A ladder leans against the side of a house. The angle of elevation of the ladder is 64 degrees
, and the top of the ladder is 13 ft from the ground. Find the length of the ladder. Round your answer to the nearest tenth.

Answer:

The theoretical probability of obtaining exactly four heads when flipping six coins is also 23.4%.

Step-by-step explanation:

Getting x successes out of n trials is a binomial distribution and is given by:

p(x) = [tex]nC_{x} p^{n-x} q^{x}[/tex]

Here, n = 6

x = 2

p = probability of one head = [tex]\frac{1}{2}[/tex]

q = 1 - p

= [tex]1-\frac{1}{2}[/tex]

= [tex]\frac{1}{2}[/tex]

Substitute these values, we get,

p(2) = [tex]6C_{2} (\frac{1}{2} )^{6-2} (\frac{1}{2} )^{2}[/tex]

= [tex]15(\frac{1}{2} )^{6}[/tex]

= [tex]\frac{15}{64}[/tex]

= 0.234

= 23.4%

We know that [tex]6C_{2} =6C_{6-2}[/tex]

[tex]6C_{2} =6C_{4}[/tex]

Now,

p(4) = [tex]6C_{4} (\frac{1}{2} )^{6-4} (\frac{1}{2} )^{4}[/tex]

= [tex]15(\frac{1}{2} )^{6}[/tex]

= p(2)

Hence, the theoretical probability of obtaining exactly four heads when flipping six coins is also 23.4%.

Answer:

W >_2/7

Step-by-step explanation:

Answer:

30 devided by half    so out here we have 30 and now half, we will take our half as 1/2 (which we all know what half is 1/2)

30 ÷ 1/2   (now here we will reciprocate the fraction on the right side as well as chnge division sign to multiplication one)

=30/1  x  2/1   (now look carefully here we have to multply 2 and 30 which will then give us our answer )

=60/1 ( as 60/1 means whole we will just write 60 as we dont need 1 out here)

=60 ANSWER

 Step-by-step explanation:

hOPE THIS HELPS MERRY CHRISTMAS

Answer:

70

Step-by-step explanation:

The first step said to take 30 and divide it by 1/2

30 ÷ 1/2

We can copy dot flip

30 * 2/1

60

Then we need to add 10

60 + 10

70

Answer:

70 feet per minute.

21 minutes

1890 feet

Step-by-step explanation:

(350 ft) / (5 min) = 70 ft/min

(1470 ft) / (70 ft/min) = 21 min

(70 ft/min) * (27 min) = 1890 ft

Answer:

Step-by-step explanation:

175 divided by 7 is 25

There are 25 rows

Answer:

25

Step-by-step explanation:

175 divided by 7 =25

Answer:

The answer would round to 55%

Step-by-step explanation:

Answer:

55%

Step-by-step explanation:

We can write an equation! So 23234008 = 41892128*x. Let x be a percent. So x=23234008/41892128 or x is about .5546151. So x is about 55%

Answer:

y = 2(x - 3)² + 5

Step-by-step explanation:

the equation of a parabola in vertex form is

y = a(x - h)² + k

where (h, k) are the coordinates of the vertex and a is a multiplier

here (h, k) = (3, 5) and a = 2, hence

y = 2(x - 3)² + 5 ← in vertex form

The equation of the quadratic function in vertex form with given vertex and leading coefficient is y=2(x-3)²+5.

The vertex form of a quadratic function is f(x) = a(x - h)² + k, where (h, k) is the vertex of the parabola. The coefficient a determines whether the graph of a quadratic function will open upwards or downwards.

Given that, the vertex is at (3,5) and has a leading coefficient of 2

Here, (h, k) = (3, 5) and a = 2

Substitute (h, k) = (3, 5) and a = 2 in f(x) = a(x - h)² + k, we get

y=2(x-3)²+5

Therefore, the equation of the quadratic function in vertex form is y=2(x-3)²+5.

