A type of steel used for bicycle frames contains 5g of magnese in every 400g of steel. how much magnese would a 2200g bicycle frame contain?

in a class of 12 boys and 9 girls, the teacher selects three students at random to write problems on the board then the probability that all the students selected are boys is 0.165

given that a class consists of 12 boys and 9 girls. The teacher picks three students to present their work to the rest of the class  and says that the three students are being selected at random

Here selecting any 3 students from the group of total 21 students is combination because order does not matter.

Total no of ways of selecting any 3 from total 21 = 21C3 = 1330

No of ways of selecting only 3 boys = No of ways of selecting random 3 boys from total 12 boys

= 12C3 =220

the probability be that all three students

selected are boys=220/1330 = 0.165

Hence , the probability that all the students selected are boys is 0.165

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The surface area of the cylinder is approximately 401.92 square centimeters. To find the surface area of the cylinder, we need to add the area of the top and bottom circles to the area of the lateral surface.

The formula for the surface area of a cylinder is:

SA = 2πr² + 2πrh

where r is the radius of the base, h is the height of the cylinder, and π ≈ 3.14.

Given that the radius is 8 cm and the height is also 8 cm, we can plug in the values in the formula:

SA = 2π(8²) + 2π(8)(8)

SA = 401.92

Rounding to the nearest hundredth, we get:

SA ≈ 401.92 square centimeters

Therefore, the surface area of the cylinder is approximately 401.92 square centimeters.

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Answer:

Formula : V = I (1 + R)^T  , Deers after 5 years ≈  556

Step-by-step explanation:

Exponential formula for  final value 'v' - for initial value 'i' at growth rate 'r' for a period of time 't'

V = I (1 + R)^T

As per given deer case, I = 330 & R = 11% = 0.11

V = 330 ( 1 + 0.11 )^t

Predicted deers after 5 years, V = 330 (1.11)^5

330 x 1.685 = 556.05

Step-by-step explanation:

The lengths of the sides of the rectangular field should be 40 ft (smaller value) and 60 ft (larger value) respectively.

Let L = length of rectangle area and W = width of rectangle area.

Let the length of the side that divides the area be parallel to the width of the area.

The total length of fencing F = 2L + 2W + W

F = 2L + 3W

Since the area is a rectangle, its area is A = LW

Since the area = 2400 square feet,

LW  = 2400 ft²

So, L = 2400/W

Substituting L into F, we have

F = 2L + 3W

F = 2(2400/W) + 3W

F = 4800/W + 3W

To find the value at which F is minimum, we differentiate F with respect to W.

So, dF/dW = d(4800/W + 3W)/dW

dF/dW = -4800/W² + 3

Equating dF/dW to zero, we have

-4800/W² + 3 = 0

-4800/W² = - 3

W² = -4800/-3

W² = 1600

W = √1600

W = 40 ft

To determine if this is a value that gives minimum F, we differentiate F twice to get

d²F/dW² = d(-4800/W² + 3)/dW

d²F/dW² = 14400/W³ + 0

d²F/dW² = 14400/W³

substituting W = 40 into the equation, we have

d²F/dW² = 14400/(40)³

d²F/dW² = 14400/64000

d²F/dW² = 0.225

Since d²F/dW² = 0.225 > 0, W = 40 is a minimum point for F

Since L = 2400/W

So, L = 2400/40

L = 60 ft

So, the lengths of the sides of the rectangular field should be 40 ft (smaller value) and 60 ft (larger value) respectively.

Answer:

I'm not sure if i'm doing this right, but I got 75

Step-by-step explanation:

(5-2)5*5^1 =  75

Therefore \(x/6=12/4\).\(5x=16ft\)The height of the tree will be 16ft.the correct answer is (c).

The study of the correlation between a right-angled triangle's sides and angles is the focus of one of the most significant areas of mathematics in history: trigonometry. Hipparchus, a Greek scholar, introduced this idea. In this article, we will study the fundamentals of trigonometry, including its formulas, tables, ratios, functions, and many solved examples. What are similar triangles If the respective sides of two triangles are proportional and the corresponding angles are congruent, then the triangles are said to be similar. To put it another way, similar triangles have the same shape but may differ in height. In addition, if the matching sides of the triangles are equal in length, the triangles are congruent. In the given figures, these are two similar triangles as the form the same angle with the ground The height of the tree will be 16ft using the property of similar triangles.

by the question.

