Answers
Answer:
Step-by-step explanation:
Since they are in a row, add all the measurements
4 ft 10 in
5 ft 6 in add ft with the ft and in with in
3 ft 3 in
12 ft 19 in
There are too many inches. So you can take away 12 of those inches and and turn it into 1 more foot. That would make 13 ft. You'd be left with 7 in.
12 ft + 1 ft 19 in - 12 in
13 ft 7in
Related Questions
Adult men have heights with a mean of 69.0 inches and a standard deviation of 2.8 inches. Find the z-score of a man who is 66.7 inches tall. (to 4 decimal places)
Answers
Answer:
!
Step-by-step explanation:
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
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
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
which of the following rational functions is graphed below? A. F(x) = 1/(x-1)² B. F(x) = 1/(2+1)² C. F(x) = 1/x2 D. F(x) = 1/x2+1
Answers
Answer:
c c c c c c c c c c c c c c c c c c c c c c c c c c c c c
Evaluate the function for f(2)
f(x) = 8x + 7
Answers
Answer:To evaluate the function for f(2), we simply substitute x = 2 into the function
:f(2) = 8(2) + 7
Simplifying the expression:
f(2) = 16 + 7f(2) = 23
Therefore, f(2) = 23.
Step-by-step explanation:
14. As shown in the figure, the area of square ABCD is known to be 1320 square centimeters, E is the midpoint of AB, F is a quarter point of BC close to point B, and the intersection points of CE, DB and DF are P and Q , find the area of the quadrilateral BPQF.
Answers
The coordinates of all four vertices of quadrilateral BPQF, we can use the shoelace formula to find its area. The shoelace formula states that the area of a polygon with vertices (x1, y1), (x2,
What is the triangle?A triangle is a closed, two-dimensional geometric shape that has three sides and three angles. It is one of the basic shapes in geometry and can be formed by connecting three non-collinear points. Triangles can be classified based on their side lengths and angles.
To solve this problem, we can use the fact that the area of a triangle is equal to half the product of its base and height. Let's first find the length of the sides of the square.
Since the area of the square is 1320 square centimeters, we can find its side length by taking the square root of 1320:
√(1320) ≈ 36.32
So the side length of the square is approximately 36.32 cm.
Next, let's find the coordinates of points E and F. Since E is the midpoint of AB, its coordinates are:
E = ((0+36)/2, (36+0)/2) = (18, 18)
Similarly, since F is a quarter point of BC close to point B, its coordinates are:
F = (36, (3/4)36) = (36, 27)
Now let's find the equation of line CE. Since we know two points on the line (C and E), we can use the point-slope form of a linear equation to find its equation:
y - y1 = m(x - x1)
where m is the slope of the line and (x1, y1) is one of the points on the line. We can find the slope of the line by taking the difference in y-coordinates and dividing by the difference in x-coordinates:
m = (0 - 36)/(36 - 18) = -2
Using the point-slope form with point C, we get:
y - 0 = -2(x - 36)
y = -2x + 72
Similarly, the equation of line DB can be found using points D and B:
m = (0 - 36)/(0 - 18) = 2
y - 0 = 2(x - 0)
y = 2x
Finally, we can find the coordinates of point P by solving the system of equations:
y = -2x + 72
y = 2x
Setting the two expressions for y equal to each other, we get:
-2x + 72 = 2x
4x = 72
x = 18
Substituting x = 18 into either equation, we get:
y = 2x = 36
So the coordinates of point P are (18, 36). To find the coordinates of point Q, we can use the fact that it lies on line DF. Since we know two points on the line (D and F), we can again use the point-slope form of a linear equation:
m = (27 - 0)/(36 - 0) = 3/4
y - 0 = (3/4)(x - 0)
y = (3/4)x
To find the intersection point of lines DF and CE, we need to solve the system of equations:
y = (3/4)x
y = -2x + 72
Setting the two expressions for y equal to each other, we get:
(3/4)x = -2x + 72
(11/4)x = 72
x = 64/11
Substituting x = 64/11 into either equation, we get:
y = (3/4)(64/11) ≈ 14.73
So the coordinates of point Q are (64/11, 14.73).
Hence, Now that we have the coordinates of all four vertices of quadrilateral BPQF, we can use the shoelace formula to find its area. The shoelace formula states that the area of a polygon with vertices (x1, y1), (x2,
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The menu board at a local pizza restaurant shows all the ordering options. Customers can choose up to one item from each category for a one-topping pizza.
