Answer:
sin45°=x/16
or, 1/√2 = x/16
or, x=16/√2
or, x=8√2 or 11.31 #
Phil Dunphy, a real estate agent, is considering whether he should list an unusual $262,023 house for sale. If he lists it, he will need to spend $3,111 in advertising, staging, and fresh cookies. The current owner has given Phil 6 months to sell the house. If he sells it, he will receive a commission of $19,752. If he is unable to sell the house, he will lose the listing and his expenses. Phil estimates the probability of selling this house in 6 months to be 40%. What is the expected profit on this listing?
Answer: $4,789.80
Step-by-step explanation:
If Phil is able to sell the house, the profit he makes will be;
= Commission - expenses
= 19,752 - 3,111
= $16,641
If he is unable to sell in 6 months he will lose $3,111.
His expected profit will be a weighted average of the two possibilities;
= (40% * 16,641) + ( 60% * -3,111)
= 6,656.40 + (-1,866.6)
= $4,789.80
Given rhombus QRST, find the
perimeter if QU = 3 and RU equals 4.
Q
R
T
U
X
S
The perimeter of the rhombus in this problem is given as follows:
19.8 units.
What is the perimeter of a polygon?The perimeter of a polygon is given by the sum of all the lengths of the outer edges of the figure, that is, we must find the length of all the edges of the polygon, and then add these lengths to obtain the perimeter.
The diagonal length can be obtained as follows:
QU = US = 3.RU = UT = 4.RU + UT = 7.
Applying the Pythagorean Theorem, the side length is obtained as follows:
x² + x² = 7²
2x² = 49
\(x = \sqrt{\frac{49}{2}}\)
x = 4.95.
Then the perimeter is given as follows:
P = 4 x 4.95
P = 19.8 units.
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10-2 eeaaasadaddadeeee
Answer:thwe answer is 8
Step-by-step explanation:
Answer:88
Step-by-step explanation:
Please help me with this I need the help
PLS QUICK How did the mountainous geography of Athens influence the economy?
The people of Athens mined gold for trade.
The people of Athens were unable to raise any crops.
The people of Athens focused on the military to protect their region.
The people of Athens relied on sea trade.
Option D. The mountainous geography of Athens influence the economy as The people of Athens relied on sea trade.
How did the terrain of Athens influence the economy ?Greece's rugged terrain caused some areas, particularly Athens, to become dependent on trade. Many Greeks went on to become seafaring tradesmen and merchants. Greeks engaged in trade with other Mediterranean people for pottery, wine, and olive oil. They communicated with the outside world by sailing to neighboring islands.
The geography of the area influenced the ancient Greeks' political system and way of life. Mountains, seas, and islands formed natural barriers between the Greek city-states, forcing the Greeks to relocate to coastal areas.
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1. The expression ax^2 + bx takes the value 6 when x = 1 and 10 when x = 2. Find its values when x = 5
The value of the quadratic expression ax² + bx when x = 5 is 10.
What is a quadratic expression?A quadratic expression is an expression in which the highest power of the unknown is 2.
Since we have the expression ax² + bx takes the value 6 when x = 1 and 10 when x = 2. We need to find its values when x = 5.
We proceed as follows.
Let y = ax² + bx.
When x = 1, y = 6. So, substituting these into the equation, we have that
y = ax² + bx
a(1)² + b(1) = 6
a + b = 6 (1)
Also, when x = 2, y = 10. So, substituting these into the equation, we have that
y = ax² + bx
a(2)² + b(2) = 10
4a + 2b = 10 (2)
From (1) a = 6 - b (3).
So, substituting equation (3) into (2), we have that
4a + 2b = 10
4(6 - b) + 2b = 10
24 - 4b + 2b = 10
24 - 2b = 10
-2b = 10 - 24
-2b = -14
b = -14/-2
b = 7
Substituting b into (3). we have that
a = 6 - b
= 6 - 7
= - 1
So, substituting a = - 1 and b = 7 into the quadratic expression, we have that
y = ax² + bx
= -1x² + 7x
= -x² + 7x
So, the value of the expression when x = 5 is
= -x² + 7x
= -(5)² + 7(5)
= -25 + 35
= 10
So, the value is 10
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ead the situations below and determine which relationship is not functional.
Situation 1: a cell phone bill to the amount of minutes used
Situation 2: the perimeter of a square to the length of one of the sides of a square
Situation 3: the total amount of money charged monthly on credit cards to the number of credit cards owned
Situation
does not represent a function.
This is because
.
