Answer:
(2x+1)(2x−1)
Step-by-step explanation:
Step-by-step explanation:
I hope it helps man Hope you will understand my answer
1) Which expression represents the volume
of a shipping box?
Answer:
(s+2)^3
Step-by-step explanation:
I think this is referring to a square as a box, so the length of a jewelry box would be s. We learn that a shipping box is 2 inches longer, so s+2 = the length of the shipping box.
Volume = Length*Width*Height, but if square, all dimensions are the same, so s+2 to the power of 3 would be your answer.
Answer:answer (s+2)^3
Step-by-step explanation: ( I did it on iready
vertex (0,0) focus (0,-1)
A) y=1/4 x^2
B) y=-1/4x^2
C) y=1/16x^2
D) y=-1/16x^2
Answer:B
Step-by-step explanation:
6. A rectangle with a length of 15 feet has a
diagonal that measures 17 feet. Find the
perimeter of the rectangle.
Answer:
46 feet
Step-by-step explanation:
it is a 8-15-17 Pythagorean Triple (or you can use the Pythagorean theorem)
P=8+8+15+15=46
The perimeter of the rectangle with a length of 15 feet and has a diagonal that measures 17 feet is: A. 46 feet.
What is the Perimeter of a Rectangle?To find the perimeter of the rectangle, we need to know the width of the rectangle. Let's call the width of the rectangle W.
In a rectangle, the diagonal, length, and width are related by the Pythagorean theorem:
Diagonal² = Length² + Width²
In this case, the diagonal (D) is 17 feet, and the length (L) is 15 feet. So we have:
17² = 15² + W²
289 = 225 + W²
Now, let's solve for W:
W² = 289 - 225
W² = 64
W = √64
W = 8 feet
Now that we know the width is 8 feet, we can calculate the perimeter (P) of the rectangle:
Perimeter = 2 * (Length + Width)
= 2 * (15 + 8)
= 2 * 23
Perimeter = 46 feet
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Triangle rst has sides measuring 22 inches and 13 inches and a perimeter of 50 inches. what is the area of triangle rst? round to the nearest square inch.
The area of the triangle is 94.9 square inches
For given question,
We have been given triangle RST has sides measuring 22 inches and 13 inches and a perimeter of 50 inches.
Let x be the third side of ΔRST
⇒ 22 + 13 + x = 50
⇒ x = 50 - 35
⇒ x = 15
Let s = sum of three sides of the triangle / 2
s = (22 + 13 + 15)/2
s = 25
Now using the formula for the area of the triangle,
A = √[s × (s-a) × (s-b) × (s-c)]
Let a = 22 inches, b = 13 inches, c = 15 inches
Substituting the values,
⇒ A = √[25 × (25 - 22) × (25 - 13) × (25 - 15)]
⇒ A = √(25 × 3 × 12 × 10)
⇒ A = √9000
⇒ A = 94.9 square inches
Therefore, the area of the triangle is 94.9 square inches
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The area of triangle rst which have sides 22 inches and 13 inches with perimeter 50 inches is 95 square inches.
We are given that the two sides of the triangle rst are 22 inches and 13 inches respectively. Also perimeter of the triangle rst is 50 inches.
We have to find the area of triangle to the nearest square inches.
Let the third side of the triangle rst be x.
Hence,
22 + 13 + x = 50 inch
35 + x = 50 inch
x = 50 - 35
x = 15 inches
Hence, the third side of the triangle is 15 inches.
We will use the Heron's formula here to find the area of the triangle.
Heron's formula = \(\sqrt{s(s-a)(s-b)(s-c)}\)
Here,
s = Semi- perimeter
a, b, and c are sides of the triangle.
