The space sample would include the lotion, spray and gel, with the SPF and there are 15 possible outcomes.
How to find the sample space ?The enumeration of sample space and all potential results can be achieved by duly considering various combinations of SPF and sunscreen variety. It is achievable to list the entire gamut of possibilities when each type of sunscreen is matched with every value of SPF:
The sample space would look like this:
SPF 10 LotionSPF 10 SpraySPF 10 GelSPF 15 LotionSPF 15 SpraySPF 15 GelSPF 30 LotionSPF 30 SpraySPF 30 GelSPF 45 LotionSPF 45 SpraySPF 45 GelSPF 50 LotionSPF 50 SpraySPF 50 GelThis shows that there are 15 possible outcomes in the sample space.
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Jackie's car is in the shop and she drives a rental for five days she wrote down miles she drove on the rental car each day this week and recorded them in the table below what is the approximate average number of miles she put on a rental car each day
The approximate average number of miles she put on a rental car each day is C. 42.
What is the average?The average is the quotient of the total value divided by the number of data items.
The average is also described as the mean data value.
The mean is one of the basic centers of measurement.
The total number of miles driven by Jackie's car for the five days = 209.1 miles
The number of days of driving undertaken by Jackie = 5 days
The average miles per day = 41.81 (209.1 ÷ 5)
41.81 miles per day is approximately = 42 miles per day
Thus, we can confidently conclude that Jackie's car drove 42 miles dai on the average.
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The monthly profit P (in dollars) a company makes depends on the amount x (in dollars) the company spends on advertising according to the model
P-550 + 130x²
Find the amount spent on advertising that will yield a monthly profit of $9,000
The amount spent on advertising that will yield a monthly profit of $9,000 is $8.57.
What is profit?Profit is the amount of money or financial gain that a business or an individual makes after deducting all the expenses and costs associated with producing or providing a product or service.
According to question:According to the model, the profit P (in dollars) is dependent on the sum x (in dollars) that the business invests in advertising:
P = 130x² - 550
We want to find the amount spent on advertising that will yield a monthly profit of $9,000. In other words, we want to solve for x when P = 9000:
130x² - 550 = 9000
Adding 550 to both sides, we get:
130x² = 9550
Dividing both sides by 130, we get:
x² = 73.46
x = ±8.57
Since we are dealing with a real-world scenario, the amount spent on advertising must be a positive value. Therefore, we take the positive root:
x = 8.57
Therefore, the amount spent on advertising that will yield a monthly profit of $9,000 is $8.57.
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Into how many regions, or parts, do two lines that are in general position divide a plane?
Answer:
Two lines that are in general position divide a plane into four regions or parts.
When two lines intersect at a point, they divide the plane into four distinct regions, called quadrants. However, if the two lines are parallel, they do not intersect, and the plane is divided into only two regions, called half-planes.
In general position, two lines in a plane have different slopes and different y-intercepts, which means that they are neither parallel nor coincident. Therefore, the two lines must intersect at a point, dividing the plane into four regions.
Hope this helps!
PLEASE HELP QUICKLY!! (20 points)
Which function has the greatest slope?
A. g(x)
B. f(x)
C. h(x)
D. k(x)
E. all if the slopes are the same
i think its d but im not sure please answer quickly
Answer: E
Step-by-step explanation:
Put each function into the slope-intercept form y=mx+b. Notice that m=1 for each function, and because m represents the slope, all slopes are the same.
Which number line shows the solution set for |d| > 3?
Answer:
Last number line
Step-by-step explanation:
Solving |d| > 3,
d^2 > 9
d = +-3
Using the graph y=x^2,
d < -3, d > 3
Hence, it's the last number line i.e. the one with blank dots.
Hope this helps and be sure to mark this as brainliest! :)
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.
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 with explanation
Answer:
Area = 36 [tex]units^{2}[/tex]
Perimeter = 26 units
Step-by-step explanation:
Helping in the name of Jesus.
