Julian's carpet has an area of 160 square feet. He hires the Carpet Pro carpet cleaning service, which is able to clean 9 square feet of his carpet every minute. Therefore, in the first minute, CarpetPro is able to clean 9 square feet of Julian's carpet (leaving 151 square feet remaining to be cleaned). In the second minute, the cleaner is again able to clean 9 square feet of carpet (leaving 142 square feet to be cleaned), etc. Which of the following functions expresses the number of square feet that still remain to be cleaned after t minutes from the time that the carpet cleaner began cleaning this carpet. O A(t) = 220 - 9t O A(t) = 220 - 0.1^t O A(t) = 220(0.1)^t O A(t) = 220(0.9t) O A(t) = 220 - 0.9t
Answers
The function that expresses the area of the 160 square feet carpet remaining after t minute is; A(t) = 160 - 9·t
What is a mathematical function?A function is a rule that maps the elements of a set known as the input of the function, to the elements of another set, known as the output of the function, such that each element of the input is mapped to exactly one element of the output set.
The area Julian's carpet covers = 160 square feet
The area the Carpet Pro cleaning service is able to clean every minute = 9 square feet.
A table of values showing the area of the carpet remaining after each minute of cleaning by Carpet Pro, can be presented as follows;
Time, t (minute) \({}\) Area remaining to be cleaned (square feet), A(t)
0 \({}\) 160
1 \({}\) 151
2 \({}\) 142
3 \({}\) 133
4 \({}\) 124
5 \({}\) 115
The change in the area of the carpet remaining is a constant and therefore, the first difference of the values in the above table is a constant which indicates that the relationship is a linear relationship, with an equation of the form y = m·x + c
Where;
m = The slope = (151 - 160)/(1 - 0) = -9
c = The y-intercept The value of the function when the input (time) is zero, which is 160
c = 160
x = The number of minutes that elapse, t
y = The number of square feet remaining after t minutes, A(t)
Plugging in the above value, we get;
A(t) = -9·yt + 160
The function that expresses the number of square feet remaining A(t) after t minutes from the time the carpet cleaner began cleaning the carpet is; A(t) = 160 - 9·t
The possible options based on a similar question posted online and the 160 square feet area of the carpet specified in the question are;
A(t) = 160 - 9·t
A(t) = 160 - 0.1^t
A(t) = 160·(0.1)^t
A(t) = 160·(0.9·t)
A(t) = 160 - 0.9·t
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Related Questions
What is the circumference of the circle if the radius is 10 cm?
Answers
Answer for this question
The circumference of the circle is 62.8cm.
The Circumference of the circle is given by the formula,
Circumference = 2*\(\pi\)*r cm.........equation 1
Given, r = 10cm
On substituting the radius value in equation 1
Circumference = 2*\(\pi\)*10
Circumference = 62.8 cm
Therefore, the circumference of the circle is 62.8cm.
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A soccer team traveled to a game in 4 vans. Each van held 6 players. Two of the players are goalkeepers. How many of the players are not goalkeepers?
Answers
Work:
4 * 6 = 24
24 - 2 = 22
Answer:
22
Step-by-step explanation:
(6x4)-2
multiply the number of vans by the number of player in each van which equals 24 then subtract the 2 goal keepers which equals 22.
g The weight of a certain type of apple is normally distributed with a mean of 10.56 ounces and standard deviation of 0.9 ounces. What is the first quartile, Q subscript 1, of the weight of this type of apple?
Answers
Answer:
First Quartile Q1 = 9.9525
Step-by-step explanation:
For a standard normal distribution,
First quartile Q1 = μ - 0.675 σ
From the question mean μ = 10.56
Standard deviation σ = 0.9
Plugging these values into the first quartile equation, we have;
Q1 = 10.56 -0.675(0.9)
Q1 = 10.56 - 0.6075
Q1 = 9.9525
HELP WILL GIVE BRAINLIST: Answers A: $26.81 b: $22.98 c: $19:98 D $3.83
Answers
Answer:
B 22.98
Step-by-step explanation:
divided 11.49 by 3, you get 3.83, then multiply it by 6. thats your answer
Answer:
B: $22.98
Step-by-step explanation:
The first thing we need to do for this question is find a pattern. Find a pattern between the prices of 3 pizzas, 4 pizzas, and 5 pizzas. Once we have this pattern, we can solve for x.
To find the pattern, we must first subtract the price of 4 pizzas from the price of 3 pizzas. This difference is 3.83, so we know the price went up $3.83. Next, subtract the price of 5 pizzas from the price of 4 pizzas. This is also 3.83, so we know that for every extra pizza added, the price goes up $3.83.