Hence,
\(s=\frac{50}{2} \\\\s=25 inches\)
a = 22 inches
b = 13 inches
c = 15 inches
Hence,
Area of the triangle rst = \(\sqrt{25(25-22)(25-13)(25-15)}\\\\ \sqrt{25(3)(12)(10)} =\sqrt{5*5*3*3*2*2*5*2}=5*3*2\sqrt{5*2}=30\sqrt{10}\)
We know that,
\(\sqrt{10}\) ≈ 3.162277
Hence,
\(\sqrt{10} * 30\) ≈ 94.86831 ≈ 95 square inches.
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A circular skating rink has a radius of 40 feet. Which expression can be used to find the circumference of the skating rink, in feet?
2.40.π is the expression can be used to find the circumference of the skating rink.
What is Circle?A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre.
Given that a circular skating rink has a radius of 40 feet.
Radius = 40 ft.
We need to find the expression can be used to find the circumference of the skating rink.
The formula for circumference of circle is 2πr.
Circumference=2.40.π.
Hence, 2.40.π is the expression which can be used to find the circumference of the skating rink.
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Answer: 2 x 40 x pie
Step-by-step explanation:
The width of a rectangle is w + 4 and the length of the rectangle is 2w + 3. Which expression represents the area of the rectangle?
Answer:
A= 2w^2 + 11w +12
Step-by-step explanation:
(w + 4)(2w + 3) = l x b = A
2w^2 + 3w +8w +12 = A
A= 2w^2 + 11w +12
1.Suppose a chef ices and decorates cupcakes in batches of 100. Each batch requires 40 minutes to setup the equipment, and each cupcake in the batch takes 1.25 minutes to process. Each unit in the batch must wait for the entire batch to be processed before moving on to packaging. What is the throughput capacity (in cupcakes and/or minutes) of the icing stage? Pick the closest answer.
.6
.8
1
1.25
1.65
2
2. Refer to the previous question. What is the throughput time for a batch of cookies, in minutes? Pick the closest answer.
1.25
2.5
40
125
140
The closest answer is 80 cupcakes per minute, so the correct option is .8. The closest answer is 165 minutes, so the correct option is 165.
The throughput capacity of the icing stage can be calculated by dividing the number of cupcakes in a batch (100) by the time required to process each cupcake (1.25 minutes).
Throughput capacity = Number of cupcakes in a batch / Time to process each cupcake
Throughput capacity = 100 cupcakes / 1.25 minutes
Throughput capacity = 80 cupcakes per minute
The closest answer is 80 cupcakes per minute, so the correct option is .8.
The throughput time for a batch of cupcakes is the time required to process the entire batch, including the setup time.
Throughput time = Time for setup + (Number of cupcakes in a batch * Time to process each cupcake)
Throughput time = 40 minutes + (100 cupcakes * 1.25 minutes per cupcake)
Throughput time = 40 minutes + 125 minutes
Throughput time = 165 minutes
The closest answer is 165 minutes, so the correct option is 165.
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answer each of the following questions. a. if a hen and a half lay an egg and a half in a day and a half, how long will it take a dozen hens to lay a dozen eggs? b. if 10 painters can paint 15 houses in 9 days, how many days will it take 20 painters to paint 20 houses? c. if 5 painters can paint 3 houses in 7 days, how many days will it take 8 painters to paint 10 houses?
a. It will take a dozen hens the same amount of time, a day and a half, to lay a dozen eggs.
Determine the same amount of time?The given information states that a hen and a half (1.5 hens) lay an egg and a half (1.5 eggs) in a day and a half. This implies that each hen lays 1 egg in 1 day.
Therefore, a dozen hens (12 hens) will lay a dozen eggs (12 eggs) in the same time frame, which is a day and a half.
b. It will take 9 days for 20 painters to paint 20 houses.
Determine how many days?Given that 10 painters can paint 15 houses in 9 days, we can calculate the rate at which painters can paint houses.
This means that each painter can paint 1.5 houses in 9 days.
Therefore, to paint 20 houses, we need 20 painters, and the number of days required remains the same. So, 20 painters will also take 9 days to paint 20 houses.
c. It will take 14 days for 8 painters to paint 10 houses.
