1. Working on a circle of radius 10cm, explain in detail how to determine the values of each of the following trigonometric expres- sions. Include a picture for each to help with your explanations.
(a) cos(5π)
(b) sin(−9π/2)
(c) sin(183π/2)

2. Approximate the value of cos π◦. Explain your reasoning. Do not use a calculator. Include a picture to help with your explanation.

Answer:

Step 1:

a.) 16 pets in total (1 + 0 + 2 + 0 + 3 + 8 + 0 + 2)

b.) the mean is 2 (16 is the total number of pets, divide that by 8 which is the total number of students asked, 16/8 = 2)

Step 2:

a.) 0, 0, 0, 1, 2, 2, 3, 8 (zero, one, two, three, four, five, six, seven, eight.)

b.) 0 and 3 are the middle numbers (center.)

c.) 3/2 = 1.5 (0+3 = 3 divided by 2 = 1.5)

Step 3:

- most of the students did not have any pets, so the mode would be 0 (it is zero because zero appears in the set of numbers 3 times. More than any other number).

Step 4:

They should use the mean of the amount of pets the students have; this is because the mean is the average amount of pets counting everyone in class—regardless on if there were zeros in the list.

_________________________________

_________________________________

Answer:

$6,840

Step-by-step explanation:

The critical value that should be used in constructing the confidence interval is 2.132 (rounded to three decimal places).

What is Critical value ?

In statistics, a critical value is a threshold value that is used to determine whether to reject or fail to reject the null hypothesis in a statistical test. It is typically based on the significance level of the test, which is the probability of rejecting the null hypothesis when it is actually true.

To find the critical value for a 90% confidence interval with n = 5, we need to use a t-distribution with (n-1) degrees of freedom.

Using a t-distribution table or a calculator, we can find the critical value with a 90% confidence level and 4 degrees of freedom (n-1 = 5-1 = 4) to be approximately 2.132.

Therefore, the critical value that should be used in constructing the confidence interval is 2.132 (rounded to three decimal places).

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Answer:

Yes, it's a parallelogram bcz the opposite sides are parallel and equal.

Answer: 48

Step-by-step explanation:

180-132=48

Answer:

48

Step-by-step explanation:

angle = 132

supplementary angle = 180

measure of supplementary angle = 180 - 132 = 48

thus the measure of the supplement is 48

hope you got your answer.

Answer:

[tex]\dfrac{\boxed{2}}{\boxed{3}} \times \dfrac{\boxed{1}}{\boxed{2}} = \dfrac{\boxed{1}}{\boxed{3}}[/tex]

Step-by-step explanation:

The square is 1 unit long and 1 unit wide
There are 3 smaller rectangles in the horizontal direction

Length of each rectangle is therefore 1/3 unit

There are 6 rectangles along the vertical direction

The height of each rectangle is therefore 1/6 unit

The shaded area is 2 rectangles wide and 3 rectangles in height

Width of shaded area = 2 x 1/3 = 2/3

Height of shaded region = 3 x 1/6 = 1/2

Area of shaded rectangle is

[tex]\dfrac{\boxed{2}}{\boxed{3}} \times \dfrac{\boxed{1}}{\boxed{2}} = \dfrac{\boxed{1}}{\boxed{3}}[/tex]

a) An exponential equation in the form of y = a(b)ˣ that can model the amount of money (future value) in Patrick's account, y, x years after starting the account is y = 894(1.02)ˣ.

b) If Patrick makes no other deposits or withdrawals, after 5 years or approximately 6 years his account will have more than $1,000 (future value).

An exponential equation is a mathematical function, written in the form of y = a(b)ˣ, where y is the ending value, a is the initial value, b is the growth or decay rate, and x is the exponent or number of years.

Thus, there are two types of exponential functions: exponential growth and exponential decay functions.

y = 894(1.02)^6

1,000 ≤ 894(1.02)ˣ

I/Y (Interest per year) = 2%

Present Value = $894

FV (Future Value) ≥ $-1,000

Results:

x = 5.658

x ≈ 6 years

= $1,006.79

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Patrick spent last summer working in construction with his dad, and he put $894 of his earnings into a new high-yield savings account. The money in this savings account will increase by 2% each year.

a) Write an exponential equation in the form of y = a(b)ˣ that can model the amount of money in Patrick's account, y, x years after starting the account. Use whole numbers, decimals, or simplified fractions for the values of a and b.

y =

b) If Patrick makes no other deposits or withdrawals, after how many years will his account have more than $1,000?

