The rectangular prism is filled with 1
-centimeter cubes.

Count the cubes to find the volume of the How many centimeter cubes fit in the rectangular prism?
centimeter cubes
What is the volume of the rectangular prism?
cubic centimeters

Answers

Answer 1

Each cube has a volume of 1 cm³, and the rectangular prism contains 320 cubes, so the volume of the rectangular prism is 320 cm³.

What is volume?

Volume is a physical quantity that measures the amount of space occupied by an object or a substance. It is typically measured in cubic units such as cubic meters (m³) or cubic centimeters (cm³).

Here,

Length side = 4 cubes

= 5 cm

Width side = 2 cubes

= 2 cm

Height side = 2 cubes

= 2 cm

The length of the rectangular prism is 4 cubes which are equal to 5 cm each, so the length is 4 x 5 cm = 20 cm. The width of the rectangular prism is 2 cubes which are equal to 2 cm each, so the width is 2 x 2 cm = 4 cm. The height of the rectangular prism is 2 cubes which are equal to 2 cm each, so the height is 2 x 2 cm = 4 cm.

To find the volume of the rectangular prism, we multiply the length by the width by the height:

Volume = length x width x height

Volume = 20 cm x 4 cm x 4 cm

Volume = 320 cubic cm

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Complete question:

Each cube in this rectangular prism is 1 cm³. What is the volume of the rectangular prism?

The Rectangular Prism Is Filled With 1-centimeter Cubes.Count The Cubes To Find The Volume Of The How

Related Questions

A BCom graduate bought a small apartment for R151 000.00 with a down payment of R51 000.00. If the graduate secures a mortgage bond with a bank for the balance at 15% per annum, compounded monthly, with a term of 20 years. What are the monthly payments?

Answers

The solution of calculate the monthly payments on a mortgage bond, we can use the formula for the present value of an annuity.

what is present value and annuity

Present value (PV) is the current value of a future sum of money, discounted to reflect the time value of money and the risk of non-payment or default.

An annuity is a financial product that pays out a fixed stream of payments to an individual over a specified period of time.

According to the given information:

To calculate the monthly payments on a mortgage bond, we can use the formula for the present value of an annuity:

PV = (PMT / i) x (1 - [tex](1+n)^{-n}[/tex])

Where:

PV = present value (the amount borrowed)

PMT = monthly payment

i = monthly interest rate (15% per annum / 12 months = 1.25%)

n = number of monthly payments (20 years x 12 months per year = 240 months)

First, we need to calculate the present value of the loan, which is the amount borrowed minus the down payment:

PV = R151 000.00 - R51 000.00

PV = R100 000.00

Next, we can plug in the values into the formula:

R100 000.00 = (PMT / 0.0125) x (1 - [tex](1+0.0125)^{-240}[/tex])

Solving for PMT, we get:

PMT = R1,080.80

Therefore, the monthly payments on the mortgage bond will be R1,080.80.

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Classify the solid.

Explain your reasoning.

Image below.

Answers

The solid displayed in the image is a trapezoidal prism.

What is a trapezoidal prism?

A trapezoidal prism is a three-dimensional solid with two parallel trapezoids as its bases, and rectangular or parallelogram sides connecting them. The top and bottom faces are identical, and the side faces are parallelograms.

To classify the solid, look at its properties. The solid has two parallel trapezoids as its bases, and the side faces are parallelograms. Therefore, it is a prism.

Since the bases are not identical rectangles or squares, it is not a rectangular or square prism. However, since the bases are trapezoids, it is a trapezoidal prism.

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Two buses leave a station at the same time and travel in opposite directions. One bus travels 20 mi/h faster than the other. If the two buses are 576 miles apart after 4 hours, what is the rate of each bus?

Answers

The first bus would be going 54 MPH, and the second bus would be going 66 MPH!

Solve for x:-
2^x=32

Answers

Answer:

x=5

Step-by-step explanation:

2^x= 32

2^x=2^5

(comparing, common denominator)

therefore x=5.

Use the graph to answer the question.

graph of polygon ABCD with vertices at 1 comma 5, 3 comma 1, 7 comma 1, 5 comma 5 and a second polygon A prime B prime C prime D prime with vertices at 8 comma 5, 10 comma 1, 14 comma 1, 12 comma 5

Determine the translation used to create the image.

