The topsoil will be 4.05 inches deep
Calculating depthFrom the question, we are to determine how many inches deep the topsoil will be
From the given information,
The volume of the topsoil = 1 cubic yard
Convert to cubic feet
1 cubic yard = 27 cubic feet
∴ The volume of the topsoil = 27 cubic feet
Then,
The depth of the topsoil will be = 27/(8 ×10)
Depth of topsoil = 27/80
Depth of topsoil = 0.3375 foot
Now, convert to inches
1 foot = 12 inches
∴ 0.3375 foot = 0.3375×12 inches
= 4.05 inches
Hence, the topsoil will be 4.05 inches deep
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The difference between twice a number, x, and a smaller number, y, is 3. The sum of twice the number and the smaller
number is -3. Which equations represent this situation?
Oy=2x-3 and y=-2x-3
Oy-2x-3 and y=-2-2
O y=2x+3 and y=-2x-3
Oy-2x+3 and y=-x-
3. Help meeee
Answer:
y=2x+3 and y=-2x-3
Step-by-step explanation:
First situation:
2x-y=3
making y subject
y=2x+3
Second situation:
2x+y=-3
making y subject
y=-2x-3
una familia compuesta por 4 personas van a celebrar el cumpleaños de su hijo para lo cual compran una torta y realizan el siguiente reparto: una familia compuesta por 4 personas van a celebrar el cumpleaños de su hijo para lo cual compran una torta y realizan el siguiente reparto: la mamá recibe 1/7 de pastel; el papá recibe 3/14 de pastel; el hijo mayor recibe 2/7de pastel; ¿qué cantidad recibió el cumpleañero?
Durante la celebración familiar del cumpleaños y aplicando las propiedades de los números fraccionarios, el hijo menor recibió 5/14 de la torta.
¿Cuánta proporción del pastel recibió el cumplimentado?
En esta pregunta tenemos una torta de cumpleaños, que asumimos de forma circular. Si leemos con cuidado el enunciado, encontramos que la proporción del pastel correspondiente al cumplimentado mediante la siguiente sustracción de fracciones:
x = 1 - 1/7 - 3/14 - 2/7
x = 6/7 - 3/14 - 2/7
x = 4/7 - 3/14
x = 8/14 - 3/14
x = 5/14
Durante la celebración familiar del cumpleaños y aplicando las propiedades de los números fraccionarios, el hijo menor recibió 5/14 de la torta.
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What is the coefficient of [tex]x^7[/tex] in the expansion of [tex](3 - x)^{11}[/tex]?
Answer:
-26730
Explanation:
To find the coefficient of [tex]x^7[/tex] in the expansion of [tex](3 -x)^{11}[/tex]
Use Binomial Expansion:
[tex](x+y)^n = \ ^n C_0 x^n + \ ^n C_1 x^{n-1} y + \ ^n C_2 x^{n-2}y^2 + ...+ \ ^n C_n y^n[/tex]
In this expansion,
[tex](3-x)^{11}[/tex]
The coefficient of [tex]x^7[/tex]
[tex]= 11C_{7} (3)^{11-7} (-x)^7[/tex]
[tex]= (330) (81) (-x^7)[/tex]
[tex]= -26730x^7[/tex]
Could someone help me out with this question?
The simplified form of the difference quotient of equation [tex]9x^2+5x-1[/tex] . in the form 9x + 9h + 5.
In question for equation [tex]9x^2+5x-1[/tex], simplified to difference quotient in the form of Ax+Bh+C where A, B, C are integers
equation is the relationship between variable and represented as [tex]9x^2+5x-1[/tex] is example of polynomial equation.
We know that,
for difference quotient
[tex]=\frac{f(x+h)-f(x)}{h} \\\frac{9(x+h)^2+5(x+h)-1-9x^2-5x+1}{h}\\\frac{9h^2+9hx+5h}{h}\\9x+9h+5[/tex]
While, compared with Ax+Bh+C
we have A=9, B=9, C=5.
