Answer:
3 x (5 + 2)
Step-by-step explanation:
Just use the distributive property, it's very simple.
simplify the following monomials (-a²b)ª
Answer:
[tex]\displaystyle{(-1)^aa^{2a} b^a}[/tex]
Step-by-step explanation:
The following expression can be rewritten as:
[tex]\displaystyle{\left((-1)\cdot a^2 \cdot b\right)^a}[/tex]
In this case, we have to separate -1 out of a² since if a becomes even, the value of (-a)ª will become positive while (-a)ª becomes negative when a is odd.
We can apply the law of exponent when:
[tex]\displaystyle{\left(a \cdot b \cdot c \right)^m = a^m \cdot b^m \cdot c^m}[/tex]
Therefore:
[tex]\displaystyle{\left((-1)\cdot a^2 \cdot b\right)^a = (-1)^a\cdot a^{2a}\cdot b^a}\\\\\displaystyle{\left((-1)\cdot a^2 \cdot b\right)^a = (-1)^aa^{2a} b^a}[/tex]
This will make when a = even numbers, the expression is positive while negative when a is odd.
And no, the answer is not [tex]-a^{2a} b^a[/tex] since this will make the expression negative only but the problem can be positive when a = even number which is why we have to separate -1 out of -a² so that it meets the condition.
Hence, the answer is [tex]\displaystyle{(-1)^aa^{2a} b^a}[/tex]
In a club with 99 male and 1616 female members, how many 77-member committees can be chosen that have (a) all men? (b) all women? (c) 44 men and 33 women?
The probability for the question as per the information that has been provided, can be solved in the following manner:
a) Probability for picking an all men committee
P = picking a Male probability
= 99/1715
Now, P = picking a female probability
= 1616/1715
The number of 77-member committee is Binomial [1715,77]
The number of 77-member committee being male is Binomial [99,77]
The probability of 77 men committee is Binomial [1715,77] / Binomial [99,77] or 99C77/1715C77
b) Probability for picking an all women committee
P = picking a Male probability
= 99/1715
Now, P = picking a female probability
= 1616/1715
The number of 77-member committee is Binomial [1715,77]
The number of 77-member committee being women is Binomial [1616,77]
The probability of 77 men committee is Binomial [1715,77] / Binomial [1616,77] or 1616C77/1715C77
c) Probability for picking 44 men and 33 women
Desired set is 44 men and 33 women, which can be done in 99C44 and 1616C33 ways.
So, P(44 men and 33 women) = 99C44 × 1616C33 / 1715C77
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help with these questions pls, thanks :)
Answer: Based on the formula I was taught, for your first problem it'd be the option that says 813.9 ft and for the second one it'd be your option with 2076.3 square inches.
Answer: D) 813.9 inches
Step-by-step explanation:
Formula for surface area of cylinder is:
A=2πrh+2πr2
r = 6
h = 15.6
A = 2π(6)(15.6) + 2π(6)^2
A = 187.2π + 2π(36)
A = 187.2π + 72π
A = 259.2π
If π is 3.14,
A = 259.2(3.14) = 813.9
A number increased by 15 is greater than 124. Find the smallest integer that satisfies the inequality.
The smallest integer that satisfies the inequality is 110
How to find the smallest integer to satisfy the inequalityThe least number is calculated by first generation g the inequality equation
The statement "A number increased by 15 is greater than 124" is written in an equation form, assuming the number is x
x + 15 > 124
Solving for x with the generated expression
x + 15 > 124
isolating x
x + 15 - 15 > 124 - 15
x > 124 - 15
x > 109
since x is greater than 109 the least integer greater than 109 is 110
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what does a table with two rows and columns of data represent?
-two separate linear functions
-a diagram
-two ordered pairs
-a linear function
A table with two rows and columns of data represent a linear function.
How is a linear function represented in a table?A table of values is linear if the rate of change is constant. A graph that is not vertical and is a straight line is linear. A linear equation is one that has the form y = mx + b. A value table is linear if the rate of change is constant.A straight line on the coordinate plane is represented by a linear function. As an illustration, the equation y = 3x – 2 depicts a linear function since it is a straight line in the coordinate plane.A table with two rows and columns of data represent a linear function.To learn more about linear function refer to:
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Give your answer in point notation with the x and y coordinates. If there are
multiple solutions, separate the answers with commas and no spaces. For example,
if your answers are (0,2) and (-3,1), you would type it as: (0,2),(-3,1). Order does not
matter.
V
N
AV
The points (2,2) and (-2,2) are both solutions to the equation y=2.
