Compute the determinant using cofactor expansion along any row or column that seems convenient.
tan(theta) sin(theta) cos(theta)
cos(theta) 0 −sin(theta)
sin(theta) 0 cos(theta)

At a 5% level of significance, if the calculated p-value is less than 0.05, we reject the null hypothesis and conclude that the performance of Chicago O'Hare airport is significantly different from the nation as a whole.

To determine whether the performance of Chicago O'Hare airport differs from the nation as a whole, a hypothesis test can be conducted.

Let the null hypothesis, H0, be that the mean departure delay time for Chicago O'Hare airport is equal to the mean departure delay time for the nation.

The alternative hypothesis, Ha, is that the mean departure delay time for Chicago O'Hare airport is not equal to the mean departure delay time for the nation.

A two-sample t-test can be used to determine whether the difference between the means is statistically significant.

At a 5% level of significance, if the calculated p-value is less than 0.05, we reject the null hypothesis and conclude that the performance of Chicago O'Hare airport is significantly different from the nation as a whole.

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Answer:

The coordinates of the point S could be;

A. (-1, -1)

Step-by-step explanation:

The given parameters are;

The ratio of the length of the line RS to the length of the line RT = 1:2

The coordinates of point R = (2. 5)

The coordinates point T = (-4, -7)

Therefore, we have;

\(\dfrac{The \ length \ of \, RS}{The \ length \ of \, RT} = \dfrac{1}{2}\)

\(\therefore {The \ length \ of \, RS} = \dfrac{1}{2} \times The \ length \ of \, RT\)

The length of the line RT = √(((2 - (-4))² + (5 - (-7))²) = 6·√5

Therefore, we have;

\({The \ length \ of \, RS} = \dfrac{1}{2} \times 6\cdot \sqrt{5} = 3 \cdot \sqrt{5}\)

When the coordinates of the point S = (-1, -1), we have;

The length of the line RS = √(((2 - (-1))² + (5 - (-1))²) = √45 = 3·√5

Therefore, the coordinates of the point S could be (-1, -1)

Answer:

A)Deductive

B)Deductive

C)Inductive

D) Deductive

Step-by-step explanation:

The number sentence to find how many people are on all the buses is 7 x10 = ?. (Option C)

A number sentence refers to an equation or inequality which expresses using numbers and mathematical symbols. Examples of number sentences include 32 + 57 = ? or 5 x 6 = ?. In the given situation, Jack sees 7 buses and each bus has 10 people on it. In order to determine the total number of buses on all the buses, multiplication operation is used. Multiplication, one of the four basic mathematical operations of arithmetic, refers to an operation that represents the basic idea of repeated addition of the same number. Hence, it is used to combine groups of equal sizes. As in the given case, the group of equal size i.e., the number of people on each bus is seen in 7 buses, the total number of people would be the product of two and would be represented by 7 x10 = ?.

Note: The question is incomplete. The complete question probably is: Jack sees 7 buses. Each bus has 10 people on it. Which number sentence can be used to find how many people are on all the buses? A. 7 + 10 = ? B. 10 – 7 = ? C. 7 x10 = ? D. 10 ÷ 7 = ?

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Answer:

C. order

Step-by-step explanation:

The associative property of addition allows you to change the of numbers without affecting the sum.

Answer: Grouping

Step-by-step explanation:

Changing the grouping of addends does not change the sum. For example, ( 2 + 3 ) + 4 = 2 + ( 3 + 4 ) (2 + 3) + 4 = 2 + (3 + 4) (2+3)+4=2+(3+4)left parenthesis, 2, plus, 3, right parenthesis, plus, 4, equals, 2, plus, left parenthesis, 3, plus, 4, right parenthesis.

Answer:

10 ≥ 2(2.99) + 0.67b  

10 ≥ 5.98 + 0.67b

4.02 ≥ 0.67b

6 ≥ b

David can buy 6 pounds of bananas at most.

Step-by-step explanation:

Its A OR B

make me brainest please

Without additional information about the room, cheese location, and mouse behavior, it is difficult to provide an exact probability of the mouse finding cheese in the long run. However, it is safe to say that the more the mouse explores and the more determined it is, the higher its probability of finding cheese.

The probability of a mouse finding cheese in the long run depends on various factors such as the size and layout of the room, the location of the cheese, and the behavior of the mouse. Assuming that the room is small and the cheese is located in a fixed position, the probability of the mouse finding cheese increases as it explores more areas of the room. However, if the cheese is hidden or difficult to reach, the probability of the mouse finding it may decrease.

Furthermore, the behavior of the mouse can also impact its probability of finding cheese. If the mouse is determined and persistent, it may continue searching for the cheese until it is found. However, if the mouse is easily distracted or gives up easily, its probability of finding cheese may decrease.

