The given expression is
[tex]\frac{v+8}{v}=\frac{1}{2}[/tex]First, we multiply 2v on each side.
[tex]\begin{gathered} 2v\cdot\frac{v+8}{v}=2v\cdot\frac{1}{2} \\ 2v+16=v \end{gathered}[/tex]Then, we subtract v on each side.
[tex]\begin{gathered} 2v-v+16=v-v \\ v+16=0 \end{gathered}[/tex]At last, we subtract 16 on each side.
[tex]\begin{gathered} v+16-16=-16 \\ v=-16 \end{gathered}[/tex]Therefore, the solution is -16.According to a report from a particular university, 46% of female undergraduates take on debt. Find the probability that none of the female undergraduates have taken on debt if 9female undergraduates were selected at randomWhat probability should be found?MA PO female undergraduates take on debt)OB P(9 female undergraduates take on debt)OC P(1 female undergraduate takes on debt)OD P(2 female undergraduates take on debt)The probability that none of the female undergraduates take on debt is I(Type an integer or decimal rounded to three decimal places as needed)1}0vo(0.MorexHelp Me Solve ThisView an ExampleGet More HelpClear AllCheck Answer
For this exercise we use the probability function of the binomial distribution, also called the Bernoulli distribution function, is expressed with the formula:
[tex]P(x)=\frac{n!}{(n-x)!\cdot x!}\cdot p^x\cdot q^{n-x}[/tex]Where:
• n, = the number of trials
,• x, = the number of successes desired
,• p,= probability of getting a success
,• q, = probability of getting failure
From the exercise we can identify:
[tex]\begin{gathered} n=9 \\ x=0 \\ p=0.46 \\ q=1-p \\ q=0.54 \end{gathered}[/tex]Replacing in the equation of the binomial distribution:
[tex]\begin{gathered} P(0)=\frac{9!}{(9-0)!\cdot0!}\cdot(0.46)^0\cdot(0.54)^{9-0} \\ P(0)=0.0039 \\ P(0)=0.004 \end{gathered}[/tex]The answer is P(0 female undergraduates tak on debt)
build build a machine that can automatically clean a coffee mug Bill wants the machine to be able to do an amount of work represented by the inequality x + y greater than or equal to 2 while using battery power that remains at level represented by the inequalities for x + y greater than or equal to -1 where X and Y both represent the number of minutes spent on cleaning different parts of the tank at the machine Spence 5 in three minutes on X & Y respectively does he meet those requirements?
We have to meet these restrictions:
Amount of work:
[tex]x+y\ge2[/tex]Battery power:
[tex]x+y\ge-1[/tex]If the values of x and y are x=5 and y=3, then we have to evaluate each restriction:
[tex]\begin{gathered} x+y=5+3=8\ge2\longrightarrow\text{true} \\ x+y=5+3=8>-1\longrightarrow true \end{gathered}[/tex]Answer: Yes, they meet the requirements.
find the equation of the line with slope 6 and containing the point (3,1). Write the equation in function notation
ANSWER
f(x) = 6x - 17
EXPLANATION
The equation of a line with slope m and y-intercept b is:
[tex]f(x)=mx+b[/tex]We know the slope of this line, m = 6, so we have this equation:
[tex]f(x)=6x+b[/tex]To find the y-intercept we have to replace f and x with the given point: f(3) = 1:
[tex]\begin{gathered} 1=6\cdot3+b \\ 1=18+b \\ b=1-18 \\ b=-17 \end{gathered}[/tex]The equation is:
[tex]f(x)=6x-17[/tex]Solve each system of equations using linear combination.1.3x +5y = 82x - 5y = 22
x = 6, y = -2
Explanations:The given system of equations is:
3x + 5y = 8..................................(1)
2x - 5y = 22................................(2)
Add equations (1) and (2) together
(3x + 5y) + (2x - 5y) = 8 + 22
3x + 2x + 5y - 5y = 30
5x = 30
x = 30/5
x = 6
Substitute x = 6 into equation (1)
3x + 5y = 8
3(6) + 5y = 8
18 + 5y = 8
5y = 8 - 18
5y = -10
y = -10/5
y = -2
The solution to the system of equations is:
x = 6, y = -2
Rewrite the equation below so that it does not have fractions. 3+ = x= = Do not use decimals in your answer.