7 units to the right
7 units to the left
3 units to the right
3 units to the left

Answers

To create the image, in order to transform polygon ABCD into polygon A' B' C' D', a translation of `7 units to the right` was used.

Can someone help me with this problem please? :(

Answers

Answer:

y =- [tex]\frac{3}{4}[/tex] x + 1

Step-by-step explanation:

This is a linear equation: y = mx + b

First, you are going to find the y-intercept, b, which in this case is 1.In order to find the slope just use the [tex]\frac{rise}{run}[/tex] method, which in this problem it goes down 3 and 4 to the right.

Angular speed describes how fast something is turning. Linear speed describes how far it travels while it is turning. Linear speed depends on the circumference of a circle (C = 27r) and the number of revolutions per minute. Vinyl records were not the same size. A 45 rpm record had a diameter of 7 inches, a 33+ a diameter of 12 inches, and a 78 had a diameter of 10 inches. a. If a fly landed on the outer edge of a 45 rpm record, how far would it travel in 1 minute? b. How far if it was perched on the outside edge of a 33 rpm record? c. How far if it was perched on the outside edge of a 78 rpm record?​

Answers

a. On a 45 rpm record (7-inch diameter), the fly would travel 990 inches in 1 minute.

b. On a 33 rpm record (12-inch diameter), the fly would travel 1,245.6 inches in 1 minute.

c. On a 78 rpm record (10-inch diameter), the fly would travel 2,430 inches in 1 minute.

How to solve

Radius of 45 rpm record = 3.5 inches (7/2)

Circumference = 2 * π * r = 2 * π * 3.5 ≈ 22 inches

Distance in 1 minute = Circumference * rpm = 22 * 45 = 990 inches

Thus, it can be seen that On a 45 rpm record (7-inch diameter), the fly would travel 990 inches in 1 minute.


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If $c$ is a constant such that $9x^2+10x+c$ is equal to the square of a binomial, then what is $c$?

Answers

c=25/9 for the given condition of the bionomial.

We can solve this problem by using the technique of completing the square.

First, let's assume that [tex]9x^2 + 10x + c[/tex] is equal to the square of a binomial:

[tex](3x + b)^2 = 9x^2 + 6bx + b^2[/tex]

If we compare the above expression with [tex]9x^2 + 10x + c[/tex], we can see that:

6bx = 10x, which implies that b = 5/3

b^2 = c, which implies that [tex]c = (5/3)^2 = 25/9[/tex]

Therefore, c = 25/9 is the constant that satisfies the condition

[tex]9x^2 + 10x + c[/tex] is equal to the square of a binomial.

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The model below represents the division problem 2\frac{1}{5}\div\frac{4}{5}2
5
1

÷
5
4

.

Answers

The equivalent value of the fraction is A = 11/4

Given data ,

Let the fraction be represented as A

Now , let the first fraction be p = 2 1/5

Let the second fraction be q = 4/5

Now , A = p/q

On simplifying the equation , we get

A = ( 2 1/5 ) / 4/5

A = ( 11/5 ) / ( 4/5 )

On further simplification , we get

A = ( 11/5 ) x ( 5 / 4 )

A = 11/4

Therefore , the value of A is 11/4

Hence , the fraction is A = 11/4

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Which of the points below correctly plots the point (4,4π/3)?

Answers

Answer: the correct answer is B

Step-by-step explanation:

Remember that the coordinates (4,4π3) tell us the radius r=4 and the angle θ=4π3. So the point should be on the circle labeled 4 and form an angle of 4π3 with the positive x-axis. Point B is the correct point.

The area of a rhombus is 20 square miles. One of its diagonals is 10 miles. What is the length of the missing diagonal?

Answers

Answer:

The length of the missing diagonal is 4 miles.

