The ratio of the number of baskets made by Tony to the number of baskets made by Collin is 2 to 3. Tony made 10 baskets. How many baskets did Collin make?

The probability that a randomly chosen manufactured light bulb will be removed by the packer is 0.034.

In order to calculate this probability, we need to consider two scenarios: (1) the light bulb is defective and (2) the light bulb is not defective.

For the first scenario, the probability that the light bulb is defective is given as 0.04. In this case, the packer detects the defective bulb with a probability of 0.96 and removes it correctly. Therefore, the probability that a defective bulb is removed is 0.04 ×  0.96 = 0.0384.

For the second scenario, the probability that the light bulb is not defective is 1 - 0.04 = 0.96. In this case, the packer mistakenly removes a working bulb with a probability of 0.01. Therefore, the probability that a working bulb is mistakenly removed is 0.96 × 0.01 = 0.0096.

To find the overall probability that a randomly chosen bulb will be removed by the packer, we sum up the probabilities from both scenarios: 0.0384 + 0.0096 = 0.048. Rounded to the third decimal, the probability is 0.034.

Therefore, the probability that a randomly chosen manufactured light bulb will be removed by the packer is 0.034.

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The median of the employees' ages is 27.

The median is the value that splits the mathematical numbers or expressions in the half. The median value is the middle number of data point. To find the median, firstly arrange the data points in ascending order.

The ages of the workers at a small company are given.

Employees’ ages are 17, 22, 56, 45, 34, 18, 21, 62, 25, 29.

To find the median,

firstly, arrange the data points in ascending order.

17, 18, 21, 22, 25, 29, 34, 45, 56, 62.

The total element in the data set is 10.

And 10 is an even number.

Then the median is the simple average of the middle two numbers.

And the middle numbers are 25 and 29.

So, 25 + 29 / 2

= 54/2 = 27

Therefore, the median is 14.

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Answer:

$24

Step-by-step explanation:

50% of 40 = 20

10% of 40 = 4

20+4=$24

5+2y=13, y-5=2(x-1), y/2 = x+7, x=-4 are linear equations.

An equation is said to be linear if the maximum power of the variable is consistently 1.

Another name for it is a one-degree equation.

A linear equation with one variable has the conventional form Ax + B = 0.

In this case, the variables x and A are variables, while B is a constant.

A linear equation with two variables has the conventional form Ax + By = C.

Here, the variables x and y, the coefficients A and B, and the constant C are all present.

As explained above about linear equation from given option we can verify that

5+2y = 13 can be written as 2y = 8 or 2y-8=0 which represents linear equation in one variable.

\(y = \frac{1}{2x^{2} +7}\) cannot be written in any linear form and its highest degree is 2. So, it is not linear equation.

y-5= 2(x-1) can be written as 2x-y=-3 which is in the form of linear equation in two variables. So, it is linear equation in two variables.

x = -4 can be written as x + 4 = 0 which represents linear equation in one variable.

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To prove that the argument is valid using propositional logic, we can apply logical rules and deductions. Let's break down the argument step by step:

(A + B) ^ (C V -B) ^ (-D --> C) ^ A ^ D

We will represent the proposition as follows:

P: (A + B)

Q: (C V -B)

R: (-D --> C)

S: A

T: D

From the given premises, we can deduce the following:

P ^ Q (Conjunction Elimination)

P (Simplification)

Now, let's apply the rules of disjunction elimination:

P (S)

A + B (Simplification)

Next, let's apply the rule of disjunction introduction:

C V -B (S ^ Q)

Using disjunction elimination again, we have:

C (S ^ Q ^ R)

Finally, let's apply the rule of modus ponens:

-D (S ^ Q ^ R)

C (S ^ Q ^ R)

Since we have derived the conclusion C using valid logical rules and deductions, we can conclude that the argument is valid.

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By critically observing the basketball hoop (see attachment), we can logically deduce that the basket's height from Lisa's horizontal sight is the same as the length of the shortest leg of the right-angle triangle:

Shortest leg = 8.5 - 5

Shortest leg = 3.5 feet.

In Geometry, the sum of all the angles in a triangle is equal to 180°:

x + y + z = 180

x + y + 90 = 180

x + y = 180 - 90

x + y = 90° (complementary angle).

Therefore, the angle of depression is complementary to the angle of elevation.

Also, you should use the inverse tangent function because the lengths of the opposite and adjacent sides of the right-angle triangle are known.

Angle of depression = tan⁻¹(Opposite/Adjacent)

Angle of depression = tan⁻¹(3.5/10)

Angle of depression = 19.29° ≈ 19°.