Her next step in obtaining the area of the triangle is replacing the numeric values of h and y into the area formula.

The area of a rectangle of base b and height h is given by half the multiplication of dimensions, as follows:

A = 0.5bh.

The dimensions for this problem are given as follows:

Hence the formula is:

A = 0.5yh.

Hence the actual values of y and h must be inserted into the formula to obtain the area of the triangle.

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The estimate of the cost for a 20-ft cord is given as follows:

$74.66.

To find the regression equation, which is also called called line of best fit or least squares regression equation, we need to insert the points (x,y) in the calculator.

The points in the context of the problem are given as follows:

(3, 12.75), (5, 16), (6, 25.99), (50, 185).

Inserting these points into a calculator, the regression equation is given as follows:

y = 3.6794x + 1.06462.

Hence the estimate of the cost for a 20-ft cord is obtained when x = 20 as follows:

y = 3.6794(20) + 1.06462

y = $74.66.

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The median number of newspapers sold is 202 newspaper. So, correct option is C.

To find the median, we need to arrange the given data in ascending or descending order.

The given data in ascending order: 71, 81, 113, 202, 242, 248, 269

Since there are 7 data points, the median will be the fourth value in the sorted list. Therefore, the median number of newspapers sold is 202.

Hence, the correct answer is option C, which states that the median number of newspapers sold is 202.

The median is the middle value of a dataset when arranged in order, and it's a measure of central tendency that is less affected by outliers than the mean. In this case, the median value represents the value at which half the data points are below it and half are above it.

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Complete question is:

A store manager kept track of the number of newspaper sold each week over a seven week period. the result were as fellows 71,81,202,113,269,248,242​

Find the median number of newspapers sold.

A. 175 newspapers

B. 113 newspapers

C. 202 newspapers

D. 242 newspapers

Answer:

Let's start by using algebra to solve for the original amount that Alex paid for his shares.

Let X be the original amount that Alex paid for his shares.

We know that his shares dropped in value by 35%, so after the drop, he had 65% of his original investment left:

0.65X = $72,800

Solving for X:

X = $72,800 / 0.65

X = $112,000

Therefore, Alex paid $112,000 for his shares to begin with.

The adjusting entry that Tanning Company will make for Allowance for Doubtful Account will be:

Data:

Total credit sales = $1,000,000

Accounts receivable balance = $310,000

Estimated uncollectible receivables = $21,700

The adjusted balance for allowance for doubtful accounts will be:

= Credit balance + Estimated uncollectible receivables

= $2,200 + $21,700

= $23,900

So, the Company will make an adjusting entry by debiting Bad Debt Expense for $21,500 and crediting Allowance for Doubtful Accounts for $21,500 which will increase the balance of the allowance for doubtful accounts to $23,900.

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Answer:

No I don't. The editor will receive 360 undelivered mail.

Step-by-step explanation:

He sends 12000 emails, 3/100 of them come back undelivered.

Multiply to find the answer:

12000 x 3/100 = 36000/100 = 360

Simple as that; the editor will find that 360 of his sent emails will come back undelivered.

Answer:

B’ = (-11, 1)

Step-by-step explanation:

Because the triangle is reflected across the line x = -2, it is being reflected across a vertical line.

Therefore only the x-coordinate will change.

As B is 9 units right of the line x = 2, the coordinates of B’ will be (-2 - 9, 1)

Which will be (-11, 1)

The biggest length stick that will fit is 16.49 units long.

The length stick which will fit into Elaina's 12* 8*8 tank can be found using the Pythagorean theorem.

The diagonal length, of tank will be equal to square root of the sum of the squares of its length, width and height.

So, the diagonal length of the tank, using Pythagorean theorem, is

= √(12² + 8² + 8²)

= √(144 + 64 + 64)

= √272

≈ 16.49.

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Answer:

The correct answer is (C) 310.

Multiplying the given expression by 36 gives:

(32)(38) + (35)(35) - (33)(37)

= 1216 + 1225 - 1221

= 1220

So the equivalent expression is 1220.

Option (C) 310 is not equivalent to 1220.

The State Cash Flow Statement using the direct method.

                                                         OP                       INV                  FIN

Personnel emolument                  2,000,000

CRF charges                                 1,000,000

Statutory revenue allocation       20,000,000

Proceeds from sale of fixed assets                          100,000

Purchase of marketable securities                           50,000

Purchase & construction of fixed assets                  500,000

Share of VAT                                 200,000

Share of excess crude oil            100,000

Internally generated revenue    10,000,000

Gratuities and pension              15,000,000

Miscellaneous income                50,000

Overhead expenses                   36,000

Recurrent grant made                20,000

Miscellaneous expenses          10,000

Servicing & repayment of public debts                                            100,000

Grants & subventions from NGO                                                     200,000

Proceeds from loan & other borrowings                                         300,000

Dividends received                                                                           100,000

                                            12,234,000             -450,000              500,000  

  Net Cash Flow for the year ended 31 December 2006: 12,284,000  

To prepare the State Cash Flow Statement using the direct method, we'll classify cash flows into three categories: Operating Activities (OP), Investing Activities (INV), and Financing Activities (FIN). Then, we'll calculate the net cash flow for each category and add them together to find the net cash flow for the year.

Operating Activities:

(-2,000,000 - 1,000,000 + 20,000,000 + 200,000 + 100,000 + 10,000,000 - 15,000,000 + 50,000 - 36,000 - 20,000 - 10,000) = 12,234,000

Investing Activities:

(100,000 - 50,000 - 500,000) = -450,000

Financing Activities:

(-100,000 + 200,000 + 300,000 + 100,000) = 500,000

Net Cash Flow for the year ended 31 December 2006:

12,234,000 (Operating Activities) - 450,000 (Investing Activities) + 500,000 (Financing Activities) = 12,284,000

The above answer is in response to the question below;

The following information has been extracted from the records of WELFARE STATE of Nigeria for the year ended 31 December 2006:

Personnel emolument                  2,000,000

CRF charges                                 1,000,000

Statutory revenue allocation       20,000,000

Proceeds from sale of fixed assets  100,000

Purchase of marketable securities  50,000

Purchase & construction of fixed assets  500,000

Share of VAT                                 200,000

Share of excess crude oil            100,000

Internally generated revenue    10,000,000

Gratuities and pension              15,000,000

Miscellaneous income                50,000

Overhead expenses                   36,000

Recurrent grant made                20,000

Miscellaneous expenses          10,000

Servicing & repayment of public debts      100,000

Grants & subventions from NGO               200,000

Proceeds from loan & other borrowings       300,000

Dividends received                                       100,000

You are required to:

Prepare the State Cash Flow Statements for the year ended 31 December 2006 using the direct method approach (ICAN May 2008)

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The circumference of the circle with a radius of 10 cm is 20π cm, option (C) is correct.

A circle's perimeter, or the distance encircling it, is known as its circumference. It is determined by multiplying the circle's diameter by pi. But in this case, we are given the radius of the circle, which is half of the diameter.

To get a circle's circumference, use the following formula:

C = 2πr

where;

r = radius of the circle

π = mathematical constant pi (approximately equal to 3.14).

Given the radius of the circle as 10 cm, we can use the formula to find its circumference:

C = 2πr

C = 2π(10 cm)

C = 20π cm

Hence, option C is correct.

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The correct question is:

What is the circumference of the circle with radius = 10 cm (leave your answer of π).

A) 10π cm

B) 5π cm

C) 20π cm

D) 10π cm

Answer:

2.5 cm

Step-by-step explanation:

The small arrow is 1/2 the side of the large arrow.  1/2 of 5 is 2.5 or 2 1/2.

Helping in the name of Jesus.

The answer is $11,092.63.

This could be calculated using the proportion. If the value of the car decreases by 15% each year, that means that after each year the value of the car is 85% of the value from the first year.

After 1st year:

$25,000 : 100% = x1 : 85%

x1 = $25,000 · 85% ÷ 100%

x1 = $21,250

After 2nd year:

$21,250 : 100% = x2 : 85%

x2 = $21,250 · 85% ÷ 100%

x2 = $18,062.5

After 3rd year:

$18,062.5 : 100% = x3 : 85%

x3 = $18,062.5 · 85% ÷ 100%

x3 = $15,353.12

After 4th year:

$15,353.12 : 100% = x4 : 85%

x4 = $15,353.12 · 85% ÷ 100%

x4 = $13,050.15

After 5th year:

$13,050.15 : 100% = x5 : 85%

x5 = $13,050.15 · 85% ÷ 100%

x5 = $11,092.63

Therefore, the value of the car 5 years after it is purchased is $11,092.63.

Answer:

$95

Step-by-step explanation:

Carmen invested $2,000 in a mutual fund with a loading rate of 4.75%. To calculate the loading charge, we can multiply the amount invested by the loading rate: $2,000 * 4.75% = $95. So, the loading charge for this mutual fund was $95.

Answer: C: 5/8

Step-by-step explanation:

Simply 5/8 of the bar is filled in

Using probability, we can find probability of the random variable, x falling in the shaded region as to be 5/8.

Here, we have,

Probability is the ratio of favorable outcomes to all other potential outcomes of an event. The symbol x can be used to express the quantity of successful outcomes for an experiment with 'n' outcomes. The following formula can be used to determine an event's probability.

Positive Outcomes/Total Results = x/n = Probability(Event)

Let's look at a simple example to better understand probability. Imagine that we need to predict whether it will rain or not. The right response to this question is "Yes" or "No." Whether it rains or not is uncertain. Probability is used to predict the outcomes when tossing coins, rolling dice, or drawing cards from a deck of cards.

Here in the question,

Total region = 8.

Shaded region = 5

So, probability of falling in the shaded region = 5/8

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Answer:

  B. CPCTC

  D.  opposite sides are congruent

Step-by-step explanation:

You want to know the necessary claims for proving opposite angles are congruent in a parallelogram.

Given parallelogram ABCD and diagonal AC, you can prove opposite angles congruent in this way:

  AB≅CD and BC≅DA . . . . . opposite sides are congruent

  AC≅CA . . . . . . . . . . . . . . reflexive property of congruence

  ∆ABC≅∆CDA . . . . . . . . . . . SSS congruence

  ∠B ≅ ∠D . . . . . . . . . . . . Corresponding parts of congruent triangles

When doing the proof, the necessary claims are ...

  B. Corresponding parts of congruent triangles are congruent

  D. Opposite sides are congruent.

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The percentage increase in the number of water bottles from February to April is 19%.

A company manufactures water bottles. The list describes the amount of water bottles manufactured in three months.

Therefore,

February: 4100 water bottles

March: 7% more water bottles than in February

April: 500 more water bottles than in march

Therefore,

Number of water bottles in march = 4100 + 7% of 4100

Number of water bottles in march =4100 + 7 / 100 × 4100

Number of water bottles in march = 4100 + 287

Number of water bottles in march =  4387

Hence,

Number of water bottles manufactured in April = 4387 + 500 = 4887

Therefore,

percentage increase from February to April = 4887 - 4100 / 4100 × 100

percentage increase from February to April = 787 / 4100 × 100

percentage increase from February to April = 78700 / 4100

percentage increase from February to April = 19.1951219512

percentage increase from February to April = 19%

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The correct numbers for Derrek and Thomas' football teams are :

According to the information given, Thomas's football team lost 3 yards in their first drive, which means they moved backward 3 yards from the line of scrimmage. This can be represented as -3 on the number line.

On the other hand, Derrek's football team gained 5 yards in their first drive, which means they moved forward 5 yards from the line of scrimmage. This can be represented as +5 on the number line.

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A conclusion on the null hypothesis is C. Reject H_{0} because the P-value is less than or equal to a.

Stated in the initial description is the null hypothesis, establishing that adults who possess a desire to eliminate all personal information available online would equate to or exceed 53%, while the alternative conjecture rests on this percentage being under 53%.

The statistical significance level at hand designated as alpha equals 0.05 indicates that a P-Value having less than or equal value of 0.05 is necessary for declining the null hypothesis. As provided by the task's question, the computed P-value registers a score of 0.0059 which falls below the established significance level of 0.50 and thus resulting in null hypothesis rejection.

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Answer:

[tex]=\left(x-2\right)\left(x-3\right)\\[/tex]

Step-by-step explanation:

Given:

[tex]x^2-5x\:+6[/tex]

To find:

Equivalent to x^2-5x+6

Explanation:

[tex]x^2-5x+6\\=\left(x^2-2x\right)+\left(-3x+6\right)\\=x\left(x-2\right)-3\left(x-2\right)\\\mathrm{Factor\:out\:common\:term\:}x-2\\=\left(x-2\right)\left(x-3\right)[/tex]

Final Answer:

(x-2)(x-3)