Let's first find the ratio of Jack's height to his shadow length:

Jack's height / Jack's shadow length = 6 / 4

Simplifying this ratio, we get:

\(Jack's height / 4 = 3 / 2\)

Multiplying both sides by 4, we get:

\(Jack's height = 6\)

Now, let's find the ratio of the tree's height to its shadow length:

Tree's height / Tree's shadow length = x / 12

Since the two triangles are similar, we know that these ratios are equal. So, we can write:

Jack's height / Jack's shadow length = Tree's height / Tree's shadow length

Substituting the known values, we get:

\(6/4=x/12\)

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Answer:

a.) Total amount spent on gasoline and oil = $ ( 3.95g + 4.45c )

b.) Total amount spent by Maria = $ 74.02

Step-by-step explanation:

As given,

Cost of gasoline = $ 3.95 gallon

Cost of oil per can = $ 4.45

Also given,

Maria bought g gallons of gasoline and c cans of oil

⇒ Total cost of g gallons of gasoline = g×3.95 = $3.95g

   Total cost of c cans of oil  = c×4.45 = $4.45c

Now,

a.)

Total amount spent on gasoline and oil = $ ( 3.95g + 4.45c )

b.)

As given ,

Maria buy gasoline , g = 8.6 gallons

Maria buy cans of oil , c = 6

So,

Total amount spent = $ 3.95(8.6) + 4.45(9)

                                = $ 33.97 + 40.05 = $ 74.02

⇒Total amount spent by Maria = $ 74.02

The numbers that do not form a fact family are solved

Given data ,

A fact family consists of a set of related addition and subtraction facts that use the same numbers. For example, the numbers 3, 5, and 8 form a fact family because:

3 + 5 = 8

5 + 3 = 8

8 - 5 = 3

8 - 3 = 5

Numbers that do not form a fact family are any set of numbers that do not follow this pattern. For example, the numbers 2, 4, and 7 do not form a fact family because no combination of addition and subtraction using these numbers produces the other two numbers.

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Answer:

C, both plans will work for achieving the goal.

Step-by-step explanation:

For plan A, you must multiply 7.20 by 9, then multiply the product by 8. The answer is 526.4 This means that plan A will work, and more than the original goal will be saved up.

For plan B, you must multiply 6.50 by 15, then multiply the product by 6. The answer is 585. This is more than the original goal, so plan B would work as well.

This means that C is correct, because both plans will work for achieving the goal.

Answer:

C

Step-by-step explanation:

Edged 2022

The required decimal numbers are 8.43, 8.403, 8.403, and 8.43.  

In mathematics, place value is the value of a digit in a number based on its position. For example, in the number 123, the digit 3 is in the one's place, representing the value of 3 ones.

Decimal notation is a system of writing numbers using a base value of 10 and the digits 0-9. In decimal notation, each digit in a number represents a multiple of a power of 10. For example, in the number 123.45, The digit 4 is in the tenth place, representing the value of 4 tenths.

Here we have 8.43

The number can be expressed as follows

8.43 = 843 hundredths = 8.43

8.43 = 84 tenths and 3 thousandths = 8.403

8 ones 4 hundredths and 3 thousandths  = 8.403

8.43 = 8 + 0.4 + 0.03 = 8.43  

Therefore,

The required decimal numbers are 8.43, 8.403, 8.403, and 8.43.  

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Answer: The box is large enough to ship the coat.