First we have to find the least common multiple between the denominators ( 3 and 7). Since they are prime numbers the LCM is : 3*7 = 21
Then, multiply each term of the equation by 21 and simplify
[tex]\begin{gathered} 3\cdot21+21\cdot\frac{2}{3}x=\frac{2}{7}\cdot21 \\ 63+7\cdot2x=2\cdot3 \\ 63+14x=6 \end{gathered}[/tex]The answer is 63 + 14x = 6
solve x 9/× = x/4 what is x
evaluate [tex]3 {x}^{2} - 4[/tex]when x=2.
3x^2 - 4 , at 2 is = 3•2^2 - 4
. = 12 - 4 = 8
Law of Exponents. Simplify each expression. Answers should be written with positive exponents.(-5p^6 times r^-9)^0
Solution:
Given the expression:
[tex](-5p^6\cdot r^{-9})^0[/tex]Simplifying using the law of exponents,
[tex]\begin{gathered} (-5p^6\cdot r^{-9})^0=(-5\times p^{-6}\times r^{-9})^0 \\ \end{gathered}[/tex]but
[tex]a^{-b}=\frac{1}{a^b}[/tex]thus, we have
[tex]\begin{gathered} (-5\times p^{-6}\times r^{-9})^0=(-5\times\frac{1}{p^6}\times\frac{1}{r^9})^0 \\ =(-\frac{5}{p^6r^9})^0 \end{gathered}[/tex]From the zero index law of exponents,
[tex]a^0=1[/tex]This implies that
[tex](-\frac{5}{p^6r^9})^0=1[/tex]Hence, the solution to the expression is 1
Describe how the graph of y = ln (-x) relates to the graph of its parent function y = ln x.
The graph of function f(-x) can be obtained from graph of pareant funcion f(x) by refecting the graph over y-axis.
We need to obtain the graph of ln (-x) from parent function ln x, which is nothing but replace of x by -x. So graph of ln (-x) is obtained by reflection of graph of function ln (x) over y-axis.
Answer: y-axis reflection
use the distributive property to write an equivalent expression for 88 plus 55
We are asked to use the distributive property to write an equivalent expression for 88 plus 55.
Let us first understand what is distributive property?
[tex]a\cdot(b+c)=a\cdot b+a\cdot c[/tex]The above property means that multiplying the sum of two or more addends by a number will give the same result as multiplying each addend individually by the number and then adding the products together.
But we have only two numbers 88 and 55 so how are we going to apply this property?
We need to break these numbers.
Let us find out the GCF (greatest common factor) of these two numbers.
11 is the greatest common factor of numbers 88 and 55
So, we can break the numbers as
[tex]\begin{gathered} 88=11\cdot8 \\ 55=11\cdot5 \end{gathered}[/tex]Now we have three numbers so let us apply the distributive property.
[tex]\begin{gathered} a\cdot(b+c)=a\cdot b+a\cdot c \\ 11\cdot(8+5)=11\cdot8+11\cdot5 \end{gathered}[/tex]Therefore, the equivalent expression for 88 plus 55 is
[tex]88+55=11\cdot(8+5)_{}[/tex]Liam wants to find the average of the following numbers. 53, 46, 57, 52, 49 He estimates the average as 50 and then finds the average. Which describes how close Liam is to his estimate?
You find the average by adding all of the numers and then divide by the ammount of numbers that were added:
[tex]A=\frac{53+46+57+52+49}{5}\Rightarrow A=51.4[/tex]So the average is 51.4 and therefore Liam was off by 1.4 units.
Given the definitions of f(x) and g(2) below, find the value of g(f(-3))f(x) = -3x – 12g(x) = 3x2 – 2x – 14
Given data:
Itis given that
[tex]\begin{gathered} f(x)=-3x-12 \\ g(x)=3x^2-2x-14 \end{gathered}[/tex]Now to calcualte g(f(-3)) first let us calculate f(-3)
[tex]\begin{gathered} f(-3)=-3(-3)-12 \\ =9-12 \\ =-3 \end{gathered}[/tex]Now, g(f(-3)) will be
[tex]\begin{gathered} g(f(-3))=g(-3) \\ =3(-3)^2-2(-3)-14 \\ =3(9)+6-14 \\ =27-8 \\ =19 \end{gathered}[/tex]So, value of g(f(-3)) is 19.
