ALGEBRA 1 HW!! I WILL GIVE BRAINLYEST​

ALGEBRA 1 HW!! I WILL GIVE BRAINLYEST

Answers

Answer 1

The average rate of change of P between t = 3 and t = 5 is -18 people/hour.

A possible value of people in line at t = 6, given the average rate of change would be 50.

How to find the average rate of change ?

To find the average rate of change of P between t = 3 and t = 5, we can use the formula:

Average rate of change = (P(5) - P(3)) / (5 - 3)

From the table, we know P(3) = 85 and P(5) = 49.

Average rate of change = (49 - 85) / (5 - 3) = (-36) / 2 = -18 people/hour

To find the possible number of people at t = 6, Let P(6) = x. First, we will find the average rate of change between t = 3 and t = 6:

(P(6) - P(3)) / (6 - 3) = (x - 85) / 3

This value must be negative. Now, we will find the average rate of change between t = 5 and t = 6:

(P(6) - P(5)) / (6 - 5) = (x - 49) / 1

This value must be positive. Since (x - 49) is positive, we know that x > 49. Now we need to find a value for x that also satisfies the condition that the average rate of change between t = 3 and t = 6 is negative. Since (x - 85) / 3 is negative, we know that x < 85.

So, a possible value for P(6) is between 49 and 85. For example, we could choose P(6) = 50, which satisfies both conditions.

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Related Questions

find the sum of money that amounts to Rs- 3450 in 4 monts at the rate of 4½ %. per annam.​

Answers

Answer:

To find the sum of money that amounts to Rs- 3450 in 4 months at the rate of 4.5% per annum, we can use the formula for simple interest:

Simple Interest = (Principal * Rate * Time) / 100

Where,

Principal = the sum of money borrowed or invested

Rate = the rate of interest per annum

Time = the time period in years

Since the time period given is 4 months, we need to convert it to years by dividing it by 12:

Time = 4/12 years = 1/3 years

Now, we can plug in the given values and solve for Principal:

Simple Interest = (Principal * Rate * Time) / 100

3450 = (Principal * 4.5 * 1/3) / 100

3450 * 100 = Principal * 4.5 * 1/3

11500 = Principal * 1.5

Principal = 11500 / 1.5

Principal = 7666.67 (rounded off to two decimal places)

Therefore, the sum of money that amounts to Rs- 3450 in 4 months at the rate of 4.5% per annum is Rs- 7666.67.

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A train moves southward at 400 km/hr. How long will it take to make a 1,200 km trip?

Answers

Answer:

3 hours

Step-by-step explanation:

1200/400=3

does anyone know how to find the particular solution for this nonhomogeneous equation:
y"+3y'-3y=3xe^-1​

Answers

Using the equations, the particular solution is y_p(x)=-3x+1+2e⁻ˣ.

What are non-homogeneous differential equations?

As we already know, homogeneous equations have zero on the right side of the equation. Thus, it is said that non-homogenous differential equations are those with a function on the right side of their equation.

We are given a non-homogeneous differential equation in the form:

y′′+3y′-3y=3xe^-1​

The differential equation is called non-homogeneous because it is known to have a non-zero right-hand side.

To solve this differential equation, we first need to find the complementary function, which is the solution to the corresponding homogeneous differential equation y′′+3y′-3y=0.

We then take the first and second derivatives of y_p(x) and substitute them into the differential equation, y′′+3y′-3y=3xe^-1​ and simplify.

This leads to the system of equations:

a + 3c = 3

a + 3b - 3c = 0

a + b + 3c = 1

Solving this system of equations, we find that a=-3, b=1, and c=2. Therefore, the particular solution is y_p(x)=-3x+1+2e⁻ˣ.

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This set of equations can be solved, and the results show that a=-3, b=1, and c=2. As a result, the specific answer is [tex]y_{p(x)} =-3x+1+2e^{-x}[/tex].

What are non-homogeneous differential equations?

Homogeneous equations, as we already know, have "0" on the right side of the equation. Therefore, it is said that differential equations with a function on the right side of the equation are non-homogenous differential equations.

