Hi there!
[tex]\large\boxed{9(x - 1)^{2}}[/tex]
9x² - 18x + 9
We can begin by factoring out a 9 from each term:
9(x² - 2x + 1)
Now, find two terms that add up to -2 and equal 1 when multiplied. We get:
9(x - 1)(x - 1)
Or:
9(x - 1)²
Lunch break: In a recent survey of 643 working Americans ages 25-34, the average weekly amount spent on lunch as $43.21 with standard deviation $2.95. The weekly amounts are approximately bell-shaped. Part: 0 / 30 of 3 Parts Complete Part 1 of 3 Your Answer is incorrect (a) Estimate the percentage of amounts that were less than $40.26. Round the answer to one decimal place. Approximately % of the amounts were less than $40.26.
Answer:
107%
Step-by-step explanation:
Round up all possible algorithms
Which of the following is the value of a when the function (x) - 3|xlis written in the standard form of an absolute value
function?
Answer:1
Step-by-step explanation:2
2
The value of a when the function f(x) = 3|xl is written in the standard form of an absolute value function is 3.
What is meant by an absolute function ?An absolute function is defined as a function which consists of an algebraic expression that is within absolute value symbols.
Here,
The standard form of the absolute value function is written by,
f(x) = a|x|
Given that,
f(x) = 3|x|
Comparing this with the standard form, we get,
a|x| = 3|x|
Therefore, a = 3
Hence,
The value of a when the function f(x) = 3|xl is written in the standard form of an absolute value function is 3.
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what is the difference between the products of the digits in 425 and the sum of the digits in the numeral 92784
Answer: 10
Step-by-step explanation:
4 x 2 x 5 = 40
9 + 2 + 7 + 8 + 4 = 30
40 - 30 = 10
= 10
halla la suma y el producto de la PG 3,9,27,81,243
Answer:
huh ano yan huhu paki ayos ng sagot
Step-by-step explanation:
hahahhaa
CAN SOMEONE PLEASE HELP
A six sided number cube rolled once. what is the probability of landing on a multiple of 2. write the probability as a fraction, percent and decimal.
probability (as fraction)=
probability (as percent)=
probability (as decimal)=
Answer:
P( fraction) = 1/2
P ( percent) = 50%
P ( decimal) = .5
Step-by-step explanation:
The possible outcomes on a six sided cube are 1,2,3,4,5,6
Multiples of 2 are 2,4,6
P( multiple of 2) = number of multiples of 2 / total outcomes
= 3/6 = 1/2
P( fraction) = 1/2
P ( percent) = 50%
P ( decimal) = .5
prove that
[tex]2 \tan30 \div 1 + tan ^{2} 30 = sin60[/tex]
prove that
.
Step-by-step explanation:
2tan 30° / 1 + tan² 30° =
2(⅓√3) /1 + (⅓√3)² =
⅔√3 / 1+ ⅓ =
⅔√3 / 4/3 =
2/4 √3 =
½√3 = sin 60° (proven)
Which of the following is not true regarding the flow of information from the adjusted trial balance on the end-of-period spreadsheet?
The correct statement about the flow of information from the adjusted trial balance on the end-of-period spreadsheet is A. The revenue and expense account balances flow into the income statement.
What is an Adjusted Trial Balance?This refers to the general ledger balance after some changes have been done an account balance such as accrued expenses, depreciation, etc.
Therefore, we can see that from the complete information, the statement that is false about the adjusted trial balance on the end-of-period spreadsheet is option A because the revenue and expense account balances does not flow into the income statement.
The other options from the complete text are:
a. The revenue and expense account balances flow into the income statement.b. The asset and liability account balances flow into the retained earnings statement.c. The revenue and expense account balances flow into the retained earnings statement.d. The retained earnings and dividends account balances flow into the balance sheet.
