A. 9
B. 0
C. -9
D. 6

Answer:

2

Step-by-step explanation:

Answer: 2

I got it right on ed

In a right triangle, the trigonometric ratio x must be positive. There isn't an x solution that meets the requirements. The cosine and sine function values given are incompatible with a correct right triangle. x = -0.40

A right triangle is one with a 90 degree inner angle. The two arms of a right angle are made up of height and base.

The sum of the angles B and C's measurements in a right triangle is 90 degrees (since angle A is 90 degrees).

So we have:

B + C = 90

And since sin C = 3x + 0.31, we know that:

C = sin⁻¹(3x + 0.31)

B + sin⁻¹(3x + 0.31) = 90

Subtracting sin⁻¹(3x + 0.31) from both sides, we get:

B = 90 - sin⁻¹(3x + 0.31)

Now we can use the fact that cos B = x - 0.49:

cos(90 - sin⁻¹(3x + 0.31)) = x - 0.49

Using the identity cos(90 - θ) = sin(θ), we can rewrite this as:

sin(sin⁻¹(3x + 0.31)) = x - 0.49

Simplifying the left side using the inverse sine function, we get:

3x + 0.31 = x - 0.49

Subtracting x and 0.31 from both sides, we get:

2x = -0.80

Dividing both sides by 2, we get:

x = -0.40

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14 + 5 equals a value of 19. Roman numeral 19 is hence XIX.

Roman numerals are a set of numbers that was first used in ancient Rome and remained to be widely used in European until the Late Middle Ages.

The fixed positive numbers are represented by alphabets in roman numerals. I, II, III, IV, V, VI, VII, VIII, IX, and X are roman numerals that stand for the numbers 1, 2, 3, 4, 5, 6, 7, 8, 9, and 10 respectively.

The roman numbers XI for 11, XII for 12, XII for 13,... to XX for 20 come after 10.

So, roman numerals require that the number be written in extended form, i.e:

19 = 20 – 1

19 = XX – I

19 = XIX

Therefore, 14 + 5 equals a value of 19. Roman numeral 19 is hence XIX.

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Answer: (13,-7)

Step-by-step explanation:

By using the formula \((x_{m},y_{m}) =(\frac{x_{1}+x_{2} }{2},\frac{y_{1}+y_{2} }{2} )\)

\((x_{m},y_{m})\\\) is the coordinates of the midpoint.

For finding the midpoint X variable do:

\((\frac{4+22}{2})=13\)

For finding the midpoint Y variable do:

\(\frac{-10+(-4)}{2} = -7\) (you can either keep the parenthesis or take them out. Either way, the answer is the same.

Considering coordinate numbers follow the format: (x,y), you'll simply just substitute the numbers found above into their respective places.

x: 13

y: -7

(13,-7).

Answer:

im sorry but can you post like something to go with it cause i dont get it like you only put numbers

Step-by-step explanation:

There are 680 ways can Marie choose 3 pizza toppings from a menu of 17 toppings if each topping can only be chosen once.

We have to given that;

Marie choose 3 pizza toppings from a menu of 17 toppings.

Hence, To find ways can Marie choose 3 pizza toppings from a menu of 17 toppings if each topping can only be chosen once,

We can formulate;

⇒ ¹⁷C₃

⇒ 17! / 3! 14!

⇒ 17 × 16 × 15 / 6

⇒ 680

Thus, There are 680 ways can Marie choose 3 pizza toppings from a menu of 17 toppings if each topping can only be chosen once.

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Answer:

500 students

Step-by-step explanation:

Change the percent to a fraction in its simplest terms

Then solve 2/3×1250

Answer:

500 students ride the bus

Step-by-step explanation:

Easy:

If the total number of students is 1250 and you know 40% ride the bus all you have to do is figure out 40% of 1250. Once you get that you will get 500 people. You can use a calculator for this problem.

x/1250 = 40/100

x = number of students riding bus

Solve for x

100x = 1250*4 - after you cross mulitply

solve for x

x = 500

Option A. In observational studies, the variable of interest can be either numerical or categorical, so it does not have to be numerical.

Observational studies are a type of study in which researchers observe and record data on variables of interest without manipulating them directly. These studies are often used in fields such as epidemiology, social sciences, and psychology to investigate relationships between variables and identify potential risk factors for diseases or other outcomes.

The variable of interest in an observational study can be either numerical or categorical. Numerical variables are those that can be measured and expressed as a numerical value, such as age, height, weight, or blood pressure. Categorical variables are those that are qualitative or nominal in nature, such as gender, race, or smoking status.

