Answer: -x+12
Step-by-step explanation:
tested
A home improvement contractor is painting the walls and ceiling of a rectangular room. The volume of the room is 875.00 cubic feet. The cost of wall paint is $0.08 per square foot and the cost of ceiling paint is $0.14 per square foot. Find the room dimensions that result in a minimum cost for the paint.
Answer:
The room dimensions for a minimum cost are: sides of 10 feet and height of 8.75 feet.
Step-by-step explanation:
We have a rectangular room with sides x and height y.
The volume of the room is 875 cubic feet, and can be expressed as:
[tex]V=x^2y=875[/tex]
With this equation we can define y in function of x as:
[tex]x^2y=875\\\\y=\dfrac{875}{x^2}[/tex]
The cost of wall paint is $0.08 per square foot. We have 4 walls which have an area Aw:
[tex]A_w=xy=x\cdot \dfrac{875}{x^2}=\dfrac{875}{x}[/tex]
The cost of ceiling paint is $0.14 per square foot. We have only one ceiling with an area:
[tex]A_c=x^2[/tex]
We can express the total cost of painting as:
[tex]C=0.08\cdot (4\cdot A_w)+0.14\cdot A_c\\\\C=0.08\cdot (4\cdot \dfrac{875}{x})+0.14\cdot x^2\\\\\\C=\dfrac{280}{x}+0.14x^2[/tex]
To calculate the minimum cost, we derive this function C and equal to zero:
[tex]\dfrac{dC}{dx}=280(-1)\dfrac{1}{x^2}+0.14(2x)=0\\\\\\-\dfrac{280}{x^2}+0.28x=0\\\\\\0.28x=\dfrac{280}{x^2}\\\\\\x^3=\dfrac{280}{0.28}=1000\\\\\\x=\sqrt[3]{1000} =10[/tex]
The sides of the room have to be x=10 feet.
The height can be calculated as:
[tex]y=875/x^2=875/(10^2)=875/100=8.75[/tex]
The room will have sides of 10 feet and a height of 8.75 feet.
In which set does -15/2 belong? Answer choices: Rational numbers
Integers
Whole numbers
All of the above
Answer:
Rational numbersStep-by-step explanation:
When an integers or a whole number is divided by another integer or whole number the result is a whole number.
Hence [tex]\frac{-15}{2}[/tex] is a rational number
This is because both -15 and 2 are integer numbers
Answer:
rational
Step-by-step explanation:
Can someone please help me?
Answer:
''0 is neither a rational number nor an irrational number.''
Step-by-step explanation:
Zero is a rational number. Zero can be written as a fraction, where p/q = 0, where p = 0 and q is any non-zero integer. Hence, 0 is a rational number.
A taxi company charges based on the function rule P(t) = 0.5t + 2.5, where t is the
time taken for a trip (in minutes) and P(t) is the amount in dollars. If a trip takes 30 minutes, how much will it cost the client?
Answer:
$17.5
Step-by-step explanation:
hello,
we need to compute P(30)
P(30) = 0.5*30 + 2.5 = 15 + 2.5 = 17.5
hope this helps
Rectangle is 5ft in length and 3 ft in height. What is the area of the rectangle
Answer: 15
Step-by-step explanation:
to find the area multiply the length by height
in this case it’s 5ft and 3ft
5 • 3 = 15
A=15
The city of Oakdale wishes to see if there is a linear relationship between the temperature and the amount of electricity used (in kilowatts). Using the estimated regression equation found by using Temperature as the predictor variable, find a point estimate Kilowatt usage when the Temperature is 90 degrees outside?
The question is incomplete. The complete question is as follows.
The city of Oakdale wishes to see if there is a linear relantionship between the temperature and the amount of electricity used (in kilowatts). Using the estimated regression equation found by using Temperature as the predictor variable, find a pont estimate Kilowatt usage when the Temperature is 90 degrees outside?
Temperature(x) Kilowatts(y)
73 680
78 760
85 910
98 1510
93 1170
83 888
92 923
81 837
76 600
105 1800
Answer: The point estimate is 1132.5 Kilowatts
Step-by-step explanation: Regression analysis is used to find an equation that fits the data. Once this equation is found, it's used to make predictions. One of the regressions is linear regression.