Size Sauce Cheese Toppings
Small
Medium
Large
Garlic
Marinara
Mozzarella
Provolone
Parmesan
Pepperoni
Sausage
Ham
Pineapple
Onions
Peppers
What is the probability that a randomly selected one-topping pizza will not have onions on it? Express your answer as a simplified fraction.
Answers
Answer: 4/5
Step-by-step explanation: In decimal form: 0.8
39. Firefighters must reach a fire anywhere
in the city within 7 minutes. They are
currently reaching fires in 3.5 minutes
less than the maximum time allotted.
Which equation shows how much time
it takes them to reach a fire?
A. t + 3.5=7
B. t - 3.57
C. t - 7 = 3.5
D. t + 7 = 3.5
Answers
A random number generator picks a number from 7 to 69 in a uniform manner. Round answers to 4 decimal places when possible.
Find the maximum for the lower quartile
(100PTS)
Answers
Answer:
The lower quartile corresponds to the 25th percentile of the data set. To find the maximum value for the lower quartile, we need to find the largest number that is at or below the 25th percentile.
The range of the numbers that the random number generator can pick is 69 - 7 + 1 = 63. The 25th percentile corresponds to the value that is 25% of the way through this range, which is:
0.25 * 63 = 15.75
Since we can't pick a fractional number, we need to round down to 15. Therefore, the maximum value for the lower quartile is 15.
PLEASE HELP QUICKLY(20 POINTS!!)
what is the slope of this function
A. 1/2
B. -2
C. 2
D. -1/2
E. -3/2
F. -3
Answers
Answer:
A
Step-by-step explanation:
calculate the slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (- 6, - 6) and (x₂, y₂ ) = (6, 0) ← 2 points on the line
m = [tex]\frac{0-(-6)}{6-(-6)}[/tex]= [tex]\frac{0+6}{6+6}[/tex] = [tex]\frac{6}{12}[/tex] = [tex]\frac{1}{2}[/tex]
What is the median
9,7,7,7,8,8,6
Answers
To arrange in sequence like :-
9,7,7.7,8,8,6
Like
6.7,7,7,8,8,9
An then 6+7+7+7+8+8+9 =52 and divide with six
Answer is 7
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
Answers
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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Every page of the newspaper is a rectangle measuring 43 cm by 28 cm, both correct to the nearest
centimetre.
Calculate the upper bound of the area of a page.
Answers
Answer: 1204 cm²
Step-by-step explanation:
The upper bound of the area of a page would be the area of a rectangle with the upper bound of the length and width measurements.
Given that each page of the newspaper is a rectangle measuring 43 cm by 28 cm, both correct to the nearest centimetre, the upper bound of the length would be 43.5 cm (since we round up to the nearest centimetre) and the upper bound of the width would be 28.5 cm.
Therefore, the upper bound of the area of a page would be:
43.5 cm x 28.5 cm = 1240.25 cm²
Rounding this value to the nearest whole number, we get:
1204 cm²
So, the upper bound of the area of a page is 1204 cm².
Answer:
1204 cm 2
Step-by-step explanation:
Supplementary angles. I will be giving out points
Answers
Answer: Angle aeb
Step-by-step explanation: To be supplementary, the angle(s) must add up to 180. Angle AEB and angle DEA add to 180. Another way to find this is to find the angle that the angle is adjacent to in a straight line.
A circle is centered on point
B points a c and d lie on its
circumference. if
Answers
The measure of the angle ADC is: 20°
How to find the angle at the circumference?The parameters are given as:
∠ABC = 40°
∠ADC = ?
We know from circle geometry that:
Angle subtended at the center is twice the angle subtended at the circumference.
Therefore:
∠ABC = 2 x ∠ADC
On substituting the value we get:
40° = 2 * ∠ADC
∠ADC = 20°
Therefore, the measure of the angle ADC is 20°
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Complete question is:
A circle is centered on point B. Points A, C and D lie on it's circumference.
If ABC measures 40 degrees, what does ADC measure?
Find the value of x in each triangle
Answers
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
1. Undemeath each number write I for Irrational or R for Rational
3.2 x 10³
4/3
1.423...