Now that we have our pattern, we can solve for x. Because the price goes up $3.83 for every extra pizza added, we can add $3.83 to the price of 5 pizzas. This will give us $22.98. We now know the value of x and the price of 6 pizzas.
I hope this helps. Please let me know if you need any more help. Have a great day and good luck!
Alondra is asked about her age. She answers as follows. "My age is 6 more than four times the age of my son." How old is her son if Alondra is 46 years old?
Answers
Answer:
10 years old
Step-by-step explanation:
lets break it down:
6 more means +6
four times means *4
so if her son is x years old, she is 4x+6
since we know she's 46, we know that 4x+6=46
now we just solve the equation
4x+6=46
-6 on both sides
4x=40
/4 on both sides
x=10
only people who know the answer
Jose wants to put a fence around his rectangular garden. His garden measures 33 feet by 39 feet. The garde has a path around it that is 3 feet wide. How much fencing material does Jose need to enclose the garden path?
Answers
Answer:
156ft of material.
Step-by-step explanation:
Since the garden path borders the garden and is 3 feet wide, it increases the side lengths of his garden by 3 feet on each side. Then we just find the perimeter using the new values:
\(P=36+36+42+42=156\)
If this helped, a brainliest answer would be greatly appreciated!
2. this data came from a pre-employment drug screening. positive test result negative test result (drug use is indicated) (drug use is not indicated) subject uses drugs 44 6 (true positive) (false negative) subject is not a drug user 90 860 (false positive) (true negative) (a) false positive find the probability of selecting a subject with a positive test result given that the subject does not use drugs. (b) false negative find the probability of selecting a subject with a negative test result given that the subject uses drugs.
Answers
a) The probability of selecting a subject with a positive test result given that the subject does not use drugs is equals to the 0.09473.
b) The probability of selecting a subject with a negative test result given that the subject uses drugs is equals to the 0.12.
The confusion matrix of the pre employment drug screening data is present above. It contains positive test result, Negative test result and Total.
Subject uses drugs 44 6 = 50
Subject does not use drugs 90 860 = 950
Similarly , 90 + 44 = 134 , 860 + 6 = 886 and 950 + 50 = 1000.
a) We have to determine the probability of selecting a subject with a positive test result that the subject does not use drug. Let A be the event that the subject with a positive test result and B be the event that subject does not use drug. We have to determine P(A/B). From conditional probability, P(A/B) = P(A and B)/P(B)
= 90/950 = 0.09473
Hence, the probability of selecting a subject with a positive test result given that the subject does not use drug is 0.09473.
b) We have to calculate the probability of selecting a subject with a negative test result that the subject use drugs. Let R be the event that the subject with a negative test result and S be the event that subject uses drug. We have to calculate the value of P(R/S). By using Bayes theorem, P(R/S) = P(R and S) /P(S)
= 6/50 = 0.12
Hence, the probability of selecting a subject with a negative test result given that the subject uses drug is 0.12.
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Complete question:
The above table complete the question.
2. this data came from a pre-employment drug screening. positive test result negative test result (drug use is indicated) (drug use is not indicated) subject uses drugs 44 6 (true positive) (false negative) subject is not a drug user 90 860 (false positive) (true negative) (a) false positive find the probability of selecting a subject with a positive test result given that the subject does not use drugs. (b) false negative find the probability of selecting a subject with a negative test result given that the subject uses drugs.
For the following vectors, (a) find the dot product v•w ; (b) find the angle between v and w , (c) state whether the vectors are parallel, octagonal, or neither. V=-3i-4j, w=6i+8j
A- v•w
B-the angle between v and w is theta ^•?
C- the vectors v and w are?
Answers
B) The angle between vectors v and w can be found using the formula: cos(theta) = (v • w) / (||v|| ||w||), where ||v|| and ||w|| are the magnitudes of vectors v and w respectively.
First, we need to find ||v|| and ||w||:
||v|| = sqrt((-3)^2 + (-4)^2) = 5
||w|| = sqrt((6)^2 + (8)^2) = 10
Now, we can substitute in the values to get:
cos(theta) = (-50) / (5 * 10) = -1
theta = arccos(-1) = pi radians or 180 degrees.
Therefore, the angle between vectors v and w is 180 degrees.
C) Two vectors are parallel if their directions are the same, which can be determined by comparing their unit vectors.
