Find the area of the shaded part of the trapezoid.

Answer:

C. All parallelograms are quadrilaterals.

Step-by-step explanation:

Quadrilateral are 2D shapes that are closed sides, with 4 sides.

Using the hypergeometric distribution, it is found that there is a

The cards are chosen without replacement, hence, the hypergeometric distribution is used to solve this question.

Hypergeometric distribution:

\(P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}\)

\(C_{n,x} = \frac{n!}{x!(n-x)!}\)

The parameters are:

In this problem:

To draw 2 clubs, it is P(X = 2) when \(k = 13\), as there are 13 clubs in a deck. Hence:

\(P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}\)

\(P(X = 2) = h(2,52,2,13) = \frac{C_{13,2}C_{39,0}}{C_{52,0}} = 0.0588\)

0.0588 = 5.88% probability of drawing two clubs from a standard deck of 52 cards.

To draw 2 faces, it is P(X = 2) when \(k = 12\), as there are 12 faces in a deck. Hence:

\(P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}\)

\(P(X = 2) = h(2,52,2,12) = \frac{C_{12,2}C_{40,0}}{C_{52,0}} = 0.0498\)

0.0498 = 4.98% probability of drawing two faces from a standard deck of 52 cards.

To draw 2 aces, it is P(X = 2) when \(k = 4\), as there are 4 aces in a deck. Hence:

\(P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}\)

\(P(X = 2) = h(2,52,2,4) = \frac{C_{4,2}C_{48,0}}{C_{52,0}} = 0.0045\)

0.0045 = 0.45% probability of drawing two aces from a standard deck of 52 cards.

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Write the equation in slope-intercept form for the line that passes through the given point and is parallel to the given equation, x - 2y = 9 and passes through (4, 5)

_________________________

The equation in slope-intercept form

y = mx + b

The slope is m

_____________________________

Two parallel lines have the same slope

_____________________________

To find the slope

x - 2y = 9

x - 9 = 2y

2y = x - 9

y= 1/2 x - 9/2

y = mx + b

The slope is 1/2

___________________________

Passes through (4, 5) = (x1, y1)

(y-y1) = m (x-x1)

(y- 5 ) = 1/2 (x- 4 )

y = 1/2 x - 4/2 +5

y= 1/2 x -2 +5

y= 1/2 x + 3

_____________________________________

The equation in slope-intercept form is y= 1/2 x +3



Answer:

C

Step-by-step explanation:

Answer:

-6+541=535

Step-by-step explanation:

Answer:

In picture.

Step-by-step explanation:

To do this answer, you need to count the boxes up to the mirror line. This will give us the exact place to draw the triangle.

The picture below is the answer.

Answer:

 0

Explanation:

Given expression:

\(\sf 6 - (1 \times 4) -2\)

Use BODMAS method:

brackets, order, division, multiplication, addition, subtraction

First simplify variables inside brackets

\(\sf 6 - (4) -2\)

Then simply use subtract integers

\(\sf 0\)

\({ \qquad\qquad\huge\underline{{\sf Answer}}} \)

Let's get it done using Bodmas Rule ~

\(\qquad \sf  \dashrightarrow \: 6 - (1 \times 4) - 2\)

\(\qquad \sf  \dashrightarrow \: 6 - (4) - 2\)

\(\qquad \sf  \dashrightarrow \: 6 - ( 4 + 2)\)

\(\qquad \sf  \dashrightarrow \: 6 - 6\)

\(\qquad \sf  \dashrightarrow \: 0\)

We will get the end result 0, on simplification ~

Answer:

19) x=4

20) x=7

21) x=15.5

22) x= -7

23) x=9

24) x=5

25) x=-6 (Im pretty sure)

26)x=4

27)x=10

28) x=-9

Step-by-step explanation:

Answer: A: It will cost $936.00 to carpet the floor.

B: It will cost $297.00 to wallpaper all four walls.

C: It will cost $33.25 to paint the ceiling.

D: The cost of the entire project will be $1266.25.

