The area of ΔEFG is approximately 6.7 square centimeters.
To find the area of ΔEFG with given sides g = 5.2 cm, e = 5.1 cm, and ∠F = 42°, you can use the formula for the area of a triangle when two sides and the included angle are known. This formula is:
Area = (1/2)ab * sin(C)
In this case, a = g, b = e, and C = ∠F. Plug in the values:
Area = (1/2)(5.2 cm)(5.1 cm) * sin(42°)
Area ≈ 6.675 square centimeters
So, the area of ΔEFG is approximately 6.7 square centimeters to the nearest 10th of a square centimeter.
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LA and LB are vertical angles. If mLA= (4x+6)° and mLB=(2x+18)°, then find the value of x
NEED HELP ASAP PLEASE
Answer:
C
Step-by-step explanation:
All the other ones aren't increasing with the same proportion
Only C is increasing by same number each time (which is 26)
Find the values of x and y that make the quadrilateral a parallelogram
DEFG
5x-4
3y+9
10x-24
2y+16
Answer:
x = 4, y = 7
Step-by-step explanation:
3y + 9 = 2y + 16
y = 7
10x - 24 = 5x - 4
5x = 20
x = 4
values of x is 4 and y is 7
Question One:
Zahir bought a house 15 years ago, and it is now valued $548 900.00.
Determine the initial value of the home when Zahir purchased it, if it's value
has grown at a rate of 4.8% compounded annually. (2 marks)
Question Two:
Kiran purchases a sofa for $1791.99 (taxes already included). The
department store offers her a promotion of 0% interest with no payments
for one year. If Kiran does not pay the amount in full within one year,
interest will be charged from the date of purchase at an annual rate of
27.93%, compounded monthly.
a) If Kiran does not make any payments, what will the department store bill
her one year after the date of purchase? Show your work. (2 marks)
b) Describe a different compounding period such that the overall cost of the
sofa is lower than if the annual interest rate were compounded monthly. Use
an example to help your explanation. (2 mark)
A. Kiran will be billed approximately $2,284.33 one year after the date of purchase if she does not make any payments.
B. In this case, the overall cost of the sofa would be approximately $2,284.08
How to solve the problemsTo find the initial value of the home when Zahir purchased it, we can use the compound interest formula:
Future Value = Initial Value * (1 + (interest rate))^years
Let Initial Value be P. We are given the Future Value as $548,900, the interest rate as 4.8%, and the number of years as 15.
548,900 = P * (1 + 0.048)^15
Now, we'll solve for P:
P = 548,900 / (1 + 0.048)^15
P ≈ 305,113.48
a. Future Value = Initial Value * (1 + (interest rate / number of periods))^(years * number of periods)
Initial Value = $1,791.99
Interest Rate = 27.93% (0.2793)
Number of periods = 12 (monthly)
Years = 1
Future Value = 1,791.99 * (1 + (0.2793 / 12))^(1 * 12)
Future Value ≈ 2284.33
Kiran will be billed approximately $2,284.33 one year after the date of purchase if she does not make any payments.
b. interest were compounded annually:
Future Value = Initial Value * (1 + interest rate)^years
Future Value = 1,791.99 * (1 + 0.2793)^1
Future Value ≈ 2284.08
In this case, the overall cost of the sofa would be approximately $2,284.08, which is slightly lower than if the interest were compounded monthly ($2,284.33).
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Question 3
CLASS PRESIDENT In a poll for senior class president, 68 of the 145 male students said they planned to vote for Santiago. Out of 139
female students, 89 planned to vote for his opponent, Measha.
Construct a conditional relative frequency table based on voter preference. Show your calculations on a separate sheet of paper. Round to
the nearest whole percent if necessary
The given data is tabulated for conditional relative frequency table as follows.
Total male = 145, Total female = 139
Total male votes for Santiago = 68, Total female votes for Measha = 89
Total female votes for Santiago = 50, Total male votes for Measha = 77
Now total votes for Santiago = 68+50=118
Total votes for Measha = 166
Total votes casted = 284
The above data is formulated in tables attached below.
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To conduct a science experiment, it is required to decrease the temperature from 36 c at the rate of 4 c every hour. what will be the temperature 10 hours after the process begins?
To conduct the science experiment, the temperature needs to be decreased from 36°C at a rate of 4°C every hour.