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A student estimated based on the video that the ball left my hand 1.65 meters off the ground, and after 0.58 seconds the ball reached the maximum height of 3.26 meters. Use this information to find an equation of the form h = a ( t − t 1 ) 2 + h 1 for the height of the ball, in meters, after t seconds. h =
9514 1404 393
Answer:
h = -4.79(t -0.58)^2 +3.26
Step-by-step explanation:
The coordinates (t1, h1) are the time and height at the maximum. Then 'a' can be found from ...
h = a(t -t1)^2 +h1
1.65 = a(0 -0.58)^2 +3.26
-1.61 = 0.3364a . . . . . subtract 3.26
-4.786 = a . . . . . . . divide by the coefficient of a
The equation is ...
h = -4.79(t -0.58)^2 +3.26
The accompanying data represent the homework scores for material for a random sample of students in a college algebra course.
36
47
54
58
60
66
66
68
69
70
72
75
77
77
78
78
78
79
79
79
79
79
80
82
84
85
86
86
86
87
89
89
91
92
92
93
93
94
96
99
(a) Construct a relative frequency distribution with a lower class limit of the first class equal to 30 and a class width of 10.
(b) What is the probability a randomly selected student fails the homework (scores less than 70)? (The standard deviation is 13.64)
Simplify your answer to two decimal places.
Answer:
[tex]\begin{array}{ccc}{Class} & {Frequency} & {Relative\ Frequency} &{30-39} & {1} & {0.025} & {40-49} & {1} & {0.025} & {50 - 59} & {2} & {0.050} & {60 - 69} & {5} & {0.125} & {70 - 79} & {13} & {0.325} & {80 - 89} & {10} & {0.250} & {90 - 99} & {8} & {0.200} &{Total} & {40} & {1}\ \end{array}[/tex]
[tex]P(x < 70) = 0.225[/tex]
Step-by-step explanation:
Given
[tex]Lower = 30[/tex]
[tex]Width = 10[/tex]
Solving (a): The relative frequency table
First, we construct the frequency table using the given parameters.
[tex]\begin{array}{cc}{Class} & {Frequency} &{30-39} & {1} & {40-49} & {1} & {50 - 59} & {2} & {60 - 69} & {5} & {70 - 79} & {13} & {80 - 89} & {10} & {90 - 99} & {8} & {Total} & {40}\ \end{array}[/tex]
The relative frequency (RF) is calculated as:
[tex]RF = \frac{Frequency}{Total}[/tex]
Using the above formula to calculate the relative frequency, the relative frequency table is:
[tex]\begin{array}{ccc}{Class} & {Frequency} & {Relative\ Frequency} &{30-39} & {1} & {0.025} & {40-49} & {1} & {0.025} & {50 - 59} & {2} & {0.050} & {60 - 69} & {5} & {0.125} & {70 - 79} & {13} & {0.325} & {80 - 89} & {10} & {0.250} & {90 - 99} & {8} & {0.200} &{Total} & {40} & {1}\ \end{array}[/tex]
Solving (b): [tex]P(x < 70)[/tex]
To do this, we add up the relative frequencies of classes less than 70.
i.e.
[tex]P(x < 70) = [30 - 39] + [40 - 49] + [50 - 59] + [60 - 69][/tex]
So, we have:
[tex]P(x < 70) = 0.025 + 0.025 + 0.050 + 0.125[/tex]
[tex]P(x < 70) = 0.225[/tex]
How many outcomes (sample points) for a deal of two cards from a 52-card deck are possible? Report your answer as an integer.
Answer:
1326
Step-by-step explanation:
[tex]{52\choose2}=\frac{52!}{(52-2)!2!}=\frac{52!}{50!*2!}=1326[/tex]
Suppose that you are offered the following "deal.
You roll a six-sided die.
If you roll a 6, you win $8.
If you roll a 3, 4 or 5, you win $1.
Otherwise, you pay $7.
Complete the Probability Distribution table shown below.
Let X represent your profit and list the X values from smallest to largest. Roond to 4 decimal places where
appropriate.
