expression as 3⁷.
The exponent 7 indicates that the base number, which is 3, should be multiplied by itself 7 times. So, 3⁷ means 3 multiplied by itself 7 times.
When we calculate 3⁷, we get the result 2187.
Therefore, the expression 3x3x3x3x3x3x3 is equivalent to 3⁷.
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What is the decimal value of the 2 in the hexadecimal number f42ac16?
The decimal value of the 2 in the hexadecimal number f42ac16 is 2.
Explanation:The hexadecimal number f42ac16 can be split into individual digits, where each digit represents a power of 16. Starting from the rightmost digit, the 2 represents the digit in the 16^0 (1) place, which is simply 2. Therefore, the decimal value of the 2 in the hexadecimal number f42ac16 is 2.
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The manager of a store selling tea plans to mix a more expensive tea that cost $7 per pound with a less expensive tea that cost $4 per pound to create a hundred forty pound blend that will sell for $6.10 per pound. How many pounds of each type of tea are required?
One side of a rectangle is five times as long as the other side. If the perimeter is 72 meters, what is the length of the shorter side?
What is the difference between sin and cosine
Find the volume of the figure. A) 33 in3 B) 150 in3 C) 233 in3 D) 425 in3
The Volume of Figure is 233 inch³.
What is Volume?Volume is a three-dimensional quantity used to calculate a solid shape's capacity. That means that the volume of a closed form determines how much three-dimensional space it can fill. Volume is a three-dimensional quantity used to calculate the capacity of a container.
Given:
Top Cuboid:
length = 12 inch
width = 3 inch
Height = 3 inch
Bottom Cube:
Edge = 5 inch
So, the Volume of Figure
= Volume of Top Cuboid + Volume of Cube
= 12 x 3 x 3 + 5 x 5 x 5
= 72 + 125
= 233 inch³
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Brent conducted a survey in his school regarding whether students ride their bikes to school each day. he surveyed a random sample of 150 students and 40 said they rode their bikes to school each day. there are 450 students who attended school. based on the results of Brents survey, about how many students in the school ride their bikes to school each day
HELP ASAP PLS Solve and check c-4/c-2=c-2/c+2-1/2-c the solution is c = ? How many extraneous solutions are there?
Answer : the solution of c is 14.
Explanation :
Since we have given that
[tex]\frac{c-4}{c-2}=\frac{c-2}{c+2}-\frac{1}{2-c}\\\\\frac{c-4}{c-2}=\frac{c-2}{c+2}+\frac{1}{c-2}\\\\\frac{c-4}{c-2}=\frac{(c-2)^2+c+2}{(c+2)(c-2)}\\\\\frac{c-4}{c-2}=\frac{c^2+4-4c+c+2}{(c+2)(c-2)}\\\\(c-4)(c+2)=c^2+6-3c\\\\c^2-8-2c=c^2+6-3c\\\\-2c+3c=6+8\\\\c=14[/tex]
So, c = 14
So, the solution of c is 14.
There is no extraneous solution as if we put the value of c i.e. 14 in the equation it does not make the equation not defined . so by putting the value of c we get a defined value,
Hence , there is no extraneous solution.
Answer: The solution is C = 14
And there is zero extraneous solutions
Step-by-step explanation: Because I said so :-)
What are the direction indices for a vector that passes from point 34 1 12 to point 14 12 1 in a cubic unit cell? please indicate negative directions by a "-" sign before the integer and omit spaces between numbers?
The direction indices for a vector passing from point (34, 1, 12) to point (14, 12, 1) are calculated by subtracting the coordinates of the starting point from the ending point, resulting in the indices [-20 11 -11].
Explanation:The student asked for the direction indices of a vector passing from point (34, 1, 12) to point (14, 12, 1) in a cubic unit cell. To determine the direction indices, we need to subtract the coordinates of the initial point from the coordinates of the final point. The resulting vector ∆r will have components ∆x, ∆y, and ∆z as follows:
∆x = 14 - 34 = -20∆y = 12 - 1 = 11∆z = 1 - 12 = -11Therefore, the direction indices for the vector are written without spaces and with negative signs for negative directions. In this case, the direction indices would be [-20 11 -11].
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Evaluate 10x^2y^-1 for x=3 and y=2
Answer:
[tex]10x^{2} y^{-1}[/tex] for x=3 and y=2 is 45.
Step-by-step explanation:
In order to evalue the given expression [tex]10x^{2}y^{-1}[/tex] you have to rewrite it as a fraction, using the property for a negative exponent which says that [tex]y^{-1}[/tex] can be written as [tex]\frac{1}{y}[/tex]
You obtain: [tex]\frac{10x^{2} }{y}[/tex]
Now, you have to replace the given values of x and y in the previous expression:
x=3 and y=2
[tex]\frac{10(3)^{2} }{2}[/tex]
Solving the square:
[tex]\frac{(10)(9)}{2}[/tex]
Solving the multiplication and division:
[tex]\frac{90}{2} = 45[/tex]
The answer is 45
what's the square root of 89
What must be true of the discriminant the soulution to a quadratic equation is a set of 2 different real numbers?
which equation are true for x=-2 and x=2 check all that apply
Answer:
A. [tex]x^2-4=0[/tex]
D. [tex]4x^2=16[/tex]
Step-by-step explanation:
To check which of the given equations have solution [tex]x=-2\text{ and }x=2[/tex], we will solve our given equations one by one.