Complementary angles.
Answer: Angle EGF
Step-by-step explanation: Angle EGF is complementary to FGA because the two angles add up to 90 degrees, which is what it means to be complementary.
Math: Please very important and urgent!! I’ll give brainliest for it if it’s correct
The value of k in the given wave equation is determined as 1/2.
What is the value of k in the wave equation?
The value of k in the given wave equation is calculated as follows;
The wave equation; y = a sin (bθ)
where;
a is the amplitude of the waveb is the coefficient of the phase anglewhen y = 24/25, the value of k is calculated as follows;
24/25 = 2 x sinbθ
sin bθ = 24/50
bθ = sin⁻¹ (24/50)
bθ = 0.5
bθ = ¹/₂
Thus, the value of k in the given wave equation corresponds to value of b and it is determined as 1/2.
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please help answer these two i beggg
Answer:
i can only answer 1 but the first one is c
Step-by-step explanation:
What is the horizontal distance from (−9, −4) to (15, −4)? −24 units −6 units 6 units 24 units
Answer:
Step-by-step explanation:
Answer: D 24 units i did the quiz
Step-by-step explanation:
Find the exact length of the curve. x = et − t, y = 4et/2, 0 ≤ t ≤ 6
Length of the curve is e² - 1 .
In arithmetic, a function from a group X to a group Y assigns to every part of X precisely one part of Y. The set X is termed the domain of the function and therefore the set Y is termed the codomain of the function
Main body:
A parametric curve is a function expressed in components form, such that;
x = f(t) , y = g(t).
The length of a parametric curve on the interval a ≤ t ≤ b is given by the definite integral :
L = [tex]\int\limits^a_b {\sqrt{\frac{dx}{dt}^2 + {\frac{dy}{dt}^2 } } } \, dx[/tex]
Let's begin by getting the first derivative of the components of the function with respect to the variable t.
x = e^t - t
dx / dt = e^t−1
And, y = 4 e^t/2
dy /dt = 2 e^t/2
Substitute the derivatives into the following definite integral which computes the length of the parametric curve on the interval
[a,b]=[0,2].
L = [tex]\int\limits^a_b {\sqrt{\frac{dx}{dt}^2 + {\frac{dy}{dt}^2 } } } \, dx[/tex]
L= [tex]\int\limits^2_0 {\sqrt{\ (e^t - 1)^2 + ({\(2e^{t/2}) ^2 } } } \, dx[/tex]
L = [tex]\int\limits^2_0 {e^t - 1} \, dx[/tex]
Evaluate the solution at the limits of integration to get the length.
L = (e² - 1 )- (e⁰ - 1)
L = e² - 1 - 1 + 1
L= e² - 1
Hence , length of the curve is e² - 1 .
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good buy electronics has a markup of 150% on a keyboard that cost the retailer $25. find the retail "selling" price and show your work
The retail selling price of the keyboard is $43.75.
What is the percentage?
A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%", although the abbreviations "pct.", "pct" and sometimes "pc" are also used. A percentage is a dimensionless number; it has no unit of measurement.
To find the retail selling price of the keyboard, we need to add the markup to the cost of the keyboard.
The markup of 150% means that the retailer is adding 150% of the cost to the selling price.
To calculate this, we can first find the dollar amount of the markup:
Markup = 150% of $25
Markup = 0.5 * 150 * $25
Markup = $18.75
This means that the retailer is adding $18.75 to the cost of the keyboard to get the selling price. To find the selling price, we can add the markup to the cost:
Selling price = Cost + Markup
Selling price = $25 + $18.75
Selling price = $43.75
Therefore, the retail selling price of the keyboard is $43.75.
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Suppose f(x) = x² and g(x) = (x). Which statement best compares the
graph of g(x) with the graph of f(x)?
A. The graph of g(x) is the graph of f(x) shifted units left.
B. The graph of g(x) is the graph of f(x) vertically stretched by a
factor of 5.
