given the Venn diagram below what is the probability that both event A and B will occur

Yes, because the ladder will reach 16 feet high

The relationship between the three sides of a right-angled triangle is explained by the Pythagoras theorem, commonly known as the Pythagorean theorem.

According to the Pythagoras theorem, the square of the hypotenuse of a triangle, which has a straight angle of 90 degrees, equals the sum of the squares of the other two sides.

Given:

Hypotenuse= 20 feet

base= 12 feet

Using Pythagoras theorem

H²= P² + B²

20² =12² +P²

P²= 400-144

P²= 256

P= 16 FEET.

Hence, Yes, because the ladder will reach 16 feet high

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Answer:

See below

Step-by-step explanation:

ANSWER

EXPLANATION

We want to solve the given linear equation:

To do this, divide both sides of the equation by -6 to isolate u and simplify:

That is the solution to the linear equation.

1

Step

Multiple both numerator and both denominator

2

3

4

The amount of wall surface in square feet is there to paint is: 364 square ft. While the floor area is 169.58sq ft. See the calculations below:

The square foot is an imperial measure of area and a customary unit of area in most countries. It is defined as the area of a square with one-foot sides.

The calculation for the above solution is given as:

Step I - Recall the Given Stats:

Dimensions of the room are:

12′-4″ by 13′-9″ with an 8′-0″ ceiling height has one door 3′ × 7′ and two windows 4′ square.

Let Lenght (l) = 13'9" = 13(9/12) ft = 13(3/4) = 55/4 ft.

Let Width(w) = 12'4" = 12(4/12) ft = 12(1/3)ft = 37/3 ft

Let Height h = 8'0" = 8ft.

Recall that we have a door with dimensions 3' x 7' and two windows 4'x4'

Step II - A) Surface area of the wall to be painted is:

Area of 4 walls less (area of door plus area of window)

Surface Area = 2LH + 2WH - ((3 x7) + 2(4x4))

= 2(l +w)h - (21 + 32)
= 2 ((55/4) + (37/3))8 -53

= 220 + 592/3 - 53
= 167 + 592

= (501+ 592)/3
= 1093/3

Hence,

The Surface Area to be painted is = 364.33 Sq ft.

Step III - B) The Area of the Floor = Lx W

= (55/4) x (37/3)

= 2035/12

= 169.583333333

Hence,

Area of the Floor is approximately = 169.58

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Full Question:

A room 12′-4″ by 13′-9″ with an 8′-0″ ceiling height has one door 3′ × 7′ and two windows 4′ square.

Answer the following questions. Assume there is no waste in materials, and round off your answer to the next largest unit. Show both exact and rounded figures in the blanks provided.

A. How much wall surface in square feet is there to paint?

B. What is the floor area?

1) [tex]VX=ZX, \angle XVY=\angle XZW[/tex] (given)

2) [tex]\angle X=\angle X[/tex] (reflexive property)

3) [tex]\triangle VXY \equiv \triangle ZXW[/tex] (ASA)

We are given the following equation:

In the first step we will use the distributive property on the left side:

In step 2, we will add like terms on the left side using associative properties of addition and subtraction and we will subtract 20 from both sides, we get:

Solving the operations we get:

In step 3 we will add 34x to both sides, this is the inverse additive inverse:

Solving the operations:

In step 4, we divide both sides by 17, this is the division property of equality:

Solving the operations:

Given the two sides measurement,

• Assuming that the other side represent x and the other side represent y,( 4cm;6cm) , and that we are drawing a right angle triangle .We can constuct a triangle as follows :

• We can find the value of side h by using Pythagorean theorem:

• Subsequently, we will find angle angle , as shown in the diagram above as follows:

• Since we have angle ,= 56.3 °, ,we can find, angle :

• + + 90° = 180 °,....(angles in a triangle adds up to 180°)

∴ = 180° -90° -56.3°

=33.7°

A.

[tex]3n =19 - 1 \\ 3n = 18 \\ \frac{3n}{3} = \frac{18}{3} \\ n = 6[/tex]

B.

[tex]21 + 5 = - 2p \\ 2p = - 26 \\ \frac{2p}{2} = \frac{26}{2} \\ p = 13[/tex]

HOPE THIS HELPS.

