angle measure is a complement of an angle whose measure is 62 degrees=90-62=28.
Answer:
D 28 is your answer
Suppose a home improvement contractor is painting the walls and ceiling of a rectangular room. The volume of the room is 288 cubic feet. The cost of wall paint is $0.06 per square foot and the cost of ceiling paint is $0.16 per square foot. Let x, y, and z be the length, width, and height of a rectangular room respectively. Identify the room dimensions that result in a minimum cost for the paint and use these dimensions to find the minimum cost for the paint. Round your answer to the nearest cent.
Answer:
The minimum cost is $17.30c
Step-by-step explanation:
Given
[tex]V = 288[/tex] --- Volume
[tex]C_1 = 0.06[/tex] --- cost of wall paint
[tex]C_2 = 0.16[/tex] ---cost of ceiling paint
Required
Minimum cost of paint
The volume is calculated as:
[tex]V =xyz[/tex]
Substitute 288 for V
[tex]288 =xyz[/tex]
Make z the subject
[tex]z = \frac{288}{xy}[/tex]
The surface area is calculated as:
[tex]Area = 2(yz + xz) + xy[/tex]
Because xy represent the dimension of the ceiling and the opposite of the ceiling (the floor) will not be painted. Hence, it does not require a coefficient of 2
The cost is:
[tex]C = 0.06 * 2(yz + xz) + 0.16 * xy[/tex]
Substitute [tex]z = \frac{288}{xy}[/tex]
[tex]C = 0.06 * 2(y*\frac{288}{xy} + x*\frac{288}{xy}) + 0.16 * xy[/tex]
[tex]C = 0.06 * 2(\frac{288}{x} + \frac{288}{y}) + 0.16 * xy[/tex]
[tex]C = 0.12(\frac{288}{x} + \frac{288}{y}) + 0.16 * xy[/tex]
[tex]C = (\frac{34.56}{x} + \frac{34.56}{y}) + 0.16 * xy[/tex]
[tex]C = (\frac{34.56}{x} + \frac{34.56}{y}) + 0.16 xy[/tex]
Differentiate w.r.t x and y
[tex]C_x = -\frac{34.56}{x^2} + 0.16y[/tex]
[tex]C_y = -\frac{34.56}{y^2} + 0.16x[/tex]
By comparison: [tex]x = y[/tex]
Set them equal to 0
[tex]C_y = -\frac{34.56}{y^2} + 0.16x=0[/tex]
[tex]-\frac{34.56}{y^2} + 0.16x=0\\[/tex]
Substitute x for y
[tex]-\frac{34.56}{x^2} + 0.16x=0[/tex]
[tex]0.16x=\frac{34.56}{x^2}[/tex]
Cross multiply
[tex]0.16x^3 = 34.56[/tex]
[tex]x^3 = \frac{34.56}{0.16}[/tex]
[tex]x^3 = 216[/tex]
Take the cube root of both sides
[tex]x = \sqrt[3]{216}[/tex]
[tex]x = 6[/tex]
[tex]x=y= 6[/tex]
Substitute 6 for x and for y in [tex]C = (\frac{34.56}{x} + \frac{34.56}{y}) + 0.16 xy[/tex]
[tex]C = (\frac{34.56}{6} + \frac{34.56}{6}) + 0.16 * 6* 6[/tex]
[tex]C = (\frac{2*34.56}{6}) + 5.76[/tex]
[tex]C = 11.52 + 5.76[/tex]
[tex]C = 17.28[/tex]
[tex]C = 17.3[/tex] --- approximated
Jim had 16 gallons of orange juice. What is the total number of cups of orange juice Jim has?
Answer:
I think it's 256
Step-by-step explanation
Answer:
256
Step-by-step explanation:
why well
it goes like this
write the 2 number as shown
16 gallons cups
what is more gallons or cups
its gallons so
large to small
lagre to small is mutipling and small to large is dividing so u need to mutiply the amout of cups are in a gallon wichis 16 so 16 times 16 is 256 so there u go
help pleaseee, this is for math class
Answer:
Step-by-step explanation:
3h = 3×7, not 37.
3h + 13 = 3×7 + 13 = 34
Use the description of an experiment done in a children's hospital.
A music therapist was interested in investigating whether listening to music or composing music had an influence on both anxiety levels and oxygen saturation in children who were hospitalized for asthma-related illnesses. Thirty-two children spent 20 minutes listening to classical waltzes played on a piano. On a different day, they spent 20 minutes composing their own short pieces of music using a software program.
When listening to music: For the physiological measure, the critical value for t was larger than the test statistic for the observed data. For the anxiety measure, the critical value for t was smaller than the test statistic for the observed data.
When composing music: For the physiological measure, the critical value for t was larger than the test statistic for the observed data. For the anxiety measure, the critical value for t was larger than the test statistic for the observed data.