A. [tex]x^2-4=0[/tex]
[tex]x^2-4+4=0+4[/tex]
[tex]x^2=4[/tex]
[tex]\sqrt{x^2}=\pm\sqrt{4}[/tex]
[tex]x=\pm 2[/tex]
[tex]x=-2\text{ or }x=2[/tex]
Therefore, option A is the correct choice.
B. [tex]x^2=-4[/tex]
To solve our given equation, we need to take square root of both sides of equation. Since square root is not defined for negative numbers, therefore, option B is not a correct choice.
C. [tex]3x^2+12=0[/tex]
[tex]3x^2=-12[/tex]
[tex]x^2=-4[/tex]
To solve our given equation, we need to take square root of both sides of equation. Since square root is not defined for negative numbers, therefore, option C is not a correct choice.
D. [tex]4x^2=16[/tex]
[tex]x^2=4[/tex]
[tex]\sqrt{x^2}=\pm\sqrt{4}[/tex]
[tex]x=\pm 2[/tex]
[tex]x=-2\text{ or }x=2[/tex]
Therefore, option D is the correct choice.
E. [tex]2(x-2)^2=0[/tex]
[tex](x-2)^2=0[/tex]
[tex]\sqrt{(x-2)^2}=\sqrt{0}[/tex]
[tex]x-2=0[/tex]
[tex]x=2[/tex]
Therefore, option E is not a correct choice.
Yvonne put $4000 in a savings account. At the end of three years, the account had earned $960 in simple interest. A. How much does she have in her own account at the end of three years? B. What annual simple interest rate did the account grow? Show your work. C. How many more dollars would she have in her account if the interest rate were 1% greater? Show your work.
The area of a rectangle is 56 cm.the length is 2 cm more than x and the width is 5 cm less than twice x.solve for x
Answer:
x = 6 cm
Step-by-step explanation:
The area is the product of length (x +2) and width (2x -5). It is 56 cm², so for all dimensions in cm, we can write ...
(x +2)(2x -5) = 56
2x² -x -66 = 0 . . . . . subtract 56 to put into standard form
(x -6)(2x +11) = 0 . . . . factor
Solutions to the equation are values of x that make the factors zero:
x = 6, x = -11/2
The negative solution is extraneous, so the solution of interest is ...
x = 6 cm
the product of twice a number and two is the same as the difference of three times the number and 8/3. find the number
Lin has 13 coins in her pocket that equal 40 cents. All the coins are dimes, d, and pennies, p. Which combination of coins does Lin have? Use the table to answer the question.
The combination of coins are:
3 dimes and 10 pennies.
Step-by-step explanation:Let there are d number of dines and p number of pennies.
Now as there are a total of 13 coins this means that:
d+p=13------(1)
and also the total value of the coins is 40 cents.
1 dime=10 cents
Hence, d dime= 10 d cents
Also, 1 penny= 1 cent
Hence p penny= p cents
Hence, we get:
10d+p=40------(2)
On subtracting equation (1) from (2) we get:
9 d=27
on dividing both side by 9 we get:
d=3
On putting the value of d in equation (1) we get:
3+p=13
i.e. p=13-3
i.e. p=10
The combination is:
3 dimes and 10 pennies
A picture contains 2/3 quart of lemonade If an equal amount of lemonade is poured into each of six classes how much lemonade will each class contain
The perimeter of a rectangle is 44 ft. the length is 6 ft longer than the width. find the dimensions. write a system of linear equations and solve the resulting system. let x be the length and y be the width.
Fabian harvests 10 pounds of tomatoes from his garden he needs 2 2/5 pound to make a batch of soup. If he sets aside 2.8 pounds of tomatoes to make spaghetti sauce, how many batches of soup can He make
With 7.2 pounds of tomatoes, Fabian can make 3 batches of soup since each batch requires 2.4 pounds of tomatoes.
Explanation:First, let's understand the total quantity of tomatoes Fabian has to make soup. He harvested a total of 10 pounds and set aside 2.8 pounds for spaghetti sauce. So, he has 7.2 pounds of tomatoes left to make soup. Every batch of soup needs 2 2/5 pounds of tomatoes which is equivalent to 2.4 pounds. To find out how many batches of soup he can make, divide the total weight of tomatoes he has for the soup by the weight each batch needs. Therefore, 7.2 divided by 2.4 gives 3 batches of soup.
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