Probability Distribution
Table
Х
P(X)
Find the expected profit. $
(Round to the nearest cent)
Answer:
expected profit is - $0.50
Step-by-step explanation:
1 $(7.00) 0.166666667 $(1.17)
2 $(7.00) 0.166666667 $(1.17)
3 $1.00 0.166666667 $0.17
4 $1.00 0.166666667 $0.17
5 $1.00 0.166666667 $0.17
6 $8.00 0.166666667 $1.33
$(0.50)
evaluate the expression when c= -4 and x=5
x-4c
Answer:
21
Step-by-step explanation:
Fill in x into 5 and c into -4
5-4(-4)
21
Answer: -11
Step-by-step explanation:
x=5
and
c=4
the equation written in numbers is:
5-4x4 which simplified equals 5-16
this equals 5-5-11 so it should be -11
Which of these is an example of technology?
an idea for a story
the first wheel ever built
an engineer
Answer:
the first wheel ever built
Answer:
The first wheel ever built
Step-by-step explanation
(*) Sorry for my late answer but I hope this helps others that are looking for this.
100% in the test :)
Find the distance between the two points.
(3,-9) and (-93,-37)
Answer:
100
Step-by-step explanation:
√(x2 - x1)² + (y2 - y1)²
√(-93 - 3)² + [-37 - (-9)]
√(-96)² + (-28)²
√9216 + 784
√10000
= 100
What is the inverse of function f? f(x)=3-x/7
Answer:
[tex] {f}^{ - 1} (x) = \frac{x}{3} + \frac{7}{3} [/tex]
hence option d is the correct option.
Answer:
Option C is answer.
Step-by-step explanation:
Hey there!
Given;
f(x) = (3-x) /7
Let f(x) be "y".
y = (3-x) /7
Interchanging "x" and "y".
x = (3-y)/7
7x = 3-y
y = 3-7x
Therefore, f'(x) = 3-7x.
Hope it helps!
will give brainyest (m^2/3 n^-1/3)^6
Step-by-step explanation:
here is the answer to your question
Round off to the underlined place values. 1 0.5242 2. 2.1616 3. 5.4852 4. 0.5862 5. 5.9658 6. 2.8959 7. 8.2584 8. 8.8956 9. 4.1492 1 5481
Answer:
wheres the underline pls let me know what is underlined ill answer it on comment
Make a substitution to express the integrand as a rational function and then evaluate the integral. int_(25)^(81) sqrt(x)/(x-1) dx
Let y = √x, so that y ² = x and 2y dy = dx. Then the integral becomes
[tex]\displaystyle \int_{25}^{81} \frac{\sqrt x}{x-1}\,\mathrm dx = \int_{\sqrt{25}}^{\sqrt{81}} \frac y{y^2-1}(2y\,\mathrm dy) = 2 \int_5^9 \frac{y^2}{y^2-1}\,\mathrm dy[/tex]
Now,
y ² / (y ² - 1) = 1 + 1 / (y ² - 1) = 1 + 1/2 (1/(y - 1) - 1/(y + 1))
so integrating gives us
[tex]\displaystyle 2\int_5^9\frac{y^2}{y^2-1}\,\mathrm dy= \int_5^9\left(2+\frac1{y-1}-\frac1{y+1}\right)\,\mathrm dy \\\\= (2y+\ln|y-1|-\ln|y+1|)\bigg|_5^9 \\\\= \boxed{8+\ln\left(\dfrac65\right)}[/tex]
Thirty-six percent of customers who purchased products from an e-commerce site had orders exceeding 110. If 17% of customers have orders exceeding 110 and also pay with the e-commerce site's sponsored credit card, determine the probability that a customer whose order exceeds 110 will pay with the sponsored credit card.
Answer:
The right solution is "0.5".