So, after 1 hour, the temperature will be 36°C - 4°C = 32°C. After 2 hours, the temperature will be 32°C - 4°C = 28°C. Continuing this pattern, after 10 hours, the temperature will be 36°C - (4°C x 10) = 36°C - 40°C = -4°C.
However, this temperature is below freezing and unlikely to be accurate for a science experiment.
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Which phase of the process cycle for customer relationship management represents the actual implementation of the customer strategies and programs?
The phase of the process cycle for customer relationship management that represents the actual implementation of the customer strategies and programs is the "Execution" phase.
This is where the plans and strategies that were formulated in the earlier phases of the process cycle are put into action to interact with customers and build strong relationships with them.
During the Execution phase, the focus is on carrying out specific tactics to engage with customers and meet their needs, such as targeted marketing campaigns, personalized communication, and efficient service delivery.
The success of this phase relies heavily on the quality of the planning and preparation done in the earlier phases, as well as ongoing monitoring and adaptation to customer feedback and changing market conditions.
Effective execution of customer strategies and programs is crucial for building loyal and satisfied customers, and ultimately driving business growth.
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Choose which option shows the plan, which
option shows the front elevation and which
option shows the side elevation of this 3D
shape.
side
front
A
D
G
B
E
H
C
F
Looking at the triangular prism, the options showing the plan, front elevation and side elevation are:
Plan - A Front elevation - F Side elevation - J How to show the elevations ?To show the elevations of a triangular prism, you would need to draw a two-dimensional representation of each of the six faces of the prism, including the top, bottom, and four side faces.
For each face, you would draw the shape of the face, including any dimensions or angles necessary to accurately represent the face. Finally, you would draw lines to show the elevations of each face, indicating how they are connected to form the three-dimensional shape of the prism.
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Help me— My brain goes brrr in this question word problem thing ; - ;
A table tennis ball has a radius of 0. 04m. Estimate how many table tennis balls you could fit into the coin building! [search up what it is—]
( Width: 20m | height: 110m )
- How did you calculate your estimate?
- Explain how accurate you think your prediction is?
( Show Work. )
Number of balls ≈ [tex]1.03 * 10^9[/tex]
To calculate how many table tennis balls can fit into the coin building, we need to first figure out the volume of the building and the volume of the table tennis ball.
Then, we can divide the volume of the building by the volume of the ball to get an estimate of the number of balls that can fit inside.
The volume of a table tennis ball can be calculated using the formula for the volume of a sphere, which is:
V = (4/3)πr³
where V is the volume, π is pi (approximately 3.14), and r is the radius of the ball. In this case, the radius is given as 0.04m, so we can plug that in and get:
V = (4/3) x 3.14 x 0.04³
[tex]V =2.14 * 10^{-5} m^3[/tex]
Next, we need to find the volume of the coin building. The building has a width of 20m and a height of 110m, but we don't know its depth.
Let's assume that the building is a rectangular prism with a depth of 10m. Then, we can calculate its volume using the formula:
V = l x w x h
where l is the length, w is the width, and h is the height. Plugging in the given values, we get:
V = 20 x 10 x 110
V = 22000 m³
Now, we can divide the volume of the building by the volume of the ball to get an estimate of how many balls can fit inside:
Number of balls ≈ [tex]V_building / V_ball[/tex]
Number of balls ≈ 22000 / 2.14 x [tex]10^-5[/tex]
Number of balls ≈ [tex]1.03 * 10^9[/tex]
So we can estimate that approximately 1.03 billion table tennis balls can fit into the coin building.
As for the accuracy of this prediction, it's important to keep in mind that we made some assumptions and estimations in our calculations.
For example, we assumed that the building is a rectangular prism with a depth of 10m, which may not be completely accurate.
Additionally, we rounded some of our values and used approximations for pi.
Therefore, our estimate should be considered as a rough approximation rather than an exact calculation. Nonetheless, it gives us an idea of the scale of the building and how many objects it can hold.
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Connor invests $1,400 in a savings account that compounds annually at a 9% interest rate. Determine how much money Connor will have after 4 years. Round to the nearest cent
Connor will have $ 1975.4 if he invests $1,400 with a 9% interest rate that compounds annually for 4 years.