5. Input Output 4 3 3 1
It is not a function because a function should assign one element in the domain to one and only one in the range.
A researcher studied the relationship between the number of times a certain species of cricket will chirp in one minute and the temperature outside. Her data is expressed in the scatter plot and line of best fit below. What is the meaning of the yy-value on the line when x=80x=80?
The line of best fit approximates the relationship between the independent and the dependent variables. Here, the x-values give us the number of chirps per minute while the y-values give us the temperature in degrees Fahrenheit.
When x = 80, the number of chirps per minute is 80. The corresponding y is approximately 62.5 degrees Fahrenheit, which is the predicted temperature when the x-value is 80.
So, the answer is the first option: The predicted temperature in degrees Fahrenheit if the cricket has chirped 80 times.
Hello!I have (m^3n^5)^1/4 and I do not know how to take the n out since it is n^5/4.Thanks
We are given
[tex](m^3n^5)^{\frac{1}{4}}[/tex]
We want to take n out
Solution
Given
[tex]\begin{gathered} (m^3n^5)^{\frac{1}{4}} \\ (m^3\times n^4\times n)^{\frac{1}{4}} \\ (m^3)^{\frac{1}{4}}\times(n^4)^{\frac{1}{4}}\times(n)^{\frac{1}{4}} \\ (m^3)^{\frac{1}{4}}\times n^{}\times(n)^{\frac{1}{4}} \\ n\times(m^3)^{\frac{1}{4}}^{}\times(n)^{\frac{1}{4}} \\ n(m^3n)^{\frac{1}{4}} \end{gathered}[/tex]Martha drove her car east for a total of 9 hours at a constant velocity. In one-third of that time, she drove 180 kilometers. What was her velocity?
time = one third of 9 hours = 1/3 x 9 = 3 hours
Distance = 180 km
Velocity = Distance / time
Replacing:
V = 180 km/3 h = 60 km per h
Daniel and his mother flew fromMiami, Florida to Maine to visit family.When they left Miami, the temperaturewas 84°. When they arrived in Maine itwas -7°. What was the temperaturechange Daniel and his mother?
the temperature change will be the difference or the subtraction between bout temperatures so it will be:
[tex]84-(-7)=91º[/tex]so there are 91º of temperature difference
please i need your help i will appreciate it
The value of c is 5/2 that satisfy the conclusions of the mean value theorem.
Given Function:
f(x) = x^2-3x+3 on interval [1,4].
The Mean Value Theorem states that for a continuous and differentiable function f(x)=x^2-3x+3 on the interval [1,4] there exists such number c from the interval [1,4] that [tex]f'(c)=\frac{f(4)-f(1)}{4-1}[/tex].
f(4) = 4^2-3*4+3
= 16-12+3
= 4+3
= 7
f(1)=1^2-3*1+3
= 1-3+3
= 1
f'(c) = 2c -3
2c-3 = 7 - 1 / 4 - 1
2c - 3 = 6/3
2c -3 = 2
2c = 5
c = 5/2
Therefore the value of c = 5/2 that satisfy the conclusions of the mean value theorem.
Learn more about the mean value theorem here:
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Calculate the limitlim x => -4 [tex] \frac{x {}^{2} + 2x - 8}{x {}^{2} + 5x + 4} [/tex]
The limit to be calculated is:
[tex]\lim _{x\to-4}\frac{x^2+2x-8}{x^2+5x+4}[/tex]Notice that:
[tex]\begin{gathered} \frac{x^2+2x-8}{x^2+5x+4}=\frac{(x-2)(x+4)}{(x+1)(x+4)} \\ =\frac{(x-2)}{(x+1)},x\ne-4 \end{gathered}[/tex]Remember that, in the limit when x->-4, the value of x approaches to -4, but it never is -4. Thus, we can use the last line of the identity above,
[tex]\begin{gathered} \Rightarrow\lim _{x\to-4}\frac{x^2+2x-8}{x^2+5x+4}=\lim _{x\to-4}\frac{(x-2)(x+4)}{(x+1)(x+4)}=\lim _{x\to-4}\frac{(x-2)}{(x+1)}=\frac{(-4-2)}{(-4+1)}=-\frac{6}{-3}=2 \\ \Rightarrow\lim _{x\to-4}\frac{x^2+2x-8}{x^2+5x+4}=2 \end{gathered}[/tex]The answer is 2.
