If a circular arc of the given length s subtends the central angle θ on a circle, find the radius of the circle.
s = 3 km, θ = 20°

The eigenvectors v1 and v2 are such that when multiplied by matrix A, they result in scalar multiples of themselves (scaled by their respective eigenvalues).

An eigenvector is a non-zero vector that, when multiplied by a matrix, results in a scalar multiple of itself. In other words, if A is a square matrix and v is an eigenvector of A, then Av = λv, where λ is the eigenvalue associated with v.

Given the eigenvalues and eigenvectors for matrix A as λ1 = 2, v1 = [-5 1]ᵀ and λ2 = 6, v2 = [5 4]ᵀ, we can say that:

- Av1 = λ1v1 = 2[-5 1]ᵀ = [-10 2]ᵀ
- Av2 = λ2v2 = 6[5 4]ᵀ = [30 24]ᵀ

Therefore, the eigenvectors v1 and v2 are such that when multiplied by matrix A, they result in scalar multiples of themselves (scaled by their respective eigenvalues).

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Answer:

Area of the square: 36

Step-by-step explanation:

6.1+8.2+9.7=24. Squares have 4 sides so 24/4=6. Area= base times highet, Base=6 Highet=6. 6 times 6=36!

Answer:

A=36 cm²

Step-by-step explanation:

the perimeter of triangle=a+b+c

P=6.1+8.2+9.7

P= 24 cm

P of triangle = P of square ( square has 4 equal sides):

24=4a

a=24/4=6

Area of square : a²

A=6² = 36 cm²

Answer:

32

Step-by-step explanation:

Well I don't really have a way to make this equation any simpler than just adding 1 to 31.

31 + 1 = 32

Hope you pass the quiz!!

The batting order for a baseball team is a permutation

This is permutation because repetition is not allowed and the order of the items matters. In the context of the batting order for a baseball team, the order in which the players are arranged in the lineup is significant.

Each player has a specific position in the order, and the arrangement affects the strategy and dynamics of the game. Additionally, in a typical baseball game, each player can only occupy one position in the lineup, so repetition is not allowed. Therefore, the batting order is an example of a permutation.

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Answer:

$8882.9

Step-by-step explanation:

A=p(1+(r/n))^nt

Given:P=7000, r=(3÷100%)=0.03 , n=2, t=8

A = 7000(1+(.03/2))^(2×8)

A = 7000 (1+0.015)^16

A = 7000 × 1.015^16

A = $8882.9

Since X² (68.732) > X²₀.₀₁ (13.277), we reject the null hypothesis and conclude that There is evidence that political views and level of marijuana usage are related.

The alternative hypothesis states that political beliefs and marijuana use depend on one another within the population, contrary to the null hypothesis that asserts these two variables are independent.

H₀ : Pij = Pi · Pj ; i = 1, 2, 3 ; j = 1, 2, 3

Ha : at least one Pij ≠ Pi · Pj

We want to test whether there is a relationship between political views and marijuana usage levels. The results of a random sample of size n = 1353 are derived from the following formula;

e = (Row total) x (Column total) /Total sample size

We are told to use the 0.01 level of significance to test the null hypothesis. Thus, α = 0.01. The table has r = 3 rows and c = 3 columns. An r × c table has degrees of freedom df = (r - 1) x (c - 1). So, a 3×3 table has degrees of freedom df = (3 - 1) x (3 - 1) = 4. From formula the df = 4 and α = 0.01, χ²₀.₀₁ = 13.277. Reject the null hypothesis if X² ≥ 13.277 where

x² =Σ(a - e)²/e

Substituting the observed and expected frequencies summarized in the table above into the formula for x², we get

X² = 68.732

Rejection Region → X² ≥ 13.277

Test statistic → X² = 68.732

Since X² (68.732) > X²₀.₀₁ (13.277), we reject the null hypothesis and conclude that There is evidence that political views and level of marijuana usage are related.

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Answer:

Total probability = 0.002 or 1 / 495

Step-by-step explanation:

Given:

Number of men = 8

Number of women = 4

Total number of person = 12

Find:

All four members will be women

Computation:

1st women probability = (4/12)

2nd women probability = (3/11)

3rd women probability = (2/10)

4th women probability = (1/9)

Total probability = (4/12)×(3/11)×(2/10)×(1/9)

Total probability = 24 / 11,880

Total probability = 0.002 or 1 / 495

The probability that all four members of the search committee will be women is 1.42%.

Since a board of directors consists of eight men and four women, and a four-member search committee is randomly chosen to recommend a new company president, to determine what is the probability that all four members of the search committee will be women the following calculation should be performed:

Therefore, the probability that all four members of the search committee will be women is 1.42%.

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When a double cone is sliced at the apex by a plane perpendicular to the base of the cone, the resulting conic section is a parabola.

Option B is the correct answer.

We have,

A parabola is a type of conic sect ion that can be defined as the locus of points equidistant from a fixed point (the focus) and a fixed line (the directrix).

In the case of slicing a double cone at the apex, the resulting conic section will have the characteristic shape of a parabola.

The slicing plane intersects both sides of the double cone, creating a curved shape that opens upward or downward, depending on the orientation of the cone.

The vertex of the parabola corresponds to the point of intersection of the slicing plane with the double cone.

Therefore,

When a double cone is sliced at the apex by a plane perpendicular to the base, a parabola is formed.

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The complete question:

Which degenerate conic is formed when a double cone is sliced at the apex by a plane perpendicular to the base of the cone?

A. Circle

B. Parabola

C. Ellipse

D. Hyperbola

Answer: $15

Step-by-step explanation:  1.25 X 12 = 15

Answer:

The price before the discount is $ 16

Step-by-step explanation:

Answer:

x - 11

Step-by-step explanation:

f(x) = -5x - 4

g(x) = 6x - 7

Find f(x) + g(x).

To find the sum of f(x) and g(x), we must substitute f(x) and g(x) with the given equations:

(-5x - 4) + (6x - 7)

To solve, we combine like terms.

-5x + 6x = x

-4 + (-7) = -11

Therefore, we end up with x - 11.

Hope this helps.

Marcella would not be able to win the competition because her kite string (159.75 feet) is less than 162 feet.

An equation is an expression that shows the relationship between two or more numbers and variables.

Trigonometric ratio is used to show the relationship between the sides and angles of a right angled triangle.

Let l represent the length of the string, hence:

sin(28) = 75/l

l = 159.75 feet

Marcella would not be able to win the competition because her kite string (159.75 feet) is less than 162 feet.

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Answer:

DE's length is 1/2 of BC's length, due to it being a mid segment (13)((You can tell it is a mid segment due to the congruency lines)). AD's length is 12, due to there being a midpoint. EC's length is 10, also due to the congruency lines.

Expression which represents the amount of money spend by each woman is equal to [ 9 + 1.35 + (one- half)(3.50 + 1.74)].

As given in the question,

Condition for the expression:

Sally and Anne both went for a movie.

Each one purchased a drink.

Shared one popcorn and one veggie bought by them.

Consider movie ticket price = 9

drink price = 1.35

Popcorn price = 3.50

Veggie price = 1.74

Explanation for different expressions are:

1. one-half (9 + 1. 35 + 3. 50 + 1. 74)

Here sum of all the amount is divided equally, which is not correct as movie ticket and drink they have purchased individually.

2.  9 + 1. 35 + one-half (3. 50 + 1. 74)

This is correct option as it represents :

Movie ticket price = 9

Drink = 1.35

one-half (3. 50 + 1. 74) = one popcorn and one veggie divided equally.

3. 18 + 2. 70 + one-half (3. 50 + 1. 74)

As per consideration of price this is not correct option.

Movie ticket price =18

Drink = 2.70

one-half (3. 50 + 1. 74) = one popcorn and one veggie divided equally.

4. 9+1. 35+2(3. 50+1. 7)

This is not correct option as popcorn and veggie price is doubled.

Therefore, expression which represents the amount of money spend by each woman is equal to [ 9 + 1.35 + (one- half)(3.50 + 1.74)].

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The class that had more than half 2.5 or better GPAs for the five decades is the Senior (Sr) class.

GPAS refers to Grade Point Average (GPA) that is calculated by adding the total number of grade points earned and dividing by the total number of credits attempted.

A decade is a period of ten years, used especially as a unit of time or history. It is often used in everyday speech and various fields such as science, technology, and history.

The senior class had more than half 2.5 or better GPAs for the five decades. So, the correct answer is option D (Sr).

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The amount of interest that Coach Cliffman earned is $108

Coach Cliffman made a deposit of $1,800 into an account that earns 2% annual simple interest.

The principle amount is $1800

The rate of interest is 2%

The time period is 3years

SI = prt/100

= 1800 x 2 x 3/100

= 108

Therefore after 3 years,  the amount of interest that Coach Cliffman earned is $108

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Answer:

the slope is 12

Step-by-step explanation:

The points i used were (0,-80)and (5,-20) You rise 60 and run 5.  Rise/run would be 60/5 which gives you 12 as your final answer.  Hope this helps.  

Take 2 points

Slope:-

\(\\ \tt\hookrightarrow m=\dfrac{-20+80}{5-0}=\dfrac{60}{5}=12\)

The selling price of each mango is sh 18

What is selling price?

Selling price can b described as the amount at which a particular product is sold at the market

Write out the parameters

160 mangoes are sold at Sh 10

The calculation can be done as follows

cost price= 160 × 10

= 1600

Sh 200 was paid for transportation

The total cost price is 1600 + 200

= 1800

Formula

selling price= cost price (1+r/100)

= 1800(1 + 60/100)

= 1800( 1+ 0.6)

= 1800(1.6)

= 2880

Therefore the selling price of each mango can be calculated as follows

= 2880/160

= 18

Hence the selling price of each Mango is Sh 18

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Answer:

Step-by-step explanation:

Given the value of a family's home, in Camrose AB, given by the following exponential function f(x) = 130000(1.06)^x, where x is the number of years after the family purchases the house for $130,000. In order to calculate the best estimate for the instantaneous rate of change in the value of the home when the family has owned it for 5 years, we will have to substitute x =5 in the given function and solve as shown;

f(x) = 130000(1.06)ˣ

f(5) = 130000(1.06)⁵

f(5) = 130000*(1.06)⁵

f(5) = 130000*1.338226

f(5) = 173,969.38

Hence, the instantaneous rate of change in the value of the home when the family has owned it for 5 years is approximately  $173,969

Answer:

p=-6

Step-by-step explanation:

w =2 y =4

p=7w - 5y

p = 7(2) - 5(4)

p= 14 - 20

p= -6

Answer:

-6

Step-by-step explanation:

Substituting 2 for w and 4 for y, we get:

P=7w - 5y  =>  P=7(2) - 5(4)  =  14 - 20  =  -6

Answer: $21.52

Step-by-step explanation: 2.69 times 8 = $21.52

Answer:

The angles are 110, 110 and 140

Step-by-step explanation:

Let the equal angles be x.

So we have angles x, x and another third one

Now, the other third angle is 30 degrees larger than x, this means that the other third angle is 30 + x

Since they are angles at a point, adding the three together will make or give 360.

Thus,

x + x + x + 30 = 360

3x + 30 = 360

3x = 360-30

3x = 330

x = 330/3

x = 110

So the other third angle is 110 + 30 = 140

So the angles are 110, 110 and 140

The probability that a student who has an A is a male is 60%.

To find the probability that a student who has an A is a male, we need to calculate the ratio of the number of male students with an A to the total number of students with an A.

Given that there are 19 students in total, and 6 of them are female, we can determine that there are 19 - 6 = 13 male students. Out of these male students, 7 do not have an A. Therefore, the number of male students with an A is 13 - 7 = 6.

Now, we know that there are 10 students in total who have an A. Therefore, the probability that a student with an A is a male can be calculated as the ratio of the number of male students with an A to the total number of students with an A:

Probability = Number of male students with an A / Total number of students with an A

Probability = 6 / 10

Probability = 0.6 or 60%

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Answer: D or x-y=3 and x-3y=-9

Step-by-step explanation: I got 100% on the quiz

Answer:d

Step-by-step explanation:

Answer:

13.2 g

Step-by-step explanation:

let x = grams sugar in a 200 ml glass

16.5 g sugar / 250 ml = x g sugar / 200 ml

x(250) = (16.5)(200)

x =  (16.5)(200) / (250) = 3300 / 250 = 13.2

Answer:  there are 13.2 g sugar in a 200 ml glass of juice

The theoretical probability of choosing a prime number from the natural numbers 1 to 10 is 2/5 (option D).

To find the theoretical probability of choosing a prime number from the natural numbers 1 to 10, follow these steps:

1. Identify the prime numbers within the given range (1 to 10). Prime numbers are numbers greater than 1 that have no divisors other than 1 and themselves. In this case, the prime numbers are 2, 3, 5, and 7.

2. Count the total number of prime numbers you found in step 1. There are 4 prime numbers.

3. Count the total number of natural numbers in the given range. There are 10 natural numbers from 1 to 10.

4. Divide the number of prime numbers (step 2) by the total number of natural numbers (step 3) to find the probability. This gives you 4/10, which simplifies to 2/5.

The theoretical probability of choosing a prime number from the natural numbers 1 to 10 is 2/5 (option D).

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The direct variation equation between x and y is 4x = y.

Here, we are given that x and y are in direct variation. In other words, this means that x and y are directly proportional to each other.

Thus, if k is a constant term, then the relation between x and y can be represented as-

x = ky

Now, we are given that if y = 12, x = 3

⇒ 3 = 12k

12k = 3

k= 3/12

k= 1/4

Thus, we found the value of k, the relation will become-

x = y/4

or 4x = y

Thus, the direct variation equation between x and y is 4x = y.

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The range of the function g(x) = |x - 12| - 2 is {y | y > -2}, indicating that the function can take any value greater than -2.

To find the range of the function g(x) = |x - 12| - 2, we need to determine the set of all possible values that the function can take.

The absolute value function |x - 12| represents the distance between x and 12 on the number line. Since the absolute value always results in a non-negative value, the expression |x - 12| will always be greater than or equal to 0.

By subtracting 2 from |x - 12|, we shift the entire range downward by 2 units. This means that the minimum value of g(x) will be -2.

Therefore, the range of g(x) can be written as {y | y > -2}, which means that the function can take any value greater than -2. In other words, the range includes all real numbers greater than -2.

Visually, if we were to plot the graph of g(x), it would be a V-shaped graph with the vertex at (12, -2) and the arms extending upward infinitely. The function will never be less than -2 since we are subtracting 2 from the absolute value.

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In conclusion the correct solution is 1.54 as the spending multiplier.

The spending multiplier is a measure of the impact of changes in spending on overall economic output. It represents the amount by which a change in spending is multiplied throughout the economy. In this case, the question provides a marginal propensity to consume (MPC) of 0.65.

The MPC represents the portion of additional income that individuals choose to spend rather than save. Since the MPC is 0.65, it means that for every additional dollar earned, individuals will spend 65 cents and save the remaining 35 cents.

To calculate the spending multiplier, we take the reciprocal of the MPC. In this case, the reciprocal of 0.65 is approximately 1.54. This means that a change in spending of $1 will result in a total change in economic output of approximately $1.54.

For example, if there is an increase in government spending by $100 million, the total impact on the economy will be approximately $154 million. This is because the initial increase in spending will lead to additional income for individuals, who in turn will spend a portion of that income, leading to further rounds of spending and economic activity.

Therefore, the correct answer is 1.54 as the spending multiplier.

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