C. The graph of g(x) is the graph of f(x) horizontally stretched by a
factor of 5.
D. The graph of g(x) is the graph of f(x) horizontally compressed by a
factor of 5.
cu
(b) The graph of g(x) is the graph of f(x) vertically stretched by a factor of 5.
Comparing the functions f(x) and g(x)From the question, we have the following parameters that can be used in our computation:
f(x) = x²
g(x) = (1/5x)²
The graph of g(x) is the graph of f(x) vertically stretched by a factor of 5.
To see this, we can rewrite g(x) as g(x) = (1/5)²(x²) = (1/5²)f(x).
This means that g(x) is equal to f(x) scaled vertically by a factor of 5² = 25.
Therefore, the graph of g(x) will be the same shape as the graph of f(x), but stretched vertically by a factor of 25.
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Find the value of x in each triangle
Answer:b 40
A60
Step-by-step explanation:
Answer:
Step-by-step explanation:
so for figure a:
we can find x by using sin which is sin = opposite/hypotenuse so
- sin30= x/10cm(sin30 is equivalent to 1/2 or 0.5)
- 0.5= x/10cm or 1/2=x/10cm (i'm gonna use the 2nd option)
- 10cm * 1/2=x
-x=5cm
and for figure b:
here we also use sin
- sin 50= x/8cm (sin 50 is equivalent to 0.7660 )
- 0.7660= x/ 8cm
-0.7660 * 8cm=x
- x= 6.128cm and when estimated x= 6cm
Given NE and TE are tangents to the circle below, what is the length of segment NE
If "NE" and "TE" are tangents of circle, then length of segment NE is 53 units.
We find the length of the segment "NE" by using the fact that tangents drawn to a circle from an external point are equal in length.
So, We have,
⇒ NE = TE ...(because they are tangents to the same circle from the same external point E),
So we can set the "two-expressions" of tangent equal to each other:
We get,
⇒ 13x - 12 = 7x + 18,
⇒ 6x - 12 = 18,
⇒ 6x = 30,
⇒ x = 5,
now, we substitute the value of x in "NE", to find the length of segment NE.
We get,
⇒ NE = 13x - 12,
⇒ NE = 13(5) - 12,
⇒ NE = 65 - 12,
⇒ NE = 53.
Therefore, length of NE is = 53 units.
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The given question is incomplete, the complete question is
Given NE and TE are tangents to the circle below, what is the length of segment NE?
Let v be the vector from initial point P₁ to terminal point P2. Write v in terms of i and j.
P₁ = (-5,3), P2=(-2,-7)
V=
(Type your answer in terms of i and j.)
The value of the vector from initial point P₁ to terminal point P₂ is,
⇒ V = 3i - 10j
We have to given that;
Points are,
P₁ = (-5, 3)
P₂ = (-2, -7)
Hence, The value of the vector from initial point P₁ to terminal point P₂ is,
⇒ V = (x₂ - x₁) i + (y₂ - y₁)j
⇒ V = (- 2 + 5) i + (- 7 - 3) j
⇒ V = 3i - 10j
Thus, The value of the vector from initial point P₁ to terminal point P₂ is,
⇒ V = 3i - 10j
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A plane cruising at an altitude of km starts descending so that its altitude decreases at the rate m/min. Find the equation for its altitude h (in m) as a function of time t and sketch the graph for t0 to t10 min.
The equation for its altitude h (in m) as a function of time t is h(t) = h₀ x 1000 - rt and the graph of the equation is illustrated below.
Let's begin by defining our variables. We know that the initial altitude of the airplane is given as h₀, which is in km. We also know that the rate at which the altitude decreases is given as r, which is in m/min. Our objective is to determine the altitude h of the airplane at any given time t, in minutes, during the descent.
To find the equation for the altitude of the airplane, we need to first convert the initial altitude from km to m. This can be done by multiplying h₀ by 1000. Therefore, the initial altitude in meters is h₀ × 1000.