Determine how many days?If 5 painters can paint 3 houses in 7 days, we can calculate the rate at which painters can paint houses.
This means that each painter can paint 0.6 houses in 7 days. Therefore, to paint 10 houses, we need 8 painters, and we can calculate the time required.
Hence, each painter can paint 0.6 houses in 7 days, so to paint 10 houses, 8 painters will take 14 days.
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Determine whether the given relation is an implicit solution to the given differential equation. Assume that the relationship does define y implicitly as a function of x and use implicit differentiation.
If it is not true, then the relation is not an implicit solution to the differential equation.
You have not provided the given relation and differential equation, so I will provide general steps to determine whether a given relation is an implicit solution to a differential equation using implicit differentiation and assuming that the relation defines y implicitly as a function of x.
1. Differentiate the relation with respect to x using implicit differentiation.
2. Substitute y' for dy/dx.
3. Simplify the resulting expression by collecting like terms.
4. Substitute the original relation into the simplified expression to obtain a statement that must be true if the relation is an implicit solution to the differential equation.
5. Check whether the resulting statement is true for all values of x and y that satisfy the original relation. If it is true, then the relation is an implicit solution to the differential equation.
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A video game that usually costs $30.65 is marked down 60%. Kelvin determined that the new price of the game would be $18.39. Look at Kelvin's work and find his error.
Answer: The answer is provided below
Step-by-step explanation:
A price markdown is a reduction that is deliberate when selling a product. From the question, we are informed that a video game that usually costs $30.65 is marked down 60%.
The find the new price of the video game, we have to subtract the amount reduced from the original price. The amount reduced is:
= 60% of $30.65
= 60/100 × $30.65
= 0.6 × $30.65
= $18.39
The new selling price = $30.65 - $18.39
= $12.26
The error that Kelvin made when he determined that the new price of the game would be $18.39 was that he didn't subtract the value from the original price of the video game.
A project under consideration has a 10-year projected life. The initial investment for the project is estimated to have a mean of $10,000 and a standard deviation of $1,000. The annual receipts are independent, with each year’s expected return having a mean of $1,800 and a standard deviation of $200. MARR is 12 percent. Assuming that initial investment and annual receipts are independent and normally distributed, estimate the probability that the present worth is negative using NORM.INV function in excel.
This value represents the present worth below which the probability is 0.5, indicating a negative present worth.
To estimate the probability that the present worth is negative using the NORM.INV function in Excel,
we need to calculate the present worth of the project and then determine the corresponding probability using the normal distribution.
The present worth of the project can be calculated by finding the sum of the present values of the annual receipts over the 10-year period, minus the initial investment. The present value of each annual receipt can be calculated by discounting it back to the present using the minimum attractive rate of return (MARR).
Using the given information, the present value of the initial investment is $10,000. The present value of each annual receipt is calculated by dividing the expected return of $1,800 by \((1+MARR)^t\),
where t is the year. We then sum up these present values for each year.
We can use the NORM.INV function in Excel to estimate the probability of a negative present worth. The function requires the probability value, mean, and standard deviation as inputs.
Since we have a mean and standard deviation for the present worth,
we can calculate the corresponding probability of a negative present worth using NORM.INV.
This value represents the present worth below which the probability is 0.5. By using the NORM.INV function,
we can estimate the probability that the present worth is negative based on the given data and assumptions.
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g a student takes an exam containing 5 true or false questions. if a student randomly guesses on the entire exam, what is the standard deviation of the number of incorrect answers? round your answer to two decimal places.
The standard deviation of the number of incorrect answers in an exam will be equal to 1.12.
If a student randomly guesses on an exam containing 5 true or false questions, the number of incorrect answers will follow a binomial distribution with n = 5 (the number of questions) and p = 0.5 (the probability of guessing incorrectly on each question). The standard deviation of a binomial distribution is given by the formula:
sd = √(np(1-p))
Plugging in the values n = 5 and p = 0.5, we get:
sd = √(50.5(1-0.5)) = √(50.50.5) = √(1.25) = 1.12
Rounding to two decimal places, the standard deviation of the number of incorrect answers is 1.12.