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Answer:

g=44°

k=70°

h= 136°

m= 110°

Answer:

h= 136°

g=44°

m= 110°

k=70°  

Step-by-step explanation:

Have a nice day!

False. if you are given a graph with two shif table lines, the correct answer will always require you to move both lines.

In a graph with two shiftable lines, the correct answer may or may not require moving both lines. It depends on the specific scenario and the desired outcome or conditions that need to be met.

When working with shiftable lines, shifting refers to changing the position of the lines on the graph by adjusting their slope or intercept. The purpose of shifting the lines is often to satisfy certain criteria or align them with specific points or patterns on the graph.

In some cases, achieving the desired outcome may only require shifting one of the lines. This can happen when one line already aligns with the desired points or pattern, and the other line can remain fixed. Moving both lines may not be necessary or could result in an undesired configuration.

However, there are also situations where both lines need to be shifted to achieve the desired result. This can occur when the relationship between the lines or the positioning of the lines relative to the graph requires adjustments to both lines.

Ultimately, the key is to carefully analyze the graph, understand the relationship between the lines, and identify the specific criteria or conditions that need to be met. This analysis will guide the decision of whether one or both lines should be shifted to obtain the correct answer.

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The missing value, rounded to the nearest hundredth, is approximately 54.46 degrees.

The equation sin ___ = 7/12 suggests that we need to find an angle whose sine is equal to 7/12. To determine the missing value, we can use the inverse sine function, also known as arcsine or sin^-1.

Using the inverse sine function, we can write the equation as ___ = sin^-1(7/12). Evaluating this expression with a calculator or a trigonometric table, we find that sin^-1(7/12) is approximately 54.46 degrees.

It's important to note that trigonometric functions have periodicity, meaning that there are multiple angles that have the same sine value. Therefore, there are other angles, such as 180 degrees minus 54.46 degrees, that also satisfy sin ___ = 7/12. However, when finding a single missing value, we typically consider the principal value within a specified range, often from -90 degrees to 90 degrees.

Thus, rounding to the nearest hundredth, the missing value that satisfies sin ___ = 7/12 is approximately 54.46 degrees.

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The depreciation expense for 2022, based on the purchase price for the computer of $8,600, the revised estimate in 2022, using the straight-line method is $2,410 per year

The straight-line depreciation method is method for calculating the depreciation of an asset in which the value of the asset is uniformly reduced within each period until the salvage value of asset is reached.

The depreciation on the computer = $8,600 - $900 = $7,700

The annual depreciation rate for the computer in the first two years, using the straight line depreciation method is; $7,700/5 = $1,540 per year

The depreciation of the computer by the end of 2021 = 2 × $1,540 = $3,080

Therefore, the net book value of the computer at the end of 2021 = $8,600 - $3,080 = $5520

The estimates are revised with Pharoah expecting to use the computer until December 2022, to sell for $700, therefore;

The revised depreciable amount for the computer = $5,520 - 700 = $4,820

The revised depreciation rate for the years, 2022 and 2023 is therefore;

Depreciation = $4,820/2 = $2,410 per year

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Occupants are 10 times more likely to be killed in a crash when not buckled in. option c.

Wearing a seatbelt is one of the simplest ways to protect oneself while in a vehicle. When properly worn, it decreases the likelihood of being seriously injured or killed in a collision by as much as 50%. When an individual is not wearing a seatbelt, they are putting their lives at risk. Wearing a seatbelt should be a routine habit whenever an individual sits in a vehicle.

Buckling up is the easiest and most effective way to prevent injuries and fatalities on the road. If drivers, passengers, and children buckle up every time they travel in a vehicle, the likelihood of being killed or injured in a collision is greatly reduced. When occupants of a vehicle do not buckle up, they are 10 times more likely to be killed in a crash. This means that the likelihood of being killed is significantly higher when not wearing a seatbelt.

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A function type that could model the given situation is a linear function.

The rate of change in the truck's worth per year is -1400.

A model that describes this situation is y = -1400x + 43500

In Mathematics, the slope of any straight line can be determined by using this mathematical equation;

Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope (m) = rise/run

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Substituting the given data points into the slope formula, we have the following;

Slope (m) = (36,500 - 43,500)/(2020 - 2015)

Slope (m) = -7,000/5

Slope (m) = 1,400.

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By looking at the table, you can see that we have an x

that is paired with two different y's so this does not fit the

definition of a function which states that each x must

be paired with exactly one y.

Answer: x = 4

Step-by-step explanation:

Answer:

X= 4

Step-by-step explanation:

You add the six to both sides and get 3x+5x=32. Add the 3 with the %x to get 8X. Divide 32 by 8 to get 4.

Therefore, the directional derivative of f at P=(1,-1,-2) in the direction of A=3i+2j-6k is -2.

