A storage shed is to be built in the shape of a box with a square base. It is to have a volume of cubic feet.
The dimensions of the most economical shed are height = 10 ft and side 5 ft
Taken data
volume = 250 cubic feet
base costs = $4 per square foot
material for the roof costs = $6 per square foot
material for the sides costs = $2.50 per square foot
to find out the dimensions of the most economical shed solution
let us consider length of side x and height is h
so we can say x²h = 250
and h = 250 / x²
now cost of material = cost of base + cost top + cost 4 side
cost = x²(4) + x²(6) + 4xh (2.5)
cost = 10 x² + 10xh
put here h = 250 / x²
cost = 10 x² + 10x (250/ x² )
cost = 10 x² + (2500/ x )
if we differentiate and we get
c' = 20 x - 2500 / x²
put c' = 0 solve x
20 x - 2500 / x² = 0
x = 5
so we say one side is 5 ft base
and height is h = 250 / x²
h = 250 / 5²
height = 10 ft
Hence the answer is, the dimensions of the most economical shed are height = 10 ft and side 5 ft
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The string of a kite is 120 m long and makes an angle of 70° with the horizontal. What is the height of the kite? show work!
The height of the kite is approximately 112.763 meters above the ground.
How to determine the height of a kite above the ground
The situation is represented by the following geometric diagram, a right triangle with a known hypotenuse (r), in meters, and a known acute angle (θ), in degrees. The height of the kite (h), in meters, is represented by the leg opposite to the acute angle and can be found by trigonometric functions:
sin θ = h / r
h = r · sin θ
h = 120 · sin 70°
h ≈ 112.763 m
The height of the kite is approximately 112.763 meters.
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a website advertises job openings on its website, but job seekers have to pay to access the list of job openings. the website recently completed a survey to estimate the number of days it takes to find a new job using its service. it took the last 30 customers an average of 60 days to find a job. assume the population standard deviation is 10 days. calculate a 95% confidence interval of the population mean number of days it takes to find a job.
(56.42155, 63.57845) is the 95% confidence interval of the population mean number of days it takes to find a job.
What is confidence interval ?In frequency statistics, a confidence interval is the range of estimated values for an unknown parameter. Confidence intervals are computed at the specified confidence level. A 95% confidence level is the most common, but other levels such as 90% and 99% are sometimes used.
CalculationGiven a=0.05, Z(0.025)=1.96
SO 95% confidence interval is
xbar+/-Z*s/vn
--> 60+/- 1.96*10/sqrt(30)
-> (56.42155, 63.57845)
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Based on the time recorded for 500 attendees at an amusement park, the average amount of time spent at the park was 6.75 hours with a margin of error of ±1.45 hours. if 2,000 people attended the park on a given day, what is the estimated range of total hours the attendees spent in the park? 2,725 to 5,375 total hours spent in the park 3,842 to 4,893 total hours spent in the park 10,600 to 16,400 total hours spent in the park 13,600 to 19,400 total hours spent in the park
Answer:10,600 to 16,400
Step-by-step explanation:
First you subtract the margin of error to find the least amount of hours.
6.75 - 1.45 = 5.3 x 2,000(people) = 10,600 (least amount of hours)
Then you add the margin of error to find the most amount of hours.
6.75 + 1.45 = 8.2 x 2,000(people) = 16,400 (most amount of hours)
The margin of error just shows that people spent at least 5.3 and at most 8.2 hours at the park.
You multiply those numbers with how many people went to the park. 2,000
That means the answer is C: 10,600 TO 16,400.
Plus.....I took the test and got it right!
Lincoln Elementary has 651 students and 31 teachers. The total number of students in the elementary and middle school is 1,197. How many teachers does the middle school have if it has the same teacher-student ratio as the elementary school?
