Answers
Answer:
[tex]\begin{aligned}&\phantom{=.} \dfrac{1}{8}x \cdot \dfrac{-4}{5}x\\\\&=\dfrac{1}{2} \cdot \dfrac{\boxed{-1}}{5} \cdot x \cdot \boxed{x}\\\\& = \dfrac{\boxed{-1}}{\boxed{10}} \;x\;^\boxed{2}\end{aligned}[/tex]
Step-by-step explanation:
According to the Commutative Property Law of Multiplication, changing the order or position of the numbers does not change the end result.
Therefore, collect like terms by moving the fractions to the left and the variables to the right.
As the denominator of the first fraction has been divided by 4, the numerator of the second fraction should also be divided by 4.
Therefore:
[tex]=\dfrac{1}{2} \cdot \dfrac{\boxed{-1}}{5} \cdot x \cdot \boxed{x}\\[/tex]
[tex]\textsf{Apply\;the\;fraction\;rule} \quad \dfrac{a}{c}\cdot \dfrac{b}{d}=\dfrac{ab}{cd}.[/tex]
[tex]\textsf{Apply\;the\;exponent\;rule}\quad \:aa=a^2.[/tex]
Therefore:
[tex]=\dfrac{\boxed{-1}}{\boxed{10}} \;x\;\boxed{^2}[/tex]
Related Questions
grace and jack are playing a game with a gigantic bucket of markers. jack took a random sample of markers from the bucket and counted 121212 yellow markers, 373737 blue markers, and 111 red marker. use the observed frequencies to create a probability model for the color of the next randomly selected marker from the gigantic bucket of markers. input your answers as fractions or as decimals rounded to the nearest hundredth.
Answers
If grace and jack are playing a game with a gigantic bucket of markers. The probability are yellow 0.24, blue 0.74, red 0.02.
ProbabilityGiven data:
Yellow markers = 12
Blue markers =37
Red marker =1
Total number of markers = 12 + 37 + 1
Total number of markers = 50
Probability of an event occuring= Favorable number of outcomes / Total number of outcomes
Probability of getting an yellow marker = 12/50
Probability of getting an yellow marker = 0.24
Probability of getting an blue marker = 37/50
Probability of getting an blue marker = 0.74
Probability of getting an red marker = 1/50
Probability of getting an red marker = 0.02
Probability model
Type of maker Frequency Probability
Yellow 12 0.24
Blue 37 0.74
Red 1 0.02
Therefore the probability are 0.24, 0.74, 0.02.
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in endurance horse racing, people over the age of 15 are called seniors and people 15 years or younger are called juniors. an endurance horse race consists of 30 seniors and 6 juniors. (give answer as a fraction or a decimal out to at least 4 places. if your answer is very small use scientific notation for example 3.3421e-6.)
Answers
a)P(all seniors) =(25C3)/(30C3) =0.5665
b)P(All Juniors)=(5C3)/(30C3) =0.0025
c)P(2 senior and 1 Junior) =(25C2)(5C1)/(30C3) =0.3695
d)P(1 senior and 2 Junior) =(25C1)(5C2)/(30C3) =0.0616
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What is 80,023 written in scientific notation? A. 8.0023 x 10^3 B. 8.0023 x 10^4 C. 8.0023 x 10^5D. 8.0023 x 10^6
Answers
ANSWER
[tex]B\text{. 8.0023 }\cdot10^4[/tex]EXPLANATION
We want to write the number given in scientific notation. The number is 80,023
Putting a number in scientific notation involves writing that number as a product of a number between 1 and 10 and a power of 10.
We do this by moving the decimal point from behind the last digit of the number (3) to just after the first digit (8).
We move the decimal point 4 times to the left, that is why the power of 10 is +4.