Compound interest is given by the formula:
A = P [tex](1 + \frac{r}{n})^{nt[/tex]
where A is the amount
P is the principal
r is the rate of interest
n is the frequency with the interest is compounded in a year
t is the time
P = $ 1,400
r = 9% or 0.09
t = 4 years
Since the interest is compounded annually the frequency of the compounding is 1.
n = 1
A = 1400 [tex](1 +\frac{0.09}{1})^{1*4[/tex]
= 1400 [tex](1.09)^4[/tex]
= 1400 * 1.411
= $ 1975.4
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You work at Dave's Donut Shop. Dave has asked you to determine how much each box of a dozen donuts should cost. There are 12 donuts in one dozen. You determine that it costs $0. 32 to make each donut. Each box costs $0. 18 per square foot of cardboard. There are 144 square inches in 1 square foot.
The total cost for one dozen donuts include the cost to make the donuts and the cost of the box. Create an expression to model the cost for one dozen donuts where t represents the total surface area of the box
create an expression to model the total cost for one dozen donuts where t represents the total surface area of the box in square feet.
help please :(
The cost for one donut is $0.32, so the cost for one dozen donuts is:
12 donuts x $0.32/donut = $3.84
The cost for the cardboard box is $0.18 per square foot of cardboard, and there are 144 square inches in 1 square foot, so the cost per square inch of cardboard is:
$0.18 / 144 sq in = $0.00125/sq in
If t represents the total surface area of the box in square inches, then the cost of the box is:
t x $0.00125/sq in
To convert square inches to square feet, we divide by 144:
t/144 square feet x $0.18/square foot = t x $0.00125/sq in
Thus, the expression to model the total cost for one dozen donuts where t represents the total surface area of the box in square feet is:
$3.84 + (t/144) x $0.18
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Find the equation of a line that goes throught point -2,-5 and is parallel to y = x + 2
The equation of the line that goes through the point (-2, -5) and is parallel to y = x + 2 is y = x - 3.
To find the equation of a line that goes through the point (-2, -5) and is parallel to y = x + 2, we will follow these steps:
1. Identify the slope of the given line.
2. Use the slope and the given point to find the equation of the new line.
Step 1: Identify the slope of the given line.
The equation of the given line is y = x + 2. This is in slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept. In this case, the slope (m) is 1, as it is the coefficient of x.
Step 2: Use the slope and the given point to find the equation of the new line.
Since the new line is parallel to the given line, it will have the same slope. Therefore, the slope of the new line is also 1.
Now, we will use the point-slope form of a linear equation, which is given by y - y1 = m(x - x1), where m is the slope, and (x1, y1) is the given point.
Plugging in the values, we have:
y - (-5) = 1(x - (-2))
y + 5 = 1(x + 2)
Now, let's rewrite the equation in slope-intercept form:
y + 5 = x + 2
y = x + 2 - 5
y = x - 3
So, the equation of the line that goes through the point (-2, -5) and is parallel to y = x + 2 is y = x - 3.
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Please help
Factor out the GCF.
6x²-3x - 18
Factor completely and show/explain each step.
Answer:
3(x - 2)(2x + 3)
Step-by-step explanation:
6x² - 3x - 18 ← factor out GCF of 3 from each term
= 3(2x² - x - 6) ← factor the quadratic
consider the factors of the product of the coefficient of the x² term and the constant term which sum to give the coefficient of the x- term
product = 2 × - 6 = - 12 and sum = - 1
the factors are - 4 and + 3
use these factors to split the x- term
2x² - 4x + 3x - 6 ( factor the first/second and third/fourth terms )
= 2x(x - 2) + 3(x - 2) ← factor out (x - 2) from each term
= (x - 2)(2x + 3) ← in factored form
then
6x² - 3x - 18 = 3(x - 2)(2x + 3)
The antiderivative ofeᵏˣ, where k is any constant, is... ½ eᵏˣ + c keᵏˣ + c eᵏˣ + c In(kx)+C
The antiderivative of e^(kx), where k is any constant, is (1/k)e^(kx) + C, where C is the constant of integration.
1. As we can see, you are asked to find the antiderivative of the function e^(kx).
2. Recall that the antiderivative of a function is the function that, when differentiated, gives you the original function.
3. The derivative of the function (1/k)e^(kx) is e^(kx), as the constant k in the exponent gets multiplied by the (1/k) factor, canceling each other out.