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Please help very urgent! A fair maiden can sew the border of a tapestry in six hours. Her sister works twice as fast. If they are working together, how long will it take them to finish the border?
Let's call the time it takes the fair maiden to sew the border of the tapestry "t". So, her sister can sew the border in t/2 hours.
Working together, they can sew the border in t + t/2 = 1.5t hours.
Since we know the fair maiden can sew the border in 6 hours, we can substitute this into the equation to find t:
6 + 6/2 = 1.5t
Simplifying the right side of the equation:
6 + 3 = 1.5t
9 = 1.5t
Dividing both sides of the equation by 1.5:
t = 6
So the fair maiden can sew the border in 6 hours and her sister can sew the border in 6/2 = 3 hours.
Working together, it would take them 6 + 3 = 9 hours to sew the border of the tapestry.
Kyle earns $68.75 for mowing 3 lawns.
How much will he earn for mowing 8 lawns?
Answer:
I think the answer is 183.28
Step-by-step explanation: I divided 68.75 by 3 and got 22.91
so I multiplied 22.91 and 9.
Consider the series ∑n=1[infinity]1/n(n+5) Determine whether the series converges, and if it converges, determine its value. Converges (y/n): Value if convergent (blank otherwise):
To get an explicit value for this convergent series is not straightforward and may not be possible using elementary methods. Therefore, I can't provide you with the exact value if convergent.
To determine whether the series ∑n=1[infinity] 1/n(n+5) converges or not, we can use the comparison test. The comparison test states that if 0 ≤ a_n ≤ b_n for all n and the series ∑b_n converges, then the series ∑a_n also converges. Conversely, if the series ∑b_n diverges, then the series ∑a_n also diverges.
Your series is: ∑n=1[infinity] 1/n(n+5)
Let's compare it with the series: ∑n=1[infinity] 1/n^2
First, note that 0 ≤ 1/n(n+5) ≤ 1/n^2 for all n. Since the series ∑n=1[infinity] 1/n^2 is a p-series with p=2, which is greater than 1, it converges. Therefore, by the comparison test, the series ∑n=1[infinity] 1/n(n+5) also converges.
Converges (y/n): y
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Suppose the function shown below was expressed in standard form, v = a * x ^ 2 + bx + c What is the value of a?
Answer:
a = v / x ^ 2 - b / x - c / x ^ 2 :))))))
Answer:
2
Step-by-step explanation:
The answer is 2=a
just got it correct on the quiz
The weight of a honeybee is 1.2\cdot10^{-1}\text{ g}1.2⋅10 −1 g1, point, 2, dot, 10, start superscript, minus, 1, end superscript, start text, space, g, end text. The weight of the pollen collected by the bee on one trip is 6.0 \cdot 10^{-2} \text{ g}6.0⋅10 −2 g6, point, 0, dot, 10, start superscript, minus, 2, end superscript, start text, space, g, end text.
Answer:1.8*10^-1
Step-by-step explanation:
Answer: 1.8 x 10^−1
Step-by-step explanation:
Geometry math i need help
Answer:
Isn't the scale factor 1.28...I haven't done this in a while but last time I checked you divide it to find the scale factor so I believe its 32/25 which is 1.28.
How wide is the chasm between what men and women earn in the workplace? According to a 2015 analysis from a national women's group, women lose $435,049 over the course of a career because of the pay gap. The bar graph to the right shows the average earnings in the United States for men and women at ages and. This exercise involves the graphs of models for the data shown in the rectangular coordinate system to the right. Complete parts (a) through (c) below
The pay gap, on the other hand, rapidly becomes much more substantial as workers advance in their careers, peaking at age 59, when men earn more than double what women earn, with an average of $119,000 for men and $54,000 for women.