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Answer:

3.5

congruent

inverse tangent

19

Step-by-step explanation:

Answer: -1,6 maybe

Step-by-step explanation:

The ratio of their corresponding side lengths is 7:10

A scale factor is defined as the ratio between the scale of a given original object and a new object.

scale factor is expressed as;

scale factor = new dimension / old dimension

The linear scale factor is the ratio of their corresponding side lengths.

The relationship between area scale factor and linear scale factor is;

area scale factor =( linear scale factor)²

Since area scale factor = 49/100

the linear scale factor = √49/√100

= 7/10

therefore the ratio of their side length is 7:10

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Answer:

16x^11

Step-by-step explanation:

2x^3 x 8x^8

= 2 x 8 ( x^8 x x^3 )

= 16 ( x ^8 + 3 )

= 16x^11

\(\huge\textsf{Hey there!}\)

\(\mathsf{2x^3\times8x^8}\\\textsf{There arent any like terms so we \underline{do not} have to compare them together}\\\mathsf{= \mathsf{2\times8 \rightarrow \bf 16}}\\\mathsf{= 3+8\rightarrow\bf 11}\\\mathsf{= 16\times x^{11}}\\\mathsf{= \bf 16x^{11}}\\\\\\\\\boxed{\boxed{\large\textsf{Answer: \bf 16x}\mathsf{\bf ^{11}}}}\huge\checkmark\\\\\\\large\textsf{Good luck on your assignment and your day!}\\\\\\\\\frak{Amphitrite1040:)}\)

If T is the midpoint of PQ and PT = 3x+3, TQ = 7x-9, then PT = 12 units.

Determining the Value of PT

It is given that,

T is the midpoint of PQ ........ (1)

PT=3x+3 ......... (2)

TQ=7x-9 .......... (3)

From (1), the distance from P to T and the distance from T to Q will be equal.

⇒ PT = TQ [Since, a midpoint divides a line into two equal segments]

Hence, equating the equations of PT and TQ given in (2) and (3) respectively, equal, we get the following,

3x + 3 = 7x - 9

or 7x - 9 = 3x + 3

or 7x - 3x = 9 + 3

or 4x = 12

or x = 12/4

⇒ x = 3

Substitute this obtained value of x in equation (2)

PT = 3(3) + 3

PT = 9 + 3

PT = 12 units

Thus, if T is the midpoint of PQ, then the measure of PT and TQ is equal to 12 units.

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Answer:

72.4$

Step-by-step explanation:

We can use cross multiplication here

\(\frac{18.10}{originalbill} = \frac{25}{100}\)

18.10 x 100 = 25 x original bill

1810 = 25 x original bill

72.4 = original bill

The equation of the circle, obtained by applying the completing the square method to the specified equation indicates that the center and radius of the circle are;

Center (0, 6) and radius 7.5

The general form of the equation of a circle is; (x - h)² + (y - k)² = r², where;

(h, k) = The coordinates of the center of the circle

r = The measure of the length of the radius

The possible equation obtained from a similar question on the internet can be presented as follows;

x² + y² - 12·y - 20.25 = 0

The above equation can be evaluated using the completing the square method and excluding the x² term as follows;

y² - 12·y - 20.25 = 0

y² - 12·y = 20.25

y² - 12·y + (-12/2)² = 20.25 + (-12/2)²

y² - 12·y + (-6)² = 20.25 + (-6)² = 56.25

(y - 6)² = 56.25

Therefore;

y - 6 = √(56.25) = ±7.5

The possible equation of the circle obtained by plugging in the x² term therefore is; (x - 0)² + (y - 6)² = 7.5²

The center of the circle is therefore;

(h, k) = (0, 6)

The radius of the circle, r = 7.5

The possible correction is therefore, option (a), where the 5 is a typing error

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Answer:

aye bro i hate doing homework at night

Step-by-step explanation:

ye

The required fraction of chicken,whose are laying eggs irregularly.

Multiply the numerators and denominators independently to track down the item. At the point when you need to duplicate divisions, increase the 2 numerators together first and compose it on top. Then duplicate the denominators together and compose it on the lower part of the portion. Work on your response in the event that you would be able so it is in the least terms.

9/15 chickens are laying eggs regularly and 2/15 chickens never lay eggs.

Then,fraction of chicken

1 - 9/15 - 2/15

15 - 9 - 2/15

4/15

Thus, the fraction of chicken are 4/15

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Correct question:

9/15 of David's chickens lay

eggs every day. 2/15 of the chickens never lay any eggs. What fraction of the chickens lay eggs irregularly.

Answer:

1 small box

5 medium box

2 large box

Step-by-step explanation:

Let x be the small box, y be the medium box and z be the large box.

