Part A
x = amount of money she starts with
(4/9)x = cost of the dress
(5/9)x = amount of money leftover after buying the dress
note that 4/9 and 5/9 add to 1 to represent 100% of her money
(3/4)*(5/9)x = (15/36)x = (5/12)x = amount spent on shoes
We see that she spent 5/12 of her original amount of money on shoes.
-----------------------
We can look at a more concrete example if the previous section does not make sense.
Let's multiply the denominators 9 and 4 to get 9*4 = 36. Doing this trick will mean that the later steps won't involve decimal values.
Let's say she starts off with $36
Multiply that with 4/9 to get (4/9)*36 = 16. So in this hypothetical situation, the dress costs $16 and she's left with 36-16 = 20 dollars.
Multiply that 20 by 3/4 to get (3/4)*20 = 15
In this situation, the shoes cost $15
We'll then divide the cost of the shoes (15) over the original amount of money she started with (36)
15/36 = (3*5)/(3*12) = 5/12
-----------------------
Answer: 5/12=======================================================
Part B
From the first section in part A, we found that:
(4/9)x = amount of money spent on the dress(5/12)x = amount of money spent on shoesAdd those two expressions
(4/9)x + (5/12)x = (16/36)x + (15/36)x = (31/36)x
This indicates that buying the dress and shoes will cost (31/36)x dollars, where x is the original amount of money Jing has to start with.
The amount left over is (5/36)x because 5/36 adds with 31/36 to get 1.
Take 1/3 of this to get:
(1/3)*(5/36)x = (5/108)x
Then set this equal to 18 and solve for x
(5/108)x = 18
5x = 18*108
5x = 1944
x = 1944/5
x = 388.80
--------------------
Let's check the answer
If she starts with 388.80 dollars, then the dress costs (4/9)*388.80 = 172.80
She's left with 388.80 - 172.80 = 216 dollars after buying the dress.
She then spends the remaining 3/4 of that on shoes. So (3/4)*216 = 162 dollars is spent on the shoes.
Jing now has 216 - 162 = 54 dollars left over.
1/3 of which is spent on the shoe bag, meaning it costs (1/3)*54 = 18 dollars
This confirms our answer.
--------------------
Answer: $388.80The price of a home (in thousands of dollars) is associated with the number of square feet in a home. Home prices in Smavile can be modeled using the equation p = 150 + 0.041a where p is the price of the home in thousands of dollars and a is the area of the house in square feet Home prices in Fancyville can be modeled using the equation p = 250 + 0.198a Ngoc saw a real estate advertisement for a 2800 square foot home that was selling for $280,000. Which city should she predict that the home is in?
Ngoc should predict that the home is located in Smavile based on the real estate advertisement
How to determine the city she should predict that the home is in?From the question, we have the following parameters that can be used in our computation:
Function 1: p = 150 + 0.041a (Smavile)
Function 2: p = 250 + 0.198a (Fancyville )
Where
a = area
p = price
From the question, we have
a = area = 2800
p = price = 280000
Using the above as a guide, we have the following:
So, we have
Function 1: p = 150 + 0.041 * 2800 (Smavile)
Evaluate the expression
p = 264.8 -- false
Function 2: p = 250 + 0.198 * 2800 (Fancyville )
Evaluate the expression
p = 804.4 --- false
264.8 is closer to 280 than 804.4
Hence, the home is in Smavile
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A girl read a book that had 1,159 pages. She read 72 pages on the first day. She then read 40 pages per day until she finished the book. Which equation can be used to find how many more days, d, it took her to read the book after the first day?
Answer:
The girl read 1,159 - 72 = 1,087 pages after the first day.
Let d be the number of days after the first day that she took to finish the book.
The total number of pages she read on these d days is 40d.
The equation that can be used to find how many more days it took her to read the book after the first day is:
40d = 1,087
Solving for d:
d = 1,087/40
d ≈ 27.175
Therefore, it took her approximately 27 more days to finish reading the book after the first day.
A group of 6 students was asked, "How many hours did you watch television last week?" Here are their responses: 19, 9, 18, 16, 14, 19 Find the mean and median number of hours for these students.
Answer:
Mean = 15.83 hours
Median = 17 hours
Step-by-step explanation:
The first step to follow when dealing with data distributions is to arrange the data in either an ascending or descending order.