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In observational studies, the variable of interest ____

A. cannot be numerical.

B. must be numerical.

C. is controlled.

D is not controlled.

The contour lines closer to the origin

Let's start by understanding the equation given: y = f(x,t) = cos(t)sin(x)

Here, t represents time in milliseconds and x represents the distance in millimeters from the left end of the string. The function f(x,t) gives the displacement of the string at a given point (x,t) from its equilibrium position.

To graph the traces f(x,0) and f(x,pi/2), we need to fix the value of t and plot the function against x.

f(x,0) = cos(0)sin(x) = 0, as the displacement of the string is zero when t = 0.

f(x,pi/2) = cos(pi/2)sin(x) = sin(x), which gives us the displacement of the string at time t = pi/2 milliseconds.

The x-axis represents the distance from the left end of the string in millimeters, and the y-axis represents the displacement of the string in millimeters.

The trace f(x,0) represents the initial position of the string when it is at rest. The trace is a straight line at y=0, indicating that all points on the string are in their equilibrium positions.

The trace f(x,pi/2) represents the displacement of the string at time t = pi/2 milliseconds. It shows the shape of the string when it has completed a quarter of its vibration cycle. The curve starts at 0 when x = 0 and reaches a maximum displacement of 1 at x = pi/2. The curve then goes back to 0 at x = pi, indicating that the string has completed one cycle of vibration.

Now, let's graph the traces f(0,t) and f(pi/2,t):

f(0,t) = cos(t)sin(0) = 0, as the displacement of the string at x=0 is zero.

f(pi/2,t) = cos(t)sin(pi/2) = cos(t), which gives us the displacement of the string at time t for all points x = pi/2.

The x-axis represents time in milliseconds, and the y-axis represents the displacement of the string in millimeters.

The trace f(0,t) represents the displacement of the left end of the string, which is fixed at x=0. As expected, the trace is a straight line at y=0, indicating that the left end of the string remains stationary throughout the vibration cycle.

The trace f(pi/2,t) represents the displacement of the midpoint of the string, which is x=pi/2. The trace is a cosine curve, which indicates that the midpoint of the string oscillates back and forth between positive and negative displacements with a frequency of one cycle per millisecond.

The x-axis represents the distance from the left end of the string in millimeters, and the y-axis represents time in milliseconds. The contours represent the displacement of the string at a given point (x,t) from its equilibrium position.

The contour lines are labeled with the displacement values in millimeters. The contour lines closer to the origin

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Answer:

$1.50 per filled donut and $0.72 per regular donut

Step-by-step explanation:

We need to set up a system of equations to find the price of each type of donut:

Since Bill bought 4 regular donuts and 8 filled donuts for $14.88, we can use the equation 4R + 8F = 14.88

Since Mary Ann bought 7 regular donuts and 7 filled donuts for $15.54, we can use the equation 7R + 7F = 15.54

From first glance, it is clear that elimination will be the best method to solve:

\(4R+8F=14.88\\7R+7F=15.54\\\\7(4R+8F=14.88)\\-4(7R+7F=15.54)\\\\28R+56F=104.16\\-28R-28F=-62.16\\28F=42\\F=1.5\\\\4R+8(1.5)=14.88\\4R+12=14.88\\4R=2.88\\R=0.72\)

A and B commute if a - d = 7b and a = b = d = 0.

To show that A and B commute, we need to show that AB = BA.

First, let's calculate AB:
AB = [2a + b, 2b + b, a + d, b + 5d]

Next, let's calculate BA:
BA = [2a + b, a + d, 2b + b, b + 5d]

We can see that the first and fourth elements of both matrices are the same. However, the second and third elements are different. In order for AB and BA to be equal, we need the second and third elements to also be the same.

This means that we need:
2b + b = a + d
and
a + d = 2b + b

Subtracting 2b from both sides of the first equation gives us:
b = a + d - 2b

Subtracting a from both sides of the second equation gives us:
d - a = 2b + b

Now, we can use the given equation a - d = 7b to substitute for a in the first equation:
b = (7b + d) + d - 2b
b = 9b + 2d

And we can use the same equation to substitute for d in the second equation:
(7b + a) - a = 2b + b
7b = 2b + b

Simplifying both equations gives us:
8b = -2d
and
4b = 0

This means that b = 0 and d = 0. Substituting these values back into the original equation gives us:
a - 0 = 7(0)
a = 0

So, the only solution for A and B to commute is if a = b = d = 0. Therefore, A and B commute if a - d = 7b and a = b = d = 0.