So, we have that 80,023 becomes:
[tex]80,023\text{ = 8.0023 }\cdot10^4[/tex]
Complete the table and graph the solutions of the equation y =-3x + 3. X -1 0 1 2 у co -7 -6 -5 -4 -3 -2 -1. 0 2 3
Answers
1) Since the equation is y= -3x+3, let's fill in that table by plugging into them the given values for x
x | y= -3x +3 | y
-1 | y=-3(-1)+3 | 6
0 | | 3
1 | | 0
2| | -3
2) Let's plot that equation for points (-1,6) (0,3), (1,0) and (2,-3)
The mass of the Rock of Gibraltar is 1.78-102 kilograms. The mass of the Antarctic iceberg is 4.55-103 kilograms. Approximately how many more kilograms is the mass of the Antarctic iceberg than the mass of
the Rock of Gibraltar? Show your work and write your answer in scientific notation (10 points)
Answers
4.372 × [tex]10^{13}[/tex] more kilograms the mass of the Antarctic iceberg than the mass of the Rock of Gibraltar.
Mass of the Antarctic iceberg = 4.55 × [tex]10^{13}[/tex]
Mass of the rock of Gibraltar = 1.78 × [tex]10^{12}[/tex]
Excessive mass of Antarctic Icebergs than the rock of Gibraltar,
4.55 × [tex]10^{13}[/tex] - 1.78 × [tex]10^{12}[/tex]
Subtract easily both should be in the same power of ten,
= 4.55 × [tex]10^{13}[/tex] - 1.78 × [tex]10^{12}[/tex]
= 43.72 × [tex]10^{12}[/tex]
= 4.372 × [tex]10^{13}[/tex]
Scientific notation is used to express quantities that are either too large or too little to be represented by decimals. Scientific format, standard index format, and standard format are other terms for the same thing.
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Roy ate 2/3 of his personal pizza Roxy ate 3/5 of hers robbi ate 0.45 of hers and Russ ate 9/12 of his who ate the most of his or her pizza?
Answers
We will see that the largest number is 9/12, and Russ ate 9/12 of his pizza, so he is the one that ate most of his pizza.
Who ate the most of his/her pizza?Here we know that:
Roy ate 2/3 of his pizza.Roxy ate 3/5 of her pizza.Robby ate 0.45 of his pizza.Russ ate 9/12 of her pizza.So we just need to see which of the given numbers is the largest one.
We can rewrite the fractions as:
2/3 = 0.66
3/5 = 0.6
9/12 = 3/4 = 0.75
The largest number is 0.75, in this way we conclude that Russ is the one that ate more pizza.
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How many minutes are in two fifths of a day?
Answers
Answer:576 minutes
Step-by-step explanation:
4.8h x 60(minutes)
288min x 2
576 min
Andrew writes the algebraic expression 2s+ 2.79 to represent the cost of his
lunch. He bought 2 sandwiches and a large drink. Identify any variables,
coefficients, and terms in the expression. Tell what each represents.
Answers
The sandwich's price is represented by the variable s , 2 is the coefficient of s and 2.97 represents both the cost of a big drink and a constant
What is Algebraic Expression?
An algebraic expression is one that has been constructed using integer constants, variables, and algebraic operations. For instance, the algebraic formula 3x2 2xy + c
The cost of Andrew's lunch is written as the algebraic expression
2s + 2.79 as a given. He bought a huge drink and two sandwiches.
In the algebraic expression given;
2s + 2.79
Here, 2 stand in for the coefficients of s, which stands for the quantity of sandwiches he purchased.
The sandwich's price is represented by the variable s, which is a function of the coefficient.
And 2.97 represents both the cost of a big drink and a constant since no further letters have been added.
Hence, sandwich's price is represented by the variable s , 2 is the coefficient of s and 2.97 represents both the cost of a big drink and a constant
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PLS HELPPPP
Is this right????
Answers
Answer:
yes that is the correct answers
In a class of 28 students, 6 are female and 7 have an A in the class. There are 17 students who are male and do not have an A in the class. What is the probability that a student is a male given that they have an A?
Answers
Step-by-step explanation:
a probability is always
desired cases / totally possible cases
28 students in total.
6 are female.
so, we have 28-6 = 22 male students.