A non-homogeneous differential equation of the following shape is provided to us:

[tex]y^{''} +3y^{'} -3y=3xe^{-1}[/tex]

Since the right-hand side of the differential equation is known to be non-zero, it is referred to as non-homogeneous.

Finding the complementary function, which is the answer to the related homogeneous differential equation [tex]y^{''} +3y^{'} -3y=0[/tex], is the first step in solving this differential equation.

The differential equation [tex]y^{''} +3y^{'} -3y=3xe^{-1}[/tex] is then simplified by taking the first and second derivatives of [tex]y_{p(x)}[/tex] and substituting them into

the equation.

This results in the formulae system:

a + 3c = 3

a + 3b - 3c = 0

a + b + 3c = 1

This set of equations can be solved, and the results show that a=-3, b=1, and c=2. As a result, the specific answer is  [tex]y_{p(x)} =-3x+1+2e^{-x}[/tex].

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Seven different single-digit numbers are written in the circles of the diagram shown with one number in each circle. The product of the three numbers in each of the three lines of three numbers is the same. Which number is written in the circle containing the question mark?​

Answers

Answer:

Without an image or a more detailed description of the diagram, it's difficult to provide an exact answer to this problem. However, we can use some logical reasoning to try to solve it.

Let's assume that the three lines of three numbers are arranged in a Tic-Tac-Toe grid, like this:

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A B C

D E F

G H I

We know that the product of the three numbers in each line is the same. Let's call this product "P". Then we can write:

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A * B * C = P

D * E * F = P

G * H * I = P

If we divide the second equation by the first equation, we get:

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(D * E * F) / (A * B * C) = 1

Since all the numbers are single-digit, this means that either D or F is equal to A, B, C, or 1. If D or F is equal to 1, then E is also equal to 1, which means that the entire middle row is filled with 1s, and that cannot be the case since all the numbers are different.

Therefore, we can assume that either D or F is equal to one of the numbers in the top row. Without further information, we cannot determine which one it is, but we know that the product of the numbers in the bottom row must be divisible by the product of the numbers in the top row. This means that the number in the circle containing the question mark must be a factor of this product, and it must be different from all the other numbers in the diagram.

Again, without more information, we cannot determine the exact number in the circle containing the question mark, but this logic should help narrow down the possibilities.

Step-by-step explanation:

13. Higher Order Thinking Name two rays with the same endpoint in the figure below. Do they form an angle? Explain.

Answers

The two rays with the same endpoint in the figure below are AB and BC. Although they share a common endpoint (B), they do not form an angle since they are collinear and lie on the same line. Two non-collinear rays that share an endpoint create an angle. In this case, AB and BC lie on line AC and do not form an angle.


An angle is formed by two rays that originate from a common endpoint. In the given figure, AB and BC share the same endpoint (B), but they do not form an angle since they lie on the same line. A line is an infinite set of points that extends in both directions, while a ray is a portion of a line that starts at a particular point and extends infinitely in one direction. When two rays share a common endpoint, they form an angle only if they are not collinear, i.e., they do not lie on the same line. In this case, since AB and BC lie on line AC, they do not form an angle. Therefore, AB and BC are collinear and do not form an angle.

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Can you solve this question?
A) f'(x)=?
B) slope at x=2: ?
slope at x=3: ?
C) tangent line at x=2: y= ?
tangent line at x=3: y= ?
D) value(s) of x=?

Answers

A. The derivative of f'(x) = 26x + 5is 26x + 5

B. Slope at x = 2 is 57

Slope at x = 3 is 83

c. The equation of the tangent line at x = 3 is y - 122 = 83(x - 3), or y = 83x - 179.

D. The value of x where the tangent line is horizontal is x = -5/26.

How to calculate the value

(A) f'(x) = 26x + 5.