Thus, The required value of difference Quotient in the form Ax+Bh+c where A, B and C is 9, 9 and 5 respectively
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Find n in this equation: 308P(n,2)=P(16,4)
Answer:
24
Step-by-step explanation:
7x4
Solve for x in the diagram below.
Vertical angles are congruent, so:
[tex]4x+50=150\\\\4x=100\\\\x=\boxed{25}[/tex]
The vertex of this parabola is at (3,-2). When the x-value is 4, the
y-value is 3. What is the coefficient of the squared expression in the
parabola's equation?
O
O
A-1
B. 7
C. 1
D. 5
Answer:
5
Step-by-step explanation:
f(x) = a(x-3)² - 2
When x = 4, y = 3, so:
3 = a(4-3)² - 2
5 = a
v = u + 2at
Where v is the final velocity (in m/s), u is the initial velocity (in m/s), a is the acceleration (in m/s²) and t is the time (in seconds).
Find v when u is 19 m/s, a is 3 m/s², and is 21 seconds.
Answer:
145 m/s
Step-by-step explanation:
v = u + 2at
v = 19 + 2(3)(21)
v = 19 + 126
v = 145
answer
V=145
Step-by-step explanation:
V=U+2at
v=19+2×3×21
v=19+126
v=145
please help me asap thank you so so much u are so amazing!!
You have 20 coins (8 silver dollars, 7 quarters, and 5 dimes) and plan to sell 8 at random. What is the probability that you sell 3 silver dollars, 2 quarters, and 3 dimes?
Answer: 0.01225%
Step-by-step explanation:
[tex]\frac{8}{20} *\frac{8}{20} *\frac{8}{20} *\frac{7}{20} *\frac{7}{20} *\frac{5}{20} *\frac{5}{20} *\frac{5}{20} = \frac{49}{400000} =0.0001225=0.01225[/tex]%
Are the grades shown in the math class below normally distributed? Explain your answer.
Since the histogram is not symmetric, the grades shown in the math class below are not normally distributed.
When does a histogram represent a normal distribution?A histogram represents a normal distribution if it symmetric.
In this problem, we have that:
57% of the grades are on the left tail.25% of the grades are on the center.18% are on the right tail.Since the percentages at the tails are different, the histogram is not symmetric, and the grades shown in the math class below are not normally distributed.
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An insurance policy sells for $600. Based on past data, an average of 1 in 50 policy holders
will file a $5,000 claim, an average of 1 in 100 policyholders will file a $10,000 claim, and an average
of 1 in 200 policyholders will file a $30,000 claim.
(a) Find the expected value (to the company) per policy sold.
(b) If the company sells 10,000 policies, what is the expected profit or loss?
Using the expected value of a discrete distribution, the values are given as follows:
a) $250.
b) $2,500,000.
What is the mean of a discrete distribution?The expected value of a discrete distribution is given by the sum of each outcome multiplied by it's respective probability.
The distribution of the company's earnings is given as follows:
P(X = -4400) = 0.02.P(X = -9400) = 0.01.P(X = -29400) = 0.005.P(X = 600) = 0.965.Considering that the policy sells for $600, for example, a $5000 claim is a loss of $5000 - $600 = $4,400 for the company, which explains the above distribution.
Item a:
The expected value for a policy sold is given by:
E(X) = 600(0.965) - 4400(0.02) -9400(0.01) - 29400(0.005) = 250.
Item b:
Considering the value found in item a for a single policy, for 10,000 policies, the expected profit is given by:
E = 10000 x 250 = 2,500,000.
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in your own words , what is drecrete math
Answer:
Discrete mathematics is the study of mathematical structures that can be considered "discrete" rather than "continuous". Objects studied in discrete mathematics include integers, graphs, and statements in logic.
_____ ÷ ( - 9 ) = ( - 8 )
pls pls answer me question
Interest = $42.68, time 7.08%. Find the principal. Round to the nearest hundredth place. = 7 years, rate =
Answer:
trust me its c i did the test on edge for me
Step-by-step explanation:
i did the test on edge
Answer:
$63.83
Step-by-step explanation:
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The diameter of a wrecking ball used to tear down buildings is 3.5 ft. What is the volume ( to the nearest hundredth) Use 3.14 for pi and round each approximation to the nearest hundredth.