Step-by-step explanation:

GIVEN :

Area of rhombus = 20 square milesDiagonals of rhombus = 10 miles

TO FIND :

Length of missing diagonals

USING FORMULA :

[tex] \longrightarrow{\sf{Area \: of \: rhombus = \dfrac{d_1 \times d_2}{3}}}[/tex]

SOLUTION :

Substituting the given values in the formula to find the length of the missing diagonal :

[tex] \longrightarrow{\sf{Area \: of \: rhombus = \dfrac{d_1 \times d_2}{3}}}[/tex]

[tex] \longrightarrow{\sf{20 = \dfrac{10 \times d_2}{2}}}[/tex]

[tex] \longrightarrow{\sf{20 \times 2= 10 \times d_2}}[/tex]

[tex] \longrightarrow{\sf{40= 10 \times d_2}}[/tex]

[tex] \longrightarrow{\sf{d_2 = \dfrac{40}{10}}}[/tex]

[tex] \longrightarrow{\sf{d_2 = \cancel{\dfrac{40}{10}}}}[/tex]

[tex]\longrightarrow{\sf{\underline{\underline{d_2 = 4 \: miles}}}}[/tex]

Hence, the length of the missing diagonal is 4 miles.

Answer:

The length of the missing diagonal is 4 miles.

Step-by-step explanation:

To find the length of the missing diagonal, we can use the formula for the area of a rhombus, which is:

[tex]\sf\qquad\dashrightarrow Area_{(Rhombus)} = \dfrac{(Diagonal_1 \times Diagonal_2)}{2}[/tex]

We know that the area is 20 square miles and one of the diagonals is 10 miles, so we can substitute these values into the formula as follows:

[tex]\sf\qquad\dashrightarrow20 = \dfrac{(10 \times Diagonal_2)}{2}[/tex]

Simplifying the equation, we get:

[tex]\sf\qquad\dashrightarrow 40 = 10 \times Diagonal_2[/tex]

Dividing both sides by 10, we get:

[tex]\sf\qquad\dashrightarrow \boxed{\bold{\:\:Diagonal_2 = 4\:\:}}\:\:\:\bigstar[/tex]

Therefore, the length of the missing diagonal is 4 miles.

The average high temperatures in degrees for a city are listed.

58, 61, 71, 77, 91, 100, 105, 102, 95, 82, 66, 57

If a value of 120.5° is added to the data, how does the mean change and by how much?

Answers

The answer is 3.08 more

Find the missing measurements in the triangle.

Angles should be to the nearest degree.

Side lengths should be rounded to the nearest tenth.

Answers

Answer: angle b= 63

Ac= 23.6

Ab=26.4

Step-by-step explanation:

angle b= 63

Ac= 23.6

Ab=26.4

Angle B is 63 degrees, the length of AC is approximately 22.23 units, and the length of AB is approximately 26.42 units.

What is right angle triangle?

A triangle in which one of its angles measures 90 degrees is called a right-angled triangle .

The side opposite the right angle is called the hypotenuse while the other two sides are called the legs or the adjacent and opposite sides.

According to given figure angle C is a right angle, we know that the sum of angles A and B must be 90 degrees.

So, angle B = 90 - angle A = 90 - 27 = 63 degrees.

To find the length of AC, we can use trigonometry. Since we know the length of the opposite side (BC) and the angle opposite the side we want to find (angle A), we can use the tangent function:

tan A = opposite / adjacent

tan 27 = BC / AC

AC = BC / tan 27

AC = 12 / tan 27

AC ≈ 22.23

Now,

[tex]AB^2 = AC^2 + BC^2 \\ AB^2 = 22.23^2 + 12^2 \\ AB^2 ≈ 697.57 \\ AB ≈ 26.42[/tex]

Therefore, Angle B is 63 degrees, the length of AC is approximately 22.23 units, and the length of AB is approximately 26.42 units.

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If you repeat this experiment 360 times, how many repetitions do you predict will result in the same letter being spun for both spins?

Answers

Answer:

  90

Step-by-step explanation:

You want to know the number of times in 360 trials that the same letter will appear twice in a row using a fair 4-letter spinner.

Probability

The table shows 4 outcomes of the 16 possible that have the same letter repeated. That's a probability of a repeated letter of 4/16 = 1/4.

Expected number

The expected number of repeated letters in 360 trials is the number of trials times the probability of a repeat:

  expected repeats = 360 × 1/4 = 90

You predict there will be 90 repetitions in 360 trials.

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Ahmad received a $1100 bonus. He decided to invest it in a 2-year certificate of deposit (CD) with an annual interest rate of 1.14% compounded daily.
Answer the questions below. Do not round any intermediate computations, and round your final answers to the nearest cent. If necessary, refer to the
list of financial formulas. Assume there are 365 days in each year.
(a) Assuming no withdrawals are made, how much money is in Ahmad's
account after 2 years?