Step-by-step explanation:
elementary school has 651 students and 31 teachers.
the teacher/student ratio is therefore 31/651 or simplified 1/21.
elementary and middle school together have 1197 students. that means the middle school has
1197 - 651 = 546 students
their teacher student ratio is then
x/546
and that must be the same as for the elementary school.
so,
x/546 = 1/21
x = 546/21 = 26
so, the middle school has 26 teachers.
Find the solution(s) to the equation sine (startfraction x over 2 endfraction) cosine x minus 1 = 0 on the interval 0 ≤ x 2π. check all that apply. 0 startfraction pi over 3 endfraction startfraction pi over 6 endfraction startfraction 3 pi over 2 endfraction startfraction 5 pi over 3 endfraction
All apply values to the equation are:
0 ⇒ A
π/3 ⇒ B
5π/3 ⇒ E
What is an equation?
A formula known as an equation shows the equality of two expressions by joining them with the equals sign =.
Main Body:
∵ 0 ≤ x ≤ 2π is the domain for angle x
∴ 0 ≤x/2 ≤ π is the domain of angle
∵ sin(x/2) + cos(x) - 1 = 0
→ To solve the equation we should use the rule of cosine double angle
∵ cos(x) = 1 - 2 sin²(x/2)
→ Substitute it in the equation above
∴ sin(x/2) + (1 - 2 sin²(x/2) = 0
∴ sin(x/2) + 1 - 2 sin²(x/2) = 0
→ Add the like terms
∴ sin(x/2) + (1 - 1) - 2 sin²(x/2) = 0
∴ sin(x/2) - 2 sin²(x/2) = 0
→ Take sin(x/2) as a common factor
∴ sin(x/2) [1 - 2sin(x/2)] = 0
→ Equate each factor by 0
∵ sin(x/2) = 0
→ The value of sine equal zero on the x-axis
∴ x/2 = 0, π, 2π
∵ The domain of x/2 is 0 ≤ (x/2) ≤ π
∴ x/2 = 0 and π ⇒ 2π refused because ∉ the domain
→ Multiply both sides by 2 to find x
∴ x = 0 and 2π
∵ 1 - 2sin(x/2) = 0
→ Subtract 1 from both sides
∴ - 2sin(x/2) = -1
→ Divide both sides by -2
∴ sin(x/2) = 1/2
→ The sine is positive in the 1st and 2nd quadrants
∴ (x/2) lies on the 1st OR 2nd quadrants
∵ (x/2) = sin⁻¹(1/2)
∴ (x/2) = π/6 = ⇒ 1st quadrant
→ Multiply both sides by 2
∴ x = π/3
∵ (x/2) = π -π/6 = 5π/6 ⇒ 2nd quadrant
→ Multiply both sides by 2
∴ x = 5π/3
∴ The values of x are 0,π/3 , 5π/3 , 2π
Hence apply values are:
0 ⇒ A
π/3⇒ B
5π/3⇒ E
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Cdm = 108 abc = 32 whats CMN
The measure of angle 1 is 48°.
The measure of angle 2 is 132°.
The measure of angle 3 is 132°.
What are the measure of angles?
Angle 1 and angle 48 are vertically opposite angles. Verticly opposite angle have the same values. Thus, angle 1 would be 48.
Angle 1 and 2 are interior opposite angles. Thus, both angles should add up to 180 degrees.
180 - 48 = 132
Angle 2 and 3 are alternate external angles. Thus, they are equal.
Angle 3 would be 132.
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The value of y varies directly with x. If x=15, then y=9. Find the value of y if x=9
Answer:
y = 3/5 x
Step-by-step explanation:
Direct variation:
y = kx
We need to find k.
x = 15; y = 9
9 = k × 15
k = 9/15 = 3/5
Answer: y = 3/5 x
Triangle ABC is congruent to triangle XYZ. Side BC corresponds to what side in triangle XYZ?
