Answer:
Step-by-step explanation:
“One number is larger than the other by 4 2/3”
x = y + 4⅔
“The difference of the numbers is equal to the smaller number.”
x-y = y
x = 2y
y + 4⅔ = 2y
y = 4⅔
x = 2y = 9⅓
“The sum of the numbers is natural number”
x+y ∈ ℕ
9⅓ + 4⅔ = 14 ∈ ℕ
Answer:
9 1/3 and 4 2/3
Step-by-step explanation:
:)
can someone help me?
9514 1404 393
Answer:
8.39
Step-by-step explanation:
In the right triangle, the hypotenuse and side opposite the angle are shown. The applicable trig relation is ...
Sin = Opposite/Hypotenuse
Opposite = Hypotenuse × Sin
x cm = (15 cm)×sin(34°)
x ≈ 8.39
A spherical tank is 3 m tall and therefore has a capacity of about 14000 L (NOTE that 3m is its diameter, and one cubic meter is 1000 L). You have been asked to put level lines on the tank showing the depths where the tank contains 1000, 5000, and 10000 L of liquid. (a) Use calculus to determine the height of each line (to the nearest cm). (b) Plot the circular cross-section of the tank and the level lines (NOTE the lines do not have to stay within the circle).
Answer:
(a) 1) When V = 1000 L, the height of the liquid in the tank is approximately 62 cm
2) When V = 5,000 L, the height of the liquid in the tank is approximately 106 cm
3) When V = 10,000 L, the height of the liquid in the tank is approximately 202 cm
b) The drawing of the spherical tank showing the height of the liquid level for each volume created with Microsoft Excel is attached
Step-by-step explanation:
(a) The height of the spherical tank = 3 m
The diameter of the spherical tank, d = 3 m
The capacity of the spherical tank = 14,000 L
The volume of a sphere, V = (4/3) × π × r³ =
Where, r = d/2
∴ r = 3 m/2 = 1.5 m
V = (4/3) × π × (1.5)³ ≈ 14.1371669412 m³
Using calculus, we have;
[tex]V = 2 \times \pi \times \int\limits^r_{0} {(r^2 - y^2)} \, dx = 2 \times \pi \times \left[r^2 \cdot y - \dfrac{y^3}{3} \right]^y_0[/tex]
For the two halves, we have;
[tex]V = \pi \times \left[r^2 \cdot y - \dfrac{y^3}{3} \right]^{\dfrac{y}{2}} _0 + \pi \times \left[r^2 \cdot y - \dfrac{y^3}{3} \right]^y_{\dfrac{y}{2}}[/tex]
[tex]V = 2 \times \pi \times \left[y^3- \dfrac{y^3}{3} \right]^y_0 = \dfrac{4 \cdot \pi \cdot y^3}{3}[/tex]
1) For V = 1000 L, we have;
[tex]1000 \ L = \dfrac{4 \cdot \pi \cdot y^3}{3}[/tex]
1000 L =
When V = 1000 L, we have;
[tex]y = \sqrt[3]{\dfrac{3 \times 1 \, m^3}{4 \times \pi } } \approx 0.62 \ m[/tex]
The liquid level, y ≈ 0.62 m = 62 cm
2) When V = 5,000 L, we have;
[tex]y = \sqrt[3]{\dfrac{3 \times 5 \, m^3}{4 \times \pi } } \approx 1.06 \ m[/tex]
The liquid level, y ≈ 1.06 m = 106 cm
3) When V = 10,000 L, we use the height of the unfilled volume at the top which is the volume of the sphere less the 10,000 L as follows;
For the volume of the sphere of 14,000 L, we have;
Volume at the top = 14,000 L - 10,000 L = 4,000 L = 4 m³
Therefore
[tex]y_{top} = \sqrt[3]{\dfrac{3 \times 4 \, m^3}{4 \times \pi } } \approx 0.985 \ m[/tex]
The height of the liquid in the tank, y = d - [tex]y_{top}[/tex]
∴ y = 3 m - 0.985 m = 2.015 m
The liquid level, y ≈ 2.015 m = 201.5 cm ≈ 202 cm
b) Please find attached the drawing of the spherical tank created with Microsoft Excel
a) (i) The level line for 1000 liters is set at a height of 0.486 meters.