7 of the 28 students have an A.
17 male students do not have an A.
that means 22-17 = 5 male students have an A.
and that means 7-5 = 2 of the female students have an A.
"given that they have an A".
that reduces our totally possible cases to 7.
the probability that an A-student is male is therefore
5/7 = 0.714285714...
and FYI
the probability that an A student is female is
2/7 = 0.285714286...
The probability that a student is male given that they have an A is approximately 0.538.
What is probability?It is the chance of an event to occur from a total number of outcomes.
The formula for probability is given as:
Probability = Number of required events / Total number of outcomes.
Example:
The probability of getting a head in tossing a coin.
P(H) = 1/2
We have,
We can use Bayes' theorem.
P(male | A) = P(A | male) x P(male) / P(A)
We are given:
P(A | male) = 7/17
(7 students are male and have an A, out of 17 male students)
P(male) = 17/28
(17 students are male, out of 28 total students)
P(A) = (6+7) / 28
(13 students have an A, out of 28 total students)
Plugging in these values.
P(male | A) = (7/17) x (17/28) / (13/28) = 0.538
Therefore,
The probability that a student is male given that they have an A is approximately 0.538.
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6. Critical Thinking
Suppose point P divides the directed line segment XY so that the ratio of XP to PY is 3 to 5. Describe the
point that divides directed line segment YX so that the ratio of YP to PX is 5 to 3.
Answers
Using proportions, the coordinates of the point that divides directed line segment YX so that the ratio of YP to PX is 5 to 3 are given by:
[tex](x,y) = \left(\frac{3}{8}(x_y - x_x) + x_x, \frac{3}{8}(y_y - y_x) + y_x\right)[/tex]
What is a proportion?A proportion is a fraction of a total amount, and equations can be built to find the desired measures in the problem using basic arithmetic operations such as multiplication or division from the given ratios.
Division of line segments is one application of proportions. The entire length of the line segment with endpoints XY is given by:
Y - X.
Now we have point P, dividing the line segment YX so that the ratio of YP to PX is 5 to 3, meaning that XP is 3/8 of XY, that is:
[tex]P - X = \frac{3}{8}(y - x)[/tex]
Then the x-coordinate of P is found as follows:
[tex]x - x_x = \frac{3}{8}(x_y - x_x)[/tex]
[tex]x = \frac{3}{8}(x_y - x_x) + x_x[/tex]
The y-coordinate is found applying the same rule with the y-coordinates of points X and Y, as follows:
[tex]y - y_x = \frac{3}{8}(y_y - y_x)[/tex]
[tex]y = \frac{3}{8}(y_y - y_x) + y_x[/tex]
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The average flight time for the pilots is found to be 8.12 hours. The
standard deviation reported by the FAA is 0.72 hours, and there
were 81 pilots in the sample. What is the t-statistic for this
hypothesis test? Report to two decimal points
(Flights generally limit pilots to 8 hours of flight time during a 24-hour period)
Answers
The test statistic for this hypothesis test is; t = 1.5
What is the Test Statistic?
The formula for test statistic is;
t = (x' - μ)/(σ/√n)
where;
x' is sample mean
μ is population mean
σ is standard deviation
n is sample size
We are given;
Sample mean; x' = 8.12 hours
Population mean; μ = 8 hours
Standard deviation; σ = 0.72 hours
sample size ; n = 81 pilots
Thus;
t = (8.12 - 8)/(0.72/√81)
t = 0.12/0.08
t = 1.5
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a triangle base is 6 inches long and it’s height is 5 inches. what the area of the triangle?
Answers
Answer:
Answer:The area of the triangle is 60 in.
explanation:
Because we have 6inches in the weigth and 5inches in the height .
A=1/2bhA=1/2x 5 x 6A=30A=1/2 ÷30A=60inPLS HELPPOO!!!!!!!!!
