The area of the largest possible norman window with a perimeter of 25 ft is 43.75 ft²
Let r = the semicircle's radius
h = the rectangle's radius
2r = the window's width
C = 2πr is the formula for the perimeter of a circle,
The perimeter of the semicircle =πr
The perimeter of the window is
P=πr + 2h + 2r = 25
2h + (π +2)r = 25
h = ½[25 - (π + 2)r]
h = 12.5 - (π/2 +1)r ...............(1)
The formula for the area of a circle is A= πr², so
½πr² = the perimeter of the semicircle
The area of the window is
A = ½πr² + 2rh.............. (2)
Substitute (1) with (2).
A = ½πr² + 2r[12.5 - (π/2 +1)r] = ½πr² + 25r - (π +2)r²
A = 25r - (π + 2 - π/2)r²
A = -(π/2 + 2)r² + 25r ........(3)
One way to notice the vertex is to set the first derivative equal to zero.
dA/dr =-2(π/2 + 2)r + 25 = 0
-(π + 4)r + 25 = 0
r = 25/(π + 4)
r ≈ 3.50 ft .......... (4)
Substitute (4) with (1).
h = 12.5 - (π/2 +1)(3.50) = 12.5 - (2.571× 3.50)
h = 12.5 - 9.00 = 3.50
h = 3.50 ft
Area = 1.571(3.50)² + 2×3.50×3.50 = 19.25 + 24.50
Area = 43.75 ft²
So, the area is 43.75 ft².
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i need help. like... really need help.
The domain of the function graphed in this problem is given as follows:
{x | x ≥ -4}.
How to obtain the domain of the function?The domain of a function is the set composed by all the input values that the function accepts.
On the graph, the domain of the function is given by the values of x.
From the graph of the function, the function has a closed interval at x = -4, and is defined for all the values for the right of that, that is, greater than -4, hence the notation for the domain is given as follows:
{x | x ≥ -4}.
Meaning that the correct option is given by the second option.
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How many sides does a regular
polygon have if an interior
angle measures 150°?
n = [?]
The number of sides of a regular polygon with an interior angle that measures 150° is equal to 12 sides.
What is a regular polygon?In Euclidean geometry, a regular polygon simply refers to a form of polygon which has all of its sides and interior angles being equal.
In Geometry, the sum of the interior angles of both a regular and irregular polygon is given by this formula:
Sum of interior angles = 180 × (n - 2)
Where:
n represents the number of sides of a regular polygon.
Similarly, the number of sides of a regular polygon with a given interior angle can be calculated by using this mathematical expression:
Interior angles = 180 × (n - 2)/n
150° = 180(n - 2)/n
150n = 180n - 360
180n - 150n = 360
30n = 360
n = 360/30
n = 12 sides.
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a medical researcher is comparing the results of two surgical techniques to correct a skeletal deformity. there are many obvious risks of participating in this treatment trial, and participants are carefully informed about the likelihood of infection, poor treatment outcome, further damage, etc. the research design includes a questionnaire given to patients about their quality of life before and after the surgery. because this is just a simple paper and pencil questionnaire, it does not add any risks to the overall study design. is this true or false?
The questionnaire given to patients about their quality of life before and after the surgery included in the research design does add risks to the overall study design. Hence, the given statement is false.
Even though the questionnaire itself may not cause any additional physical risks, it can still have an impact on the overall study design. The questionnaire can add additional burden to the participants, who may already be dealing with physical and emotional stress from the surgery. Also, the questionnaire results may not be accurate if participants are not fully honest or unable to understand the questions being asked. Therefore, the inclusion of such a questionnaire in the research design should be carefully considered after evaluating its potential impact on the overall study.
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A company manufactures a wash-down motor that is used in the food processing industry. The motor is marketed with a warranty that guarantees it will be replaced free of charge if it fails within the first 12,000 hours of operation. On average, the wash-down motors operate for 14,000 hours with a standard deviation of 1, 050 hours before failing. The number of operating hours before failure is approximately normally distributed.
a. What is the probability that a wash-down motor will have to be replaced free of charge?
b. What percentage of wash-down motors can be expected to operate for more than 16,100 hours?
c. If the company wants to design a wash-down motor so that no more than 1% are replaced free of charge, what would the average hours of operation before failure have to be if the standard deviation remains at 1,050 hours?