(ii) The level line for 5000 liters is set at a height of 1.203 meters.
(iii) The level line for 10000 liters is set at a height of 1.926 meters.
b) The sphere is represented by the equation [tex]x^2+(y-1.5)^{2} = 2.25[/tex] and the level lines are represented by the linear functions [tex]y = 0.486[/tex], [tex]y = 1.203[/tex] and [tex]y = 1.926[/tex]. Please see the second image attached.
How to determine and plot the heights of a spherical tanka) First, we derive an expression for the volume of a spherical section ([tex]V[/tex]), in cubic meters, in terms of tank radius ([tex]R[/tex]), in meters, and liquid height ([tex]h[/tex]), in meters. The volume can be found by using the slicing method integral equation:
[tex]V = \int\limits^{H}_{0} {A(h)} \, dh[/tex] (1)
Where:
[tex]A(h)[/tex] - Area of the infinitesimal circular cross section, in square meters. [tex]H[/tex] - Required height of the liquid, in meters.If we know that [tex]A = \pi\cdot [R^{2}-(R-h)^{2}][/tex], then the volume formula is:
[tex]V = \pi\int\limits^H_0 {h\cdot (2\cdot R-h)} \, dh[/tex]
[tex]V = 2\pi\cdot R\int\limits^{H}_{0} {h} \, dh - \pi \int\limits^{H}_{0} {h^{2}} \, dh[/tex]
[tex]V = \pi\cdot R\cdot H^{2}-\frac{\pi\cdot H^{3}}{3}[/tex]
Then we obtain the following third order polynomial:
[tex]\frac{\pi\cdot H^{3}}{3}-\pi\cdot R\cdot H^{2}+V = 0[/tex] (2)
Now we proceed to solve numerically for each case:
Case 1 - [tex]R = 1.5\,m[/tex], [tex]V = 1\,m^{3}[/tex][tex]H = 0.486\,m[/tex]
The level line for 1000 liters is set at a height of 0.486 meters. [tex]\blacksquare[/tex]
Case 2 - [tex]R = 1.5\,m[/tex], [tex]V = 5\,m^{3}[/tex][tex]H = 1.203\,m[/tex]
The level line for 5000 liters is set at a height of 1.203 meters. [tex]\blacksquare[/tex]
Case 3 - [tex]R = 1.5\,m[/tex], [tex]V = 10\,m^{3}[/tex][tex]H = 1.926\,m[/tex]
The level line for 10000 liters is set at a height of 1.926 meters. [tex]\blacksquare[/tex]
b) The sphere is represented by the equation [tex]x^2+(y-1.5)^{2} = 2.25[/tex]level lines are represented by the linear functions [tex]y = 0.486[/tex], [tex]y = 1.203[/tex] and [tex]y = 1.926[/tex]. By a graphing tool we have the following result. [tex]\blacksquare[/tex]
To learn more on volumes, we kindly invite to check this verified question: https://brainly.com/question/1578538
A family has four children. If the genders of these children are listed in the order they are born, there are sixteen possible outcomes: BBBB, BBBG, BBGB, BGBB, GBBB, BGBG, GBGB, BGGB, GBBG, BBGG, GGBB, BGGG, GBGG, GGBG, GGGB, and GGGG. Assume these outcomes are equally likely. Let represent the number of children that are girls. Find the probability distribution of . Part: 0 / 20 of 2 Parts Complete Part 1 of 2 Your Answer is incorrect (a) Find the number of possible values for the random variable . There are possible values for the random variable .