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Answer:

To determine if fractions are equivalent, you need to get a common denominator.  When the denominators are the same, if the numerators are the same, the fractions are equivalent

Step-by-step explanation:

To determine if fractions are equivalent, you need to get a common denominator.  When the denominators are the same, if the numerators are the same, the fractions are equivalent

Answer:

diagonal^2 = side^2 + side^2

144*10 = 2s^2

144*5 = s^2  

side = 12sqrt(5) f

Step-by-step explanation:

Answer:

Step-by-step explanation:

(y+6)=(1/2)x

Answer: x = 7 (choice C)

"sum of 1 and 3 times a number" means we have the expression 1+3*x for some unknown number x. This is set equal to 22, and we isolate x. The idea is to follow the order of operations PEMDAS in reverse. So start with subtraction and try to undo it. If it's not present, then undo addition, and so on, until x is all by itself on one side.

1+3x = 22

3x+1 = 22

3x+1-1 = 22-1 ... see note 1 below

3x = 21

3x/3 = 21/3 .... see note 2 below

x = 7

note1: Undoing addition. We undo the "+1" by subtracting 1 from both sides

note2: Undoing multiplication. 3x means "3 times x". The inverse of this is division which means we divide both sides by 3

Answer:

Alright well the Answers to your question is

- 2 Hope this helps have a nice day :)

Step-by-step explanation:

Since the equation can be written in the form y = kx, y varies directly with x and. The constant of variation, k, is - 2

Hope this help's as well Hope u have a nice day :)

Answer:

This is direct variation with the constant of variation being -2.

Step-by-step explanation:

The equation for direct variation is y = kx

We have the equation y = -2x

This is direct variation with the constant of variation being -2.

Answer:

c = 5 and t = 20

Step-by-step explanation:

t = 2c + 10, t = 4c

so

2c + 10 = 4c

-2c = -10

c = 5

t = 4(5)

t = 20

Answer:

c=5 t=20

Step-by-step explanation:

Answer:

There will be 18 3/4 Inches on each side of the frame!

Hope this helped:)

Step-by-step explanation:

4*12=48

48-10.5=37.5

37.7/2=18.75

Answer:

Step-by-step explanation:

We know that, the picture is 10.5 inches wide, and the wall is 4 feet wide.

First we have to transform feet to inches and subtract. So, we know that 1 feet is 12 inches, how much inches would be 4 feet?

[tex]4 \ ft\frac{12 \ in}{1 \ ft}=48 \ in[/tex]

So, the wall is 48 inches wide.

Now,

[tex](48 - 10.5)in=37.5in[/tex]

There's 37.5 inches of space. If the picture is in the middle, then each side would be have:

[tex]\frac{37.5}{2}=18.75 \ in[/tex]

Therefore, there's 18.75 inches of space at each side of the picture.

To solve triangle ABC, we use the Law of Cosines to find angle C and the Law of Sines to find angles A and B. Plugging in the given values, we find that angle C is approximately 103.39 degrees, angle A is approximately 25.70 degrees, and angle B is approximately 50.91 degrees.

Given that c = 82, b = 2, and a = 12, we can use the Law of Cosines to solve for the missing angles.

Using the Law of Cosines, we have:

c^2 = a^2 + b^2 - 2ab*cos(C)

Plugging in the values, we get:

82^2 = 12^2 + 2^2 - 2(12)(2)*cos(C)

6724 = 144 + 4 - 48cos(C)

660 = -48cos(C)

cos(C) = -660/48

C = acos(-660/48)

Using a calculator, we find that C ≈ 103.39 degrees.

To find angle A, we can use the Law of Sines:

a/sin(A) = c/sin(C)

Plugging in the values, we get:

12/sin(A) = 82/sin(103.39)

Solving for sin(A), we get:

sin(A) = (12*sin(103.39))/82

A = asin((12*sin(103.39))/82)

Using a calculator, we find that A ≈ 25.70 degrees.