Step-by-step explanation:
According to the question,
P(pay with the sponsored credit card | order exceeds $110)
= [tex]\frac{P(Pay \ with \ the \ sponsored \ credit\ card\ and\ order\ exceeds\ 110)}{P(order \ exceeds \ 110)}[/tex]
= [tex]\frac{P(A \ and \ B)}{P(A)}[/tex]
By putting the values, we get
= [tex]\frac{0.17}{0.34}[/tex]
= [tex]0.5[/tex]
Thus, the above is the right solution.
Let (-5. 4) be a point on the terminal side of ø
Find the exact values of cos, csc , and tan
Answer:
[tex] \cos(x) = - \frac{5}{ \sqrt{41} } [/tex]
[tex] \csc(x) = \frac{ \sqrt{41} }{4} [/tex]
[tex] \tan(x) = - \frac{4}{5} [/tex]
Step-by-step explanation:
We know that (-5,4) is the terminal side. This means out legs will measure 5 and 4 if we graph it on a triangle.
We need to find the cos, csc, and tan measure of this point.
We can find cos by using the formula of
[tex] \cos(x) = \frac{adj}{hyp} [/tex]
The adjacent side is -5 and we can find the hypotenuse by doing pythagorean theorem.
[tex] { - 5}^{2} + {4}^{2} = \sqrt{41} [/tex]
So using the info the answer is
[tex] \cos(x) = \frac{ - 5}{ \sqrt{41} } [/tex]
We can find tan but first me must find sin x.
[tex] \sin(x) = \frac{opp}{hyp} [/tex]
[tex] \sin(x) = \frac{4}{ \sqrt{41} } [/tex]
So now we just use this identity,
[tex] \tan(x) = \sin(x) \div \cos(x) [/tex]
[tex] \tan(x) = \frac{ \frac{4}{ \sqrt{41} } }{ \frac{ - 5}{ \sqrt{41} } } = - \frac{4}{5} [/tex]
So tan x=
[tex] - \frac{ 4}{5} [/tex]
We can find csc by taking the reciprocal of sin so the answer is easy which is
[tex] \frac{ \sqrt{41} }{4} [/tex]
Barnaby decided to count the number of ducks and geese flying south for the winter. On the first day he counted 175 ducks and 63 geese. By the end of migration, Barnaby had counted 4,725 geese. If the ratio of ducks to geese remained the same (175 to 63), how many ducks did he count?
Answer:
13,125 ducks
Step-by-step explanation:
The ratio of ducks:geese on the first day was:
175:63
On the last day (end of migration), he counted 4,725 geese.
To find the number of ducks using the same ratio, we are first going to divide 4,725 by 63 to find what number all the ducks and geese multiplied by:
4,725/63 = 75
The geese multiplied by 75. This means the ducks also multiplied by 75:
175*75 = 13,125
Barnaby counted 13,125 ducks.
Hope it helps (●'◡'●)
had
n=2
n²-n-2
n² – 5n+6
Answer:
0，0
Step-by-step explanation:
n=2，
[tex] {2}^{2} - 2 - 2 = 0 [/tex]
[tex] {2}^{2} - 5 \times 2 + 6 = 0[/tex]
1. Willow Brook National Bank operates a drive-up teller window that allows customers to complete bank transactions without getting out of their cars. On weekday mornings, arrivals to the drive-up teller window occur at random, with an arrival rate of 24 customers per hour or 0.4 customers per minute.
a. What is the mean or expected number of customers that will arrive in a five-minute period?
b. Assume that the Poisson probability distribution can be used to describe the arrival process. Use the arrival rate in part (a) and compute the probabilities that exactly 0, 1, 2, and 3 customers will arrive during a five-minute period.
c. Delays are expected if more than three customers arrive during any five-minute period. What is the probability that delays will occur?
2. In the Willow Brook National Bank waiting line system (see Problem 1), assume that the service times for the drive-up teller follow an exponential probability distribution with a service rate of 36 customers per hour, or 0.6 customers per minute. Use the exponential probability distribution to answer the following questions:
a. What is the probability that the service time is one minute or less?
b. What is the probability that the service time is two minutes or less?
c. What is the probability that the service time is more than two minutes?
