Answer:
Rewrite using the commutative property of multiplication.
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Anything raised to
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Multiply
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Rewrite the expression using the negative exponent rule
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Simplify the denominator.
Tap for more steps...
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Simplify terms.
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Eitan is on a train heading west into the city while Dmitri is on a train on the adjacent track heading east, away from the city. They start 150 miles apart. Eitan’s train is traveling at an average speed of 65 miles per hour while the average speed of Dmitri's train is 55 miles per hour. How long will it take the two trains to reach each other? How far outside the city will they be?
The time when the two trains reach each other is
.
The trains are
away from the city when they reach each other.
Answer:
1.25 hours.
68.75 miles from the city
Step-by-step explanation:
Eltan's train (E) is travelling 65mph west.
Dmitri's train (D) is travelling 55mph west.
In terms of vectors, we can write E as 65E and D as 55W
The miles travelled by each is a function of time, T, in hours.
Each train's distance is:
E: T*65E
D: T*55W
They are 150 miles apart. They will meet with the combined miles travelled is 150 miles.
150 miles = T*65E + T*55W
150 miles = T(120 miles/hour)
T = (150 miles/120 miles/hour)
T = 1.25 hours
Make Demitri's train mile 0 and Eitan's train at mile 150 at the start.
They will have travelled the following miles in 1.25 hours:
Demitri: (1.25hr)(55 m/hr) = 68.75 miles
Eitan: (1.25hr)(65 m/hr) = 81.25 miles
Total = 150 miles
Dimitri is headed away from the city. After 1.25 hours, his train will have travelled 68.75 miles when he sees Eitan passing him on the adjacent track (hopefull) headed into the city. They meet 68.75 miles from the city.
Answer:
question one is B and question 2 is C
Step-by-step explanation:
Mrs. Smith runs a dessert parlor. Her top-selling items are mixed berry smoothies and milkshakes. She sells mixed berry smoothies for $5 each and milksh
for $3 each. Mrs. Smith wants to sell at least 60 mixed berry smoothies and milkshakes in all and wants to earn at least $210. Each mixed berry smoothie ta
7 minutes to make, and each milkshake takes 3 minutes to make.
O
New folder
How many mixed berry smoothies and milkshakes should Mrs. Smith make to minimize the time she spends making the desserts, also selling at least the
minimum total number and earning at least the minimum amount of money?
Answer:
Step-by-step explanation:
0 mixed berry smoothies and 70 milkshakes
a company produces very unusual CD's for which the variable cost is 8$ per CD and the fixed costs are $30000. They will sell the CD's for $63 each. Let x be the number of CD's produced. Write the total cost C as a function of the number of CD's produced.C=$___Write the total revenue R as a function of the number of CD's produced R=$_______Write the total profit P as a function of the number of CD's producedP=$______Find the number of CD's which must be produced to break even.The number of CD's which must be produced to break even is_______
Remember that to model this kind of problems, we can use the equation of a straight line
[tex]y=mx+b[/tex]Where:
• b, are the fixed costs
,• x ,represents what varies
,• m, is the cost of what varies
1. Therefore, using the data provided, we can model the cost of production with a function where:
• x ,is the numbers of CD's produced
,• C, is the cost of producing those CD's
[tex]C=8x+30000[/tex]2. To model the revenue, we'll have to take into account that every CD sells at $68. Therefore, the money collected by selling the x CD's produced is:
[tex]R=63x[/tex]Where:
• x ,its the number of CD's produced and sold
,• R, is the total revenue
3. To get the profit, we'll have to substract the production cost to the money collected by the sale. Remember we already have two expressions, in terms of x, that describe both situations. Therefore,
[tex]\begin{gathered} P=R-C \\ \rightarrow P=63x-(8x+30000)\rightarrow P=63x-8x-30000 \\ \rightarrow P=55x-30000 \end{gathered}[/tex]Where:
• x ,its the number of CD's produced and sold
,• P, is the total revenue
4. In order to break even, the revenue (R) has to be equal to the cost of production (C), Thus,
[tex]\begin{gathered} R=C\rightarrow63x=8x+30000 \\ \rightarrow63x-8x=30000 \\ \rightarrow55x=30000\rightarrow x=\frac{30000}{55} \\ x=545.5 \\ \text{Rounding to closest integer,} \\ x=546 \end{gathered}[/tex]Therefore, 546 CD's would have to be produced to break even.
in order to determine an interval for the mean of a population with unknown standard deviation, a sample of 59 items is selected. the mean of the sample is determined to be 32. what is the associated number of degrees of freedom for reading the t value?
The associated number of degrees of freedom for reading the t-value is 58.
The aim is to determine an interval for the mean of a population.
The standard deviation is unknown to us. The sample consists of 59 items. The mean of the sample is determined to be 32. We need to calculate the associated number of degrees of freedom for reading the t value.
We know that the degree of freedom is one less than the number of items in the sample space.
The associated number of degrees of freedom for reading the t-value is 59-1.
The associated number of degrees of freedom for reading the t-value is 58.
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100pts. find the area of these questions below
Answer:
20 feet²Step-by-step explanation:
triangle area formula: A = 1/2 × b × h
Find the base7 +3 = 10 ft
Find Area1/2 10 × 4 =
5 × 4 =
20 feet²
answer please and look at the pic
Answer: slope = [tex]\frac{y}{x}[/tex]
Step-by-step explanation:
Slope means gradient which is given by change in y
change in x
on the graph, change in y = 100-0 = 100
change in x = 95-45 = 50
so, gradient is 100/50
= 2
jane wants to know what percentage of freshmen at her college purchase clothing with college logos. she decides to randomly interview 10 freshmen from each of the dorms. these people are her
Jane decides to randomly interview 10 freshmen from each of the dorms, these people are her Sample.
What is Sample?
Sampling is the process of choosing a portion of a statistical population to estimate attributes of the entire population in statistics, quality control, and survey methods. Statisticians try to get samples that are typical of the population under consideration.
A little sample or amount of someone or something that is inspected, analyzed, or otherwise investigated to learn more about the rest.
Given: Jane wants to know what percentage of freshmen at her college purchase clothing with college logos. She decides to randomly interview 10 freshmen from each of the dorms.
Therefore, by the above information, these people are her Sample.
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solve the equation, giving values of x in a form suitable for computation.
x(2√3-3)=4√3
answer = 8+4√3
(never heard of computation before
Answer:
x = 8 + 4[tex]\sqrt{3}[/tex]
Step-by-step explanation:
computation just means to calculate
x(2[tex]\sqrt{3}[/tex] - 3 ) = 4[tex]\sqrt{3}[/tex] ( divide both sides by (2[tex]\sqrt{3}[/tex] - 3 ) )
x = [tex]\frac{4\sqrt{3} }{2\sqrt{3-3} }[/tex]
rationalise the denominator by multiplying the numerator/ denominator by the conjugate of the denominator.
the conjugate of 2[tex]\sqrt{3}[/tex] - 3 , is 2[tex]\sqrt{3}[/tex] + 3
= [tex]\frac{4\sqrt{3}(2\sqrt{3}+3) }{(2\sqrt{3}-3)(2\sqrt{3}+3) }[/tex] ← expand denominator using FOIL
= [tex]\frac{24+12\sqrt{3} }{12-9}[/tex]
= [tex]\frac{24+12\sqrt{3} }{3}[/tex]
= [tex]\frac{24}{3}[/tex] + [tex]\frac{12\sqrt{3} }{3}[/tex]
= 8 + 4[tex]\sqrt{3}[/tex]
The base of this right prism is a rectangle. What is the surface area of the prism? Height = 10 ft
Surface area of a rectangular prism formula
[tex]SA=2(wl+hl+hw)[/tex]where w is width, l is length, and h is height.