(b) How much interest is earned on Ahmad's investment after 2 years?

Answers

The interest that have been earned after two years is $25.

What is the compound interest?

A type of interest known as compound interest is computed using both the original sum and any accrued interest from earlier periods. The interest that is earned on interest is, in other terms, interest.

We know that by the compound interest formula;

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

A = amount

P = principal

r = rate

n = Number of times compounded

t = time

Thus;

A = 1100(1 + 0.0114/365)^365* 2

A = $ 1125

Thus the interest after two years is;

$ 1125 - $1100

= $25

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is it true that 5 2/3 - 3 3/4= 1+2/3+3/4

Answers

In linear equation., both quantities are different from each other.

What is a linear equation in mathematics?

A linear equation in algebra is one that only contains a constant and a first-order (direct) element, such as y = mx b, where m is the pitch and b is the y-intercept.

                         Sometimes the following is referred to as a "direct equation of two variables," where y and x are the variables. Direct equations are those in which all of the variables are powers of one. In one example with just one variable, layoff b = 0, where a and b are real numbers and x is the variable, is used.

Taking LHS

  5 2/3 - 3 3/4= 17/3 - 15/4

  17/3 - 15/4 =  68 - 45/12  = 23/12

 

now solving RHS

  1+2/3+3/4  = 12 + 8 + 9/12  = 29/12

clearly, LHS≠ RHS

hence both quantities are different from each other.

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θ=1 rad when S=r. If θ=2 rad then what is the condition? :::::::(S means arc length)

Answers

If θ=2 rad then the condition when θ=2 rad is that the arc length S is equal to twice the radius r.

In this problem, we are given that when the arc length is equal to the radius (S=r), the angle is 1 radian (θ = 1 rad). Now, we are asked to find the condition when the angle is 2 radians (θ = 2 rad).

If Θ=1 rad when S=r, it means that when the angle subtended by an arc of length r is 1 radian, then the radius of the circle is also r.

Now, if θ=2 rad, we can use the same proportionality to find the arc length S that corresponds to this angle. Since the angle has doubled, we can expect the arc length to double as well. Therefore, we have:

θ/Θ = S/r

2/1 = S/r

S = 2r

Thus, the condition when θ=2 rad is that the arc length S is equal to twice the radius r.

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4) Which of the following lists are in order from least to greatest? Select TWO correct answers * 2 points

A 117.51 17.382 17.38 17.23

B 452.8 45.18 452.28 453.71

C 0.005 0.045 0.102 0.63

D 2.452 2.749 2.981 2.994

E 7.604 7.599 7.452 7.045

Answers

Answer: The two lists that are in order from least to greatest are:

C) 0.005, 0.045, 0.102, 0.63

and

E) 7.045, 7.452, 7.599, 7.604

Step-by-step explanation:

To determine which lists are in order from least to greatest, we need to compare the values and arrange them accordingly. Here is the explanation for the two correct answers:

C) 0.005, 0.045, 0.102, 0.63

This list is already in order from least to greatest. Starting from the smallest value of 0.005, each subsequent value increases until we reach the largest value of 0.63.

E) 7.045, 7.452, 7.599, 7.604

This list is also in order from least to greatest. Starting from the smallest value of 7.045, each subsequent value increases until we reach the largest value of 7.604.

For the other options:

A) 117.51, 17.382, 17.38, 17.23 - This list is not in order from least to greatest.

B) 452.8, 45.18, 452.28, 453.71 - This list is not in order from least to greatest.

D) 2.452, 2.749, 2.981, 2.994 - This list is not in order from least to greatest.

Therefore, the two lists that are in order from least to greatest are C (0.005, 0.045, 0.102, 0.63) and E (7.045, 7.452, 7.599, 7.604).

The answer is a and b

Let
x = −4, y = 0,
and
z = 7
and evaluate the expression.

Answers

Answer:you need to include the expression

Step-by-step explanation:

once you have the expression, substitute the numbers given for each variable and use order of operations to

Determine the line of reflection. Reflection across the x-axis Reflection across the y-axis Reflection across x = 5 Reflection across y = 6

Answers

The calculated line of reflection of the graph is y = -3

Determining the line of reflection.

The given graph is added as an attachment

From the graph, we can see that the shapes are symmetrical about the line y = -3

When shapes are symmetrical about a point or a line, then the point or the line is the point of reflection

This means that the line of reflection is y = -3

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Answer:

The calculated line of reflection of the graph is y = -3

Step-by-step explanation:

Help !!!!!!!!!!!!!!!!!!!!!!!!!!!

Answers

The preimage of the quadrilateral is in the second quadrant. The quadrilateral is reflected across the x-axis, the image would lie in the fourth quadrant.

What is quadrilateral?

A quadrilateral is a geometric shape that consists of four straight sides and four angles. It is a two-dimensional shape, also known as a 2D polygon, and can be defined as any closed shape that has four sides. There are many different types of quadrilaterals, each with its own unique set of characteristics.

According to given information:

The second quadrant is characterized by negative x-coordinates and positive y-coordinates, while the fourth quadrant has positive x-coordinates and negative y-coordinates.

If the preimage of the quadrilateral is in the second quadrant, then its x-coordinates are negative and its y-coordinates are positive.

When the quadrilateral is reflected across the x-axis, its x-coordinates will remain the same but its y-coordinates will become negative. Therefore, if the preimage is in the second quadrant and the quadrilateral is reflected across the x-axis, the image would lie in the fourth quadrant.

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x = sin t, y = 3 cos t

Answers

Answer:

16.39 square units.

Step-by-step explanation:

The parametric equations x = sin t and y = 3 cos t describe a curve in the xy-plane known as an ellipse.

To see this, we can use the Pythagorean identity for sine and cosine:

sin^2 t + cos^2 t = 1

Multiplying both sides by 9, we get:

9 sin^2 t + 9 cos^2 t = 9

Substituting x = sin t and y = 3 cos t, we get:

9 x^2 + y^2/3 = 9

This is the equation of an ellipse centered at the origin with semi-axes a = 3 and b = sqrt(3), where a is the length of the horizontal semi-axis and b is the length of the vertical semi-axis.

The area of an ellipse is given by the formula:

Area = pi * a * b

Substituting the values of a and b, we get:

Area = pi * 3 * sqrt(3) ≈ 16.39

Therefore, the area of the ellipse described by the parametric equations x = sin t and y = 3 cos t is approximately 16.39 square units.

NO LINKS!! URGENT HELP PLEASE!!

Please help me with #19

Answers

Answer:

a. 1.95 cm.

b. 3920 cm^2.

Step-by-step explanation:

(a) To find the length of the arc that subtends the central angle theta on a circle of diameter d, we can use the formula:

Arc Length = (theta / 360°) x (pi x d)

Substituting the given values, we get:

Arc Length = (1.6 / 360°) x (pi x 140 cm)

Arc Length ≈ 1.95 cm

Therefore, the length of the arc that subtends the central angle of 1.6 radians on a circle of diameter 140 cm is approximately 1.95 cm.

(b) To find the area of the sector determined by the central angle theta, we can use the formula:

Area of Sector = (theta / 2π) x pi x (r^2)

where r is the radius of the circle.

Since the diameter of the circle is given as 140 cm, the radius is half of that, which is 70 cm.

Substituting the given values, we get:

Area of Sector = (1.6 / (2 x pi)) x pi x (70 cm)^2

Area of Sector ≈ 3920 cm^2

Therefore, the area of the sector determined by the central angle of 1.6 radians on a circle of diameter 140 cm is approximately 3920 cm^2.

Eastern Manufacturing is involved with several situations that possibly involve contingencies. Each is described below. Eastern’s fiscal year ends December 31, and the 2024 financial statements are issued on March 15, 2025.

Answers

The income statement, and stockholders equity are given below.

