Jacob needs to know the volume of the cylinder shown. Which expression will give him the correct volume

Answer:

The value of the 4 in 2,849 is 4 x 100 = 400, while the value of the 4 in 3,824 is 4 x 10 = 40. Therefore, the value of the 4 in 2,849 is 400/40 = 10 times greater than the value of the 4 in 3,824.

Step-by-step explanation:

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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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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These fractions are equivalent fractions by algebraic property:

Case 1: YES

Case 2: NO

Case 3: YES

Case 4: NO

Case 5: YES

Case 6: YES

Case 7: NO

Case 8: YES

Case 9: YES

Case 10: YES

Case 11: NO

Case 12: YES

Case 13: NO

Case 14: YES

Case 15: YES

Case 16: YES

Case 17: NO

Case 18: YES

In this question we must check 18 cases of equivalent fractions, two fractions are equivalent if the following algebraic property is met:

a / b = (a · c) / (b · c), where a, b, c are integers and c is nonzero.

Now we proceed to determine if each pair is equivalent:

Case 1

2 / 3 = (2 · 2) / (3 · 2)

2 / 3 = 4 / 6 (YES)

Case 2

2 / 6 = (2 · 3) / (6 · 3)

2 / 6 = 6 / 18 (NO)

Case 3

9 / 9 = (9 · 4) / (9 · 4) = 36 / 36 (YES)

Case 4

3 / 11 = (3 · 3) / (11 · 3) = 9 / 33 (NO)

Case 5

7 / 8 = (7 · 2) / (8 · 2) = 14 / 16 (YES)

Case 6

4 / 6 = (4 · 5) / (6 · 5) = 20 / 30 (YES)

Case 7

5 / 6 = (5 · 2) / (6 · 2) = 10 / 12 (NO)

Case 8

2 / 7 = (2 · 4) / (7 · 4) = 8 / 28 (YES)

Case 9

6 / 12 = (6 · 2) / (12 · 2) = 12 / 24 (YES)

Case 10

4 / 9 = (4 · 5) / (9 · 5) = 20 / 45 (YES)

Case 11

9 / 10 = (9 · 3) / (10 · 3) = 27 / 30 (NO)

Case 12

1 / 5 = (1 · 5) / (5 · 5) = 5 / 25 (YES)

Case 13

12 / 12 = (12 · 3) / (12 · 3) = 36 / 36 (NO)

Case 14

8 / 11 = (8 · 4) / (11 · 4) = 32 / 44 (YES)

Case 15

5 / 5 = (5 · 4) / (5 · 4) = 20 / 20 (YES)

Case 16

6 / 9 = (6 · 4) / (9 · 4) = 24 / 36 (YES)

Case 17

3 / 7 = (3 · 8) / (7 · 8) = 24 / 56 (NO)

Case 18

10 / 12 = (10 · 4) / (12 · 4) = 40 / 48 (YES)

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The volume of a sphere of radius 9.5 cm is approximately 3589.5 cm³

From the question, we are to calculate the volume of a sphere

The volume of a sphere is given by the formula

V = 4/3 πr³

Where V is the volume of the sphere

and r is the radius of the sphere

From the given information,

r = 9.5 cm

Thus,

Volume of the sphere = 4/3 × π × 9.5³

Put π = 3.14

Volume of the sphere = 4/3 × 3.14 × 9.5³

Volume of the sphere = 3589.54333 cm³

Volume of the sphere ≈ 3589.5 cm³

Hence,

The volume of the sphere is 3589.5 cm³

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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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Answer: 7.35 km = 7350000 mm

Step-by-step explanation:

Multiply km by 1000000

7.35 * 1000000 = 7350000 mm

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:

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

Answer:

20

Step-by-step explanation:

just a substitute 3 in x so 3x3=9

11+9=20

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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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: 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 aspects of the scenario that bring the validity of the conclusion made by the representatives of the government would be:

The sample size used by the representatives in the survey was only 50 individuals, which might not be sufficient to represent the views of the entire town's population accurately. A more extensive sample size would provide a more precise approximation of the public opinion.

Moreover, the conductance of the survey on the existing boardwalk presents the possibility of sampling bias since those who visit the boardwalk could hold different opinions towards the new construction than those that do not visit.

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If the polygon A, B, C, D is transformed to polygon A', B', C', D' to the right of the first image with all points in the same position, then the transformation is a horizontal translation.

Option A is the correct answer.

We have,

A horizontal translation moves every point of a figure the same distance in the same direction.

In this case, since the second polygon is to the right of the first one, we know that every point of the polygon has been translated to the right by the same amount.

A vertical translation would move every point of the figure the same distance in the same direction, but vertically instead of horizontally.

A reflection across the x-axis would flip the figure over the x-axis, so points that were above the x-axis would end up below it and vice versa.

A 90° clockwise rotation would rotate the figure 90 degrees to the right.

Thus,

If the polygon A, B, C, D is transformed to polygon A', B', C', D' to the right of the first image with all points in the same position, then the transformation is a horizontal translation.

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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

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

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 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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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:

(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 problem describes rolling an unfair number cube which lands with 6, and asks for the number of outcomes where X=0, X=1, X=2, and X=3.

X can be 0, 1, 2, or 3 if X equals the number of times she rolls a 6 over the course of three tries.

We must count the instances where none of the three trials yields a six in order to determine the number of occurrences where X = 0. Since there is a 0.4 percent chance that the cube will fall on 6, there is a 0.6 percent chance that it won't. Therefore, there are 0.6 * 3 = 0.216, or 21.6%, of outcomes where X = 0.

To find the number of outcomes where X=1, we need to count the number of outcomes where exactly one of the three trials results in a 6. There are three ways to choose which trial will result in a 6, and each of the other two trials must not result in a 6. Therefore, the number of outcomes where X=1 is 3 × 0.4 × 0.6^2 = 0.432 or 43.2%.

We must count the outcomes where precisely two out of the three trials yield a six in order to determine the number of events where X=2. There are three options for selecting the two trials that will end in a 6, and the third trial cannot also end in a 6. The proportion of outcomes where X=2 is therefore 3 0.4 2 0.6 = 0.288 or 28.8%.

Finally, to find the number of outcomes where X=3, we need to count the number of outcomes where all three trials result in a 6. This occurs with probability 0.4^3 = 0.064 or 6.4%.

Therefore, the number of outcomes where X = 0 is 21.6%, X=1 is 43.2%, X=2 is 28.8%, and X=3 is 6.4%.

The value of this country's net capital outflow is $200 billion.

We have,

The formula for net capital outflow (NCO) is:

NCO = Domestic Investment - Foreign Investment

Since the problem only gives us information about domestic investment, we need to use another formula to calculate foreign investment.

The formula for national saving (S) is:

S = GDP - Consumption Expenditures - Government Spending

We can rearrange this formula to solve for foreign investment:

Foreign Investment = GDP - Consumption Expenditures - Government Spending - Domestic Investment

Substituting the given values, we get:

Foreign Investment = $1000 billion - $650 billion - $250 billion - $150 billion

Foreign Investment = $1000 billion - $1050 billion

Foreign Investment = -$50 billion

The negative sign indicates that there is a net capital inflow (i.e., foreign investment is greater than domestic investment).

Therefore, the value of this country's net capital outflow is:

NCO = Domestic Investment - Foreign Investment

NCO = $150 billion - (-$50 billion)

NCO = $150 billion + $50 billion

NCO = $200 billion

Thus,

The value of this country's net capital outflow is $200 billion.

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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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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.

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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