We can **estimate** that there are approximately 134 glass beads in the bin.

**What is probability?**

Probability is a measure of the likelihood of an event **occurring**.

To estimate the number of glass beads in the bin, we can use the **proportion** of glass beads in the handful that Jasper selected.

There are 15 beads in the handful, and 4 of **them** are glass. So, the proportion of glass beads in the handful is:

4/15 ≈ 0.267

We can assume that the proportion of glass beads in the bin is similar to the proportion in the handful. Therefore, we can **estimate** the number of glass beads in the bin as

0.267 x 500 ≈ 134

Therefore, we can estimate that there are approximately 134 glass beads in the bin.

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Lastly, let’s consider the alternative method of paying for college: paying with loans. You take out a loan in the amount of your tuition and fees cost for 5 years rounded up to the nearest thousand dollars (for example if the total cost is $55,787 the loan would be for $56,000). The loan has a monthly interest rate of 0.25% and a monthly payment of $250. How long will it take you to pay off the loan? Use the formula N= (-log(1-i*A/P))/(log(1+i)) to determine the number of months it will take you to pay off the loan. Let N represent the number of monthly payments that will need to be made, i represent the interest rate in decimal form, A represent the amount owed (total amount of the loan), and P represent the amount of your monthly payment. Be sure to show your work for all calculations made.

With given** compound interest**, it will take 27.25 years to pay off the loan.

**What is Compound interest?**

Compound interest is the addition of interest to the **principal **sum of a loan or deposit, or in other words, the interest that is earned on both the principal amount and any previously accumulated interest. In other words, it is interest that is calculated not only on the original amount of money but also on any interest that has been earned previously. This can result in significant growth of an investment or loan balance over time, as the interest earned on the accumulated interest can compound exponentially. Compound interest can be calculated using a specific formula that takes into account the principal amount, the interest rate, and the compounding frequency.

Now,

First, we need to calculate the total **amount **of the loan. We round up the tuition and fees cost for 5 years to the nearest thousand dollars:

Total cost = $70,000

Rounded up to nearest thousand = $70,000

So, the amount of the loan is $70,000.

Next, we can use the formula N= (-log(1-i*A/P))/(log(1+i)) to calculate the number of monthly payments needed to pay off the **loan**.

N = (-log(1-0.0025*70000/250))/(log(1+0.0025))

N = (-log(1.75))/(log(1.0025))

N = 326.45

Rounding up to the nearest whole number, it will take 327 **monthly payments **to pay off the loan.

So, it will take 327/12 = 27.25 years to pay off the loan.

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Please help me solve and show my work

The **degree** measure of the **angles** are;

1. 5π/3 = 300°

2 3π/4 = 135°

3. 5π/6 = 150°

4. -3π/2 = 90°

What is degree and radian?A **degree** is a unit of measurement which is used to measure circles, spheres, and angles while a radian is also a unit of measurement which is used to measure **angles**.

A circle has 360 **degrees** which are its full area while its **radian** is only half of it which is 180 degrees or one pi **radian**.

therefore π = 180°

1. 5π/ 3 = 5×180/3 = 300°

2. 3π/4 = 3× 180/4 = 540/4 = 135°

3. 5π/6 = 5×180/6 = 150°

4. - 3π/2 = -3 × 180/2 = -270° = 90°

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please answer in detail

**Answer:**

AB: y = 2x + 4

**Step-by-step explanation:**

Line AB is parallel to the line y = 2x + 3

When 2 lines are parallel they have the same coefficient of x.

=> AB: y = 2x + m (1)

Because line AB passes through the point (0, 4)

Replace x = 0; y = 4 into (1) => 2 × 0 + m = 4 => m = 4

So AB: y = 2x + 4

You can afford a $1000 per month mortgage payment. You've found a 30 year loan at 5.3% interest.

a) How big of a loan can you afford? (Round to the nearest cent, as needed.)

$

b) How much total money will you pay the loan company? (Round to the nearest cent, as needed.)

$

c) How much of that money is interest? (Round to the nearest cent, as needed.)

**Answer:**

a) To find out how big of a loan you can afford, we can use the formula for the monthly payment of a mortgage:

M = P [ i(1 + i)^n ] / [ (1 + i)^n - 1 ]

where M is the monthly payment, P is the principal (the amount borrowed), i is the monthly interest rate (which is the annual interest rate divided by 12), and n is the number of monthly payments (which is the number of years times 12).