Step-by-step explanation:

To calculate the costs for carpeting, wallpapering, painting, and the overall cost of the project, we need to determine the areas that need to be covered and the corresponding prices for each material.

Given dimensions:

Room length: 26 feet

Room width: 18 feet

Room height: 9 feet

Door dimensions:

Height: 6 feet 6 inches

Width: 4 feet

Window dimensions (each):

Width: 2 feet

Height: 2 feet 6 inches

A: Carpeting the floor:

To find the area of the floor, we multiply the length and width of the room:

Floor area = Length × Width = 26 feet × 18 feet = 468 square feet.

To convert to square yards (since the carpet is sold per square yard), we divide by 9:

Floor area in square yards = 468 square feet / 9 = 52 square yards.

Cost to carpet the floor = Floor area in square yards × Cost per square yard = 52 square yards × $18.00 = $936.00.

B: Wallpapering the walls:

To find the area of the walls, we calculate the perimeter of the room (2 × (Length + Width)) and multiply it by the height of the room:

Wall area = Perimeter × Height = 2 × (26 feet + 18 feet) × 9 feet = 396 square feet.

Cost to wallpaper the walls = Wall area × Cost per square foot = 396 square feet × $0.75 = $297.00.

C: Painting the ceiling:

To find the area of the ceiling, we multiply the length and width of the room:

Ceiling area = Length × Width = 26 feet × 18 feet = 468 square feet.

Since a quart of paint covers 88 square feet, we need to determine the number of quarts required:

Number of quarts = Ceiling area / Coverage per quart = 468 square feet / 88 square feet = 5.32 quarts.

Since a gallon contains 4 quarts, the number of gallons required is 5.32 quarts / 4 quarts = 1.33 gallons.

Cost to paint the ceiling = Number of gallons × Cost per gallon = 1.33 gallons × $25.00 = $33.25.

D: Cost of the entire project:

Total cost = Cost to carpet the floor + Cost to wallpaper the walls + Cost to paint the ceiling

= $936.00 + $297.00 + $33.25 = $1266.25.

Therefore:

A: It will cost $936.00 to carpet the floor.

B: It will cost $297.00 to wallpaper all four walls.

C: It will cost $33.25 to paint the ceiling.

D: The cost of the entire project will be $1266.25.

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Answer:

x =30.4 seconds

Step-by-step explanation:

We can use ratios to solve

20 drops           8 drops

---------------  = ----------------

76 seconds      x seconds

Using cross products

20x = 8*76

20x =608

Divide each side by 20

20x/20 = 608/20

x =30.4 seconds

Answer:

30.4 secs = 30secs

Step-by-step explanation:

20 drops fall in 76s

Hence 1 drop is 76/20

Therefore 8 drops would be ;

76/20 × 8 = 30.4 secs

We need to determine the equations that represents the following phrase "Bobby is 10 years younger than her sister Amy". The first step is to assign the variable "x" to Bobby's age and "y" to Amy's age. Then we need to represent Bobby's age on the left side of the equation, since Bobby is younger Amy's age "minus" 10 should be equal to Bobby's. This is shown below:

The correct option is the second one.

Answer:

z=2, y=-4, x=8

Step-by-step explanation:

since we know z is 2, we can plug it back into the equation to find y:

y+2*2=0

first, simplify:

y+4=0

then, subtract 4 from both sides:

y=-4

now we know what both z and y are, we can put the values back into the equation to find x:

x+2(-4)+3*2=6

first, simplify:

x-8+6=6

x-2=6

then, add 2 to both sides:

x=8

so the values are:

z=2, y=-4, x=8

Answer:

C

Step-by-step explanation:

3, 4 and 5 cant be a right triangle

Answer:

hi hello he they 1235

Step-by-step explanation:

hi hello he they 1235

The slope of the given lines are representing that these lines are perpendicular.

A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. Sometimes, the aforementioned is referred to as a "linear equation of two variables," with y and x serving as the variables.