To find the directional derivative of f(x,y,z) at P=(1,-1,-2) in the direction of A=3i+2j-6k, we first need to find the gradient of f at P, which is given by:

grad(f) = ∇f = (∂f/∂x)i + (∂f/∂y)j + (∂f/∂z)k

Here, f(x,y,z) = xy + yz + zx, so we have:

∂f/∂x = y + z

∂f/∂y = x + z

∂f/∂z = x + y

Thus, at P=(1,-1,-2), we have:

∇f(P) = (∂f/∂x)i + (∂f/∂y)j + (∂f/∂z)k

= (y+z)i + (x+z)j + (x+y)k

= (0+(-2))i + (1+(-2))j + (1+0)k

= -2i - 1j + 1k

Next, we need to find the unit vector in the direction of A:

|A| = sqrt(3^2 + 2^2 + (-6)^2) = 7

u = A/|A| = (3/7)i + (2/7)j - (6/7)k

Finally, we can compute the directional derivative of f at P in the direction of A as:

(DAf) | 1(1,-1,-2) = ∇f(P) · u

= (-2i - 1j + 1k) · (3/7)i + (2/7)j - (6/7)k

= -6/7 - 2/7 - 6/7

= -2

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Solution:

Given the triangle below where K is in the incenter:

Thus, we have

step 1: In the triangle DGK, find DK.

Thus, by Pythagoras theorem, we have

step 2: In the triangle KDI, find DK.

Similarly, we have

Step 3: Equate the equations in steps 1 and 2.

This gives

The value of x is

Answer:

the answer is 82

Step-by-step explanation:

here,

x°+57°+41°=180° ( sum of interior angle of a triangle)

or, x°+ 98°= 180°

or, x°=180°-98°

or, X°=82.

can u give me brailest

Answer:

Supplementary Angles

x = 62

Step-by-step explanation:

Supplementary angles equal 180.

180 - 118 = 62

I hope this helps!

Answer:

(1) Hundred

(2) Numerator

(3) Percent

Step-by-step explanation:

The probability that x is greater than 77. 5 is 0.039828

Given,

Mean, μ = 80

Standard deviation, σ = 25

We have to find z score corresponding to 77.5

z = (x-μ) / σ

   \(=\frac{77.5-80}{25} \\= 0.1\)

Now we have to find P value from Z table:

P(x<77.5) = 0.46017

P(x>77.5) = 1 - P(x<77.5) = 0.53983

P(77.5<x<80) = 0.5 - P(x<77.5) = 0.039828

The probability of x greater than 77.5 is 0.039828

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Step-by-step explanation:

\( \frac{10}{5x - 9} = \frac{7}{9} \\ 7(5x - 9) = 9 \times 10 \: \\ (cross \: multiplication) \\ 35x - 63 = 90 \\ 35x = 90 + 63 \\ 35x = 153 \\ x = \frac{153}{35} \)

.

.

.

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\(\color{yellow}\boxed{\colorbox{black}{MARK\: BRAINLIEST!❤}}\)

Answer:

wouldn't it be 3lb and 7oz

\(5(x + 3y) \\ y(2x - 3)\)

If 22 inches of wire costs 88 cents then at the same rate, 16 inches of wire will cost 64 cents.

To determine the cost of 16 inches of wire at the same rate as 22 inches, we can set up a proportion using the given information. We have that 22 inches of wire costs 88 cents. We can set up the proportion:

22 inches / 88 cents = 16 inches / x cents

By cross-multiplying, we get:

22 inches * x cents = 16 inches * 88 cents

Simplifying, we have:

22x = 1408

Dividing both sides by 22, we find:

x = 64

Therefore, 16 inches of wire will cost 64 cents at the same rate as 22 inches. The cost is directly proportional to the length of the wire, so we can use this proportion to calculate the cost of different lengths.

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Answer:

21%

Step-by-step explanation:

Out of the 25 + 9 + 12 + 21 + 12 + 21 = 100 total rolls, 6 came up 21 times so the percentage is 21/100 = 21%.

Answer:

volume = 720 in³

Step-by-step explanation:

volume = 1/3Bh = 1/3 x 72 x 30 = 720 in³

Four siblings whose ages are consecutive integers. If the sum of their ages is 86 then The eldest sibling is 20, followed by siblings 21, 22, and 23.

Consecutive means in order.  Integers are a collection of whole integers and their antipodes, such as -3, -2, 1, 0, 1, 2, 3, etc.

Let x = the one sibling

Let x + 1 = the second sibling

Let x + 2 = the third sibling

Let x+4 = the fourth sibling.

If you add the four siblings together they equal 86

(x) + (x +1) + (x + 2) + (x+3) = 86  I put the parentheses in so that you can see each sibling, but it is not needed.

x + x+ 1 +x + 2 + x+ 3 = 86  Combine like terms

4x + 6 = 86 Subtract 6 from both sides

4x = 80

x = 20

The eldest sibling is 20, followed by siblings 21, 22, and 23.

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