It should be noted that to find the derivative of f(x), we apply the power rule and the constant multiple rule:

f'(x) = d/dx (13x²+5x)

= d/dx (13x²) + d/dx (5x)

= 26x + 5

(B) ain this case, to find the slope of the graph of f(x) at x = 2 and x = 3, we plug these values into the derivative:

Slope at x = 2: f'(2) = 26(2) + 5 = 57

Slope at x = 3: f'(3) = 26(3) + 5 = 83

(C) Based on the information, to find the equation for the tangent line at x = 2 and x = 3, we use the point-slope form of a line:

Tangent line at x = 2:

We know the slope is 57, and the point (2, f(2)) is on the line.

Plugging in x = 2 to f(x) gives us f(2) = 13(2)² + 5(2) = 58.

So the equation of the tangent line at x = 2 is y - 58 = 57(x - 2), or y = 57x - 56.

Tangent line at x = 3:

We know the slope is 83, and the point (3, f(3)) is on the line.

Plugging in x = 3 to f(x) gives us f(3) = 13(3)² + 5(3) = 122.

So the equation of the tangent line at x = 3 is y - 122 = 83(x - 3), or y = 83x - 179.

D. In order to find where the tangent line is horizontal, we need to find where the slope is equal to zero. Setting f'(x) = 0 and solving for x gives:

f'(x) = 26x + 5 = 0

x = -5/26

Therefore, the only value of x where the tangent line is horizontal is x = -5/26.

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The acceleration, in feet per second per second, of an object is given by the acceleration function a(t)=2sint+1. The initial velocity is v(0)=0 and the initial position is s(0)=3. Find the equation of the velocity function. Find the position function and the average value of the position function from time t = 2 seconds to t = 5 seconds. Show all your work.

Help pls

Answers

Using the derivative of the velocity, the average value of the position function from t = 2 seconds to t = 5 seconds is 14.5.

What is the position and average value of the position function from t = 2 to t = 5?

Given:

Acceleration function, a(t) = 2sin(t) + 1

Initial velocity, v(0) = 0

Initial position, s(0) = 3

To find:

Velocity function, v(t)

Position function, s(t)

Average value of the position function from t = 2 seconds to t = 5 seconds

Solution:

We know that acceleration is the derivative of velocity, and velocity is the derivative of position. So we can find the velocity and position functions by integrating the acceleration function.

Velocity function:

[tex]v(t) = \int a(t) dt\\v(t) = \int (2sin(t) + 1) dt\\v(t) = -2cos(t) + t + C1[/tex]

We know that the initial velocity, v(0) = 0. Substituting this value in the above equation, we get:

[tex]0 = -2cos(0) + 0 + C1\\C1 = 2[/tex]

Therefore, the velocity function is:

[tex]v(t) = -2cos(t) + t + 2[/tex]

Position function:

[tex]s(t) = \int v(t) dt\\s(t) = \int (-2cos(t) + t + 2) dt\\s(t) = 2sin(t) + \frac{1}{2} t^2 + 2t + C2[/tex]

We know that the initial position, s(0) = 3. Substituting this value in the above equation, we get:

[tex]3 = 2sin(0) + 0 + 0 + C2\\C2 = 3\\[/tex]

Therefore, the position function is:

[tex]s(t) = 2sin(t) + \frac{1}{2} t^2 + 2t + 3[/tex]

Average value of the position function from t = 2 seconds to t = 5 seconds:

We can find the average value of the position function using the following formula:

[tex]Avg = (1/(b-a)) * \int(a,b) f(t) dt[/tex]

Here, a = 2 and b = 5. So, substituting the values in the above formula, we get:

[tex]Avg = (1/(5-2)) * \int(2,5) (2sin(t) + \frac{1}{2} t^2 + 2t + 3) dt\\Avg = \frac{1}{3} * [ -2cos(t) + 1/6 t^3 + t^2 + 2t ] \eval(2,5)\\[/tex]

[tex]Avg = \frac{1}{3} * [ (-2cos(5) + 1/6 (5^3) + 5^2 + 25) - (-2cos(2) + 1/6 (2^3) + 2^2 + 22) ]\\Avg = 14.5[/tex]

Therefore, the average value of the position function from t = 2 seconds to t = 5 seconds is 14.5.