There can be multiple outputs (monthly charges) for a given input (number of credit cards), violating the definition of a function. hence, Situation 3 does not represent a function.
Situation 3: the total amount of money charged monthly on credit cards to the number of credit cards owned does not represent a function.
In a function, each input (or x-value) should have a unique output (or y-value). However, in this situation, the total amount of money charged monthly on credit cards depends on the number of credit cards owned. It is possible to have different credit card numbers but still have the same total amount of money charged monthly.
For example, two people could own different numbers of credit cards but have the same monthly charges.
As a result, the definition of a function can be violated by having many outputs (monthly charges) for a single input (number of credit cards).
Because of this, case 3 does not represent a function.
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help.... i will mark you brain
Answer:
58 students
Step-by-step explanation:
11 * 5 = 55
55 + 3 = 58
Answer:
58 students
Step-by-step explanation:
11 tables have 5 students, so we multiply.
11 • 5 = 55
Add three for the last table
55+3=58 students
Given f(x) = |X - 9|.The vertex of the function moves from (0,0) nine units where?
left
right
up
down
Answer:
RightStep-by-step explanation:
Given function
f(x) = |x - 9|Let's try point x = 0
f(0) = | 0 - 9 | = | -9 | = 9So the vertex moves right
See attached
ind the fractal dimensions for the following fractal objects. Complete parts (a) through (c). Question content area bottom Part 1 a. Suppose you are measuring the length of the stream frontage along a piece of mountain property. You begin with a 10 -meter ruler and find just one element along the length of the stream frontage. When you switch to a 1 -meter ruler, you are able to trace finer details of the stream edge and you find 25 elements along its length. Switching to a 10 -centimeter ruler, you find elements along the stream frontage. Based on these measurements, what is the fractal dimension of the stream frontage
Answer: the stream frontage has a fractal dimension between 1.67 and 2
Step-by-step explanation: The equation utilized to compute the fractal dimension of stream frontage is expressed as follows: D = (log N) / (log 1/s), where N represents the total count of constituent units and 1/s denotes the scaling factor.
At the scale of 10 meters, it has been determined that N equals one and the reciprocal of s equals one. At the scale of 1 meter, the sample size (N) is equal to 25, while the sampling interval (1/s) is equivalent to 0.1, which is obtained by dividing it by 10. At a distance of 10 centimeters, the number of observed particles is equivalent to 250 and the reciprocal of the standardized sensitivity value is 0.01. By employing the applicable formula, the fractal dimension can be computed as follows:
The equation can be expressed as D, which is equal to the logarithm of N divided by the logarithm of the reciprocal of s, represented as log 1/s.
At the 10-meter scale, it can be observed that D possesses a value of 0. This signifies that, within the scope of measurement, D does not exhibit any discernible magnitude.
At a scale of 1 meter, the value of D is approximately equal to 1.67.
The value of D on a 10 centimeter scale is equivalent to 2.
Julie printed out a picture of each of the five members of her favorite band to decorate her bedroom door. Each picture measures 8
inches by 10 inches. Once decorated, how many square inches of Julie's door will be covered by these pictures?
OA.
400 square inches
OB. 320 square inches
OC. 480 square inches
OD
180 square inches
Given f(x)2x and g(x) = x^2+3 , find f(g(x)).
Answer:
2x^2 + 6.
Step-by-step explanation:
Replace the x in f(x) by g(x):
f(g(x)) = 2(x^2 + 3)
= 2x^2 + 6.
The quadratic formula can be used to solve an equation only if the highest
degree in the equation is
Α. Ο
B. 3
C. 2
D. 1
Answer:
2
Step-by-step explanation:
15 less than a number is equal to 12
Answer:
Step-by-step explanation:
x - 15 = 12
x = 27
A house is sold for $195,000. The mortgage is $168,745.60 at 8%. Annual taxes are $3,893.25. The closing will occur on June 15. What are the total prorations for interest (for the full month) and for property taxes to the nearest $100? Will the prorations be added to, or subtracted from, the seller's equity?
The total prorations for interest and property taxes to the nearest $100 are:
Proration for interest: $517
Proration for property taxes: $1,754
To calculate the total prorations for interest and property taxes, we need to determine how much the seller owes for each of these expenses up to the closing date of June 15.