Finally, we can find angle B using the fact that the sum of the angles in a triangle is 180 degrees:

B = 180 - A - C

Plugging in the values, we get:

B = 180 - 25.70 - 103.39

Using a calculator, we find that B ≈ 50.91 degrees.

A ≈ 25.70 degrees

B ≈ 50.91 degrees

C ≈ 103.39 degrees

To solve the triangle ABC, we can use the Law of Sines. The Law of Sines states. the correct answer is:option b. A≈9.59°, B≈88.41°, c≈12.17°

To solve the triangle ABC, we can use the Law of Sines. The Law of Sines states:

sinA/a = sinB/b=sinC/c

Given that C=82°, b=2, and a=12, we want to find angles A and B and side

Let's find angle A using the Law of Sines:

sinA/12=sin82°/2

Now, solve for angle A:

sinA=12⋅ sin82°/2

A=sin −1(12⋅ sin82°/2)

A≈9.59°

Now that we have angle A, we can find angle B using the fact that the sum of angles in a triangle is 180°:

B=180°−A−C

B=180°−9.59°−82°

B≈88.41°

Now, we can find side c using the Law of Sines:

sinA/a= sinC/c

sin9.59°/12= sin82°/c

Now, solve for c:

c=12⋅sin82°/ sin9.59°

c≈12.17

So, the correct answer is:

A≈9.59°,

B≈88.41°,

c≈12.17°

completed question

Given that C=82°, b=2 , and a=12 , solve triangle ABC. Round the answer to the nearest hundredth.

A. A=9.59°, B=88.41°, c=11.89

B. A=9.59°, B=88.41°, c=12.17

C. A=88.41°, B=9.59°, c=11.89

D. A=88.41°, B=9.59°, c=12.17

Answer:

B

Step-by-step explanation:

solving the inequality

9 - y > 12 ( subtract 9 from both sides )

- y > 3 ( multiply both sides by - 1 )

Remembering to reverse the inequality symbol when multiplying/ dividing by a negative quantity

y < - 3 ← reverse symbol

Thus y is less than or equal to - 3

The only value from the list which makes this true is - 6 → B

To find a solution to the inequality 9 – y > 12, one must first simplify the inequality to y < -3. After comparing all the options, the correct answer is Option B (– 6), as it is the only value that is less than -3.

The question asks to find a value of y that satisfies the inequality 9 – y > 12.

To find the solution, we need to isolate y on one side of the inequality:

Now that we have the solution to the inequality, we can evaluate the given options.

Therefore, the correct answer is Option B: – 6, because – 6 < – 3.

There is only one unique triangle that can be drawn with side lengths of 4cm, 5cm, and 10cm.

A triangle is defined by its side lengths. In order for a triangle to be formed, the sum of any two side lengths must be greater than the third side length. In this case, we have side lengths of 4cm, 5cm, and 10cm. We can check if these lengths can form a triangle by checking the triangle inequality:

Since all three inequalities are true, a triangle can be formed with side lengths of 4cm, 5cm, and 10cm. Therefore, there is only one unique triangle that can be drawn with these side lengths.

Answer:

The correct option is 1.

Step-by-step explanation:

From the given table is notices that the function f(x) is a downward parabola.

The maximum value of f(x) is 5 at x=1.

The function g(x) is

[tex]g(x)=-x^2+4x[/tex]

vertex of the parabola is

[tex](\frac{-b}{2a}, g(\frac{-b}{2a}))[/tex]

[tex](\frac{-4}{2\times 1}, g(\frac{-4}{2\times 1})[/tex]

[tex](2, g(2))[/tex]

Put x=2.

[tex]g(x)=-2^2+4(2)=4[/tex]

Therefore the vertex of g(x) is (2,4). The vertex of a downward parabola is the maximum point of the function.

Therefore ƒ(x) has the greater maximum. Option 1 is correct.

Answer:

ƒ( x) has the greater maximum.

Step-by-step explanation:

Answer:

Step-by-step explanation:

Point R is the mid point of side FE Using mid point formula coodinates of F are (3a,b)

In triangle DEF, DF = base = 4a and height = 2b.