Substituting with w = 4 ft, l = 6 ft, and h = 10 ft, we get:
[tex]\begin{gathered} SA=2(4\cdot6+10\cdot6+10\cdot4) \\ SA=2(24+60+40) \\ SA=2\cdot124 \\ SA=248\text{ ft}^2 \end{gathered}[/tex]
The difference between the two numbers is -1. Their sum is -27. Find the numbers. Let x represent the first number and y represent the second number. first number x = second number y =
Taking into account the definition of a system of linear equations, the first number is x= -14 and the second number y= -13.
System of linear equationsA system of linear equations is a set of linear equations (that is, a system of equations in which each equation is of the first degree) in which two or more unknowns are related.
Systems of linear equations have as a solution set all ordered pairs (x, y) that satisfy the equation, where x and y are real numbers. That is, solving a system of equations consists of finding the values of the unknowns, with which, when replaced in the equations, they must give the proposed solution.
This caseIn this case, a system of linear equations must be proposed taking into account that
"x" is the first number."y" is the second number.You know:
The difference between the two numbers is -1. Their sum is -27.The system of equations to be solved is
x-y= -1
x+y= -27
It is decided to solve the system of equations using the substitution method, which consists of clearing one of the two variables in one of the equations of the system and substituting its value in the other equation.
In this case, isolating the variable "x" from the first equation:
x= -1 +y
Replacing this expression in the second equation:
-1 +y +y= -27
Solving:
y +y= -27 +1
2y= -26
y= (-26)÷2
y= -13
Remembering that x=-1 +y, you get
x= -1 -13
x= -14
Finally, the numbers are -13 and -14.
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The values of the first and second numbers are - 13 and - 14 respectively.
What is a numerical expression?A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.
Let us assume that the two numbers are x and y.
Given, The difference between the two numbers is -1.
∴ x - y = - 1...(i)
And, Their sum is - 27 which is,
x + y = - 27...(ii)
Now, if we add eqn (i) to eqn (ii)
x + y = - 27
+ x - y = -1
---------------------
2x = - 28
+ y and - y get canceled and we get
∴ 2x = 26.
x = - 13.
Now, substitute the value of x in any of the eqn(i). we get y = - 14.
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by the time vince left the library he had 7/8 of his new book left to read ge read 1/10 of his book on the way home and 2/5 of the book after dinner what fraction of the book does he have left to read
We have the next information
When he left the library he read 8/8-7/8= 1/8
then he read 1/10
after dinner, he read 2/5
First, we need to sum the fraction of the book he read
[tex]\frac{1}{8}+\frac{1}{10}+\frac{2}{5}[/tex]we need to have the same denominator in order to sum the fractions
[tex]\frac{5+4+16}{40}=\frac{25}{40}=\frac{5}{8}[/tex]the book complete represent 8/8 so we need to subtract 5/8 from the fraction of the complete book
[tex]\frac{8}{8}-\frac{5}{8}=\frac{3}{8}[/tex]the fraction of the book does he have left to read is 3/8
Please help ㅤㅤ
What is the value of this expression
ㅤ
PLUG IN THE VALUES OF THE VARIABLES IN THE RIGHT POSITIONS AND SIMPLIFY.
[tex] \frac{1}{2} (12 - 4) \times \frac{1}{4} \\ = \frac{1}{2} (8) \times \frac{1}{4} \\ = \frac{8}{2} \times \frac{1}{4} \\ = \frac{8}{8} \\ = 1[/tex]
THE ANSWER IS OPTION B.
The line containing the points (14, 15) and (20, 24) crosses the y-axis at what point?
The linear equation that passes through the points (14, 15) and (20, 24) crosses the y-axis at y = -6.
How to get the y-intercept?
A general linear equation can be written as:
y = m*x + b
Where m is the slope and b is the y-intercept.