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Please answer fast!!

Answers

Answer:

Look at the green dot

Step-by-step explanation:

Average movie prices in the United States​ are, in​ general, lower than in other countries. It would cost ​$78.50 to buy three tickets in Japan plus two tickets in Switzerland. Three tickets in Switzerland plus two tickets in Japan would cost ​$74.10. How much does an average movie ticket cost in each of these​ countries?

Answers

The average movie ticket cost in Switzerland and Japan each of these​ countries is 46.97.

Let's assume that the average cost of a movie ticket in Japan is x, and the average cost of a movie ticket in Switzerland is y.

According to the problem statement, we can write two equations based on the given information:

3x + 2y = 78.5 ...(1)

2x + 3y = 74.1 ...(2)

We can solve these equations simultaneously to find the values of x and y. Here's how:

Multiply equation (1) by 2 and equation (2) by 3, then subtract equation (1) from equation (2):

(2x + 3y) - 2(3x + 2y) = 74.1 - 2(78.5)

Simplifying this equation, we get:

-y = -109.3

Therefore, y = 109.3.

Now substitute y = 109.3 into either equation (1) or (2) and solve for x:

3x + 2(109.3) = 78.5

Simplifying this equation, we get:

3x = -140.9

Therefore, x = -46.97.

However, we cannot have negative ticket prices.

Therefore, the average cost of a movie ticket is 46.97.

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which of the statements is true for the two division problems below? A: (x^2-3x-18)÷(x-6) or B: (x^3-x^2-5x-3)÷(x^2+2x+1)

A equals (x+3) and b equals (x-3)
A and b both equal (x+3)
a and b both equal (x-3)
a equals (x-3) and b equals (x+3)​

Answers

A equals (x+3) and b equals (x-3) the statement that is true for the two division problems is that a equals factor (x+3) and b equals (x-3).

For the first division problem, [tex](x^2-3x-18)[/tex]÷(x-6), the quotient is (x+3). To solve for the quotient, you first need to factor the numerator, which is (x-6)(x+3). Then, you need to divide the numerator by the denominator, which is (x-6). The quotient is (x+3). For the second division problem, [tex](x^3-x^2-5x-3)/(x^2+2x+1)[/tex], the quotient is (x-3). To solve for the quotient, you first need to factor the numerator, which is (x+1)(x-3). Then, you need to divide the numerator by the denominator, which is [tex](x^2+2x+1)[/tex]. The quotient is (x-3). Therefore, the statement that is true for the two division problems is that a equals (x+3) and b equals (x-3).

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help me please i need help im fsilinh

Answers

Answer:

b. 1/4

Step-by-step explanation:

Probability of rolling even number = 3/6 = 1/2

Probability of tails = 1/2

Multiplying these two probabilities, we have 1/4.

Is 2 x5/8 the same of 10 x1/8​

Answers

Answer:

Step-by-step explanation:

[tex]2\times \frac{5}{8} = \frac{2}{1} \times\frac{5}{8}= \frac{10}{8}[/tex]

[tex]10\times \frac{1}{8} =\frac{10}{1} \times \frac{1}{8}= \frac{10}{8}[/tex]

So yes they are the same.

Suppose that f(4)=2, g(4)=5, f'(4)=6, g'(4)=-3, f'(5)=8, and g'(2)=10.
Find h'(4) where
(a) h(x)=f(x)g(x)
(b) h(x)= g(x)/f(x)+g(x)
(c) h(x)=f(g(x))
please help

Answers

(a) Using the product rule for h(x) = f(x)g(x), h'(4) = 24

(b) Using the quotient rule, for h(x) = g(x) / (f(x) + g(x)), h'(4) = -33/49.

(c) Using chain rule for h(x) = f(g(x)), h'(4) = 80.

What is the solution of the functions?

We can use the product rule, quotient rule, and chain rule to find the derivatives of the functions h(x).