Answer:
Side YZ
Step-by-step explanation:
think of the triangles as mirrors of each other
and pay attention to the symbols that correspond from side to side, and angle to angle
what substance do you drink to get strong bones
Answer:
milk
Step-by-step explanation:
HELP ME PLSSSS I NEED HELP OR ELSE I WILL CRY
The length of the segment BD is 2.4 units and that of AB is 4 units.
According to the question,
We have the following information:
We have a figure of triangle in which there are two right-angled triangles.
Now, we can find the length of the segment BD and AB using the Pythagoras theorem.
Using it in triangle BDC:
[tex]BC^{2} = CD^{2} + BD^{2}[/tex]
Putting the values of BC and CD:
3*3 = 1.8*1.8+[tex]BD^{2}[/tex]
9 = 3.24+[tex]BD^{2}[/tex]
Subtracting 3.24 from both sides:
9-3.24 = [tex]BD^{2}[/tex]
[tex]BD^{2}[/tex] = 5.76
BD = 2.4 units
Now, using the same theorem in triangle BDA:
[tex]AB^{2} = BD^{2}+ AD^{2}[/tex]
[tex]AB^{2}[/tex] = 5.76+3.2*3.2
[tex]AB^{2}[/tex] = 5.76+10.24
[tex]AB^{2}[/tex] = 16
AB = 4 units
Hence, the length of the segment BD is 2.4 units and that of AB is 4 units.
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P is the point (0,-1) and Q is the point (5,9) find the equation of the line through P that is perpendicular to PQ
Answer:
Step-by-step explanation:
Find the slope of PQ
[tex]\frac{9 - (-1)}{5-0}=\frac{10}{5}[/tex] or just [tex]2[/tex]
The perpendicular slope is the negative reciprocal
Use a slope of [tex]-\frac{1}{2}[/tex]
Use the point-slope form of a equation and point P to find a new equation in slope-intercept form
[tex](y- (-1))=-\frac{1}{2}(x-0)[/tex]
[tex]y+1=-\frac{1}{2} x[/tex]
Subtract the 1 from both sides of the equation
[tex]y=-\frac{1}{2}x-1[/tex]
1) Solve the following equations for 0° ≤ θ ≤ 360°.
(i) 2 sin 2 θ = cos θ
(ii) tan 2θ=4 tan θ
please answer my question in the image
The value of this simplification is - 20. 72.
What is simplification?
The act of simplifying something that is simpler to carry out or understand, or the thing that is the product of this simplifying process: The group offers suggestions for streamlining business processes. This grossly oversimplifies what actually transpired.
Here, we have
Given the equation, we solve this through simplification
We get,
= {(1.88 + 2.12) × 0.1875}/{(0.625 - 0.722)÷2.888} + {(1.44 + 0.56)÷0.5}/{(7.7÷24.75 + 0.133)× 4.5}
= 0.75/(-0.033) + 4/1.988
= -22.72 + 2.00
= - 20.72
Hence, the value of this simplification is - 20. 72.
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what is the square rout of 9
Answer:3
Step-by-step explanation: 3x3=9
Answer:
3
Step-by-step explanation:
√9
=√3²
=√(3²)
=3
{as square root =1/2, 2*1/2 = 1}
I inserted a picture so it can be more clear. This is for Algebra 2, Unit 2
Answer: x=-16
Step-by-step explanation:
g^-1 is the inverse of the g(x) graph meaning that the x and g(x) values of the g(x) graph switch places. So in the table when x=-2 g(x)=-16
2 half dollars = how many dimes
2 half dollars just mean a dollar. In that case, that's 10 dimes. (10*10=100)
Answer:
10 dimes
Step-by-step explanation:
So in order to get this answer we first must know that...
1 half dollar = 50 cents
1 dime = 10 cents
So...
5 dimes = 50 cents
2 half dollars = 100 cents aka $1
10 dime = 100 cents aka $1
Therefore we can use our common sense to figure out that 2 half dollars is 10 dimes.
Find Average Rate of Change from Equation
Given the function
f(x) = x² *8x +11, determine the average rate of change of the function over the interval
-7 < x < −3.