If the line passes through two points (x₁, y₁) and (x₂, y₂), then the slope can be written as:
m = (y₂ - y₁)/(x₂ - x₁).
In this case the line passes through (14, 15) and (20, 24) so the slope is:
m = (24 - 15)/(20 - 14) = 9/6 = 3/2
y = (3/2)*x + b
To find the y-intercept we can replace the values of one of the points, like (14, 15)
15 = (3/2)*14 + b
15 = 3*7 + b
15 = 21 + b
15 - 21 = b
-6 = b
The y-intercept is -6.
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If -8x-y=-9 is a true equation, what would be the value of -8x-y+3
scores on an iq test are normally distributed. the test is designed so that the mean is 100 and standard deviation is 15. hat is the cutoff score so that only 5% of the population has a higher score?
The cutoff score so that only 5% of the population has a higher score is 124.7.
If 5% of the population has a higher score, then the probability of selecting these is 0.05.
Find the z-score that corresponds to the probability in the z-table. (see attached images)
probability = 1 - 0.05 = 0.95
z-score = 1.647
Using the formula for the z-score below, determine the cutoff score.
z-score = (x – μ) / σ
where x = individual data value = cutoff score
μ = mean = 100
σ = standard deviation = 15
1.647 = (x - 100) / 15
1.647(15) = x - 100
x = 24.705 + 100
x = 124.705
cutoff score = 125
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1.
Rule/Equation: y = slope (x) +/- y-intercept
OR y = m(x) +/- b
X
2
6
10
14
18
y
12
8
4
0
TABLES TO EQUATIONS #2
-4
Slope (growth rate):
y-intercept (starting value):
2
Equation:
Answer:
Step-by-step explanation:
x y
2 12
6 8
10 4
14 0
18 -4
The slope is the Rise/Run, or change in y over the change in x. Pick any two points. I'll choose (2,12) and (18,-4),
Rise = (-4 - 12) = -16
Run = (18 - 2) = 16
Slope = Rise/Run = -16/15, or -1
The equation becomes y = -1x + b
To find b, use any of the points in the equation and solve for b. I'll use (14,0):
y = -1x + b
0 = -1(14) + b
b = 14
The equation is y = -x + 14
See the attached graph.
What is the length of the major axis of the conic section shown below? (x + 2)(y-1) 49 25 1
From the ellipse equation
[tex]\frac{(x+h)^2}{a^2}+\frac{(y+k)^2}{b^2}=1[/tex]the length of the major axis is equal to 2a. By comparing this equation with the given one, we can note that
[tex]\begin{gathered} a=7 \\ \text{because} \\ 7^2=49 \end{gathered}[/tex]Then, the length of the major axis is 2x7 = 14
2q/5 + 4 < 2q/ - 9 what the solution set?
The solution set for the given inequality (2q/5 + 4 < 2q/-9) is q∈(-∞, - 45/7).
What is the solution set?A solution set is a group of values in mathematics that satisfy a given set of equations or inequalities.Any value of a variable that causes the given equation to hold true is a solution. A solution set is a collection of all the variables needed to solve an equation. Due to the fact that 2y + 6 = 14 and 2(4) + 6 = 14, the solution set is 4. You must first enter each value from the domain into the equation to obtain the corresponding range values before you can determine the solution set of an equation with a given domain.From these values, make ordered pairs, and then write them as a set.So, 2q/5 + 4 < 2q/ - 9:
Now, solve for the solution set as follows:
2 ∙ q/5 + 4 < 2 ∙ q/ - 92 ∙ q/5 + 4 < - 2 ∙ q/92q/5 + 4 < - 2q/9[(2q) + 5∙4]/5 < - 2q/9q ∈ ( -∞, - 45/7)Therefore, the solution set for the given inequality is q ∈ ( -∞, - 45/7).
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Select the correct answer.