So, we have:

\(\begin{array}{cccc}{} & {Oatmeal} & {Chocolate} & {Shortbread} & {x} & {1} & {1} & {0} & {y} & {2} & {1} & {1}& {z} & {2} & {2} & {3} & {Total} & {15} & {10} & {11} \ \end{array}\)

From the above table, we have the following equations:

Oatmeal:

\(x + 2y + 2z = 15\) --- (1)

Chocolate Chip

\(x + y + 2z = 10\) --- (2)

Shortbread

\(y + 3z = 11\) --- (3)

Make y the subject in (3)

\(y =11 - 3z\)

Substitute \(y =11 - 3z\) in (1) and (2)

\(x + 2y + 2z = 15\) --- (1)

\(x + 2(11-3z) + 2z = 15\)

\(x + 22 - 6z + 2z = 15\)

\(x -6z +2z = 15 - 22\\\)

\(x-4z = -7\)

\(x = 4z - 7\) --- (4)

\(x + y + 2z = 10\) --- (2)

\(x + 11 - 3z + 2z = 10\)

\(x - 3z + 2z = 10 - 11\)

\(x -z = -1\)

\(x = z - 1\) --- (5)

Equate (4) and (5)

\(4z - 7 = z - 1\)

\(4z - z = 7 - 1\)

\(3z = 6\)

\(z = 2\)

Substitute \(z = 2\) in (5)

\(x = z - 1\) --- (5)

\(x =2-1\)

\(x =1\)

Substitute \(z = 2\) in \(y =11 - 3z\)

\(y = 11 - 3 * 2\)

\(y = 11 - 6\)

\(y = 5\)

So, the solution is:

\(x =1\)     \(y = 5\)       \(z = 2\)

Answer:

Benny the tiger costs more to feed each day because he eats 12.5 pounds of meat per day, which costs $38.75 ($3.10 x 12.5). Jasmine eats 200 pounds of hay and alfalfa, which costs $0.00, since hay and alfalfa are not typically purchased with money. Therefore, Benny the tiger costs more to feed each day.

The volume of the resulting solid is (26π/3) cubic units.

To find the volume of the solid generated by rotating the region bounded by the curves x = (y - 6)², x = 25, about the axis y = 1, we will integrate the cylindrical shells along the y-axis.

The limits of integration for y are from y = 1 to y = 11, as determined earlier.

The differential volume of a cylindrical shell is given by dV = 2πrh dy, where r is the distance from the axis of rotation to the curve, h is the height of the cylindrical shell, and dy is the thickness of the shell.

In this case, the radius of the cylindrical shell is r = 1, and the height of the cylindrical shell is h = x₁ - x₂ = 25 - (y - 6)².

Thus, the differential volume becomes dV = 2π(1)(25 - (y - 6)²) dy.

We can now integrate this differential volume over the range of y = 1 to y = 11 to find the total volume V:

V = ∫[1,11] 2π(25 - (y - 6)²) dy

Expanding and simplifying the integral:

V = 2π ∫[1,11] (25 - (y - 6)²) dy

V = 2π ∫[1,11] (25 - (y² - 12y + 36)) dy

V = 2π ∫[1,11] (25 - y² + 12y - 36) dy

V = 2π ∫[1,11] (-y² + 12y - 11) dy

Integrating the terms individually:

V = 2π [-y³/3 + 6y² - 11y] |[1,11]

V = 2π [-(11³/3) + 6(11²) - 11(11)] - [-(1³/3) + 6(1²) - 11(1)]

V = 2π [-1331/3 + 726 - 121] - [-1/3 + 6 - 11]

V = 2π [-1331/3 + 726 - 121 + 1/3 - 6 + 11]

V = 2π [-604/3 + 616 + 1/3]

V = 2π [13/3]

Simplifying further:

V = (26π/3)

Therefore, the volume of the resulting solid is (26π/3) cubic units.

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The derivatives of the given functions:

1. f'(x) = (-sinh(x)(7 + cosh(x))) / (7 + cosh(x))²

2. f'(t) = 1 / tanh(t)

3. f'(x) = cosh(cosh(x)) sinh(x)

4.f'(x) = 2x sinh⁻¹(6x) + 6x² / √(1 + 36x²)

1. f(x) = 7 - cosh(x) / (7 + cosh(x))

Using the quotient rule, we differentiate numerator and denominator separately:

f'(x) = [(-sinh(x))(7 + cosh(x)) - (cosh(x))(-sinh(x))]/(7 + cosh(x))²

f'(x) = (-sinh(x)(7 + cosh(x)) + cosh(x)(sinh(x))) / (7 + cosh(x))²

f'(x) = (-sinh(x)(7 + cosh(x))) / (7 + cosh(x))²

2. f(t) = ln(sinh(t))

Using the chain rule, the derivative is:

f'(t) = (1 / sinh(t)) cosh(t)

f'(t) = cosh(t) / sinh(t)

Using the identity cosh(t) / sinh(t) = 1 / tanh(t):

f'(t) = 1 / tanh(t)