Answer:
X : ___ 0 ____ 1 _____ 2 _____ 3 _____ 4
P(x): _ 1/16 __ 1/4 ____ 3/8 ____ 1/4 ____ 1/16
Step-by-step explanation:
Given the listed possible occurrence of boys and girls :
B = boys ; G = girls
BBBB, BBBG, BBGB, BGBB, GBBB, BGBG, GBGB, BGGB, GBBG, BBGG, GGBB, BGGG, GBGG, GGBG, GGGB, and GGGG
Let x = distribution of girls
P = required outcome / Total possible outcomes
For :
x = 0 ;(BBBB) = 1
P(x) = 1/16
x = 1 ; (BBBG, BBGB, BGBB, GBBB) = 4
P(x) = 4 / 16 = 1/4
P(x = 2) ; (BGBG, GBGB, BGGB, GBBG, BBGG, GGBB) = 6
P(x) = 6 / 16 = 3/8
P(x = 3) ; (BGGG, GBGG, GGBG, GGGB) = 4
P(x) = 4 / 16 = 1/4
P(x = 4) ; (GGGG) = 1
P(x) = 1 / 16
X : ___ 0 ____ 1 _____ 2 _____ 3 _____ 4
P(x): _ 1/16 __ 1/4 ____ 3/8 ____ 1/4 ____ 1/16
can anyone help me please?
Answer:
line n
Step-by-step explanation:
5) Un pedazo de pizza cuesta $30, un jugo cuesta $15. ¿Cuánto de deben sobrar de
$500 al comprar 5 pedazos de pizza y 5 jugos?
Answer:
I think it is 275 if you are subtracting
the ratio of boys to girls in the park was 4 to 5 .if 270 children were in the park.How many girl?
Answer:
150 are girls.
Step-by-step explanation:
There is an important difference between the way counts are viewed in ratio to that in fractions.
The ratio of boys : girls
4:5
so you have 4 boys and 5 girls making the whole count in its simplest form.
4+5=9
So to change the ratio proportion into fraction proportion we have:
Boys: 4/9
Girls: 5/9
It is given that the whole is 270 therefore the count of girls is:
5/9 x 270 = 150
To make meatloaf. mix 2 pounds of beef and 0.5 of a cup of breadcrumbs. How many pounds of beef
would you mix with 4.5 cups of breadcrumbs
Answer:
18 pounds of beef.
Step-by-step explanation:
For every 0.5 cups of breadcrumbs there's 2 pounds of beef.
0.5 x 9 = 4.5
9 x 2 = 18 or 2 x 9 = 18
multiples of two: 2 4 6 8 10 12 14 16 18
This shows that when we multiply 2 nine times we get 18!
Determine the 12th term of the following Arithmetic sequence, 5 ; 12; 19;... (2)
Answer:
26-33-40-47-54-61-68-75-82-89-96
del puerto de cabo San Lucas México salen dos barcos el barco México 1,navega con una trayectoria de x+y=88;el barco México 2 navega con una trayectoria de 2x + 2y= -176 en que punto se encontrarán los dos barcos?
What value of x and y will make the polygon a parallelogram
105°
V
15x
Answer
60
Step-by-step explanation:
105+15= 120
180-120=60
I think this is the correct answer but I dont know
What is the area of the real object that the scale drawing models?
Answer:
90 cm²
Step-by-step explanation:
since the ratio is 1:6 for every one little box the bigger box increases 6 times.
so 15·6= 90 cm²
Answer:
D. 90 square cm
Coaching companies claim that their courses can raise the SAT scores of high school students. Of course, students who retake the SAT without paying for coaching generally raise their scores. A random sample of students who took the SAT twice found 427 who were coached and 2733 who were uncoached. Starting with their verbal scores on the first and second tries, we have these summary statistics:
Try 1 Try 2 Gain
x s x s x s
Coached 500 92 529 97 29 59
Uncoached 506 101 527 101 21 52
Let's first ask if students who are coached significantly increased their scores.