Answer:
Step-by-step explanation:
1
Find the quotient (x³ + 2x² − x − 2) ÷ (x + 2)
Answer: The quotient is x²- 1
Please help quick thanks
Answer:
Step-by-step explanation:
( [tex]x_{1}[/tex] , [tex]y_{1}[/tex] )
( [tex]x_{2}[/tex] , [tex]y_{2}[/tex] )
d = [tex]\sqrt{(x_{2} -x_{1} )^2+(y_{2} -y_{1} )^2}[/tex]
~~~~~~~~~~~~~~~
A ( 3 , 6 )
B ( 0 , 1 )
C ( 4 , 0 )
AB = [tex]\sqrt{(0-3)^2 + (1-6)^2}[/tex] = 3√5 ≈ 6.71
AC = [tex]\sqrt{(4-3)^2 + (0-6)^2 }[/tex] = √37 ≈ 6.08
BC = [tex]\sqrt{(4-0)^2 + (0-1)^2 }[/tex] = √17 ≈ 4.12
AB ≠ AC ≠ BC ⇒ Δ ABC is a scalene triangle
an actual distance of 50km corresponds to 4cm on the map
Using the given information, the scale of the map is 1 : 1250000
Determining the scale of a mapFrom the question, we are to determine the scale of the map.
From the given information,
An actual distance of 50km corresponds to 4cm on the map
To determine the scale of the map,
First, we will convert 50 km to cm
50 km = 50000 m
50000m = 5000000 cm
∴ 50 km = 5000000 cm
Thus,
An actual distance of 5000000 cm corresponds to 4cm on the map
That is,
4 cm represents 5000000 cm
Dividing by 4
Then,
1 cm represents 1250000 cm
Hence,
The scale is 1 : 1250000
Here is the complete question:
What is the scale if: an actual distance of 50km corresponds to 4cm on the map.
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The sum of three times a and four is the same as 5
times a.
Answer: 2
Step-by-step explanation:
Equation: 3a + 4 = 5a
-5a+3a+4 = 5a-5a
-2a+4 = 0
-2a+4-4 = 0-4
-2a = -4
a = 2
Done!
Please help and show your work and steps please
Solve for W
P = 2L + 2W
Answer:
W= P/2 - L
By doing the algebraic work you get W=P/2 - L
Carlos harvests cassavas at a constant rate. he needs 353535 minutes to harvest a total of 151515 cassavas. write an equation to describe the relationship between t, the time, and ccc, the total number of cassavas.
Carlos harvests cassavas at a constant rate. He needs 353535 minutes to harvest a total of 151515 cassavas.
The ratio of the change in dependent values or outputs to the change in independent values or inputs is known as the rate of change. The change, which also refers to the function's slope, represents the shift in values between two points on a coordinate plane. The formula for the rate of change is (y2 - y1)/, where y stands for the dependent variable and x for the independent variable (x2 - x1).
Given:
Carlos gives 353535 minutes to harvest a total of 151515 cassavas.
Find:
We have to find the total number of cassavas.
Solution:
Carlos harvests cassava at constant rate is 353535 minutes per 151515 cassavas
= 151515/353535
= 0.429
A formula for the quantity of cassava (C) that Carlos harvests each time (T).
This means that after 353535 minutes, 151515 cassavas have been harvested, after 700000 minutes, 300000 cassavas, and so on.
Hence, the required constant rate is 0.429T.
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On Monday, jake could lift 25lbs. One month later he could lift 45lbs. What is the percent change in the number of pounds he can lift? Round to the nearest whole number.
what Is the answer
The percent change in the number of pounds that Jake can lift is 80%.
How to calculate the percentage?From the information illustrated, Jake could lift 25lbs and one month later he could lift 45lbs.
The percentage change will be:
= Change in pounds / Original pounds × 100
= (45 - 25) / 25 × 100
= 20 / 25 × 100
= 4 / 5 × 100
= 80%
The percentage change is 80%.