To find the linear regression model:
1) Create a table with the following: ∑y; ∑x; ∑xy; ∑x²; ∑y²;
2) Use these equations to find coefficients a and b:
a = (∑y)(∑x²) - (∑x)(∑yx) / n(∑x²) - (∑x)²
b = n(∑xy) - (∑x)(∑y) / n(∑x²) - (∑x)²
3) Substitute the coefficients into the equation of form: y = a + bx
For the table above, the linear regression equation is:
y = - 2004 + 34.85x
When Temperature is 90, i.e. x = 90:
y = - 2004 + 34.85*90
y = 1132.5
The estimate Kilowatt is 1132.5.
a. Draw a geometric diagram of this scenario using two parallel lines and one
transversal. (Remember that a transversal is a line which cuts across
parallel lines.) Label the angles, parallel lines, and transversal as indicated
in the diagram above.
Answer:
See Attachment
Step-by-step explanation:
I have attached the geometric diagram of the scenario below.
Lines t and u are the two parallel linesLine v is the transversal line.The angles which t makes with v are 1 and a respectively.The angles which u makes with v are b and 2 respectively.parallel lines = lines t and u, transversal line = line v, the angles which t makes with v are 1 and a, the angles which u makes with v are b and 2.
Please answer this correctly
Answer:
Skateboard:
Scooter:
Bike:
Step-by-step explanation:
19 + 14 + 17 = 50 (there were 50 customers)
19 out of 50 = 38%
14 out of 50 = 28%
17 out of 50 = 34%
Hope this helps!
A box containing 15 DVDs is selling for $156.00. The box contains some
DVDs worth $11.00 each and some DVDs worth $9.00 each. Which system of
equations can be used to determine x, the number of $11.00 DVDs, and y, the
number of $9.00 DVDs?
Answer:
Step-by-step explanation:
x + y = 15
11x + 9y = 156
For each ordered pair, determine whether it is a solution to x=-3.
Answer: no, no, no, yes
Step-by-step explanation:
x=-3 is a vertical line. It goes straight up and down at x=-3. In order for the points to be on this line, the x-axis has to be -3. Looking at all the choices, all points are not a solution with the exception of (-3,0) which is right on the line.
Answer:
no no no yes
Step-by-step explanation:
i think
Verify the identity. Please explain step by step.
Step-by-step explanation:
sin²α − sin⁴α
Factor out sin²α.
sin²α (1 − sin²α)
Use Pythagorean theorem.
(1 − cos²α) cos²α
Distribute.
cos²α − cos⁴α
an oil company conducts a geological study that indicates that an exploratory oil well should have a 20% chance of striking oil. assuming independence, what is that probability that the third strike comes on the seventh well drilled
Answer:
4.92% probability that the third strike comes on the seventh well drilled
Step-by-step explanation:
For each drill, there are only two possible outcomes. Either it is a strike, or it is not. Each drill is independent of other drills. So we use the binomial probability distribution to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
20% chance of striking oil.
This means that [tex]p = 0.2[/tex]
What is that probability that the third strike comes on the seventh well drilled
2 stikers during the first 6 drills(P(X = 2) when n = 6)[/tex]
Strike during the 7th drill, with 0.2 probability. So
[tex]P = 0.2P(X = 2)[/tex]
In which
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 2) = C_{6,2}.(0.2)^{2}.(0.8)^{4} = 0.2458[/tex]
Then
[tex]P = 0.2P(X = 2) = 0.2*0.2458 = 0.0492[/tex]
4.92% probability that the third strike comes on the seventh well drilled
A restaurant sees about 600 orders on Tuesday. This is down from last Tuesday by about 0.85%. How many did they see last Tuesday
Answer:
Number of orders seen on last Tuesday = 605
Step-by-step explanation:
Number of orders seen on Tuesday = 600
It is given that it is 0.85% less than last Tuesday.
Let number of sales on last Tuesday = [tex]x[/tex]
As per question statement:
Number of order on last Tuesday - 0.85% of Number of order on last Tuesday = 600
OR
i.e. if we subtract 0.85% of x from x, it must be equal to 600.
[tex]x-\dfrac{0.85}{100}x =600\\\Rightarrow x-\dfrac{0.85}{100}x =600\\\Rightarrow \dfrac{100-0.85}{100}x =600\\\Rightarrow \dfrac{99.15}{100} \times x =600\\\Rightarrow x =\dfrac{600\times 100}{99.15}\\\Rightarrow x =\dfrac{60000}{99.15}\\\Rightarrow x \approx 605[/tex]
So, there were about 605 order seen last Tuesday.
