26=-9w-2w-18?????????????????

Probability of answering exactly 4 questions correctly = 0.206

P (More than 2) = 0.475

1.

ind P(4): Probability of answering exactly 4 questions correctly.

P(X=4) = (10C4) * (0.25^4) * (0.75^6)

10C4 = 10! / (4! * (10-4)!) = 210

P(X=4) = 210 * (0.25^4) * (0.75^6)

= 0.206

P(X=0) = (10C0) * (0.25^0) * (0.75^10) ≈ 0.056

P(X=1) = (10C1) * (0.25^1) * (0.75^9) ≈ 0.187

P(X=2) = (10C2) * (0.25^2) * (0.75^8) ≈ 0.282

Now, calculate P(X>2):

P(X>2)

= 1 - (P(X=0) + P(X=1) + P(X=2))

= 1 - (0.056 + 0.187 + 0.282)

= 1 - 0.525

= 0.475

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Answer: 7.35 km = 7350000 mm

Step-by-step explanation:

Multiply km by 1000000

7.35 * 1000000 = 7350000 mm

The only graph that represents a function is: Graph D

A function is defined as a relationship or expression that involves one or more variables. It typically has a set of input and outputs.  Each input has only one output. The function is the description of how the inputs relate to the output.

A function is a relation which describes that there should be only one output for each input (or) we can say that a special kind of relation (a set of ordered pairs), which follows a rule i.e., every X-value should be associated with only one y-value is called a function.

From the graphs, we can see that:

Graph A has 2 outputs at x = -2

Graph B has 2 outputs at x = 0

Graph C has two outputs at x = -1

Graph D has a unique output for every input and as such it is a function

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Answer:

y = x + 2

Step-by-step explanation:

y = mx + b

Point (0, 2) shows that the y-intercept is 2, so b = 2.

y = mx + 2

Now we find the slope using the 2 points, (0, 2) and (2, 4).

m = (4 - 2)/(2 - 0) = 1

y = x + 2

The required mean will increase to about 12.6 when another student of age 15 joins the class, and the correct answer is C.

The original mean is the sum of the ages divided by the number of students:

Mean = (10 + 10 + 11 + 12 + 12 + 13 + 13 + 14 + 14 + 15) / 10

Mean = 124 / 10

Mean = 12.4

If another student of age 15 joins the class, the new sum of the ages is:

Sum = 10 + 10 + 11 + 12 + 12 + 13 + 13 + 14 + 14 + 15 + 15

Sum = 139

The new mean is the new sum of ages divided by the new number of students:

New mean = Sum / (Number of students + 1)

New mean = 139 / 11

New mean = 12.63636... or about 12.6 (rounded to one decimal place)

Therefore, the mean will increase to about 12.6 when another student of age 15 joins the class, and the correct answer is C.

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By expanding and simplifying the algebraic expression (y + 7)(y - 5), we have the result y² + 2y - 35

To expand an algebraic expression in brackets, we need to use the distributive property to make is easy for simplification, thus we expand and simplify the expression as follows:

(y + 7)(y - 5) = y(y - 5) + 7(y - 5) {distributive property}

(y + 7)(y - 5) = y² - 5y + 7y - 35

by simplification, we have;

(y + 7)(y - 5) = y² + 2y - 35

Therefore, the expansion and simplification of the algebraic expression (y + 7)(y - 5), gives the result y² + 2y - 35.

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Answer:

Step-by-step explanation:

m/1 = m  (Any number, except zero, divided by itself is 1)

m : 8 = 133 : 1

m = 8 * 133 : 1

m = 1064

----------------------

check

1064 : 8 = 133 : 1

133 = 133

the answer is good

The correct option is D, the equation has two complex solutions.

Here we can see that we have the graph of a quadratic equation.

It opens upwards, and we can see that it has a vertex at (1, 4), which intercepts the y-axis at y = 5.

Now, we say that the solutions of a quadratic are the values of x such that the function becomes zero.

Particualrly, in this graph we can see that the graph never intercepts the x-axis, that means that this equation has no real roots.

Then the correct option is:

"Function f has exactly two complex solutions."

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Answer:

  58.85°

Step-by-step explanation:

You want to know the measure of the angle in the right triangle that has hypotenuse 29 and adjacent side 15.

The cosine function relates angles and sides by ...

  Cos = Adjacent/Hypotenuse

  cos(x) = 15/29

The inverse function is used to find the angle value:

  x = arccos(15/29) ≈ 58.85°

The value of x is about 58.85°.

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Answer:

20

Step-by-step explanation:

just a substitute 3 in x so 3x3=9

11+9=20

False. When Jane turns left 40 degrees and walks 60 meters, she is farther away from her starting position than when she crossed the finish line.