In this case, we know that M = $1,000, i = 0.053/12, and n = 30 x 12 = 360. We want to solve for P, the principal we can afford.

Substituting these values into the formula, we get:

$1,000 = P [ 0.004416(1 + 0.004416)^360 ] / [ (1 + 0.004416)^360 - 1 ]

Simplifying and solving for P, we get:

P = $183,928.72

Therefore, you can afford a loan of approximately $183,928.72.

b) The total money paid to the loan company will be the monthly payment multiplied by the number of payments over the life of the loan. In this case, we have:

Total money paid = $1,000 x 360 = $360,000

Therefore, the total amount of money paid to the loan company will be $360,000.

c) To find out how much of that money is interest, we can subtract the principal from the total amount paid. In this case, we have:

Interest paid = Total money paid - Principal = $360,000 - $183,928.72 = $176,071.28

Therefore, the amount of money paid in interest will be $176,071.28.

Suppose that the function h is defined as follows.

if

-2

-1

h(x)= 0

1

2

Graph the function h.

-3.5
if-2.5
if-1.5
if -0.5
if 0.5 ≤x≤1.5

+

X

Ś

The required **graph **of the function given; h (x) has been attached.

In mathematics, graph theory is the study of graphs, which are mathematical structures used to represent pairwise interactions between objects. In this definition, a network is made up of nodes or points called **vertices** that are connected by edges, also called links or **lines**. In contrast to directed graphs, which have edges that connect two vertices asymmetrically, undirected graphs have edges that connect two vertices symmetrically. Graphs are one of the primary areas of study in discrete mathematics.

Here as per the question the graph of the function, h (x) has been attached.

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PLEASE HELP

Find the Area

2cm

___cm^2

**Answer:**

3.14 cm^2

**Step-by-step explanation:**

1. Find radius:

If diameter is 2, divide it by 2 to get radius = 1

2. Find formula:

A=πr^2

3. Plug in:

A = π(1)^2

4. Solve (multiply):

A = π(1)^2:

3.14159265359

Or

3.14 cm^2

**Answer:**

3.14 cm^2

**Step-by-step explanation:**

A=[tex]\pi[/tex]r^2

r=2

2/2=1

A=[tex]\pi[/tex](1)^2

=[tex]\pi[/tex]1

≈3.14x1

≈3.14cm^2

Which geometric term describes ∠ T A G ?

**Answer:**

angle

**Step-by-step explanation:**

since there is a < sign, that makes it an angle. I'm not sure if that is the whole problem, or if It is missing a picture. Hope this helps!

**Answer: i know it is acute**

if f(x)= -3, then f'(x)=?

**Answer:**

0

**Step-by-step explanation:**

0

Find the surface area. Round to the nearest hundredth

**Answer:**

122.30 cm²

**Step-by-step explanation:**

Divide the polyhedron into shapes:

+) 2 triangles with the same area.

The area of the triangle is

(4.3×11)÷2 = 23.65 cm².

And with two triangles of the same area we take the sum of both areas

23.65 + 23.65 = 47.3 cm²

+) 3 rectangles with different areas.

(3×6) + (3×8) + (3×11) = 75 cm²

So the surface area is the sum of areas of the triangles and rectangles

47.3 + 75 = 122.3 = 122.30 cm²

Triangle PQR is drawn with coordinates P(0, 2), Q(0, 5), R(1, 4). Determine the translation direction and number of units if R′(−7, 4).

8 units down

8 units up

8 units to the right

8 units to the left

It follows that the **translation** direction is 8 units to the left and 0 units up or down.

A translation is a geometric change in** Euclidean geometry **where each point in a figure, shape, or space is moved uniformly in one direction. A translation can either be thought of as moving the** origin **of the coordinate system or as adding a constant vector to each point

The new vertices of a triangle with vertex locations of (0,0), (1,0), and (0,1), for instance, would be (2,3, (3,3), and (2,4) if the triangle were translated 2 units to the right and 3 units up.

We can use the following procedures to get the translation direction and number of units for R′(7, 4):

1. Determine the difference between R and R′'s x-coordinates: −7 − 1 = 8

2. Determine the difference between R and R′'s y coordinates: 4 − 4 = 0

It follows that the translation direction is 8 units to the left and 0 units up or down.

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Given the expression 3x+2 evaluate the expression for the given values of x when x=(-2)

**Answer:**

...............................

Answer:

The answer is -4.

Explanation:

First, plug the value of x in.

