x = (4 - 3x)/k
solve for x

Answer:

Anna

Step-by-step explanation:

Hers grew 2.5 inches each time

Angle measure of the smaller angle in two complement angles = x

Angle measure of the bigger angle = x + 20

Their sum = 90° ( the sum of two complementary angles is always equal to 90° )

This can be written in an equation as =

= x + x + 20 = 90

= 2x + 20 = 90

= 2x = 90 - 20 ( transposing +20 from LHS to RHS changes +20 to -20 )

= 2x = 70

= x = 70 ÷ 2 ( transposing ×2 from LHS to RHS changes ×2 to ÷2 )

= x = 35

Then the value of the smaller angle = x = 35°

The value of the bigger angle = x + 20 = 35 + 20 = 55°

Therefore , the measure of degrees in the the smaller angle is :

Answer:

The thousandth goes past the decimal point 3 places.

This would be the first option, i.e. 22.524 :)

Answer:

[tex]-\frac{15}{7}[/tex]

Step-by-step explanation:

Isolate the variable by dividing each side by factors that don't contain the variable.

Answer:

it should be -[tex]\frac{15}{7}[/tex]

Step-by-step explanation:

Answer:

(3,-1)

Step-by-step explanation:

(y,-x) is the "formula" to use on this ordered pair to find the counterclockwise rotation of 270 degrees (you should probably memorize these for your test). This means that (1,3) would become (3,-1) after flipping the x- and y-coordinates and making the x-coordinate negative.

The image of the point (1,3) after a counterclockwise rotation of 270° is (3, -1).

The given coordinate point is (1, 3).

We need to find the image of the point (1,3) after a counterclockwise rotation of 270°.

A rotation is a type of transformation that takes each point in a figure and rotates it a certain number of degrees around a given point.

When we rotate a figure of 270° counterclockwise, each point of the given figure has to be changed from (x, y) to (y, -x) and graph the rotated figure.

So, points (1,3) changed to (3, -1).

Therefore, the image of the point (1,3) after a counterclockwise rotation of 270° is (3, -1).

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Answer: fourth

Step-by-step explanation: the terminal ray of a 300 angle lies in the FOURTH quarter.

This angle measures (5/3) radians.

Answer:

-fourth

-5/3pi

Step-by-step explanation:

Answer:

Try doing the ratio

Step-by-step explanation:

like it would be -15 to 20

The sample consists of three scores: 7, 8, and 9. The mean is 8, the median is 8, there is no mode, and the range is 2.

In statistics and probability, a sample refers to a subset of a population that is used to make inferences or draw conclusions about the entire population. In this case, the sample consists of the scores you obtained in 5 quizzes. The scores are as follows: 7, 8, and 9.
To analyze this sample, there are several key measures that can be calculated:
1. Mean: The mean, also known as the average, is calculated by summing up all the scores and dividing it by the number of scores. In this case, the mean can be calculated as (7 + 8 + 9) / 3 = 8.
2. Median: The median is the middle value when the scores are arranged in ascending order. In this case, since there are three scores, the median is the middle score, which is 8.
3. Mode: The mode is the score that appears most frequently in the sample. In this case, none of the scores repeat, so there is no mode.
4. Range: The range is the difference between the highest and lowest scores in the sample. In this case, the highest score is 9 and the lowest score is 7, so the range is 9 - 7 = 2.
5. Standard Deviation: The standard deviation is a measure of how spread out the scores are from the mean. It quantifies the amount of variation or dispersion in the sample. To calculate the standard deviation, you would need the full set of scores, not just the three provided.

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The lifetime of a light bulb is known to have an exponential distribution with mean 200 days. The formula for the exponential distribution is: f(x) = (1/λ) * e^(-x/λ), where x ≥ 0 and λ > 0 are constants.

Here, the mean is 200 days, so λ = 1/200 = 0.005.

Both X and Y are independent.

Therefore, we can find the probability that X fails within 10 days of Y, and multiply it by the probability that Y fails within 10 days of X.

Hence, the probability that the bulbs fail within 10 days of each other is the sum of these probabilities.

Let Z = X - Y, then P(X ≤ Y + 10) = P(X - Y ≤ 10) = P(Z ≤ 10).

Now, we can transform Z into a standard normal variable, as follows: Z = (X - Y - E[Z]) / σ[Z].