We have to show the income statement

The income statement for Coyote Corporation for the year ended December 31, 2024, is as follows:

Coyote Corporation

Income Statement

For the Year Ended December 31, 2024

Service Revenue $55,000

Less: Expenses

Salaries Expense $27,000

Rent Expense $6,000

Utilities Expense $6,000

Interest Expense $5,000

Total Expenses $44,000

Net Income $11,000

The statement of stockholders' equity for Coyote Corporation for the year ended December 31, 2024, is as follows:

Coyote Corporation

Statement of Stockholders' Equity

For the Year Ended December 31, 2024

Retained Earnings, December 31, 2023 $35,000

Add: Net Income for 2024 $11,000

Less: Dividends $0

Retained Earnings, December 31, 2024 $46,000

Classified Balance Sheet:

Assets

Current Assets

Cash $27,000

Accounts Receivable $26,000

Prepaid Rent $6,000

Supplies $5,000

Total Current Assets $64,000

Property, Plant, and Equipment

Land $55,000

Total Property, Plant, and Equipment $55,000

Total Assets $119,000

Liabilities and Stockholders' Equity

Current Liabilities

Accounts Payable $90,000

Salaries Payable $375,000

Interest Payable $6,000

Total Current Liabilities $471,000

Long-term Liabilities

Notes Payable (due in two years) $55,000

Total Liabilities $526,000

Stockholders' Equity

Common Stock $35,000

Retained Earnings $46,000

Total Stockholders' Equity $81,000

Total Liabilities and Stockholders' Equity $119,000

Therefore, the classified balance sheet for Coyote Corporation as of December 31, 2024, is as follows:

Coyote Corporation

Classified Balance Sheet

As of December 31, 2024

Assets

Current Assets

Cash $27,000

Accounts Receivable $26,000

Prepaid Rent $6,000

Supplies $5,000

Total Current Assets $64,000

Property, Plant, and Equipment

Land $55,000

Total Property, Plant, and Equipment $55,000

Total Assets $119,000

Liabilities and Stockholders' Equity

Current Liabilities

Accounts Payable $90,000

Salaries Payable $375,000

Interest Payable $6,000

Total Current Liabilities $471,000

Long-term Liabilities

Notes Payable (due in two years) $55,000

Total Liabilities $526,000

Stockholders' Equity

Common Stock $35,000

Retained Earnings $46,000

Total Stockholders' Equity $81,000

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complete question:

Kindly check if the photo below of income statement is wrong and correct which one is wrong in a excel or anything that makes it clear to me.

100 Points! Write a polynomial function of least degree with integral coefficients that have the given zeros of -1,1,i√6. Photo attached. Please show as much work as possible. Thank you!

Answers

The required polynomial  [tex]f(x) = x^4+5x^2-6[/tex] has the zeros -1, 1, [tex]i\sqrt6[/tex], and [tex]-i\sqrt6[/tex].

What is a polynomial ?

A polynomial is a mathematical expression that consists of variables and coefficients, combined by addition, subtraction, and multiplication, but not division by a variable.

To write a polynomial function of least degree with integral coefficients that has zeros of -1, 1, and [tex]i\sqrt{6[/tex], we need to include their conjugates as well. This is because complex roots always come in conjugate pairs.

The conjugate of  [tex]i\sqrt{6[/tex] is  [tex]-i\sqrt{6[/tex], so our polynomial function will have the following zeros: -1, 1,  [tex]i\sqrt{6[/tex], and  [tex]-i\sqrt{6[/tex].

To find the polynomial function, we can use the fact that the product of the factors of a polynomial is equal to the polynomial itself. So, we can start by multiplying out the factors:

[tex](x+1)(x-1)(x-i\sqrt6)(x+i\sqrt6)[/tex]

Expanding this out gives:

[tex](x^2-1)(x^2+6)[/tex]

Multiplying these two expressions gives:

[tex]x^4+5x^2-6[/tex]

So the polynomial function of least degree with integral coefficients that has zeros of -1, 1, and [tex]i\sqrt{6[/tex] is [tex]f(x) = x^4+5x^2-6[/tex]

To verify that this polynomial has the desired zeros, we can factor it using the difference of squares:

[tex]x^4+5x^2-6 = (x^2-1)(x^2+6) = (x-1)(x+1)(x^2+6)[/tex]

And the quadratic factor has no real roots, so it must be the factorization [tex](x-i\sqrt6)(x+i\sqrt6)[/tex].

Therefore, [tex]f(x) = x^4+5x^2-6[/tex] has the zeros -1, 1, [tex]i\sqrt6[/tex], and [tex]-i\sqrt6[/tex], as required.

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A box contains 5 orange pencils, 8 yellow pencils, and 8 green pencils. Two pencils are selected, one at a time, with replacement. Find the probability that the first pencil is green and the second pencil is yellow.

