Answer: (x-2)
Step-by-step explanation:
This problem is a middle-term factorization, or factoring by splitting the middle term.
We have the equation
x^2 - 18x + 32
This equation represents the area, and area = length x width for all rectangles. We also know the width, x-16, which makes it easier for us. The length must also be in the same format.
x^2 - 18x + 32
= x^2 - 16x - 2x + 32
= x(x-16) - 2(x - 16)
= (x-16) (x-2) -------> we get this through taking (x-16) common
We could also pretend that the length is x - y, where y is the number we need to finish the equation.
x^2 - 18x + 32
= (x-16) (x-y)
= x^2 -16x - xy + 16y
-16 minus 2 is -18, which is our middle term.
Therefore, y = 2. This is also verified because is 16y = 32, the constant term, then through transposing we get y = 2.
Our answer is that the length is (x-2).
IF THE PROBABILITY THAT A FOOTBALL TEAM WILL WIN THEIR NEXT GAME IS 80%,
WHAT ARE THE ODDS IN FAVOR OF THEM WINNING?
The odds in favor of them winning is 20%
How to determine the probability
From the information given, we have that the probability of them winning the next game is 80%
P( winning) = 80% = 0. 8
The odds against them winning is given as;
1 - probability of winning
We have;
= 1 - 0. 8
= 0. 2
The odds in favor of them winning is simply the probability of them losing;
= 0. 2 × 100
= 20%
Thus, the odds in favor of them winning is 20%
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What is the first step to solve the equation A. Square both sides of the equation. B. Add 5 to both sides of the equation. Square. 5, and -3. C. D. None, because there is no solution. 2x-5--3?
Hi :)
I'd start by adding 5 to both sides of the equation. That would make the equation easier.
[tex]\boldsymbol{\sqrt{2x}-5=3}}[/tex]
[tex]\boldsymbol{\sqrt{2x}=2}[/tex]
The next step is to get rid of the radical sign.
Which operation will undo the square root? Squaring.
So that's why we square both sides:
[tex]\boldsymbol{2x=4}[/tex]
And Now we just divide both sides by 2
[tex]\boldsymbol{x=2}[/tex]
~[tex]\textit{\textbf{Learn More; Work Harder}}[/tex]~
:)
The graph of a cosine function has an amplitude of 5, a vertical shift of −1, and a period of 4. These are the only transformations of the parent function.
Use the Sine tool to graph the function.
The first point must be on the midline, and the second point must be a maximum or minimum value on the graph closest to the first point.
See attachment for the graph of the cosine function f(x) = 5 cos(π/2x) - 1
How to graph the cosine function?From the question, the given parameters are:
Amplitude, A = 5
Vertical shift, D = -1
Period, T = 4
A cosine function is represented as:
f(x) = A cos(B(x + C)) + D
Where
Amplitude = A
Period = T
Horizontal shift = C
Vertical shift = D
Since the horizontal shift is not stated in the question, we can assume that the horizontal shift is 0
i.e. C = 0
So, the equation of the cosine function becomes
f(x) = A cos(Bx) + D
Calculate the value of B using
B = 2π/T
So, we have:
B = 2π/4
Evaluate
B = π/2
So, we have:
f(x) = A cos(π/2x) + D
Substitute the known values of A and D in the above equation
f(x) = 5 cos(π/2x) - 1
Next, we plot the graph of the cosine function on a graphing tool
See attachment for the graph of the cosine function f(x) = 5 cos(π/2x) - 1
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The total cost to rent 5 chairs and 3 tables is $27. The total cost to rent 2 chairs and 12 tables is $81. What is the cost to rent each chair and each table
The cost to rent each chair is $1.5 and cost to rent each table is $6.5
Applications of systems of linear equationsFrom the question, we are to determine the cost to rent each chair and each table
Let c represent chair
and
t represent table
From the given information,
The total cost to rent 5 chairs and 3 tables is $27
That is,
5c + 3t = 27 ------------ (1)
Also,
The total cost to rent 2 chairs and 12 tables is $81
That is,
2c + 12t = 81 ---------- (2)
Now, solve the equations simultaneously
5c + 3t = 27 ------------ (1)
2c + 12t = 81 ---------- (2)
Multiply equation (1) by 2 and multiply equation (2) by 5
2 × [5c + 3t = 27 ]
5 × [2c + 12t = 81 ]
10c + 6t = 54 ------------- (3)
10c + 60t = 405 ------------- (4)
Subtract equation (4) from equation (3)
10c + 6t = 54
10c + 60t = 405
---------------------------
-54t = -351
t = -351/-54
t = 6.5
Substitute the value of t into equation (2)
2c + 12t = 81
2c + 12(6.5) = 81
2c + 78 = 81
2c = 81 - 78
2c = 3
c = 3/2
c = 1.5
∴ The cost of chair is $1.5 and cost of table is $6.5
Hence, the cost to rent each chair is $1.5 and cost to rent each table is $6.5
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Is 3 1/4 a rational or irrational number?