(a) h(x) = f(x)g(x)

Using the product rule, we have:

h'(x) = f'(x)g(x) + f(x)g'(x)

At x = 4, we have:

h'(4) = f'(4)g(4) + f(4)g'(4) = 6(5) + 2(-3) = 24

Therefore, h'(4) = 24.

(b) h(x) = g(x) / (f(x) + g(x))

Using the quotient rule, we have:

h'(x) = [g'(x)(f(x) + g(x)) - g(x)f'(x)] / (f(x) + g(x))^2

At x = 4, we have:

h'(4) = [g'(4)(f(4) + g(4)) - g(4)f'(4)] / (f(4) + g(4))^2

= [(-3)(2 + 5) - 5(6)] / (2 + 5)^2

= -33 / 49

Therefore, h'(4) = -33/49.

(c) h(x) = f(g(x))

Using the chain rule, we have:

h'(x) = f'(g(x))g'(x)

At x = 4, we have:

h'(4) = f'(g(4))g'(4)

= f'(5)(10)

= 8(10)

= 80

Therefore, h'(4) = 80.

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Riley is dividing a batch of 7 1/2 cups of salsa into equal servings that are 3/4 cup each. Select all of the expressions that can be used to find the number of servings Riley will have.

Answers

Thus, from the all given expressions, the number of servings Riley will ve using is 15/2 ÷  3/4.

Explain about the mixed fraction?

Once kids have a firm grasp on proper fractions, they are introduced to mixed numbers and incorrect fractions. A mixed number combines an integer (whole number) and a fraction. It is also sometimes referred to as a mixed fraction (part of a whole number).

The composite number's fractional component needs to be a legal fraction (less than one whole). The numerator (top number) of a correct fraction is less than its denominator (bottom number),

Given data:

Total batch of cup of salsa = 7 1/2Serving cup size = 3/4 each cup

Convert the mixed fraction 7 1/2 in the proper fraction:

= 7 1/2

= (7*2 + 1)/2

= 15/2

Number of serving cups =  Total amount of salsa / Serving cup size

Number of serving cups =  15/2 ÷  3/4

Thus, from the all given expressions, the number of servings Riley will ve using is 15/2 ÷  3/4.

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Complete question:

Riley is dividing a batch of 7 1/2 cups of salsa into equal servings that are 3/4 cup each. Select all of the expressions that can be used to find the number of servings Riley will have.

2/15 ÷ 3/415/2 ÷  3/42/15 ÷  4/515/2 ÷  4/315/2 ÷  3/4

solve the equation 25a=10a squared

Answers

Answer: The answer is [tex]\frac{5}{2}[/tex].

Step-by-step explanation:

We are given

25a = 10[tex]a^{2}[/tex].

First, we divide both sides by a

25 = 10a

Then we divide both sides by 10

[tex]\frac{5}{2}[/tex] = a

3. In triangle ABC, 4A is a right angle, and m<B = 45°. What is the length of BC? If your answer is not an integer, leave it in simplest radical form.

A. 18 ft.
B. 18√2
C. 18√3
D. 36
what is the answer? thank you​

Answers

Option B is correct, check the diagram below, the question has been solved.. if you need an online tutor, please let me know +2347047917708

Find the vertex and the

x​- and

y​-intercepts of the equation

=

2

2


8
y=x
2
−2x−8
Then, use the points to graph the parabola.

a) What is the vertex of the parabola? Enter your answer as an ordered pair.
Vertex
Preview

​b) Identify the

x​-intercept(s) of the parabola. Enter your answers as ordered pairs. Use a comma to separate answers as needed. If there are none, enter
None
None​.

x-intercept
Preview

​c) Identify the

y​-intercept of the parabola. Enter your answer as an ordered pair.

y-intercept
Preview

d) Use the points you found to graph the parabola.

Answers

Answer:

Step-by-step explanation:

As seen in earlier sections, the process of completing the square is a useful tool in finding noninteger values of quadratic equations, especially intercepts. When a quadratic equation of the

form f (x) = ax2

+ bx + c is put through the process of completing the square it yields an

equation of the form f (x) = a(x – h)2

+ k . The conversion of the equation to this form will

yield critical information about the equation’s characteristics before you begin to graph it.