In the United States, there exists a substantial wage gap between men and women. According to a 2015 analysis by a national women's group, women lose $435,049 over the course of their careers due to the pay gap. The average earnings of men and women are shown in the bar graph to the right at various ages. The disparity between men's and women's earnings in the workplace is a critical problem.
According to the graph above, the average earnings for women and men vary widely as they age. The pay gap at the start of a woman's working career is modest, but it grows rapidly and becomes much more substantial as she ages and advances through her career. As depicted in the graph, the average earnings for men and women are reasonably similar at the beginning of their working careers, with both sexes earning an average of roughly $20,000 at age 20.
The pay gap, on the other hand, rapidly becomes much more substantial as workers advance in their careers, peaking at age 59, when men earn more than double what women earn, with an average of $119,000 for men and $54,000 for women. The chasm between what men and women earn in the workplace, according to the data provided, is considerable.
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The pay gap, on the other hand, rapidly becomes much more substantial as workers advance in their careers, peaking at age 59, when men earn more than double what women earn, with an average of $119,000 for men and $54,000 for women.
In the United States, there exists a substantial wage gap between men and women. According to a 2015 analysis by a national women's group, women lose $435,049 over the course of their careers due to the pay gap. The average earnings of men and women are shown in the bar graph to the right at various ages. The disparity between men's and women's earnings in the workplace is a critical problem.
According to the graph above, the average earnings for women and men vary widely as they age. The pay gap at the start of a woman's working career is modest, but it grows rapidly and becomes much more substantial as she ages and advances through her career. As depicted in the graph, the average earnings for men and women are reasonably similar at the beginning of their working careers, with both sexes earning an average of roughly $20,000 at age 20.
The pay gap, on the other hand, rapidly becomes much more substantial as workers advance in their careers, peaking at age 59, when men earn more than double what women earn, with an average of $119,000 for men and $54,000 for women. The chasm between what men and women earn in the workplace, according to the data provided, is considerable.
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How wide is the chasm between what men and women earn in the workplace? According to a 2015 analysis from a national women's group, women lose 5435,049 over the course of a career because of the pay gap. The bar graph to the right shows the average carnings in the United States for men and women at ages 22 and 57 This exercise Involves the graphs of models for the data shown in the rectangular coordinate system to the right. Complete parts (6) through (c) below. Average Yearly Eamings in the US by Gender and Age 70 GO (COL) ಠ ಠ Average aty Earrings (51000) ကို နိုင် ငံ မှ 370 560. 550 TROPY 540 530 5200 00.21 $10 50 0 10 20 30 40 50 Years Age 22 10 Age Use the two points for men shown on the graph to find a function in the form M(x)= mx + b that models average yearly earnings for men x years after age 22 M(x)- (Use integers or decimals for any numbers in the expression. Round to two decimal places as needed)
There were 26 balloon in the party room, 12 red and 14 blue. Half of the blue balloon
popped. How many balloons are left?
Answer:
There would be 19 ballons left
Step-by-step explanation:
Cinema A can seat 2100 people. It can seat 1477 people more than cinema B find the total number of people that both cinemas can seat?
Easy
Answer:
5677
Step-by-step explanation:
2100 +1477 = 3577
2100+3577= 5677
whats 10 times 10? also 6 times 6
Answer:
10 x 10 = 100
6 x 6 = 36
:)
Answer:
10*10=100 | 6*6=36
Step-by-step explanation:
Well, 100/10=10
36/6=6
--------------
10+10+10+10+10+10+10+10+10+10=50+50=100
6+6+6+6+6+6=18+18=36
A polling organization announces that the proportion of American voters who favor congressional term limits is 64 percent, with 95% confidence and margin of error of 3 percent. This means that
Answer:
We are 95% confident that the proportion of American voters who favor congressional term limits is 64 percent with a difference of 3% for small sample size.