Now, E[Z] = E[X - Y] = E[X] - E[Y] = 200 - 200 = 0, and

σ[Z]^2 = Var[X - Y] = Var[X] + Var[Y] = (1/λ^2) + (1/λ^2) = 2/λ^2.

Hence, σ[Z] = √(2/λ^2) = √2 * 200 ≈ 282.84.

Therefore, P(Z ≤ 10) = P[(X - Y) / σ[Z] ≤ 10 / σ[Z]] = P(Z' ≤ 10 / σ[Z]) ≈ P(Z' ≤ 0.0354), where Z' is a standard normal variable.

The probability of Z' being less than or equal to 0.0354 is equal to 0.5120.

Therefore, the probability that two bulbs fail within 10 days of each other is

P(X ≤ Y + 10 and Y ≤ X + 10) = P(X ≤ Y + 10) * P(Y ≤ X + 10) = P(Z ≤ 10) * P(Z ≤ -10) = P(Z ≤ 10)^2 ≈ (0.5120)^2 = 0.2621.

The probability that two bulbs fail within 10 days of each other is 0.2621.

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To calculate the annual interest rate required to earn if you want a $600 per month contribution to grow to $45,000 in six years, we can use the formula for future value of an annuity: FV = PMT x [((1 + r)n - 1) / r]where,FV = future value of an annuityPMT = the payment you will make in each periodr = the interest rate per periodn = the number of periods.

Using the given values, we have:FV = $45,000PMT = $600n = 6 x 12 = 72 (since we are given in months, and there are 12 months in a year)r = ?To solve for r, we can use trial and error or a financial calculator. Here, we will use a financial calculator.

To solve this problem, we will use the formula for future value of an annuity:FV = PMT x [((1 + r)n - 1) / r]where,FV = future value of an annuity PMT = the payment you will make in each periodr = the interest rate per periodn = the number of periods.

We are given:FV = $45,000PMT = $600n = 6 x 12 = 72 (since we are given in months, and there are 12 months in a year)r = ?To solve for r, we can use a financial calculator or trial and error. Here, we will use a financial calculator. We enter the values into the financial calculator and solve for r. We get

:r = 8.81% (rounded to two decimal places)Therefore, the annual interest rate required to earn if you want a $600 per month contribution to grow to $45,000 in six years is approximately 8.81%.

The annual interest rate required to earn if you want a $600 per month contribution to grow to $45,000 in six years is approximately 8.81%.

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Answer:

Option 1 or 16 + h = 24

Step-by-step explanation:

Tyrone ate 16 hamburgers today.

Tyrone had 24 hamburgers.

Hamburger = h.

We want to find how much Tyrone had left so:

h = 24 - 16

OR (we can move 16 to the other side)

h + 16 = 24

Option 1 is the answer

6.22 +1-1-1-2+4= 7.22

Answer:

6.22 +1-1-1-2+4= 7.22

Step-by-step explanation:

Depending on q, the boy who gets a strictly higher payoff in the SPE is different.  The correct statement is: Which boy gets strictly higher payoff depends on q.

First we will find the Subgame Perfect Equilibrium (SPE) of the game.

Subgame 1: Let's find the SPE of the first subgame. Boy 1 proposes a deal.

There are only two possible deals, so we can compute the payoff for each.

If a = 80, Boy 2 will accept, because he gets 20 and Boy 1 gets 80.

If a = 50, Boy 2 will reject, and the game will move on to subgame 2.

For subgame 2, Boy 2 proposes a deal.

There are only two possible deals, so we can compute the payoff for each.

If a = 80, Boy 1 will reject, because he gets 20 and Boy 2 gets 80.

If a = 50, Boy 1 will accept, because he gets 50 and Boy 2 gets 50.

Payoffs of each player for each decision rule:

Now let's analyze the payoffs of the boys in the SPE under any q.

When q < 0.5, there is a high probability that the cat will come and steal the pizza in subgame 1, so Boy 1's best offer is 50.

In subgame 2, Boy 2's best offer is 50, because Boy 1 is indifferent between 50 and 80, but 50 provides a higher expected payoff in case the pizza is stolen.

When q > 0.5, there is a high probability that the game will move on to subgame 2, so Boy 1's best offer in subgame 1 is 80.

In subgame 2, Boy 1's best offer is 50, because Boy 2 is indifferent between 50 and 80, but 50 provides a higher expected payoff in case the pizza is stolen

The correct statement is: Which boy gets strictly higher payoff depends on q.