1.) The value of h is the distance left (if negative) or right (if positive) the graph

translates from the standard position.

2.) The value of k is the distance up (if positive) or down (if negative) the graph

translates from the standard position.

3.) The values of h and k, when put together as an ordered pair, give the vertex i.e.

(h, k).

4.) The equation x = h is the formula for the axis of symmetry.

The following example demonstrates how to find the following critical information of the

equation:

a.) vertex

b.) axis of symmetry

c.) y intercept (if any)

d.) x intercepts (if any)

Example 1: Find the vertex, axis of symmetry, x-intercept(s), and y-intercept and gr

In a recent year and author wrote 191 check, use the poisson distribution to find the probability that on a random select today he wrote at least one check

Answers

The probability that on a random select today he wrote at least one check is 0.407

How to solve

Let X be the no.of checks the author wrote in a day

   Average,

u = 191 checks per year

191/365                        

= 0.5233/ day

       X~Poisson ( u- 0.5233)

The p.m.f of X is given by

P(X=x) =

The probability​ that, on a randomly selected day, he wrote at least one check = P(

               = 1 - P( X < 1)

               = 1 - P(X=0)

               = 1 - e^-0.5233 x 0.5233^0/0!

               = 1 - e^-0.5233 x 1/

               = 1 - 0.59256

               = 0.407

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Roman opened a savings account and started out the account with $45. He adds $18 each month. He currently has $207 in his account. How many months has he been saving?​

Answers

Answer:

9

Step-by-step explanation: each month adding 18 starting at 45 and currently at 207 means he gained 162 and divided by 18,9 months.

Three students need to produce a prime factorization of
48. Donna states that the first factors in the tree should
be 6 and 8. Larry states that the first factors in the tree
should be 4 and 12. Trish states that the initial factors of
48 do not affect the prime factorization. Explain why Trish
is correct.

Answers

Answer:

students need to produce a prime factorization of 48. Donna states that the first factors in the tree should be 6 and 8. Larry states that the first factors in the tree should be 4 and 12. Trish states that the initial factors of 48 do not affect the prime factorization. Explain why Trish is correct.Trish is correct because the initial factors of 48 do not affect the prime factorization. Prime factorization is the process of breaking down a composite number into its prime factors. The prime factors of a number are those factors that are prime numbers. The prime factorization of 48 is 2 x 2 x 2 x 2 x 3, which means that 48 can be expressed as a product of these prime factors. The order in which we choose the initial factors to start the prime factorization does not affect the result, as long as we continue to break down the resulting factors into their prime factors until we cannot break them down any further. Therefore, Trish is correct that the initial factors of 48 do not affect the prime factorization.

Trish is correct because the prime factorization of 48 will be the same regardless of which factors are chosen as the initial factors in the tree.

To see why, let's look at the prime factorization of 48:

48 = 2 × 2 × 2 × 2 × 3

No matter which factors are chosen as the initial factors, the same prime factors will eventually be found.

For example, if Donna's method is used, we could start with 6 and 8:

6 = 2 × 3

8 = 2 × 2 × 2

Then we could continue to factor each of these numbers until we reach prime factors:

6 = 2 × 3

8 = 2 × 2 × 2

= 2 × 2 × 2 × 3

= 2³ × 3

Now we have found all of the prime factors of 6 and 8, and we can combine them to get the prime factorization of 48:

48 = 2 × 2 × 2 × 2 × 3

If Larry's method is used, we could start with 4 and 12:

4 = 2 × 2

12 = 2 × 2 × 3

Then we could continue to factor each of these numbers until we reach prime factors:

4 = 2 × 2

12 = 2 × 2 × 3

= 2² × 3

Now we have found all of the prime factors of 4 and 12, and we can combine them to get the prime factorization of 48:

48 = 2 × 2 × 2 × 2 × 3

As we can see, the same prime factors are found regardless of which factors are chosen as the initial factors in the tree. Therefore, Trish is correct that the initial factors of 48 do not affect the prime factorization.