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Answer:

39

Step-by-step explanation:

1- Put your numbers in acending order

2- cross out the first number and the last number until you are in the middle number

3- the number is 39

Answer: 39

Step-by-step explanation: I took the quiz myself and that was the answer.

Answer:

x = 4

Step-by-step explanation:

m = (y2-y1)/(x2-x1)

m = (10 - -2)/(4 - 4) = 12/0

so slope is undefined

therefore the line is a vertical line, which is x = 4

Step-by-step explanation:  

#1 Surface area of the rectangular box:

The formula for the surface area of a rectangular box is given by:

SA= 2lw + 2lh + 2wh, where

In this rectangular box, the length is 5 cm, the width is 7 cm, and the height is 2 cm.  

Thus, we can plug in 5 for l, 7 for w, and 2 for h in the rectangular box formula to find SA, the surface area of the rectangular box in square cm:

SA = 2(5 * 7) + 2(5 * 2) + 2(7 * 2)

SA= 2(35) + 2(10) + 2(14)

SA = 70 + 20 + 28

SA = 118

Thus, the surface area of the rectangular box is 118 cm^2.

#1 Volume of the rectangular box:

The formula for the volume of a rectangular box is given by:

V = lwh, where

Thus, we can plug in 5 for l, 7 for w, and 2 for h in the rectangular box formula to find V, the volume of the rectangular box in cubic units:

V = 5 * 7 * 2

V = 70

Thus, the volume of the rectangular box is 70 cm^3.

#2 Surface area of the cube:

The formula for the surface area of a cube is given by:

SA = 6s^2, where

Thus, we can plug in 4.5 for s in the surface area formula to find SA, the surface area of the cube in square in.:

SA = 6(4.5)^2

SA = 6(20.25)

SA = 121.5

Thus, the surface area of the cube is 121.5 in^2.

#2 Volume of the cube:

The formula for the volume of a cube is given by:

V = s^3, where

Thus, we can plug in 4.5 for s in the volume formula to find V, the volume of the cube in square in.:

V = 4.5^3

V = 91.125

Thus, the volume of the cube is 912.125 in^3.

#3 Surface area of the triangular prism:

One formula we can use for the surface area of a triangular prism is given by:

SA = bh + L(s1 + s2 + s3), where

In this triangular prism, the base is 6 in., the height is 8 in., the length is 6 in., and the three side lengths of one of the triangles are 8 in., 6 in., and 10 in.

Thus, we can plug in 6 for b, 8 for h, 6 for L, and 8, 6, and 10 for s1, s2, and s3 in the triangular prism surface area formula to find SA, the surface area of the triangular prism in square meters:

SA = 6 * 8 + 6(8 + 6 + 10)

SA = 48 + 6(24)

SA = 48 + 144

SA = 192

Thus, the surface area of the triangular prism is 192 m^2.

#3 Volume of the triangular prism:

The formula for the volume of a triangular prism is given by:

V = 1/2bhl, where

Thus, we can plug in 6 for b, 8 for h, and 6 for l in the triangular prism volume formula to find V, the volume of the triangular prism in cubic meters:

V = 1/2(6)(8)(6)

V = 3 * 48

V = 144

Thus, the volume of the triangular prism is 144 m^3.

#4 Surface area of the triangular prism:

Because this figure is also a triangular prism, we can use the same formulas to surface area and volume as we used for #3.  

Since the formula for surface area of a triangular prism is given by:

SA = bh + L(s1 + s2 + s3), we can plug in 12 for b, 8 for h, 12 for L, and 10, 10, and 12 for s1, s2, and s3 in the surface area formula to find SA, the surface area of the triangular prism in cubic ft:

SA = 12 * 8 + 12(10 + 10 + 12)

SA = 96 + 12(32)

SA = 96 + 384

SA = 480

Thus, the surface area of the triangular prism is 480 ft^2.

#4 Volume of the triangular prism:

Since the volume for the volume of a triangular prism is given by:

V = 1/2bhl, we can plug in 12 for b, 8 for h, and 12 for l in the triangular prism volume formula to find V, the volume of the triangular prism in cubic ft:

V = 1/2(12)(8)(12)

V = 6 * 96

V = 576

Thus, the volume of the triangular prism is 576 ft^3.

#5 Surface area of the cylinder:

The formula for the surface area of a cylinder is given by:

SA = 2πrh + 2πr^2, where

In the cylinder, the radius of one of the circles is 2 yd and the height of the cylinder is 5 yd.