4. So, the antiderivative of e^(kx) is (1/k)e^(kx) + C, where C is the constant of integration.
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This equation gives the light intensity, I (in lumens), in water at a depth of feet: d= -425log(I/12). I) What is the intensity of the light at a depth of 300 feet? Please show all work. Ii) At what water depth is the intensity 5 lumens? Please show all work. Iii) What is the light intensity at the surface of the water? Please show all work
i) The light intensity at a depth of 300 feet is approximately 0.131 lumens.
ii)The light intensity of 5 lumens is reached at a depth of approximately 106.6 feet.
iii)The light intensity at the surface of the water is 12 lumens.
The equation given is:
[tex]d= -425log(\frac{I}{12} )[/tex]
where d is the depth in feet, and l is the light intensity in lumens.
i)To find the intensity of light at a depth of 300 feet:
[tex]d= -425log(\frac{I}{12} )[/tex]
[tex]or, \frac{d}{-425}=log(\frac{I}{12})[/tex]
[tex]or, 10^{\frac{d}{-425}}=\frac{I}{12}[/tex]
[tex]or, 12 X 10^{\frac{d}{-425}}=I[/tex]
Given, d= 300 feet. Hence,
[tex]or, 12 X 10^{\frac{300}{-425}}=I[/tex]
or, I = 0.131 lumens (approx.)
ii) We have been given the equation :
[tex]d= -425log(\frac{I}{12} )[/tex]
when I =5 lumens
[tex]d= -425log(\frac{5}{12} )[/tex]
or, d = 106.6 feet (approx.)
iii) For finding the light intensity at the surface of the water d=0
[tex]d= -425log(\frac{I}{12} )[/tex]
Putting d = 0 we get
[tex]0= -425log(\frac{I}{12} )[/tex]
[tex]or, log(\frac{I}{12})=0[/tex]
[tex]or, \frac{I}{12} = 10^0 = 1[/tex]
or, I = 12 lumens
Therefore the light intensity at the surface of the water is 12 lumens.
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To integrate f(x, y, z) = ~ over the region ? consisting of the points (2, Y, 2)
such that
•0≤o≤1,
•0≤y≤2,and
• 0 ≤ 2 ≤ 3x + 4y.
If we want to use the bounds of integration, what kind of integration would we use?
We first integrate with respect to z from 2 to (3x + 4y), then with respect to y from 0 to 2, and finally with respect to x from 0 to 1.
To integrate the given function over the region, we would use triple integration with the bounds of integration as follows:
∫ from 0 to 1 ∫ from 0 to 2 ∫ from 2 to (3x + 4y) f(x, y, z) dz dy dx
This is because the region is defined by the inequalities 0 ≤ x ≤ 1, 0 ≤ y ≤ 2, and 0 ≤ z ≤ (3x + 4y).
Therefore, we first integrate with respect to z from 2 to (3x + 4y), then with respect to y from 0 to 2, and finally with respect to x from 0 to 1.
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The equation, with a restriction on x, is the terminal side of an angle theta in standard position. 5x + y = 0, x ≥ 0 Give the exact values of the six trigonometric functions of theta. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. sin theta = (Simplify your answer. Use integers or fractions for any numbers in the expression. Type an exact answer, using radicals as needed. Rationalize all denominators.) B. The function is undefined.