Answer:
22.44 ft
Step-by-step explanation:
The radius is equal to half of the diameter or 1.75 ft (in this case).
The volume of a sphere is defined as the equation:
V = 4/3 * pi * radius ^ 3
V = 4/3 * 3.14 * 1.75 ^ 3
V = 4/3 * 3.14 * 5.36
V = 22.44 ft
The functions f(x)=x²-1 and g(x) = -x² + 4 are shown on the graph.
Explain how to modify the graphs of f(x) and g(x) to graph the solution set to the following system of inequalities. How can the solution set be identified?
The solution to the given graph is (-√5/2, √5/2)
Quadratic graphGiven the following quadratic graph f(x)=x²-1 and g(x) = -x² + 4
The solution will be the point of intersection of the two curves.
Equate the functions
x²-1 = -x² + 4
Equate to zero
x²+x² - 1- 4 = 0
2x² -5 = 0
2x² = 5
x² = 5/2
x = ±√5/2
Hence the solution to the given graph is (-√5/2, √5/2)
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You know the area (A = 300 ft^2) and the width (w = 4 ft), but not the length. Rewrite the formula by dividing both sides by the width.
length = Answer
Answer:
Length equals to 75 ft
Step-by-step explanation:
A=l x w Area of a rectangle formula.
A/w=l Solve for length
300=l x 4
300=l x 4
4 4
300/4=l
75=l
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How many 4-letter words with at least one vowel can be constructed from the letters A, B, C, D, and E? (Note that A and E are vowels, any word is valid, not just English language words, and letters may be used more than once.)
Answer:
544 words
Step-by-step explanation:
The number of 4 letter words can be constructed from ABCDE would be 5^4 = 625
The number of 4 letter words can be constructed using BCD would be 3^4 = 81
So the number of words that use at least one vowel would be 5^4 - 3^4 = 625-81 = 544
A cook needs 7 cups of vegetable stock for a soup recipe. How much is this in pints? Write your answer as a whole number or a mixed number in simplest form. Include the correct unit in your answer. Ú 08 Explanation Check fl oz qt X values: One... gal pt S .? © 2022 McGraw HilllLS ALL
Answer:
3 1/2 pints
Step-by-step explanation:
A pint is two cups
7 cups / 2cups/pint = 7/2 pint = 3 1/2 pints
18
(cos+ i sin ) ¹8
6
Answer:
-1.
Step-by-step explanation:
1) according to the DeMoivre's theorem:
[tex]1*(cos\frac{ \pi}{6} +isin\frac{ \pi}{6})^{18}=1^{18}(cos(18*\frac{ \pi}{6})+isin(18*\frac{ \pi}{6}))=cos3\pi +isin3\pi =cos\pi +isin\pi ;[/tex]
2) if cos(π)=-1 and sin(π)=0, then cosπ+i*sin(π)=-1.
Write an equation of a circle with the given center and radius
Center(-7,-6) Radius = 2
The equation of the circle is (x + 7)² + (y + 6)² = 4 if the center and radius are (-7,-6) and 2 respectively.
What is a circle?It is described as a set of points, where each point is at the same distance from a fixed point (called the center of a circle)
We have center of the circle(h, k) = (-7, -6)
The radius of the circle r = 2
The standard form of a circle:
(x - h)² + (y - k)² = r²
(x - (-7))² + (y - (-6))² = 2²
(x + 7)² + (y + 6)² = 4
Thus, the equation of the circle is (x + 7)² + (y + 6)² = 4 if the center and radius are (-7,-6) and 2 respectively.
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Yall I need help asap pls
question 7
You work as an assistant for a local musical theatre group, the Main Street Theatre Company. The company is putting on a production of Les Misérables this year, and they need your help planning it.