a) The probability that a wash-down motor will have to be replaced free of charge - 1,904
b) A percentage of wash-down motors can be expected to operate at 2,28 %
c) The average hours of operation before failure would be 13500 h
Normal Distribution
μ₀ = 14000 hours and σ = 1050 hours
a) Probability of X (replacement of motor free of charge)
Z = ( X - μ₀ ) / σ
Z = ( 12000- 14000) / 1050
Z = - 2000/1050
Z = - 1,904
From z Table we get
for z = -1.904 P [ X ≤ 12000 ] = 0.0262
P [ X ≤ 12000 ] = 0.0262 or 2.62 %
b) What % of motors can be expected to operate more than 16100 hours
z = ( 16100 - 14000) / 1050
z = 2100/1050 ⇒ 2
From the z table, we find with z = 2 total number of f motors operating up to 16100 hours
From the z table, we find 0,9772
Then the probability of motors operating for more than 16100 hours is:
P [ X > 16100] = 1 - 0.9772 = 0,0228
Then
P [ X > 16100] = 0,0228 or 2,28 %
c) The average hours of operation before failures if only 1% of motors would be replaced free of charge is:
1% = 0,01 Probability then z score is z = 0,4960
0,4960 = ( 14000 - X ) / 1050
0,4960 * 1050 = ( 14000 - X )
520,8 - 14000 = - X
X = 13479,2 hours as is not common such offer company could set up a guarantee for 13500 h
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Suppose you are trying to find your longitude and start looking for when the shadows are shortest at your house. You discover that this happens at 1:14:20 p. M. EDT (Eastern Daylight Savings Time). What is this time in GMT? Remember that EDT = GMT – 4. 2Points Be sure to show your work to earn full credit
Time in GMT is 5:14:20 P.M (GMT)
Eastern Daylight Saving Time is four hours behind GMT (Greenwich Mean Time).
The time on the Earth's meridian, or zero-degree line of longitude, is known as Greenwich Mean Time (GMT). This passes via the Old Royal Observatory in the London district of Greenwich on its way from the North Pole to the South Pole.
This is,
Eastern Standard Time is equal to Greenwich Mean Time plus four.
Therefore,
1:14:20 p.m. EDT (Eastern Daylight) will be equivalent to;
1:14:20 p.m + 4 hours (GMT)
5:14:20 P.M (GMT)
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Consider two stars, star A and star B. Star A is 22 light-years from Earth, and star B is 34 light-years from
Earth. Viewing from Earth, the angle between them is 60 degrees. What is the distance between star A
and star B in light-years? (Round your answer to the nearest hundredth.)
The distance that exists between star A and B is given as 29.87 light years
How to solve for the distance that exists between the the starsWe can solve this by creating a triangle where Point a Is star a, point b is star b and the point c is earth
the angle is given as 60 degrees
AC = 22 light years
BC = 34 light years
ab² = ac² + bc² - 2 *ac * bc* cos60
we would have to put in the values
ab² = 22² + 34² - 2 * 34 * 22 * cos 60
ab² = 484 + 1156 - 748
ab² = 892
square both sides
ab = 29.87 light years
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what is (8/9)^2 pls i need it
Answer: about 0.79
Step-by-step explanation:
First divide 8 by 9 --> (8/9) = about 0.8889
then square that value --> (0.8889)^2 = about 0.79.
PEMDAS is your friend!
Multiple Choice 1. Which proportion can be used to determine what number is 15% of 30? (1 point) 15/30=x/100 15/100=x/30 15/100=x/30 30/100=x/15
Answer:4.5
Step-by-step explanation:
can someone help me with 11 and 12
Answer:
see below
Step-by-step explanation:
11: write 3 equiv ratio of 1:3, so it' could be 3:9, 2:6, 4:12
12. 20:15 = 4:3, 12:9, 8:6
I really need help with this question please and thank you
Answer:
9. reduction, 1/2
10. enlargement, 3/2
11. enlargement, 3
12. reduction, 1/3
Step-by-step explanation:
You want to know whether the dilations shown are reduction or enlargement.
Dilation
If the image (figure B) is larger, the dilation is an enlargement. (10, 11)
If the image (figure B) is smaller, the dilation is a reduction. (9, 12)
Scale FactorThe scale factor is the ratio of a length on the image to the corresponding length on the original figure. It will also be the ratio of distances from the center of dilation (the origin) of corresponding points.
9.The ratio of line lengths B/A is 3/6, a reduction by a factor of 1/2.
10.The ratio of distances from the origin on the x-axis is 3/2, an enlargement by a factor of 3/2.