Once this is done, we have the responses as
responses: 9. 14, 16, 18, 19, 19
The mean of the distribution can be obtained by dividing the total sum of the values, by the number of respondents.
this is \(9 +14 + 19 + 18 + 16 + 14 + 19/ 6= 95/6 = 15.83\)
The mean of the distribution is 15.83 hours
The median is obtained by picking out the middle number of the distribution. However, our distribution is even, and hence has two middle numbers. To solve this , we simply add the two numbers and divide by 2
= (16 + 18 )/2 = 34/2 = 17
Answer:
(a) The average television hours for the six students in the previous week was 15.83 Hours.
(b) The median number of hours would be 17 Hours
Step-by-step explanation:
Mean
The mean of a group of numbers is the average of the numbers. The mean can be gotten with the expression in equation 1.
Mean = Σx / n ...............1
Where Σx is the sum of the numbers
n is the number of values
Substituting our values into equation 1 we have;
Mean = (19+9+18+ 16+14+19) ÷ 6
Mean = 95 ÷ 6
= 15.83 Hours
Therefore the average television hours for the six students in the previous week were 15.83 Hours.
MedianThe median of a group of numbers is the middle term of the numbers when arranged in ascending or descending order.
Given the television hours of the six students, we have;
19, 9, 18, 16, 14, 19
We arrange the numbers in ascending order from the smallest to the biggest;
9, 14, 16, 18, 19, 19
Since the number of value is even the median would be obtained by finding the mean of the two middle terms.
From our arranged data, 9, 14, 16, 18, 19, 19
the two middle numbers are 16, 18
Therefore the mean would be
(16+18) /2
=34/2
= 17 hours
Thus the median number of hours would be 17 Hours
What value of y makes the number sentence shown true?
y−3=15
Answer:
18
Step-by-step explanation:
y-3=15
+3 +3
if you add 3 to the other side, you would get:
y=18
y= -x +3 and y = x - 1
Answer:
x=2 and y=1
Step-by-step explanation:
Rewrite equations:
y=−x+3;y=x−1
Step: Solve
y=−x+3
Step: Substitute−x+3foryiny=x−1:
y=x−1
−x+3=x−1
−x+3+−x=x−1+−x(Add -x to both sides)
−2x+3=−1
−2x+3+−3=−1+−3(Add -3 to both sides)
−2x=−4−2x−2=−4−2
(Divide both sides by -2)
x=2
Step: Substitute2forxiny=−x+3:
y=−x+3
y=−2+3
y=1(Simplify both sides of the equation)
Hope this Helps you :)
Find the values of x and y that make k || j and m || n. x = ° y = °
By using properties of parallel lines, the results obtained are
x = 80°, y = 130°
What are parallel lines?
Parallel lines
Two lines are said to be parallel if on extending them indefinitely, they will never intersect
Transversal is a line that intersects two or more parallel lines
Here, by using properties of parallel lines,
x + 50 + x - 30 = 180 [Co interior angles are supplementary]
2x + 20 = 180
2x = 180 - 20
2x = 160
x = \(\frac{160}{2}\\\)
x = 80°
x - 30 + y = 180 [Co interior angles are supplementary]
80 - 30 + y = 180
50 + y = 180
y = 180 - 50
y = 130°
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Complete Question
The diagram has been attached
Find the values of x and y that make k || j and
m || n.
x =
y =
Please help me with this question
Answer:
m < ABC is "The measure of angle ABC"
Step-by-step explanation:
The m < ABC denotes that it is the measure of the angle, < ABC.
The letter in the middle of the angle’s name has to be the point of the angle’s vertex. We know from the name <ABC that point B is the vertex of the angle in question. Since B is the vertex, any other name we could give to that same angle would have to stay true to which point is the angle’s vertex, meaning that B would have to be in the middle of the angle’s name.
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Help
Look at the picture it says what it needs.
The value of x and y for the angles are 4 and 9 respectively.
What is an equation?An exponential equation is an expression that shows how numbers and variables using mathematical operators.
10x - 4 = 6(x + 2) (opposite angles are equal to each other)
10x - 4 = 6x + 12
4x = 16
x = 4
Also:
18y - 18 = 16y
2y = 18
y = 9
The value of x and y are 4 and 9 respectively.
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A~B, what is the scale factor from B to A?
A. 1/2
B. 2/5
C. 2
D. 5/2
Answer:
I cant help you completely but it has to be C or D because it is bigger and not smaller
Step-by-step explanation:
make x subject of m =n + x/p
Answer:
\(x = p(m-n)\)
Step-by-step explanation:
m = n + \(\frac{x}{p}\)
Subtracting n to both sides
=> m-n = \(\frac{x}{p}\)
Multiplying p to both sides
=> \(x = p(m-n)\)
Answer:
x=p(m-n)
Step-by-step explanation:
m =n + x/p
x/p=m-n
x=p(m-n)
A study at a college on the west coast reveals that, historically, 36% of the students are minority students. If a random sample of 100 students is selected, what is the probability that between 31.2% and 50.4% students in the sample will be minority students?