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Answer:

It's 60 degrees. if you look carefully at the image, there is 2 angles. it can't be 93 since it is way too narrow.

Step-by-step explanation:

I'm on the question on edge, ill keep you updated if it's wrong.

update: it was correct. hope this helped!

Based on the alternate interior angle theorem, the measure of angle 2 in the diagram given is: C. 60°

The alternate interior angle theorem states that the measure of two alternate interior angles are congruent.

Angle 2 and 60° are alternate interior angles, therefore:

Angle 2 = 60° [alternate interior angle theorem].

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Answer:

n = -2

Step-by-step explanation:

Answer:

-2

Step-by-step explanation:

Answer:

more than 200 calls

Step-by-step explanation:

Suppose number of calls = x

According to plan 1: Total monthly charge is $24

According to plan 2: Fix charge is $16 and $0.04 per call

cost of x's call = $0.04x

and monthly charge according to plan 2 = 0.04x + 16

a)  Plan 1 is more economical than plan 2.

0.04x + 16 > 24

solve it for x

.04x > 8

x > 200

b)   So,  if more than 200 calls are made then Plan 1 is more economical.

Answer:

None of the provided choices accurately represents the probability that the area of the rectangle is more than 1/2.

Step-by-step explanation:

To find the probability that the area of the rectangle is more than 1/2, we need to consider the possible combinations of lengths for the adjacent sides of the rectangle. Since the sides are chosen from independent and identically distributed uniform distributions over the interval [0, 1], we can think of it as randomly selecting two numbers from the interval [0, 1] to represent the lengths of the sides.

The area of a rectangle is given by the product of its length and width. Let's assume that the length of the rectangle is represented by X and the width by Y. To calculate the probability that the area is more than 1/2, we can find the probability that X * Y > 1/2.

Since X and Y are uniformly distributed over the interval [0, 1], their joint probability density function is f(x, y) = 1 for 0 ≤ x, y ≤ 1.

To find the desired probability, we need to integrate the joint density function over the region where X * Y > 1/2.

Integrating the joint density function over this region will give us the probability of interest. However, the calculation involves solving a double integral, which is beyond the scope of a simple multiple-choice answer format.

Therefore, none of the provided choices accurately represents the probability that the area of the rectangle is more than 1/2.

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The distance AB across the river is 417.04 m when BC = 351 m, B = 112°10′ and C = 17°15′ across the river. Hence, the correct answer is AB = 417.04m.

We are given that BC = 351 m, B = 112°10′ and C = 17°15′.

We need to find the distance AB across the river, given that angle BAC = 90°.

To find AB, we will use the sine rule.

According to the sine rule,

AB / sin ∠BAC = BC / sin ∠BCA

Substituting the given values, we get,

AB / sin 90° = 351 / sin (112°10′ + 17°15′)

We know that sin 90° = 1 and sin (112°10′ + 17°15′) = sin 129°25′

So,

AB = 351 / sin 129°25′ = 351 / 0.8413

AB = 417.04 m

Therefore, the distance AB across the river is 417.04 m when BC = 351 m, B = 112°10′ and C = 17°15′ across the river. Hence, the correct answer is AB = 417.04m.

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Answer:

738cm^3

Step-by-step explanation:

You just multiply everything together

12.3 * 7.5 * 8 = 738cm^3

To determine the unit requirements for producing A and C from D and E, the problem provides a product structure and inventory information. The number of units of D needed to make one unit of A is not explicitly given. However, it can be inferred by analyzing the product structure and inventory quantities. The number of units of D needed to make one unit of C is also not directly specified. However, by examining the product structure, we can determine the relationship between C and D. Finally, to produce 10 units of A, the number of units of E required can be calculated based on the given inventory levels and the product structure.

a) the number of units of D required to make one unit of A is not explicitly stated. The given information provides a product structure that includes A, B, D, E, and C. To determine the unit requirements for A, it would be necessary to examine the specific relationship between A and D. However, without this information, the exact number of units of D needed for one unit of A cannot be determined.
b) similarly, the number of units of D required to make one unit of C is not explicitly given in the problem statement. To determine this relationship, the product structure needs to be examined more closely. The information provided suggests that C is connected to D through E. However, the exact quantity of D required to produce one unit of C cannot be determined without additional information.
c) To calculate the number of units of E needed to produce 10 units of A, we can analyze the given inventory levels and product structure. The problem states that there are 5 units of D available. To produce A, we require B and E. However, the number of units of B available is not specified. Considering the product structure, it is indicated that each unit of A requires 2 units of B and 2 units of E. Thus, to produce 10 units of A, we would need 20 units of B and 20 units of E. However, since the availability of B is unknown, the exact number of units of E needed cannot be determined with the given information.