Hence area of triangle DEF = 1/2 hy = 4ab

In triangle QRP, base QR = line joining mid points of sides DE and EF

= 1/2 (DF) = 2a

Height =b

So area of triangle DEF = 1/2 (2a)b = ab

i.e. Area of triangle DEF = 4 times triangle QRD

It follows that in an isosceles triangle, if QR is the mid points of isosceles sides, then triangle QRD has 1/4 times area of triangle DEF

Answer:

6/16

Step-by-step explanation:

12/16-3/8

12/16-6/16

6/16=3/8

6/16

12/16-3/8

12/16-6/16

6/16=3/8

Answer:

62.8 in

Step-by-step explanation:

Circumfrence=pi x diameter

3.14 x 20=62.8

Final answer:

Given π as approximately 3.14159, the circumference is found to be about 62.8318 inches.

Explanation:

The question asks for the circumference of a circle with a diameter of 20 inches. To find the circumference (C), we use the formula C = πd, where π (Pi) is approximately 3.14159, and d is the diameter of the circle. Given the diameter (d) of 20 inches, the circumference is calculated as follows: C = 3.14159 × 20.

Substituting the values into the equation provides: C = 62.8318 inches. Hence, the circumference of the circle with a diameter of 20 inches is approximately 62.8318 inches.

Alright, so we are given a triangle where all the angles are the same. Now - we need to write a proof that when IE bisects KM, it creates equal angles.

Given:

IKM is equiangular

IE is perpendicular to KM

This is enough to prove that IKE is congruent to IME because:

IEK and IEM are both 90 degrees, since IE is perpendicular to KM

KIE and MIE are the same degree measure, since I is being bisected.

This leaves us with only one angle remaining, and since we already know that the first two angles are congruent to their counterpart - we also know that IKE is congruent to IME because all interior angles of triangles add up to 180°, and we know the other two angle sets to be congruent.

The first step is to calculate the difference between the original selling price and the sale price. Then divide the markdown amount by the original selling price and multiply by 100 to find the percent markdown.

The first step in finding the percent markdown is to calculate the difference between the original selling price and the sale price. Subtract the sale price from the original selling price to find the markdown amount. Then, divide the markdown amount by the original selling price and multiply by 100 to find the percent markdown.

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The percent markdown is approximately 14.99%.

The first step in finding the percent markdown is to calculate the difference between the original selling price and the sale price.

In this case, the difference is $175.80 - $149.42 = $26.38.

Next, divide the difference by the original selling price and multiply by 100 to find the percent markdown.

So, $26.38 / $175.80 × 100 = 14.99%.

Therefore, the percent markdown is approximately 14.99%.

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Answer:  Circumference of cake board is 35π cm.

Step-by-step explanation:

Since we have given that

Diameter of a round cake = 30 cm

Diameter of a cake board is 5 cm longer than the diameter of a round cake.

So, Diameter of a cake board = 30+5=35 cm

So, radius of a cake board will be

[tex]r=\frac{35}{2}[/tex]

As we know the formula for " Circumference of Circle ":

So, According to question, we get,

[tex]C=2\pi r\\\\C=2\pi\times \frac{35}{2}\\\\C=35\pi[/tex]

Hence, Circumference of cake board is 35π cm.

Answer:

35pi

Step-by-step explanation:

Answer:

The answer would be D.

Step-by-step explanation:

You can use an online graphing calculator to see the lines for each equation.

Answer: D

Step-by-step explanation: The slope of a line is rise/run or change in y values/change in x values. We will use the two points (-4, 1) and (0,0) for this problem. 0-1/0-(-4) = -1/4

Answer:

3

√

−

216

x

9

Rewrite  

−

216

x

9

as  

(

−

6

x

3

)

3

.

3

√

(

−

6

x

3

)

3

Pull terms out from under the radical, assuming positive real numbers.

−

6

x

3

Step-by-step explanation:

Hope This Helped