The probability that between 31.2% and 50.4% of the students in the sample will be minority students is approximately 0.7154, or 71.54%.
To solve this problem, we can use the normal approximation to the binomial distribution, assuming that the sample size is large enough. The mean (μ) of the binomial distribution is given by n * p, where n is the sample size and p is the probability of success. In this case, the sample size is 100 and the probability of success is 0.36.
μ = n * p = 100 * 0.36 = 36
The standard deviation (σ) of the binomial distribution is given by the square root of n * p * (1 - p).
σ = √(n * p * (1 - p)) = √(100 * 0.36 * (1 - 0.36)) ≈ 4.16
To calculate the probability between 31.2% and 50.4%, we need to convert these percentages into z-scores using the formula:
z = (x - μ) / σ
where x is the observed value, μ is the mean, and σ is the standard deviation.
For 31.2%:
z1 = (31.2 - 36) / 4.16 ≈ -1.06
For 50.4%:
z2 = (50.4 - 36) / 4.16 ≈ 3.37
Next, we need to find the cumulative probabilities associated with these z-scores using a standard normal distribution table or calculator. The cumulative probability can be interpreted as the area under the normal curve up to a given z-score.
P(31.2% ≤ x ≤ 50.4%) = P(-1.06 ≤ z ≤ 3.37)
Using a standard normal distribution table or calculator, we can find the corresponding cumulative probabilities:
P(-1.06 ≤ z ≤ 3.37) ≈ 0.8577 - 0.1423 ≈ 0.7154
Therefore, the probability that between 31.2% and 50.4% of the students in the sample will be minority students is approximately 0.7154, or 71.54%.
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1.A five pack of theater tickets cost $88.75 what is the unit price per ticket?
2.A 4 pack of monster cards costs $6.56, what is the unit price per card?
3.An 8 pack of stickers cost $0.64, what is the unit price per sticker?
4. An 9 pack of apple cost $6.30, what is the unit price per apple?
5. A 5 pack of muffins costs $6.25, what is the unit price per muffin?
6. A 9 pack of lollipops costs $5.85, what is the unit price per lollipop?
7. A 3 pack of batteries costs $ 4.65, what is the unit price per battery?
8. A 6 pack of pencils cost $4.80, what is the unit price per pencil?
9. A 2 pack of books costs $24.80, what is the unit price per book?
10. A 5 pack of stamps cost $5.95, what is the unit price per stamp?
11. An 8 pack of eggs costs $4.80, what is the unit price per eggs?
12. A 10 pack of candy bars costs $5.70, what is the unit price per candy bar?
Answer:
1. 17.75 per ticket
2. 1.64 per card
3. 0.08 per sticker
4. 0.07 per apple
5. 1.25 per muffin
6. 0.65 per lolipop
7. 1.55 per battery
8. 0.80 per pencils
9. 12.40 per book
10. 1.19 per stamp
11. 0.60 per egg
12. 0.57 per candy bar
Step-by-step explanation:
price divided by ammount
convert this equation into standard form
y=-0.25(x+0)(x-8)
Solve the following initial value problem. + 1/2 y₁ = −6y₁ = -2y1 3y2 y₁(0) = 5, y2(0) = 3. Enter the functions y₁(x) and y2(x) (in that order) into the answer box below, separat
A differential equation is a type of mathematical equation that connects the derivatives of an unknown function.
The differential equation is 1/2 y₁ = −6y₁ = -2y1 3y2.
The initial conditions are
y₁(0) = 5, y2(0) = 3.
The solution of the differential equation is: First we solve the differential equation for
y1:1/2 y₁ = −6y₁−2y1⇒
1/2y₁ + 6y₁ = 0+2y₁⇒
13/2 y₁ = 0⇒
y₁ = 0.
Therefore, y₁(x) = 0 is the solution to the differential equation. Now we solve the differential equation for
y2:3y2 = 0⇒
y2 = 0.
Therefore, y2(x) = 0 is the solution to the differential equation. The initial conditions are
y₁(0) = 5, y2(0) = 3.
So the solution to the differential equation subject to the initial conditions is
y₁(x) = 5 and
y2(x) = 3.
