3. Mr. Jackson could think about his experiment a little differently. How many times should he expect to roll a 4 if he rolls his number cube 30 times? This is called the mean, or expected value. You can find it if you know the number of trials and the probability of success for an individual trial. Use the formula μx = np to find the expected value.

Answer:

yes

Step-by-step explanation:

The quotient of z₁ by z₂ in trigonometric form is:

7/21 * (cos(584°) + i sin(584°))

To find the quotient of z₁ by z₂ in trigonometric form, we'll express both complex numbers in trigonometric form and then divide them.

Let's represent z₁ in trigonometric form as z₁ = r₁(cosθ₁ + isinθ₁), where r₁ is the magnitude of z₁ and θ₁ is the argument of z₁.

We have:

z₁ = 7(cos(577°) + i sin(577°))

Now, let's represent z₂ in trigonometric form as z₂ = r₂(cosθ₂ + isinθ₂), where r₂ is the magnitude of z₂ and θ₂ is the argument of z₂.

From the given information, we have:

z₂ = 21(cos(-7°) + i sin(-77°))

To find the quotient, we divide z₁ by z₂:

z₁ / z₂ = (r₁/r₂) * [cos(θ₁ - θ₂) + i sin(θ₁ - θ₂)]

Substituting the given values, we have:

z₁ / z₂ = (7/21) * [cos(577° - (-7°)) + i sin(577° - (-7°))]

= (7/21) * [cos(584°) + i sin(584°)]

The quotient of z₁ by z₂ in trigonometric form is:

7/21 * (cos(584°) + i sin(584°))

Option C, 21(cos(-7°) + i sin(-77°)), is not the correct answer as it does not represent the quotient of z₁ by z₂.

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The total surface area of the building block is therefore (4×l×w) + (2×(b×h)/2), which is equal to (2×l×w) + bh.

Surface area is the total exposed area of a three-dimensional object, including the object's base area and lateral area. It is the area of the surface or outer boundary of an object and is measured in units squared such as square meters or square centimeters. Surface area is an important concept in mathematics, physics, and engineering, as it is used to calculate the amount of material needed to construct an object.

The total surface area of the building block can be found by adding the area of the six faces of the block together. To calculate the surface area of the block, we first need to find the area of each face. The six faces of the building block are four rectangular faces and two triangular faces. The area of each rectangular face can be found using the formula A=l×w, where l is the length and w is the width. The area of each triangular face can be found using the formula A=(b×h)/2, where b is the base and h is the height.

By adding the area of each face together, the total surface area of the building block can be found. The total surface area is equal to the sum of the four rectangular faces plus the two triangular faces. The total surface area of the building block is therefore (4×l×w) + (2×(b×h)/2), which is equal to (2×l×w) + bh.

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let's bear in mind that complex roots never come alone, their conjugate sister is always with her, so if we have the complex root of "i" or namely "0 + i", her conjugate is also coming along, or "0 - i", so we really have four roots, so

\(\begin{cases} x = 0+i &\implies x -i=0\\ x = 0-i &\implies x +i=0\\ x = \sqrt{2} &\implies x -\sqrt{2}=0\\ x = 3 &\implies x -3=0\\ \end{cases} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{original~polynomial}{a ( x -i )( x +i )( x -\sqrt{2} )( x -3 ) = \stackrel{0}{y}}\hspace{5em}\stackrel{\textit{we are assuming that}}{a=1} \\\\\\ 1( x -i )( x +i )( x -\sqrt{2} )( x -3 ) = y\implies ( x -i )( x +i )( x -\sqrt{2} )( x -3 ) = y \\\\[-0.35em] ~\dotfill\)

\(\stackrel{ \textit{difference of squares} }{( x -i )( x +i )}\implies x^2 - i^2\implies x^2-(-1)\implies x^2+1 \\\\[-0.35em] ~\dotfill\\\\ (x^2+1)( x -\sqrt{2} )( x -3 )\implies (x^2+1)(x^2-3x-x\sqrt{2}+3\sqrt{2}) \\\\\\ (x^2+1)[x^2-x(3+\sqrt{2})+3\sqrt{2}] \\\\\\ x^4-x^3(3+\sqrt{2})+3x^2\sqrt{2}+x^2-x(3+\sqrt{2})+3\sqrt{2} \\\\\\ \boxed{x^4-x^3(3+\sqrt{2})+x^2(3\sqrt{2}+1)-x(3+\sqrt{2})+3\sqrt{2}~~ = ~~y}\)

Answer:

11 buses

Step-by-step explanation:

Declarative sentences are those which state a fact, describe something, or make a statement. A declarative sentence is a simple statement that gives some information. It ends with a period and always has a subject and a predicate.