Step-by-step explanation:
95 % confidence means that we are 95 % confident that the the proportion of American voters who favor congressional term limits is 64 percent.
95 % confidence means that of all the sample about 95 % values are within in the given range.
And only 5% sample are not included in the given parameter.
Margin of error is the amount of miscalculation or difference in change of circumstances from the obtained data.
3% margin of error usually occurs when the data size is small.
As the data size increases the margin of error decreases.
So this statement tells us that we are 95% confident that the proportion of American voters who favor congressional term limits is 64 percent with a difference of 3% for small sample size.
Margin of error= z *σ/√n→
This indicates that as the sample size decreases the margin of error increases and vice versa.
Halp! Brainliest to correct answer!!!!
Answer: 11c^2
Step-by-step explanation:
(3c^2 - 8c^1 + 5) + (1c^2 - 8c^1 - 6)
5c^1 + 5 = 10c^1 + 1c^2 - 8c^1
-7c^1 - 6
K C C
7+ -6 = -1c^1
10c^1 + 1c^1= 11c^2
Answer:
The final expression is:
\(4c^{2}-16c-1\)
So, the option (B) is the correct one.
Step-by-step explanation:
The expression is as such:
\((3c^{2}-8c+5)+(c^{2}-8c-6)\)
Step 1: Remove the brackets:
\((3c^{2}-8c+5)+(c^{2}-8c-6)\\=3c^{2}-8c+5+c^{2}-8c-6\)
Step 2: Collect the like terms together:
\(3c^{2}-8c+5+c^{2}-8c-6\\=3c^{2}+c^{2}-8c-8c+5-6\)
Step 3: Take the common variable as a factor, and add accordingly:
\(3c^{2}+c^{2}-8c-8c+5-6\\\\\text{Take}~c^{2}~\text{as the factor between the first two terms:}\\(3+1)c^{2}-8c-8c+5-6\\\\\text{Take}~c~\text{as the factor between the third and fourth terms:}\\(3+1)c^{2}+(-8-8)c+5-6\\\\\text{Since the last two terms are integers, we can just add them normally}\\\\\text{Add the like terms and the integers now:}\\(3+1)c^{2}+(-8-8)c+5-6\\=(4)c^{2}+(-16)c-1\\\\\text{Remove the brackets:}\\4c^{2}-16c-1\)
a common everyday counting unit that is used to mean 12 of an object is a____
A common everyday counting unit that is used to mean 12 of an object is a Dozen
Dozen is derived from the Old French word "douzaine" which means twelve each. In most situations, a dozen is used to refer to a group of twelve items. The term dozen is also used in informal situations to refer to a very large number of objects. For example, one might say "I have dozens of friends!" to mean that they have a lot of friends.
Dozen is a useful term when counting items. It allows for large numbers to be easily broken down into manageable groups. For example, if you have 120 pencils, you could easily count them by saying that you have 10 dozen pencils. It can also be useful when talking about fractions. For example, instead of saying "one and a half of an item," one could say "one and a half dozen of an item."
Dozen is a common everyday counting unit that is used to mean 12 of an object. It is a useful term when counting items and when talking about fractions, and can be used in both formal and informal settings.
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you ask a neighbor to water a sickly plant while you are on vacation. without water the plant will die with probability 0.85. with water it will die with probability 0.6. you are 82 % certain the neighbor will remember to water the plant. when you are on vacation, find the probability that the plant will die.
The probability that the plant will die when you're on vacation is 0.645 or 0.726 (rounded to three decimal places).
The probability that the plant will die when you're on vacation is 0.726. Here's how to get it:
Given that without water, the plant will die with probability 0.85, and with water, it will die with probability 0.6. Then, the probability that the plant will survive is:
1 - probability of dying without water - probability of dying with water= 1 - 0.85 - 0.6= -0.45 (Not possible since probability cannot be negative)
Thus, the probability that the plant will die is 0.45. Also, given that you are 82% certain that the neighbor will remember to water the plant, the probability that they will forget to water it is 1 - 0.82= 0.18.Then, the probability that the plant will die if the neighbor forgets to water it is 0.85, and the probability that it will die if the neighbor waters it is 0.6.