A coordinate pair(2,2),(3,1)When solving a system of equations, one way to find the solution is by graphing.To graph the given system of equations, start by plotting the two equations on the coordinate plane.The first equation, x + y = 4, can be written in the form y = -x + 4.Plot this line on the coordinate plane, with any two points that satisfy the equation. In this case, the two points could be (0,4) and (4,0).Plot the second equation, x - y = 2, in the same way.This line can be written in the form y = x - 2.Plot two points that satisfy this equation, such as (0,-2) and (2,0).After plotting the two lines, look for the point of intersection, which is the solution to the system.In this case, the point of intersection is (2,2) and (3,1).Therefore, the solution to the system is (2,2),(3,1).This equation is a line that has a y-intercept of 2, meaning that the line crosses the y-axis at the point (0,2). The slope of the line is 0, meaning that the line is vertical and does not cross the x-axis.Therefore, any point along this line will have the same y-coordinate, which in this case is 2. In other words, for any given x-coordinate, the y-coordinate will always be 2. This means that both (2,2) and (-2,2) are valid solutions for the equation y=2.To learn more about a coordinate pair refer to:
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answer choices:
x=22
x=68
x=90
x=112
Answer: I think x=22.
Step-by-step explanation:
If you look at half of the circle you can see a line in it right? This line measures to 180 degrees. This is a right triangle. Usually triangles have a little box in the corner to tell you that is it indeed a right triangle. I don't know why this one doesn't. anyways, if you add 90+68, you get 158. Now you need to get to 180 by simply adding 22. Thats why i think the answer is 22. Sorry if im wrong.
Create the number line that represents the solution to the inequality of 3x - 8 greater than 7
The number line in the image below shows the solution to the inequality 3x - 8 > 7.
How to Create a Number Line that Shows the Solution of an Inequality?
Before we can create a number line that represents the solution of an inequality, we have to solve to find the solution first.
Given the inequality 3x - 8 > 7, solve for x:
3x - 8 + 8 > 7 + 8 (addition property of equality)
3x > 15
3x/3 > 15/3 (division property of equality)
x > 5
The solution is x > 5, therefore, the image attached below shows the number line of the solution.
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Find the slope of the line.
On a coordinate plane, a line goes through (0, negative 6) and (2, 0).
a.
Negative one-third
c.
3
b.
One-third
d.
Negative 3
Answer:
3
Step-by-step explanation:
The equation for slope is (y2-y1)/(x2-x1)
We have (0, -6) as our x1 and y1 and (2,0) as our y1 and y2. So now it's plug and play!
=(0-(-6))/(2-0)
=(0+6)/(2-0)
=(6)/(2)
Simplifying this we get 3/1 or in simple terms... 3
true or false: a parallel gateway with three sequence flows would have three tokens leaving the gateway.
A parallel gateway with three sequence flows would have three tokens leaving the gateway - True.
Reason: Each path has a token.
A parallel gateway can synchronize or merge the parallel flows once more, or split the sequence flow into two or more parallel flows. Awaiting the arrival of all incoming sequence flows is synchronization. After that, the flow resumes.
Instead, two concurrent jobs in a business flow are represented by a parallel gateway. In a UML activity diagram, it is equivalent to a fork. The business process in the example below uses a parallel gateway because the company is trying to have its cake and eat it too. With Lucid chart, diagramming is quick and simple.
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A water sample shows 0. 097 grams of some trace element for every cubic centimeter of water. Owen uses a container in the shape of a right cylinder with a radius of 6. 7 cm and a height of 13. 3 cm to collect a second sample, filling the container all the way. Assuming the sample contains the same proportion of the trace element, approximately how much trace element has Owen collected? Round your answer to the nearest tenth
The amount of trace element collected by Owen is 59.3 g.
To calculate the amount of trace element collected by Owen, we first need to find the volume of the container. Given the radius of 6.7 cm and the height of 13.3 cm, the volume of the cylinder is given by:
V = π * r^2 * h = π * (6.7)^2 * 13.3 = 615.96 cm^3
Since there are 0.097 grams of the trace element per cubic centimeter of water, the amount of trace element in the container can be calculated as:
m = V * 0.097 g/cm^3 = 615.96 cm^3 * 0.097 g/cm^3 = 59.32 g
Rounding to the nearest tenth, the answer is 59.3 g.
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PLEASE HELP!! 100 POINTS
Answer:
see explanation
Step-by-step explanation:
the total cost is dependent on the number of rides she takes, then
the number of rides is the independent variable and the total cost is the dependent variable.