You have a 1
-gallon paint can in the shape of a cylinder. One gallon is 231
cubic inches. The radius of the can is 3
inches. What is the approximate height of the paint can? Use 3.14
for pi.

Answers

Answer:

Step-by-step explanation:

Sin ² 20 +Sin² 40° +Sin ²80 simplify​

Answers

Answer:

The answer is 1.5

Step-by-step explanation:

You just calculate in calculator and you will get the answer as 1.5

If an item has an original price of $90 and has been discounted 30%, what is the sale price

Answers

Answer: 63 US$

Step-by-step explanation:

Circular sector with a radius of 12 inches and a central angle of 120 degrees​

Answers

Answer:

hope this helps

Step-by-step explanation:

simplify 300/25 fraction with steps

Answers

300/25

Divided by 5

60/5

Divided by 5

12/1

Following the basic principles and theory of simplifying fraction it is visible that this question follows the, the basic calculations involving the basic mathematics

Therefore the , let us take the given numerator that is 300 and then divide it using the denominator that is 25 ,

so, when we divide 300 /25 we get, the answer as12

because, when we divide both the numerator and denominator with 5 (because 25 and 300 are a divisible by 5 and are also multiples of )

we clearly see that 300 is divisible by 5 and the answer comes out to be 12.

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The ratio of monthly income to the monthly saving of a family is 9:2. If the
saving is Rs 4,320, find the income and expenditure of the family.

Answers

Step-by-step explanation:

Let's assume that the monthly income of the family is x.

From the problem statement, we know that the ratio of monthly income to the monthly saving is 9:2.

Therefore, we can write:

x/4320 = 9/2

To solve for x, we can cross-multiply:

2x = 9*4320

2x = 38,880

x = 19,440

So, the monthly income of the family is Rs 19,440.

To find the monthly expenditure, we can subtract the monthly savings from the monthly income:

Monthly expenditure = Monthly income - Monthly saving

Monthly expenditure = 19,440 - 4,320

Monthly expenditure = 15,120

Therefore, the monthly expenditure of the family is Rs 15,120

Please see the attached

Answers

A restaurant borrows $15,700 for two months from a nearby bank. For this loan, the neighbourhood bank charges simple interest at a yearly rate of 10%. Suppose a month is one-twelfth of a year.

a) $218.06 in interest will be due after two months.

b) In the event that the restaurant doesn't pay, the balance due after two months is $15,918.06.

a) To find the interest that will be owed after 2 months, we first need to calculate the monthly interest rate:

r = (10%)/12 = 0.00833333...

We can use the formula for simple interest to find the interest owed:

I = Prt

where P is the principal (the amount borrowed), r is the interest rate per period, and t is the time in periods. Since the loan is for 2 months, we have t = 2/12 = 1/6 years.

Substituting the values, we get:

I = 15700 * 0.00833333... * (1/6) = 218.0555...

Rounding to the nearest cent, the interest owed after 2 months is $218.06.

b) The total amount owed after 2 months is the sum of the principal and the interest. Using the same values as above, we have:

The total amount owed = Principal + Interest

= 15700 + 218.0555...

= 15918.0555...

Rounding to the nearest cent, the amount owed after 2 months is $15,918.06.

The complete question is:-

A restaurant borrows $15700 from a local bank for 2 months. the local bank charges simple interest at an annual rate of 10% for this loan. assume each month is 1/12 of a year. answer each below. do not round any intermediate computations, and round your final answers to the nearest cent, if necessary, refer to the lists of financial formulas.

a) find the interest that will be owed after 2 months.

b) assuming the restaurant doesn't make any payments, find the amount owed after 2 months.

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The mean per capita income is 21,699
dollars per annum with a standard deviation of 835
dollars per annum.

What is the probability that the sample mean would be less than 21583
dollars if a sample of 399
persons is randomly selected? Round your answer to four decimal places.

Answers

The probability that the sample mean would be less than 21583 dollars if a sample of 399 persons is randomly selected is approximately 0.0826 or 8.26% (rounded to four decimal places).