The functions y₁(x) and y2(x) (in that order) are:
y₁(x) = 5, y2(x) = 3.
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Which Of the following could be the ratio between Of the two legs Of a 30-60-90 triangle? (Apex Quiz)
The ratio of the two legs of the triangle 30-90-60 will be 1 : √3.
What is trigonometry?The branch of mathematics that sets up a relationship between the sides and the angles of the right-angle triangle is termed trigonometry.
The trigonometric functions, also known as a circular, angle, or goniometric functions in mathematics, are real functions that link the angle of a right-angled triangle to the ratios of its two side lengths.
The triangle is 30-90-60. The ratio of the two legs will be calculated as,
tan(30) = AB / BC
1 / √3 = AB / BC
Hence, the ratio of the two legs will be 1 : √3.
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Find the missing side lengths. Leave your answer as radicals in simplest form.
The values of the sides are;
41. x = 18√3. Option D
42. x = 6√3. Option A
How to determine the valuesUsing the different trigonometric identities, we have;
41. Using the tangent identity, we have;
tan 60 = 9√2/y
cross multiply the values
y =9√2 ×√3
y = 9√6
Using the sine identity;
sin 45 = y/x
1/√2 = 9√6/x
cross multiply the values, we have;
x = 9√2 ×√3 ×√2
x = 18√3
42. Using the cosine identity
cos 60 = 3√3 /x
cross multiply, we have;
x = 6√3
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there are more than 7 shades of skin color. can you offer an explanation?
First and foremost, it is important to note that human skin color is determined by a variety of factors, including genetics, environmental influences, and geographic location. In fact, skin color is the result of the amount and type of melanin pigment produced by specialized cells in the skin called melanocytes.
There are two main types of melanin pigment: eumelanin and pheomelanin. Eumelanin is responsible for producing darker skin colors, while pheomelanin produces lighter skin colors. However, the amount and distribution of these pigments can vary greatly between individuals, resulting in a wide range of skin tones.
Additionally, skin color can also be influenced by factors such as sun exposure, age, and hormonal changes. For example, prolonged sun exposure can lead to darker skin, while aging and hormonal changes can cause changes in skin pigmentation. Furthermore, it is important to note that skin color is not always clearly defined or easily categorized into specific shades. There can be a great deal of variation within a single skin tone, as well as overlap between different skin tones. This is due to the complex interplay of genetic and environmental factors that contribute to skin color.
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three cards are drawn without replacement from the 12 face cards (jacks, queens and kings) of an ordinary deck of 52 playing cards. let x be the number of kings selected and y the number of jacks selected.
The joint probability distribution function are;
P (Y = 3 | X = 1) = 1/55
P (Y = 2 | X = 2) = 3/55
P (Y = 1 | X = 3) = 12/55
P (Y = 0 | X = 4) = 1/220
To determine the joint probability distribution function, we have to find the probability of each possible outcome (x,y) for the random variables X and Y.
If X = 1, then select three cards of the same kind, that can only be a set of three jacks or three queens or three kings, or three aces.
P (Y = 3 | X = 1) = 4/220 = 1/55
If X = 2, then we are selecting two cards of one kind and one card of another kind. The first kind can be any of the four face card denominations, and the second kind can be any of the remaining three face card denominations. So, the number of possible sets is 4 × 3 = 12.
P (Y = 2 | X = 2) = 24/220 = 3/55
If X = 3, then we are selecting one card of each of three different kinds. The first kind could be any of the four face card denominations, the second kind could be any of the three remaining face card denominations, and the third kind can be any of the two remaining face card denominations.
P (Y = 1 | X = 3) = 1536/220 = 12/55
Finally, if X = 4, then we are selecting one card of each of the four different kinds, which could only be the four jacks.
P (Y = 0 | X = 4) = 1/220
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The complete question is
Three cards are drawn without replacement from the 12 face cards of an ordinary deck of 52 playing cards. Let X be the number of kinds selected and Y be the number of jacks selected. Find the joint probability distribution function.
8 elephants plus 4 elephants equal
19. find the dimensions of a right circular cylinder of maximum volume that can be inscribed in a sphere of radius 10 cm. what is the maximum volume?
A right circular cylinder with the largest volume that can fit within a sphere with a 10 cm radius will have a maximum radius of 8.165 cm and a maximum height of 11.55 cm. Additionally, the largest volume is 2417.82 cm³.