Answer:
It is a rational number.
Step-by-step explanation:
A number is only irrational if it has a decimal that never ends and doesn't have a pattern. So a number like Pi (3.141592653589...) is irrational while a number like 1/3 (0.33333333...) is rational.
Hi :)
Below is the difference between rational & irrational numbers
______________RATIONALA number that can be expressed in [tex]\sf{\dfrac{p}{q}}[/tex] form, where [tex]\large\boldsymbol{q\ne0}[/tex]Evidently,
An irrational number is a number that cannot be expressed in [tex]\sf{\dfrac{p}{q}}[/tex] formLet's test the given number, [tex]\boldsymbol{3\dfrac{1}{4}}[/tex]
Well isn't it already in [tex]\sf{\dfrac{p}{q}}[/tex] form? It is.
Thus
[tex]\longrightarrow\darkblue\boldsymbol{3\dfrac{1}{4}\:is\:rational}[/tex]
[tex]\tt{Learn\:More;Work\:Harder}[/tex]
:)
A closed box with a square base is to have a volume of 16000 cubic centimeters. The material
for the top and bottom of the box costs $3 per square centimeter while the material for the sides
costs $1.50 per square centimeter. Find the dimensions of the box that will minimize the total
cost of materials. What is the minimum total cost?
The most suitable measurements for a box with a square base are 5cm (width) x 5cm (length) x 640cm (height). This box would be worth $4875
How to calculate the minimum value of the box?To find the minimum value of a box that must have a square base and 16000 cm³, we must try different measurements to find the variable that represents the least value.
In this case, the variable that represents less value is a base of 5cm x 5cm and a height of 640cm. This means that the box would be worth $4875 as shown below.
Base
5cm × 5cm = 25cm²25cm² x 3 = $75Sides
5cm × 640cm = 3200cm²3200cm² × $1.50 = $4800$4,800 + $75 = $4,875Additionally, we can check that the volume of the box is the required 16000cm³, as shown below:
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⦁ Mr. A likes playing a game and the probability that he wins this game is p. He enters the casino and he promises himself that he plays the game until he wins one time and then he stops. Let X be the number of plays in order to win one time. ⦁ What are the values of X? ⦁ What is the probability that X=n?. Prove that it satisfies the PMF conditions. ⦁ Calculate E(X) ⦁ Calculate V(X) ⦁ Study the memoryless property of X.