3(-2)+2

Then, multiply 3 and -2 since they are next to each other and order of operations PEMDAS tells you to multiply first.

-6+2

Lastly, add -6 and 2 to get -4.

The answer is -4.

Explanation:

First, plug the value of x in.

3(-2)+2

Then, multiply 3 and -2 since they are next to each other and order of operations PEMDAS tells you to multiply first.

-6+2

Lastly, add -6 and 2 to get -4.

2. Mrs. Cooper created a triangular shaped vegetable garden and needs to put down fertilizer to cover the space. If the garden has a base of 8m and a height of 10m, how much fertilizer will she need?

**Answer:**

40 m²

**Step-by-step explanation:**

**Area of triangle:**

To find the area of triangle, multiply the base and area and then divide it by 2.

base = b = 8 m

height = h = 10m

[tex]\boxed{\bf Area \ of \ triangle = \dfrac{1}{2}*b*h}[/tex]

[tex]= \dfrac{1}{2}*8 * 10\\\\= 4 * 10\\\\= 40 \ m^2[/tex]

1. You go to the ice cream shop with your friends and you can choose an ice cream, a topping

and sprinkles. How many different sundaes can you make when you order one flavor of ice

cream, one topping and one color of sprinkles from the chart below? Show all possible

outcomes in a tree diagram.

Ice Cream

Chocolate

Vanilla

Strawberry

Topping

Fudge

Marshmallow

Sprinkles

Chocolate

Rainbow

a. How many sample spaces are there? HINT: How many possible combinations?

b. P (Chocolate, Fudge, Rainbow)

A. There are 9 **sample spaces.**

B. The **probability** of choosing Chocolate, Fudge, and Rainbow is 1/9

**What is meant by sample spaces?**

In probability theory, a sample space is the set of all **possible** outcomes of a **random** experiment or process. It is used to define the space of events and calculate probabilities.

**What is meant by probability?**

Probability is a **measure** of the likelihood of an event occurring, expressed as a number between 0 and 1, where 0 indicates impossibility and 1 indicates certainty. It is **calculated** by dividing the number of favourable outcomes by the total number of possible outcomes.

**According to the given information**

A. There are 9 possible combinations (3 ice cream flavors x 3 toppings x 1 sprinkle color), so there are 9 sample spaces.

B. The probability of choosing Chocolate, Fudge, and Rainbow is 1/9, assuming all combinations are equally likely.

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Which graph represents the hyperbola x2/52-y2/42 = 1?

For the given **equation** we have horizontal length of 5 and vertical width of 4 units. The graph that depicts this **hyperbola** is: Option B.

A hyperbola is a particular kind of **conic section** in mathematics, which is a curve created by the intersection of a cone and a plane. The collection of all points in a plane that have a constant difference between them and two **fixed points**, known as the foci, is referred to as a hyperbola. The distance between the foci is referred to as this consistent difference and is represented by the symbol 2a.

Two separate branches that are mirror reflections of one another make up a hyperbola. The vertices are the two locations where the two branches of a hyperbola are joined.

For the given equation of the parabola, the value of a and b = 5 and 4.

Thus, we have horizontal length of 5 and vertical width of 4 units

The graph that depicts this hyperbola is: Option B.

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The complete question is:

How much money would an investment of 300 at rate of 12 percent compound monthly be after 4 years

**Answer:**

data given

principal 300

rate12%

time 4 years

**Step-by-step explanation:**

from

A=P[1+r/100]^n

where

A is amount

p is principal

r is rate

n is interest period

now,

A= 300[1+12/(100×12)]^(12×4)

A=300×1.01^48

A=483.67

: .would be 483.67

What is the mean of the values in the stem-and-leaf plot?

Enter your answer in the box.

**Answer:**

mean = 24

**Step-by-step explanation:**

the mean is calculated as

mean = [tex]\frac{sum}{count}[/tex]

the sum of the data set is

sum = 12 + 13 + 15 + 28 + 28 + 30 + 42 = 168

there is a count of 7 in the data set , then

mean = [tex]\frac{168}{7}[/tex] = 24

Write an equation in point-slope form. Part I: Create an equation of a line in point-slope form. Be sure to identify all parts of the equation before writing the equation. (3 points) Part II: Using the equation of the line you wrote in Part I, write an equation of a line that is perpendicular to this line. Show your work. (3 points)

The line's equation in **point**-**slope **form is shown here. Point (2, 5) is the given point on the line, and slope 2 is the given slope of the line. The slope of this line is -1/2, which is the negative reciprocal of the slope.