11.The ratio of distances from the origin on the x-axis is 6/2, an enlargement by a factor of 3.
12.The ratio of distances from the origin on the x-axis is 2/6, a reduction by a factor of 1/3.
Heyy can anyone help me in this please IMP
Answer:
Step-by-step explanation:
Your parents are taking you and some of your friends to the movies tonight. Your parents might bring your grandparents and other adults to the movies as well. Adult tickets cost $11 each, and children's tickets cost $8 each. Write an equation that represents the total cost for the movie tickets. What is one combination of tickets that would total $57?
Answer:
57 = 33+24 = 3a+3c
Step-by-step explanation:
Let a= adults, c = children
total costs = 11a+8c
57 = 33+24 = 3a+3c
Answer: We can use the variables x and y to represent the number of adult tickets and children's tickets, respectively. The cost of adult tickets is $11 each and the cost of children's tickets is $8 each. So, we can use the following equation to represent the total cost for the movie tickets:
C = 11x + 8y
Where C is the total cost of the tickets, x is the number of adult tickets and y is the number of children's tickets
One combination of tickets that would total $57 is:
C = 11x + 8y = $57
x + y = 7 (number of tickets)
One way to satisfy this equation is to have 5 adult tickets and 2 children's tickets
x = 5
y = 2
C = 115 + 82 = $57
So, 5 adult tickets and 2 children's tickets is one combination that would total $57.
Step-by-step explanation:
If 479,000 people each receive an average refund of $4,500, based on an interest rate of 1 percent, what would be the lost annual income from savings on those refunds? (Do not round intermediate calculations. )
As per the compound interest, the lost annual income from savings on those refunds is $21,555,000
In math the term called compound interest is defined as a type of interest that not only accrues on the principal but also on the accrued interest and the interest rates on loans are quoted in terms of annual percentage rate, which does not account for the compounding of interest, and therefore understates the true cost of borrowing.
Here we know that the 479,000 people each receive an average refund of $4,500, based on an interest rate of 1 percent.
Then the lost annual income from savings on those refunds is calculated as,
As we all know that the lost annual income is the amount of interest these people could have earned on their income, in which the extra tax had not been deducted.
Then With $4,500 each person,
Then the total amount of the deducted income is calculated as,
=> 479,000 x 4,500 = 2,155,500,000.
Here we have the 1% interest rate, then the net return on these fund if they were saved
=> 2,155,500,000 x 1% = 21,555,000.
Therefore the total lost annual income is 21,555,000
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There are five possibilities for whole numbers such that radical expression 4 ≤ √3 + √x ≤ 5: {6, 7, 8, 9, 10}
How to derive an integer for a radical expression
In this problem we have the case of a radical expression, from which we need to determine at least a whole number such that following inequality is fulfilled:
4 ≤ √3 + √x ≤ 5
This can be done by algebra properties. First, determine the limits of the inequality:
4 ≤ √3 + √x
4 - √3 ≤ √x
(4 - √3)² ≤ x
x ≥ (4 - √3)²
x ≥ 16 - 8√3 + 3
x ≥ 19 - 8√3
√3 + √x ≤ 5
√x ≤ 5 - √3
x ≤ (5 - √3)²
x ≤ 25 - 10√3 + 3
x ≤ 28 - 10√3
There are five possibilities for five whole numbers: 6, 7, 8, 9, 10
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An architect is designing a building. Each floor will be 12 feet tall. Write an expression for the number of floors the building can have for a given building height. Tell what the variable in your expression represents
elect ALL factors of 15. (Be sure to select ALL correct factors for full credit).
Question 5 options:
45
5
2
3
30
15
9
1
Answer:
1,3,5,15
Step-by-step explanation:
A factor cannot be greater then the number itself so we can scratch 30 and 45. 15 is divisible by itself and 1, as every other number. 2 is not a factor of 15 because 15 is not even. Also not 9. But it does have factors 5 and 3 because 5×3=15.
Hope that helps, let me know if you have any further questions!
Translate the following into equivalent predicate statement :
i. There is an integer whose square is twice itself.
ii. No school buses are purple.
iii. If a real number is even, then its square is even.
i. ∃x ∈ Z, x² = 2x, ii. ∀y ∈ school buses, y is not purple and iii. ∀x ∈ R, if x is even, then x² is even.
i. The equivalent predicate statement for the first statement is:
∃x ∈ Z, x² = 2x
The symbol "∃" means "there exists", the symbol "∈" means "is an element of", and the symbol "Z" represents the set of integers.
ii. The equivalent predicate statement for the second statement is:
∀x, (x is a school bus) → (x is not purple)
The symbol "∀" means "for all", and the symbol "→" means "implies".
iii. The equivalent predicate statement for the third statement is:
∀x ∈ R, (x is even) → (x² is even)
The symbol "∈" means "is an element of", and the symbol "R" represents the set of real numbers.