Finally, we can find the equation for the altitude of the airplane by subtracting the amount that the altitude has decreased from the initial altitude. This gives us the following equation:
h(t) = h₀ × 1000 - rt
where h(t) is the altitude of the airplane at time t, h₀ is the initial altitude in km, r is the rate of descent in m/min, and t is the time in minutes.
To sketch the graph of this equation, we can plot altitude on the y-axis and time on the x-axis. Then we get the graph like the following.
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If you want to earn 2% annual simple interest on an investment, how much should you pay for a note that will be worth $15,500 in 10 months? (Round your answer to two decimal places.)
Answer:
Step-by-step explanation:
To solve this problem, we can use the simple interest formula:
I = P*r*t
where I is the interest earned, P is the principal (the initial investment), r is the interest rate (as a decimal), and t is the time (in years).
Here, we want to find P, so we'll rearrange the formula:
P = I/(r*t)
We know that the final value of the investment (including interest) is $15,500, and the time is 10 months (or 10/12 years). We can plug in the numbers:
I = $15,500 - P
r = 0.02
t = 10/12
P = (15,500 - P)/(0.02*(10/12))
P = (15,500 - P)/(0.1667)
P = 93,000 - 6P
7P = 93,000
P = $13,285.71
Therefore, you should pay $13,285.71 for the note if you want to earn 2% annual simple interest and have it be worth $15,500 in 10 months.
Hope that helps :)
Based on the work shown on the right, check all of the possible solutions of the equation.
-8
-2
0
2
8
Diagram not drawn to scale
Answer:
8
Step-by-step explanation:
sqrt(2x) - x = - 4
sqrt(2x) = x - 4
2x = (x - 4) ^ 2
2x = x ^ 2 - 8x + 16
o = x ^ 2 - 10x + 16
matrix 0&=& (x - 2)(x - 8) matrix )
Which number equals 3 4 exponent -2
The answer for the above expression is 16/9.
What is an expression?An expression is a combination of numbers, variables, and mathematical operations, such as addition, subtraction, multiplication, division, exponentiation, and root extraction, that represents a mathematical quantity or a mathematical statement. An expression can be as simple as a single number or variable, or it can be a complex combination of several numbers, variables, and operations.
According to the given information:
The expression "[tex](\frac{3}{4} )^{2}[/tex]" represents the fraction "3/4" raised to the power of "-2". In mathematical notation, this is written as "[tex](\frac{3}{4} )^{-2}[/tex]".
To calculate this value, we can use the rule that a negative exponent is equivalent to taking the reciprocal of the base raised to the positive exponent. Therefore, "[tex](\frac{3}{4} )^{-2}[/tex]" is equal to the reciprocal of "3/4" raised to the power of "2", or "[tex]\frac{1}{(\frac{3}{4} )^{2}}[/tex]".
Evaluating this expression, we get:
[tex](\frac{3}{4} )^{-2}[/tex]= [tex]\frac{1}{(\frac{3}{4} )^{2}}[/tex] = [tex]\frac{1}{(\frac{9}{6})^{2} }[/tex]= 16/9
So, "[tex](\frac{3}{4} )^{-2}[/tex]" is equal to 16/9.
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URGENT!! ILL GIVE
BRAINLIEST! AND 100 POINTS
Answer:
Step-by-step explanation:
We need to look at the graph:
The graph shows a pretty clear upward trend, so we can assume that as the years of college increases, income increases as well. Based on how well the data represents a straight line, we can assume there is a strong positive linear correlatino between these variables. But remember, correlation does not imply causation, so we cannot assume that # of years in college causes income to increase.
Thus, looking at our answer choices, the answer is e
A new blood pressure medication has been manufactured and a study is being conducted to determine whether its effectiveness depends on dose. When 50 milligrams of the medication was administered to a simple random sample (SRS) of 40 patients, 12 of them demonstrated lower blood pressure. When 100 milligrams of the medication was administered to another SRS of 35 patients, 14 of them demonstrated lower blood pressure. Which of the following test statistics is an appropriate hypothesis test?
a z-test for the proportional difference is the proper hypothesis test.