The possible values of X for this game are 0, 1, 2, 3, 4.......n, where n ≥ 1
How to determine the values of X?From the complete question, we understand that Mr. A wants to plays the game until he wins
This means that
He might win at the first game and he might win after n attempts
So, the values of X are
X = 0, 1, 2, 3, 4.......n
Hence, the possible values of X for this game are 0, 1, 2, 3, 4.......n, where n ≥ 1
The probability that X = nThe probability of x is represented as:
P(x) = nCx * p^x * (1 - p)^(n-x)
So, the probability that X = n is:
P(n) = nCn * p^n * (1 - p)^(n - n)
Evaluate the exponent
P(n) = nCn * p^n * 1
Evaluate the combination expression
P(n) = 1 * p^n * 1
This gives
P(n) = p^n
Hence, the probability that X = n is p^n
Prove that it satisfies the PMF conditions.The distribution satisfies PMF conditions because
The sum of the probabilities is 1 No probability is negativeEach probability value is between 0 and 1 (inclusive)Calculate E(X)The expected value E(x) is calculated using
E(x) = n * p
So, we have:
E(x) = np
Hence, the value of E(x) is np
Calculate V(X)The variance V(x) is calculated using
V(x) = √n * p * (1 - p)
So, we have:
V(x) = √np(1 - p)
Hence, the value of V(x) is √np(1 - p)
Study the memoryless property of X.The memoryless property of X is that each probability of X is independent
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For the straight line y =1/2x-4 what are the slope and y intercept
Answer:
Step-by-step explanation:
slope-- 1/2
y intercept-- -4
A private jet flies the same distance in 8 hours that a commercial jet flies in 7 hours. If the speed of the commercial jet was 144mph less than 2 times the speed of the private jet, find the speed of each jet.
Solving a system of equations, we can see that:
Speed of the private jet: 168 mi/hSpeed of the commercial jet: 192mi/hHow to find the speeds of each jet?Let's define the variables:
P = speed of the private jet.C = speed of the commercial jet.With the given information, we can write:
P*8h = D
C*7h = D
C = 2*P - 144mi/h
So we have a system of 3 equations, where D is the distance in the problem.
With the first and second equations we can write:
P*8h = D = C*7h
Isolating P, we get:
P = C*(7/8)
Now we can replace that in the last equation:
C = 2*P - 144mi/h
C = 2*C*(7/8) - 144mi/h
And now we can solve that for C.
C - 2*(7/8)*C = - 144mi/h
C*(1 - 14/8) = -144mi/h
C*(8/8 - 14/8) = - 144mi/h
C*(6/8) = 144mi/h
C = (8/6)*144mi/h = 192mi/h
Now that we know the speed of the commercial jet, we can find the speed of the private jet.
P = C*(7/8) = 192mi/h*(7/8) = 168 mi/h
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just need these 3 please and thanks in advance
The conclusion that can be made based on the hypothesis is:
1. It's a valid conclusion.
2. It is a valid conclusion.
3. It is a valid conclusion.
How to illustrate the information?According to the law of detachment, when the conditional and the hypothesis are true, the conclusion will be true.
Therefore, if 6x < 42, the value of x will also be less than 6. This is valid.
When an angle is more than 90°, it's an obtuse angle and since A is 103°, it's valid.
Also, the statement about the violin being a string instrument is logically valid.
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If f(x) = 5x, what is ƒ˜¹ (x)?
[tex]y = 5x \\ switch \: y \: and \: x \\ x = 5y \\ solve \: for \:y \\ y = \frac{x}{5} [/tex]
Instructions: Find the value of the trigonometric ratio. Make sure to simplify the fraction if needed.
Sin A= Answer
Check the picture below.
Find the measures of angles a and b when 0=44
Solve the system of equations below using a matrix equation.
2x + y = - 7
x − y = 4
Select one:
a.
( 1, 5 )
b.
( - 1, - 5 )
c.
( - 1, -2 )
d.
