If you know the radius, r, of a circle, what do you multiply rby to get the circle's CIRCUMFERENCE?

Volume of a prism: base area x height

Edge of each cube: 1 inch

Cubes used for the first layer: 42

Base area = 42 inches

height = 7 inches (or layers )

Volume = 42 x 7 = 294 cubic inches

The external auditor gathers a sample of shipping documents and matches them to entries in the sales journal to provide corroborating evidence that recorded sales represent authorized transactions.

This is because shipments of goods are recorded as sales, and shipments of goods are for authorized sales. Therefore, recorded sales were for goods that were shipped.In addition, it is essential to note that FOB (Free On Board) shipping point is a legal term that indicates that the buyer assumes ownership of the goods as soon as they leave the seller's dock. As a result, the buyer is responsible for paying for the transportation of the goods from the seller's location to their destination.

Therefore, when a rich company sells household goods and appropriately records its sales upon shipment, it indicates that the goods are shipped FOB (Free On Board) shipping point. This method is used to ensure that shipments of goods are for authorized sales and that recorded sales were for goods that were shipped.

The external auditor gathers a sample of shipping documents and matches them to entries in the sales journal to provide corroborating evidence that the recorded sales represent authorized transactions.

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Answer:

The expression is A that is -b

Answer:

150% of 45 less than 100, greater than 100 but less than 150. Or greater than 150?

Answer:

Less than 100?                                                  YES

Step-by-step explanation:

150% of 45 less than 100, greater than 100 but less than 150, or greater than 150?

"150% of 45 "

150% (45)

1.5*(45) = 67.5      

Less than 100?                                                  YES

Greater than 100 but less than 150               NO

Greater than 150?                                             NO

Answer:

27°,63°

Step-by-step explanation:

Let the two angles be a and b.

They are complementary, meaning they add up to 90. Thus:

\(a+b=90\)

And we are told their difference is 36. Therefore:

\(a-b=36\)

Solve for the system of equations. Add b to both sides in the second equation:

\(a=b+36\)

Substitute this into the first:

\((b+36)+b=90\)

Combine like terms;

\(2b+36=90\)

Subtract 36:

\(2b=54\)

Divide by 2:

\(b=27\)

So, b is 27 degrees.

Use the second equation again:

\(a-b=36\)

Now that we know b is 27, substitute:

\(a-27=36\)

Add 27 to both sides:

\(a=63\)

So, a is 63 degrees.

And we're done :)

Answer:

27 and 63

Step-by-step explanation:

x - y = 36

x + y = 90

add the equations together

2x = 126

x = 63

substitute x for x in the first equation

63 - y = 36

y = 27

The function corresponding to zeroes 6 and -4 is f(x)=(x-6)(x+4) i.e. A.

What is a function?

A function is defined as a relation between a set of inputs having one output each. In simple words, a function is a relationship between inputs where each input is related to exactly one output. Every function has a domain and co-domain or range. A function is generally denoted by f(x) where x is the input. The general representation of a function is y = f(x).

There are several types of functions in math. Some important types are:

Injective function or One to one function: When there is mapping for a range for each domain between two sets.

Surjective functions or Onto function: When there is more than one element mapped from domain to range.

Polynomial function: The function which consists of polynomials.

Inverse Functions: The function which can invert another function.

Now ,

We can find function for zeroes 6 and -4 by putting f(x)=0

Therefore,

(x-6)(x+4)=0

x-6=0 and x+4=0

Hence,

           x=6,-4

          The function corresponding to zeroes 6 and -4 is f(x)=(x-6)(x+4).

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The sum of 1039 g and 36.7 kg expressed in milligrams (mg) to the correct number of significant figures is 37,739,000 mg.

To perform the addition, we need to convert 36.7 kg to grams before adding it to 1039 g. There are 1000 grams in 1 kilogram, so we multiply 36.7 kg by 1000:

36.7 kg * 1000 g/kg = 36,700 g

Now, we can add 1039 g and 36,700 g:

1039 g + 36,700 g = 37,739 g

To convert grams to milligrams, we multiply by 1000 because there are 1000 milligrams in 1 gram:

37,739 g * 1000 mg/g = 37,739,000 mg

The final result, expressed in milligrams with the correct number of significant figures, is 37,739,000 mg.