If Jane turns left 90 degrees or 120 degrees, then she will also be farther away from her starting position than when she crossed the finish line. Turning left 90 degrees or 120 degrees will take her in a different direction, and thus she will be farther away from her starting position than when she crossed the finish line.

Therefore, the given statement is false.

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The sine of angle B is obtained dividing the length of the opposite side to angle B by the length of the hypotenuse.

The three trigonometric ratios are the sine, the cosine and the tangent, and they are defined on the bullet points below:

The problem is incomplete, hence the general procedure to obtain the sine of angle B is presented.

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length LD = 6 units

length DF = 9 units

length HF = 6 units

length LH = 9 units

length L'D' = 2 units

length D'F' = 3 units

length H'F' = 2 units

length L'H' = 3 units

Dilation is the scaling of an object, where it gets bigger or smaller.

Scale factor = new dimension/old dimension

length LD = 15-9 = 6units

length DF = 6-(-3) = 9units

length HF = 15-9 = 6 units

length LH = 6-(-3) = 9 units

Since the scale factor is 1/3, we divide the preimage dimension by 3 to get the dimensions of the new image.

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The minimum height of the second beaker must be approximately 13.5 inches to hold the solution without overflowing.

Now, For the minimum height of the second beaker, we need to find its volume first.

The volume of the first beaker is given by;

⇒ V₁ = πr₁²h₁

where r₁ is the radius and h₁ is the height.

Substituting the given values, we get:

V₁ = π(1.8)²(4.6)

V₁ ≈ 66.85 cubic inches

Since, the first beaker is filled to the top, its volume equals the volume of the solution.

Therefore, the volume of the solution is also 66.85 cubic inches.

To find the minimum height of the second beaker, we need to use the formula for the volume of a cylinder:

V₂ = πr₂²h₂

where r₂ is the radius and h₂ is the height of the second beaker.

We want to find h₂ such that V₂ is equal to 66.85 cubic inches.

Dividing both sides of the equation by πr₂², we get:

h₂ = V₂ / (πr₂²)

Substituting the given value for r₂, we get:

h₂ = 66.85 / (π(1.25)²)

h₂ ≈ 13.5 inches

Therefore, the minimum height of the second beaker must be approximately 13.5 inches to hold the solution without overflowing.

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Answer:

A = 11.4 ft²

Step-by-step explanation:

the area (A) of a trapezium is calculated as

A = [tex]\frac{1}{2}[/tex] h (b₁ + b₂ )

where h is the height between the bases

here h = 3 , b₁ = 2.4 , b₂ = 5.2 , then

A = [tex]\frac{1}{2}[/tex] × 3 × (2.4 + 5.2) = 1.5 × 7.6 = 11.4 ft²

Let's start by finding how many bags of lemons Rachel used on Monday. We know she used a whole number of bags plus a fraction, so we'll need to convert the mixed number to an improper fraction:

1 2/5 = 7/5

So Rachel used 7/5 bags of lemons on Monday.

On Tuesday, Rachel used 1 1/4 times as many lemons as on Monday. To find out how many bags of lemons that is, we can multiply the amount Rachel used on Monday by 1 1/4:

1 1/4 = 5/4

5/4 times 7/5 = 35/20 = 7/4

So Rachel used 7/4 bags of lemons on Tuesday, which is the same as 1 3/4 bags of lemons.

Therefore, Rachel used 1 3/4 bags of lemons on Tuesday.

The missing lengths and angles in the geometric systems are listed below:

Case 8: x = 60

Case 9: x = 48

Case 10: x = 5.535

Case 11: x = 5.665

Case 12: x = 9.103

Case 13: θ = 60°

Case 14: θ = 23.025°

In this problem we find two cases of geometric systems formed by triangles:

First case is analyzed by means of proportionality ratios and second case done by trigonometric functions:

Case 8

100 / x = x / 36

x² = 3600

x = 60

Case 9

x / 36 = 64 / x

x² = 36 · 64

x = 48

Case 10

x = 17 · sin 19°

x = 5.535

Case 11

x = 11 · cos 59°

x = 5.665

Case 12

x = 13 · tan 35°

x = 9.103

Case 13

cos θ = 7 / 14

cos θ = 1 / 2

θ = 60°

Case 14

tan θ = 17 / 40

θ = 23.025°

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Answer:

(x²)³ - 1 = x^6 - 1

Step-by-step explanation:

To find (gof)(x), we first need to evaluate g(x), which is x², and then use the result as input to f(x), giving us f(g(x)).