3. f(x) = sinh(cosh(x))

Using the chain rule, the derivative is:

f'(x) = cosh(cosh(x)) sinh(x)

4. f(x) = x² sinh⁻¹(6x)

Using the chain rule, the derivative is:

f'(x) = 2x sinh⁻¹(6x) + x² (1 / √(1 + (6x)²)) 6

Simplifying further:

f'(x) = 2x sinh⁻¹(6x) + 6x² / √(1 + 36x²)

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The probability of choosing a 5 and then a 6 is 1/49

From the question, we have the following parameters that can be used in our computation:

The tiles

Where we have

Total = 7

The probability of choosing a 5 and then a 6 is

P = P(5) * P(6)

So, we have

P = 1/7 * 1/7

Evaluate

P = 1/49

Hence, the probability of choosing a 5 and then a 6 is 1/49

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Question

You randomly choose one of the tiles. Without replacing the first tile, you choose a second tile. Find the probability of the compound event. Write your answer as a fraction or percent rounded to the nearest tenth. The probability of choosing a 5 and then a 6

1.) If x and y are both positive, the expression x - y is Always positive.

2.) If x is positive and y is negative, the expression x - y is Positive only if x > y.

1.) When both x and y are positive, subtracting a positive number from a positive number will always result in a positive value. Therefore, the expression x - y is always positive in this case.

2.) When x is positive and y is negative, subtracting a negative number from a positive number will result in a positive value only if the positive number (x) is greater than the negative number (-y). In other words, x - y is positive only if x > y. If x is less than or equal to y, the result would be negative or zero, making the expression not positive.

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Event A and B = 4

Event A or B = 2, 3, 4, 5, 6, 8

Complement of Event B = 1, 2, 7, 8

Event A: The marble selected has an even number.

The even numbers from 1 to 8 are 2, 4, 6, and 8. Therefore, the outcomes for Event A are: 2, 4, 6, 8.

Event B: The marble selected has a number from 3 to 6.

The numbers from 3 to 6 are 3, 4, 5, and 6. Therefore, the outcomes for Event B are: 3, 4, 5, 6.

Event A and B:

The outcomes that satisfy both Event A and Event B are the numbers that are both even and from 3 to 6. In this case, the only number that satisfies both conditions is 4.

Therefore, the outcome for Event A and B is: 4.

Event A or B:

The outcomes for Event A or Event B are the numbers that satisfy either Event A or Event B or both.

Combining the outcomes from Event A and Event B, we have: 2, 3, 4, 5, 6, 8.

Complement of Event B:

The complement of an event includes all the outcomes that are not part of the event.

In this case, the complement of Event B includes the numbers that are not from 3 to 6.

Therefore, the outcomes for the complement of Event B are: 1, 2, 7, 8.

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Complete question

A marble is selected from a bag containing eight marbles numbered 1 to 8.

The number on the marble selected will be recorded as the outcome.

Consider the following events.

Event A: The marble selected has an even number.

Event B: The marble selected has a number from 3 to 6.

Give the outcomes for each of the following events.

If there is more than one element in the set, separate them with commas.

Event A and B =

Event A or B =

Complement of the event B=

In standard nomenclature, a normally distributed dataset is represented as \(N(µ, σ^2)\), where µ is the mean and \(σ^2\)is the variance (square of the standard deviation).

A normally distributed phenomenon using standard nomenclature can be described as follows:

A dataset is said to be normally distributed if it follows a bell-shaped curve, which is symmetrical around the mean (µ) and characterized by its standard deviation (σ). In standard nomenclature, a normally distributed dataset is represented as \(N(µ, σ^2)\), where µ is the mean and \(σ^2\)is the variance (square of the standard deviation).

For example, if we consider the heights of adult males in a large population, we may observe that the distribution is normally distributed with a mean height (µ) of 175 cm and a standard deviation (σ) of 10 cm. In this case, the nomenclature for this normally distributed phenomenon would be N(175, 100), as the variance is \(10^2 = 100\).

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Answer:

The picture isnt loading, i would love to help. Maybe, repost the question?

Step-by-step explanation:

Answer: you did not put in the full equation but i got this right out of the box.

ˉx 28

r 0.82

Answer:5,149 pounds of sawdust for $1,132.78

Step-by-step explanation:

Step 1 is to convert 4 tons into pounds is:

4 tons * 2000 pounds per ton = 8000 pounds

Step 2 is to find the cost of saw dust per pound in each scenario:

Scenario 1: $1132.78 / 5149 = .22 dollars per pound

Scenario 2: $2800 / 8000 = .35 dollars per pound

Step 3 is just comparing which one is the cheapest per pound based on step 2:

.22 per pound is less than .35 per pound. So the answer is scenario 1 (5149 pounds for 1132.78) is the better buy