Sin theta = -5/sqrt(26) Is the correct option , To find the six trigonometric functions of theta, we need to first find the values of x and y on the terminal side of theta. From the given equation, 5x + y = 0 and x ≥ 0, we can solve for y in terms of x:
y = -5x
Since x ≥ 0, we know that (x, y) lies in the fourth quadrant. We can now use the Pythagorean theorem to find the length of the hypotenuse:
r =[tex]sqrt(x^2 + y^2) = sqrt(x^2 + (-5x)^2) = sqrt(26x^2)[/tex]
Now we can find the six trigonometric functions:
sin(theta) = y/r = [tex]-5x/sqrt(26x^2) = -5/sqrt(26)[/tex]
cos(theta) = x/r =[tex]x/sqrt(26x^2) = 1/sqrt(26)[/tex]
tan(theta) = y/x = -5x/x = -5
csc(theta) = r/y = [tex]sqrt(26x^2)/(-5x) = -sqrt(26)/5[/tex]
sec(theta) = r/x = sqrt(26x^2)/x = sqrt(26)/1 = sqrt(26)
cot(theta) = 1/tan(theta) = -1/5
Therefore, the exact values of the six trigonometric functions of theta are:
sin(theta) = -5/sqrt(26)
cos(theta) = 1/sqrt(26)
tan(theta) = -5
csc(theta) = -sqrt(26)/5
sec(theta) = sqrt(26)
cot(theta) = -1/5
Answer: A. sin theta = -5/sqrt(26)
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Find the derivative of the function. f(x) = (5x - 5)(Vx+3) - 1/2 O A. f'(x) = 3.33x - 1/2 - 2.5x + 15 - 1/2 OB. f'(x) = 3.33% - 1/2 - 5x + 15 O c. f'(x) = 7.5x1/2 ) - 5x - 1/2 + 15 OD/2 O D. f'(x) = 7
To get the derivative of the function f(x) = (5x - 5)(√x + 3) - 1/2, we'll first need to use the product rule and then simplify the expression. The product rule states that if you have a function g(x)h(x), its derivative is g'(x)h(x) + g(x)h'(x).
Let g(x) = 5x - 5 and h(x) = √x + 3.
Step 1: the derivatives of g(x) and h(x).
g'(x) = 5 (derivative of 5x - 5)
h'(x) = 1/(2√x) (derivative of √x + 3)
Step 2: Apply the product rule.
f'(x) = g'(x)h(x) + g(x)h'(x)
f'(x) = 5(√x + 3) + (5x - 5)(1/(2√x))
Step 3: Simplify the expression.
f'(x) = 5√x + 15 + (5x - 5)/(2√x)
This is the derivative of the function f(x) = (5x - 5)(√x + 3) - 1/2. Note that none of the given answer choices match this result, so there might be a mistake in the provided options.
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Robert uses f(x)=1000(1. 0375)^x to calculate the interest he earns each year for his savings account. What is the annual rate as a percent?
The annual rate as a percent is approximately 4.86% per year.
To find the annual rate as a percent, we first need to understand the function that Robert is using. The function [tex]f(x) = 1000(1.0375)^x[/tex] represents the amount of money Robert earns each year based on his initial investment of $1000 and the interest rate of 3.75% (as represented by the value 1.0375, which is 1 + 0.0375).
To calculate the annual rate as a percent, we need to isolate the interest rate from the function. We can do this by using logarithms. Taking the logarithm of both sides of the equation, we get:
log(f(x)) = log(1000) + x*log(1.0375)
Now, we can solve for the interest rate (represented by the value of 1.0375) by dividing both sides of the equation by x and then taking the antilog of the result:
1.0375 = antilog[(log(f(x)) - log(1000))/x]
Using this formula, we can plug in any value for x (representing the number of years Robert has held his investment) and find the corresponding interest rate. For example, if Robert has held his investment for 5 years, we can calculate the interest rate as:
1.0375 = antilog[(log(f(5)) - log(1000))/5]
This gives us an interest rate of approximately 4.86% per year. So, to answer the original question, the annual rate as a percent is approximately 4.86%.
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Reddy
algebraic expressions with exponents - instruction - level f
) amelia stores her gardening supplies in two cube-shaped boxes. the smaller box has a
volume of 100 in.. amelia wants to know the total volume of both boxes.
s = length (in) of one side of the larger box.
6) write an expression to show the total
volume of the two boxes.
The expression to show the total volume of the two boxes is:
100 + [tex]s^3[/tex] ([tex]in^3[/tex])
We can start by finding the volume of the smaller box using the formula for the volume of a cube:
Volume of smaller box = (length of one side)^3 = 100 in^3
Taking the cube root of both sides, we get:
Length of one side = ∛100 in ≈ 4.64 in
Now, we can use this value to find the volume of the larger box:
Volume of larger box = (length of one side)[tex]^3 = s^3[/tex]
The total volume of both boxes is the sum of the volume of the smaller box and the volume of the larger box:
Total volume = Volume of smaller box + Volume of larger box
Total volume = 100 in [tex]^3 + s^3[/tex]
Therefore, the expression to show the total volume of the two boxes is:
100 + [tex]s^3[/tex] (in[tex]^3[/tex])
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Which coordinates below form a rectangle that is a translation of the rectangle
shown above?