First, let's calculate the daily interest rate on the mortgage. We can do this by multiplying the principal amount of the mortgage ($168,745.60) by the annual interest rate (8%) and then dividing by 365 (the number of days in a year):
Daily interest rate = ($168,745.60 x 0.08) / 365 = $36.94
Next, we need to determine the number of days from the start of the month (June 1) to the closing date (June 15):
Number of days = 15 - 1 = 14
Using the daily interest rate and the number of days, we can calculate the proration for interest:
Proration for interest = ($36.94 x 14) = $516.76
To calculate the proration for property taxes, we need to divide the annual property taxes ($3,893.25) by 365 to get the daily property tax rate:
Daily property tax rate = $3,893.25 / 365 = $10.65
Next, we need to determine the number of days from the start of the year to the closing date (June 15):
Number of days = 165
Using the daily property tax rate and the number of days, we can calculate the proration for property taxes:
Proration for property taxes = ($10.65 x 165) = $1,754.25
Therefore, the total prorations for interest and property taxes to the nearest $100 are:
Proration for interest: $517
Proration for property taxes: $1,754
These prorations will be subtracted from the seller's equity, since they are expenses that the seller owes up to the closing date.
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The coordinate plane shows a line traveling through two points.
The coordinates that represent another point on the line are
a (3,5)
b (3,2)
c (5,3)
d (6,7)
Solve the equation: 9-15x = 28 + 4x
Answer:
x = -1
Step-by-step explanation:
To solve this, we want to isolate x:
9 - 15x = 28 + 4x
Subtract 9 from both sides:
-15x = 19 + 4x
Subtract 4x from both sides:
-19x = 19
Divide both sides by -19:
x = -1
a rectangle has a perimeter of 48 in. the length and width are scaled by a factor of 2.5. what is the perimeter of the resulting rectangle?
If a rectangle has a perimeter of 48 in. the length and width are scaled by a factor of 2.5, the perimeter of the resulting rectangle is 225 inches.
Let L be the length of the original rectangle and W be the width. Then, the perimeter of the original rectangle is P = 2L + 2W = 48 inches.
If we scale the length and width by a factor of 2.5, we get a new length of 2.5L and a new width of 2.5W. The perimeter of the new rectangle would be:
P' = 2(2.5L) + 2(2.5W)
= 5L + 5W
To find the new perimeter, we need to find the new values of L and W. Since the length and width are scaled by the same factor, we can write:
2.5L = kL
2.5W = kW
where k is the scaling factor.
Since the new rectangle is scaled by a factor of 2.5, k = 2.5. Therefore:
L' = 2.5L = 2.5(12) = 30 inches
W' = 2.5W = 2.5(6) = 15 inches
The new perimeter is:
P' = 5L' + 5W'
= 5(30) + 5(15)
= 225 inches
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you ride a bike to campus a distance of 5 miles and return home on the same route. Going to campus, you ride mostly downhill and average 9 miles per hour faster than on your return trip home. If the round trip one hour and ten minutes that is 7/6 hours; what is your average velocity on your return trip
Rectangular Garden
A rectangular garden shown above is enclosed by
60
60
feet of fencing on three sides and by a wall on the fourth side. One of the sides of the garden that is perpendicular to the wall is
x
x
feet long. In terms of
x
,
x
,
what is the length, in feet, of the side of the garden that is against the wall?
Answer:
The length, in feet, of the side of the garden that is against the wall is(60 - x - CD) ft.
Step-by-step explanation:
Consider the diagram below.
The wall is labelled as AD, the side perpendicular to the wall is labelled as AB and the side against the wall is labelled as CB.
It is provided that the rectangular garden is enclosed by 60 feet of fencing on three sides.
That is,
AB + CB + CD = 60 ft.
⇒ x + CB + CD = 60 ft.
Then the length, in feet, of the side of the garden that is against the wall is:
x + CB + CD = 60 ft.
⇒ CB = (60 - x - CD) ft.
Answer: 60-2x
Step-by-step explanation:
-11, -8,-5, -2...
What is the 100th term in this sequence?
Answer:
298.
Step-by-step explanation:
formula- n in the next term is (n+3)
basically adding three
3x100=300
-2+300=298
-2 (1 - 4x)=3x +8 is
Answer:
= 2
1. Rearrange terms
2.Distribute
3. add 2 to both sides of the equation
4.Simplify
5.Subtract 3 from both sides of the equation
6. Simplify again
7. Divide both sides of the equation by the same term
8. Simplify one more time
Anne's phone plan charges $25.00 to sign up and $.02 per minute of usage. AJ's phone plan charges $5.00 to sign up and $.04 per minute of usage. After how many minutes of usage will Anne and AJ's plan cost the same amount?