15000cm to the power of 3>10000cm to the power of 3

Step-by-step explanation:

V box=25x30x20

         =750+20

         =15000cm to the power of 3

So the box is large enough to ship the coat

The curve of critical points that satisfies an equation of the form y = f(x) is:

y = 24tan^2(t/2) + 32tan(t/2)

To find the curve of critical points that satisfies an equation of the form y = f(x), we need to first find the critical points by setting x' and y' equal to zero:

x' = y^2 - 6x^2y - 8xy = 0

y' = xy - 6x^3 - 8x^2 = 0

Simplifying the second equation, we get:

y = 6x^2 + 8x

Substituting this expression for y into the first equation, we get:

x'(6x^2 + 8x) - 6x^2(6x^2 + 8x) - 8x(6x^2 + 8x) = 0

Simplifying this equation, we get:

(6x^2 + 8x)(x' - 36x^2 - 64) = 0

Therefore, either 6x^2 + 8x = 0 or x' - 36x^2 - 64 = 0.

Solving the first equation, we get:

2x(3x+4) = 0

This gives us two critical points: x = 0 and x = -4/3.

Now, solving the second equation, we get:

x' = 36x^2 + 64

Integrating both sides with respect to x, we get:

x = 4tan(t/2)

where t = sqrt(32)(t0 - t)

Substituting this expression for x into y = 6x^2 + 8x, we get:

y = 24tan^2(t/2) + 32tan(t/2)

Therefore, the curve of critical points that satisfies an equation of the form y = f(x) is:

y = 24tan^2(t/2) + 32tan(t/2)

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The inequality based on the given data is :

d ≥ 5s + 9 .

Step 1: Eliminate fractions by multiplying all terms by the least common denominator of all fractions to solve an inequality.

Step 2 Simplify the inequality by combining like terms on each side.

Step 3 Subtract or add amounts to get the unknown on one side and the numbers on the other.

Here given,

Fixed cost = $9.00

Cost per pound of soil is $5.00

Hence, the equation will be :

d ≥ 5s + 9

Since d must be greater than or equal to this value for Kyle to be able to afford it.

∴ The inequality = d ≥ 5s + 9 .

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Answer:

68 in.

Step-by-step explanation:

Multiply 4 by 8 and get 32

Multiply 6 by 6 and get 36

Add 38 and 36

=68

Answer:

92 square inches.

Step-by-step explanation:

4 × (6+8) + (6×6)

The workers can expect to receive a bonus of $20 on average each week.

To calculate the workers expected weekly bonus, we need to first find the expected value for each possible bonus amount, and then multiply it by its corresponding probability. In this case, the possible bonus amounts are $10 and $50, with probabilities of 0.75 and 0.25 respectively.

So, the expected value for $10 bonus is:
Expected value = $10 x Probability = $10 x 0.75 = $7.50

Similarly, the expected value for $50 bonus is:
Expected value = $50 x Probability = $50 x 0.25 = $12.50

To find the workers expected weekly bonus, we need to add up the expected values for each possible bonus amount:
Expected weekly bonus = ($7.50 + $12.50) = $20.

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Answer: True

Step-by-step explanation:

In a Poisson distribution, the mean and variance are both equal to λ, where λ is the parameter that represents the average number of occurrences in a fixed interval of time or space. The probability mass function of a Poisson distribution is given by:

P(X = k) = (e^(-λ) * λ^k) / k!

where X is the random variable that represents the number of occurrences, k is a non-negative integer, e is the base of the natural logarithm, and k! is the factorial of k.

The mean of a Poisson distribution is given by:

E(X) = λ

and the variance is given by:

Var(X) = λ

Since the mean and variance are equal, it follows that:

E(X) = Var(X) = λ

Answer:$62

Step-by-step explanation: 62 becuase I took your formula and plugged it in. There are 2 kids under 12 so thats $16, then there are 3 people who are 12-59 that equals $52, then 1 person who is over 60. So $62.

Answer:

18 miles away from home

Step-by-step explanation:

This question requires you to know about displacement. Since you rode 22 miles from home, you are 22 miles away from home, obviously. Now, you walk BACK 4 miles, so take 4 away from 22 and you get 18. This means that your displacement from home is 18 miles. Interestingly, you traveled 26 miles before your mom picked you up, but the question asks for the displacement, and not the distance traveled overall.

To determine which set of data most likely has a mean closest to 29.5, we need to analyze the shape and position of the histograms in relation to the value 29.5.