Answers
Answer:
AC=8
Step-by-step explanation:
2x=2(8)
2x=16
x=16÷2
x=8
Help pls thx
King David was born in 1015 BC and died in 970 BC. The Roman Emperor Augusta was born in 63 BC and died in 14 AD. Which of these two men lived longer?
Answers
1015-970=45 (king David)
63-14=49 (augusta)
A group of friends wants to go to the amusement park. They have no more than $325 to spend on parking and admission. Parking is $13, and tickets cost $39 per person, including tax. Write and solve an inequality which can be used to determine p, the number of people who can go to the amusement park.
Answers
Using inequality, we can conclude that maximum of 14 people can visit the amusement park.
What is inequality?A relation that compares two numbers or other mathematical expressions inequitably is known as an inequality in mathematics. On the number line, size comparisons between two numbers are typically made. Inequalities are relationships between two expressions that aren't equal to one another. The symbols, >, <, ≤, ≥ and ≠ are used to denote inequalities and mean "7 is greater than" (or "is less than 7," when read left to right).So, (p) a maximum number of people who can visit the park:
They can only spend a total of $325 on parking and admission.Parking costs $13 and tickets are $39 per person, tax included.Now, calculate as follows:
13+ $39p ≤ $325$39p ≤ $325 - $13p ≤ 14Therefore, using inequality, we can conclude that maximum of 14 people can visit the amusement park.
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Rewrite the power as a product of powers (2ax)^3
Answers
The power as a product of powers can be rewritten (2ax)³ as (2ax )(2ax)(2ax )
What is the fundamental principle of multiplication?Multiplication is the mathematical operation that is used to determine the product of two or more numbers.
The product can be defined as the multiplication operation of two or more terms so that another term can be gotten the same as the one that is been given that we were asked to rewrite.
Power is defined as the degree that is been found on the terms, the degree that can be on the term is 3, then it can be expressed in three terms
Therefore, the given expression is (2ax)³ can be rewritten as;
(2ax)³ = (2ax )(2ax)(2ax )
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The distance between Dallas and Austin on a map is about 9 centimeters. The map uses a scale in which 1 centimeter represents 20 miles. What is the actual distance between Dallas and Austin in miles
please help due in an hour and i cannot fail!!!
Answers
Answer:
180
Step-by-step explanation:
9x20
The volume of a cone with height
h
and radius
r
can be found using the formula
V
=
1
3
π
r
2
h
Find the volume of a cone with radius 8 feet and height 7 feet.
Answers
The volume of the cone has a value of 410.67 cubic meters
How to determine the volume of the cone?From the question. the height and the radius of the cone are given as
Height = 7 feet
Radius = 8 feet
The volume of the cone can be calculated using the following volume formula
Volume = 1/3πr^2h
Substitute the known values in the above equation
So, we have
Volume = 1/3 * 22/7 * 8 * 7^2
Evaluate the products
Volume = 410.67
Hence, the volume is 410.67 cubic meters
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A soccer league is organizing teams. There are 60 boys to make up the boys' teams and 40 girls to make up the girls' teams. The teams should be the same size What is the largest number of people that can be on a team?The largest number of people that can be placed on a team is
Answers
There are 60 boys to make up the boys' teams and 40 girls to make up the girls' teams.
We are also told that the teams should be the same size.
This means that irrespective of the number of teams, each team should contain the same number of players.
Thus, the largest number of people that can be placed on a team is;
The highest common factor ;
The HCF is 10 x 2 = 20, therefore;
The largest number of people that can be placed on a team is 20.