----------------------------------------------------------------------------
(2)
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
given m = - 2 , then
y = - 2x + c ← is the partial equation
to find c substitute (- 4, 2 ) into the partial equation
2 = - 2(- 4) + c = 8 + c ( subtract 8 from both sides )
- 6 = c
y = - 2x - 6 ← equation of line
--------------------------------------------------------------------------
(3)
calculate the slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (- 3, 6 ) and (x₂, y₂ ) = (9, - 2 )
m = [tex]\frac{-2-6}{9-(-3)}[/tex] = [tex]\frac{-8}{9+3}[/tex] = [tex]\frac{-8}{12}[/tex] = - [tex]\frac{2}{3}[/tex] , then
y = - [tex]\frac{2}{3}[/tex] x + c ← is the partial equation
to find c substitute either of the 2 points into the partial equation
using (9, - 2 )
- 2 = - [tex]\frac{2}{3}[/tex] (9) + c = - 6 + c ( add 6 to both sides )
4 = c
y = - [tex]\frac{2}{3}[/tex] x + 4 ← in slope- intercept form
multiply through by 3 to clear the fraction
3y = - 2x + 12 ( add 2x to both sides )
2x + 3y = 12 ← equation in standard form
----------------------------------------------------------------------------
(4)
linear function has the form
y = mx + c ( m is the slope and c the y- intercept )
calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (0, 200) and (x₂, y₂ ) = (2, 500) ← 2 ordered pairs from the table
m = [tex]\frac{500-200}{2-0}[/tex] = [tex]\frac{300}{2}[/tex] = 150
the ordered pair (0, 200 ) indicates that c = 200
y = 150x + 200 ← linear equation
--------------------------------------------------------------------------
(5)
money left over f(x) is
f(x) = initial amount - expenses
= 125 - (15 + 40 + 5x)
= 125 - (55 + 5x)
= 125 - 55 - 5x
= 70 - 5x
that is
f(x) = - 5x + 70
John is making apple pies and apple cobblers to sell at his stand at the Farmer's Market.
A pie uses 4 cups of apples and 3 cups of flour.
A cobbler uses 2 cups of apples and 3 cups of flour.
John has 16 cups of apples and 15 cups of flour.
When John sells the pies and cobblers at the Farmer's Market, he will make $3.00 profit per pie and $2.00 profit per cobbler.
Let x = the number of pies John makes.
Let y = the number of cobblers John makes.
Since John cannot make a negative number of pies or cobblers, what additional constraints exist on the variables?
Since John cannot make a negative number of pies or cobblers, the additional constraints that exist on the variables include the following:
B. x ≥ 0.
y ≥ 0.
How to write an equation to model this situation?In order to write an equation that model this situation, we would assign a variable to the number of pies John makes and the total number of cobblers John makes respectively, and then translate the word problem into algebraic equation as follows:
Let the variable x represent the number of pies John makes.Let the variable y represent the total number of cobblers John makes.However, it should be noted that John cannot make a negative number of pies or cobblers and as such, the number of pies he makes must be greater than or equal to zero (0) such as 0 pies, 1 pies, 2 pies, 3 pies, 4 pies, etc. Similarly, the aforementioned constrain applies to the number of cobblers John makes.
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The midpoint of AB is M (-2,5). If the coordinates of A are (1,7), what are the coordinates of B?
Answer:
B(-5, 3)
Step-by-step explanation:
(1 + x)/2 = -2
1 + x = -4
x = -5
(7 + y)/2 = 5
7 + y = 10
y = 3
B(-5, 3)
Can you give me great examples of buildup, unit ratio, and cross multiplication for proportional relationships? I am trying to get an A on this test and dont want to mess up.
Cross multiplying will help us identify the variable if it is the same variable that is present on both sides of the equation. Let's explain with the use of examples. Solve X/5 = 5/X, for instance.
What is cross multiplication in ratio and proportion?When you multiply the denominator of one ratio by the numerator of another, you get a cross product. In the event when the cross products are equal, the ratios are proportionate. In the case of ratios and, and are proportional and can be expressed as a b = c d.So 4×32=128. Moreover, we obtain the result 726=182 when we cross-multiply these two. The fact that 182 is greater than 128 enables us to conclude that 732 is greater than 426. The number we multiplied by our numerator symbolises the matching fraction, and we must always keep this in mind.For comparison of fractions, cross multiply. The most typical application of cross multiplication is the comparison of fractions. multiplying the numerator while paying closer attention to the procedure.To learn more about Cross multiplying refer to:
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which procedure can reduce can reduce problems associated with the use of deception by a researcher? a. debriefing b. random sampling c. random assignment d. using only single-blind studies e. using only double-blind studies
Reporting on a mission, initiative, or the data obtained from it is known as debriefing. Debriefing can reduce problems associated with the use of deception by a researcher. So option a is correct.
