Solve 6 ÷ 4. Express your answer as an improper fraction.

Hello!

surface area

= 2(4 x 2) + 2(12 x 4) + 2(12 x 2)

= 160cm²

Answer:

Step-by-step explanation:

3x+y+z= 4

3x+ y = 4 - z

y = 4-z-3x

We then make parallel

y-2 = 4−z−3x

y-2 = 4-2 -z-3x

y-2 = 2-z-3x

y = -z-3x+2

Answer:

Step-by-step explanation:

Given the data representation of the strength of nine randomly selected casts​ (in psi) as 3960, 4090, 3200, 3100, 2940, 3830, 4090, 4040, 3780.

MEAN

Mean is the average of the samples

\(\overline x = \frac{\sum Xi}{N}\)

\(\sum Xi\) is thw sum of the given data

N is the sample size

\(\overline x\) is the mean

\(\overline x = \frac{3960+4090+3200+3100+2940+3830+4090+4040+3780}{9}\\\\\overline x = \frac{33,030}{9}\\ \\\overline x = 3,670psi\)

Hence the mean of the data is 3,670psi

MEDIAN

Median is the value at the middle of the data after rearrangement.

On rearranging in ascending order

2940, 3100, 3200, 3,780) 3,830 (3,960, 4040, 4090, 4090

It can be seen that the middle value is 3860. Hence the median of the data is 3860psi.

MODE

Mode is the most occurring data in the dataset. It is the data with the highest frequency. From the data, it can be seen that the only data occurring most (twice) is 4090, hence the modal value is 4090psi

Answer:

y = 4x - 11

Step-by-step explanation:

The general equation of the slope-intercept form of a line is given by:

y = mx + b, where

We can find b, the y-intercept of the line, by plugging in 4 for m and (3, 1) for (x, y) in the slope-intercept form:

1 = 4(3) + b

1 = 12 + b

-11 = b

Thus, the y-intercept is -11.

Thus, the equation of the line with a slope of 4 passing through the point (3, 1) in slope-intercept form is y = 4x - 11

The answer is:

Work/explanation:

First, we will write the equation in point slope:

\(\sf{y-y_1=m(x-x_1)}\)

where m = slope;

(x₁,y₁) is a point on the line.

Plug in the data:

\(\sf{y-1=4(x-3)}\)

Simplify

\(\sf{y-1=4x-12}\)

Add 1 on each side

\(\sf{y=4x-12+1}\)

\(\sf{y=4x-11}\)

Hi there!

\(\large\boxed{y = \pm \sqrt{x - 16}}\)

To solve for the inverse, swap the x and y variables:

x = y² + 16

Isolate for y by subtracting both sides by 16:

x - 16 = y²

Square root both sides:

√(x - 16) = y

Add the plus/minus sign:

y = ±√(x - 16)

Answer:

c

Step-by-step explanation:

The term that should be added to the expression to make the expression perfect square trinomial is 169/4. The expression then becomes : (y - 13/2)²

What is meant by a perfect square trinomial?

By multiplying a binomial by another binomial, perfect square trinomials—algebraic equations with three terms—are created. A number can be multiplied by itself to produce a perfect square. Algebraic expressions known as binomials are made up of simply two words, each of which is separated by either a positive (+) or a negative (-) sign. Similar to polynomials, trinomials are three-term algebraic expressions.

A perfect square trinomial expression can be created by taking the binomial equation's square. If and only if a trinomial satisfying the criterion b² = 4ac has the form ax² + bx + c, it is said to be a perfect square.

Given expression y² - 13y + ?

Comparing with the general equation

a = 1

b = -13

For perfect square trinomial

b² = 4ac

(-13)² = 4 * 1 * c

169 = 4c

c = 169/4

So the expression becomes,

y² - 13y + 169/4 = (y - 13/2)²

Therefore the term that should be added to the expression to make the expression perfect square trinomial is 169/4.

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The biconditional statement is: A rectangle is a parallelogram with four right angles if and only if a parallelogram has four right angles.

The term "if and only if" or biconditional statement refers to a compound statement composed of two conditional statements connected by a logical operator.

This definition is commonly utilized to describe the characteristics of a rectangle when it comes  to its correlation with a parallelogram. The opening section of the biconditional statement is comprised of a conditional statement indicating that a rectangle is defined as a parallelogram featuring four right angles.

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Write this definition as a biconditional statement.

A rectangle is a parallelogram with four right angles.

Answer:

Let's denote:

- The number of orders Diane served as `D`

- The number of orders Sam served as `S`

- The number of orders Boris served as `B`

From the problem, we know:

1. `D + S + B = 54` (the total number of orders they served)

2. `D = S - 6` (Diane served 6 fewer orders than Sam)

3. `B = 2S` (Boris served 2 times as many orders as Sam)

We can substitute equations 2 and 3 into equation 1 to solve for the variables:

Substitute `D` and `B` in equation 1:

`(S - 6) + S + 2S = 54`

Combine like terms:

`4S - 6 = 54`

Add 6 to both sides:

`4S = 60`

Divide by 4:

`S = 15`

Now that we know `S = 15`, we can find `D` and `B` by substituting `S` into equations 2 and 3:

`D = S - 6 = 15 - 6 = 9`

`B = 2S = 2 * 15 = 30`

So, Diane served 9 orders, Sam served 15 orders, and Boris served 30 orders.

To solve the equation 3,532.5 = (3.14)(r^2)(x/3) for the variable r, we can follow these steps:

Multiply both sides of the equation by 3/3 to eliminate the fraction:

3,532.5 * 3/3 = (3.14)(r^2)(x/3) * 3/3

This simplifies to:

10,597.5 = (3.14)(r^2)(x)

Divide both sides of the equation by (3.14)(x) to isolate the variable r:

10,597.5 / (3.14)(x) = (r^2)

Take the square root of both sides of the equation to solve for r:

r = sqrt(10,597.5 / (3.14)(x))

Therefore, the solution to the equation 3,532.5 = (3.14)(r^2)(x/3) for the variable r is:

r = sqrt(10,597.5 / (3.14)(x))

Answer:

\(124\:\mathrm{N}\)

Step-by-step explanation:

From Newton's 2nd Law, we have \(\Sigma F=ma\).

What we're given:

Substituting given values, we get:

\(F=62\cdot 2=\boxed{124\:\mathrm{N}}\)

Answer:

hshshshshshshshsiqkZjfdudiodjfhfbbxdudijdd

Answer:

-1 and 1

Step-by-step explanation:

Reciprocal means "one divided by...".

1/-1 = -1 and 1/1 = 1

The length of a rectangle cannot be negative, hence the length of the rectangle is 7 units.

Based on the question given, the width (W) is the length (L) minus 3 units, which can be expressed as:

W = L - 3

The formula for the area (A) of a rectangle is:

A = Length × Width

We are given that the area is 28 square units, so:

A = 28

Now, we can substitute the expressions for width (W) and area (A) into the area formula:

28 = L × (L - 3)

Now, we need to solve this quadratic equation for L. First, expand the equation:

28 = L^2 - 3L

Now, rearrange the equation in standard quadratic form

L^2 - 3L - 28 = 0

To solve this quadratic equation, you can factor it:

(L - 7)(L + 4) = 0

Now, set each factor equal to zero and solve for L:

L - 7 = 0

L = 7

L + 4 = 0

L = -4

Since the length of a rectangle cannot be negative, hence the length of the rectangle is 7 units.

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Answer:

(a) Yes, E and F are independent events.

(b) P(E and F) = P(E)P(F) = (1/2)(1/2) = 1/4

The down payment for the Martin family is $42,750, and the amount to borrow is $285,000. The monthly payment is $242,250, and the total interest paid over the 30 years is $135,622.

A down payment is a portion of the total purchase price of an item or property that is paid upfront in cash or equity, before taking out a loan or mortgage to finance the rest of the amount. In real estate, for example, the down payment is the initial payment made by a homebuyer towards the purchase of a home. The down payment is considered separate from the monthly mortgage payments that the homebuyer will make to repay the loan. The size of the down payment affects the size of the loan and the monthly payments, as well as the interest that will be charged on the loan. A larger down payment usually results in a smaller loan and lower interest charges.

11. The down payment for the Martin family would be $42,750.

To calculate this, we can use the formula:

Down Payment = Sale Price * Down Payment Percentage

Down Payment = $285,000 * 15%

Down Payment = $42,750

12. To find the monthly payment, we need to first calculate the amount they need to borrow, which is the sale price minus the down payment:

Amount to Borrow = Sale Price - Down Payment

Amount to Borrow = $285,000 - $42,750

Amount to Borrow = $242,250

Next, we'll use the formula for calculating the monthly payment for a loan:

Monthly Payment = Loan Amount * (APR/12) / (1 - (1 + (APR/12))^(-12 * Years))

Monthly Payment = $242,250 * (3.75/12) / (1 - (1 + (3.75/12))^(-12 * 30))

Rounding to the nearest cent, the monthly payment would be approximately $1,039.20.

13. To find the total of all of the monthly payments over the 30 years, we can simply multiply the monthly payment by the number of months:

Total Monthly Payments = Monthly Payment * 12 * 30

Total Monthly Payments = $1,039.20 * 12 * 30

Rounding to the nearest cent, the total of all of the monthly payments over the 30 years would be approximately $377,872.

14. To find the total interest paid over the 30 years, we'll subtract the amount borrowed from the total monthly payments:

Total Interest Paid = Total Monthly Payments - Amount to Borrow

Total Interest Paid = $377,872 - $242,250

Rounding to the nearest cent, the total interest paid over the 30 years would be approximately $135,622.

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Answer

The second derivative of an implicit function can be found using sequential differentiation of the initial equation F(x,y)=0. At the first step, we get the first derivative in the form y′=f1(x,y). On the next step, we find the second derivative, which can be expressed in terms of the variables x and y as y′′=f2(x,y).

The expressions that are completely factored are:

The expressions are considered correct because they have been completely factored, meaning they have been written in the form of "a common factor times another expression". This means that the expression on the right side of the equal sign can be simplified into its simplest form.

For example, in the expression 16a5−20a3=4a3(4a2−5), the 4a3 factor is common to both 16a5 and 20a3, so it can be factored out. The expression then becomes 4a3 times (4a2−5), which is the completely factored form.

Similarly, in the expression 12a3+8a=4(3a3+2a), the factor of 4 is common to both the expressions on the right side, so it can be factored out. This results in the completely factored form of 4 times (3a3+2a).

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Answer:

16a^5−20a^3=4a^3(4a^2−5)

and

24a^4+18=6(4a^4+3)

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:    x=67

Step-by-step explanation:

All of the angles add up to 180 for a triangle

38 + 75 + x = 180               >combine like terms (the numbers)

113 + x = 180                       >subtract 113 from both sides

x=67

Answer:

Step-by-step explanation:

We know that,

\( \sf \: By \: Using \: Angle \: sum \: property \: of \: triangle\)

\( \large \sf \: → x +38° + 75° = 180°\)

\( \large \sf \: → x + 113 = 180°\)

\( \large \sf→ x = 180°- 113°\)

\( \boxed{\large \bf→ x = 67° }\)

Answer:

1 sec

Step-by-step explanation:

Answer:

y=9x

Step-by-step explanation:

Answer:

n = 26/45

Step-by-step explanation:

If the 9⅓ and 27⅘ are supposed to be \(9^{1/3}\)  and \(27^{4/5}\), then

\(9^{1/3}\) × \(27^{n}\) = \(27^{4/5}\)

=> \((3^{2})^{1/3}\) × \((3^3)^{n}\) = \((3^3)^{4/5}\)

=> \(3^{2/3}\) × \(3^{3n}\) = \(3^{12/5}\)

=> \(3^{3n+\frac{2}{3}}\) = \(3^{12/5}\)

=> 3n+2/3 = 12/5

=> 45n + 10 = 36

=> 45n = 26

=> n = 26/45

Miranda needs to work 50 hours at her job in order to purchase the computer.

Amount is a term generally used to refer to a numerical value which represents a quantity of something. It can be used to describe the size, magnitude, or total of an object, event, or concept. Amount is often used to refer to money, but it can also be used to refer to other elements such as time, energy, weight, and volume. Amount can also be used to refer to a certain degree or level, such as a certain amount of effort or a certain amount of progress.