Thus, we can plug in 2 for r and 5 for h to find SA, the surface area of the cylinder in square yd:

SA = 2π(2)(5) + 2π(2)^2

SA = 2π(10) + 2π(4)

SA = 20π + 8π

SA = 28π

SA = 87.9645943

SA = 87.96

Thus, the surface area of the cylinder is about 87.96 yd^2.

#5 Volume of the cylinder:  

The formula for the volume of a cylinder is given by:

V = πr^2h, where

Thus, we can plug in 2 for r and 5 for h in the cylinder volume formula to find V, the volume of the cylinder in cubic yd:

V = π(2)^2 * 5

V = 4π * 5

V = 20π

V = 62.83185307

V = 62.83

Thus, the volume of the cylinder is about 62.83 yd^3.

Answer:

B.

right scalene triangle

Step-by-step explanation:

The average number of shoppers in the new store at any given time is approximately 1,839,383,838.

The owner of the new store estimates that during business hours, an average of 909090 shoppers per hour enter the store and each of them stays an average of 121212 minutes.

To calculate the average number of shoppers in the new store at any given time, we need to convert minutes to hours.

Since there are 60 minutes in an hour,

121212 minutes is equal to 121212/60

= 2020.2 hours.
To find the average number of shoppers in the store at any given time, we multiply the average number of shoppers per hour (909090) by the average time each shopper stays (2020.2).

Therefore, the average number of shoppers in the new store at any given time is approximately

909090 * 2020.2 = 1,839,383,838.

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Each child gets =7×8=56crayoms

Total boxes

Round to next whole as we can't have depict

Answer:

5 boxes

Step-by-step explanation:

There are 12 crayons in one box.

So,8×7=56

56crayons

Then divide 56 and 12

56 ÷12 =4.66

Round of 4.66 and u will get 5

So,the answer is 5 boxes

Given:

You will spin the spinner twice in which there are 4 boxes with numbered

Required:

We have to find the probability of landing on a number greater than 3 and then landing on a number less than 5 in percentage.

Explanation:

There are two possibilities of landing on a number greater than 3 which are 4 and 5.

The total number of possibilities when spinning the spinner is 4.

Hence the probability of landing on a number greater than 3 is

Since the events are independent. The possibility of landing a number less than 5 the second time is 2, 3, and 4.

Hence the probability of landing on a number less than 5 is

Therefore the required probability of landing on a number greater than 3 and then landing on a number less than 5 is

Hence the required percentage is

Final answer:

Hence the final answer is

The only solution to the equation is (6, 5).

Linear equation can be represented in slope intercept form as follows;

y = mx + b

where

Therefore, the linear equation is y = 2 / 3 x + 1 .

Therefore, let's check if  (6, 5) and (9, 8) are solution to the linear equation. We have to insert the x values in the equation to know whether we will get the y values

y = 2 / 3 x + 1 .

5 = 2 / 3(6) + 1

5 = 4 + 1

5  = 5

let's check (9, 8)

y = 2 / 3 x + 1

8 = 2 / 3 (9) + 1

8 = 6 + 1

8 ≠ 7

Therefore, only (6, 5) is a solution

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The result of an average of more than 100% in a survey of tenants on cleaning chores in shared apartments is likely due to social desirability bias.

The average tenant response of more than 100% in a study about cleaning duties in shared apartments is probably the product of social desirability bias. Social desirability bias occurs when respondents give answers that they think are socially acceptable or desirable, rather than their true opinions or behavior.

In this case, tenants may have overstated their contribution to cleaning the apartment, in order to appear more helpful or responsible, leading to an average percentage higher than 100%.

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(a) To prove the equation ||u' - v|| = √2√(1 - u · v) in R², where u and v are unit vectors, we can use the properties of the dot product and vector norms.

First, let's expand the norm on the left side of the equation:

||u' - v||² = (u' - v) · (u' - v)

Expanding the dot product, we have:

||u' - v||² = (u' · u') - 2(u' · v) + (v · v)

Since both u and v are unit vectors, their norms are equal to 1:

||u' - v||² = (1) - 2(u' · v) + (1)

Simplifying, we have:

||u' - v||² = 2 - 2(u' · v)

Now, let's focus on the right side of the equation:

√2√(1 - u · v) = √2√(1 - (u' · v))

Taking the square of both sides, we have:

2 - 2(u' · v) = 2 - 2(u' · v)

Therefore, the equation ||u' - v|| = √2√(1 - u · v) holds in R².