The sum of 1039 g and 36.7 kg, expressed in milligrams (mg) with the correct number of significant figures, is 37,739,000 mg. Remember to consider unit conversions and maintain the appropriate number of significant figures throughout the calculation.

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Answer:

slope is undefined

Step-by-step explanation:

We can use the slope formula

m = (y2-y1)/(x2-x1)

   = (-4 -1)/(8-8)

     = -5/0

We cannot divide by zero so the slope is undefined

Answer:

Slope is undefined .

Step-by-step explanation:

        y2 - y1

m =   ---------------  

         x2 - x1

           -4 - 1             -5

m =   ---------------  =  ----- -  = 0

            8 - 8             0

Answer:

Mean = 86

Median = 86

Mode = 93

Range = 20

Step-by-step explanation:

Mean is the average of a set of numbers. To find the average, you add all the numbers together and divide the product by how many numbers are in the set so:

93 + 86 + 93 + 85 + 73 = 430

430/5 = 86

Median is the middle of a set of numbers.

First put the numbers in order of smallest to biggest

73, 85, 86, 93, 93.

The middle number is 86 so the median is 86.

A mode or modes are numbers that appear most frequently in a number of sets. They’re can be multiple modes.

The most frequent number is 93 so the mode is 93

Range is the difference of the biggest number and the smallest number. The biggest is 93 and the smallest is 73.

93 - 73 = 20

The range is 20

The amount that the credit union will finance is $24169.60

We have given that the cost of the car is $22,346. 16

and the credit union required 10% down payment

and sale tax=7.6%

The license and title charges are $125. 13.

We have to determine that the  amount that the credit union will

finance Now  we have sale tax 7.6% for $22,346. 16

Therefore, we get

\(\frac{7.6}{100} \times 22,346. 16=1698.31\)

credit union finance=cost of car+sales tax+the license and title  charges.

\(=22346.16+1698.31+12.13\\=24169.60\)

Therefore, the amount that the credit union will finance is $24169.60

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Answer:

7

Step-by-step explanation:

KU=UM

3x+3=4x-4

x= 7

A Parametric equations for the tangent line at the point (v2, v2, 5):x = v2 - (√2/2)t -- (3),y = v2 + (√2/2)t -- (4),z = 5 + t -- (5).These equations describe the tangent line to the helix at the point (v2, v2, 5).

To find the tangent line to the helix given by the vector equation r(t) = 2cos(t)i + 2sin(t)j + tk at the point (v2, v2, 5), d to find the value of t at that point.

The x-coordinate and y-coordinate of the helix at any given point t are given by 2cos(t) and 2sin(t) respectively the following equations:

2cos(t) = v2 -- (1)

2sin(t) = v2 -- (2)

Dividing equation (2) by equation (1),

(2sin(t))/(2cos(t)) = v2/v2

simplifying,

tan(t) = 1

From this conclude that t = π/4 or t = 5π/4. There are infinitely many values of t that satisfy tan(t) = 1, but consider the values within the given range of t.

T(t), which represents the tangent vector at any point on the helix. differentiate the vector equation r(t) = 2cos(t)i + 2sin(t)j + tk with respect to t: r'(t) = -2sin(t)i + 2cos(t)j + k

So, the tangent vector T(t) is given by:

T(t) = -2sin(t)i + 2cos(t)j + k

Now, the value of t (t = π/4 or t = 5π/4) to find the tangent vector at the point (v2, v2, 5).

For t = π/4:

T(π/4) = -2sin(π/4)i + 2cos(π/4)j + k

= -√2/2 i + √2/2 j + k

For t = 5π/4:

T(5π/4) = -2sin(5π/4)i + 2cos(5π/4)j + k

= √2/2 i - √2/2 j + k

So, the tangent vectors at the point (v2, v2, 5) are:

T(π/4) = -√2/2 i + √2/2 j + k

T(5π/4) = √2/2 i - √2/2 j + k

Tangent vectors to write the parametric equations for the tangent line.

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Answer: They made 6 three point shots.

Step-by-step explanation:

Make your equation

(((6x1)+(27x2)+(3x)=78

Simplify

(6+54+3x=78)

60+3x=78

Subtract from both sides

3x=18

Divide from both sides

x=6

The basketball team scored 6 shots worth 3 points.

The number of baskets the players made that were worth 3 points each is 6 and the equation used for this is, total score = The number of 1-point baskets × 1 + The number of 2-point baskets × 2 + The number of 3-point baskets × 3.

A formula known as an equation uses the equals sign to denote the equality of two expressions.

Given:

Total scored by the team = 78 points,

The number of 1-point baskets = 6,

The number of 2-point baskets = 27,

If b is the number of 3-point baskets, the equation can be given as,

Total score = The number of 1-point baskets × 1 + The number of 2-point baskets × 2 + The number of 3-point baskets × 3

78 = 6 × 1 + 27  × 2 + b  ×3

b = 6

Therefore, the number of baskets the players made that were worth 3 points each is 6.

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The correct answer is option D. We can be 95% confident that the sample proportion is captured by the confidence interval.

The margin of error of plus or minus three percentage points at a 95% confidence level means that the true proportion of people who jog regularly in the population is estimated to be between 15% and 21%. We can be 95% confident that the true proportion of people who jog regularly falls within this interval.

Therefore, option B is correct. Option A is incorrect because it implies that the margin of error always holds true for any sample size, which is not the case. Option C is incorrect because it presents a range of values for the population, not for the estimate. Option E is incorrect because it refers to the proportion of samples that would find the same sample proportion, not the range of values within which the true proportion lies.

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SOLUTION

Consider the graph shown:

From the graph the equation is:

Therefore the approximate equation is:

Substitute x=4 into the equation:

True, a data warehouse allows users to specify certain dimensions or characteristics.

In a data warehouse, dimensions represent the different aspects or characteristics by which data can be categorized or analyzed. These dimensions can include various attributes or variables that provide context and organize the data.

Users of a data warehouse can specify these dimensions based on their analytical needs and the nature of the data being stored.

For example, in a sales data warehouse, common dimensions may include product, customer, time, and location.

By specifying these dimensions, users can slice and dice the data based on different criteria and gain insights from various perspectives.

By defining dimensions, users can navigate through the data warehouse and perform multidimensional analysis using tools such as OLAP (Online Analytical Processing).

Dimensions provide a structure for organizing and querying data in a way that facilitates analysis and reporting.

In summary, a data warehouse allows users to specify dimensions or characteristics that help organize and analyze the data stored in the warehouse. These dimensions provide a framework for users to navigate and explore the data from different perspectives.

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The LCM of a and c is 20.

Here we need to find the minimum possible LCM of a and c. For this a and c must have the minimum possible values.

Now,

LCM of a and b is 12

LCM of b and c is 15

Now for this to be true, b must be a number that is a common factor of 12 and 15, which is 3

Hence, b is 3.

Hence a will obviously be 4 and c will be 5.

Hence the LCM of a and c is 20.

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Complete Question

The least common multiple of a and b is 12, and the least common multiple of b and c is 15. What is the least possible value of the least common multiple of a and c?

The interest earned by Mrs Grey over the 7 years is R5670. The cost of the television set 5 years ago was R20,600.

4.1.1 To calculate the interest earned by Mrs Grey over 7 years, we use the formula for simple interest: Interest = Principal x Rate x Time. Mrs Grey's principal is R18,000 and the rate is 4.5% per annum. The time is 7 years. Using the formula, we can calculate the interest as follows:

Interest = R18,000 x 0.045 x 7 = R5670. Therefore, Mrs Grey has earned R5670 in interest over the 7 years.

4.1.2 To calculate the cost of the television set 5 years ago, we need to account for the inflation rate. The cost of the television set now is R27,660. The average rate of inflation over the last 5 years is 6.7% per annum. We can use the formula for compound interest to calculate the original cost of the television set:

Cost 5 years ago = Cost now / (1 + Inflation rate)^Time

Cost 5 years ago = R27,660 / (1 + 0.067)^5 = R20,600. Therefore, the cost of the television set 5 years ago was R20,600.

4.1.3 To determine the rate of simple interest Mrs Grey should have invested her money at 7 years ago, we can use the formula for interest: Interest = Principal x Rate x Time. We know the principal is R18,000, the time is 7 years, and the interest earned is R5670. Rearranging the formula, we can solve for the rate:

Rate = Interest / (Principal x Time)

Rate = R5670 / (R18,000 x 7) ≈ 0.0448 or 4.48% per annum. Therefore, Mrs Grey should have invested her money at a rate of approximately 4.48% per annum to have earned enough interest to purchase the television set using only her original investment and the interest earned over the 7 years.

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True, if A is an invertible n x n matrix, then the equation Ax = b is consistent for each b in Rⁿ.

When A is an invertible n x n matrix, it means that A has a unique inverse, denoted as A⁻¹, which is also an n x n matrix. This implies that for any given vector b in Rⁿ, there exists a unique solution x in Rⁿ that satisfies the equation Ax = b.

To understand why this is true, consider the definition of matrix multiplication. In the equation Ax = b, A is multiplied by x to obtain b. Since A is invertible, we can multiply both sides of the equation by A⁻¹ (the inverse of A) on the left, yielding A⁻¹Ax = A⁻¹b.

Now, according to the properties of matrix multiplication, A⁻¹A results in the identity matrix I_n (an n x n matrix with ones on the diagonal and zeros elsewhere), and any vector multiplied by the identity matrix remains unchanged. Therefore, we get I_nx = A⁻¹b, which simplifies to x = A⁻¹b.

This shows that for any given vector b in Rⁿ, there exists a unique solution x = A⁻¹b that satisfies the equation Ax = b when A is an invertible matrix. Hence, the equation Ax = b is consistent for each b in Rⁿ.

Therefore, the correct answer is True.

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The probability that a person arriving to use the machine will find it idle is 1/3 or 0.3333. Option a is correct.

Use the concept of an M/M/1 queue to calculate the probability, which models a single-server queue with exponential interarrival times and exponential service times.

In this case, the interarrival time follows an exponential distribution with a rate parameter of λ = 5 persons per hour (or 1/12 persons per minute). The service time (copying time) also follows an exponential distribution with a rate parameter of μ = 1/8 persons per minute (since each person uses the machine for an average of 8 minutes).

In an M/M/1 queue, the probability that the system is idle (no person is being served) can be calculated as:

P_idle = ρ⁰ × (1 - ρ), where ρ is the traffic intensity, defined as the ratio of the arrival rate to the service rate. In this case, ρ = λ/μ.

Plugging in the values, we have:

ρ = (1/12) / (1/8) = 2/3

P_idle = (2/3)⁰ × (1 - 2/3) = 1/3

Therefore, the probability is 1/3 or approximately 0.3333.

Thus, option (A) is the correct answer.

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Answer:

Area= l+b) ×2

6.5x+5ft +5ft

13x+20ft

Answer:

y = x + 6

x = 1

y = ¼(x - 5) + 3

Step-by-step explanation:

Vetices are;

A(1,5), B(5,3) and C(-3, -2)

Thus;

Median of AB is; D = (1 + 5)/2, (5 + 3)/2

D = (3, 4)

Median of BC is; E = (5 + (-3))/2, (3 + (-2))/2

E = (1, 0.5)

Median of AC is; F ; (-3 + 1)/2, (-2 + 5)/2

F = (-1, 1.5)

Thus, the median lines will be;

CD, AE & BF.

Thus;

Equation of CD is;

(y - (-3))/(x - (-2)) = (-2 - 4))/(-3 - 3)

(y + 4)/(x + 2) = -6/-6

y - 4 = 1(x + 2)

y = 4 + x + 2

y = x + 6

Equation of AE;

(y - 5)/(x - 1) = (0.5 - 5)/(1 - 1)

(y - 5)/(x - 1) = -4.5/0

Cross multiply to get;

0(y - 5) = -4.5(x - 1)

-4.5x = -4.5

x = 1

Equation of BF;

(y - 3)/(x - 5) = (1.5 - 3)/(-1 - 5)

(y - 3)/(x - 5) = -1.5/-6

(y - 3)/(x - 5) = 1/4

y - 3 = ¼(x - 5)

y = ¼(x - 5) + 3

Answer:

the correct options are 1, 2, 5, and 6th

1. and 2.

all functions have a dependant variable y and independent variable x, and the set of dependant variables is called its range whereas the set of independent variables is called its domain.

5. and 6.

In a horizontal line 1 input associates itself with exactly one ouput, even tho the output is constant (same) for all values of x, and that's the property of a function

Answer:

all functions have dependent variables

all functions have an independent variable

a horizontal line Is an example of a functional relationship

Step-by-step explanation:

I can explain what each item is, but I don't know exactly what it's asking

5 is a coefficient. The number attached to the left of the variable/term is always called the coefficient

x is the term/variable. Can always change the outcome, it just depends on the value inputed at that place

3 is a constant, since there's no term attached to it, it will always stay 3

Hope this helps in some way

Answer: 3

Step-by-step explanation:

32 × 3 = 96

96 ÷ 3 = 3

that means 3 dollars per student for the app.

Answer:

x= 4

Step-by-step explanation:

3x + 7 = 5x - 1

combine the like numbers: add 1 to the other side, isolating 5x

3x + 8 = 5x

Subtract 3x from 5x, isolating 8

8 = 2x

divide

4 = x

Check if it works

3(4) + 7 = 5(4) - 1

19 = 19

Yes, it is correct

Answer: There is no points

Step-by-step explanation:

Answer:

B (the second one)

Step-by-step explanation:

The thin yellow line in A only goes from 14-30. However, the correct numbers listed range from 12-30. Line B matches up with this data

Answer:

The rule for the linear function will be:

f(x) = 5/2x - 4

Step-by-step explanation:

We know that linear function can be represented using the slope-intercept formula

y = mx+b

where m is the slope and b is the y-intercept

Given the function is linear

Taking two points

Finding the slope between (0, -4) and (2, 1)

Using the formula

Slope = m =  [y₂ - y₁] /  [x₂ - x₁]  

                 =  [1 - (-4)] / [2 - 0]  

                 = 5 / 2

Thus, the slope of the line = m = 5/2

We know that the value of y-intercept can be determined by setting x = 0, and determining the corresponding value of y.

From the graph, it is clear

at x = 0, y = -4

Thus, the y-intercept b = -4

Now, substituting m = 5/2 and b = -4 in the slope-intercept form of linear function

y = mx+b

y = (5/2)x + (-4)        ∵ m = 5/2, b = -4

y = 5/2x - 4

or

f(x) = 5/2x - 4     ∵  y = f(x)

Therefore, the rule for the linear function will be:

f(x) = 5/2x - 4

Answer:

Five domain values of the function f(x) = x² - 1, are; 1, 2, 3, 4, 5

Five range values of the function f(x) = x² - 1, are; 0, 3, 8, 15, 24

Step-by-step explanation:

The values in the domain are the values of the independent or (normally) x-variable

The values i the range are the values obtained by applying the function relationship to the domain as follows;

Let 'f(x)' represent the function that generates the values of the data in the data set,

For f(x) = x² - 1, we have the following table;

\(\begin{array}{ccc}x&f(x)\\1&0\\2&3\\3&8\\4&15\\5&24\end{array}\)

Therefore;

The function is f(x) = x² - 1

The five domain values are; 1, 2, 3, 4, 5

The five range values are; 0, 3, 8, 15, 24.