A(0, 3), (0, 9), (5, 3), (5,9)
B(0, 0), (0, 3), (5, 0), (5, 3)
C(0, 0), (4,0), (0, 4)
D(7, 0), (7, 3), (12, 0), (12, 3)
Can someone help me with this, please?
Answer:
You are correct.
Hope this helps!
Step-by-step explanation:
The lines intersect at one point and that is the solution.
( The image shows a graph with infinite solutions. ( ignore the Byjus thing i was just trying to find an image that showed an example ... ) )
Which is a function of a protein macromolecule? a. keeping organisms warm b. providing quick energy for cells c. moving material in and out of cells d. passing traits to offspring
One if the functions of a protein macromolecule is: c. moving material in and out of cells
What is the Function of a Protein Macromolecule?Proteins can be described as a complex macromolecules that are responsible for several key functions such as the regulation of cells, tissue, and organs of living organisms including their structure.
Proteins also help in performing the following:
Regulation of gene expression
Structural support, and
Many other cellular processes.
Therefore, a function of a protein macromolecule is: c. moving material in and out of cells.
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A florist sells flower bouquets. the table shows the prices for various amounts and kinds of bouquets.
total price
bouquets
2
flower
daisies
tulips
roses
$23.90
$60.80
2
1
2
a
the expression (23.90 - 2) - (60.80 – 2) represents that a bouquet of daisies is
$18.45 more than a bouquet of tulips.
b
the expression (60.80 - 2) - (23.90 + 2) represents that a bouquet of tulips is
$18.45 more than a bouquet of daisies.
с
the expression 23.90 - 60.80 represents that a bouquet of tulips is $36.90 more than a
bouquet of daisies.
d
the expression 60.80 - 23.90 represents that a bouquet of daises is $36.90 more than a
bouquet of tulips.
The latter expression gives a positive result of $36.90, which means that a bouquet of daisies is $36.90 more expensive than a bouquet of tulips.
The given table shows the prices for various amounts and kinds of bouquets sold by a florist. The prices depend on the number and type of flowers in the bouquet. The table shows prices for bouquets of 2 flowers with daisies, tulips, and roses.
The expression (23.90 - 2) - (60.80 – 2) represents that a bouquet of daisies is $18.45 more expensive than a bouquet of tulips. This is because the cost of a 2-flower bouquet of daisies is $23.90 and the cost of a 2-flower bouquet of tulips is $60.80, so the difference between them is $36.90.
However, we subtract 2 from each price to get the price of the actual flowers in the bouquet, which are the same for both daisies and tulips. Therefore, we get the difference of $18.45.
Similarly, the expression (60.80 - 2) - (23.90 + 2) represents that a bouquet of tulips is $18.45 more expensive than a bouquet of daisies. Here, we subtract the price of a 2-flower bouquet of daisies plus the cost of 2 flowers from the price of a 2-flower bouquet of tulips.
Again, the actual cost of flowers in both bouquets is the same, so we get the difference of $18.45.
The expressions 23.90 - 60.80 and 60.80 - 23.90 represent the price difference between bouquets of daisies and tulips, respectively. The former expression gives a negative result of $36.90, which means that a bouquet of tulips is $36.90 more expensive than a bouquet of daisies.
The latter expression gives a positive result of $36.90, which means that a bouquet of daisies is $36.90 more expensive than a bouquet of tulips.
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You are making a 3 foot by 3 foot coffee table with a glass top surrounded by a cherry border of uniform width. The cherry border is included in the 3 x 3 measurements. You have 5 square feet of cherry border. What should the width of the border be?
Answer:
Step-by-step explanation:
The total area of the coffee table (including the cherry border) is:
3 feet x 3 feet = 9 square feet
We know that the area of the cherry border is:
5 square feet
To find the width of the cherry border, we need to subtract the area of the glass top from the total area of the coffee table:
9 square feet - area of glass top = area of cherry border
The area of the glass top is:
(3 feet - 2x) x (3 feet - 2x)
where x is the width of the cherry border.