Answers

A box contains 5 orange pencils, 8 yellow pencils, and 8 green pencils. Two pencils are selected, one at a time, with replacement.

There are a total of 21 pencils in the box.

The probability of selecting a green pencil on the first draw is 8/21, since there are 8 green pencils out of 21 total.

After replacing the first pencil, there are still 21 pencils in the box, including 8 yellow pencils.

The probability of selecting a yellow pencil on the second draw, given that a green pencil was selected first, is 8/21.

By the Multiplication Rule of Probability, we can multiply these probabilities together to find the probability of both events occurring

P(green and yellow) = P(green) × P(yellow|green)

P(green and yellow) = (8/21) × (8/21)

P(green and yellow) = 64/441

Therefore, the probability of selecting a green pencil first and a yellow pencil second is 64/441 or approximately 0.145.

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can I ask for someone to help me please?

Answers

Here we have an exponential growth were the increase is of 26%, and it can be written as.

[tex]y = a*(1 + 0.26)^t[/tex]

How to rewrite the function?

Here we want to rewrite the function

[tex]y = a*(2)^{t/3}[/tex]

In the given form for the general exponential, so let's do that.

We can expand the product to get:

[tex]y = a*(2)^{t/3}\\\\y = a*((2)^{1/3})^t\\\\y = a*(1.26)^t\\\\y = a*(1 + 0.26)^t[/tex]

To identify if it is a growth or a decay we need to see the sign of r (the thing we are adding to the 1) in this case is +0.26

When it is positive we have a growth, so here we have a growth.

And to get the percentage multiply that number by 100%, we will get:

0.25*100% = 26%

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What is the equation of the graphed line written in standard form?

a. 2x - y = -4
b. 2x - y = 4
c. y = 2x - 4
d. y = 1/2x - 4

Answers

Answer:

answer is

c. y = 2x - 4

Step-by-step explanation:

y=mx+b is standard, b is also correct but not in standard form, hope this helps

Find the area of each

Answers

The areas of each figure are 5.6 sq m, 76.8 sq km, 280.8 sq units, 173.88 sq units and 332 sq units

Finding the area of each figure

The area of a shape is the amount of space on it

Using the above as a guide, we have the following:

Figure 7:

The area is calculated as

Area = 1/2 * (sum of parallel sides) * height

So, we have

Area = 1/2 * (3.9 + 1.7) * 2

Area = 5.6 sq m

Figure 8:

The area is calculated as

Area = Base * height

So, we have

Area = 9.6 * 8

Area = 76.8 sq km

Figure 9:

The area is calculated as

Area = 6 * 1/2 * Base * height

So, we have

Area = 6 * 1/2 * 9 * 10.4

Area = 280.8 sq units

Figure 10:

The area is calculated as

Area = 7 * 1/2 * Base * height

So, we have

Area = 7 * 1/2 * 6.9 * 7.2

Area = 173.88 sq units

Figure 11:

The area is calculated as

Area = 8 * 1/2 * Base * height

So, we have

Area = 8 * 1/2 * 10 * 8.3

Area = 332 sq units

Figure 12, 13 and 14:

The areas of the figures cannot be calculated with the available details and parameters

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Kelly is making a bubble mixture for kids to play with at a backyard party. She adds 1/4 of a cup of corn syrup to 6 cups of soap and water.

She wants to make more bubble mixture and has 18 cups of the soap and water mixture to use.

How much corn syrup does she need to add?

A. 2/3 of a cup of corn syrup
B. 3 cups of corn syrup
C. 3/4 of a cup of corn syrup
D. 3 1/4 cups of corn syrup

Answers

Answer: C. 3/4 of a cup of corn syrup

Step-by-step explanation:

    We will set up a proportion to help us solve.

[tex]\displaystyle \frac{1/4\text{ cup corn syrup}}{6\text{ cups of soap and water}} =\frac{x\text{ cups corn syrup}}{18\text{ cups of soap and water}}[/tex]

    Next, we will cross-multiply.

1/4 * 18 = 6 * x

9/2 = 6x

    Lastly, we will divide both sides of the equation by 6.

x = 3/4 of a cup of corn syrup

                       C. 3/4 of a cup of corn syrup

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