What is probability?

Probability is a way to gauge how likely something is to happen. It is a number between 0 and 1, where 0 denotes an impossibility and 1 denotes a certainty that the occurrence will occur.

We can use the central limit theorem (CLT) to approximate the sampling distribution of the sample mean. According to CLT, if we have a large enough sample size (n≥30), the sampling distribution of the sample mean will be approximately normal, regardless of the underlying distribution of the population.

The mean of the sampling distribution of the sample mean is the same as the population mean, which is given as μ = 21699 dollars per annum. The standard deviation of the sampling distribution of the sample mean is equal to the standard error of the mean (SEM), which is calculated as follows:

SEM = σ/√n, where n is the sample size, and is the total standard deviation.

With the numbers from the problem substituted, we obtain:

SEM = 835/√399 = 41.767

Now, we need to find the probability that the sample mean would be less than 21583 dollars. We can standardize the sample mean using the standard normal distribution as follows:

z = (x - μ) / SEM, where the sample mean is x.

Substituting the values, we get:

z = (21583 - 21699) / 41.767 = -1.389

Using a standard normal distribution table, we can find that the area to the left of z=-1.389 is 0.0826.

Therefore, the probability that the sample mean would be less than 21583 dollars if a sample of 399 persons is randomly selected is approximately 0.0826 or 8.26% (rounded to four decimal places).

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area of a triangle vertices are (-3,1), (1,1) and (1,4)

Answers

The area of the triangle is 3 square units whose vertices are (-3,1), (1,1) and (1,4). We will use distance formulae in this question.

To find the area of a triangle whose vertices are (-3,1), (1,1), and (1,4), we can use the formula for the area of a triangle:

Area = 1/2 * base * height

where the base and height are perpendicular and are formed by any two sides of the triangle.

To apply this formula, we can choose the line segment between (1,1) and (1,4) as the base of the triangle, since it is a vertical line and therefore has a length equal to the height of the triangle. The length of this line segment is 4 - 1 = 3 units.

Next, we need to find the length of the perpendicular segment from the point (-3,1) to the line containing the base. To do this, we can use the formula for the distance between a point and a line:

distance = [tex]|ax + by + c| / \sqrt{(a^2 + b^2)[/tex]

where a, b, and c are the coefficients of the equation of the line and x, y are the coordinates of the point.

In this case, the equation of the line containing the base is x = 1, so a = 1, b = 0, and c = -1. Plugging in the coordinates of (-3,1), we get:

distance = [tex]|1*(-3) + 0*(1) - 1| / \sqrt{(1^2 + 0^2)} = 2[/tex]

Therefore, the height of the triangle is 2 units.

Finally, we can plug these values into the formula for the area of a triangle to get:

Area = 1/2 * base * height = 1/2 * 3 * 2 = 3

So the area of the triangle is 3 square units.

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a bakery has 3 types of pie.. apple, cherry, and peach. there are 4 times as many apple pie as peach pie. what is a possible percentages for each type of pie

Answers

Answer:

Apple Pie = 66.67%

Cherry Pie = 16.67%

Peach Pie = 16.67%

A possible distribution of pie percentages could be 66.67% apple, 16.67% cherry, and 16.67% peach.

Step-by-step explanation:

Let's assume that the bakery has 1 peach pie. Then, according to the problem statement, the bakery has 4 apple pies.

So, the total number of pies is 1 + 4 + 1 = 6.

To find the percentage of each type of pie, we need to divide the number of each type of pie by the total number of pies and multiply by 100%.

Percentage of apple pies: (4/6) x 100% = 66.67%

Percentage of cherry pies: (1/6) x 100% = 16.67%

Percentage of peach pies: (1/6) x 100% = 16.67%

Therefore, a possible distribution of pie percentages could be 66.67% apple, 16.67% cherry, and 16.67% peach.

It is important to note that this is just one possible distribution based on the information given in the problem. If we were given different information, such as the total number of pies, the percentages could be different.

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