Given, the pair of the equation are parallel, perpendicular, or neither y=-7/8x-1, 32x-28y=-36

Slope intercept form of both equations of a line

1)  y = -7/8x - 1

it is already in a slope intercept form

2) 32x - 28y = -36

-28y = -32x -36

y = 8/7x + 9/7

Since their slope is inverse and had a negative constant.

The slope of a perpendicular line from the slope of a given line is obtained by taking the negative reciprocal of the slope of the given line. If the slope of the given line is m1 and the slope of a perpendicular line is m2 then we have m2 = -1/m1.

Therefore, The slope of the given lines are representing that these lines are perpendicular.

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The measure of arc angle QTP is 204 degrees.

When a tangent and a secant intersect outside a circle then the measure of the angle formed is one-half the positive difference of the measures of the intercepted arcs.

Therefore, let's find the measure of arc angle QTP as follows:

90 = 0.5(x - 68)

90 = 0.5x - 34

0.5x = 124

x = 124 / 0.5

x = 248 degrees

Where

x = arc angle TSQ

Therefore,

arc QP = 44 degrees

Therefore,

arc QTP = 248 - 44

arc QTP = 204 degrees

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Answer:

715

Step-by-step explanation:

[4(17) + 3(25)] x 5

(68+3*25)*5

(68+75)*5

143*5

175

Answer:

$6.84

Step-by-step explanation:

This is quite a simple question, simply add the new deposited amount into the original balance to get your answer.

Answer:

If AB and CD intersect at point P such that P is between A and B and is also between C and D, then ∠APC and ∠BPD are a pair of vertical angles.

Step-by-step explanation:

The diagram is a sketch of a counterexample. Notice that ∠APC and ∠BPD are actually the same angles and are not vertical angles.

If P is between A and B and is also between C and D, then ∠APC and ∠BPD are vertical angles. Then the statement can be completed as:

If AB and CD intersect at point P such that P is between A and B and is also between C and D, then ∠APC and ∠BPD are a pair of vertical angles.

As a result, the experimental probability of landing on heads is 48%, probability which means that we should expect heads approximately 48 times out of 100 coin flips.

Probability is a measure of the likelihood of an event occurring. It is expressed as a number between 0 and 1, with 0 indicating an unlikely event and 1 indicating an unavoidable event. Because there are two equally likely outcomes, switching a fair coin and coin flips has a probability of 0.5 or 50%. (Either heads or tails). Probability theory, a branch of mathematics, is concerned with the investigation of random events rather than their properties. It is used in a variety of fields, including statistics, finance, science, and engineering.

The following formula can be used to calculate the relative frequency or experimental probability of landing on heads:

Number of Heads / Total Number of Flips = Experimental Probability of Heads

The number of heads in this case is 48, and the total number of flips is 100. Therefore,

Heads Experimental Probability = 48 / 100 = 0.48

We can multiply this by 100 to get a percentage:

Heads Experimental Probability = 0.48 * 100 = 48%

As a result, the experimental probability of landing on heads is 48%, which means that we should expect heads approximately 48 times out of 100 coin flips.

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The value of x in the triangle ABC is 25.

The interior angles of the triangle are given as m∠A = 3x and m∠B = 50°.

The exterior angle of the triangle is given as m∠ACD = 5x.  

The sum of angle in a triangle is equals to 180 degrees. Therefore,

3x + 50 + (180 - 5x)  = 180

3x + 50 - 5x + 180 = 180

3x - 5x + 50 + 180 = 180

-2x + 230 = 180

subtract 230 from both sides

-2x + 230 - 230 = 180 - 230

-2x = -50

divide both sidesby -2

-2x / -2 = -50 / -2

x = 25

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Answer:

y=4x+3

Step-by-step explanation:

First, see where the line intercepts at the y-axis and use the y-value(which is 3). Then to find the slope(m), use the slope equation y{2}-y{1}/x{2}-x{1}.