You could use the information given to carry out either a two-sample t test comparing Try 1 with Try 2 for coached students or a matched pairs t test using Gain. Which is the correct test? Why?
A. Two-sample test, because we are given data for the two samples which is more accurate than the data only on the gain.
B. Matched pairs test, because we are not interested in the difference in mean between the two groups, but the gain that each student has achieved.
C. Two-sample test, because matched pairs test can be performed only if we have information on every individual.
D. Matched pairs test, because we are interested in the difference in mean between the two groups - not the gain that each student has achieved.
Answer:
Matched pairs test, because we are interested in the difference in mean between the two groups - not the gain that each student has achieved.
Step-by-step explanation:
Due to the correlation which exists between the two Given samples, we need to examine the difference between the pair of each point in the dataset ; coach and uncoached point. Hence, in other to analyze the underlying pattern between each data point in the two categories, the matched pair test will be more appropriate due to the underlying relationship between the reported groups.
I need help ASAP pls
map of field: 12 in × 15 in
scale of map: 1 in = 3 ft
What are the dimensions
of the actual field?
Presented below are the financial statements for the Amphlett Corporation, as of year-end 2012 and 2013.
AMPHLETT CORPORATION
Consolidated Balance Sheets
As of Year-End ($ thousands) 2013 2012
Assets
Current
Cash $18,000 $108,000
Marketable securities 240,000 -
Accounts receivable (net) 708,000 528,000
Inventory 720,000 738,000
Total current assets 1,686,000 1,374,000
Noncurrent
Long-term investments 372,000 468,000
Property & equipment 2,160,000 1,320,000
Less: Accumulated depreciation (600,000) (600,000)
Property & equipment (net) 1,560,000 720,000
Intangibles (net) 114,000 126,000
Total noncurrent assets 2,046,000 1,314,000
Total assets $3,732,000 $2,688,000
Liabilities & Shareholders' Equity
Accounts payable $1,080,000 $1,020,000
Short-term bank debt 228,000 -
Total liabilities 1,308,000 1,020,000
Shareholders' equity
Common stock, $10 par value 930,000 810,000
Additional paid-in-capital 456,000 360,000
Retained earnings 1,038,000 498,000
Total shareholders' equity 2,424,000 1,668,000
Total liabilities & shareholders' equity $3,732,000 $2,688,000
AMPHLETT CORPORATION
Consolidated Income Statement
For Year Ended ($ thousands)
2013
2012
Revenues
$1,716,000
$1,440,000
Less: Cost of goods sold
600,000
504,000
Gross margin
1,116,000
936,000
Less: Selling, general & administrative expenses
180,000
144,000
Operating income
936,000
792,000
Gain on sale of investments
84,000
-
Net income before taxes
1,020,000
792,000
Less: Income taxes
60,000
13,200
Net income after taxes
$960,000
$778,800
The footnotes to the Amphlett Corporation's financial statements revealed the following additional information:
Property and equipment costing $540 million was sold for its book value of $240 million.
Long-term investments were sold for $180 million, which included a gain of $84 million.
Required
Using the above financial data for the Amphlett Corporation, prepare the firm's statement of cash flow for 2013 using the indirect method.
Use a negative sign with answers to indicate a decrease in cash.