(b) To prove that if x'ui = ||ui|| for all i, 1 ≤ i ≤ n, where U = {u₁, ..., un} is an orthonormal basis for Rⁿ and x ∈ Rⁿ, then x = u₁ + ... + un.

Since U is an orthonormal basis, each ui is a unit vector, and they are linearly independent, forming a basis for Rⁿ. We can write any vector x ∈ Rⁿ as a linear combination of the basis vectors:

x = c₁u₁ + c₂u₂ + ... + cnun

Now, let's calculate the dot product of x with each basis vector ui:

x · ui = (c₁u₁ + c₂u₂ + ... + cnun) · ui

= c₁(u₁ · ui) + c₂(u₂ · ui) + ... + cn(un · ui)

Since the basis vectors are orthonormal, the dot product of any two distinct basis vectors is zero:

(uj · ui) = 0 (for j ≠ i)

Therefore, the dot product simplifies to:

x · ui = ci(u · ui)

Given that x · ui = ||ui|| for all i, we have:

ci(u · ui) = ||ui||

Since ui is a unit vector, the dot product (u · ui) is equal to the norm of u:

ci ||ui|| = ||ui||

This equation holds for all i, 1 ≤ i ≤ n. Since ||ui|| is non-zero (as ui is a unit vector), we can divide both sides of the equation by ||ui||:

ci = 1

Hence, each coefficient ci is equal to 1. Therefore, we can rewrite x as:

x = u₁ + u₂ + ... + un

If x'ui = ||ui|| for all i, 1 ≤ i ≤ n, where U = {u₁, ..., un} is an orthonormal basis for Rⁿ, then x can be written as the sum of the basis vectors: x = u₁ + u₂ + ... + un.

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Answer:

154.3

Step-by-step explanation:

First off let’s calm down… next thing we are going to do is know that a ratio is also a fraction so 5:7 also equals 5/7. Then, all you need to do is multiply 5/7 by 216 to get about 154.3

:D

Answer:

f(g(x)) = 9x² - 6x - 4

Step-by-step explanation:

f(g(x) )

= f(3x - 1)

= (3x - 1)² - 5 ← expand factor using FOIL

= 9x² - 6x + 1 - 5

= 9x² - 6x - 4

Using the .01 level of significance means that, in the long run, a Type I error occurs 1 time in 100. This means that if we perform a statistical test 100 times, and we set the level of significance at .01, then we can expect to observe one false positive result due to chance alone. So, the correct option is 1).

A Type I error occurs when we reject a true null hypothesis, or when we conclude that there is a significant difference or relationship between two variables when in fact there is not.

By setting the level of significance at .01, we are minimizing the risk of making a Type I error while increasing the risk of making a Type II error, which occurs when we fail to reject a false null hypothesis. So, the correct answer is 1).

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The solution to the given differential equation 2xy(dy/dx) = y², with the initial condition y(2) = 3, is y = (27 * e⁽ˣ⁻²⁾\()^{1/4}\).

To solve the given differential equation

2xy(dy/dx) = y²

We will use separation of variables and integrate to find the solution.

Start with the given equation

2xy(dy/dx) = y²

Divide both sides by y²:

(2x/y) dy = dx

Integrate both sides:

∫(2x/y) dy = ∫dx

Integrating the left side requires a substitution. Let u = y², then du = 2y dy:

∫(2x/u) du = ∫dx

2∫(x/u) du = ∫dx

2 ln|u| = x + C

Replacing u with y²:

2 ln|y²| = x + C

Using the properties of logarithms:

ln|y⁴| = x + C

Exponentiating both sides:

|y⁴| = \(e^{x + C}\)

Since the absolute value is taken, we can remove it and incorporate the constant of integration

y⁴ = \(e^{x + C}\)

Simplifying, let A = \(e^C:\)

y^4 = A * eˣ

Taking the fourth root of both sides:

y = (A * eˣ\()^{1/4}\)

Now we can incorporate the initial condition y(2) = 3

3 = (A * e²\()^{1/4}\)

Cubing both sides:

27 = A * e²

Solving for A:

A = 27 / e²

Finally, substituting A back into the solution

y = ((27 / e²) * eˣ\()^{1/4}\)

Simplifying further

y = (27 *  e⁽ˣ⁻²⁾\()^{1/4}\)

Therefore, the solution to the given differential equation with the initial condition y(2) = 3 is

y = (27 * e⁽ˣ⁻²⁾\()^{1/4}\)

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