What is cylinder?A cylinder is a three-dimensional solid in mathematics that maintains, at a given distance, two parallel bases connected by a curving surface. These bases often have a circular form (like a circle), and a line segment known as the axis connects the centers of the two bases. The height of the cylinder is "h," while the radius of the cylinder is "r," measuring the distance from the axis to the outside surface.
Here,
radius=10 cm
r²+h²/4=10²
r²=10²-h²/4
volume=πr²h
=π(10²-h²/4).h
V=π(10²h-h³/4)
dV/dh=π(10²-3h²/4)
dV/dh=0
10²=3h²/4
10²*2²/3=h²
20/√3=h
h=11.55 cm
r²=10²-h²/4
=10²-(10²*2²/3)/4
r²=(100-400/12)
r²=100-33.33
r²=66.67
r=√66.67
r=8.165 cm
volume=πr²h
=3.14*8.165*8.165*11.55
volume=2417.82 cm³
The dimensions of a right circular cylinder of maximum volume that can be inscribed in a sphere of radius 10 cm will be 8.165 cm radius and 11.55 cm height. Also the maximum volume is 2417.82 cm³.
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Use the graph to determine the domain and range. Then state whether the relation is a function.
What is the domain of the function?
Answer:
[-2, 4]
Step-by-step explanation:
The domain of a function is the set of all x-values a relation could possibly take on to have an output. This is represented by in the graph by having the line correspond to the x-value. From the graph shown we can see that x-values from -2 to 4 have a line corresponding to them, and the dots are closed meaning it is inclusive. This would be written as: [-2, 4]
Find the area of each figure.
Answer:
132 m²
Step-by-step explanation:
The rectangle is 20 m by 6 m.
Base of triangle: 20 m - 8 m - 6 m = 6 m
Height of triangle: 10 m - 6 m = 4 m
The triangle has a base of 6 m and a height of 4 m.
A = LW + bh/2
A = 20 m × 6 m + (6 m × 4 m)/2
A = 120 m² + 12 m²
A = 132 m²
Which of the following best describes the equation below?
y = -2x2 - 4
A.
both linear and nonlinear
B.
neither linear nor nonlinear
C.
nonlinear
D.
linear
Answer:
I think it's C nonlinear
Step-by-step explanation:
Answer:
d
Step-by-step explanation:
use desmos calculator helps with these question
what is the area of a semicircle with a diameter of 12.5 ft
radius = 12.5/2 = 6.25 feet
area = \(\frac{1}{2} \pi r^{2} = \frac{1}{2}\pi (39.0625) = 19.5312\pi\) square feet
Determine the number of significant figures in each measurement. Then, choose the representation of the number where x is in place of the estimated digit from the measurement Number of Measurement Estimated Digit Significant Figures 14.8 m 3 ✓ Choo *4.8 Txa 14. $10.25 Choose... 0.05 L Choose 1.000 g/ml Choose.. 6200 cm Choose... 403 kg Choose Figures 14.8 m 3 Choose... $10.25 ✓ Choose... 10.35 10,2% 1x.25 NO.25 0.05L Choose. 1.000 g/ml Choose 6200 cm Choose. Choose.. 403 kg place of the estimated digit from the measurement. Number of Measurement Estimated Digit Significant Figures 14.8 m 3 Choose... $10.25 Choose... II 0.05 L ✓ Choose.. 0.x5 x.05 0.0x 1.000 g/mL Choose... 6200 cm Choose... 403 kg Choose... Determine the number of significant figures in each measurement. Then, choose the representation of the number where x is in place of the estimated digit from the measurement. Number of Measurement Estimated Digit Significant Figures 14.8 m Choose... 3 $10.25 Choose... 0.05 L Choose... 1.000 g/mL Choose 1.00 1.0x0 X.000 1.200 Choose... 6200 cm Choose.. 403 kg Determine the number of significant figures in each measurement. Then, choose the representation of the number where x is in place of the estimated digit from the measurement. Number of Measurement Estimated Digit Significant Figures 14.8 m Choose... 3 $10.25 Choose... Choose... 0.05 L Choose... 1.000 g/ml 6200 cm ✓ COD Bx00 x200 620x 6220 Choose 403 kg Determine the number of significant figures in each measurement. Then, choose the representation of the number where x is in place of the estimated digit from the measurement Number of Measurement Estimated Digit Significant Figures Choose... 14.8 m 3 $10.25 Choose... Choose... 0.05 L 1.000 g/mL Choose.. Choose... 6200 cm 403 kg ✓ Choose XO3 40% 4x3
The table shows the estimated digit and significant figures of each measurement and their representation with x.