find the slope (-10,8) (5,-3)
The slope can be calculated with the following formula:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]In this case, you have the following points:
[tex]undefined[/tex]values for relation g are given in the table. which pair is in g inverse
Given
Values for relation g
Find
Which pair is in g inverse.
Explanation
In the inverse function , it satisfies when y = f(x)
[tex]x=f^{-1}(y)[/tex]so , in the inverse of g
since g(4) = 9 , so
[tex]4=g^{-1}(9)[/tex]g(5) = 13 , so
[tex]13=g^{-1}(5)[/tex]g(3) = 5 , so
[tex]5=g^{-1}(3)[/tex]g(2) = 2 , so
[tex]2=g^{-1}(2)[/tex]so , (13 , 5) would be found in the inverse of g
Final Answer
Hence , the correct option is (13 , 5)
what is .8 divided by 40
Problem
0.8 divided 40
Solution
We can do the following:
[tex]\frac{0.8}{40}=\frac{0.8\cdot10}{40\cdot10}=\frac{8}{400}[/tex]and if we simplify we got:
[tex]\frac{8}{400}=\frac{4}{200}=\frac{2}{100}=\frac{1}{50}=0.02[/tex]A bag contains 6 apples and 4 bananas. If two fruits are drawn one by one with replacement, find the probability that the first one is an apple and the second one is banana.
we have
probability first one is an apple:
[tex]\frac{6}{6+4}=\frac{6}{10}[/tex]probability the second one is banana:
[tex]\frac{4}{6+4}=\frac{4}{10}[/tex]therefore, the probability that the first one is an apple and the second one is banana:
[tex]\frac{6}{10}\times\frac{4}{10}=\frac{24}{100}=\frac{6}{25}[/tex]answer: 6/25
K
There are 48 runners in a race. How many ways can the runners finish first, second, and third?
There are different ways that the runners can finish first through third.
(Type a whole number.)
The number of different ways that the runners can finish first through third. is 103776
There are 48 runners in a race
The number of options for the first place is 48, as only one can be in 1st postion and there are a total of 48 persons
The number of options for the second place is 47, as the person who became first cannot be in the second position
The number of options for the third place is 46, as the person who became first and second cannot be in the third position
There are different ways that the runners can finish first through third. is
48 x 47 x 46 = 103776
Therefore, the number of different ways that the runners can finish first through third. is 103776
To learn more about permutation refer here
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Solve the system of two linear inequalities graphically.{x<5<2x - 4Step 1 of 3: Graph the solution set of the first linear inequality.Answer3 KeypadKeyboard ShortcutsThe line will be drawn once all required data is provided and will update whenever a value is updated. Theregions will be added once the line is drawn.HOANChoose the type of boundary line:O Solid (-)Dashed ---)SEnter two points on the boundary line:10-5ज510JOO5Select the region you wish to be shaded:ОАOB101
From the problem, we have :
[tex]\begin{gathered} x<5 \\ x\ge-4 \end{gathered}[/tex]For the first inequality, x < 5
Since the symbol is "<", the boundary line is dashed line.
The boundary line is at x = 5 which has points (5, 0) and (5, 2)
and the region is to left of x = 5.
The graph will be :
Next is to graph the second inequality, x ≥ -4
Since the symbol is "≥", the boundary line is a solid line
The boundary line is at x = 4 which has points (-4, 0) and (-4, 2)
and the region is to the right.
The graph will be :
The solution to the inequalities is the overlapping region when joined together.