Debriefing is the act of reporting on a mission, project, or the data gleaned from it. After an activity or event, a structured procedure examines the actions performed.
Technically speaking, it refers to a method of active intervention that is specialized and developed into more formal meanings like operational debriefing. It is divided into various categories, including, among others, psychological, military, and experiential debriefing.
The following crucial components are often included in effective debriefings:
1. Active participation that goes beyond merely taking criticism in a passive manner.
2. Developmental aim centred on growth and learning
3. A discussion of particular incidents
4. Information from several sources
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Please help the question is a photo! We need to find the area and we use 3.14 or 22/7
The area of the circular figure which is the top of a can drink with a diameter of 3 inches is about 7.065 square inches
What is a circular figure?A circular figure is one that has no edges or sharp corners, and which is essentially round (in the form of a disc or the path described by rotary motion) in shape.
A circular object occupies the largest area per diagonal compared to other regular shapes, as the circular inscribes other regular shapes within its circumference.
The shape in the figure is a circle
The diameter of the circle, D = 3 in.
The formula for finding the area of a circle, A, for which the diameter is presented as follows;
Area of the circle, A = π·D²/4
The approximation of the value of π to be used are 3.14 or 22/7
The area is obtained by plugging in the values of D and π in the formula for the area of a circle as follows;
The area of the figure is; A = 3.14 × 3²/4 = 7.065
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Distribute: 5(2x + y -6)
Answer:
10x+5y-30
Step-by-step explanation:
5(2x+y -6)
5x2=10
5x (-6)= -30
=10x+5y-30
What is the least common denominator of 3/4 and 7/12
12 is the least common denominator between 3/4 and 7/12.
The least common denominator (LCD) of two or more fractions is the smallest number that can be divided by the denominators of each of the fractions without leaving a remainder.
What is the least common denominator in mathematics?The smallest number among all the common multiples of the denominators is the least common denominator when two or more fractions are provided.
Finding the least common multiple (LCM) of the denominators 4 and 12 will allow you to get the least common denominator of 3/4 and 7/12.
12 is the least frequent multiple of 4 and 12. Therefore, 12 is the least common denominator between 3/4 and 7/12.
Finding the denominators' multiples is another way to locate it. 43 = 12 is the least common multiple and the least common denominator, respectively.
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a square has side length of 7.37.3 inin. if the area is multiplied by 1919, what happens to the perimeter?
The perimeter should be multiplied by 1/3
The side length of the square, which is 7.3 inches,
The square's surface area
Side x Side is Area = 7.3 x 7.3 = 53.29
The square's new area is multiplied by 1/9,
so area is equal to
1/9 x 53.29 and s is equal to 2.4333.
Using the length of the new square as the new perimeter, the square's new perimeter is equal to 9.733 times its side times.
Now that we have calculated the perimeter ratios, we can see that the square's side length is 7.3.
the perimeter is equal to 7.3 times 4 and equals 29.12; nevertheless,
the ratio of the perimeters of the first and second lengths is equal to
29.12/9.733 and is
therefore 3:1.
so, perimeter multiplied by 1/3
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you work as an undergraduate student advisor and you keep track of all athlete students. your data contains information about their age, ethnicity, gender, their gpas and courses taken in year 1, year 2, year 3, and year 4. what type of data is this? cross-sectional data time-series data panel (longitudinal) data none of the above all of the above
Panel (longitudinal) data is data that is collected over multiple time points.
It is composed of repeated measurements of the same items, such as age, ethnicity, gender, GPAs, and courses taken over a period of time. This type of data allows us to compare changes in the same variables over a period of time. For example, we can compare the GPA of an athlete student in Year 1 to their GPA in Year 4 and look for changes that may have occurred. We can also observe how the courses taken in Year 1 may have had an impact on the GPA in Year 4. Panel data is useful to analyze changes in a population over time and can be used to make predictions about future trends.
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What do I put in the boxes
Step-by-step explanation:
6
7 47
42
-------
R 5
47 ÷ 7 = 6.71428571429
1/3y = 4 5/6
the options are
a. 1 11/8
b. 4 5/18
c. 12 5/6
d. 14 1/2
You are traveling west on the highway. At 1:00 you pass kilometer marker 485. At 4:30 you pass kilometer marker 154. What has your average velocity been.
technically a physical science question but i didn't know what to label it.