What is the deviation in proportions?A hypothesis test can be used to find whether the deviation in proportions impacts the medication's effectivity. We may compare the secondary hypothesis—that the proportions are different—to the null hypothesis.
which states that the dimension of patients who show cut down blood pressure is the same for the two doses of the drug (50 mg and 100 mg).
Popular test statistics like the z-test can be applied to this hypothesis test and other statistical analyses.
[tex]z = (p1 - p2) / SE[/tex]
where p1 and p2, for the 50 mg and 100 mg doses, respectively, are the sample proportions of patients who show fallen blood pressure, and SE is the standard error of the difference between the proportions.
the samples are assumed to be independent or dependent, impacts the SE formula. The samples in this instance are presumed to be independent because they came from various patients. Consequently, the equation for SE is:
[tex]SE = \sqrt(p1 \times (1 - p1)/n1 + p2 *\times(1 - p2)/n2)[/tex]
here, the sample sizes for two doses is n1 and n2.
We can compute the z-test statistic based on the sample sizes and proportions and compare the result to a critical value or p-value to decide whether to accept or reject the null hypothesis.
Therefore, a z-test for the proportional difference is the proper hypothesis test.
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Alpha, a car manufacturer, pays VAT by the credit method. In the tax period, it has the following activities: (1) Importing 1,000 air conditioners with capacity of 9,000 BTU which are designed for installation in car only with CIF price of VND 10 million/air conditioner. In the tax period, Alpha used 400 air conditioners to produce cars. The remaining imported air conditioners was sold to domestic garages with price exclusive of VAT of VND 18 million/air conditioner. (2) Producing cars and selling transactions as follow: - Selling domestically 1,500 five-seat cars with price exclusive of VAT of VND 520 million/car - Selling 10 five-seat cars and 15 24-seat cars to enterprises in EPZs with price exclusive of VAT of 533 million/car and VND 650 million/car, respectively - Using 5 five-seat cars in a promotion accordance with regulations of Trade Law Requirements: Determine the amount of customs duty, excise duty, and VAT that enterprise Alpha must declare and pay in the period. Knowing that: - Import duty rate of air conditioner is 10% - Excise duty rate of car is 30%, of air conditioners is 10%. - The VAT rate is 10%. - VAT of other purchased goods to serve production and business activities in the period VND 15,000 million - Enterprises have full legal invoices and documents, payment via bank
Answer: Enterprise Alpha must declare and pay VND 1,000 million for import duty, VND 96.44 million for excise duty, and VND 80,730 million for VAT in the period.
Step-by-step explanation:
400 adults,96 of the 400adults have high blood pressure 116adults report being willing to change. an adult choosen at random what is probability they will be willing to change diet
The probability that an adult chosen at random will be willing to change their diet is 0.29 or 29%.
what is probability?
In general terms, probability is the measure of the likelihood or chance of an event occurring. It is a mathematical concept that is used to quantify uncertainty or randomness in various situations.
In formal terms, probability is defined as the ratio of the number of favorable outcomes to the total number of possible outcomes in an event. It is usually represented as a value between 0 and 1, where 0 represents an impossible event and 1 represents a certain event.
The probability of an adult being willing to change their diet can be calculated using the given information as follows:
Probability of an adult being willing to change diet = Number of adults willing to change / Total number of adults
Total number of adults = 400 (as given in the question)
Number of adults willing to change = 116 (as given in the question)
Therefore, the probability of an adult being willing to change their diet can be calculated as:
Probability = 116/400
Probability = 0.29 or 29%
So, the probability that an adult chosen at random will be willing to change their diet is 0.29 or 29%.
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Select all of the following sets that could be the set A if A {5, 7, 11, 13, 17, 19}.