Since the glass top is square, we can set the two dimensions equal to each other:
(3 feet - 2x) = (3 feet - 2x)
Expanding the left-hand side, we get:
9 feet - 6x = 9 feet - 6x
Simplifying, we get:
0 = 0
This means that the width of the cherry border does not affect the area of the glass top. Therefore, we can set the area of the glass top equal to the total area of the coffee table minus the area of the cherry border:
(3 feet - 2x) x (3 feet - 2x) = 9 square feet - 5 square feet
Simplifying, we get:
(3 feet - 2x) x (3 feet - 2x) = 4 square feet
Expanding the left-hand side, we get:
9 feet^2 - 12 feet x + 4x^2 = 4 square feet
Subtracting 4 square feet from both sides, we get:
9 feet^2 - 12 feet x + 4x^2 - 4 square feet = 0
Simplifying, we get:
4x^2 - 12 feet x + 9 feet^2 - 4 square feet = 0
Using the quadratic formula, we get:
x = [12 feet ± sqrt((12 feet)^2 - 4(4)(9 feet^2 - 4 square feet))] / (2(4))
Simplifying, we get:
x = [12 feet ± sqrt(144 feet^2 - 4(4)(9 feet^2 - 4 square feet))] / 8
x = [12 feet ± sqrt(144 feet^2 - 144 feet^2 + 64 square feet)] / 8
x = [12 feet ±
Use the following bond listing for Pacific Bell to answer the following: Bonds Cur. Yia. Vol Close Net. Chg. 5 6. 55 5 1 1 Pac Bell 6– 34 99- 4 8 What is the coupon rate and maturity date for this bond? 5 The coupon rate is 62, the maturity date is 2034. A. B 1 The coupon rate is 8 the maturity date is 2034. 5 The coupon rate is 6. The maturity date is 2099. D. The coupon rate is 6. 55; the maturity date is in 5 years.
The coupon rate for this Pacific Bell bond is 6%, and the maturity date is in 2034. So, the correct option is B: The coupon rate is 6%, and the maturity date is 2034.
The information provided in the bond listing can be interpreted as follows:
Bond issuer: Pacific Bell
Coupon rate: 6.55
Maturity date: 2034
Volume: 511
Closing price: 99-4
Net change: 8
Therefore, the correct answer is: The coupon rate is 6.55 and the maturity date is 2034.
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Given m||n, find the value of x
Answer:
x=32°
Step-by-step explanation:
3x-2=2x+30
x-2=30
x=32°
Use the information to answer the question.
A company had a profit of -$4,758 in January and a profit of $3,642 in February. The company's profits for the months of March through May
were the same in each of these months. By the end of May, the company's total profits for the year were -$1,275.
What were the company's profits each month from March through May? Enter the answer in the box.
The company's profits for each month from March through May were $658.33.
How to find the company profits for the months of March through May?
To solve the problem, we need to use the information given and set up an equation. Let's call the profits for the months of March through May "P" (since they are the same for each month).
The company's total profits for the year can be calculated by adding up the profits for each month:
January profit + February profit + March profit + April profit + May profit = total profit
Plugging in the numbers we know:
-$4,758 + $3,642 + 3P + 3P + 3P = -$1,275
Simplifying the equation:
9P = $5,925
Dividing both sides by 9:
P = $658.33
So the company's profits for each month from March through May were $658.33.
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SIMPLIFY THE EXPRESSION:
Answer:
12x - 8y
Step-by-step explanation:
Combine like terms.
10x - 5y + 2x -3y =
= 10x + 2x - 5y - 3y
= 12x - 8y
Question 7 of 25
Emma choosing a weekly meeting time. She hopes to have two different
managers attend on a regular basis. The table shows the probabilities that
the managers can attend on the days she is proposing.
Monday
Wednesday
0. 82
0. 87
Manager A
Manager B
0. 88
0. 85
Assuming that manager A's availability is independent of manager B's
availability, which day should Emma choose to maximize the probability that
both managers will be available?
O A. Wednesday. The probability that both managers will be available is
0. 74
O B. Monday. The probability that both managers will be available is
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Emma should choose A. Wednesday to maximize the probability that both managers will be available.
A. Wednesday. The probability that both managers will be available is 0.74.
To calculate this, multiply the probabilities of each manager's availability for each day:
- Monday: Manager A (0.82) x Manager B (0.88) = 0.7216
- Wednesday: Manager A (0.87) x Manager B (0.85) = 0.7395
Since 0.7395 (Wednesday) is higher than 0.7216 (Monday), Emma should choose Wednesday to maximize the probability that both managers will be available.
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