Evaluate 6×[2−(4)×(–8)]

The number of ways they can is 40,320.

The number of ways Larry can arrive first and Sarah can arrive last is 720.

The probability that Larry arrives first and Sarah arrives last is 0.01786.

We have,

a)

Since each person can arrive at any time, the number of ways they can arrive is equal to the number of permutations of 8 people, which is:

= 8!

= 40,320

b)

To calculate the number of ways Larry can arrive first and Sarah can arrive last, we can fix their positions and then permute the remaining 6 people in the middle.

= 1 x 6! x 1

= 720

c)

To find the probability that Larry arrives first and Sarah arrives last, we need to divide the number of ways they can arrive in the desired order (720) by the total number of ways they can arrive (40,320):

= P(Larry first and Sarah last)

= 720 / 40,320

= 0.01786

So the probability is approximately 0.01786, or about 1.8%.

Thus,

The number of ways they can is 40,320.

The number of ways Larry can arrive first and Sarah can arrive last is 720.

The probability that Larry arrives first and Sarah arrives last is 0.01786.

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Answer:

Step 1: Distributive Property

Step 2: Distributive Property

Step 3: Commutative Property

Step-by-step explanation:

Step 1: This is distributing the (x + 4y + z) into the (x - 7y), so each term in the prior expression is multiplied by (x - 7y). Hence, Distributive Property.

Step 2: This is doing the same thing but to each individual term. The x in the first term is multiplied by each term in the (x - 7y), the 4y in the second term is multiplied by each term in the (x - 7y), and the same for z. Hence, Distributive Property.

Step 3: This is reordering the variables in the terms. For example, 4yx is changed to 4xy, and that is possible because of the Commutative Property. zx is also reordered into a xz and 7zy into a 7yz.

Feel free to ask any more questions. Hope this helps!!!

There is a probability of 94/315 that the problem will be solved.

We are given that P has a chance of solving the problem of 2/7, Q has a chance of solving the problem of 4/7, and R has a chance of solving the problem of 4/9. To find the probability that the problem is solved, we need to consider all possible scenarios in which the problem can be solved.

The probability of this scenario is 2/7. If P solves the problem, then it does not matter whether Q or R solve it, the problem is already solved. Therefore, the probability of the problem being solved in this scenario is 2/7.

The probability of this scenario is 4/7. If Q solves the problem, then it does not matter whether P or R solve it, the problem is already solved. Therefore, the probability of the problem being solved in this scenario is 4/7.

The probability of this scenario is 4/9. If R solves the problem, then it does not matter whether P or Q solve it, the problem is already solved. Therefore, the probability of the problem being solved in this scenario is 4/9.

The probability of this scenario is (1-2/7) * (1-4/7) * (1-4/9) = 3/35. This is because the probability of P not solving the problem is 1-2/7, the probability of Q not solving the problem is 1-4/7, and the probability of R not solving the problem is 1-4/9. To find the probability of none of them solving the problem, we multiply these probabilities together.

To find the probability of the problem being solved, we need to add the probabilities of all the scenarios in which the problem is solved. Therefore, the probability of the problem being solved is:

2/7 + 4/7 + 4/9 = 94/315

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Step-by-step explanation:

5 (4x^8) ^(-1/2)    -   2 x^-3

p ^(1/2)

r ^5/3  

The area of the triangle with base of 5 ​inches and a height of 10 inches is 25 square inches. The correct answer is C.

The formula for the area of a triangle is A = 1/2 * b * h, where A is the area, b is the base, and h is the height. Using this formula, we can calculate the area of the triangle in question.

Given that the base of the triangle is 5 inches and the height is 10 inches, we can plug these values into the formula and solve for A:

A = 1/2 * b * h

A = 1/2 * 5 * 10

A = 25

Therefore, correct answer is C.

The height of a triangle is the perpendicular distance between the base and the opposite vertex. The base is the side of the triangle on which the height is measured.

By multiplying the base and the height and dividing the result by 2, we can find the area of a triangle. This formula works for all types of triangles, regardless of their size or shape.

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Complete question is:

Find the area of a triangle with base of 5 ​inches and a height of 10 inches.

A 100 square inches

B 50 square inches

C 25 square inches

D 12.5 square inches

1. The objective of Nour's study is to sample the population to see if there is a correlation between her performance and the audience response.

2. No, because the population she sampled isn't necessarily representative

A population sample is a subgroup of people drawn from a broader population for the purpose of a study.

A population sample is often chosen such that it is a representative of the greater population. Populaton sample should consider factors such as age, gender, income, or level of education.

The answer provided is based on the full question below;

Nour wants to go on a popular TV talent show. In order to be accepted, her audition must get at least 60% positive votes from people in the crowd.

