Let x, xr , xr² be the terms of GP.
After the increase, the terms are : x+xr , xr+xr , xr²+xr
or in simplified manner : x(1+r), 2xr, xr (r+1) .
For these terms to be in Harmonic Progression, their reciprocals should be in Arithmetic Progression .
Thus,
Arithmetic mean of first and last terms should be equal to the middle term.
First term = 1/[x(1+r)] ; Middle term= 1/(2xr) ; Last term = 1/[xr(r+1)]
Assume,
A = Arithmetic mean of first and last term
A= [1/[x(1+r)]+[1/[xr(r+1)] /2
A= (1/2)[(r+1)/(xr(1+r))]
A= (1/2)(1/xr)
A= 1/(2xr)
A = Middle term
Thus, the reciprocals are in AP.
Hence x(1+r), 2xr, xr(r+1) in HP.
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TOURISM At a town with a large convention center, the cost of a hotel room has increased 5.1% annually.
If the average hotel room cost $48.00 in 1980 and this growth continues, what will an average hotel room
cost in 2012? Use y = a(1 + r)^t and round to the nearest cent.
a. $143.38
h
$235.79
$126 34
d
$87 19
Given statement solution is :- The average hotel room cost in 2012 would be $199.97, none of the provided options are correct.
To calculate the average hotel room cost in 2012, we can use the formula:
y = a(1 + r)^t
where:
y = future value (cost in 2012)
a = initial value (cost in 1980)
r = annual growth rate (5.1% or 0.051)
t = number of years (2012 - 1980 = 32)
Substituting the given values into the formula, we have:
y = $48.00(1 + 0.051)^32
Calculating the value:
y ≈ $48.00(1.051)^32
y ≈ $48.00(2.718282)^0.051(32)
y ≈ $48.00(2.718282)^1.632
y ≈ $48.00 * 4.171331
y ≈ $199.97
Rounding to the nearest cent, the average hotel room cost in 2012 would be $199.97.
Therefore, none of the provided options are correct.
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y = x² + 6x - 12
a =______
b = _____
c=______
h=______
k =_____
y-intercept=______
x-intercepts =______
and_____
Answer:
See below for answers and explanations
Step-by-step explanation:
a, b, and c are the coefficients of the quadratic, so a=1, b=6, and c=-12
(h,k) is the vertex of the parabola, so we must convert it to vertex form by completing the square:
[tex]y=x^2+6x-12\\y+21=x^2+6x-12+21\\y+21=x^2+6x+9\\y+21=(x+3)^2\\y=(x+3)^2-21[/tex]
Therefore, the vertex is (3,-21), which means h=-3 and k=-21.
The y-intercept is when x=0, or when the function passes through the x-axis:
[tex]y=x^2+6x-12\\y=0^2+6(0)-12\\y=-12[/tex]
Therefore, the y-intercept is -12 (also written as (0,-12) as an ordered pair).
The x-intercept is when y=0, or when the function passes through the y-axis:
[tex]\displaystyle x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\x=\frac{-6\pm\sqrt{6^2-4(1)(-12)}}{2(1)}\\\\x=\frac{-6\pm\sqrt{36+48}}{2}\\\\x=\frac{-6\pm\sqrt{94}}{2}[/tex]
Therefore, the x-intercepts are (-6+√94)/2 and (-6-√94)/2.
Hope this helped!
a bread making machine pours out 50 kg of mixture in 8 minutes in 8 minutes.at what rate is the mixture being poured?
To calculate the rate at which the mixture is being poured, we divide the amount of mixture poured (in kilograms) by the time it takes (in minutes):
Rate = Amount of mixture / TimeIn this case, the amount of mixture poured is 50 kg, and the time taken is 8 minutes. Plugging these values into the formula, we have:
Rate = 50 kg / 8 minDividing 50 kg by 8 min gives us:
Rate = 6.25 kg/minTherefore, the mixture is being poured at a rate of 6.25 kilograms per minute.
Use the binomial theorem to find the expansion of ( x - y + z)^3
What is the name of an angle that measures 91°?
Answer: Obtuse Angle
Step-by-step explanation: A 90 degree angle is a right angle anything larger then a right angle is a obtuse angle.
Answer:
It would be called an obtuse angle
Step-by-step explanation: so you see if it was exactly 90 degrees it would be called a right angle. Anything above 90 (b91 92 93 etc...) degrees would be an obtuse angle and anything below 90 ( 89 88 87 etc..) would be an acute angle except an 180 degree angle would be a straight angle. Hope that helps!
have a wonderful Sunday!
Janine built a raised garden bed that is 10 feet long, 5 feet wide, and 1.5 feet tall. She plans to fill the garden bed with premium soil that costs $16.31 per cubic yard. Recall that 1 yard = 3 feet. how much will it cost Janine to fill her garden bed with premium soil?
Answer: $45.31
Step-by-step explanation:
10*5*1.5=75
75/27 (formula)=2.77778
2.77778*16.31=45.31
Valerie took a job that paid $14 per hour after a pay raise she earned $15.05 per hour find the percent of increase
Answer:
Valerie's pay increased by 7.5%.