When writing the results of the music therapist's study, which of these statements reflects the correct conclusions that should be drawn from the results and then included as part of the interpretation paragraph?Question 8 options:
a) Music therapists should make pediatric asthma patients compose music in order to increase their oxygen saturation.
b) Music therapists should make pediatric asthma patients listen to music in order to reduce their anxiety.
c) Pediatric asthma patients should listen to music in order to increase their oxygen saturation.
d) Additional information is needed to draw a proper conclusion.
Answer:
d) Additional information is needed to draw a proper conclusion
Step-by-step explanation:
When listening to music;
Physiological measure
Critical t > Test statistic Accept H₀
Anxiety measure
Critical t < Test statistic Reject H₀
When composing music;
Physiological measure
Critical t > Test statistic Accept H₀
Anxiety measure
Critical t > Test statistic Accept H₀
When the test statistic is larger the critical 't' we reject the hypothesis that there is no difference in the observation, and we accept the alternative hypothesis
The test results having a larger critical 't' than the test statistics suggest that there is no difference between physiological and anxiety influence of composing music on pediatric asthma patients
However, given that when listening to music, the critical 't' is lest than the test statistic for the anxiety parameter of the participants, there is sufficient statistical evidence to suggest that there in an influence on the anxiety of pediatric asthma patients when they listen to music, however, it is not stated if the anxiety increases or decreases, therefore additional information is needed
Need help please thanks
Answer:
6.
Just count the x's on the graph...
You move right 3 units. You end at (5, 2). Where did you start?
Answer:
8,2
Step-by-step explanation:
Help me with this geometry question!!
Answer:
A) trapezoid a=141 b=69
Step-by-step explanation:
It must be a trapezoid because two of the sids are not parallel. The interior angles of any quadrilateral must equal 360, and each side of a trapezoid must equal 180, so:
A) trapezoid a=141 b=69
Answer:
a
Step-by-step explanation:
One card is randomly selected from a deck of cards. Find the odds:
in favor of getting a spade.
Answer:
1/4 chance or 0.25 or 25%
Step-by-step explanation:
One forth of cards in a deck are spades
Answer:
1/4
Step-by-step explanation:
In a deck of cards, there are 52 cards (not including jokers)
and there are 13 cards that are spades, so it's simply just 13/52 which simplifies to 1/4
Susan plans to make 4 pies for a family reunion. There will be 32 people at the reunion. How much pie will each person get if each piece is the same size?
1. 1/4
2. 1/7
3. 1/8
4. 1/32
Answer:
3
Step-by-step explanation:
to get enough pie for 32 people, each of the 4 pies would need to be 8 slices. since they each get 1 of 8 it would be 1/8
solve for x in the equation 5x-4=2x+20
The solution to the equation 5x - 4 = 2x + 20 is x = 8 which can be determined by simplification process.
To solve for x in the equation 5x - 4 = 2x + 20, we can follow these steps:
Start by isolating the x terms on one side of the equation. We can do this by subtracting 2x from both sides:
(5x - 2x) - 4 = (2x - 2x) + 20]
Simplifying:
3x - 4 = 20
Next, isolate the constant term on the opposite side of the equation by adding 4 to both sides:
(3x - 4) + 4 = 20 + 4
Simplifying:
3x = 24
Finally, solve for x by dividing both sides of the equation by 3:
(3x)/3 = 24/3
Simplifying:
x = 8
Therefore, the solution to the equation 5x - 4 = 2x + 20 is x = 8.
To know more about "equation." here
https://brainly.com/question/29174899
#SPJ2
Full Question-
Solve for x in the given equation 5x-4 = 2x+20
Mel has 1/2 gallon of milk in the refrigerator. He drinks 1/4 of the milk. How much milk does Mel drink?
Answer:
1/3
Step-by-step explanation:
Answer:
3/4
Step-by-step explanation:
The answer is 3/4 because 1/2 can be turned into 2/4 so the denominators are equal and then you add 1/4 and 3/4
2/4=1/2 because they are both a half
Can someone tell me this one?
Answer:
The answer is 45
Step-by-step explanation:
35+10=45
Ms. Wright looks at the menu in a restaurant. She wants to order a bowl of salad priced at $13.10 and a glass of fruit juice priced at $5.90. There are a 5% sales tax and a 3% meals tax on all food and beverages. Is she able to pay for her meal with $20? Explain your reasoning.
Answer:
No
Step-by-step explanation:
No, she is not able to pay for her meal with 20 dollars. The first step to solve this problem is to add up 13.10 and 5.90 so you can see how much money Ms. Wright has to spend on the food and drinks alone. 13.10 + 5.90 is 19. Since there are 5% and 3% of taxes on all food and beverages, there is 8% in total of taxes. 8% of 19 is 1.52. 19 plus 1.52 is 20.52 which is greater than 20. Therefore, Ms. Wright cannot pay for her meal with 20 dollars.