Look at the steps and find the pattern.step 1step 2step 3How many dots are in the 4th step?dotsSubmit
Answers
40
Explanation
Step 1
a)initially we have 8 dots
after that
in step 2, we have a new row and , now there are 8 dots per row, so
[tex]\begin{gathered} \text{new row} \\ and\text{ number of dots= previous +1} \end{gathered}[/tex]in step 3, we should have
[tex]\begin{gathered} new\text{ row, it means now, there are 3 rows} \\ \end{gathered}[/tex]and
[tex]\begin{gathered} and\text{ number of circles = previous +1} \\ \text{ number of circles =}8+1=9 \\ \text{ number of circles =}9 \end{gathered}[/tex]as we can see, the rule works
Step 2
now, to find the patter in step 4, just apply
[tex]a\text{ new rounds, now, there are 4 row}[/tex]and
[tex]\begin{gathered} and\text{ number of dots = previous +1} \\ \text{ number of dots = 9}+1=10 \\ \text{ number of dots=}10 \end{gathered}[/tex]finally, to know the number of dots
Multiply the number of row, by the number of dots per row, so
[tex]\begin{gathered} \text{Number of dots=4}\cdot10 \\ \text{Number of dots=}40 \end{gathered}[/tex]therefore, the answer is 40
I hope this helps you
PLEASE HELP ASAP!!!!!!!!!!!!!!!
The table describes the quadratic function h(x).
x h(x)
−3 −2
−2 −3
−1 −2
0 1
1 6
2 13
3 22
What is the equation of h(x) in vertex form?
h(x) = (x + 2)2 − 3
h(x) = (x + 1)2 − 2
h(x) = (x − 1)2 + 2
h(x) = (x − 2)2 + 3
Answers
The quadratic function of h (x) in vertex form will be;
⇒ h(x) = (x + 2)² − 3
What is substitution method?
To find the value of any one of the variables from one equation in terms of the other variable is called the substitution method.
Given that;
The values of x and h (x) for the quadratic function is given as;
x = -3, -2, -1, 0, 1, 2, 3,
h (x) = -2, -3, -2, 1, 6, 13, 22
Now,
Let the quadratic function is,
h (x) = ax² + bx + c
Substitute x = -3 and h (x) = -2 in above quadratic function we get;
h (x) = ax² + bx + c
- 2 = a × (-3)² + b × -3 + c
- 2 = 9a - 3b + c
And, Substitute x = -2 and h (x) = -3 in above quadratic function we get;
h (x) = ax² + bx + c
- 3 = a × (-2)² + b × -2 + c
- 3 = 4a - 2b + c
And, Substitute x = -1 and h (x) = -2 in above quadratic function we get;
h (x) = ax² + bx + c
- 2 = a × (-1)² + b × -1 + c
- 2 = a - b + c
After solving we get;
a = 1 , b = 4 and c = 1
Substitute all the values in above quadratic equation, we get;
h (x) = ax² + bx + c
h (x) = 1 × x² + 4x + 1
h (x) = x² + 4x + 1
h (x) = x² + 4x + 4 - 4 + 1
h (x) = (x + 2)² - 3
Thus, The quadratic function of h (x) in vertex form will be;
⇒ h(x) = (x + 2)² − 3
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is line k parallel to line /?
O a
Ob
122⁰
Yes
No
&
l
Answers
Answer:
Yes
Step-by-step explanation:
Parallel lines are 2 lines that go in the same direction that will never touch each other.
Hope that helps
For the bake sale, Lee baked 141 cookies. Esther baked 51 more cookies than Lee. How many cookies did Lee and Esther bake in all?
Answers
Answer: 333 Cookies
Step-by-step explanation:
Let E = Cookies by Esther
Let L = Cookies by Lee
The equation for amount of cookies: E+L
L=141
E=L+51
Substitute L
E=141+51=192
E+L=141+192=333
Answer:
[tex]10 \div x - 10 \div (x - 1) = 30[/tex]
-2.3x - 4.2x = -66.3
Solve the equation for x
Answers
Combine -2.3x and -4.2x since they are like terms, which equals -6.5x. Then you need to divide -66.3 by -6.5, and when you do so, you get your answer, 10.2 as x.
Answer
x=10.
Step-by-step explanation:
-2.3x-4.2x=-66.3
-2.3+-4.2=-6.5x
-6.5x÷-6.5
-66.3÷-6.5
x=10.