Number of Measurement Estimated Digit Significant Figures
14.8 m 3 ✓
$10.25 - ✓
0.05 L - ✓
1.000 g/mL - ✓
1.200 - ✓
6200 cm - ✓
403 kg - ✓
For each measurement, the estimated digit is replaced with an x to represent the number with the correct number of significant figures. The correct representations for each measurement are:
14.8 m: 15.0 m$10.25: $10.30.05 L: 0.050 L1.000 g/mL: 1.00 g/mL1.200: 1.206200 cm: 6200 cm403 kg: 400 kgNote that in some cases, the representation requires adding zeros to the right of the decimal point to indicate the number of significant figures. In other cases, the representation requires rounding up or down to the correct number of significant figures.
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a farmer has 2,000 meters 2,000 meters of fencing and wants to use it to create a rectangular area for grazing. the area will be against a stream so that only three sides will need to be fenced. what is the maximum area that can be enclosed?
The maximum rectangular area that can be fenced can be
2499 sq meters.
What are the area and perimeter of a rectangle?We know the perimeter of any 2D figure is the sum of the lengths of all the sides except the circle and the area of a rectangle is the product of its length and width.
We know for a quadrilateral, A square has the maximum area.
We also know That the product of two numbers is maximum when the difference between them is minimum.
Given, A farmer has 2,000 meters of fencing and wants to use it to create a rectangular area for grazing.
So, 2(l + b) = 2000.
l + b = 1000.
For a square, it would be 500 and 500, But to be a rectangle it can be 49 and 51.
Therefore, The maximum area would be,
= (51×49) sq meters.
= 2499 sq meters.
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A farmer has a rectangular field that measures 100 feet by 150 feet. He plans to increase the area of the field by 20%. He will do this by increasing the length and width by the same amount, x. Which equation represents the area of the new field? WILL GIVE BRAINLIEST
Answer:
(100 + x) x (150 + x) = 18,000 ft^2
Step-by-step explanation:
area of a rectangle = length x width
Area of the original field = 15,000
Area after 20% increase = 1.2 x 15,000 = 18,000
Increase i length = 100 + x
increase i width = 150 + x
Area = (100 + x) x (150 + x) = 18,000 ft^2
Answer
C
Step-by-step explanation:
It would be (100+x)(150+x) = 18,000 (incase if the answer isn't C for those)
He how do you do this
Answer:
I'm not sure. have you tried googling? Also where is comments on this site I'm kinda new
Step-by-step explanation:
the weights of bags of cement are normally distributed with a mean of 53 and a standard deviation of 2 a. what is the likelihood that a randomly selected individual bag has a weight greater than 50
The likelihood that a randomly selected bag of cement weighs more than 50 is approximately 93.32%
When dealing with normally distributed data, we use the mean and standard deviation to determine the likelihood of certain events occurring. In this case, the mean weight of bags of cement is 53 with a standard deviation of 2.
To find the likelihood that a randomly selected bag has a weight greater than 50, we need to calculate the z-score for 50. The z-score tells us how many standard deviations away a particular value is from the mean.
z = (X - μ) / σ
where X is the value we're interested in (50), μ is the mean (53), and σ is the standard deviation (2).
z = (50 - 53) / 2 = -1.5
A z-score of -1.5 means that a weight of 50 is 1.5 standard deviations below the mean. To find the likelihood of a bag weighing more than 50, we can use a z-table or a calculator to find the area to the right of this z-score.
Looking up a z-score of -1.5, we find that the area to the left is approximately 0.0668, which means the area to the right (the likelihood of a bag weighing more than 50) is:
1 - 0.0668 = 0.9332
Thus, the likelihood that a randomly selected bag of cement weighs more than 50 is approximately 93.32%.
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A grinding process has an upper specification of 1.649 inches and a lower specification of 1.507 inches. A sample of parts had a mean of 1.57 inches with a standard deviaiton of 0.026 inches.
Round your answer to four decimal places.
What is the process capability index for this system?
Answer:
The process capability index for this system is 0.9103
Step-by-step explanation:
Upper specification = 1.649 inches
Lowe Specification = 1.507 inches
Mean = 1.57 inches
Standard Deviation = 0.026 inches
Process Capability Index = PCI
PCI = (Upper specification - lower specification)/6(standard deviation)
So, we get,
PCI = (1.649 - 1.507)/((6)(0.026))
PCI = 0.142/0.156
PCI = 0.9102564
To four decimal places, we get,
PCI = 0.9103