1. Example of a closed declarative statement: A closed declarative sentence is one that has only one answer and cannot be disputed.

An example of a closed declarative statement would be: The capital of France is Paris. This is a closed declarative statement because there is no other city that is the capital of France other than Paris.

2. Example of an open declarative statement: An open declarative sentence is one that may have many possible answers and may be disputed.

An example of an open declarative statement would be: The best pizza topping is pepperoni. This is an open declarative statement because some people may disagree and have their own preferences about pizza toppings.

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9514 1404 393

Answer:

Step-by-step explanation:

Surface area

The length of the hypotenuse of the front facing triangle is given by the Pythagorean theorem:

  d^2 = 13^2 +6^2 = 169 +36 = 205

  d = √205

So, the perimeter of that triangle is ...

  P = 13 +6 +√205 = 19 +√205

The total area of the rectangular faces of this triangular prism is then ...

  rectangular face area = (base perimeter)·(prism height)

  = (19 +√205)(7) = 133 +7√205

The area of the two triangular faces will be ...

  triangular face total area = 2·(triangle area) = 2(1/2)(6)(13) = 78

Then the total surface area is ...

  total surface area = rectangular face area + triangular face total area

  total surface area = (133 +7√205) +78

  surface area = 211 +7√205 ≈ 311.22 . . . . square units

__

Volume

The volume is the product of the area of the triangular base and the height of the prism.

  V = Bh

  V = (39)(7)

  volume = 273 . . . . cubic units

Answer:

9514 1404 393

Answer:

 $67,200

Step-by-step explanation:

The amount if interest is given by the formula ...

I = Prt

where P is the amount invested, r is the annual rate, and t is the number of years. Here, we want to find P when r = 0.05 and t = 1/2 such that I = 1680.

 P = I/(rt) = $1680/(0.05·0.5) = $1680/0.025

 P = $67,200

The amount invested was $67,200.

Step-by-step explanation:

Answer:

12.25

Step-by-step explanation:

3.5*3.5=12.25

Answer:

12.25m^2

Step-by-step explanation:

3 1/2 × 3 1/2

3 1/2 is equivalent to 7/2

7/2 × 7/2= 49/4

this simplifies to 12.25

answer: 12.25 m^2

\(\cos(37^o )=\cfrac{\stackrel{adjacent}{11}}{\underset{hypotenuse}{x}} \implies x=\cfrac{11}{\cos(37^o)}\implies x\approx 13.77\)

Make sure your calculator is in Degree mode.

Answer:

The answer is approximately 14

Step-by-step explanation:

<A+<B+<C=180

y+37+90=180

y+127=180

y=180-127

y=53°

<A=53°

sinø=opp/hyp

sin67=11/x

x=11/sin53°

x≈14

Answer:

A. A donut cost 0.9 at donalds shop

B.a donut cost 0.875 at sunrise

C.the better deal is Sunrise

Step-by-step explanation:

Answer:

x(4 × 2) + x(3 × 4)

Step-by-step explanation:

The question says "which of the following equations" which infers you have already been given options. However, none were provided in the question so my answer may be slightly different than the given options as there's several ways to solve this problem.

Monday through Thursday = 4 days × 2 hours per day

Friday through Sunday = 3 days × 4 hours per day

To find the total for one week, add the two expressions together:

(4 × 2) + (3 × 4)

The question states for "x weeks" so:

x(4 × 2) + x(3 × 4)

This is one way the equation can be written

Another way is:

x[(4 × 2) + (3 × 4)]

If neither of these are answers for your mutliple choice question, then please provide the options and I will let you know which is correct

The solution of x in the inequality is x > 2

The inequality is given as:

5x + one third(3x + 6) > 14

Rewrite properly as:

5x + 1/3(3x + 6) > 14

Open the brackets

5x + x + 2 > 14

Subtract 2 from both sides of the inequality

5x + x + 2 - 2> 14 - 2

Evaluate the difference

5x + x > 12

Evaluate the like terms

6x > 12

Divide both sides of the inequality by 2

x > 2

Hence, the solution of x in the inequality is x > 2

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Answer:

x > 2, like the other guy said

Step-by-step explanation:

I hope this helps

Answer:

y = 2x + 5

Step-by-step explanation:

y - 3 = 2( x + 1 )

y = 2x + 5

Answer:

A. 5

Step-by-step explanation:

just use calculator tbh

Answer:

y = 3x + 2

Step-by-step explanation:

y = 3x + b

-4 = 3(-2) + b

-4 = -6 + b

b = 2

y = 3x + 2

You would expect to find the middle 98% of most averages for the lengths of pregnancies in the sample between approximately 264.0 days and 274.1 days.

To find the range in which you would expect to find the middle 98% of most pregnancies, you can use the concept of z-scores and the standard normal distribution.

For the given data:

Mean (μ) = 269 days

Standard deviation (σ) = 17 days

To find the range, we need to find the z-scores corresponding to the 1% and 99% percentiles. Since the normal distribution is symmetric, we can find the z-scores by subtracting and adding the respective values from the mean.

To find the z-score for the 1% percentile (lower bound):

z1 = Φ^(-1)(0.01)

Similarly, to find the z-score for the 99% percentile (upper bound):

z2 = Φ^(-1)(0.99)

Now, we can calculate the z-scores:

z1 = Φ^(-1)(0.01) ≈ -2.33

z2 = Φ^(-1)(0.99) ≈ 2.33

To find the corresponding values in terms of days, we multiply the z-scores by the standard deviation and add/subtract them from the mean:

lower bound = μ + (z1 * σ) = 269 + (-2.33 * 17) ≈ 229.4 days

upper bound = μ + (z2 * σ) = 269 + (2.33 * 17) ≈ 308.6 days

Therefore, you would expect to find the middle 98% of most pregnancies between approximately 229.4 days and 308.6 days.

Now, let's consider drawing samples of size 58 from this population. The mean and standard deviation of the sample means can be calculated as follows:

Mean of sample means (μ') = μ = 269 days

Standard deviation of sample means (σ') = σ / sqrt(n) = 17 / sqrt(58) ≈ 2.229

To find the range in which you would expect to find the middle 98% of most averages for the lengths of pregnancies in the sample, we repeat the previous steps using the mean of the sample means (μ') and the standard deviation of the sample means (σ').

Now, calculate the z-scores:

z1 = Φ^(-1)(0.01) ≈ -2.33

z2 = Φ^(-1)(0.99) ≈ 2.33

Multiply the z-scores by the standard deviation of the sample means and add/subtract them from the mean of the sample means:

lower bound = μ' + (z1 * σ') = 269 + (-2.33 * 2.229) ≈ 264.0 days

upper bound = μ' + (z2 * σ') = 269 + (2.33 * 2.229) ≈ 274.1 days

Therefore, you would expect to find the middle 98% of most averages for the lengths of pregnancies in the sample between approximately 264.0 days and 274.1 days.

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Answer:

Gsusyhsjevdy

Step-by-step explanation:

Je7zgdbbsuzi

Answer:

531441

Step-by-step explanation:

S¹² = a¹+a²+a³+.....+a¹¹+a¹²   ...(1)

S¹¹  = a¹+a²+a³+.....+a¹¹  ...(2)

(1)-(2): a¹² = 797160 - 265719 = 531441

Answer:

\(\boxed{x^2 = 16}\)

Step-by-step explanation:

Using Tangent Secant theorem:

(x)² = (2)(2+6)

x² = 2(8)

x² = 16

Jim did not buy any tickets (n_Jim = 0).

Larry bought 7 more tickets than Jim.

To determine the number of tickets Larry bought more than Jim, we need to find the values of n for Larry and Jim's ticket purchases.

For Larry:

Let's substitute C = $170 into the equation C = 24n + 2 and solve for n:

$170 = 24n + 2

Subtracting 2 from both sides:

$168 = 24n

Dividing both sides by 24:

n = 7

For Jim:

We can calculate the number of tickets Jim bought by subtracting 12 from Larry's number of tickets:

n_Jim = n_Larry - 12

n_Jim = 7 - 12

n_Jim = -5

Since we cannot have a negative number of tickets, we can conclude that Jim did not buy any tickets (n_Jim = 0).

To find the difference in the number of tickets bought, we subtract the number of tickets Jim bought from the number of tickets Larry bought:

n_difference = n_Larry - n_Jim

n_difference = 7 - 0

n_difference = 7

Therefore, Larry bought 7 more tickets than Jim.

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Question

The equation C=24n+2 represents the cost, C, in dollars, of buying n tickets to a play. J $170. How many more tickets did Larry buy than Jim? 12

Answer:

$3.24

Step-by-step explanation:

Cost for the coffee + Cost for the bagel

$1.39 + $1.85

$3.24

Answer:

x = 95

Step-by-step explanation:

The total degree of a circle is 360. The twp arcs on each side of the parallel lines are equal.

Subtract 135 and 35 from your total

360 - 135 - 35 = 190

Divide your answer by 2

190 ÷ 2 = 95

The values that are required to complete the table above indicating the distance traveled by the tortoise in the time elapsed are calculated below.

Mathematically, the distance traveled by the tortoise would be calculated by using this formula:

Distance = speed (rate) × time

When time = 1 min, we have:

D₁ = 20 × 1

D₁ = 20 meters.