Find the inverse of function f.
f (x) = 9x + 7
A. f^{\small -1}(x)\ =\ 7x\ +\ 9
B. f^{\small -1}(x)\ =\ -9x\ -\ 7
C. f^{\small -1}(x)\ =\ \frac{1}{9}x\ -\ \frac{7}{9}
D. f^{\small -1}(x)\ =\ \frac{7}{9}x\ -\ \frac{1}{9}
Answer:
[tex]\dfrac{x-7}{9}[/tex]
which corresponds to choice
C : [tex]f^{\small -1}(x)\ =\ \frac{1}{9}x\ -\ \frac{7}{9}[/tex]
Step-by-step explanation:
The inverse of a function y = f(x) can be found by interchanging x and y and solving for y
Let y = f(x)
y = 9x + 7
Interchange x and y:
x = 9y + 7
9y + 7 = x (switch sides)
subtract 7 both sides
→ 9y + 7 - 7 = x - 9
→ 9y = x - 9
Divide both sides by 9
→ [tex]y = \dfrac{x - 7}{9} = \dfrac{x}{9} - \dfrac{7}{9}[/tex]
which corresponds to choice C
A triangle has sides with lengths of 20 cm, 15 cm, and 10 cm. Substitute these values into the Pythagorean Theorem to determine if the sides form a right triangle.
Answer:
10^2 + 15^2 = 20^2
100+225≠400
so no, it's not a right angled triangle
:)
Select all rational numbers.
All of the rational numbers that we have in the question that we have here are:
-√25√100√0.36√0.0144What is a rational number?This is the term that is used to refer to the ratio of two numbers that when they are expressed as a ratio of two different numbers, the denominator does not have to be 0.
The rational numbers when they are solved would not give us terminating decimals. That is they would be able to be expressed as fractions.
-√25 = -5
√0.0144 = 0.12
√0.36 = 0.6
√100 = 10
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-√25, √100, √0.36, and √0.0144n are the rational number. Options B, D, E, and F are correct.
As of the given data, numbers are given we have to determine which of the number are rational numbers.
Rational numbers are numbers that can be structured in the form of the fraction of integers. Eg- 5/6, 2/3 etc.
Here,
All the numbers are irrational numbers except -√25, √100, √0.36, and √0.0144 because the number picked out is required rational number.
Thus, -√25, √100, √0.36, and √0.0144n are the rational number. Options B, D, E, and F are correct.
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If m2 = 12x - 15 and m27 = 3x + 21, what is the measure of 21?
In the given figure, m∠2 and m∠7 are "Alternate Exterior Angles" and they are always congruent (equal).
So we can equate them and solve for x.
[tex]\begin{gathered} m\angle2=m\angle7 \\ 12x-15=3x+21 \\ 12x-3x=21+15_{} \\ 9x=36 \\ x=\frac{36}{9} \\ x=4 \end{gathered}[/tex]So, m∠2 is
[tex]\begin{gathered} m\angle2=12x-15 \\ m\angle2=12(4)-15 \\ m\angle2=48-15 \\ m\angle2=33\degree \end{gathered}[/tex]According to the straight-line angle property, the sum of m∠1 and m∠2 must be equal to 180°
[tex]\begin{gathered} m\angle1+m\angle2=180\degree \\ m\angle1+33\degree=180\degree \\ m\angle1=180\degree-33\degree \\ m\angle1=147\degree \end{gathered}[/tex]Therefore, the measure of m∠1 is 147°
Which function is the inverse of f(x) = 8x + 4?A. 5-18) = —841 – 4)B. 7-14x) = 554OC. 5-11%) = 8.1 – 4)OD. 1x) = -1
ANSWER:
[tex]f^{-1}(x)=\frac{x-4}{8}[/tex]STEP-BY-STEP EXPLANATION:
We have the following function:
[tex]f(x)=8x+4[/tex]We calculate the inverse function as follows:
[tex]\begin{gathered} x=8\cdot f^{-1}(x)+4 \\ 8\cdot f^{-1}(x)=x-4 \\ f^{-1}(x)=\frac{x-4}{8} \end{gathered}[/tex]Given v = 60sinθ, what is the instantaneous voltage when θ = 30⁰?Question 11 options:6034.643051.96
30
Explanations:
Given the expression for the instantaneous voltage expressed as:
[tex]v=60\sin \theta[/tex]Given the following parameter:
θ = 30⁰
Substitute the given parameter into the formula to have:
[tex]\begin{gathered} v=60\sin 30^0 \\ v=60(0.5) \\ v=30 \end{gathered}[/tex]Therefore the instantaneous voltage when θ = 30⁰ is 30.