Based on the charges to Anne's phone plan and that of AJ, the number of minutes of usage till Anne and AJ's plan cost the same is 1,000 minutes.
How long till Anne and AJ are charged the same?Assuming that the number of minutes till Anne and AJ are charged the same is x, then Anne's phone plan can be represented as:
= 25 + 0.02x
AJ plan is:
= 5 + 0.04x
The number of minutes till both are the same is:
25 + 0.02x = 5 + 0.04x
25 - 5 = 0.04x - 0.02x
20 = 0.02x
x = 1,000 minutes
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there are how many distinct website graphics to be created?
According to the question there are 35 distinct website graphics that can be created by using at least four of seven different bitmap images.
What is website?A website is a collection of related web pages, images, videos, and other digital assets that are hosted on a web server and can be accessed by users over the internet. A website is typically identified by a unique domain name and can be accessed by typing the URL into a web browser.
Using the formula for calculating the number of combinations of size k from a set of size n (n choose k), we can calculate the number of distinct website graphics that can be created by using at least four of seven different bitmap images as follows:
n = 7 (7 different bitmap images)
k = 4 (at least 4 of the 7 bitmap images)
Number of distinct website graphics = (7 choose 4) = 35
Therefore, there are 35 distinct website graphics that can be created by using at least four of seven different bitmap images.
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Inverse f(x)=x+6/x-5,x=5
Answer: \(\frac{x+5+\sqrt{x^2+10x+1}}{2},\:\frac{x+5-\sqrt{x^2+10x+1}}{2}\)
Steps:
\(1.{A\:function\:g\:is\:the\:inverse\:of\:function\:f\:if\:for}\:y=f\left(x\right),\:\:x=g\left(y\right)\:\)
2. Replace x with y: \(x=y+\frac{6}{y}-5\)
3. Solve for y, x = y + \(\frac{6}{5}\) - 5. This will get you the correct answer.
Amy is trying to find a lid for a pot with a radius of 12 inches. How big is the lid?
Answer:
24 in
Step-by-step explanation:
the radius would be half of the whole amount
Bigco Corporation is one of the nation’s leading distributors of food and related products to restaurants, universities, hotels, and other customers. A simplified version of its recent income statement contained the following items (in millions).
Cost of sales $ 11,571
Income taxes 249
Interest expense 23
Net earnings 1,442
Sales 16,400
Earnings before income taxes 1,691
Selling, general, and administration expense 3,543
Other revenues 428
Total expenses (excluding income taxes) 15,137
Total revenues 16,828
Prepare an income statement for the year ended June 30, current year. (Hint: First order the items as they would appear on the income statement and then confirm the values of the subtotals and totals.)
Step-by-step explanation:
I hope this answer is helpful ):
The graph shows Derek’s pay compared to the hours he has worked.
What is Derek’s hourly rate of pay?
Charlie earns $52.25 in 5 hours of work. What is Charlie’s hourly rate of pay?
Who gets paid more per hour? How much more?
Answer:
Charlie gets paid more then Derek. Charlie gets paid per hour $52.25
A transponder for a toll bridge costs $58.50. With the transponder, the toll is $4 each time you cross the bridge. The only other option is toll-by-plate, for which the toll is $6.25 each time you cross the bridge with
an additional administrative fee of $2.25 for each crossing. How many times would you need to cross the bridge for the costs of the two toll options to be the same?
You need to cross the bridge times.
Using linear functions, you need to cross the bridge 13 times.
What is a linear function?A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.Considering the transporter cost as the intercept and the cost per cross as the slope, the functions are given as follows:
A(x) = 58.5 + 4x.B(x) = (6.25 + 2.25) = 8.5x.The costs are the same when:
A(x) = B(x)
58.5 + 4x = 8.5x
4.5x = 58.5
x = 58.5/4.5
x = 13.
You need to cross the bridge 13 times.
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Graph the set. in number line
(1, ∞) ∩ (−10, ∞)
See attachment for the graph of the set (1, ∞) ∩ (−10, ∞)
How to graph the set on a number line?The set is given as:
(1, ∞) ∩ (−10, ∞)
The above means that the numbers inclusive in the set are numbers between the following set:
(1, ∞): All real numbers greater than 1(−10, ∞): All real numbers greater than -10The intersection of the above set is (1, ∞)
This means that the set (1, ∞) ∩ (−10, ∞) is a set of all real numbers greater than 1
Having done the above illustration, next we plot the set on a number line
See attachment for the graph of the set (1, ∞) ∩ (−10, ∞)
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