Amphlett Corporation
Statement of Cash Flows
For Year Ended 2013
(in thousands)
Cash flow From Operations BLANK
Net Income $Answer
Add:
Depression Expense Answer
Amortization expense Answer
Less:
Gain on Sale of Investments Answer
Accounts receivable (net) Answer
Inventory Answer
Accountable Payable Answer
Cash Flow From Operations Answer
Cash Flow for Investing BLANK
Marketable securities Answer
Long-term investments Answer
Purchase of property and equipment Answer
Sale of Property and Equipment Answer
Cash Flow for Investing Answer
Cash From Financing BLANK
Short-term bank debt Answer
Common stock + additional paid in capital Answer
Dividends Paid Answer
Cash From Financing Answer
Decrease in Cash Answer
Cash, beginning of year Answer
Cash, end of year $Answer
Answer:
For Year Ended 2013
(in thousands)
Cash flow From Operations BLANK
Net Income 792,000
Add:
Depression Expense 300,000
Amortization expense 12,000
Less:
Gain on Sale of Investments
Accounts receivable (net) -180,000
Inventory 18,000
Accountable Payable Answer 60,000
Cash Flow From Operations 1,002,000
Cash Flow for Investing
Marketable securities -240,000
Long-term investments 96,000
Purchase of property and equipment -1,380,000
Sale of Property and Equipment 280,000
Cash Flow for Investing -1,244,000
Cash From Financing
Short-term bank debt 228,000
Common stock + additional paid in capital 96,000
Dividends Paid 8,000
Cash From Financing 332,000
Decrease in Cash 90,000
Cash, beginning of year 18,000
Cash, end of year 108,000
108,000
0
Step-by-step explanation:
Assets
Current
Cash $18,000 $108,000
Marketable securities 240,000
Accounts receivable (net) 708,000 528,000
Inventory 720,000 738,000
Total current assets 1,686,000 1,374,000
Noncurrent
Long-term investments 372,000 468,000
Property & equipment 2,160,000 1,320,000
Less: Accumulated depreciation -600,000 -600,000
Property & equipment (net) 1,560,000 720,000
Intangibles (net) 114,000 126,000
Total noncurrent assets 2,046,000 1,314,000
Total assets $3,732,000 $2,688,000
Liabilities & Shareholders' Equity
Accounts payable $1,080,000 $1,020,000
Short-term bank debt 228,000
Total liabilities 1,308,000 1,020,000
Shareholders' equity
Common stock, $10 par value 930,000 810,000
Additional paid-in-capital 456,000 360,000
Retained earnings 1,038,000 498,000
Total shareholders' equity 2,424,000 1,668,000
Total liabilities & shareholders' equity $3,732,000 $2,688,000
AMPHLETT CORPORATION
Consolidated Income Statement
For Year Ended ($ thousands) 2013 2012
Revenues $1,716,000 $1,440,000
Less: Cost of goods sold 600,000 504,000
Gross margin 1,116,000 936,000
Less: Selling, general & administrative expenses 180,000 144,000
Operating income 936,000 792,000
Gain on sale of investments 84,000
Net income before taxes 852,000 792,000
Less: Income taxes 60,000 13,200
Net income after taxes $792,000 $778,800
For Year Ended 2013
(in thousands)
Cash flow From Operations BLANK
Net Income 792,000
Add:
Depression Expense 300,000
Amortization expense 12,000
Less:
Gain on Sale of Investments
Accounts receivable (net) -180,000
Inventory 18,000
Accountable Payable Answer 60,000
Cash Flow From Operations 1,002,000
Cash Flow for Investing
Marketable securities -240,000
Long-term investments 96,000
Purchase of property and equipment -1,380,000
Sale of Property and Equipment 280,000
Cash Flow for Investing -1,244,000
Cash From Financing
Short-term bank debt 228,000
Common stock + additional paid in capital 96,000
Dividends Paid 8,000
Cash From Financing 332,000
Decrease in Cash 90,000
Cash, beginning of year 18,000
Cash, end of year 108,000
108,000
0
Solve for x: 3 < x + 3 < 6
6 < x < 9
6 > x > 9
0 < x < 3
0 > x > 3
Answer:
Subtract - 3 in each term
3 - 3 < x+3 - 3 < 6- 3
0 < x < 3
Estimate 307‾‾‾‾√ between two consecutive whole numbers. Enter the numbers in the boxes below.