A line's point slope form equation is [tex]y - y_1 = m(x - x_1)[/tex]. Consequently, y - 0 = m(x = 0), or y = mx, is the **equation** of a line passing through the origin with a slope of m.

We require a point on the line and the slope of the line in order to create a line equation in point-slope form. In point-slope form,

[tex]y - y1 = m(x - x1)[/tex]

As an illustration, suppose we want to formulate the **equation **of the line passing through the **coordinates** (2, 5) and having a slope of 2. The values can be entered into the point-slope form as follows:

y - 5 = 2(x - 2)Let's say the given line has the equation [tex]y - y1 = m(x - x1)[/tex], where (x1, y1) is a point on the line and m is the **slope **of the line.

we can use the given point (2, 5). Then we can plug in the values into the point-slope form:

[tex]y - 5 = (-1/2)(x - 2).[/tex]

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Primary Level 2 3 4 5 6 7. 8 children/funny monkeys thin/rake strong/ox eagle/aeroplane my room/ clean/ whistle swimmer/fish Exercise 2 Read the story. Look for the simile (as/like) When Mr. Bumble is angry, he shouts as loud as thunder. His eyes look like fire. He bangs his hands which feel as heavy as lead. Mr. Bumble stamps his feet like an et All the pupils keep as quiet as lambs when Mr. Bumble behaves like e

The **similes **in the story are:

A **simile** is a figure of speech that compares two things using the words "like" or "as." It is a type of **metaphor **that helps to create a vivid and engaging image in the reader or listener's mind.

Similes are often used in **literature, poetry, **and everyday language to make a comparison more relatable and understandable. For example, "He is as brave as a lion" or** "She sings like an angel."** These similes help to convey a certain quality or trait by comparing it to something else that is well-known or familiar.

Note: It seems there may be a** typo in the last sentence** of the story, where the word "e" appears instead of "elephant" or another word that would make sense in **context**.

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Write an equation for the polynomial graphed below

The **polynomial** in **factor form** is y(x) = - (1 / 6) · (x + 3) · (x + 1) · (x - 2) · (x - 3).

How to derive the equation of the polynomial

In this problem we find a representation of **polynomial** set on Cartesian plane, whose expression is described by the following formula in **factor form**:

y(x) = a · (x - r₁) · (x - r₂) · (x - r₃) · (x - r₄)

Where:

x - Independent variable.r₁, r₂, r₃, r₄ - Roots of the polynomial.a - Lead coefficient.y(x) - Dependent variable.Then, by direct inspection we get the following information:

y(0) = - 3, r₁ = - 3, r₂ = - 1, r₃ = 2, r₄ = 3

First, determine the **lead coefficient**:

- 3 = a · (0 + 3) · (0 + 1) · (0 - 2) · (0 - 3)

- 3 = a · 3 · 1 · (- 2) · (- 3)

- 3 = 18 · a

a = - 1 / 6

Second, write the complete expression:

y(x) = - (1 / 6) · (x + 3) · (x + 1) · (x - 2) · (x - 3)

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Given that sin 0 = 20/29 and that angle terminates in quadrant III, then what is the value of tan 0?

The **value **of Tanθ is 20/21.

**What is Pythagorean Theorem?**

A **right triangle's** three sides are related in Euclidean geometry by the Pythagorean theorem, also known as Pythagoras' theorem. According to this statement, the areas of the squares on the other two sides add up to the size of the square whose side is the **hypotenuse**.

Here, we have

Given: sinθ = -20/29 and that angle terminates in quadrant III.

We have to find the value of tanθ.

Using the definition of sine to find the known sides of the unit circle right triangle. The **quadrant **determines the sign on each of the values.

Sinθ = Perpendicular/hypotenuse

Find the adjacent side of the unit **circle **triangle. Since the hypotenuse and opposite sides are known, use the Pythagorean theorem to find the remaining side.

Adjacent = - √Hypotenuse² - perpenducualr²

Replace the known values in the **equation**.

Adjacent = -√29² - (-20)²

Adjacent = -21

Find the value of **tangent**.

Tanθ = Perpendicular/base

Tanθ = -20/(-21)

Hence, the value of Tanθ is 20/21.

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The monthly cost (in dollars) of a long-distance phone plan is a linear function of the total calling time (in minutes). The monthly cost for 35 minutes of calls is $16.83 and the monthly cost for 52 minutes is $18.87. What is the monthly cost for 39 minutes of calls?