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SHOW WORK FOR BRAINLIST
Answer:
x = 16, y = -1
Step-by-step explanation:
3x - 12y = 60------> x - 4y = 20
x + 2y = 14--------> x + 2y = 14
---------------
-6y = 6
y = -1
x + 2(-1) = 14
x - 2 = 14
x = 16
You have $14 in your pocket. A bike rental costs $5 plus $2.50 per hour. What is maximum amount of time you can rent a bike for without spending all of your money?
Answer:
3 hours
Step-by-step explanation:
3 hours will cost 2.50*3 which is 7.50 + the base price of 5.
So that would be $12.5 leaving you with $1.5
Which of the following equations represents the parabola with vertex at (2, 4) and directrix y = 7?
The equation of parabola with vertex at (2, 4) and directrix y = 7 is (x - 2)^2 = -12(y - 4)
We know that the equation of standard parabola is (x - h)^2 = 4p(y - k), where p≠ 0.
here, the vertex = (h, k)
and the directrix is the line y = k - p.
We have been given vertex at (2, 4) and directrix y = 7
so, h = 2, k = 4
k - p = 7
4 - p = 7
- p = 7 - 4
p = -3
so, equation of parabola would be, (x - 2)^2 = 4(-3)(y - 4)
(x - 2)^2 = -12(y - 4)
Therefore, the equation of parabola with vertex at (2, 4) and directrix y = 7 is (x - 2)^2 = -12(y - 4)
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On the fourth trial of this experiment, a student places some discs on the car by mistake. In 1-2 sentences, explain how this mistake will affect the graphs produced by the computer.
The acceleration produced by a car will decrease as its mass rises. Less acceleration will be recorded by the computer system, which will cause a drop in the acceleration value on the graph.
Graph:
An organized visual representation of any data in mathematics is called a graph. The graph shows the correlation between the variable values. In graph theory, a graph is used to represent the collection of objects that are somehow connected to one another. In essence, the objects' vertices or nodes are mathematical concepts, and the connections between the nodes are represented by the edges. Different types of graphs are used in mathematics and statistics to visually display data. The discipline of graph theory is the study of points and lines. It is a field of mathematics that specializes in the study of graphs. This image visually illustrates the mathematical truth. The graph theory is used to study relationships.
Complete question:
Use the image to answer the question. Students are using the experimental setup shown in the image in which the two ends of a string are attached to a car and to a hanger. The students conduct three trials in which they place metal discs on the hanger to manipulate the force applied to the car. As a result, the car accelerates along the table while two photogate probes collect motion data. On the fourth trial of this experiment, a student places some discs on the car by mistake. In 1-2 sentences, explain how this mistake will affect the graphs produced by the computer.
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What is the slope of the line that passes through the points (1, 1)(1,1) and (4, 4)(4,4)? Write your answer in simplest form.
Answer:
Slope = 1
Step-by-step explanation:
To find the slope you must do this equation: [tex]m=\frac{y_{2} - y_{1}}{x_{2}-x_{1}}[/tex]. [tex]y_{2}[/tex]=4 [tex]y_{1}[/tex]=1 [tex]x_{2}[/tex]=4 [tex]x_{1}[/tex]=1. Then do the math, 4-1=3 divided by 4-1=3. You will then get 3/3=1. 1 is your slope.
Anne worked out at the gym for
an hour. She spent 25 minutes on the
treadmill, 20 minutes lifting weights,
and the rest of the time stretching.
What percent of the time did Anne
spend stretching?
Answer:
Anny consumed 25% time in stretching
Total time taken by anny in gym = 1 hour.
Time spent by anny on the treadmill= 25 minutes.
Time spent by anny in lifting weights= 20 minutes.
And remaining time anny spent on streching,
we have to find what percent did anny spend on streching.
Therefore anny consumed 25% time in streching.
Answer is 25%.
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