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20/3 / 1/6 what is the miles per gallon
Answer: 20/3 / 1/6 is a division problem that can be simplified as follows:
20/3 divided by 1/6 = (20/3) * (6/1) = (206) / (31) = 120/3 = 40
The value of the division is 40. However, without knowing the context, it is impossible to know what the meaning of this value is. In particular, without knowing the units of 20/3 and 1/6, it is not possible to interpret the division as miles per gallon or any other unit.
It is important to note that 20/3 and 1/6 should be represented as mixed numbers (6 2/3 and 1/6) or as decimal numbers (6.66 and 0.16666) in order to be able to proceed with the division.
Step-by-step explanation:
What is the slope of the line in the graph below?
undefined
−2
2
0
Answer:
Step-by-step explanation:
The slope of the given line in the graph is "undefined".
Define the term slope of the line?Slope, usually referred to as rise over run, is the "steepness" of the line.
By dividing the difference in y values between two points by the difference in x values, we may determine slope.
A line's slope does not summarily characterize it. As a result, even if you know a line's slope, you cannot identify the exact spots the line passes through.Any two lines with the same slope are said to be parallel. When a line is rotated 90 degrees, it becomes perpendicular and becomes parallel. A horizontal line is one that has a slope of 0. Positive lines are those that rise as they move further to the right.The y-axis is an example of a vertical line that is believed to have an "undefined" slope.Thus, as the line is passing through the y axis and parallel to the x axis, the slope of the given line is undefined.
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I NEED HELP ASAP
A toy manufacturer is designing a new triangular-shaped toy. The company would like the toy to have a specific area. Write the equation for the area of a triangle. Solve your formula for the height. The company specified that the area of the toy must be 60 square inches and the length of the base must be 12 inches. Use your formula to determine the height of the new toy.
The height of the triangle with area of 60 square inches and the base of 12 inches is 10 in.
What is an equation?An equation is an expression that shows the relationship between numbers and variables.
The area of a triangle is the amount of space it occupies. The area is the product of the base and height divided by 2. It expressed as:
Area = (1/2) * base * height
Given that the area is 60 square inches and the length of the base must be 12 inches. Let h represent the height
Therefore:
Area = (1/2) * base * height
60 = (1/2) * 12 * h
6h = 60
h = 10 in
The height of the triangle is 10 in.
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the coefficients of the terms on the right side of a ___ equation are the numbers in the triangle.
The figures in the triangle represent the coefficients of the terms on the right side of a binomial equation.
Binomial Theorem: The expansion grows complex and time-consuming to calculate as the power rises. The Binomial Theorem can be used to quickly calculate a binomial statement that has been raised to a very high power. Find out everything there is to know about the binomial theorem, including its definition, characteristics, and uses.
An expression that has been raised to any finite power can be expanded using the binomial theorem. A useful expansion technique with applications in probability, probability theory, and algebra is the binomial theorem.
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Lenny has 104 coins in his pocket made up of nickels and dimes worth
$22.00. Write and solve a system of equations to find out how many
nickels and quarters he has.
On solving the equations x + y = 104 and 0.05x + 0.25y = 22, the number of nickels and quarters Lenny has is 20 and 84 respectively.
What is an equation?
A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("=").
The value of 1 nickel is = $0.05
The value of 1 quarter is = $0.25
The total amount of coins is = $22.0
The total number of coins is = 104
Let the number of nickel be = x
Let the number of quarter be = y
The equation for total number of coins =
x + y = 104 ....(1)
The equation for total amount of coins =
0.05x + 0.25y = 22 ...(2)
Multiply equation (1) by 0.05 -
0.05(x + y) = 104 × 0.05
0.05x + 0.05y = 5.2 ... (3)
Subtracting equation (3) from (2) -
0.05x + 0.25y - (0.05x + 0.05y) = 22 - 5.2
0.05x + 0.25y - 0.05x - 0.05y = 22 - 5.2
0.20y = 16.8
y = 84
Substitute the value of y in equation (1) -
x + 84 = 104
x = 104 - 84
x = 20
Therefore, the value for x and y is obtained as x = 20 and y = 84.