Apply this formula to the coordinates(0,3) and (1,7):

This will then equal to

This can be simplified to:

Applying the y-intercept value 3 and the slope 4 to the equation:

Answer

=sin (u -v)

Step-by-step explanation:

sin ( u-v):     sin(u-v)

Answer:

by measuring in feet

Step-by-step explanation:

its the easiest way to find what your looking for

Answer:

You can find the length of an unknown leg using the Pythagorean theorem

Step-by-step explanation:

\(a^2+b^2=c^2\)

or

\(c^2-a^2=b^2\)

or

\(c^2-b^2=a^2\)

note c = hypotenuse and b and a = legs

Answer:

7/11

Step-by-step explanation:

The linear functions that define their distances are given as follows:

The number of hours after noon in which they will be the same distance away from the stadium is of:

8 hours.

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

In which the parameters are given as follows:

In the context of this problem, the meaning of each parameter is:

They will be the same distance away at the point of intersection of the graph given at the end of the answer, which is of 8 hours.

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Answer:

D. (5, -6)

Step-by-step explanation:

The claim made by the soft drink consumption a researcher is valid as analyzed by the data provided.

According to one study, the average yearly usage per person is 52 gallons.

The sample size (n) is 53.

The consumption mean (x) is 52.2.

3.5 gallons is the standard deviation .

the α = 0.01 .

Let us consider the hypothesis,

H₀ : μ = 52 and

H₁ : μ ≠ 52 .

The test statistics are as follows: z = (x -mean )/( SD / n )

the rejection zone (critical value): {z : |z| ≥ z₀.₀₂₅ = 1.26 }

So , z = (52.2- 52)/(3.5/√53)

To make things even easier,

we get ,

z = 0.416

We accept H0 because the absolute value of the test statistics is smaller than the crucial threshold of 1.96.

As a result, the claim is valid.

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The probability to choose a group of four tiles with each tile worth one point is 0.200.

What is probability?

The area of mathematics known as probability deals with numerical descriptions of how likely it is for an event to happen or for a proposition to be true. A number between 0 and 1 is the probability of an event, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes its certainty.

Let there are total 25 tiles.

From this 20 tiles having one point each and 5 tiles having more than one point.

We have to choose a group of four tiles with each tile worth one point.

So,

probability = 4/20 = 0.200

Hence, the probability to choose a group of four tiles with each tile worth one point is 0.200.

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The solution to the system of equations is x = 6 and  y = -5, which is the same as we obtained using the elimination method.

A system of equations is a collection of one or more equations that are considered together. The system can consist of linear or nonlinear equations and may have one or more variables. The solution to a system of equations is the set of values that satisfy all of the equations in the system simultaneously. The given system of equations is:

2x + y = 7 ---(1)

x + y = 1 ---(2)

To solve this system, we can use the method of elimination or substitution.

Method 1: Elimination

In this method, we eliminate one of the variables by adding or subtracting the two equations. To do this, we need to multiply one or both equations by a suitable constant so that the coefficients of one of the variables become equal in magnitude but opposite in sign.

Let's multiply equation (2) by -2, so that the coefficient of y in both equations becomes equal in magnitude but opposite in sign:

-2(x + y) = -2(1) --

Multiplying equation

(2) by -2-2x - 2y = -2

Now we can add the two equations (1) and (-2x - 2y = -2) to eliminate y:

2x + y = 7(-2x - 2y = -2)0x - y = 5

We now have a new equation in which y is isolated.

To solve for y, we can multiply both sides by -1:

-1(-y) = -1(5)y = -5

Now that we know y = -5, we can substitute this value into equation (2) to find x:x + y = 1x + (-5) = 1x = 6

Therefore, the solution to the system of equations is (x,y) = (6,-5).

Method 2: Substitution

In this method, we solve one of the equations for one variable in terms of the other variable and substitute this expression into the other equation to get an equation with only one variable.

From equation (2), we can solve for y in terms of x:y = 1 - x

We can then substitute this expression for y into equation (1):2x + y = 72x + (1 - x) = 7 --Substituting y = 1 - xx + 1 = 7x = 6

Now that we know x = 6, we can substitute this value into equation (2) to find y:x + y = 16 + y = 1 --Substituting x = 6y = -5

Therefore, the solution to the system of equations is (x,y) = (6,-5), which is the same as we obtained using the elimination method.

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