OMGGGGGGGGGGGGGGGGGGGGGGGGGGGGG
Answer:
y axis-(0,6) x axis-(5,0) quad 1-(8.7,2.3) quad 2-(-1,10) quad 3-(-1/4,-6 1/2) quad 4-(5,-2)
Step-by-step explanation:
What is the equation of the line in slope-intercept form? 1,6 and 2,-6
The equation of the line in slope-intercept form would be; y = -12x + 18
How to get the slope-intercept form of a straight-line equation?If the slope of a line is m and the y-intercept is c, then the equation of that straight line is given as:
y = MX +c
To find the slope of a line, we the rate at which the value of 'y' is increasing as we increase the value of 'x' by one unit.
We have been given the point (1,6) and (2,-6)
y-y₁ = m(x-x₁)
m = (-6-6)/(2 -1)
m = -12/1
Now substitute;
y-y₁ = m(x-x₁)
y- 6 = -12(x- 1)
y- 6 = -12x + 12
y = -12x + 18
Hence, the equation of the line in slope-intercept form would be; y = -12x + 18
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Solve the inequality b+ 5 ≥ -12
The solution of the inequality is b ≥ -17.
Given inequality:-
b + 5 ≥ -12
We have to find the solution of the inequality.
Subtracting 5 from the given inequality, we get
b + 5 - 5 ≥ -12 - 5
b + (5 - 5) ≥ -17
b + 0 ≥ -17
b ≥ -17
Hence, b can be equal to or greater than -17.
Inequality
An inequality is a relation which makes a non-equal comparison between two numbers or other mathematical expressions. It is used most often to compare two numbers on the number line by their size.
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PLEASE HELP ME ILL RATE YOU 5 STARS AND GIVE U BRAINLY
The ascending order of the set of numbers is √3 - 1, 2√10 ÷ 5, √14, 3√2, √19 + 1, 6
Given,
A set of numbers;
3√2, √3 - 1, √19 + 1, 6, 2√10 ÷ 5, √14
We have to arrange this numbers from least to greatest. That is, in ascending order.
Ascending order;
Numbers can be arranged in ascending order, from least value to highest value. The arrangement is left to right. Increasing order is another name for ascending order.
Here,
First we have to find the values of the square roots in the numbers.
3√2 = 4.24
√3 - 1 = 0.73
√19 + 1 = 5.36
6
2√10 ÷ 5 = 1.26
√14 = 3.74
Then,
6 is the greatest number and √3 - 1 is the least number.
That is,
The ascending order of the set of numbers is √3 - 1, 2√10 ÷ 5, √14, 3√2, √19 + 1, 6
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Use the Product Property for Exponents: thoroughly explain why x · x = x^2.
1) We need to consider that whenever we have a variable its exponent is raised to the 1st power, even when we don't write it as a superscript.
2) So we can write out the following steps to get that product as x²:
[tex]\begin{gathered} x=x^1 \\ x^1\cdot x^1=x^{1+1}=x^2 \end{gathered}[/tex]That's why we can write that, applying the property of exponents.
Graph the linear equations 65 points
Answer:
Step-by-step explanation: