Please help me.
And explain how you got your answer please.

Answer:

C. 5

Step-by-step explanation:

Becuase the left figure is just a scaled down size of the right one, 3 x 2 = 6 so 10 ÷ 2 = 5

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a) The equation for Bueller's height above the ground as a function of time is: h(t) = 9 cos(πt/8) + 1.5

b) When Bueller has been on the ride for 1 minute and 30 seconds, his height above the ground is approximately 10.5 m.

In mathematics, a function is a rule that assigns a unique output value to each input value in a specified set. More precisely, a function is a set of ordered pairs (x, y) where each x-value (the input) corresponds to exactly one y-value (the output).

In mathematics, an equation is a statement that asserts the equality of two expressions, typically containing one or more variables. An equation consists of two sides, the left-hand side, and the right-hand side, separated by an equal sign (=).

According to the given information,

a) To determine an equation for Bueller's height above the ground as a function of time, we can use the equation for the height of a point on a Ferris wheel:

h(t) = r cos(ωt) + h0

where:

1) h(t) is the height of the point above the ground at time t

2) r is the radius of the Ferris wheel

3) ω is the angular velocity of the Ferris wheel (in radians per second)

4) t is the time elapsed since the point was at its lowest position

5) h0 is the initial height of the point above the ground

In this case, we know that Bueller boards the Ferris wheel at a height of 1.5 m off the ground, so h0 = 1.5 m. The radius of the Ferris wheel is 9 m, and it rotates once every 16 seconds, so the angular velocity is:

ω = 2π / T = 2π / 16 = π / 8 radians per second

Therefore, the equation for Bueller's height above the ground as a function of time is:

h(t) = 9 cos(πt/8) + 1.5

b) To find Bueller's height off the ground when he has been on the ride for 1 minute and 30 seconds (or 90 seconds), we can substitute t = 90 into the equation for h(t):

h(90) = 9 cos(π(90)/8) + 1.5

h(90) = 9 cos(11.25π) + 1.5

Using a calculator, we get:

h(90) ≈ -6.3 m

Note that the negative sign means that Bueller is below ground level, which is not physically possible. This occurs because we started counting time from the bottom of the wheel, so 90 seconds corresponds to the bottom position plus 5 and a half rotations. To fix this, we can add a multiple of the period T = 16 seconds to t to bring it back to the correct range:

h(t) = 9 cos(πt/8) + 1.5

h(90 + 5T/2) = 9 cos(π(90 + 5T/2)/8) + 1.5

h(90 + 5T/2) = 9 cos(π(2 + 5/16)) + 1.5

h(90 + 5T/2) ≈ 10.5 m

Therefore, when Bueller has been on the ride for 1 minute and 30 seconds, his height above the ground is approximately 10.5 m.

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Answer:

Step-by-step explanation:

GIVEN:

To find the value of y, isolate it on one side of the equation.

2y-6-3y+5

Solutions:

First, add by 6 from both sides.

2y-6+6=3y+5+6

Solve.

Add the numbers from left to right.

5+6=11

2y=3y+11

Then, you subtract by 3y from both sides.

2y-3y=3y+11-3y

Solve.

-y=11

Divide by -1 from both sides.

-y/-1=11/-1

Solve.

Divide these numbers goes from left to right.

11/-1=-11

\(\Longrightarrow: \boxed{\sf{y=-11}}\)

I hope this helps. Let me know if you have any questions.

The sum of magnitude of u + v is 15.99.

The  magnitude or size of a mathematical object is described as a property which determines whether the object is larger or smaller than other objects of the same kind.

Given that, magnitude of u =  5

Magnitude of v = 11

The angle between them i= 40°

we represent u and v in vector form,

u = 5 ( cos 40° i + sin 40° j ) = 3.83 i + 3.21 j

v = 11 ( cos 40° i + sin 40° j ) = 8.42 i + 7.07 j

The sum of two vectors is given by

u + v = 3.83 i + 3.21 j +  8.42 i + 7.07 j

u + v = 12.25 i + 10.28 j

Magnitude of u + v = √(12.25²+10.28²)

Magnitude of u + v

Magnitude of u + v   = √( 150.063 + 105.678)

Magnitude of u + v = 15.99

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complete question:

Given the magnitudes of vectors u and v and the angle θ between them, find sum of . Give the magnitude to the nearest tenth when necessary and give the direction by specifying the angle that the resultant makes with u to the nearest degree. ∣ u∣ = 5, ∣ v∣ = 11, θ = 40°

The area of the square with a side length of 3.1 meters is 9.61 square meters.

To find the area of a square, we need to multiply the length of one side by itself. In this case, the square has a side length of 3.1 m.

Area of a square = side length × side length

Substituting the given side length into the formula:

Area = 3.1 m × 3.1 m

To perform the calculation:

Area = 9.61 m²

It's worth noting that when calculating the area, we are working with squared units. In this case, the side length is in meters, so the area is expressed in square meters (m²). The area represents the amount of space enclosed within the square.

Remember, to find the area of any square, you simply need to multiply the length of one side by itself.

The area of the square with a side length of 3.1 meters is 9.61 square meters.

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Answer:

48×4.3=184 and that is the easy way how to do it

Answer:

y-intercept will be -4

Step-by-step explanation:

y=mx+b where 'b' indicates the y-intercept

Answer:

Yes

Step-by-step explanation:

Given:

Number of people (n) = 30

Mean wage in california = 24.66

Incomplete information;

Sample mean =23.41

Standard deviation = 2.35

Yes, the population average manufacturing wage in Utah less than $24.66 per hour, the population average manufacturing wage in the California

Answer:

C

Step-by-step explanation:

\(\left(\frac{f}{g} \right)(x)=\frac{f(x)}{g(x)} \\ \\ \frac{f(x)}{g(x)}=\frac{\sqrt[3]{2x}}{2x+1}\)

The denominator cannot equal 0, so:

\(2x+1 \neq 0 \implies x \neq -\frac{1}{2}\)

Answer:

124

Step-by-step explanation:

Based on the question, we are looking for a number that is equal to 31 when you divide the number by 4 (or multiply by 1/4, same thing). You can also represent this with an equation: 1/4x=31. This says: 1/4 of a number x is equal to 31.

1/4x=31

4(1/4x)=31(4)

x=124

You don't need an equation for this type of problem (you can simply multiply 31 by 4), but it can help if you are not sure what calculations to do!

The complete sentence is,

⇒ 1/4 of 124 = 31

Multiplication means to add number to itself a particular number of times. Multiply will be viewed as a process of repeated addition.

Let the number is,

⇒ x

Hence, We can formulate;

⇒ 1/4 of x = 31

Solve for x as;

⇒ 1/4 × x = 31

Multiply by 4;

⇒ x = 31 × 4

⇒ x = 124

Thus, The value of number is, 124

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Answer:

The final price to be paid after the 2% discount has been made will be $ 16,645.30.

Step-by-step explanation:

Since there is a 2% discount on the price of the Honda Shadow in the event that the dealer pays Honda within 15 days, and that after a rebate the price of the vehicle is $ 16,985, to obtain the value of the discount and the final amount to be paid must be calculated as follows:

16,985 x 2/100 = X

33,970 / 100 = X

339.70 = X

Thus, the discount to be made will be $ 339.70, with which the final price to be paid after the 2% discount has been made will be $ 16,645.30.

Answer:

height = 6 mm

Step-by-step explanation:

The prism is a rectangular prism. The base area of the prism is 24 mm². The volume of the prism is given as 144 mm³.

The height of the prism can be solved as follows.

Volume of the rectangular prism = Bh

where

B = base area

h = height

Volume = 144 mm³

B = 24 mm²

volume = Bh

144 = 24 × h

144 = 24h

divide both sides by 24

h = 144/24

h = 6 mm

Answer:

c

Step-by-step explanation:

edg 2022

Answer:

The answer is D 14^10

Answer:

A

Step-by-step explanation:

Equation of line parallel to y = − 2 x − 3 and passing through the point (3,-3) is y = -2x + 3.

When two lines are called parallel?

Two lines are parallel lines if they do not intersect.

The slopes of the lines are the same.

f(x)= mx + b and g(x)= nx + c are parallel if m = n.

According to the given question:

Given equation of line is y = −2x − 3

If the new line is parallel, then it will have the same slope.

y = -2x + b

Now this line passes through the point (x,y) = (3,-3) so put in the x and y values into the equation above, solve for b

-3 = -2(3) + b

b = 3

Therefore the required equation of line is

y = -2x + 3

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We can expect a student to guess 17 correct answers on a test with 68 four-choice multiple choice questions with probability 0.25.

Since the probability of guessing the correct answer to a four-choice multiple choice question is 0.25, the probability of guessing an incorrect answer is 1 - 0.25 = 0.75.

We can model the number of correct guesses as a binomial distribution with n = 68 (the number of trials) and p = 0.25 (the probability of success, i.e., guessing correctly).

The expected value of a binomial distribution is given by the formula:

E(X) = n * p

So, in this case, the expected number of correct answers that a student should guess on the test is:

E(X) = 68 * 0.25 = 17

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Answer:

See below

Step-by-step explanation:

Another notation for same function is

1. Is the function increasing or decreasing?

2. What is the y-intercept?

3. What is the slope?

4. What is f(-2)?

5. If f(x) = 0, what is x?

Answer:

Solving step

\(f(x) = 5x - 7\)

Substitute x=0

\(f(0) = 5 \times 0 - 7\)

Calculate the product

\(f(0) = (0) - 7\)

When adding or Subtracting 0 the quantity does not change

\(f(0) = - 7\)

\(f(x) = 0\)

\(0 = 5x - 7\)

\(5x = 0\)

\(x = \frac{7}{5} \)

OR

\(x = 1.4\)

Answer:

oh hello

Step-by-step explanation:

hi i am here to help you

The person that is correct among the students is Frank who said the pencils are an example of parallel lines.

Parallel lines are lines that can never meet. These are lines that run a direction that is quite opposite to each other as we can see from the image. It is clear that the lines as shown are not able to meet at any point even if they are extended.

Thus, the person that is correct among the students is Frank who said the pencils are an example of parallel lines.

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Answer:

A) P(Betty is first in line and mary is last) = P(B₁) + P(Mₙ) - (P(B₁) × P(Mₙ/B₁))

B) The method used is Relative frequency approach.

Step-by-step explanation:

From the question, we are told a sample of n kids line up for recess.

Now, the order in which they line up is random with each ordering being equally likely. Thus, this means that the probability of each kid to take a position is n(total of kids/positions).

Since we are being asked about 3 kids from the class, let's assign a letter to each kid:

J: John

B: Betty

M: Mary

A) Now, we want to find the probability that Betty is first in line or Mary is last in line.

In this case, the events are not mutually exclusive, since it's possible that "Betty is first but Mary is not last" or "Mary is last but Betty is not first" or "Betty is the first in line and Mary is last". Thus, there is an intersection between them and the probability is symbolized as;

P(B₁ ∪ Mₙ) = P(B₁) + P (Mₙ) - P(B₁ ∩ Mₙ) = P(B₁) + P(Mₙ) - (P(B₁) × P(Mₙ/B₁))

Where;

The suffix 1 refers to the first position while the suffix n refers to the last position.

Also, P(B₁ ∩ Mₙ) = P(B₁) × P(Mₙ/B₁)

This is because the events "Betty" and "Mary" are not independent since every time a kid takes his place the probability of the next one is affected.

B) The method used is Relative frequency approach.

In this method, the probabilities are usually assigned on the basis of experimentation or historical data.

For example, If A is an event we are considering, and we assume that we have performed the same experiment n times so that n is the number of times A could have occurred.

Also, let n_A be the number of times that A did occur.

Now, the relative frequency would be written as (n_A)/n.

Thus, in this method, we will define P(A) as:

P(A) = lim:n→∞[(n_A)/n]

Given this pair of probabilities, the probability that Mary is the first is  n(A) = n-1!, while the probability that Betty is last is  n(A) = n-1!

There are n! ways of making this arrangement

We have probability of A: Betty is the first person in this line

Probability of B: Mary is the last person

A U B = p(A) + p(B) - p(A ∩ B)

n(A) = n-1 that is given that Betty is the first person on the line.

then n(A) = n-1!

As the last person on the line P(B) = n-1!

Probability of (A∩B) =( n-2)!  this has Mary as the first and Betty as the last person.

Remaining students that would have to be on this line are n-2

Prob(A∪B) = n(A ∪ B)/n!

= 2(n-2)/n(n-1)

This is the theory that talks about the chances or the likelihood of an event occuring in a pair of events.

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The simplified form of -20/2(7 2/3) is -230/3.

To solve the expression -20/2(7 2/3), we need to follow the order of operations, which states that we should perform the operations inside parentheses first, then any multiplication or division from left to right, and finally any addition or subtraction from left to right.

First, let's convert the mixed number 7 2/3 to an improper fraction.

7 2/3 = (7 * 3 + 2) / 3 = 23/3

Now, let's substitute the value back into the expression:

-20/2 * (23/3)

Next, we simplify the multiplication:

-10 * (23/3)

To multiply a fraction by a whole number, we multiply the numerator by the whole number:

-10 * 23 / 3

Now, we perform the multiplication:

-230 / 3

Therefore, the simplified form of -20/2(7 2/3) is -230/3.

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Answer:

20 minutes

Step-by-step explanation:

Distance= 40 km

Speed= 120 km/h

Time= distance/speed= 40/120= 1/3 hour= 20 min

Answer:

Time = 0.33 hrs

Step-by-step explanation:

Given:

Speed = 120 km/hr

Distance = 40 km

Required :

Time = ?

Formula:

Speed = Distance/Time

Solution:

Time = Distance / Speed

Time = 40/120

Time = 0.33 hrs

Research Report:

Title: The Number of Coins Carried by Teachers

Introduction:

This research report aims to investigate the number of coins carried by teachers. The study seeks to understand the reasons behind carrying coins and whether there are any patterns or correlations between the number of coins and certain factors such as age, gender, and occupation.

The data was collected through a survey distributed among teachers from various educational institutions. The findings of this study provide insights into teachers' habits and preferences when it comes to carrying coins.

Results and Analysis:

A total of 300 teachers participated in the survey. The data revealed that the majority of teachers (60%) carry less than 5 coins, while 25% carry between 5 and 10 coins. Only a small percentage (15%) reported carrying more than 10 coins.

Further analysis based on demographic factors indicated that age and occupation had a significant influence on the number of coins carried. Older teachers were more likely to carry fewer coins, with 70% of teachers above the age of 50 carrying less than 5 coins.

Additionally, primary school teachers tended to carry more coins compared to secondary school teachers.

Discussion and Interpretation:

The findings suggest that the number of coins carried by teachers is influenced by various factors.

Teachers may carry coins for a range of reasons, such as purchasing small items, providing change for students, or utilizing vending machines.

The lower number of coins carried by older teachers could be attributed to a shift towards digital payment methods or a preference for carrying minimal cash.

The discrepancy between primary and secondary school teachers could be due to differences in daily activities and responsibilities.

This research provides valuable insights into the habits and preferences of teachers regarding the number of coins they carry.

Understanding these patterns can assist in designing more efficient payment systems within educational institutions and potentially guide the development of tailored financial solutions for teachers.

Further research could explore the reasons behind carrying coins in more depth and investigate how the digitalization of payments affects teachers' behavior in different educational contexts.

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Step-by-step explanation:

here,

let MP be x then,

SP=x-20%of X

=x - 20x/100

=x- 0.2x

=0.8x

CP= x- 30% of x

= x- 30x/100

=x- 0.3x

=0.7x

now,profit (P) = SP -CP

= 0.8x-0.7x

=0.1x

so,

P%=( P\CP ) ×100%

= (0.1x/0.7x) ×100%

= 14.28 %

It could be 400 sets of 4 digits.

combination and permutation are two different ways of grouping elements of a set into subsets. In a combination, the elements of the subset can be listed in any order The components of the subset are listed in a permutation in a certain order.

Given that: Alan is aware that the first digit is nine and the final digit is greater than five.

Optional first digit: 1 (9)

10 choices for the second digit (0 to 9)

10 choices for the third digit (9 to 9)

Optional fourth digits: 4. (6, 7, 8, 9)

Possibility of sets:

1×10×10×4 = 400

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Answer:

12

Step-by-step explanation:

Given that,

f(x) = 2x² - 3x + 7

To find the value of f ( 2.5 ), replace x with 2.5 and solve the equation.

Let us solve it now.

f(2.5) = 2(2.5)² - 3×2.5 + 7

f(2.5) = 12.5 - 7.5 + 7

f(2.5) = 12

Answer:

\(f(x) = 2 {x}^{2} - 3x + 7 \\ f(2.5) = 2 {(2.5)}^{2} - 3(2.5) + 7 \\ f(2.5) = 12.5 - 7.5 + 7 \\ \boxed{f(2.5) = 12}\)

Answer:

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

Find the slope of AB:

Use point-slope form and point A(2, 4) to determine the line:

Multiply both sides by 9 to clear fraction:

Open parenthesis and convert the equation into ax + by + c = 0:

Answer:

A. (x-5)(x-7)

B. It means the zeroes of the graph are at (5,0) and (7,0)

Step-by-step explanation:

A

find what + what equals -12, and multiples to 35.

List all multiples of 35.

1 35

5 7

- 12 is negative so that means it is -5 and -7

(x-5)(x-7)

B

The factor numbers are where the zeroes on a graph are, but whatever is in parenthesis, the number is opposite on a graph (e.g. if it was (x-3), the zero would be (3,0)

Answer:

A. (x-5)(x-7)

B. It means the zeroes of the graph are at (5,0) and (7,0)

Step-by-step explanation:

The solution for the given expression is 16.

There are different power rules, see some them:

1. Multiplication with the same base: you should repeat the base and  add the exponents.

2. Division with the same base: you should repeat the base and  subctract the exponents.

3.Power. For this rule, you should repeat the base and multiply the exponents.

4. Zero Exponent. When you have an exponent equals to zero, the result must be 1.

First, you apply the Power Rules - Power for  \((\frac{2^2x^2y}{xy^3} )^2}\). For this rule, you should repeat the base and multiply the exponents. Thus, the result will be:\(\frac{16x^4y^2}{x^2y^6}\).

After that, you should apply the  Power Rules - Division . For this rule, you should repeat the base and  subctract the exponents. Thus, the result will be:\(\frac{16x^2}{y^4}\).

Now, you should replace the variable x by 4 and the variable y by 2. Thus, the result will be:\(\frac{16*4^2}{2^4}=\frac{16*16}{16} =16*1=16\)

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An example of a boundary value problem is the Sturm-Liouville problem, which entails determining the eigenvalues and eigenfunctions of a differential equation that complies with specific boundary requirements.

The general formula for the Sturm-Liouville problem's solution in x is y(x) = a * f(x) + b * g(x), where a and b are constants and f(x) and g(x) are the differential equation's eigenfunctions. When the differential equation and boundary conditions are solved, the eigenvalues and eigenfunctions are discovered.

For instance, if the differential equation has the following form: -y" + q(x)y = lambda* w(x)y where y is the dependent variable, y" is the second derivative of y, q(x) and w(x) are functions of x, and lambda is the eigenvalue, the boundary conditions can be of the following

form: where L is the length of the interval on which the differential equation is defined, y(0) = 0, and y(L) = 0.

The general solution in x can be expressed in the form: y(x) = a * f(x) + b * g(x), where a and b are constants and f(x) and g(x) are the eigenfunctions of the differential equation. The eigenvalues and eigenfunctions can be discovered by solving this differential equation and the boundary conditions.

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