( 0, - 7 )
Answer: B. (-1, -5)
Step-by-step explanation:
Given equations
2x + y = -7
x - y = 4
Concept
[tex]A^{-1}=\frac{1}{ad-bc}\left[\begin{array}{ccc}a&b\\c&d\\\end{array}\right][/tex]
[tex]A*A^{-1}=A^{-1}*A=I~(Which~is~basically~1)[/tex]
Convert into matrix
[tex]\left[\begin{array}{ccc}2&1\\1&-1\\\end{array}\right] \left[\begin{array}{ccc}x\\y\\\end{array}\right]=\left[\begin{array}{ccc}-7\\4\\\end{array}\right][/tex]
Calculate the inverse of the matrix
[tex]A=\left[\begin{array}{ccc}2&1\\1&-1\\\end{array}\right][/tex]
[tex]A^{-1}=\frac{1}{ad-bc}\left[\begin{array}{ccc}a&b\\c&d\\\end{array}\right][/tex]
[tex]A^{-1}=-\frac{1}{3} \left[\begin{array}{ccc}-1&-1\\-1&2\\\end{array}\right][/tex]
Solve by multiplying the inverse of the matrix
[tex]A*A^{-1}=A^{-1}*A=I[/tex]
[tex]-\frac{1}{3} \left[\begin{array}{ccc}-1&-1\\-1&2\\\end{array}\right]\left[\begin{array}{ccc}2&1\\1&-1\\\end{array}\right] \left[\begin{array}{ccc}x\\y\\\end{array}\right]=-\frac{1}{3} \left[\begin{array}{ccc}-1&-1\\-1&2\\\end{array}\right]\left[\begin{array}{ccc}-7\\4\\\end{array}\right][/tex]
[tex]1*\left[\begin{array}{ccc}x\\y\\\end{array}\right]=-\frac{1}{3}\left[\begin{array}{ccc}3\\15\\\end{array}\right][/tex]
Simplify by multiplication
[tex]\left[\begin{array}{ccc}x\\y\\\end{array}\right]=\left[\begin{array}{ccc}-1\\-5\\\end{array}\right][/tex]
Therefore, the answer is [tex]\Large\boxed{(-1,~-5)}[/tex]
Hope this helps!! :)
Please let me know if you have any questions
Find the x-intercept.
x + 3
X-2
y =
([?], [_])
Answer: 1
Step-by-step explanation: It's subtraction and add ion look at the right side
Which value of w makes 14 = 11 + w/8 x 6 a true statemen?
choose 1 answer:
w = 1
w = 4
w = 16
w = 24
answer
is true statement w= 4
Classify the figure. Identify its vertices, edges and bases.
Write the direct variation function given that y varies directly with x, and y = 1.5 when x = 5.
1. x = 0.3y
2. y = 0.3x
3. y = 3x
4. y = 0.25x
The direct variation function is y = 0.3x
How to determine the direct variation function?The direct variation from y to x is represented as:
y = kx
When y = 1.5 and x = 5, we have
1.5 = 5k
Divide by 5
k = 0.3
Substitute k = 0.3 in y = kx
y = 0.3x
Hence, the direct variation function is y = 0.3x
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Alyssa was given a gift card for a coffee shop each morning Alyssa uses the gift card to buy one cup of coffee let a represent the amount of money of money remaining on the card after buying X cups of coffee that the table below has selected values showing the liner relationship between X and a determine the original amount of money on the gift card
Answer:20.00
Step-by-step explanation: next time include the table but i managed to find it anyway
Mrs. Smith has a total of 28 kids in her class. There are 5 more boys than there are girls. Write a system of equations to model this.
Answer:
x+(x+5)=28
Step-by-step explanation:
girls(g)should be equal to x
boys(b) will therefore be x+5
x+(x+5)=28
A rectangle has a width w that is 5units longer than its lenght/. Which equation expresses the rectangle's area, A?
Area equals Length times Width.
since the width of this equation is 5 units Longer then its Length
W = L + 5
To put this area in a equation we could say
L(L+5)=A
Simplify the equation, L^2 + 5L = A.
the size of the second application is 3.45 MB less than he first application. What is the size of the second application
The size of the second application given the size of the first application and the expression ( x - 3.45 mb) for the size of the second application is 293.55 MB.
EquationLet
Size of the first application = xSize of the second application= x - 3.45 mbFor instance,
if the size of the first application is 297 MB
Size of the second application= x - 3.45 mb
= 297 MB - 3.45 MB
= 293.55 MB
Therefore, the size of the second application given the size of the first application and the expression for the size of the second application is 293.55 MB
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Can someone help on this?
Step-by-step explanation:
this just means that the first function with input value x = 0 is calculated. that result becomes the input value x for the second function. and that result becomes the input value x for the 3rd function. and that result is then our result.
to answer a and b we only need to look at the main operation of each function :
the first one uses only basic multiplication and subtraction.
the second one uses squaring.
the third one is a 1/x operation.
a.
since the final result is a negative number (-31), the second function with the square operation cannot be last.
because a square operation always delivers a positive result.
+a × +a = +a²
-a × -a = +a²
remember, for a square operation we multiply the same number by itself. therefore we cannot mix signs like -a × +a, because then they would not be the same numbers anymore.
b.
since the initial input value is 0, the third function (1/x) cannot be the first, because 1/0 is not defined.
c.
because of the "large" -32 term in the first function I guess that this will be the last one to create such a low negative result of -31.
since 1/x cannot be first, (x - 2)² is then first. that makes 1/x second, and (4x - 32) third, as mentioned.
let's try :
x = 0
(x - 2)² = (0 - 2)² = (-2)² = 4
x = 4
1/x = 1/4
x = 1/4
4x - 32 = 4×1/4 - 32 = 1 - 32 = -31
hurrah ! we are correct !
Find the area of this kite
Answer:
26 units^2
Step-by-step explanation:
the area of a kite is (d1 * d2)/2
d1 = 2 + 2 = 4
d2 = 6 + 7 = 13
4 * 13 = 52
52 / 6 = 26
26 units^2 is your answer
Answer: 26
Step-by-step explanation:
Solve the following equation for W.
P=2L+2W
**Disclaimer** Hi there! I assumed the question is to represent W in terms of all other variables (P, L). The following answer corresponds to this understanding. If it is incorrect, please let me know and I will modify my answer.
Answer: W = (P/2) - L
Step-by-step explanation:
Given equation
P = 2L + 2W
Factorize 2 out
P = 2 (L + W)
Divide 2 on both sides
P / 2 = 2 (L + W) / 2
P / 2 = L + W
Subtract L on both sides
(P / 2) - L = L + W - L
[tex]\Large\boxed{W=\frac{P}{2} -L}[/tex]
Hope this helps!! :)
Please let me know if you have any questions
Answer:
[tex]\displaystyle{W = \dfrac{P}{2} - L}[/tex]
Step-by-step explanation:
To solve for W, we have to isolate the W-variable. First, we can factor the expression 2L + 2W to 2(L+W):
[tex]\displaystyle{P = 2(L+W)}[/tex]
Next, we'll be dividing both sides by 2:
[tex]\displaystyle{\dfrac{P}{2} = \dfrac{2(L+W)}{2}}\\\\\displaystyle{\dfrac{P}{2} = L+W}[/tex]
Then subtract both sides by L:
[tex]\displaystyle{\dfrac{P}{2} - L= L+W-L}\\\\\displaystyle{\dfrac{P}{2} - L= W}[/tex]
Therefore, we'll obtain W = P/2 - L.
Note that the given formula is perimeter formula of a rectangle where Perimeter = 2 * Length + 2 * Width.
So if we solve for W (Width) then we'll get Width = Perimeter / 2 - Length which can be useful to find width with given perimeter and length.
Suppose 45% of the population has a college degree.
If a random sample of size 437 is selected, what is the probability that the proportion of persons with a college degree will differ from the population proportion by greater than 3%? Round your answer to four decimal places.
Using the normal distribution, there is a 0.2076 = 20.76% probability that the proportion of persons with a college degree will differ from the population proportion by greater than 3%.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.By the Central Limit Theorem, for a proportion p in a sample of size n, the sampling distribution of sample proportion is approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1 - p)}{n}}[/tex], as long as [tex]np \geq 10[/tex] and [tex]n(1 - p) \geq 10[/tex].The proportion estimate and the sample size are given as follows:
p = 0.45, n = 437.
Hence the mean and the standard error are:
[tex]\mu = p = 0.45[/tex][tex]s = \sqrt{\frac{p(1 - p)}{n}} = \sqrt{\frac{0.45(0.55)}{437}} = 0.0238[/tex]The probability that the proportion of persons with a college degree will differ from the population proportion by greater than 3% is 2 multiplied by the p-value of Z when X = 0.45 - 0.03 = 0.42.
Hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem:
[tex]Z = \frac{X - \mu}{s}[/tex]
Z = (0.42 - 0.45)/0.0238
Z = -1.26
Z = -1.26 has a p-value of 0.1038.
2 x 0.1038 = 0.2076.
0.2076 = 20.76% probability that the proportion of persons with a college degree will differ from the population proportion by greater than 3%.
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I need help with the solution
The answer is Pedro.
is it possible to see the answer without paying?
Answer:
yes dear u need not to pay before viewing answer
You should at least answer 1 question to view the answers.
ball is thrown vertically upward at an initial speed of Its height (in feet) after t seconds is given by h(t)t(16t). After how many seconds does the ball reach its maximum height? Round answer to two decimal places.
If the height of ball is shown by h(t)=52t-16[tex]t^{2}[/tex] then the ball will reach after 1.625 seconds.
Given that height in t seconds is shown by h(t)=52t-16[tex]t^{2}[/tex].
We are required to find the time after which the ball will attain its maximum height.
The maximum height is the y coordinate of vertex of the parabola. Then we can use the following value of t.
h(t)=52t-16[tex]t^{2}[/tex]
Differentiate with respect to t.
dh/dt=52-32t
Again differentiate with respect to t.
[tex]d^{2}h/dt^{2}[/tex]=-32t
Because tim cannot be negative means the height is maximum.
Put dh/dt=0
52-32t=0
-32t=-52
t=52/32
t=1.625
Hence if the height of ball is shown by h(t)=52t-16[tex]t^{2}[/tex] then the ball will reach after 1.625 seconds.
Question is incomplete as the right and complete equation is
h(t)=52t-16[tex]t^{2}[/tex] .
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You are volunteering to help with the soccer team's Valentine's Day fundraiser. Each 16-ounce bag of nuts the team sold must include at least 60% chocolate-covered nuts inside.
However, instead of receiving a shipment of separated plain nuts and chocolate nuts, they delivered two large containers of mixed nuts. The first says it is 50/50 plain and chocolate covered. The second contains 80% chocolate-covered nuts.
The team is dismayed, but you come up with a solution. You suggest combining
ounces* of the 50/50 nuts with
ounces* of the 80% chocolate-covered nuts, to create the 60% mixture required for each bag.
*estimate
Then Bob, another student on the team says, "Wait, we promised at least 60%. So if we just do half and half, won't we be giving them at least 60%?"
Bob
correct.
Proportionately, if they do half and half of 50% and 80% of the two bags, Bob is correct.
What is a proportion?A proportion is a mathematical measure that compares two variables or numbers.
Proportions can be stated in percentages or ratios, as decimals or fractions.
Data and Calculations:Content of 16-ounce bag of nuts = 60% chocolate-covered nuts
Content of first bag = 50/50 plain and chocolate-covered nuts
Content of second bag = 80% chocolate-covered nuts
A mixture of half of 50% bag with half of 80% bag will result in 65% (50% + 80%)/2.
Thus, since the promise for each 16-ounce bag is for at least 60% chocolate-covered nuts, Bob is correct.
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Question Completion:Is Bob correct?
Jasmine got a new puppy for her birthday. He's full of energy, so she takes him for a walk along a 1.2-mile loop in a nearby park. If they walked a total of 3.6 miles, how many loops did they do?
Answer: 3 loops
Step-by-step explanation: The loop is 1.2 miles, and the total walk is 3.6 miles. You want to find out how many laps are in the 3.6 miles. This can be found using division. 3.6/1.2= the number of 1.2 mile laps inside the 3.6 mile walk, which is 3 laps. hope this helped!