The equation of the line 4x-20y = -160 in the slope intercept form is y = x/5 + 8 .

The equation of the line in slope intercept form is written as

y = mx + c ,

where m is the slope of the line , and c is the y intercept .

In the question ,

the equation of the line is given

equation of line is given as 4x-20y = -160

to convert the equation in slope intercept form , we rewrite it as

20y = 4x+160

dividing both sides by 20 ,

we get

20y/20 = 4x/20 + 160/20

y = x/5 + 8

hence ,the slope intercept form is y = x/5 + 8 , where 8 is the y intercept and 1/5 is the slope .

Therefore , the equation of the line 4x-20y = -160 in the slope intercept form is y = x/5 + 8 .

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Answer:

-286

Step-by-step explanation:

45(-6)-16

= -270 - 16

= -286

Step-by-step explanation:

45x - 16

x = -6

45(-6) - 16

-270 - 16

-286

Hope this helps! :)

The sectorial area of the circle is equal 31.3cm^2

The formula for the b of the sector of a circle is /360o (r2) where r is the radius of the circle and  is the angle of the sector.

Area of a Sector of Circle = (θ/360º) × πr^2, where, θ is the sector angle subtended by the arc at the center, in degrees, and 'r' is the radius of the circle.

Data;

The area of the sector can be calculated using the formula given

[tex]A = \frac{\theta }{360} * \pi r^2[/tex]

Substituting the values into the formula;

[tex]A = \frac{\theta }{360} * \pi r^2\\A = \frac{56}{360}* \pi * 8^2\\A = 31.27cm\\A = 31.3cm^2[/tex]

The area is equal 31.3cm^2

Translation:

The area of a circular sector of a circle with radius equal to 8cm and central angle equal to 56 degrees.

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Answer:

-42/7 and 42/-7

Explanation:

The absolute value of a number is represented by:

The lines represent absolute value of a number x, and what it does is that it makes everything into a positive number.

For example |-5|=5 and |5|=5, so we always have two options with an absolute value: that it comes from a negative number or that it comes from a positive number.

In this case we have that a number with an absolute value of 42 (it could be |-42|=42 or |42|=42) divided by a number with an absolute value of 7 (it could be |-7|=7 or |7|=7) the quotient is -6.

One possible numberic equation is:

Since this meets all the above conditions

Another possible numeric equation is:

Since this too meets all the above conditions.

Answer:

3x - 4

Step-by-step explanation:

"Difference" is a clue word that tells you to use subtraction. The other clue word is "times" but that means times, or multiplication and is pretty straight forward.

"Three times a number" means to multiply a number, but we don't know the number, so we use a variable (a letter). I put x but you could use n or c or almost any letter for the variable.

"the difference of ___ and ___" means to subtract those two things.

So we get 3x - 4

The ordered pair that describes the location of N is (2,6)

Given:

N's coordinates are: (-2,-6)

Point N ′ is produced by reflecting point N over the y-axis.

By reflecting point N' over the x-axis, the final point N" is produced.

x , y = -x , y

N(-2 -6) = N'(2 6)

To locate the ordered pair describing where N" is located.

Point N's coordinates are (-2,-6). Point N ′ is produced by reflecting point N over the y-axis.

x , y = -x , y

N(-2 -6) = N'(2 6)

The resultant point N" is created by reflecting point N' over the x-axis.

The ordered pair for point N" is therefore (2,6) gives its location.

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The price that Misu can pay for a comforter based on the markup percentage is $103.57.

From the information, the Bedspread shop knows his customers will pay no more than $145 for a comforter Misu wants a 40 percent markup on selling price.

Let the selling price be represented as x. Based on the information given, this will be illustrated as:

x + (40% × x) = 145

x + 0.4x = 145

1.4x = 145

Divide

x = 145/1.4.

x = 103.57

The selling price will be $103.57.

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Answer:

Slope formula is given as (y2-y1) ÷ (x2-x1) or (y1-y2) ÷ (x1-x2), where x and y are the coordinates of the points.