Using the law of total probability, the probability that the plant will die is:
P(Die) = P(Die | Water) P(Water) + P(Die | No water) P(No water)
Now substituting in the given values:
P(Die) = 0.6 × 0.82 + 0.85 × 0.18= 0.492 + 0.153= 0.645
Thus, the probability that the plant will die when you're on vacation is 0.645 or 0.726 (rounded to three decimal places).
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Eric is a great skateboard fan. He visits a shop named SKATERS to check some prices. At this shop you can buy a complete board. Or you can buy a deck, a set of 4 wheels, a set of 2 trucks and a set of hardware, and assemble your own board. The prices for the shop's products are:
Eric has 120 zeds to spend and wants to buy the most expensive skateboard he can afford. How much money can Eric afford to spend on each of the 4 parts? Put your answer in the table below.
Answer:
Deck | 60 zed
wheels | 14 zed
trucks. | 16+16 32 zed
Hardware | 10 zed
total. | 116 zed
remaining 4 zed
Step-by-step explanation:
hope this helps
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What do you like doing in your free time?what time do you get up on Mondays?which musical instrument do you have to pluck when you play it?
in my free time I watch TV I I play with my phone on Mondays are usually get up on 9 a.m. and I don't have an instrument any musical instrument I don't
A population has a mean of 400 and a standard deviation of 25. a sample of 100 observations will be taken. the probability that the sample mean will be greater than 405 is:________
The probability that the sample mean will be greater than 405 can be determined using the Central Limit Theorem. Assuming the population follows a normal distribution, we can calculate the probability using the standard deviation of the population and the sample size.
According to the Central Limit Theorem, when the sample size is large enough, the distribution of sample means will approach a normal distribution, regardless of the shape of the population distribution. In this case, the population mean is 400 and the standard deviation is 25.
To calculate the probability that the sample mean will be greater than 405, we need to convert the sample mean to a standard score (z-score) by subtracting the population mean and dividing by the standard deviation divided by the square root of the sample size.
z = (sample mean - population mean) / (standard deviation / sqrt(sample size))
= (405 - 400) / (25/\(\sqrt{100\))
= 5 / (25 / 10)
= 5 / 2
= 2.5
We can then use a standard normal distribution table or a statistical software to find the area under the curve to the right of the z-score 2.5. This area represents the probability that the sample mean will be greater than 405.
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əz 22. Suppose z= z(x, y) is implicitly determined by ln(x+y+z) = x+2y+3z. Then dy (z.y.a)=(-1,5,-3)
the derivative dy/dx is equal to 1/3 based on the given information. It's important to note that this calculation assumes that the partial derivatives (∂F/∂x) and (∂F/∂y) are not zero at the given point (z.y.a).
n the given problem, we have an implicit equation ln(x+y+z) = x+2y+3z that defines z as a function of x and y. We are given the values dy = (-1, 5, -3).
To find the derivative dy/dx, we can use the total derivative formula and apply it to the implicit equation. The total derivative is given by dy/dx = - (∂F/∂x)/(∂F/∂y), where F = ln(x+y+z) - x - 2y - 3z.
Differentiating F partially with respect to x and y, we have (∂F/∂x) = 1/(x+y+z) - 1 and (∂F/∂y) = 1/(x+y+z) - 2.
Plugging in the given values of dy = (-1, 5, -3), we can calculate dy/dx = - (∂F/∂x)/(∂F/∂y) = -(-1)/(5-2) = 1/3.
Therefore, the derivative dy/dx is equal to 1/3 based on the given information. It's important to note that this calculation assumes that the partial derivatives (∂F/∂x) and (∂F/∂y) are not zero at the given point (z.y.a).
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