The sets that is part of Set A are:
{5, 7}{}{17}{5, 7, 11, 13, 17, 19}What is the sets about?To be able to get the set A, a set need to have the same elements as {5, 7, 11, 13, 17, 19}. So the set that has six number is one that can be the set A.
Hence:
The set {5, 7} exclusively comprises elements present in the initial set.
Any set contains the empty set within its subsets.
The set {17} consists of a single element that is present in the initial set.
The set {5, 7, 11, 13, 17, 19} is a subset of the original set as it encompasses all of its elements.
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See text below
Select all of the following sets that could be the set A if A ⊆⊆ {5, 7, 11, 13, 17, 19}.
{5, 7}
{}
{7, 8, 9}
{17}
{5, 7, 11, 13, 17, 19}
{4, 5, 6}
What is the area of a sector when r=2 and 0=1.75 radians.
Answer:
To calculate the area of a sector, we can use the formula:
A = (θ/2) * r^2
where:
A is the area of the sector,
θ is the central angle of the sector in radians, and
r is the radius of the sector.
Given:
r = 2 (radius)
θ = 1.75 radians (central angle)
Plugging in the given values into the formula:
A = (1.75/2) * 2^2
A = 0.875 * 4
A = 3.5
So, the area of the se
A spherical tank of radius 8 feet is half full of oil that weighs 50 pounds for cubic font .find the work required to pump the oil out through a hole to the top of the tank.
The work required to pump the oil out through a hole to the top of the tank is approximately 6,476,160π/3 foot-pounds.
To solve this problemWe can find the work required to pump the oil out of the tank by using the formula:
W = ∫[V1, V2]ρgh dV
Where
W is the work required (in foot-pounds)ρ is the density of the oil (in pounds per cubic foot)g is the acceleration due to gravity (in feet per second squared)h is the height of the oil column being pumped (in feet)dV is an infinitesimal volume elementFirst, we need to find the density of the oil. We are told that the oil weighs 50 pounds per cubic foot, so:
ρ = 50 lb/ft^3
Next, we need to find the height of the oil column being pumped. The tank is half full, so the height of the oil column is:
h = r - (r/2) = r/2 = 8/2 = 4 feet
Now, we need to find the volume of oil being pumped. Since the tank is half full, the volume of oil is:
V = (1/2)(4/3)πr^3 = (1/2)(4/3)π(8)^3 = 1,024π/3 cubic feet
Finally, we can integrate the work formula to find the total work required:
W = ∫[V1, V2]ρgh dV
W = ∫[0, 1,024π/3] (50 lb/ft^3)(32.2 ft/s^2)(4 ft) dV
W = (6,476,160π/3) ft-lb
Therefore, the work required to pump the oil out through a hole to the top of the tank is approximately 6,476,160π/3 foot-pounds.
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Use the discriminant to determine the number of real roots for the equation 5x2 −19x − 4 = 0.
discrminant :
number of real roots:
Step-by-step explanation:
5x² - 19x - 4
use the discriminant formula
D = b² - 4ac
label the coefficients
5 = a -19 = b -4 = c
D = -19² - 4(5)(-4)
D = -281
since the discriminant is negative this eqaution ahs no real solutions
According to the USDA, a small family farm has an average area of 231 acres.
a. What is this area in square miles? Use this fact that 1 square mile is 640 acres.
b. What is this area in square feet? Recall: 1 mile = 5,280 ft.
Answer:
Therefore, the area of a small family farm in square feet is 9,923,640.
Step-by-step explanation:
a. To convert acres to square miles, we divide the number of acres by 640:
231 acres / 640 acres/square mile = 0.36 square miles
Therefore, the area of a small family farm in square miles is 0.36.
b. To convert acres to square feet, we first need to convert acres to square yards (since there are 9 square feet in a square yard):
231 acres x 4840 square yards/acre x 9 square feet/square yard = 9,923,640 square feet
Therefore, the area of a small family farm in square feet is 9,923,640.