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PLSSS HELP IF YOU TULRY KNOW THISSSS
Answer: The answer is 7
Step-by-step explanation:
Answer: x = 7
Step-by-step explanation:
Subtract 7 on each side to isolate X
7 + x = 14
-7 -7
x = 7
On a team, 3 girls and 2 boys scored a total of 27 points. The difference between the number of points scored by the 3 girls and the number of points scored by the 2 boys is 15. Each girl scored the same number of points, and each boy scored the same number of points. Find the number of points scored by each girl and each boy.
Answer:
We can start solving the problem by using algebra. Let x be the number of points scored by each girl, and y be the number of points scored by each boy. Then, based on the information given in the problem, we have the following equations:
x + y = 27 (the total number of points scored by the team)
3x - 2y = 15 (the difference between the number of points scored by the 3 girls and the 2 boys)
To solve for x and y, we can use the second equation to eliminate one of the variables. Multiplying both sides of the second equation by 2, we get:
6x - 4y = 30
Now we can substitute this into the first equation:
6x - 4y + y = 27
6x = 27 + 4y
x = (27 + 4y)/6
Now we can substitute this back into the second equation:
3((27 + 4y)/6) - 2y = 15
27 + 2y - 2y = 15
27 = 15
This is a contradiction, so the given information is insufficient to find the number of points scored by each girl and each boy.
Step-by-step explanation:
The figure shows the measurements, in inches, of a rectangular prism. 8 in 12 in 7 in What is the volume of the prism
A:92 in B: 236 in C: 472 D: 672
Answer:
672 in.³
Step-by-step explanation:
V = LWH
V = 8 in. × 12 in. × 7 in.
V = 672 in.³
Answer: D 672
Step-by-step explanation: The formula for volume is L x W x H = V so if you plug all those numbers in and multiply u get 672
The ratio of the number of Mimi’s Eminem cd’s to the number of Rita’s Eminem cd’s is 5:8. Rita has 18 more Eminem cd’s than Mimi. If Rita gives 22cd’s to Mimi, what will be the new ratio of the number of Mimi’s Eminem cd’s to Rita’s?
2:1 is the new ratio of the number of Mimi’s Eminem cd’s to Rita’s.
What is Ratio?A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0.
let Rita has X CDs.
Then Mimi has x-18 CDs.
x-18/x=5/8
8(x-18)=5x
Apply distributive property
8x-144=5x
Subtract 5x+144 on both sides
3x=144
Divide both sides by 3
x=48
Now Rita has 48-22= 26 CDs .
Mimi has 30+22= 52 CDs.
Required Ratio = 52:26 = 2:1
Hence, 2:1 is the new ratio of the number of Mimi’s Eminem cd’s to Rita’s.
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Find the measure of angles 1 and 2
Answer:
angle 1 = 118 deg
angle 2 = 62 deg
Step-by-step explanation:
To find angle one you must know that angles 1 and 118 deg are alternate angles. Therefore since these lines are parallel, angles 1 and 118 are equal.
To find angle 2 to you must know that angle 1 + angle 2 = 180.
angles on a straight line always equal 180 deg
therefore:
180
118 -
62 deg
hope this helps :)
Answer:
m<1 = 118°
m<2 = 62°
Step-by-step explanation:
The horizontal lines are parallel.
Angles 1 and 118° are alternate interior angles of parallel lines cut by a transversal, so they are congruent.
m<1 = m<2 = 118°
Angles 1 and 2 are a linear pair, so they are supplementary. That means that their measures add to 180°.
m<1 + m<2 = 180°
118° + m<2 = 180°
m<2 = 62°
Please help!!
Which of the following statements is true about the triangles below
Answer: ASA
Step-by-step explanation: Hello! You can use ASA to prove that the triangles ABC and ABD are congruent. This is because you are given two angles of each triangle. You know that your answer should be ASA or AAA, which are the only two triangle congruence postulates that involve two or more congruent angles. Lastly, you can use the reflexive property. An example of reflexive property is 3 = 3, which means anything is congruent to itself. You know that both triangles share line segment AB, meaning that they have one side and two angles that are congruent. Since you know that the two angles and the included side are congruent, ASA proves that both triangles ABC and ABD are congruent. I hope this helps you!
What would the answer be?
Answer: AAS → Makes the most sense
- They give two angles and a side for both triangles
Step-by-step explanation:
Plot a point on the coordinate plane to represent each of the ratio values in the table.