Give the equation of the line parallel to a line through (-3, 4) and (-5, -6) that passes through the origin. y = 5x
Answer:
y = 5x
Step-by-step explanation:
First, find the slope of the first equation by doing rise/run
This gets you -10/-2 or 5
A parallel line will have the same slope. Since it goes through the origin, the y-intercept and b value will be zero
The equation will be y = 5x
What sentence represents the number of points in the problem below?
A test is worth 50 points. Multiple-choice questions are worth 1 point, and
short-answer questions are worth 3 points. If the test has 20 questions, how
many multiple-choice questions are there?
Answer:
Choice D.
Step-by-step explanation:
The number of points is obtained by the number of points of each multiple choice question times the number of multiple choice questions added to the number of points of each short answer question times the number of short answer questions.
Since the total number of points is 50, then the number of points from the multiple choice questions plus the number of points from the short answer questions add up to 50 points.
Answer: Choice D.
Answer:
D
Step-by-step explanation:
The number of points is 50, and short answer questions are 3 pts. Multiple choices are 1 pts.
So we have 3s+m=50
s the last book a person in City Upper A read a discrete random variable, continuous random variable, or not a random variable? A. It is a continuous random variable. B. It is a discrete random variable.
Answer:
Not a random variable
Step-by-step explanation:
The last book a person read in City A is not a random variable because it is not a number as there is no numerical description for the outcome of this experiment.
Thus, the last book read by someone in City A is not a random variable.
Answer:
not random
Step-by-step explanation:
in a classroom 5/8 of the students are wearing blue shirts and 1/4 for wearing white shirts there are 24 students in the classroom how many are wearing shirts other than blue shirts and
Answer:
3
Step-by-step explanation:
Those wearing a shirt of another color are ...
1 - 5/8 -1/4 = 8/8 -5/8 -2/8 = 1/8
of the total number of students in the classroom
(1/8)×(24 students) = 3 students . . . . wearing another color
_____
Alternate solution
With the given information, you know ...
(5/8)(24) = 15 . . . students wear blue
(1/4)(24) = 6 . . . . students wear white
24 -15 -6 = 3 . . . students wear another color
In the following graph, the ordered pairs from the table represent points on line \blueD mmstart color #11accd, m, end color #11accd. Complete the missing values in the table. xxx yyy 222 555 666 888
Answer:
im guessing thats on khan so 4=4 and 8 = 2:)
Step-by-step explanation:
Answer: Both
Step-by-step explanation: Both equal y intercept
Write the slope-intercept inequality for the graph below. If necessary, use <=
for s or >= for 2.
(5,0)
(0,-3)
Help please
Answer:
Slope intercept y>=3/5x-3
Step-by-step explanation:
Slope intercept of the line: y=3/5x-3
Shaded above, so y>=3/5x-3
A contractor is considering whether he should take on a project that promises a profit of $8800 with a probability of 0.83 or a loss (due to bad weather, strikes, etc.) of $2900 with a probability of 0.17. What is the expected profit for the contractor
Answer: 6811
Step-by-step explanation:
in this problem the values are 8800 and -2900 and the respective probabilities are 0.83 and 0.17
--
so the expected profit o# sum = (x*P(x))=8800*(0.83)+(-2900)*(0.17)=6811
A game require rolling a six sided die numbered fro 1 to 6. What is the probability of rolling a 1 or a 2?
Answer:
1/3
Step-by-step explanation:
hello,
probability of 1 = 1/6
probability of 2 = 1/6
probability of 1 or 2 = 1/6+1/6 as probability of 1 and 2 = 0
so the answer is 2/6=1/3
find the value of ∛27
Answer:
3
Step-by-step explanation:
3^3 = 27
what is between 1/3 and 7/8 answer
Answer:
The number which is exactly in between 1/3 and 7/8 will be their average. The average = (1/3 + 7/8) / 2 = (8/24 + 21/24) / 2 = (29/24) / 2 = 29/48.
Sophie has 60 pencils. How many blunt pencils does she have if the ratio of
sharpened pencils to blunt pencils is 4:1?