Looking at the histograms described:

The first histogram ranges from 9 to 48, and the upward trend starts from 1 and ends at 33, followed by a downward trend. This histogram suggests that there may be values lower than 29.5, which would bring the mean below 29.5.

The second histogram ranges from 15 to 48, with an upward trend from 1 to 30 and then a downward trend. Similar to the first histogram, it suggests the possibility of values lower than 29.5, indicating a mean below 29.5.

The third histogram ranges from 12 to 56, and the upward trend starts from 1 and ends at 32, followed by a downward trend. This histogram covers a wider range but still suggests the possibility of values below 29.5, indicating a mean below 29.5.

The fourth histogram ranges from 15 to 54 and exhibits multiple trends. While it has fluctuations, it covers a wider range and includes both upward and downward trends. This histogram suggests the possibility of values above and below 29.5, potentially resulting in a mean closer to 29.5.

Based on the descriptions, the fourth histogram, with its more varied trends and wider range, is most likely to have a mean closest to 29.5.

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Answer:

its 94 on deltamath just did it

Step-by-step explanation:

Let t=0 represent the year 1997

Starting Value: 690

Write function:

y=690(b)^t

Now find the b-value:

y=390 when t=4 (2001−1997)

390=690(b)^4

390/690=690(b)^4/690

0.56521739=b^4

(0.56521739)^1/4=(b^4)^1/4

0.86706944=b

Write Complete Function:

y=690(0.86706944)^t

Find value in 2011 (use t=14):

y=690(0.86706944)^14

y=93.67062063

y≈94

(a) The range of c₁ (the objective coefficient of x₁) for which this BFS remains optimal is c₁ ≤ 2.

(b) The range of b₂ (the right-hand side of the second constraint) for which this BFS remains optimal is 3 ≤ b₂ < 4.

(c) The dual price of the second constraint is 0.

(a) The optimality condition for a linear programming problem requires that the objective coefficient of a non-basic variable (here, x₁) should not increase beyond the dual price of the corresponding constraint. In this case, the dual price of the second constraint is 0, indicating that increasing the coefficient of x₁ will not affect the optimality of the basic feasible solution. Therefore, the range of c₁ for which the BFS remains optimal is c₁ ≤ 2.

(b) The range of b₂ for which the BFS remains optimal is determined by the allowable range of the corresponding dual variable. In this case, the dual price of the second constraint is 0, implying that the dual variable associated with that constraint can vary within any range. As long as 3 ≤ b₂ < 4, the dual variable remains within its allowable range, and thus, the BFS remains optimal.

(c) The dual price of a constraint represents the rate of change in the objective function value per unit change in the right-hand side of the constraint, while keeping all other variables fixed. In this case, the dual price of the second constraint is 0, indicating that the objective function value does not change with variations in the right-hand side of that constraint.

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Answer:

x = 12

Step-by-step explanation:

Given a line parallel to a side of the triangle and it intersects the other 2 sides then it divides those sides proportionally, that is

\(\frac{x}{24}\) = \(\frac{5}{10}\) ( cross- multiply )

10x = 120 ( divide both sides by 10 )

x = 12

The correct answer is (a) event. An event is a subset of outcomes from the sample space. It represents a specific outcome or set of outcomes that we are interested in. Events can be simple, consisting of a single outcome, or they can be compound, consisting of multiple outcomes.

For example, consider rolling a fair six-sided die. The sample space is {1, 2, 3, 4, 5, 6}. Let's say we are interested in the event of rolling an even number. The event in this case would be {2, 4, 6}, which is a subset of the sample space.

Events can also be mutually exclusive, meaning they cannot occur at the same time, or they can be independent, meaning the occurrence of one event does not affect the probability of the other event occurring.

In summary, an event is a subset of outcomes from the sample space and represents a specific outcome or set of outcomes that we are interested in. It is an important concept in probability theory.

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Linear equations are a subset of non-linear equations, and the equation 3xy = 9 is a non-linear equation.