**Answer: We can use the two given points to find the equation of the line and then plug in 39 for the calling time to find the corresponding monthly cost.**

**Let x be the calling time (in minutes) and y be the monthly cost (in dollars). Then we have the following two points:**

**(x1, y1) = (35, 16.83)**

**(x2, y2) = (52, 18.87)**

**The slope of the line passing through these two points is:**

**m = (y2 - y1) / (x2 - x1) = (18.87 - 16.83) / (52 - 35) = 0.27**

**Using point-slope form with the first point, we get:**

**y - y1 = m(x - x1)**

**y - 16.83 = 0.27(x - 35)**

**Simplifying, we get:**

**y = 0.27x + 7.74**

**Therefore, the monthly cost for 39 minutes of calls is:**

**y = 0.27(39) + 7.74 = $18.21**

**Step-by-step explanation:**

solve the equation

a) y''-2y'-3y= e^4x

b) y''+y'-2y=3x*e^x

c) y"-9y'+20y=(x^2)*(e^4x)

**Answer:**

a) To solve the differential equation y''-2y'-3y= e^4x, we first find the characteristic equation:

r^2 - 2r - 3 = 0

Factoring, we get:

(r - 3)(r + 1) = 0

So the roots are r = 3 and r = -1.

The general solution to the homogeneous equation y'' - 2y' - 3y = 0 is:

y_h = c1e^3x + c2e^(-x)

To find the particular solution, we use the method of undetermined coefficients. Since e^4x is a solution to the homogeneous equation, we try a particular solution of the form:

y_p = Ae^4x

Taking the first and second derivatives of y_p, we get:

y_p' = 4Ae^4x

y_p'' = 16Ae^4x

Substituting these into the original differential equation, we get:

16Ae^4x - 8Ae^4x - 3Ae^4x = e^4x

Simplifying, we get:

5Ae^4x = e^4x

So:

A = 1/5

Therefore, the particular solution is:

y_p = (1/5)*e^4x

The general solution to the non-homogeneous equation is:

y = y_h + y_p

y = c1e^3x + c2e^(-x) + (1/5)*e^4x

b) To solve the differential equation y'' + y' - 2y = 3xe^x, we first find the characteristic equation:

r^2 + r - 2 = 0

Factoring, we get:

(r + 2)(r - 1) = 0

So the roots are r = -2 and r = 1.

The general solution to the homogeneous equation y'' + y' - 2y = 0 is:

y_h = c1e^(-2x) + c2e^x

To find the particular solution, we use the method of undetermined coefficients. Since 3xe^x is a solution to the homogeneous equation, we try a particular solution of the form:

y_p = (Ax + B)e^x

Taking the first and second derivatives of y_p, we get:

y_p' = Ae^x + (Ax + B)e^x

y_p'' = 2Ae^x + (Ax + B)e^x

Substituting these into the original differential equation, we get:

2Ae^x + (Ax + B)e^x + Ae^x + (Ax + B)e^x - 2(Ax + B)e^x = 3xe^x

Simplifying, we get:

3Ae^x = 3xe^x

So:

A = 1

Therefore, the particular solution is:

y_p = (x + B)e^x

Taking the derivative of y_p, we get:

y_p' = (x + 2 + B)e^x

Substituting back into the original differential equation, we get:

(x + 2 + B)e^x + (x + B)e^x - 2(x + B)e^x = 3xe^x

Simplifying, we get:

-xe^x - Be^x = 0

So:

B = -x

Therefore, the particular solution is:

y_p = xe^x

The general solution to the non-homogeneous equation is:

y = y_h + y_p

y = c1e^(-2x) + c2e^x + xe^x

c) To solve the differential equation y" - 9y' + 20y = x^2*e^4x, we first find the characteristic equation:

r^2 - 9r + 20 = 0

Factoring, we get:

(r - 5)(r - 4) = 0

So the roots are r = 5 and r = 4.

The general solution to the homogeneous equation y" - 9y' + 20y = 0 is:

y_h = c1e^4x + c2e^5x

To find the particular solution, we use the method of undetermined coefficients. Since x^2*e^4x is a solution to the homogeneous equation, we try a particular solution of the form:

y_p = (Ax^2 + Bx + C)e^4x

Taking the first and second derivatives of y_p, we get:

y_p' = (2Ax + B)e^4x + 4Axe^4x

y_p'' = 2Ae^4x +

Help me pleas whith this

The answer is c out of the options the third one

solve for the unknown to find the unit rate

1/5 ?