So, we have:

g(x) = x²

f(g(x)) = f(x²) = (x²)³ - 1 = x^6 - 1

Therefore, (gof)(x) = g(f(x)) = (f(x))² = (x³ - 1)² = x^6 - 2x^3 + 1.

To find (fog)(x), we first need to evaluate f(x), which is x³ - 1, and then use the result as input to g(x), giving us g(f(x)).

So, we have:

f(x) = x³ - 1

g(f(x)) = g(x³ - 1) = (x³ - 1)² = x^6 - 2x^3 + 1

Therefore, (fog)(x) = f(g(x)) = (x²)³ - 1 = x^6 - 1.

Answer:

The area is 13 feet squared.

Step-by-step explanation:

To find the area, first separate the composite figure into two shapes: a rectangle and a triangle.

Find the area of each shape separately, and then add the areas together.

First, the rectangle:

length= 4.5 feet

width = 2 feet

[tex]2*4.5=9 ft^{2}[/tex]

The area of the rectangle is 9 feet squared.

Next, the triangle:

The base is 2 feet + 1 foot + 1 foot = 4 feet

The height is 6.5 feet - 4.5 feet = 2 feet

The formula to find the area of a triangle is [tex]\frac{h*b}{2}[/tex] (height times base over two)

[tex]\frac{2*4}{2}=4ft^{2}[/tex]

the area of the triangle is 4 feet squared.

Add the two areas together to find the total area of the composite figure:

[tex]9ft^{2} +4ft^{2}=13ft^{2}[/tex]

The area is 13 feet squared.

The value of 3u - (2v-w) is  -6i + 25j.

We have,

u = -2i+9j, v = 2i- j, and w= -4i.

Now, 3u - (2v - w)

= 3(-2i + 9j) - [ 2(2i - j) - (-4i)]

= -6i + 27j - [4i - 2j + 4i]

= -6i + 27j - 4i - 2j + 4i

= -6i + 25j

Thus, the value of 3u - (2v-w) is  -6i + 25j.

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Answer:0.98

2.17 are correct

Step-by-step explanation:

-u^2 - 4u + 4 = 0

Multiplying both sides by -1, we get:

u^2 + 4u - 4 = 0

Now we can use the quadratic formula to solve for u:

u = (-b ± sqrt(b^2 - 4ac)) / 2a

where a = 1, b = 4, and c = -4. Substituting these values, we get:

u = (-4 ± sqrt(4^2 - 4(1)(-4))) / 2(1)

u = (-4 ± sqrt(32)) / 2

u = (-4 ± 4sqrt(2)) / 2

u = -2 ± 2sqrt(2)

Therefore, either:

Note that given the angle of elevation, the distance from pont A to Point B is approximately 627.6ft.

See the attached image.

As shown in the attached figure:

L = AO Tan 8°

L = 1035 * Tan 8°

L = 1035 * 0.14054083470239144683811769343281

L = 1035 * 0.14054083470239144683811769343281

L = 145.46 Feet


BO = L/Tan 5°
BO =  145.459763917 / 0.08748866352592400522201866943496
BO = 1662.61270952
BO = 1662.6 Feet

Since AB = BO-AO
AB = 1662.6-1035

AB = 627.6 Ft.

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Answer: He would be spending $15.25 for each person including himself

Step-by-step explanation:

step 1. you need to find out how many people are getting food

step 2. divide that number (5) by how much the total cost is ($76.25) to get 15.25

The required exact value of tan(5π/12) is (2 + √3) / 3.

We can use the half-angle identity for a tangent:

tan(x/2) = [1 - cos(x)] / sin(x)

to find the exact value of tan(5π/12), since 5π/12 is a half-angle of 5π/6.

First, we find the values of sin(5π/6) and cos(5π/6) using the unit circle:

sin(5π/6) = sin(π - π/6) = sin(π/6) = 1/2

cos(5π/6) = cos(π - π/6) = -cos(π/6) = -√3/2

Now we can use the half-angle identity for a tangent with x=5π/6:

tan(5π/12) = tan[(5π/6)/2] = [1 - cos(5π/6)] / sin(5π/6)

                = [1 - (-√3/2)] / (1/2)

               = (2 + √3) / 3

Therefore, the exact value of tan(5π/12) is (2 + √3) / 3.

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The number of the different outfits do David have to choose is 768.

Here we will use the concept of Combinations,

Combinations are the way of selecting objects or elements from a group of objects or collections, in such a way the order of the objects does not matter.

Different outfits do Damian have to choose, will be;

⇒ 8C₁×4C₁×8C₁×3C₁

⇒ 8×4×8×3

⇒ 768

Hence, the number of the different outfits do David have to select is 768.

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