Answer:
17, 18
Step-by-step explanation:
closest perfect square that is lower than 307 is 289
closest perfect square that is greater than 307 is 324
[tex]\sqrt{289} < \sqrt{307} < \sqrt{324}[/tex]
[tex]17<\sqrt{307} <18[/tex]
i need help with
−5 × −8 =
Answer:
40
Step-by-step explanation:
-5 * (-8) = 40
Answer:
40
Step-by-step explanation:
Because multiplication of subtract will be added
1 and 3/16 - 7/8????
Answer:
0.3125
Step-by-step explanation:
Answer:
5/16 or 0.3125
Step-by-step explanation:
Based only on the information given in the diagram, which congruence
theorems or postulates could be given as reasons why AADCH ADEP
Check all that apply
A. LA
B. MAS
C. HL
D. HA
E. SAS
F. LL
D. HA
1234567890oplkjhgrewsertyuiopoiuytr
Answer:
Step-by-step explanation:
Its
D and E
1. You have three standard decks of cards in front of you. What is the probability of drawing a heart card from all three decks?
2.12%
9.38%
1.56%
17.31%
Answer:
1.56%
Step-by-step explanation:
A standard deck of cards has 52 cards, and 13 of these are hearts, as there are 4 suits, and 52/4=13. This means the probability of choosing a heart card from a deck of cards is 1/4, or 25%. Now to find the probability of doing this from 3 decks in a row, we simply cube 1/4 to get 1/64, and in percentage this is ~1.56%.
Answer: 1.56%
Step-by-step explanation: there's really nothing to explain here.
Quiz From Buzz (Acceleration Education)
Hope it helps you!
Let C represent the cost in dollars and R represent the revenue in dollars. What is the break-even point? Use a table to help if necessary. C=15x+150 And R=45x
Answer:
[tex]x = 5[/tex]
[tex]R = C = 225[/tex]
Step-by-step explanation:
Given
[tex]C = 15x + 150[/tex]
[tex]R = 45x[/tex]
Required
The break even point
To do this, we make use of:
[tex]R =C[/tex]
[tex]45x=15x + 150[/tex]
Collect Like Terms
[tex]45x-15x = 150[/tex]
[tex]30x = 150[/tex]
[tex]x = 5[/tex]
Substitute 5 for x in [tex]R = 45x[/tex]
[tex]R = 45 * 5[/tex]
[tex]R = 225[/tex]
Hence, the break even point is:
[tex]x = 5[/tex]
[tex]R = C = 225[/tex]
determine the value of n 25+2-15÷3=n
Pls help me ASAP thank you
The answer to your question was..:
24.5
It is 100% correct, and I hope you get it right! :D
(Love your username! >:3)
please help me please i really need help please
Answer:
x = -22/3 and y = -1
Step-by-step explanation:
First, simplify the equation 12x + 20y = -108 by dividing both sides by 4:
3x + 5y = -27
now, you can subtract the two equations:
3x + 5y = -27
- (3x - 12y = -10)
17y = -17
y = -1
plug y = -1 into the equation 3x - 12y = -10
3x - 12 *(-1) = -10
3x + 12 = -10
3x = -22
x = -22/3
Answer:
-(22/3,-1)
Step-by-step explanation:
Jack knows that one-third of his total trip is 640 miles. How far is Jack's total trip?
[tex]-(x+9)2=64[/tex]
Find the total of a
1560 meal with 15%
tip and 8% tax.
The difference between 3 times a number x and 2 is 19. What is the value of x?
ILL MARK AS BRAINLYEST
Answer:
the value of x is 7.
Step-by-step explanation:
2+19=21
21÷3=7
Check:
3×7=21
21-2=19
Therefore, 7 is the answer.
Y varies directly with x. If y = 150 when x = 3, what is x when y = 600
Answer:
Step-by-step explanation:
Y varies directly with x:
y=kx
for some non-zero constant k
substitute y=150 and x=3:
150=3k
k=50
When y=600:
600=(50)x
x=12