TT/6
Answers
The numbers are characterized as rational and irrational numbers as below
1. 3.2 x 10³ - R (Rational)
2. 4/3 - R (Rational)
3. 1.423... - I (Irrational)
4. TT/6 - I (Irrational)
What are rational and irrational numbers?Rational numbers harmonized with a fraction of two integers where the denominator must not be zero. In simpler terms, it can be conveyed as p/q whereby both "p" and "q" are integers while "q" is unequal to zero.
As opposed to rational numbers, irrational ones cannot be expressed in a fraction or quotient of two integers. It's not possible to write them down in terms of the figure p/q whereby "p" and "q" are integers, differing from one another, and "q" is also inequivalent to zero.
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PLEASE HELP QUICKLY(25 points)!!
Match the description with the correct answer.
(questions)
———————
y-intercept -
slope-
domain-
range-
is this graph increasing, decreasing or both-
x-intercept-
———————
(answer choices)
(4,0), (0,4), (-2,0), (0,-2), +2, -4,
input values, increasing, decreasing,
both increasing and decreasing, output values
———————
please help quickly its worth 10.34 points on my test
Answers
Answer: In that picture the slope is increasing
Step-by-step explanation: positive rise and positive run (uphill from left to right)
Select any of these that are LINEAR. (Select MORE THAN ONE answer !)
Responses
A
A
B
B
C
C
D
D
Answers
The linear equations from the options given are expressed as: y = 5 and y = -2/5x + 4.
How to Determine an Equation that is Linear or Non-linear?An equation is linear can be expressed in the following forms:
y = mx + b
x = b
y = b
In the above, y is the dependent variable and x is the independent variable, m = slope, and b = y-intercept.
Note that in a linear equation the exponent of the variable is always 1. On the other hand, a nonlinear equation has an exponent that is not equal to 1 and can be expressed as:
y = x²
Therefore, the equations that are linear are:
y = 5 and y = -2/5x + 4.
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find the discriminant x^2-5x+22=7x+2
Answers
[tex]x^2-5x+22=7x+2\implies x^2-12x+20=0 \\\\[-0.35em] ~\dotfill\\\\ \qquad \qquad \qquad \textit{discriminant of a quadratic} \\\\\\ \stackrel{\stackrel{a}{\downarrow }}{1}x^2\stackrel{\stackrel{b}{\downarrow }}{-12}x\stackrel{\stackrel{c}{\downarrow }}{+20}=0 ~~~~~~~~ \stackrel{discriminant}{b^2-4ac}= \begin{cases} 0&\textit{one solution}\\ positive&\textit{two solutions}\\ negative&\textit{no solution} \end{cases} \\\\\\ (-12)^2-4(1)(20)\implies 144-80\implies 64[/tex]
In a triathlon, Farhan swims a distance of 1.5 km at an average speed of 2.5 km/h,
hours.
cycles 40 km in 12 hours and runs at an average speed of 9 km/h for 1
Find his
average speed for the entire competition.
Answers
Answer:
We can use the formula:
average speed = total distance / total time
To find the total distance, we add the distances for each event:
total distance = 1.5 km (swimming) + 40 km (cycling) + 1 km (running) = 42.5 km
To find the total time, we add the times for each event:
time for swimming = distance / speed = 1.5 km / 2.5 km/h = 0.6 hours
time for cycling = 40 km / 12 km/h = 3.33 hours
time for running = 1 km / 9 km/h = 0.11 hours
total time = 0.6 hours + 3.33 hours + 0.11 hours = 4.04 hours
Now we can calculate the average speed:
average speed = total distance / total time = 42.5 km / 4.04 hours ≈ 10.52 km/h
Therefore, Farhan's average speed for the entire competition is approximately 10.52 km/h.
What does this problem mean |x+3| if x>5
Answers
Answer:
x+3 . . . . if x > 5
Step-by-step explanation:
You want the meaning of |x+3| if x > 5.
Absolute valueThe absolute value function is a piecewise defined function:
[tex]y=|x|=\begin{cases}-x&\text{for }x < 0\\x&\text{for }x\ge0\end{cases}[/tex]
ApplicationThe expression (x+3) is zero when x=-3. So, your absolute value function will have the piecewise definition ...
[tex]|x+3|=\begin{cases}-(x+3)&\text{for }x < -3\\x+3&\text{for }x\ge-3\end{cases}[/tex]
You are interested in the value for x > 5, which is definitely greater than -3. That means only the second part of this definition is applicable.
x+3 . . . . if x > 5
__
Additional comment
The attache graph shows the given absolute value expression (dashed red line). The blue line is (x+3) for x > 5. You can see that it matches the given expression in that region.