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Answer:

Answer 1 is 3712000000

answer 2 is 8.624X10^10

answer 3 is 820

answer 4 is 380

answer 9 is 9200

answer 10 is 400

answer 11 is 8832000000

answer 12 is 1.3104X10^10

Answer:

2.5 million

Step-by-step explanation:

Given that :

Population in 2003 = 10.5 million

Population in 2003 = 3 million + (3 * population in 1950)

Hence from both expressions :

Let population in 1950 = p

3,000,000 + (3 * p) = 10,500,000

3,000,000 + 3p = 10,500,000

3p = 10,500,000 - 3,000,000

3p = 7,500,000

p = 7,500,000 / 3

p = 2,500,000

Hence, population in 1950 is 2.5 million

Answer:

than it is any number between -2 and +5

we need to find the values of sin(10°) and cos(10°) to compute sin(20°).

To find the value of sin 20°, we can use the trigonometric identity sin(2θ) = 2sin(θ)cos(θ).

Given sin(θ) = √3/2 and 0° < θ < 90°, we can find the value of sin 20° as follows:

sin(20°) = 2sin(10°)cos(10°)

We need to find the values of sin(10°) and cos(10°) to compute sin(20°).

Given cos(θ) = -√2/2 and -π/2 < θ < 0, we can find the value of sin 20° as follows:

sin(20°) = 2sin(10°)cos(10°)

Similarly, we need to find the values of sin(10°) and cos(10°) to compute sin(20°).

Since you provided conflicting information for the values of sin 0 and cos 0, it is not possible to determine the value of sin 20° without accurate values for sin 0 and cos 0. Please provide the correct values, and I will be happy to help you further.

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Answer:

(-4) (3)= -12

Step-by-step explanation:

because negative times a positive =a negative

Answer:

x= -2 y= -5

Step-by-step explanation:

X+y=-7

x+-y-7

-5(-y-7)+y=5

5y+35+y=5

6y+35=5

6y=5-s5

6y=-30

y=-5

-5x+(-5)=5

-5x=5+5

-5x=10

x=-2

a) The probability of having less than 3 breakdowns during the next three months is approximately 0.6767.

To find the probability of having less than 3 breakdowns during the next three months, we can use the Poisson distribution formula:

P(X < 3) = e^(-λ) * (λ^0/0!) + e^(-λ) * (λ^1/1!) + e^(-λ) * (λ^2/2!)

Here, λ is the mean number of breakdowns per month, which is 2.

Substituting the value of λ into the formula, we have:

P(X < 3) = e^(-2) * (2^0/0!) + e^(-2) * (2^1/1!) + e^(-2) * (2^2/2!)

Calculating each term:

P(X < 3) = 0.1353 + 0.2707 + 0.2707 = 0.6767

b) The probability that 8 out of the 10 machines will not be used during the next two months is approximately 0.000128.

If each machine works independently and there are 10 machines, we can consider the probability for each machine not being used (having more than 4 breakdowns in two months) and then multiply those probabilities together.

The probability of a single machine not being used is:

P(not used) = P(X > 4)

Using the Poisson distribution formula with a mean of 2 breakdowns per month:

P(not used) = 1 - [P(X ≤ 4)]

P(not used) = 1 - [e^(-2) * (2^0/0!) + e^(-2) * (2^1/1!) + e^(-2) * (2^2/2!) + e^(-2) * (2^3/3!) + e^(-2) * (2^4/4!)]

Calculating this probability, we find:

P(not used) = 0.1429

The probability that 8 out of 10 machines will not be used is calculated by raising the probability of a single machine not being used to the power of 8 (since each machine's status is independent):

P(8 out of 10 not used) = (P(not used))^8

P(8 out of 10 not used) = (0.1429)^8

Calculating this probability, we get:

P(8 out of 10 not used) = 0.000128

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Answer:

[tex] \frac{7}{6} or \: 1 \frac{1}{6} [/tex]

Answer:

Step-by-step explanation:

Formula for linear velocity

Converting the angle measure from degrees to radians

Substituting values