The unit vector of v is:
v_hat = v / ||v|| = (-3/5)i + (-4/5)j
The unit vector of w is:
w_hat = w / ||w|| = (6/10)i + (8/10)j = (3/5)i + (4/5)j
We can see that the unit vectors are in opposite directions, which means that the vectors are anti-parallel or opposite. Therefore, the vectors v and w are neither parallel nor orthogonal.
simplify the expression: 14-|-10+3|
Answers
Answer:
7
Step-by-step explanation:
14-|-10+3|
First find what is in the absolute value
14-|-7|
Take the absolute value
14 - 7
7
I hopes this helped .
Bye !
The area of a square is 36 sq.cm, then its perimeter is a) 24 cm b) 6 cm c) 144 cm d) 36 cm
Answers
Answer:
Step-by-step explanation:
3.6*
It is very easy to find the perimeter of a square when its area is given in the question. For that, you only ned to know one fomula. That formula is: Area = side^2
For this particular question, the given value for the area of the square is 36 sq.cm. So, we can solve for the side(s) by substituting the given value in the above mentioned formula.
We get
36 = s^2
Now, we need to get the square root of both sides, which gives us
s = √36 s = 6 cm
Since all the sides of a square are equal in length, the side length is 6 cm. Now to determine the perimeter, we must multiply the side length by 4 (because there are 4 equal sides in a square). That gives us Perimeter = 4 x side length Perimeter = 4 x 6 cm.
Therefore, the perimeter of the square is 24 cm.
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Jordan has more than 25 coins in his collection.
Which inequality shows the number of coins in Jordan's collection?
Answers
Answer:
x + 25 is an expression, not an inequality.
Jordan has more than 25 coins, so this means that the > symbol will be used.
The answer with this symbol is B. x>25.
Step-by-step explanation:
Which function is graphed below?
Answers
Y=3(1/3)^x
Petra jogs 6 miles in 42 minutes. At this rate, how long would it take her to jog 8 miles?
Answers
Distance 1 / Time 1 = Distance 2 / Time 2
Using the information given:
6 miles / 42 minutes = 8 miles / Time 2
To solve for Time 2, we can cross-multiply and then divide:
6 miles * Time 2 = 8 miles * 42 minutes
6 * Time 2 = 8 * 42
6 * Time 2 = 336
Now, we divide both sides by 6 to isolate Time 2:
Time 2 = 336 / 6
Time 2 = 56 minutes
Therefore, it would take Petra 56 minutes to jog 8 miles at the same rate.
Answer:
56 minutes
Step-by-step explanation:
We can use proportions to solve.
6 miles 8 miles
------------ = ------------------
42 minutes x minutes
Using cross products.
6x = 42 *8
Divide each side by 6
x = 42/6 * 8
x = 7*8
x = 56
What is the place value of 1 of 574.8931.
Answers
I need help
Can you help me please!!!
Answers
Answer:
Step-by-step explanation:
The triangles are similar.
x/(x+4) = 7.2/12
x/(x+4) = 0.6
x = 0.6(x+4)
0.4x + 2.4
x = 6
Guests staying at Marada Inn were asked to rate the quality of their accommodations
as being excellent (E), above average (AA), average (A), below average (BA), or poor
(P). The ratings provided by a sample of 20 guests are shown below. Give the
frequencies, in order, for the frequency distribution shown.
Α ΒΑ ΑΑ E E
AA P ΒΑ ΑΑ Α
A P A BA A A E A PA
Answers
If guests staying at Marada Inn were asked to rate the quality of their accommodations as being excellent (E), above average (AA), average (A), below average (BA), or poor (P). The frequency is : 1, 8, 6, 3, 2.
FrequencyAnalysis
E = E =1
AA= AA +AA + AA + AA + AA+ AA + AA +AA = 8
A= A + A+ A+ A+ A+ A = 6
BA = BA + BA + BA =3
P = P + P =2
Hence,
Class frequency
E 1
AA 8
A 6
BA 3
P 2
Total 20
Therefore 1, 8, 6, 3, 2 is the frequency .
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Which is the standard form for this number?
(9 × 10) + (3 × 1) + (5 ×
1
10
) + (6 ×
1
1,000
)
Answers
Answer:
66,143
Step-by-step explanation:
is question the following: (9 x 10) + (5 x 10) + (6 x 11,000)??
PLEASE HELP!
A game board with 17 spaces. Start, green, green, star, quesiton mark, question mark, star, question mark, green, cat town, green, green, star, question mark, green, green, star, green, end.
You are playing a board game and your playing piece begins the game at START. You roll a single number cube numbered 1 to 6 to find out how many spaces you can move.
What is the theoretical probability of landing on a question mark space on your first roll.