Answer:
1.
a. 2
b. 0.1353 probability that exactly 0 customers will arrive during a five-minute period, 0.2707 that exactly 1 customer will arrive, 0.2707 that exactly 2 customers will arrive and 0.1805 that exactly 3 customers will arrive.
c. 0.1428 = 14.28% probability that delays will occur.
2.
a. 0.4512 = 45.12% probability that the service time is one minute or less.
b. 0.6988 = 69.88% probability that the service time is two minutes or less.
c. 0.3012 = 30.12% probability that the service time is more than two minutes.
Step-by-step explanation:
Poisson distribution:
In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:
[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]
In which
x is the number of sucesses
e = 2.71828 is the Euler number
[tex]\mu[/tex] is the mean in the given interval.
Exponential distribution:
The exponential probability distribution, with mean m, is described by the following equation:
[tex]f(x) = \mu e^{-\mu x}[/tex]
In which [tex]\mu = \frac{1}{m}[/tex] is the decay parameter.
The probability that x is lower or equal to a is given by:
[tex]P(X \leq x) = \int\limits^a_0 {f(x)} \, dx[/tex]
Which has the following solution:
[tex]P(X \leq x) = 1 - e^{-\mu x}[/tex]
The probability of finding a value higher than x is:
[tex]P(X > x) = 1 - P(X \leq x) = 1 - (1 - e^{-\mu x}) = e^{-\mu x}[/tex]
Question 1:
a. What is the mean or expected number of customers that will arrive in a five-minute period?
0.4 customers per minute, so for 5 minutes:
[tex]\mu = 0.4*5 = 2[/tex]
So 2 is the answer.
Question b:
[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]
[tex]P(X = 0) = \frac{e^{-2}*2^{0}}{(0)!} = 0.1353[/tex]
[tex]P(X = 1) = \frac{e^{-2}*2^{1}}{(1)!} = 0.2707[/tex]
[tex]P(X = 2) = \frac{e^{-2}*2^{2}}{(2)!} = 0.2707[/tex]
[tex]P(X = 3) = \frac{e^{-2}*2^{3}}{(3)!} = 0.1805[/tex]
0.1353 probability that exactly 0 customers will arrive during a five-minute period, 0.2707 that exactly 1 customer will arrive, 0.2707 that exactly 2 customers will arrive and 0.1805 that exactly 3 customers will arrive.
Question c:
This is:
[tex]P(X > 3) = 1 - P(X \leq 3)[/tex]
In which:
[tex]P(X \leq 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)[/tex]
The values we have in item b, so:
[tex]P(X \leq 3) = 0.1353 + 0.2707 + 0.2707 + 0.1805 = 0.8572[/tex]
[tex]P(X > 3) = 1 - P(X \leq 3) = 1 - 0.8572 = 0.1428[/tex]
0.1428 = 14.28% probability that delays will occur.
Question 2:
[tex]\mu = 0.6[/tex]
a. What is the probability that the service time is one minute or less?
[tex]P(X \leq 1) = 1 - e^{-0.6} = 0.4512[/tex]
0.4512 = 45.12% probability that the service time is one minute or less.
b. What is the probability that the service time is two minutes or less?
[tex]P(X \leq 2) = 1 - e^{-0.6(2)} = 1 - e^{-1.2} = 0.6988[/tex]
0.6988 = 69.88% probability that the service time is two minutes or less.
c. What is the probability that the service time is more than two minutes?
[tex]P(X > 2) = e^{-1.2} = 0.3012[/tex]
0.3012 = 30.12% probability that the service time is more than two minutes.
Please help i need answer asap
Answer:
23
Step-by-step explanation:
7. What is given in the problem?
A. Radius of 80m C. Radius of 80 ft.
B. Diameter of 40 ft. D. Diameter of 40 m paki sagot
Answer:
radius of 80cm is the answer
Given points A(-1, -2) and B(2, 4) where AP: BP=1:2, find the locus of point P.