A total surface area is _ square inches
please help :) thanks !
Answer:
Step-by-step explanation:
b
How many square feet of outdoor carpet will
we need for this hole?
For every 5 pounds of tomatoes ordered, the restaurant orders 9 pounds of onions. If Everly orders
108 pounds of onions, how many pounds of tomatoes will she need to order?
Type or write your answers in the box below.
Answer:
[tex]\left[ 60- pounds][/tex]
Step-by-step explanation:
Ratio of tomatoes to onions = 5:9
so now it will be
5x: 108
we can solve it by doing this
x = 108/9
x = 12
so we multiply
5*x = 5x
5*12 = 60
She would need 60 pounds
the following list contains the number of movies That a group of 8 students saw in theaters in the past 12 months.
7,11,14,6,16,11,11,18
Find the median number of movies that the students saw.
Answer:
I'm pretty sure its 11
first orginize the numbers in numerical order
second the medj an is the middle numbe, if they are to find the mean of those two only
i dont understand what im doing wrong
Answer:
8
Step-by-step explanation:
-2 x -2 = 4
4 - (-28 / 7 = -4)
4- -4 = 8
Trevor is interested in purchasing the local hardware/electronic goods store in a small town in South Ohio. After examining accounting records for the past several years, he found that the store has been grossing over $850 per day about 60% of the business days it is open. Estimate the probability that the store will gross over $850
This question is incomplete, the complete question is;
Trevor is interested in purchasing the local hardware/electronic goods store in a small town in South Ohio. After examining accounting records for the past several years, he found that the store has been grossing over $850 per day about 60% of the business days it is open. Estimate the probability that the store will gross over $850 at least 6 out of 10 business day
Answer:
P( at least 6 out of 10 business days ) = 0.6312
Step-by-step explanation:
Given the data in the question;
p = 60% = 0.6
q = 1 - p = 1 - 0.6 = 0.4
Using Binomial distribution;
P( X = r ) = [tex]^nC_r p^rq^{n-r[/tex]
where [tex]^nC_r = n!/(r!(n-r))[/tex]
we substitute
P( at leas 6 ) = P(6) + P(7) + P(8) + P(9) + P(10)
= [¹⁰C₆ × 0.6⁶ × 0.4⁴] + [¹⁰C₇ × 0.6⁷ × 0.4³] + [¹⁰C₈ × 0.6⁸ × 0.4²] + [¹⁰C₉ × 0.6⁹ × 0.4¹] + [¹⁰C₁₀ × 0.6¹⁰ × 0.4⁰]
= [0.250] + [0.214] + [0.1209] + [ 0.0403] + [ 0.00604 ]
= 0.6312
Therefore, P( at least 6 out of 10 business days ) = 0.6312
6(2b+5)=12b×30
What did Joseph do wrong and whats the correct answer
Answer:
he placed a * sign instead of an add sign in the second part of the equation
Step-by-step explanation:
6(2b+5)=6*2b + 6*5 = 12b + 30
what is the slope of the line.
Answer:
m=3/2 or m=1.5
Step-by-step explanation:
slope formula:
m=(y1-y2)/(x1-x2)
in order to get this we need two points such as (3,0) and (1,-3) which are points on this line. So:
m=(0-(-3))/(3-1)
m=3/2 or m=1.5
80% of c is 20. What is c ?
Answer:
25
Step-by-step explanation:
If set M =[even digits from 2 to 8]. Find n(M)
Answer:
n(M) = 4
Step-by-step explanation:
M = (2,4,6,8)
n(M) = Number of values in set M.
n(M) = 4
Please help me find what ? Is
Answer:
My answer is 43 its that rigth
Mast
Gabi tried to solve an equation step by step.
Skill
= 80
10
algeb
1
j
· 10 = 80 · 10 Step 1
10
ne-
j = 800
Step 2
Find Gabi's mistake.
ne-
Choose 1 answer:
cual
Answer:
the answer is c
Step-by-step explanation:
Answer:
c
Step-by-step explanation:
PLEASE PLEASE PLEASEEEEE HELP!!!!!!!!!
Amir thinks of a number,
He triples it and adds 9 to get 54.
What number did he think of?
Answer:
The number he think of is 15
Step-by-step explanation:
Let x be the number
3x + 9 = 54
x = (54-9) / 3
x = 15
The number he think of is 15
Answer:
15
Step-by-step explanation:
3x + 9 = 54
x = (54-9) / 3
x = 15
Find the perimeter of the figure. due today
Answer:
62
Step-by-step explanation:
Since you are simply finding the perimeter, I assume they just want you to add all the sides. 13 + 15 + 10 + 10 + 14 = 62
Veronica can hit a bucket of 144 golf balls in 2 hours. how many golf balls can Veronica hit in 5 hours
Answer:
360
Step-by-step explanation:
144/2=72
5×72=360
...........