A 1/6
B 1/4
C 1/3
D 1/2
Answers
Answer:
C 1/3
Step-by-step explanation:
out of the 6 possible moves you have the possibility of landing on question mark twice. 2/6 -> 1/3
1,547.1892 rounded to the nearest hundredth
Answers
Answer:
I, 550
Step-by-step explanation:
Is the nearest hundredth
write an equation in slope intercept form for the line that has a slope of 1/3 and passes through the point (3, -20)
Answers
y = 1/3x - 21 is the equation of the line in slope-intercept form.
What is a slope?
Slope is a measure of the steepness or incline of a line. It describes how much the dependent variable (usually y) changes for a given change in the independent variable (usually x).
The slope-intercept form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept.
We are given that the slope is 1/3 and that the line passes through the point (3, -20). We can use the point-slope form of a linear equation to find the equation of the line:
y - y1 = m(x - x1)
where (x1, y1) is the point through which the line passes, and m is the slope. Plugging in the values we have:
y - (-20) = 1/3(x - 3)
Simplifying this equation:
y + 20 = 1/3x - 1
Subtracting 20 from both sides:
y = 1/3x - 21
This is the equation of the line in slope-intercept form.
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Given that 9 x − 4 y = 20 Find y when x = − 2 Give your answer as an improper fraction in its simplest form
Answers
Answer:
\(\boxed{\df\ \dfrac{-19}{2}}\)
Step-by-step explanation:
Hi,
x=-2
it gives
9*(-2)-4y=20
<=> -18-4y=20
<=> 18-18-4y=20+18=38
<=> -4y=38
<=> y = -38/4=-19/2
hope this helps
Determine the period of this Function.
Answers
Answer:
4p
Step-by-step explanation:
The period is basically the difference in x from one "peak" to the other "peak".
The peaks are the highest points of a sinosodial function, and the figure them out, use the formula:
\(|peak_1-peak_2|=period\)
We know the first peak is at about x=0\(\pi\)
We know the second peak is at about x=4\(\pi\)
So plugging this in:
\(|0-4\pi |=4\pi\)
So the period is \(4\pi\)
I am assuming "p" stands for \(\pi\), so the answer should be 4p.
There are other ways to find the period, for instance if you are given a sinusodial function in writing instead of a graph.
Here is an example:
5sin(5x+2)+3
If we want to find period, we need to find what we call "b"
b is the number in front of x, which we can identify as bx, which in this case is 5x above.
Now what do we do with this "b"?
This is the value we need to find our period.
If you know b, you can use this formula to find the period:
\(\frac{2\pi }{b}=p\)
And when we plug in b:
\(\frac{2\pi }{5}\)
=
1.257, which would be your period.
THis can also be reworked so that you can find b:
If the formula for period is \(\frac{2\pi }{b}=p\), then the opposite formula would be \(\frac{2\pi }{ p}=b\)
And when you plug the period you have in:
\(\frac{2\pi }{1.257}\)
=
5
Anyway, your answer is 4p.
Hope this helps!
The scale on a map shows that 10 kilometers is represented by 4 centimeters. Which proportion can be used to find
the actual distance, x, represented by 20 centimeters on the map?
Answers
\(\frac{10}{4}\) = \(\frac{x}{20}\) proportion can be used to find the actual distance 'x' represented by 20 centimeters on the map.
What is the formula of unitary method?The unitary method is used to find the value of a single unit from a given multiple.
For example: 50 boxes are of 500 rupees so what will be the price of 1 box
50 boxes → Rs. 500
1 box → 500/50
1 box → Rs. 10
This method is mostly used for ratio and proportion concept.
Here, we have given that the scale on a map shows that 10 kilometers is represented by 4 centimeters.
so,
4 centimeters → 10 kilometers
1 centimeter → 10/4 kilometers ------- ( i )
for 20 centimeters
20 centimeter → x kilometers
1 centimeter → x / 20 kilometers ------- ( ii )
on equating both the equations ( i ) and ( ii )
x / 20 = 10 / 4
x = 50 kilometers
Hence, \(\frac{10}{4}\) = \(\frac{x}{20}\) proportion can be used to find the actual distance 'x' represented by 20 centimeters on the map.