3 math questions multiple choice
Answers
1) the equation is:
[tex]2y+x=4[/tex]So we can rewrite the equation as a slope intercept so:
[tex]\begin{gathered} 2y=-x+4 \\ y=-\frac{1}{2}x+2 \end{gathered}[/tex]So the slope is -1/2
2) the equation is:
[tex]3x-2y=5[/tex]Now we evaluete the coordinates to see which one is not on the line so for (1,-1)
[tex]\begin{gathered} 3(1)-2(-1)=5 \\ 3+2=5 \\ 5=5 \end{gathered}[/tex]So is on the line
for (-1,-4)
[tex]\begin{gathered} 3(-1)-2(-4)=5 \\ -3+8=5 \\ 5=5 \end{gathered}[/tex]So it is on the line
for (3,2)
[tex]\begin{gathered} 3(3)-2(2)=5 \\ 9-4=5 \\ 5=5 \end{gathered}[/tex]So it is on the line
Finally for (1,2)
[tex]\begin{gathered} 3(1)-2(2)=5 \\ 3-4=5 \\ -1\ne5 \end{gathered}[/tex]So (1,2) is not on the line
3) if the slope is -2 and goes to the point (3,-1) we can use the equation of a line to find the intercept so:
[tex]\begin{gathered} y=-2x+b \\ -1=-2(3)+b \\ -1=-6+b \\ -1+6=b \\ 5=b \end{gathered}[/tex]So the intercept is 5 so the equation is:
[tex]y=-2x+5[/tex]Graph the image of the figure using the transformation given.
Answers
A graph of the image of triangle V'W'X' after a rotation of 90° counterclockwise about the origin is: graph A.
What is a rotation?A rotation is a type of transformation which moves every point of the object through a number of degrees around a given point, which can either be clockwise or counterclockwise (anticlockwise) direction.
In Geometry, rotating a point 90° about the origin in a counterclockwise (anticlockwise) would produce a point that has the coordinates (-y, x).
Note: Each interval on this graph represents 1 unit.
By applying a rotation of 90° counterclockwise to triangle VWX, the coordinates of the vertices of the image triangle V'W'X' include the following:
(x, y) → (-y, x)
Point V = (-2, -4) → Point V' = (-(-4), -2) = (4, -2)
Point W = (-2, -2) → Point W' = (-(-2), -2) = (2, -2)
Point X = (-5, -4) → Point X' = (-(-4), -5) = (4, -5)
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what is the radius of the circle?
Answers
Answer:
The radius is from the middle to the edge, in this case it looks the radius is 4
if f(x)=2x^2+3x Find f(−5) step by step plese
Answers
The value of x for quadratic equation f(x) = 2x² + 3x when f(-5) is 35.
Given, f(x) = 2x² + 3x
To find: f(-5)
For the quadratic equation f(x) = 2x² + 3x substitute the value -5 in place of x as the f(-5) has been mentioned in the question.
So,
f(-5) = 2(-5)² + 3(-5)
A Square of -5 is 25 and 3 multiplied by -5 is 15,
f(-5) = 2(25) + (-15)
Multiple of 25 and 2 is 50 subtracted by 15,
f(-5) = 50 - 15
At last, subtract 50 by 15,
f(-5) = 35
∴ For equation f(x) = 2x² + 3x when f(-5), the value of x = 35.
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Solve: 5k = 100k =
A. 20
B. 10
C. 500
D. 50
Answers
Answer:
A,) 20
Step-by-step explanation:
First, I am assuming that the problem is 5k = 100, not "5k = 100k =" as it was written.
We need to end up with "k equals some number." This is called solving for k. In order to do this we need to have k by itself. We look at the problem and ask, "what is preventing k from being by itself?" In this case k has a "times 5" with it. How can we get rid of that? Well we can do the opposite of "times 5," and that is to divide the left side by 5. That leaves k by itself which is exactly what we need. But if do something to one side of an equation, we need to do it to the other side for the equation to still be true. So in this case we also have to divide the right side by 5 also, which gives us 20 on the right side. So in our original problem:
5k = 100
Divide both sides by 5 and we have the answer:
k = 20