Slope = (-7-(-6)) ÷ (0-(-8))

= (-7+6) ÷ (0+8)

= -1/8

The formula for the volume of a cone is a third of the product of pi, its height h and the square of its radius r. Then, it is:

Answer: C

The probability that a family’s first child will be born with down syndrome is 1/5000

Number of first borne babies  = 30000

Number of first borne babies having Down syndrome = 6

Probability is defined as the ratio of number of favorable outcomes to the total outcome.

Probability =  (number of favorable outcomes)/(total outcome)

We have to find the probability that a family’s first child will be born with down syndrome. So, Number of first borne babies having Down syndrome is equal to the total number of favorable outcomes and  Number of first borne babies will also be equal to total outcome. Hence we can write,

Probability = (number of favorable outcomes)/(total outcome)

Probability = 6/30000

Probability = 1/5000

So, the required probability is 1/5000.

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Answer: [tex]9x-4[/tex]

Step-by-step explanation:

Reflecting across the y-axis means [tex]f(x) \longrightarrow f(-x)[/tex].

[tex]g(x)=-9(-x)-4=9x-4[/tex]

Answer

Options A, F, G, N

The line segments include

QR

QS

QT

RS

RT

ST

Note that the segments only have a dash on top of them and not an arrow.

Explanation

A line segment is a region of a line bounded by two different endpoints and contains all the points on the line that are between the two endpoints.

From the attached image, we can see that there is a line with infinite length (the arrows at the two endpoints indicate that this line continues till infinity), has points Q, R, S and T.

So, the line segments will be any space from one endpoint to another. They'll include

QR

QS

QT

RS

RT

ST

Note that the segments only have a dash on top of them and not an arrow.

Hope this Helps!!!

Answer:

10 m

Step-by-step explanation:

Area of a square

[tex]A=s^2[/tex]

where s is the side length.

If the area of the floor is 6 m²:

[tex]\begin{aligned}A&=s^2\\\implies 6&=s^2\\\sqrt{6}&=\sqrt{s^2}\\s&=\sqrt{6}\end{aligned}[/tex]

Therefore, the side length of the square is √6 m.

Perimeter of a square

[tex]P=4s[/tex]

where s is the side length.

Substitute the found value for s into the formula to find the perimeter:

[tex]\begin{aligned}P&=4s\\\implies P&=4 \cdot \sqrt{6}\\P&=4 \sqrt{6}\\P&=9.79795897...\\ P&=10 \sf \;m\;(nearest\:integer)\end{aligned}[/tex]

Therefore, the perimeter is 10 m to the nearest integer.

We know that the mean is 80, the median is 90, and the mode is 70. This means that the majority of students got an 80 on the test.

However, the median is 90, which means half of the class is below 90 where Tom's grade is placed.

We have to reflect the triangle across the y-axis.

If we have a point P = (x,y) and we reflect it across the y-axis, we will change the x-coordinate to its opposite value and and the y-coordinate is kept the same.

The image point then is P' = (-x,y).

Then, to reflect the triangle, we have to reflect the three vertices and then join the vertices.

We can then reflect the vertices as:

Answer: x=-3, x=3

Step-by-step explanation:

Answer:

4-[x]=1

-4.    -4

-[x]=-3

x=3

To answer this question, we will use the following diagram as reference:

To determine the tangent of θ, we have to find the value of x.

To find x, we use the Pythagorean theorem and get:

Therefore:

Therefore:

Answer:

Answer:

Part A: C(x) = 0.068x+0.8

Part B: 1.28

Part C: 9.76

Explanation:

Part A:

The cost C equals

cost = revenue - profit

which is

Part B:

The cost of producing 7 units is found by putting in x = 7 into the above equation. This gives

Hence, the cost of producing 7 items is 1,28 million dollars.

Part C:

To break even, the cost must equal the revenue

or

subtracting 0.068 from both sides gives

dividing both sides by 0.082 gives

which is the break-even point

Given:

Slope = 1/3

Contain the point = ( -3,-1 )

Find-:

The equation of a line.

Explanation-:

The general equation of a line is:

Where,

Given the slope is 1/3, then the equation of the line become.

The value of y-intercept is:

The point (-3,-1) contains the line so its satisfied the equation.

So equation of line become:

The final equation of line is:

where A is the first value, B the second value and x the percent

we can solve x

this is the equation

and this is the percent:

the percent is 20%