When time = 2 min, we have:

D₂ = 20 × 2

D₂ = 40 meters.

When time = 3 min, we have:

D₃ = 20 × 3

D₃ = 60 meters.

When time = 4 min, we have:

D₄ = 20 × 4

D₄ = 80 meters.

When time = 5 min, we have:

D₅ = 20 × 5

D₅ = 100 meters.

When time = 6 min, we have:

D₆ = 20 × 6

D₆ = 120 meters.

When time = 7 min, we have:

D₇ = 20 × 7

D₇ = 140 meters.

When time = 10 min, we have:

D₁₀ = 20 × 10

D₁₀ = 200 meters.

When time = 15 min, we have:

D₁₅ = 20 × 15

D₁₅ = 300 meters.

When time = 20 min, we have:

D₂₀ = 20 × 20

D₂₀ = 400 meters.

When time = 25 min, we have:

D₂₅ = 20 × 25

D₂₅ = 500 meters.

When time = 30 min, we have:

D₃₀ = 20 × 30

D₃₀ = 600 meters.

When time = 35 min, we have:

D₃₅ = 20 × 35

D₃₅ = 700 meters.

When time = 40 min, we have:

D₄₀ = 20 × 40

D₄₀ = 800 meters.

When time = 50 min, we have:

D₅₀ = 20 × 50

D₅₀ = 1,000 meters.

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Answer:

A

Step-by-step explanation:

Answer:

34.6 pounds

Step-by-step explanation:

18.8% = 0.188

0.188 X 184 = 34.592 = 34.6 pounds (to nearest one tenth)

Answer:

To determine the most James Bennett can consume in his youth, we need to find the maximum amount he can borrow from the bank to invest in the opportunity, while still being able to pay back the loan with interest in his old age.

Let x be the amount that James borrows from the bank in his youth. He invests this amount in the opportunity and receives a payoff of $15,000 in his old age. With this payoff, he can pay back the loan plus interest, which is:

Loan + interest = x + 0.18x = 1.18x

So, he needs to have at least $1.18x in his old age to be able to pay back the loan. He will also receive an inheritance of $3000 in his old age, so his total wealth in his old age will be:

Total wealth in old age = $1.18x + $3000

To determine the maximum amount he can consume in his youth, we need to subtract the cost of the investment opportunity and the amount borrowed from the bank from his initial wealth:

Initial wealth = $0 (no cash currently)

Maximum consumption in youth = Initial wealth - Cost of investment - Amount borrowed

Maximum consumption in youth = -$12,000 - x

Since James wants to maximize his consumption in his youth, we need to find the value of x that maximizes the expression -$12,000 - x, subject to the constraint that his total wealth in his old age is at least $1.18x + $3000.

To find this value of x, we can set up the following optimization problem:

Maximize -$12,000 - x

Subject to: $1.18x + $3000 >= $1.18x (i.e., his total wealth in old age is at least $1.18x + $3000)

Simplifying the constraint, we get:

$3000 >= 0

This constraint is always satisfied, so it does not affect the solution. Therefore, we can simply maximize the objective function -$12,000 - x:

d/dx (-$12,000 - x) = -1

Setting the derivative equal to 0 to find the maximum, we get:

-1 = 0

This is never true, so there is no maximum value of -$12,000 - x. This means that James cannot afford to invest in the opportunity and still have a positive wealth in his old age. Therefore, he cannot consume anything in his youth, since he has no cash currently and cannot invest in the opportunity.

Step-by-step explanation:

The expression for the volume of the cylinder is:

\(v = 3.14*(9in)^2*h\)

For a cylinder of radius r and height h, the volume is:

\(v = 3.14*r^2*h\)

Where 3.14 = π

Here we know that the diameter is 18 inches, then the radius is half of that, we will have:

r = 18in/2 = 9in

Then the volume equation is:

\(v = 3.14*(9in)^2*h\)

So the correct option is the first one.

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Answer:

x = 31°

Step-by-step explanation:

the sum of the 3 angles in a triangle = 180° , that is

x + 54° + 95° = 180°

x + 149° = 180° ( subtract 149° from both sides )

x = 31°

Answer:

\(x=8, y=3\)

Step-by-step explanation:

Recall that if a matrix multiplication of two matrices is defined, then the number of columns of the first matrix is equivalent to the number of rows of the second matrix.

Since matrix M has (11-x) columns and matrix N has y rows, and MN is defined, so it follows:

\(y=11-x----(1)\)

Since matrix N has (y+5) columns and matrix M has x rows, and NM is defined, so it follows:

\(y+5=x----(2)\)

Substitute (1) into (2):

\(11-x+5=x\\2x=16\\\therefore x=8--(3)\)

Substitute (3) into (1):

\(y=11-8=3\)