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I need help with this
Answers
The statement that is equivalent to |6x-3|=3 is: 6x-3=3 or 6x-3=-3
For the equation to be true, two scenarios need to be considered:
When the expression 6x-3 is positive and equals 3:
6x-3 = 3
When the expression 6x-3 is negative and equals -3:
6x-3 = -3
By solving these two equations, we can find the equivalent statement:
Solving 6x-3 = 3:
Adding 3 to both sides gives us:
6x = 6
Dividing both sides by 6:
x = 1
Solving 6x-3 = -3:
Adding 3 to both sides gives us:
6x = 0
Dividing both sides by 6:
x = 0
Therefore, the equivalent statement to |6x-3|=3 is:
6x-3=3 or 6x-3=-3, which can be further simplified to:
6x-3=3 or 6x-3=-3
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i’ll mark brainliest
Answers
Answer:108xy^3
Step-by-step explanation:
theme: random variables, probability distributions and expected valueJanet plays a dice game. If she rolls a 1, she wins $3 while if she rolls a 2, she wins $1. If she rolls a 3,4, or5, she loses $1 and if a 6 is rolled, she doesn't win or lose. Find the expected value of this dice game. •Round to the nearest cent. Do not round until the final calculation.
Answers
Expected value = $0.17
Explanation:
we find the probability of each numbers
Total numbers = 6
probability of 1 = 1/6
probability of 2 = 1/6
probability of 3 = 1/6
probability of 4 = 1/6
probability of 5 = 1/6
probability of 6 = 1/6
Expected value = sum of (the probabilty of each number × the amount for rolling each)
A win = positive while a loss is negative
no win or loss = 0
rolls a 1, wins $3; if she rolls a 2, she wins $1. If she rolls a 3,4, or5, she loses $1 and if a 6 is rolled, she doesn't win or lose
Expected value = (1/6 × 3) + (1/6 × 1) - (1/6 × 1) - (1/6 × 1) - (1/6 × 1) + (1/6 × 0)
= 3/6 + 1/6 - 1/6 - 1/6 -1/6 + 0 = 1/2 -2/6 = 1/2 - 1/3
Expected value = 0.5 - 0.33
Expected value = 0.17 (nearest cent)
Hence, it means Janet gained money.
unction g is a transformation of the parent tangent function such that
. Which graph represents function g?
A.
The graph shows trigonometric functions intercept the x-axis at minus 3, 0.2, and 3.5 units also pass parallel to the g of the x-axis.
B.
The trigonometric functions intercept the x-axis at minus 4.2, minus 1.1, 2, and 5 units also pass parallel to the g of the x-axis.
C.
The trigonometric functions intercept the x-axis at minus 3.5, minus 0.2, and 3 units also pass parallel to the g of the x-axis.
D.
The trigonometric functions intercept the x-axis at minus 5, minus 2, 1, and 4.2 units also pass parallel to the g of the x-axis.
Answers
Answer:
A.
The graph shows trigonometric functions intercept the x-axis at minus 3, 0.2, and 3.5 units also pass parallel to the g of the x-axis.
last question pls help :))
Answers
Answer:
4/5
Step-by-step explanation:
( 4x² - 5x + 1) + (-3x² + x +5)
Answers
Answer:
x^2-4x+6
Step-by-step explanation:
\((4x^2 -5x +1) +(-3x^2 +x+5)\\\\\mathrm{Remove\:parentheses}:\quad \left(a\right)=a\\=4x^2-5x+1-3x^2+x+5\\\\\mathrm{Group\:like\:terms}\\=4x^2-3x^2-5x+x+1+5\\\\\mathrm{Add\:similar\:elements:}\:4x^2-3x^2=x^2\\=x^2-5x+x+1+5\\\\\mathrm{Add\:similar\:elements:}\:-5x+x=-4x\\=x^2-4x+1+5\\\\\mathrm{Add\:the\:numbers:}\:1+5=6\\=x^2-4x+6\)
Answer:
Step-by-step explanation:
4x^2 - 3x^2 - 5x + x + 1 + 5
x^2 - 4x + 6
Calculate: x/y = z/100
y= 137
x = 86.33
What is z?
Answers
The value of z is 8633/137 or 63.01, approximately.
Step-by-step explanation:1. Write the expression.\(\frac{x}{y} =\frac{z}{100}\)
2. Multiply both sides of the equaton by "100".\(\frac{x}{y}*100 =\frac{z}{100}*100\\ \\100\frac{x}{y} =z\\ \\z=100\frac{x}{y}\)
3. Substitute "x" and "y" by the given values and calculate "z".\(z=100\frac{(86.33)}{(137)}\\ \\z=\frac{8633}{137}=63.01\)
4. Verify using the exact value of "z".If the calculated value of "z" is correct, then the original equation should return the same value on both sides of the equal symbol (=) when substiting all the variables by their respective value.
\(\frac{86.33}{137} =\frac{\frac{8633}{137}}{100}\\ \\0.63=0.63\)
That's correct!
Hence, the value of z is 8633/137 or 63.01.
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