Answer:
[tex]12[/tex]
Step-by-step explanation:
[tex]\frac{60}{4+1}[/tex]
[tex]\frac{60}{5} =12[/tex]
[tex]4:1[/tex]
[tex]4 \times 12: 1 \times 12[/tex]
[tex]48:12[/tex]
2 Points
If f(x) = x + 8 and g(x) = -4x - 3, find (f+ g)(x).
O A. (f+ g)(x) = -3x + 5
O B. (f+ g)(x) = 5x + 11
O C. (f+g)(x) = -5x - 11
O D. (f+ g)(x) = 3x - 5
SUBMI
Answer: A
Step-by-step explanation:
(f+g)(x) means f(x)+g(x). Since we are given f(x) and g(x), we cna add them together.
x+8+(-4x-3)
x+8-4x-3
-3x+5
Heights of Women. Heights of adult women are distributed normally with a mean of 162 centimeters and a standard deviation of 8 centimeters. Use the Table B.3 Areas under the Normal Curve (page 519 of the textbook) to find the indicated quantities: a) The percentage of heights less than 150 centimeters b) The percentage of heights between 160 centimeters and 180 centimeters
Answer:
a) 6.68% of heights less than 150 centimeters
b) 58.65% of heights between 160 centimeters and 180 centimeters
Step-by-step explanation:
When the distribution is normal, we use the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this question, we have that:
[tex]\mu = 162, \sigma = 8[/tex]
a) The percentage of heights less than 150 centimeters
We have to find the pvalue of Z when X = 150. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{150 - 162}{8}[/tex]
[tex]Z = -1.5[/tex]
[tex]Z = -1.5[/tex] has a pvalue of 0.0668
6.68% of heights less than 150 centimeters
b) The percentage of heights between 160 centimeters and 180 centimeters
We have to find the pvalue of Z when X = 180 subtracted by the pvalue of Z when X = 160.
X = 180
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{180 - 162}{8}[/tex]
[tex]Z = 2.25[/tex]
[tex]Z = 2.25[/tex] has a pvalue of 0.9878
X = 160
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{160 - 162}{8}[/tex]
[tex]Z = -0.25[/tex]
[tex]Z = -0.25[/tex] has a pvalue of 0.4013
0.9878 - 0.4013 = 0.5865
58.65% of heights between 160 centimeters and 180 centimeters
could you help me with this problem
Answer:
For x
We use cosine
cos 45° = 2/x
After solving
x = 2√2
Since we have the value of x we use it to get the value of y
we use cosine
cos 60° = 2√2/y
y =2√2/cos 60
y = 4√2
We use Pythagoras theorem to find z
(4√2)² = (2√2)² + z²
z² = 32 - 8
z² = 24
z = √24
z = 2√6
Therefore x = 2√2
y = 4√2
z = 2√6
Hope this helps.
What do you want to find out? > The rate at which Bill puts shringles on a rood. What do you know? > Bill and Chip each finished half of the roof. > Bill needs 7 hours to put the same number of shingles on the roof that Chip does in 4 hours. > For each worker, the time multiplied by the rate equals the number of shringles > Chip's rate is 30 shringles more per hour than Bill's rate. What is Chip's rate in terms of Bill's rate? Let b = Bill's rate. Chip's rate = Bill's rate (b) ( - ) ( 4 ) ( 30 ) ( 7 ) ( + )
Answer:
(a) b = (4/7)c
(b) Bill: 40 shingles/hour; Chip: 70 shingles/hour
Step-by-step explanation:
Let b and c represent Bill's and Chip's rates in shingles per hour, respectively. Then we have ...
7b = 4c
c - b = 30 . . . . shingles per hour difference in rates
(a) Bill's rate in terms of Chip's rate can be found by dividing the first equation by 7
b = (4/7)c . . . . . Bill's rate is 4/7 of Chip's rate
__
(b) To find the rates, we can multiply the second equation by 7 and substitute using the first equation:
7c -7b = 210
7c -4c = 210
c = 210/3 = 70
b = (4/7)(70) = 40
Bill's rate is 40 shingles per hour; Chip's rate is 70 shingles per hour.
in a bag there are 2 red, 3 yellow, 4 green, 6 blue marbles.
what is the probability of p (blue)?
Answer:
2/5
Step-by-step explanation:
2 red, 3 yellow, 4 green, 6 blue marbles. = 15 marbles
P( blue) = blue / total
=6/15
=2/5
Which best describes her prediction?