----- = -----

1/20 1

**Answer: 4**

**Step-by-step explanation:**

**To find the unit rate, we can cross-multiply the fractions. **

**Multiplying the numerator of the first fraction by the denominator of the second fraction, we get 1/5. **

**Multiplying the numerator of the second fraction by the denominator of the first fraction, we get 1/20. **

**Now we have the equation 1/5 = 1/20. **

**To solve for the unknown, we can cross-multiply again, which gives us 20 * 1/5 = 4. **

**Therefore, the unit rate is 4.**

Complete the truth table for (A ⋁ B) ⋀ ~(A ⋀ B).

The **truth table** for (A ⋁ B) ⋀ ~(A ⋀ B) is:

A B (A ⋁ B) ⋀ ~(A ⋀ B)

0 0 0

0 1 0

1 0 0

1 1 0

The truth table is what?A truth table is a table that displays all possible combinations of truth values (true or false) for one or more propositions or logical **expressions**, as well as the truth value of the resulting compound proposition or expression that is created by combining them using logical **operators **like AND, OR, NOT, IMPLIES, etc.

The columns of a truth table reflect the propositions or expressions themselves as well as the compound expressions created by applying logical operators to them. The rows of a truth table correspond to the various possible combinations of truth values for the propositions or expressions.

To complete the truth table for (A ⋁ B) ⋀ ~(A ⋀ B), we need to consider all possible combinations of truth values for A and B.

A B A ⋁ B A ⋀ B ~(A ⋀ B) (A ⋁ B) ⋀ ~(A ⋀ B)

0 0 0 0 1 0

0 1 1 0 1 0

1 0 1 0 1 0

1 1 1 1 0 0

So, the only case where the expression is true is when both A and B are true, and for all other cases it is false.

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6. Two out of every five Canadians read at least 10 books a year. What percent of Canadians read at least 10 books a year?

40% of Canadians read at least 10 books a **year**.

A percentage is a way of expressing a portion or a part of a **whole **as a **fraction **of 100. It is represented by the symbol "**%**". Percentages are often used to compare different quantities or to describe how much of a total is made up by a specific **amount **or group. For example, if you score 80 out of 100 on a test, your **score** can be expressed as 80%, meaning you got 80 out of 100 possible points.

If two out of every five Canadians read at least 10 books a year, then we can write this as a fraction:

2/5

We can multiply this fraction by 100 to turn it to a percentage:

(2/5) x 100 = 40%

Therefore, 40% of Canadians read at least 10 books a year.

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See the photo below

This problem involves **integration** and **algebraic manipulation**, and belongs to the subject of **calculus**. The solutions are:

[tex]A) $\int_{0}^{2} (f(x) + g(x)) dx = -3$[/tex]

[tex]B) $\int_{0}^{3} (f(x) - g(x)) dx = -4$[/tex]

[tex]C) $\int_{2}^{3} (3f(x) + g(x)) dx = -32$[/tex]

What is the explanation for the above response?

This is a problem that asks us to find the values of some definite integrals using given values of other **definite integrals**. We are given three definite integrals, and we are asked to compute three other integrals involving the same functions, using the given values.

The problem involves some algebraic manipulation and the use of the **linearity **of the integral.

It also involves finding the **constant **"a" that makes a definite integral equal to zero. The integral involves two functions, "f(x)" and "g(x)," whose definite integrals over certain intervals are also given.

See the attached for the full solution.

Learn more about **integration **at:

https://brainly.com/question/18125359

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Oliver and Mike each place some apples and oranges into the same bowl.

• The ratio of apples to oranges Oliver places in the bowl is 2:3

• The ratio of apples to oranges Mike places in the bowl is 1:2

• They each place 6 oranges in the bowl.

Write the total number of apples and oranges they place in the bowl.

**Answer: 5 * 5 = 20**

**20 divided by 1 = 20**

**If there are 5 apples with an apple:orange ratio of 1:4, there are 20 oranges.**

The diameter of a circle is 38 feet.what is the circles circumfrence. Use 3.14 for pi

**Answer:**

**The circumference of the circle is 119.32 ft.**

**Step-by-step explanation:**

The circumference of a circle can be solved through the formula:

*C = πd*

where d is the diameter

Given: d = 38 ft

π = 3.14

Solve:

C = πd

C = 3.14 (38 ft)

**C = 119.32 ft**

how am i supposed to prove that theyre collinear

**Answer:**

They are collinear if they are on the same line

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