The company's first task is to cast the lead female roles of Fantine, adult Cosette, and Éponine, and the lead male roles of Jean Valjean, Inspector Javert, and Marius. You have received headshots and resumes from 28 women and 22 men who are interested in auditioning for these parts.
A: If no one has been cast yet, how many different ways are there to cast Jean Valjean from the 22 men?
B: If Jean Valjean has already been cast, how many different ways are there to cast Inspector Javert from the remaining men?
C: If Jean Valjean and Inspector Javert have already been cast, how many different ways are there to cast Marius from the remaining men?
Select one answer choice for part A, one answer choice for part B, and one answer choice for part C.
A: 22P3
A: 22!
B: 21!
C: 20P1
B: 21
B: 21P2
C: 20!
A: 22
C: 20
Question 2:
A: Which of the following expressions will calculate the number of ways the three lead male roles could be cast?
B: Evaluate the permutation from part A.
Select one answer choice for part A, and one answer choice for part B.
A: 22P19
B: ≈1.12×1021
B: 9240
A: 3P22
A: 22P3
B: ≈1.87×1020
The permutation illustrates that if no one has been cast yet, the different ways that are there to cast Jean Valjean from the 22 men is 22.
How to compute the value?The ways to cast Jean will be:
= 22!/(22 - 1)!
= 22!/21!
= 22
When Jean Valjean has already been cast, the different ways that are there to cast Inspector Javert from the remaining men will be:
= 21!/(21 - 1)!
= 21!/20!
= 21
When Jean Valjean and Inspector Javert have already been cast, the different ways that are there to cast Marius from the remaining men will be:
= 20!/(20 - 1)!
= 20!/19!
= 20
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The area of the right triangle shown is 24 square feet. Which equations can be used to find the lengths of the legs of the triangle? Select three options. 0.5(x)(x + 2) = 24 x(x + 2) = 24 x2 + 2x – 24 = 0 x2 + 2x – 48 = 0 x2 + (x + 2)2 = 100
The equations to calculate the legs are 0.5(x)(x + 2) = 24, x^2 + 2x - 48 = 0 and x^2 + (x + 2)^2 = 100
How to determine the legs of the triangle?The complete question is in the attached image
The given parameters are:
Area = 24
Legs = x and x + 2
The area of the triangle is calculated as:
Area = 0.5 * Base * Height
This gives
0.5 * x * (x + 2) = 24
So, we have:
0.5(x)(x + 2) = 24
Divide through by 0.5
(x)(x + 2) = 48
Expand
x^2 + 2x = 48
Subtract 48 from both side
x^2 + 2x - 48 = 0
Hence, the equations to calculate the legs are 0.5(x)(x + 2) = 24, x^2 + 2x - 48 = 0 and x^2 + (x + 2)^2 = 100
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?????????????????????????
Answer:
[tex]\sqrt[10]{4}[/tex]
Step-by-step explanation:
Apply power to power rule on the exponents, [tex]\frac{2}{5}*\frac{1}{4} = \frac{1}{10}[/tex] when simplified
[tex]4^\frac{1}{10}[/tex] is also the same as [tex]\sqrt[10]{4}[/tex]
Answer:
[tex]\sqrt[10]{4}[/tex]
Step-by-step explanation:
We know that,
[tex](a^{x} )^y=a^x^y\\\sqrt{x} =x^{\frac{1}{2} } \\x^\frac{1}{y} =\sqrt[y]{x}[/tex]
By following those, let us solve the given expression.
[tex](4^\frac{2}{5} )^\frac{1}{4} \\\\4^\frac{2*1}{5*4} \\\\4^\frac{2}{20} \\\\4^\frac{1}{10}\\\\\sqrt[10]{4}[/tex]
Are the expressions –0.5(3x 5) and –1.5x 2.5 equivalent? explain why or why not.
Answer:
not equivalent; signs don't match
Step-by-step explanation:
Apparently, you want to compare the expressions ...
-0.5(3x +5)-1.5x +2.5Distributive propertyThe distributive property allows you to eliminate parentheses by multiplying each term inside parentheses by the factor outside.