To make sure she's not going to embarrass herself, she performed her act in front of 100 random people from her school. About 90% of the people said they would give her a positive vote. She calculated the margin of error and found it's well within the range above 60%, so she decided to go to the audition.

What is the objective of Nour's study?

Is the study appropriate for the statistical questions it's supposed to answer?

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12 baseball and 9 basketball players are there. The frequency of a value in the data is its occurrence.

One approach to display data is in a frequency table. To summarise bigger collections of data, the data are organised and counted. You can examine the distribution of the data across various values using a frequency table. The frequency of a value in the data is its occurrence. We can immediately see how frequently each value appears in a table. 12 baseball and 9 basketball players are there.

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Answer:

To calculate the height of the large bottle, we can use proportions. We know that the small bottle has a width of 5.5 cm and a height of 10 cm. We also know that the large bottle has a width of 9.9 cm. If we set up a proportion with the widths and heights of the two bottles, we can solve for the height of the large bottle.

5.5 cm / 10 cm = 9.9 cm / h

Multiplying both sides by h, we get:

5.5 cm * h = 10 cm * 9.9 cm

Dividing both sides by 5.5 cm, we get:

h = (10 cm * 9.9 cm) / 5.5 cm

h = 18 cm

Therefore, the height of the large bottle is 18 cm.

Step-by-step explanation:

The area of the following composite figures is 78 square units.

The area of the square is computed as 36 (length x width) or 2(Length).

The area of the triangle is computed as (base x height) ÷ 2.

The areas of the composite figures are added to determine the total area.

Line AD = 6

Line DC = 6

Line AB = 20

Base of the triangle = 14 (20 - 6)

Area of triangle = (h x b) ÷ 2

= (6 x 14) ÷ 2

= 42

Area of square portion = 36 (6 x 6)

Total area = 78 square units

Thus, we can conclude that the area of the composite figures are 78 square units.

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A function of the form y= A sin (Bx-C)+D that has period 8, phase shift -2, and the range -12 ≤y≤-4 is y = 4 sin (π/4 x + π/2) - 8

To write a function of the form y = A sin (Bx - C) + D that has a period of 8 and phase shift of -2, we can use the general formula:

y = A sin [(2π/P)(x - C)] + D

where P is the period, C is the phase shift, and D is the vertical shift. In this case, P = 8 and C = -2, so we have:

y = A sin [(2π/8)(x + 2)] + D

Simplifying the equation, we get:

y = A sin (π/4 x + π/2) + D

To find the amplitude A and vertical shift D that satisfy the range -12 ≤ y ≤ -4, we can use the fact that the sine function oscillates between -1 and 1. If we set A = 4, then the maximum value of y is 4 + D, and the minimum value of y is -4 + D. To ensure that the range is -12 ≤ y ≤ -4, we need to choose D such that:

4 + D ≤ -4 and -4 + D ≥ -12

Solving these inequalities, we get:

-8 ≤ D ≤ 0

Therefore, a function that satisfies the given conditions is:

y = 4 sin (π/4 x + π/2) - 8

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Few families can survive on a single salary is true statement

Many families rely on dual incomes to make ends meet, especially in areas with high living costs.

However, there are still many families that rely on a single salary to support themselves.

While it may be challenging to make ends meet on a single salary, it is still possible for families to survive and even thrive in these circumstances.

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Answer:

all real numbers

Step-by-step explanation:

if you subtract x from both sides, you get x=x. This is true for basically any number

The equation of tangent plane to the surfacez = 8x² - 9y² at the point (2,1,23) is 32(x - 2) - 18(y - 1) -1(z - 23) = 0

Here, the equation of the surface is

z = 8x² - 9y²

Let us assume that f(x, y, z) =  8x² - 9y² - z

The partial derivative of f(x, y, z) would be:

[tex]\frac{\partial f}{\partial x}[/tex] = 16x

[tex]\frac{\partial f}{\partial y}[/tex] = -18y

[tex]\frac{\partial f}{\partial z}[/tex] = -1

At point (2, 1, 23) the partial derivative of f(x, y, z),

[tex]\frac{\partial f}{\partial x}[/tex] = 32

[tex]\frac{\partial f}{\partial y}[/tex] = -18

[tex]\frac{\partial f}{\partial z}[/tex] = -1

So, the equation of tangent plane would be,

32(x - 2) - 18(y - 1) -1(z - 23) = 0

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The ratio of the sides of the medium box to the small box is 3:1, the ratio of the area of the bases is 9:1, and the ratio of the volumes is 27:1 and the volume of the medium box is 5832 cubic inches.

Let's denote the side length of the small cube as "s". Since it is a cube, all sides are equal.

Given that the volume of the small box is 216 cubic inches, we can set up the equation;

Volume of small box = s³ = 216

Taking the cube root of both sides, we get;

s = ∛216 = 6 inches

So, the side length of the small cube is 6 inches.

For the medium box, the length, width, and height are all tripled, so the new side length of the medium cube is 3 times the side length of the small cube:

Side length of medium cube = 3s = 3 × 6 = 18 inches

Now, let's calculate the ratio of the sides, area of the bases, and volumes of the small and medium boxes;

Ratio of sides: Side length of medium cube / Side length of small cube = 18 / 6 = 3

Ratio of area of bases: (Side length of medium cube)² / (Side length of small cube)² = (18)² / (6)² = 9

Ratio of volumes: (Volume of medium box) / (Volume of small box) = (Side length of medium cube)³ / (Side length of small cube)³ = (18)³ / (6)³ = 27

So, the ratio of the sides of the medium box to the small box is 3:1, the ratio of the area of the bases is 9:1, and the ratio of the volumes is 27:1.

The volume of the medium box is given by;

Volume of medium box = (Side length of medium cube)³ = 18³

= 5832 cubic inches

Therefore, the volume of the medium box is 5832 cubic inches.

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Answer:θ ≈ 2.57 radians

θ ≈ 0.58 radians

Step-by-step explanation:We can solve this quadratic equation in sin(θ) by factoring:

4sin^2(θ) + 7sin(θ) - 5 = 0

(4sin(θ) - 1)(sin(θ) + 5) = 0

Therefore, either:

4sin(θ) - 1 = 0

sin(θ) = 1/4

or:

sin(θ) + 5 = 0

sin(θ) = -5 (not possible, since sin(θ) is between -1 and 1)

So, we have sin(θ) = 1/4. Since 0 ≤ θ < 2π, we can find the two solutions in the interval [0, 2π) by using the inverse sine function:

θ = arcsin(1/4)

Using a calculator, we find:

θ ≈ 0.2531 or θ ≈ 2.8887

Therefore, in radians, the solutions for θ are approximately:

0.2531 (which is less than 2π)

2.8887 (which is greater than 2π)

So the only answer that satisfies 0 ≤ θ < 2π is:

Answer: 7

Step-by-step explanation: he spends 7 hours a day take 3 away from 10.

Answer:

x = 3

c(x) = 3x² + 5x + 22

⇒ c(3) = 3(3²) + 5(3) + 22

⇒ c(3) = 3(9) + 15 + 22

⇒ c(3) = 27 + 15 + 22

⇒ c(3) = 64

j(x) = 12x

⇒ j(3) = 12(3)

⇒ j(3) = 36

a(x) = 9x

⇒ a(3) = 9(3)

⇒ a(3) = 27

c(x) = 3x² + 5x + 22 is the function that has the largest value when x = 3.

False. Not all functions are equal at x = 3.

Each pound of bananas costs $1.49 for the 10-pound package and $1.51 for the 8-pound package.

The 10 pounds of bananas is the better buy because $1.49 is the cheaper price per pound.

We have,

Part A:

To find the cost of each pound of bananas in each case,

We can use the unit rate.

- For 10 pounds of bananas at $14.90, the cost per pound is:

$14.90 ÷ 10 pounds

= $1.49 per pound

- For 8 pounds of bananas at $12.08, the cost per pound is:

$12.08 ÷ 8 pounds

= $1.51 per pound

Part B:

The better buy is the one with the lower cost per pound.

Since $1.49 is less than $1.51, the 10-pound package is the better buy.

The 10 pounds of bananas is the better buy because $1.49 is the cheaper price per pound.

Therefore,

Each pound of bananas costs $1.49 for the 10-pound package and $1.51 for the 8-pound package.

The 10 pounds of bananas is the better buy because $1.49 is the cheaper price per pound.

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Using inverse variation, the value of x = -19.2

Inverse variation is when a quantity varies inversely as the other.

Given: y varies inversely with x.

If y=-24 when x =36, what is the value of x when y = 45.

To splve this, we proceed as follows

Since y varies inversely with x, we have that

y ∝ 1/x

y = k/x where k = constant of proportionality

So, making k subject of the formula, we have that

k = yx

Now, If y=-24 when x =36, we have that

k = - 24 × 36

= -864

So, substituting k into y, we have that

y = k/x

= -864/x

So, to find the value of x when y = 45, making x subject of the formula, we have that

x = -864/y

So, substituting y into the equation, we have that

x = -864/y

= -864/45

= -19.2

So, the value of x = -19.2

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Answer:

The amount of Uranium-233 produced after 20 days will be approximately 65.1 pounds.

Step-by-step explanation:

The length of AB is 4.6 inches.

An arc is a part of a circle i.e. an incomplete circle. It can be either a major arc or a minor arc of a given circle.

The length of an arc can be determined by;

length of an arc = (θ/ 360)*2πr

Where r is the radius of the circle, and θ is the measure of its central angle.

In the given diagram, the arc AB is a minor arc. So that;

AB = (θ/ 360)*2πr

r = d/2

 = 22/2

r = 11 inches

AB = (24/ 360)*2*3.14*11

     = 4.6053

AB = 4.6 inches

The length of arc AB is 4.6 inches.

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The value of f (-1) by virtue of the given absolute value function graph as required is; 8.

It follows from the task content that the value of the function instance; f (-1) is required to be determined.

On this note, the value of the function instance can be determined as the point of intersection of the line; x = -1 with the given graph.

Ultimately, the value of the instance f (-1) is; 8.

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Answer:2.71

0.43 are correct

Step-by-step explanation:We can solve this quadratic equation in sin(θ) by using the substitution u = sin(θ):

-u^2 - 2u + 1 = 0

Multiplying both sides by -1, we get:

u^2 + 2u - 1 = 0

We can use the quadratic formula to solve for u:

u = (-b ± sqrt(b^2 - 4ac)) / 2a

where a = 1, b = 2, and c = -1. Substituting these values, we get:

u = (-2 ± sqrt(4 + 4)) / 2

u = (-2 ± 2sqrt(2)) / 2

Therefore, either:

The value of the function ƒ(x) at each point is  ƒ(–1) = 5, ƒ(0) = 3, ƒ(1) = 5, ƒ(2) = 11, ƒ(3) = 21, the correct option is B.

We are given that;

f(-1)=5 f(0) = 3 f(1) = 5 f(2) = 11 f(3) = 21

Now,

The function ƒ(x) maps each value of x to a corresponding value of y. For example, when x = –1, y = 5, so ƒ(–1) = 5. Similarly, when x = 0, y = 3, so ƒ(0) = 3, and so on. The other options are incorrect because they either reverse the order of x and y, or they do not match the values given in the mapping.

Therefore, by the given domain and range the answer will be ƒ(–1) = 5, ƒ(0) = 3, ƒ(1) = 5, ƒ(2) = 11, ƒ(3) = 21.

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The complete question is;

Use the mapping shown above to show the value of the function ƒ(x) at each point. Question options: A) ƒ(1) = 5, ƒ(0) = 3, ƒ(1) = 5, ƒ(2) = 11, ƒ(3) = 21B) ƒ(–1) = 5, ƒ(0) = 3, ƒ(1) = 5, ƒ(2) = 11, ƒ(3) = 21C) ƒ(–1) = 5, ƒ(0) = 3, ƒ(1) = 5, ƒ(2) = 21, ƒ(3) = 11D) ƒ(5) = –1, ƒ(3) = 0, ƒ(5) = 1, ƒ(11) = 2, ƒ(21) = 3.

Answer:

Since the disease doubles every 7 days, the number of cases on day 21 will be 2^3 times the number of cases on day 14, which will be 2^2 times the number of cases on day 7, which will be 2^1 times the number of cases on day 1.

Starting with 3 cases on day 1, we can use the formula:

N = 3 * 2^(t/7)

where N is the number of cases after t days.

Plugging in t = 21, we get:

N = 3 * 2^(21/7) = 3 * 2^3 = 24

Therefore, there will be 24 cases by the end of day 21.

Step-by-step explanation:

The solution is : the weighted-average accumulated expenditures are $101,269.5.

Explanation:

Calculation to determine the weighted-average accumulated expenditures

Weighted-average accumulated expenditures=$202,539* (3/12 + 2/12 + 1/12)

Weighted-average accumulated expenditures=$202,539*0.5

Weighted-average accumulated expenditures=$101,269.5

Therefore In determining the amount of interest cost to be capitalized, the weighted-average accumulated expenditures are $101,269.5.

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The value of area of the figure is,

⇒ 10√10 units²

We have to given that;

To find the area of figure.

Here, We have to find length of AD and AB for area of figure.

Coordinate of A = (- 2, 2)

Coordinate of B = (- 4, -4)

Coordinate of D = (3, 2)

Since, The distance between two points (x₁ , y₁) and (x₂, y₂) is,

⇒ d = √ (x₂ - x₁)² + (y₂ - y₁)²

Hence, Length of AD;

AD = √ (-2 - 3)² + (2 - 2)²

AD = √25

AD = 5

Length of AB;

AB = √ (- 2 + 4)² + (2 + 4)²

AB = √4 + 36

AB = √40

AB = 2√10

Thus, The value of area of the figure is,

⇒ AD x AB

⇒ 5 × 2√10

⇒ 10√10

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Answer:

8sin²a + cot²a sin²a = 1 is true.

Step-by-step explanation: