Mathematics College

Comprehensive

Angel Company has prepared its financial statements for the year ended December 31, 2019, and for the 3 months ended March 31, 2020. You have been asked to prepare a statement of cash flows for the 3 months ended March 31, 2020. The company's balance sheet data at December 31, 2019, and March 31, 2020, and its income statement data for the 3 months ended March 31, 2020, follow. You are satisfied as to the correctness of the amounts presented.

Balance Sheet Data
December 31,
2019 December 31,
2020
Cash $ 25,300 $ 79,400
Marketable investments (at cost) 17,500 8,300
Allowance for decrease in value (1,000) (900)
Accounts receivable 24,320 49,320
Inventory 31,090 48,590
Total current assets $ 97,210 $184,710
Land 40,000 18,700
Building 250,000 250,000
Equipment — 81,500
Accumulated depreciation (15,000) (16,250)
Equity investment (30% ownership of Titan Company) 61,220 67,100
Other assets 15,100 15,100
Totals $448,530 $600,860
Accounts payable $ 21,220 $ 38,417
Income taxes payable — 13,529
Total current liabilities $ 21,220 $ 51,946
Bonds payable 50,000 115,000
Discount on bonds payable (2,300) (2,150)
Deferred taxes payable 510 846
Preferred stock 30,000 —
Common stock 80,000 110,000
Unrealized decrease in value of marketable investments (1,000) (900)
Dividends declared — (8,000)
Retained earnings 83,100 147,118
Other liabilities 187,000 187,000
Totals $448,530 $600,860

Income Statement Data
for the 3 Months Ended
March 31, 2020
Sales $242,807
Gain on sale of marketable investments 2,400
Equity method earnings from Titan investment (30% ownership) 5,880
Ordinary gain on condemnation of land 8,560
Total revenues $259,647
Cost of sales $157,354
General and administrative expenses 22,010
Depreciation 1,250
Interest expense 1,150
Income taxes 13,865
Total expenses $195,629
Net income $ 64,018
Your discussion with the company's controller and a review of the financial records have revealed the following information:

On January 7, 2020, the company sold marketable securities for cash. These securities had cost $9,200, and had a fair value of $8,600 at December 31, 2019. The remaining marketable securities were adjusted to their $7,400 fair value on March 31, 2020, by adjustment of the related allowance account. The dividend and interest revenue on these marketable securities is not material.
The company's preferred stock was converted into common stock at a rate of one share of preferred for two shares of common. The preferred stock and common stock have par values of $2 and $1, respectively.
On January 16, 2020, 3 acres of land were condemned. An award of $29,860 in cash was received on March 24, 2020. Purchase of additional land as a replacement is not contemplated by the company.
On March 25, 2020, the company purchased equipment for cash.
On March 26, 2020, bonds payable were issued by the company at par for cash.
The equity investment representing a 30% ownership interest in Titan Company included an amount of $9,600 attributable to an increase in the recorded value of depreciable assets at December 31, 2019. This increase is being depreciated at a quarterly rate of $480.
Required:

Prepare a spreadsheet to support the statement of cash flows for Angel for the 3 months ended March 31, 2020. Use the minus sign to indicate cash outflows, a decrease in cash or cash payments.

Answers

Answer 1

Statement of Cash Flows (Indirect Method)

For the 3 months ended March 31, 2020

Angel Company

Net income $64,018

Adjustments to reconcile net income to net cash provided by

operating activities:

Depreciation 1,250 Depreciation

Equity method earnings from Titan investment (5,880) Equity investment earnings

Increase in value of marketable investments (100) Allowance for decrease in value

Deferred taxes payable 336 Deferred taxes

Gain on sale of marketable investments (2,400) Gain on sale of marketable investments

Changes in assets and liabilities:

Accounts receivable (25,000) Accounts receivable

Inventory (17,500) Inventory

Accounts payable 17,197 Accounts payable

Income taxes payable 13,529 Income taxes payable

Other assets - -

Bonds payable 65,000 Bonds payable

Net cash provided by operating activities $44,570

Investing activities:

Proceeds from sale of marketable securities $11,400 Proceeds from sale of securities

Proceeds from condemnation award 29,860 Condemnation award proceeds

Purchase of equipment (81,500) Equipment purchases

Net cash used in investing activities (40,240)

Financing activities:

Issuance of bonds payable $65,000 Bond issuance

Dividends paid (8,000) Dividends paid

Issuance of common stock 30,000 Common stock issuance

Net cash provided by financing activities 87,000

Net increase in cash $91,330

Cash at beginning of period 25,300 Cash, beginning of period

Cash at end of period $116,630 Cash, end of period

Answer 2
To prepare the statement of cash flows for the 3 months ended March 31, 2020, we need to use the indirect method. The statement of cash flows shows the inflows and outflows of cash during the period and is divided into three sections: operating activities, investing activities, and financing activities.

First, we need to calculate the change in cash from December 31, 2019, to March 31, 2020:

Change in cash = Cash at March 31, 2020 - Cash at December 31, 2019
Change in cash = $79,400 - $25,300
Change in cash = $54,100

Next, we need to analyze the transactions during the 3 months ended March 31, 2020, and classify them into the appropriate section of the statement of cash flows.

Operating activities:
- Cash received from customers: $242,807
- Cash paid to suppliers: $108,600
- Cash paid for income taxes: $13,529
Net cash provided by operating activities: $120,678

Investing activities:
- Purchase of equipment: $81,500
- Sale of marketable investments: $9,200
Net cash used in investing activities: $72,300

Financing activities:
- Issuance of common stock: $30,000
- Issuance of bonds payable: $65,000
- Payment of dividends: $8,000
Net cash provided by financing activities: $87,000

Finally, we can prepare the statement of cash flows for the 3 months ended March 31, 2020, as follows:

Angel Company Statement of Cash Flows for the 3 Months Ended March 31, 2020
Cash flows from operating activities:
Cash received from customers $242,807
Cash paid to suppliers ($108,600)
Cash paid for income taxes ($13,529)
Net cash provided by operating activities $120,678

Cash flows from investing activities:
Purchase of equipment ($81,500)
Sale of marketable investments $9,200
Net cash used in investing activities ($72,300)

Cash flows from financing activities:
Issuance of common stock $30,000
Issuance of bonds payable $65,000
Payment of dividends ($8,000)
Net cash provided by financing activities $87,000

Net increase in cash $54,100

Therefore, the net increase in cash for the 3 months ended March

Related Questions

How many radians are in a full circle?

Answers

Answer: 2 Radians

Step-by-step explanation:

    A full circle is 2 full radians, also known as 2π. Half of a circle is equal to 180 degrees, which is equal to one radian, π.

    I have attached a picture of the unit circle below, this picture comes form www.remind.com, but you can find many online.

Angles in a Triangle

Answers

Answer:

Step-by-step explanation:

Z:

the angle b/n z and  65 is 90 b/c its a square and they are found on a straight line (180)

- 65 + 90 + z = 180

-155 + z = 180

-z= 180 - 155= 25

x:

-x + 90 = 180

- x= 180 - 90 = 90

y:

in this case now we have an inner triangle which has only one missing angle so as we know for any triangle ABC; <A + <B + <C = 180 so

- y + x + 65=180

-y+ 90 + 65= 180

-y=180 - 155

- y = 25

Joseph bought a T-shirt for $10.30 and another T-shirt for $18.90. what is the total amount spent

Answers

Answer:

29.2

Step-by-step explanation:

10.30+18.90=29.2

Answer:

$29.20

Step-by-step explanation:

$10.30

+$18.90

=$29.20

HELP URGENT PLEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEZE

Answers

350 is the answer

Step-by-step explanation:

I hope it helps

Mrs Smith oatmeal cookie recipe calls for 2/5 of a cup of sugar how much sugar which she need to make 1/2 of a batch of cookies

Answers

If Mrs. Smith's oatmeal cookie recipe calls for 2/5 of a cup of sugar to make a full batch of cookies, then to make half a batch of cookies, she will need half the amount of sugar.

So, to find out how much sugar Mrs. Smith needs to make half a batch of cookies, we can use the following calculation:

Sugar needed for half a batch = (2/5 cup sugar) x (1/2 batch)

Simplifying this expression, we get:

Sugar needed for half a batch = 2/10 cup sugar

Which can be further simplified to:

Sugar needed for half a batch = 1/5 cup sugar

Therefore, Mrs. Smith will need 1/5 cup of sugar to make half a batch of oatmeal cookies.

The figure below shows the transformation A to become rectangle B.
Which steps describe the transformation shown in figure?

A. a dilation with a factor of 1 1/2 followed by a translation to the left

B. a dilation with a factor of 2/3 followed by a translation to the left

C. a translation with a factor of 1 1/2 followed by a dilation to the left

D. a translation with a factor of 2/3 followed by a dilation to the left

Answers

Answer:

Step-by-step explanation:

A is correct

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For this graph, write the limits which describe the end-behavior of this graph.

Answers

The limits which describe the end behavior of the function are given as follows:

[tex]\lim_{x \rightarrow -\infty} f(x) = 1[/tex][tex]\lim_{x \rightarrow \infty} f(x) = 0[/tex]

What is the end behavior of a function?

The end behavior of a function refers to how the function behaves as the input variable (typically denoted as x) approaches positive or negative infinity. In other words, the end behavior describes the long-term behavior of the function as x becomes very large (either positively or negatively).

We can see that the left of the graph approaches y = 1, hence the limit is given as follows:

[tex]\lim_{x \rightarrow -\infty} f(x) = 1[/tex]

The right of the graph approaches y = 0, hence the limit is given as follows:

[tex]\lim_{x \rightarrow \infty} f(x) = 0[/tex]

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Clinton and Stacy decided to travel from their home near Austin, Texas, to Yellowstone National Park in their RV.
- The distance from their home to Yellowstone National Park is 1,701 miles.
- On average the RV gets 10.5 miles per gallon.
- On average the cost of a gallon of gasoline is $3.60.

Based on the average gas mileage of their RV and the average cost of gasoline, how much will Clinton and Stacy spend on gasoline for the round trip to Yellowstone National Park and back home?

A. $1,166.40
B. $2,480.63
C. $583.20
D. $64,297.80

Answers

Answer:

The answer is A. $1,166.40

Step-by-step explanation:

Find subject and predicate 1. Down went the Cumberland

Answers

Subject: The Cumberland
Predicate: Went down
Subject: the Cumberland
Predicate: went down

Two points on a circle of radius 1 are chosen at random. Find the probability that the distance between the two points is at most 1.5.

Answers

The probability that the distance between two points on a circle of radius 1 is at most 1.5 is approximately 0.477 or 47.7%, which corresponds to the range of central angles less than or equal to 3 radians out of the total central angle of 2π radians.

Let's consider two points on a circle of radius 1, labeled A and B. The distance between A and B is given by the length of the arc AB on the circle, which is a fraction of the circumference of the circle. The circumference of a circle of radius 1 is 2π, so the length of the arc AB is given by

d = θ/2π * 2πr = θ

where d is the distance between A and B, θ is the central angle between A and B (in radians), and r is the radius of the circle (which is 1 in this case).

To find the probability that the distance between A and B is at most 1.5, we need to find the range of central angles that correspond to arc lengths less than or equal to 1.5. Let's call this range of angles θ₁. We have

θ₁ = 2d/r = 2(1.5)/1 = 3

This means that the central angle between A and B must be less than or equal to 3 radians for the distance between A and B to be at most 1.5. Since the total central angle of the circle is 2π radians, the probability of selecting two points with a central angle less than or equal to 3 radians is

P(θ ≤ 3) = θ/2π = 3/2π ≈ 0.477

Therefore, the probability that the distance between two points on a circle of radius 1 is at most 1.5 is approximately 0.477 or 47.7%.

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Three pipes in a school building are
leaking. After 30 minutes, pipe A has leaked 3/4 gallon of water. After 45 minutes, pipe B has leaked 1 1/4 gallons of water. After 20 minutes, pipe C has leaked 1/2 gallon of water.
Which sentence is true?

A. Pipe A is leaking at the fastest rate

B. Pipe C is leaking at the slowest rate.

C. Pipe A and C are leaking at the same rate.

D. Pipes A and B are leaking at a faster rate than Pipe C.

Answers

Answer:  Option C

Step-by-step explanation: To compare the rates at which the pipes are leaking, we can find the amount of water each pipe leaks per minute.

For Pipe A:

3/4 gallon ÷ 30 minutes = 1/40 gallon per minute

For Pipe B:

1 1/4 gallon ÷ 45 minutes = 5/36 gallon per minute

For Pipe C:

1/2 gallon ÷ 20 minutes = 1/40 gallon per minute

Therefore, Pipes A and C are leaking at the same rate, which means option C is true. Option A and D are false, as Pipe B has the fastest leak rate. Option B is false, as both Pipe A and Pipe C are leaking at the same rate.

Find the y intercept of the equation 5x-2y=28

Answers

Answer:

y- intercept = - 14

Step-by-step explanation:

the y- intercept is the point on the y- axis where the line crosses.

at any point on the y- axis, the x- coordinate is zero.

let x = 0 in the equation and solve for y , the y- intercept

5(0) - 2y = 28

0 - 2y = 28

- 2y = 28 ( divide both sides by - 2 )

y = - 14 ← y- intercept

To find the y-intercept of the equation 5x - 2y = 28, we need to set x to zero and solve for y. When x = 0, the equation becomes:

5(0) - 2y = 28

Simplifying the equation, we get:

-2y = 28

Dividing both sides by -2, we get:

y = -14

Therefore, the y-intercept of the equation 5x - 2y = 28 is -14.

Use the fact that m/LCR = 90° in circle C below to answer the following items.
a. If CQ is an angle bisector of ZLCR, what is
m/LCQ?
b. Identify two major arcs.
c. Name two congruent minor arcs.
d. Name three adjacent arcs that form a semicircle.

Answers

Answer:

a. 45°

b. Arc KPR and Arc RLP

c. Arc PR and Arc RL

d. Arc LQ, Arc QR, and Arc RP

Step-by-step explanation:

a. 90/2=45°

b. Observation

c. They both have measures of 90 degrees

d. Arc Addition Postulate

Answer:

see below

Step-by-step explanation:

angle lcr appears to be a right angle

therefore if a line bisects LCR it would split the angle into 2 congruent halves:

so

90/2=45

m<LCR=45

b) arc KP and arc PR

c)

arc KL and arc LQ

d) arc PR, arc RQ and arc QL

Question 1
10 pts
Caroline conducted a survey to see if there is a relationship between the number of hours spent in a mall and the amount of money spent. The table provides the data she collected during her survey.
Respondent 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Time Spent (in hours) 2. 3.5 2.0 2.0 4.0 5.5 3.5 6.5 7.0 1.5 4.0 5.0 6.5 1.5 6.5
Amount Spend (in dollars) 85 75 50 125 35 60 50 120 150 65 120 135 175 80 165
Caroline wants to make a scatter plot of her survey. What scales should she use for the axes on her scatter plot? Select all that apply.

For the y-axis she should use a scale from 0 to 170 in 10-dollar intervals.

For the x-axis she should use a scale from 0 to 8 in one-hour intervals.

For the x-axis she should use a scale from 0 to 180 in 10-dollar intervals.

For the y-axis she should use a scale from 0 to 8 in 15-minute intervals.

For the x-axis she should use a scale from 0 to 8 in half-hour intervals.

For the y-axis she should use a scale from 0 to 180 in 5-dollar intervals.

Answers

The scale she use for the axes on her scatter plot are:

For the y-axis she should use a scale from 0 to 180 in 10-dollar intervals.

For the x-axis she should use a scale from 0 to 8 in one-hour intervals.

What is scatter plot?

A scatter plot is a type of graph that displays values for two variables as a set of points on a two-dimensional coordinate system.

According to given information:For the y-axis she should use a scale from 0 to 180 in 10-dollar intervals.For the x-axis she should use a scale from 0 to 8 in one-hour intervals.

These are the appropriate scales for the axes on Caroline's scatter plot as they will allow for a clear visualization of the relationship between the number of hours spent in the mall and the amount of money spent.

The y-axis should show the amount of money spent, and a scale from 0 to 180 in 10-dollar intervals will provide enough range to accommodate the highest value in the data set (175 dollars) and allow for clear and easy-to-read axis labels.

Similarly, the x-axis should show the time spent in the mall, and a scale from 0 to 8 in one-hour intervals will also provide enough range to accommodate the highest value in the data set (7 hours) and allow for clear and easy-to-read axis labels.

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Does tom have a legitament gripe?

Answers

Tom can choose from 7,000 possible schedules if every possible course is available at the time he's registering.

Tom can choose 22,400 possible schedules when the number of acceptable courses is doubled. The number of possible schedules is increased by a factor of approximately 3.2

What is the course available?

(a) If every possible course is available at the time Tom is registering, he can choose from:

5 choices for English x 5 choices for History x 5 choices for Math/Stats x 8 choices for Computer Science x 7 choices for general Science

= 5 x 5 x 5 x 8 x 7

= 7000 possible schedules.

(b) If the number of acceptable courses in each of the five areas is doubled, Tom can choose from:

10 choices for English x 10 choices for History x 10 choices for Math/Stats x 16 choices for Computer Science x 14 choices for general Science

= 10 x 10 x 10 x 16 x 14

= 22400 possible schedules.

The number of possible schedules is increased by a factor of:

22400 / 7000 = 3.2 (approximately)

So the number of possible schedules is increased by a factor of approximately 3.2 when the number of acceptable courses is doubled in each of the five areas.

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See text below

While making up his schedule for spring semester, Tom complains that he doesn't have very many choices of schedule because of the general education requirements he has to meet. His advisor tells Tom that he has to take one course from each of English (5 choices), History (5 choices), Math/Stats (5 choices), Computer Science (8 choices), and general Science (7 choices). Does Tom have a legitimate gripe?

(a) If every possible course is available at the time he's registering, how many possible schedules can he choose from (disregarding when the classes meet)?

Tom can choose   -------- from possible schedules.

(b) In an unprecedented effort to make the general education requirements more accessible, the dean of Tom's college decides to double the number of acceptable courses in each of those five areas. What effect does this have on the number of possible schedules?

Tom can choose ----------- from possible schedules when the number of acceptable courses are doubled. The number of possible schedules is increased by a factor of-------

The heights of tomato plants are Normally distributed with a mean of 3.56 feet and a standard deviation of 0.25 foot.

About what percent of tomato plants have a height less than or equal to 3.88 feet?

About what % of tomato plants have a height less than or equal to 3.88 feet. Round the percent to two decimal places, if necessary.

Answers

Answer:

We need to find the percentage of tomato plant that has a height less than or equal to 3.88 feet.

We know that the tomato plant heights are normally distributed with a mean of 3.56 ft and a standard deviation of 0.25 ft.

Thus, the percentage P(x≤3.88) of the heights being less than 3.88 can be calculated using the z-score z, given

Answer

About 89.97% of tomato plants.

Answer:

89.97%

Step-by-step explanation:

You design a tree house using
a coordinate plane in which
the coordinates are measured
in meters (m ). The vertices of
the rectangular floor are
(6, 7), (-3, 7), (-3,2),
and (6,2).

What is the perimeter of the tree house?

What is the area of the tree house floor?

Answers

Perimeter = 28 yards

Area 49 square yards.

Anthony, Peter, Francis, and Christopher
are in a race. The first three to finish will
receive ribbons. Which is more probable-
that both Anthony and Peter will receive
ribbons, or that Peter will finish ahead of
Francis and Christopher?​

Answers

Answer: it is more probable that Peter will finish ahead of Francis and Christopher than that both Anthony and Peter will receive ribbons.

Share Prompt

Step-by-step explanation:

Lily has a storage box shaped like a rectangular prism with a length of 4 feet, a width of 3 feet, and a height of 2 feet. She has a fishing pole that is 6 feet long. Can she store the fishing pole in the box?

Answers

Answer:

Volume L× W × H

Volume 4 × 3 × 2

4 × 3 × 2 =24

If the fish poke is 6 feet long and she has a rectangular prism of 24 since 4 × 3 ×2 equals 24 then yes she can store the fishing pole in the box

24

i need help with this one, thank you

Answers

Answer: 288.62

Step-by-step explanation:

10.4^2 + 15.3^2 = 342.25,

c^2 = 342.25

c (hypotenuse of the right triangle & length of rectangle) = 18.5

7(8) + 10.4(15.3) = 288.62

Suppose that $2000 is invested at an interest rate of 4.75% per year, compounded continuously. After how many years will the initial investment be doubled?
Do not round any intermediate computations, and round your answer to the nearest hundredth.

Answers

The initial investment will be doubled after approximately 14.6 years.

How long is required to double at a continuous compounding interest rate?

The formula for continuous compounding is given by the formula A = Pe^(rt). We we want to find the time it takes for the initial investment to double, so we can set A = 2P and solve for t:

2P = Pe^(rt)

e^(rt) = 2

Taking the natural logarithm of both sides, we get:

rt = ln(2)

t = ln(2)/r

Substituting the values:

t = ln(2)/0.0475

t = 14.5925722223

t ≈ 14.6 years.

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-3+8n=-5 for 7th grade math equation algebra

Answers

Answer: -0.25

Step-by-step explanation:

Start by undoing with PEMDAS (order of operations, P-parenthesis, E-exponents, etc)

+3 on both sides of equal sign, which gives you

8n=-2

then divide by 8 on both sides (undo the times 8)

n=-0.25

Answer: -0.25

Step-by-step explanation:

Start by undoing with PEMDAS (order of operations, P-parenthesis, E-exponents, etc)

+3 on both sides of equal sign, which gives you

8n=-2

then divide by 8 on both sides (undo the times 8)

n=-0.25

Find the area of the triangle. The area is yd² (Simplify your answer.) 17.5 yd 42 yd 45.5 yd​

Answers

To find the area of the triangle, we can use Heron's formula, which states that the area of a triangle with side lengths a, b, and c is given by:

Area = sqrt(s(s-a)(s-b)(s-c))

where s is the semiperimeter of the triangle, given by:

s = (a + b + c)/2

In this case, the side lengths of the triangle are given as 17.5 yd, 42 yd, and 45.5 yd. We can use these values to calculate the semiperimeter:

s = (17.5 yd + 42 yd + 45.5 yd)/2 = 52 yd

Now we can use Heron's formula to find the area:

Area = sqrt(52 yd(52 yd - 17.5 yd)(52 yd - 42 yd)(52 yd - 45.5 yd))

Area = sqrt(52 yd * 34.5 yd * 10.5 yd * 6.5 yd)

Area = sqrt(120022.5) yd²

Area ≈ 346.3 yd²

Therefore, the area of the triangle is approximately 346.3 yd².

Plot the numbers -2 1/2 and 1 3/4 on the number line below.

Answers

Answer:

picture

Step-by-step explanation:

The distance between each big tick mark is 1, (for example take 2 and 1, 2 minus 1 equals to 1), however, in between each of these big tick marks are four small tick marks. The distance between each small tick mark is the distance between each big tick mark divided by the amount of small tick marks plus 1 (1 divided by 4, which is 1/4).

So in this number line you count by 1/4.

What is the critical value t* for constructing a 95% confidence interval for a mean from a sample size of n=20 observations?

Answers

The critical value t* for a two-tailed 95% confidence interval with 19 degrees of freedom is approximately 2.093.

How to determine the  critical value t

The critical value t* depends on the degrees of freedom (df) and the desired level of confidence. For a 95% confidence interval and a sample size of n=20, the degrees of freedom would be df = n-1 = 19.

Using a t-distribution table with 19 degrees of freedom (since n-1=20-1=19), we can find the value of t* that corresponds to a 95% confidence level. For a two-tailed test (which is typically used for a confidence interval), the area in each tail is 0.025 (since 1 - 0.95 = 0.05, and we need to split this evenly between the two tails).

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61) If an ellipse has vertices at (-7.0). (7.0), (0.4), and (0-4), what is its domain? What is its range?

Answers

The domain of the ellipse is [-7, 7].

The range of the ellipse is [-4, 4].

What is a domain?

In mathematics, the domain of a function is the set of all possible input values for which the function is defined. In other words, it is the set of all values of the independent variable (usually denoted by x) for which the function produces a valid output (usually denoted by y).

What is the range?

In mathematics, the range of a function is the set of all possible output values that the function can produce for a given set of input values. In other words, it is the set of all values of the dependent variable (usually denoted by y) that can be obtained from the function.

According to the given information

To find the domain and range of an ellipse, we need to identify the minimum and maximum x-coordinates and y-coordinates of the points on the ellipse.