To find the amount of hours Miranda needs to work in order to purchase the computer, the following equation can be used:

12 x = Computer Price x 0.6

Where 12 is the hourly wage Miranda earns, x is the amount of hours Miranda needs to work, and 0.6 is the percentage (60%) of Miranda’s earnings that will be used to purchase the computer.

The computer price is not given, so let’s assume it to be $1000. Plugging in the values, the equation becomes:

12 x = 1000 x 0.6

Simplifying the equation, we have:

12 x = 600

Dividing both sides by 12, we get:

x = 600/12

x = 50

Therefore, Miranda needs to work 50 hours at her job in order to purchase the computer.

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Answer:

So Alina can make a box with dimensions 8.445 inches by 8.445 inches by 8.445 inches (with a metal top) that will hold approximately 606.526 cubic inches.

Step-by-step explanation:

Let's assume that the length of one side of the square base of the box is "x". Then the height of the box is also "x" to maximize the volume.

The surface area of the box (excluding the top) is given by:

2(x^2) + 4(x^2) = 6(x^2)

The surface area of the metal top is:

x^2

The total surface area of the box is the sum of the surface area of the box and the surface area of the metal top:

6(x^2) + x^2 = 7(x^2)

The cost of the wood for the box is:

5 cents per square inch * 6(x^2) = 30x^2 cents

The cost of the metal for the top is:

12 cents per square inch * x^2 = 12x^2 cents

The total cost of the box is:

30x^2 + 12x^2 = 42x^2 cents

We want to find the maximum volume of the box that can be made with $30, which is 3000 cents. Therefore, we can set up the equation:

42x^2 = 3000

Solving for x, we get:

x^2 = 71.429

x ≈ 8.445

Therefore, the maximum volume of the box is:

V = x^2 * x = (8.445)^3 ≈ 606.526 cubic inches.

So Alina can make a box with dimensions 8.445 inches by 8.445 inches by 8.445 inches (with a metal top) that will hold approximately 606.526 cubic inches.

Answer:

The answer is B) 1

Step-by-step explanation:

balls

Answer:

117\(\pi\)/4

Step-by-step explanation:

see attached for step-by-step

Answer:

A. between 38 and 46 waves

Step-by-step explanation:

Step 1: Given data

Hernando estimated about 42 waves give or take 4 waves. That is, the average is 42 waves and 4 waves define the confidence interval.

Step 2: Calculate the minimum number of waves

We have to subtract 4 waves from the average, that is 42 - 4 = 38 waves

Step 3: Calculate the maximum number of waves

We have to add 4 waves to the average, that is 42 + 4 = 46 waves

The true statement about the system of equations is the fourth one:

"(8, 2) is a solution to one equation but not the other one, so it is not a solution to the system."

The system of equations is:

x - 3y = 2

y = x + 6

We want to see which statement is true, all of them refer to the point (8, 2), so let's see if it is a solution of the system.

Replacing the values in the first equation we will get:

8 - 3*2 = 2

8 - 6  =2

2 = 2

For the second equation:

2 =8 + 6

2 = 14

This is false, so (8, 2) is not a solution of the second equation.

Then the true statement is:

" (8, 2) is a solution to one equation but not the other one, so it is not a solution to the system."

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Work Shown:

\(\cos(\text{angle}) = \frac{\text{adjacent}}{\text{hypotenuse}}\\\\\cos(65^{\circ}) = \frac{d}{e}\\\\e\cos(65^{\circ}) = d\\\\e = \frac{d}{\cos(65^{\circ})}\\\\\)

Answer:

49 square units

Step-by-step explanation:

A line connecting two points is known as a line segment

Since ABCD is a square, this means that the length of each side is equal to each other:

Length of

line segment AB = line segment BC = line segment CD = line segment AD

The length of a horizontal line on a graph can be determined by taking the difference of the x-coordinates of the two points.

∴Length of line segment AD = \((9 - 2)\) units

                                                 = 7 units

This means each side of the square measures a length of 7 units

∴Area of square ABCD = \(l^{2}\) \(units^{2}\)

                                       = \(7^{2}\) \(units^{2}\)

                                       = \(49\) square units