The average velocity is 94.6km / hour
What is average velocity?Average velocity is defined as the change in position or displacement (∆x) divided by the time intervals (∆t) in which the displacement occurs. The average velocity can be positive or negative depending upon the sign of the displacement. The SI unit of average velocity is meters per second (m/s or ms-1).
therefore average velocity = change in displacement / change in time
change in displacement = 485 - 154 = 331 km
change in time = 4:30-1:00 = 3 hours 30minutes = 3½ hrs
average velocity = 331/3.5
= 94.6km/hour
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How do you do this problem
Answer: C)39
Step-by-step explanation:
6x+507+317+3x=122
9x+824=122
9x=122-824
9x=-702
x=-78
6x+507
6(-78)+507
-468+507
=39
243 (0) If 8; 2x; 2y forms an arithmetic sequence and 2x; 2y; 36 forms a geometric sequence determine the values of x and y.
Answer:
(x, y) = (0.5, -3) or (8, 12)
Step-by-step explanation:
You want x and y such that 8, 2x, 2y is an arithmetic sequence and 2x, 2y, 36 is a geometric sequence.
Arithmetic sequenceThe difference of successive terms is a constant for an arithmetic sequence.
2x -8 = 2y -2x
2x -4 = y . . . . . . . . divide by 2, add x
Geometric sequenceThe ratio of successive terms is a constant for a geometric sequence.
2y/2x = 36/2y
y² = 18x . . . . . . . . . simplify and cross multiply
SolutionWe can substitute the expression for y from the arithmetic sequence into the expression for y² in the geometric sequence:
(2x -4)² = 18x
4x² -16x +16 = 18x . . . . . expand
2x² -17x +8 = 0 . . . . . . . divide by 2, subtract 9x
(2x -1)(x -8) = 0 . . . . . . . factor
The values of x that make the factors zero are x = 1/2 and x = 8. The corresponding values of y are 2{1/2, 8} -4 = {1, 16} -4 = {-3, 12}.
The values of x and y are (1/2 and -3) or (8 and 12).
__
Additional comment
The two sequences are ...
8, 1, -6 and 1, -6, 36 — difference of -7, ratio of -6
or
8, 16, 24 and 16, 24, 36 — difference of 8, ratio of 3/2
if I have 645 markers, and they can fit 15 in a pack how many packs of markers do I have
You can have 43 packs of the 645 markers (645 ÷ 15 = 43)
Step-by-step explanation:
First, you can make 42.33 packs of markers with 645 markers and 15 markers per pack. This is calculated by dividing the total number of markers (645) by the number of markers per pack (15), which gives you 42.33.
Find the product. (4m + 3)(4m − 3)
Answer:
= 16m² - 9
Step-by-step explanation:
(4m+3)(4m-3)
= 4m*4m + 4m*3 + 3*4m + 3*-3
= 16m² + 12m -12m - 9
= 16m² - 9
a survey was conducted on 218 undergraduates from duke university who took an introductory statistics course in spring 2012. among many other questions, this survey asked them about their gpa and the number of hours they spent and studying per week. based on this study, can we conclude that studying longer hours leads to higher gpas?
No, we cannot conclude that studying longer hours leads to higher GPAs based on this survey.
This survey only provides us with the average GPAs and average hours per week spent studying for a sample of 218 undergraduates from Duke University who took an introductory statistics course in spring 2012. This is not enough information to draw a conclusion about the correlation between hours of study and GPA. To do this, we would need to look at the correlation between the two variables. To calculate the correlation, we would need the individual data points of the GPAs and hours of study for each respondent. We could then calculate the Pearson correlation coefficient and the significance of the correlation. This would provide us with a more definitive answer to our question.
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Question #14:
Brandon is filling a flower bed with soil. The flower bed is shaped like a rectangular prism and
measures 15 feet long and 3 feet tall. If it holds 405 cubic feet of soil, how many feet wide is
Brandon's flower bed?
The width of rectangular prism shaped Brandon's flower bed is 9 meters.
As per the known information, the formula to calculate volume of rectangular prism is -
Volume of rectangular prism = length × width × height
Keep the values in formula to find the volume of rectangular prism
405 = 15 × 3 × width of rectangular prism
Performing multiplication on Right Hand Side of the equation
405 = 45 × width of rectangular prism
Rewriting the equation
Width of rectangular prism = 405/45
Performing division
Width of rectangular prism = 9 meters
Thus, the width is 9 meters.
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