ApplicationWhen we do that to the first expression, we get ...
-0.5(3x +5) = (-0.5)(3x) +(-0.5)(5) = -1.5x -2.5
Note that the signs of the terms inside parentheses are the same, and the signs of the terms after removing parentheses are the same. (Both terms have their signs changed by the negative factor multiplying the parentheses.)
The expanded expression -1.5x -2.5 is not equivalent to -1.5x +2.5, which has terms of different signs.
Solve for x. Round to the nearest hundredth if necessary.
Answer:
Step-by-step explanation:
[tex]\frac{19}{x}[/tex] = tan 29°
x = [tex]\frac{19}{tan29^o}[/tex] ≈ 34.28
PLEASE ANSWER AS FAST AS POSSIBLE PLEASE! I WILL MARK BRAINLIEST!
Three equations are listed below.
*y=x(3x+2)
*y= x/3+2
*y=2-3x
IDENTIFY ONE LINEAR EQUATION AND ONE NONLINEAR EQUATION FROM THE LIST. STATE A REASON WHY EACH QUESTION YOU IDENTIFIED IS LINEAR OR NON LINEAR.
1. WHAT IS THE LINEAR EQUATION?
WHY IS THAT THE LINEAR EQUATION
2. WHAT IS THE NONLINEAR EQUATION
WHY IS THAT THE LINEAR EQUATION
please finish this, i hate math.
Answer:
WHAT IS THE LINEAR EQUATION?
y=2-3x and y=x/3+2
WHY IS THAT THE LINEAR EQUATION
Linear functions are those whose graph is a straight line. A linear function has one independent variable and one dependent variable. The independent variable is x and the dependent variable is y
WHAT IS THE NONLINEAR EQUATION
Y = x(3x+2)
WHY IS THAT THE LINEAR EQUATION
A nonlinear function has more than one independent variable. The independent variable is x.
y= x(3x-2) is non linear equation.
y= x/3 + 2 is linear equation.
y= 3 -2x is linear equation.
What is Linear Equation?Linear equations are the equations of degree 1.
It is the equation for the straight line.
The standard form of linear equation is ax+by+c =0, where a ≠ 0 and b ≠ 0.
We know that the linear equation have highest degree 1.
First, y= x(3x-2)
y= 3x² -2x
Here, the highest degree is 2 which is non linear equation.
Now, y= x/3 + 2 have highest degree 1 which is linear equation.
and, y= 3 -2x have highest degree 1 which is linear equation.
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7+5y=-13 solve for y
[tex]\large\displaystyle\text{$\begin{gathered}\sf 7+5y=-13 \end{gathered}$}[/tex]
Subtract 7 from both sides.
[tex]\large\displaystyle\text{$\begin{gathered}\sf 5y=-13-7 \end{gathered}$}[/tex]
Subtract 7 from −13 to get −20.
[tex]\large\displaystyle\text{$\begin{gathered}\sf 5y=-20 \end{gathered}$}[/tex]
Divide both sides by 5.
[tex]\large\displaystyle\text{$\begin{gathered}\sf y=\frac{-20}{5} \end{gathered}$}[/tex]
Divide −20 by 5 to get −4.
[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf y=-4 \end{gathered}$} }\large\displaystyle\text{$\begin{gathered}\sf \ \ \to \ \ \ Answer \end{gathered}$}[/tex]
VerificationWe let y = -4.
[tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{7+5\times-4=-13 \ \ \to \ \ [ Multiply] } \end{gathered}$}[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{7-20 \ \ \to \ \ [Subtract] } \end{gathered}$}[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{-13=-13 \ \ \to \ \ [ Equality \ holds ]} \end{gathered}$}[/tex]
{ Pisces04 }Answer:
5y= -13-7
5y=-20
5y = -20
5 = 5
y = -4
list three keywords that refer to multiplication ?
Answer:
full list of words from this list
factor anything that contributes causely to a result
multiply the number by which multiplicant is multiplied
multiply the number that is multiplied by a multiplier
project and refer that has been created by someone or some process