The center of the ellipse is the midpoint of its major axis, which is the line segment connecting its vertices (-7,0) and (7,0). The midpoint is ((-7+7)/2, (0+0)/2), or (0,0). This means the center of the ellipse is at (0,0).

The semi-major axis is the distance from the center of the ellipse to one of its vertices, which is 7. The semi-minor axis is the distance from the center of the ellipse to one of its co-vertices, which is 4.

So, the equation of the ellipse can be written in standard form as:

(x - 0)²/7² + (y - 0)²/4² = 1

Simplifying, we get:

x²/49 + y²/16 = 1

To find the domain and range, we need to consider the x-coordinates and y-coordinates separately.

For the x-coordinates, we can rearrange the equation as:

x² = 49 - 49y²/16

This tells us that the minimum and maximum values of x occur when y is at its extremes, which are -4 and 4. Substituting these values, we get:

x² = 0 and x² = 49

Taking the square root, we get:

x = 0 and x = ±7

So, the domain of the ellipse is [-7, 7].

For the y-coordinates, we can rearrange the equation as:

y² = 16 - 16x²/49

This tells us that the minimum and maximum values of y occur when x is at its extremes, which are -7 and 7. Substituting these values, we get:

y² = 0 and y² = 16

Taking the square root, we get:

y = 0 and y = ±4

So, the range of the ellipse is [-4, 4].

Therefore, the domain of the ellipse is [-7, 7], and the range of the ellipse is [-4, 4].

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Answers

The profit for one small cake is £1.31.

How to calculate the profit

Let's first determine the overall count of parts demonstrated in the ratio 5:7:12, which is equal to 24. Subsequently, each part would hence correspond to a quantity of nine cakes as per the equation below:

216 cakes / 24 = 9 cakes

5 parts x 9 cakes/part = 45 cakes

Likewise, similarly calculating the number of medium cakes leads us to 63 cakes, while that of large cakes sums up to 108 cakes:

7 parts x 9 cakes/part = 63 cakes

12 parts x 9 cakes/part = 108 cakes

Considering what the profit for one small cake is denoted by "x", and similarly, the profit for one medium cake is "2x" and the profit for one large cake is "3x", we can express the total gain as follows:

45x + 63(2x) + 108(3x) = 648.45

After similifying and solving for "x", we obtain an answer of £1.31 after rounding it off to two decimal places:

495x = 648.45

x = 1.31 (rounded to two decimal places)

Thus, the income earned from selling one single small cake is estimated at £1.31.

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PLEASE HELP!! find angle RVU​

Answers

Answer:

110.5

Step-by-step explanation:

The first step is to find the measure of angle RVT

Angle Formed by Two Chords= 1/2(SUM of Intercepted Arcs)

RVT = 1/2 ( 97+42)

RVT =1/2 ( 139)

RVT = 69.5

Now RVT and RVU equals a straight line so they add to 180

RVT + RVU = 180

69.5 + RVU = 180

RVU = 110.5

Choose a correct name for the line shown. C B A overleftrightarrow BB overleftrightarrow AB AC BC

Answers

Note that the best name for the line segment indicated is  [tex]\overleftrightarrow {AB}[/tex]

What is a line segment?

A line segment is a section of a straight line that is bounded by two different end points and contains every point on the line between them. The Euclidean distance between the ends of a line segment determines its length.

Other types of lines are:

Lines that are parallel. Two lines in the same plane, either intersecting or not.

Lines that cross. Intersecting lines are two or more lines that cross in a plane.

Lines that are concurrent. Concurrent lines are defined as numerous lines that cross through each other at the same place.

Points that are curved.

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Full Question:

See attached image.

Need help asap please!

Answers

Answer:

[tex]2 \dfrac{1}{2}[/tex]     OR     [tex]\dfrac{5}{2}[/tex]

Step-by-step explanation:

We can see that there are 2 whole shaded circles, and there is 1 half shaded circle.

Therefore, we can represent the shaded area as [tex]\bold{2 \dfrac{1}{2}}[/tex] circles.

We can convert this mixed number to an improper fraction by multiplying the whole number by the denominator and adding the resulting value to the numerator.

[tex]2 \dfrac{1}{2}[/tex]

[tex]= \dfrac{(2 \times 2) + 1}{2}[/tex]

[tex]= \dfrac{5}{2}[/tex]

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