Answer:
[tex]x^2 + 4x + y^2 +8y = 0[/tex]
Step-by-step explanation:
Given
[tex]A = (-1,-2)[/tex]
[tex]B = (2,4)[/tex]
[tex]AP:BP = 1 : 2[/tex]
Required
The locus of P
[tex]AP:BP = 1 : 2[/tex]
Express as fraction
[tex]\frac{AP}{BP} = \frac{1}{2}[/tex]
Cross multiply
[tex]2AP = BP[/tex]
Calculate AP and BP using the following distance formula:
[tex]d = \sqrt{(x - x_1)^2 + (y - y_1)^2}[/tex]
So, we have:
[tex]2 * \sqrt{(x - -1)^2 + (y - -2)^2} = \sqrt{(x - 2)^2 + (y - 4)^2}[/tex]
[tex]2 * \sqrt{(x +1)^2 + (y +2)^2} = \sqrt{(x - 2)^2 + (y - 4)^2}[/tex]
Take square of both sides
[tex]4 * [(x +1)^2 + (y +2)^2] = (x - 2)^2 + (y - 4)^2[/tex]
Evaluate all squares
[tex]4 * [x^2 + 2x + 1 + y^2 +4y + 4] = x^2 - 4x + 4 + y^2 - 8y + 16[/tex]
Collect and evaluate like terms
[tex]4 * [x^2 + 2x + y^2 +4y + 5] = x^2 - 4x + y^2 - 8y + 20[/tex]
Open brackets
[tex]4x^2 + 8x + 4y^2 +16y + 20 = x^2 - 4x + y^2 - 8y + 20[/tex]
Collect like terms
[tex]4x^2 - x^2 + 8x + 4x + 4y^2 -y^2 +16y + 8y + 20 - 20 = 0[/tex]
[tex]3x^2 + 12x + 3y^2 +24y = 0[/tex]
Divide through by 3
[tex]x^2 + 4x + y^2 +8y = 0[/tex]
The first five terms of an arithmetic sequence are shown below:
20, 17, 14, 11, 8, . . .
Let n represent the term number and f(n) the term in the sequence.
Choose a function that represents the sequence.
The answer to this question is f(n) = -3 + 23
Now my question is, how do you find the solution? I was taught the explicit formula is f(n) = m(n) + b, but no matter how many times I've tried to plug in the numbers I cannot seem to get the right answer. Please help me and do show the entire process and the steps.
Answer:
The function represents the sequence is - 3 n + 23.
Step-by-step explanation:
20. 17, 14, 11, 8,......
Here, the first term is
a = 20
Common difference, d = -3
Let the nth term is Tn.
Tn = a + (n -1) d
Tn = 20 + (n -1) x (-3)
Tn = 20 - 3 n + 3
Tn = 23 - 3 n = - 3 n + 23
So, the function represents the sequence is - 3 n + 23.
Answer:
Y'all know what it is already, but I want points, so: f(n) = -3n + 23
For the following inequality, find a solution for the variable. Show all of your work and use complete sentences to explain the solving process that you used to find a solution for the inequality. Be sure to include at least two terms from the word bank. 1/4 x ≤-3
Answer:
x ≤ -12
Step-by-step explanation:
To get x by itself you simply multiply both sides by 4, since 1/4 * 4 = 1.
for maths answer this question please
4x-9=6-9
Answer:
x = 1.5
Step-by-step explanation:
First, calculate 6-9, which is -3.
Then we add 9 on both sides so that on the left, we only have 4x, and on the right, we have 6.
Then divide by 4 on both sides to get x = 1.5
Tara makes 30 cups of donut topping by mixing sugar and cinnamon. The ratio of sugar to cinnamon is 3:2
How much sugar did Tara use in the donut topping?
Answer:
18
Step-by-step explanation:
3:2 means 3/2 or 3÷2
but its better to leave it as
3/2