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
Answers
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.
What is the value of x in this triangle?
Answers
Answer:
83 degrees
Step-by-step explanation:
See attachment below:
Use synthetic division to find the quotient and remainder when is divided by by completing the parts below.
Answers
After using synthetic division, the answer are given as follows;
first row = -4, 4, 12
Second Row = -2 2 -6 -5
Answer = 6 + [-5/x-2]
What is the full calculation?-2x^3+6x^2-10x+7 / x-2
Coefficient of the numerator polynomial are:
- 2, 6, -10 , 7
the zeros of the denominator are:
x -2 = 0
x = 2
X³ X³ X¹ X⁰
-2 6 -10 7
2
X³ X³ X¹ X⁰
-2 6 -10 7
2 ↓ -4 4 -12
-2 2 -6 -5
So the quotient is -2x² +2x - 6 remainder -5
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400 adults,96 of the 400 have high blood pressure 116 report being willing to change. an adult choosen at random what is probability they will be willing to change diet
solution is what
Answers
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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Gracie walks around the edge of a circular lake exactly 15 times. If she walks 2178 m in total, what is the diameter of the lake? If your answer is a decimal, give it to 1 d.p.
Answers
The diameter of the lake is 6.2 m.
What is the diameter?The diameter is the distance from one edge of the circle to the next across the center.
The diameter can be determined given the circumference and pi, since circumference is pi x diameter.
The number of times Gracie walks around the circular lake = 15 times
The total distance covered by the walk = 2,178 meters
The circumference (the distance around the edge of the circular lake) is 145.2 m (2,178 ÷ 15).
Circumference = C = 2πr = πd
Diameter = C/π
145.2 ÷ 3.143
= 46.2 m
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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:
Answers
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
help with calculus. determine wheter each labeled point is an absolute maximum or minumum OR a relative maximum or minimum or neither
Answers
The curve is defined as follows
A. absolute minima
B. absolute maxima
C. neither
D. relative minima
E. relative maxima
F. neither
G. neither
What is absolute minima and maxima?
When examining a function, its absolute minimum refers to the lowest possible value it can reach throughout its entire domain.
In a similar manner, absolute maximum pertains to the highest value that said function is capable of attaining within the same specified range, without consideration of separate intervals or regions.
To reiterate, these values denote the smallest and largest outcomes the function can yield over its complete set of input values, regardless of where those values may be located.
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Find the length of the arc, s, on a circle of radius r intercepted by a central angle θ. Express the arc length in terms of π. Then round your answer to two decimal places.
Radius, r = 16 inches; Central angle θ = 75°
(Simplify your answer. Type an exact answer in terms of π. Use integers or fractions for any numbers in the expression.)
Answer in form of Pi and Inches
Answers
The length of the arc of the circle that has a radius of 16 inches and a central angle of 75 degrees is calculated as 6.66π inches (to two decimal places).
What is the Length of an Arc?The length of an arc is calculated using the formula below:
arc length = θ/360 * 2 * π * r
Given the variables:
Central angle (θ) = 75 degrees
radius (r) = 16 inches
Plug in the values:
arc length = 75/360 * 2 * π * 16
length of arc ≈ 6.66π inches (to two decimal places).
Learn more about the length of arc on:
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A passbook savings account has a rate of 5%. Find the effective annual yield, rounded to the nearest tenth of a percent, if the interest is compounded semiannually.
Answers
Answer: 5.1%
Step-by-step explanation:
The formula for calculating the effective annual yield when the interest is compounded semiannually is given by:
(1 + (r/n))^n - 1
where r is the annual interest rate and n is the number of times the interest is compounded in a year.
In this case, r = 5% and n = 2 (since the interest is compounded semiannually). Substituting these values into the formula, we get:
(1 + (0.05/2))^2 - 1
= (1.025)^2 - 1
= 1.050625 - 1
= 0.050625
Multiplying this value by 100 gives the effective annual yield as a percentage:
0.050625 x 100 = 5.0625%
Rounding this to the nearest tenth of a percent, we get:
Effective annual yield = 5.1%
Therefore, the effective annual yield for the given savings account, rounded to the nearest tenth of a percent, is 5.1%.