This will be :
The overlapping region is the middle region or region in between the boundary line which is also -4 ≤ x < 5
chance the pilot of a boeing 727 flew e plane so it took off at an angle of elevation 21 degrees. after flying one kilometer, what is the altitude (height) of the plane that chance was flying rounded to the nearest meter? (1 km= 1000 meters)
To solve the exercise, it is convenient to first draw a picture of the situation posed by the statement:
As you can see, a right triangle is formed. So to find the height at which the plane was when the pilot had flown one kilometer, you can use the trigonometric ratio sin(θ):
[tex]\sin (\theta)=\frac{\text{Opposite side}}{\text{ Hypotenuse}}[/tex]Then, in this case, you have
[tex]\begin{gathered} \sin (21\text{\degree})=\frac{\text{ Altitude}}{1000m} \\ \text{ Multiply by 1000m on both sides of the equation} \\ \sin (21\text{\degree})\cdot1000m=\frac{\text{ Altitude}}{1000m}\cdot1000m \\ \sin (21\text{\degree})\cdot1000m=\text{ Altitude} \\ 358.37m=\text{ Altitude} \\ \text{ Rounding to the nearest meter} \\ 358m=\text{ Altitude} \end{gathered}[/tex]Therefore, the altitude or height of the plane after flying one kilometer is 358 meters.
Q4 O center (-1,3), radius = 1 What is the center and radius of the circle, 2 2 r + y + 2x - 6y +9=0 - 9 center (1,-3), radius = 1 center (-1,3), radius = 9 center (1,-3), radius = 3
Step 1: Write out the formula
The equation of a circle given by
[tex](x-a)^2+(y-b)^2=r^2[/tex][tex]\begin{gathered} \text{where} \\ (a,b)\text{ is the center of the circle} \\ r\text{ is the radius of the circle} \end{gathered}[/tex]Step 2: Write out the given equation and rewrite it in the form shown above
[tex]x^2+y^2+2x-6y+9=0[/tex][tex]\begin{gathered} x^2+2x+y^2-6y+9=0 \\ \text{ By completing the square, we have} \\ (x+1)^2-(+1)^2+(y-3)^2-(-3)^2+9=0 \\ \end{gathered}[/tex][tex]\begin{gathered} (x+1)^2+(y-3)^2-1-9+9=0 \\ (x+1)^2+(y-3)^2=1=1^2 \end{gathered}[/tex]By comparing the equation with the formula above, we have
[tex]a=-1,b=3,r=1[/tex]Therefore,
center (-1,3), radius = 1
The volume of a large tank is 350 ft. It is 65 ft wide and 4 ft high. What is the length of the tank?
The volume of a rectangular prism can be calculated by the formula
[tex]V=l\cdot w\cdot h[/tex]in which l, w and h represent the length, width, and heght respectively.
clear the equation for l
[tex]l=\frac{V}{w\cdot h}[/tex]replace with the data given
[tex]undefined[/tex]can you please help me
Answer
The graph of y = -3x + 1 is presented below
Explanation
We are asked to plot the graph of y = -3x + 1
We will use intercepts to obtain two points on the line and connect those two points
y = -3x + 1
when x = 0
y = -3x + 1
y = -3(0) + 1
y = 0 + 1
y = 1
First point on the line is (0, 1)
when y = 0
y = -3x + 1
0 = -3x + 1
3x = 1
Divide both sides by 3
(3x/3) = (1/3)
x = ⅓ = 0.333
Second point on the line is (⅓, 0) or (0.333, 0)
The graph of this question is presented under 'Answer' above.
Hope this Helps!!!
Use a net to find the surface area of the prism.25 cm3.5 cm13 cmThe surface area of the prism is (Simplify your answer.)
A rectangle prism of sides 25, 3.5 and 13 cm can be drawn as:
It will have 6 faces (4 lateral, a base and a top face)
Each face has a surface area that is the product of two of the sides. We have two faces for each pair of sides.
So if we have sides a, b and c, the surface area can be written as:
[tex]S=2(a\cdot b+a\cdot c+b\cdot c)[/tex]With the sides of our prism we can calculate the surface area as:
[tex]\begin{gathered} S=2(25\cdot3.5+25\cdot13+3.5\cdot13) \\ S=2(87.5+325+45.5) \\ S=2\cdot458 \\ S=916\operatorname{cm}^2 \end{gathered}[/tex]Answer: The surface area of the prism is 916 cm^2