The equation 3xy = 9 is not a linear equation. It is a non-linear equation. Linear equations are first-degree equations, meaning that the exponent of all variables is 1. A linear equation is represented in the form y = mx + b, where m and b are constants.

The variables in linear equations are not raised to powers higher than 1, making it easier to graph them. In contrast, non-linear equations are any equations that cannot be written in the form y = mx + b. Non-linear equations have at least one variable with an exponent that is greater than or equal to 2. Non-linear equations are harder to graph than linear equations.

The answer is false, the equation 3xy = 9 is a non-linear equation, not a linear equation. Non-linear equations are any equations that cannot be written in the form y = mx + b. They have at least one variable with an exponent that is greater than or equal to 2.

Linear equations are a subset of non-linear equations, and the equation 3xy = 9 is a non-linear equation.

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The volume of a cone is one-third of the product of the area of the base times the height, i.e. Now multiply that by the number of cones: 6 * 75.40 cm^3 = 452.40 cm^3.

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The probability that the mean number of moths in a sample of size 50 is greater than or equal to 0.6 is 8.08%

The CLT states that the distribution of the sample means of a random variable with a finite mean and standard deviation approaches a normal distribution as the sample size increases.

In this case, the population mean is 0.5, and the population standard deviation is 0.7. Since we have a sample size of 50, the standard deviation of the sample means would be

=> 0.7 / √(50) = 0.099.

Next, we need to calculate the z-score, which measures the number of standard deviations from the mean.

In this scenario, we want to find the probability that the mean number of moths in a sample of size 50 is greater than or equal to 0.6. So, we would plug in x = 0.6, μ = 0.5, σ = 0.7, and n = 50 into the z-score formula. This gives us

=> (0.6 - 0.5) / (0.7 / √(50)) = 1.41.

Using a standard normal distribution table or calculator, we can find that the probability of a z-score of 1.41 or higher is approximately 0.0808. Therefore, the estimated probability that the mean number of moths in a sample of size 50 is greater than or equal to 0.6 is 0.0808 or about 8.08%.

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Complete Question:

The gypsy moth is a serious threat to oak and aspen trees. A state agriculture department places traps throughout the state to detect the moths. Each month, an SRS of 50 traps is inspected, the number of moths in each trap is recorded, and the mean number of moths is calculated. Based on years of data, the distribution of moth counts is discrete and strongly skewed, with a mean of 0.5 and a standard deviation of 0.7. Estimate the probability that the mean number of moths in a sample of size 50 is greater than or equal to 0.6.

Answer:The solution is in the attached file

Step-by-step explanation:

The total spending figures indicate that Joe's demand for pizza is elastic as his total spending decreases when the price decreases, suggesting he is responsive to price changes.

a. The demand curve for Joe's pizza can be plotted by using the equation Q = 30 - 2P, where Q represents the quantity of pizza consumed and P represents the price per slice.

On the graph, the vertical axis represents the price (P), and the horizontal axis represents the quantity (Q). The vertical intercept occurs when Q is 0, which corresponds to P = 15. The horizontal intercept occurs when P is 0, which corresponds to Q = 30.

b. The total spending on pizza at P = 5 is $100, and the total spending at P = 4 is $88. This information indicates that Joe's total spending decreases as the price of pizza decreases.

Based on this, we can infer that Joe's elasticity of demand for pizza between P = 5 and P = 4 is elastic. When the price decreases from $5 to $4, the total spending decreases, indicating that the demand is responsive to price changes.

c. When P = 9, we can substitute this value into the demand function to calculate the corresponding quantity: Q = 30 - 2(9) = 30 - 18 = 12. To calculate Joe's consumer surplus, we need to find the area of the triangle formed by the demand curve and the price line.

The consumer surplus is given by (1/2) ˣ  (9 - P) ˣ  Q = (1/2) ˣ (9 - 9) ˣ  12 = 0.d. If the price of pizza rises to $15 per slice, we can again substitute this value into the demand function to find the corresponding quantity: Q = 30 - 2(15) = 30 - 30 = 0.

Joe's consumer surplus at this new price would be zero since he is not consuming any pizza at that price, resulting in no surplus.

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