Step-by-step explanation:
The percent increase in Valerie's pay can be calculated as follows:
Percent increase = ((New pay - Old pay) / Old pay) x 100%
Substituting the given values, we get:
Percent increase = ((15.05 - 14) / 14) x 100%
Percent increase = (1.05 / 14) x 100%
Percent increase = 0.075 x 100%
Percent increase = 7.5%
Step-by-step explanation:
She now gets $1.05 per hour more .....1.05 is what percent of 14.00 ?
$ 1.05/ $ 14 x 100% = 7.5% increase
Whats the surface area
The surface area of the prism is S = 36 feet²
Given data ,
Let the surface area of the prism be represented as S
Now , the base of the prism is B
where B = l x w
And , length of prism = l and width of prism is = w
The formula for the surface area of a prism is SA=2B+ph, where B, is the area of the base, p represents the perimeter of the base, and h stands for the height of the prism
Surface Area of the prism = 2B + ph
The area of the triangular prism is A = ph + ( 1/2 ) bh
S = 2 ( 1/2 ) ( 3 x 4 ) + ( 4 x 2 ) + ( 3 x 2 ) + ( 5 x 2 )
On simplifying , we get
S = 12 + 8 + 6 + 10
S = 36 feet²
Hence , the surface area is S = 36 feet²
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e:
3) Find the value of x if RZ-2x+7 and SW= 5x-23
Applying the properties of the diagonal of a rectangle, the value of x is calculated as: x = 37.
How to Find the Value of x Using the Properties of the Diagonals of a Rectangle?A rectangle is a quadrilateral that has two equal diagonals which bisect each other, to form equal segment. Rectangle RSTW has two diagonals RT and SW, therefore:
2(RZ) = SW
Given the following:
RZ = 2x + 7
SW = 5x - 23
Plug in the values:
2(2x + 7) = 5x - 23
4x + 14 = 5x - 23
4x - 5x = -14 - 23
x = 37
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What is the sale price of a pillow originally priced at 12 dollars
The sale price of a pillow originally priced at 12 dollars is given as follows:
$9.
How to obtain the sale price?The sale price of a pillow originally priced at 12 dollars is obtained applying the proportions in the context of the problem.
The original price is given as follows:
$12.
The markdown rate for this problem is given as follows:
25%.
Hence the sale price of a pillow originally priced at 12 dollars is given as follows:
0.75 x 12 = $9.
(markdown of 25% means that 75% of the price is paid).
Missing InformationThe complete problem is:
"A pillow was marked down at 25%. What is the sale price of a pillow originally priced at 12 dollars?"
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help solve and explain
Answer:
6
Step-by-step explanation:
(3√3)^2/3 = (∛3)² X ∛(√3)²
= 3
27^2/3 = (∛27)²
= 3² = 9
9^-1/2 = 1/√9
= 1/3
so the answer is 3 + (9 X 1/3)
= 3 + 3
= 6
Solve for m/MNP ifm/MNO = 132° and m/PNO = 40°.
Answer:
Step-by-step explanation:
To solve for m/MNP if m/MNO = 132° and m/PNO = 40°, we can use the fact that the sum of the angles in a triangle is 180 degrees.
First, we can find the measure of angle MNO:
m/MNO + m/PNO + m/MNP = 180
132 + 40 + m/MNP = 180
m/MNP = 8
Copy
Therefore, m/MNP = 8 degrees.
I hope this helps! Let me know if you have any other questions.
MARKING AS BRAINLIST PLEASE HELP!!
The correct probability that either event will occur is 0.533.
What is probability?A measure of the likelihood of an event to occur.
P(A or B) = P(A) + P(B).
Probability = Number of favorable outcomes/Total number of outcomes
P(A) = 1/5 = 0.3
P(B) = 1/3 = 0.33
P(A) + P(B) = 1/5 +1/3
= 0.533
Probability = 0.533.
Therefore, the probability that either event will occur is 0.533.
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If you are trying to determine which company has higher salaries, which measure of center should you use?
A table titled, Salaries of Current Employees, listing 6 salaries for 2 companies. Company A salaries are: 45,000, 55,000, 53,000, 51,000, 49,000, and 42,000. Company B salaries are: 54,000, 39,000, 51,000, 52,000, 44,000, and 48,000.
mean median mode
To determine which company has higher salaries, you can use the mean, median, or mode as measures of center. Let's calculate each of these measures for the given data:
Company A salaries: 45,000, 55,000, 53,000, 51,000, 49,000, and 42,000.
Mean (Average):
To calculate the mean, sum up all the salaries and divide by the total number of salaries.
Mean of Company A salaries = (45,000 + 55,000 + 53,000 + 51,000 + 49,000 + 42,000) / 6 = 295,000 / 6 = 49,167
Median:
To find the median, you arrange the salaries in ascending order and find the middle value. If there is an even number of values, you take the average of the two middle values.
Arranging the Company A salaries in ascending order: 42,000, 45,000, 49,000, 51,000, 53,000, 55,000
Median of Company A salaries = (49,000 + 51,000) / 2 = 50,000
Mode:
The mode represents the value(s) that appear most frequently in the dataset.
In Company A salaries, all the values occur only once, so there is no mode.
Now let's calculate the same measures for Company B salaries:
Company B salaries: 54,000, 39,000, 51,000, 52,000, 44,000, and 48,000.
Mean of Company B salaries = (54,000 + 39,000 + 51,000 + 52,000 + 44,000 + 48,000) / 6 = 288,000 / 6 = 48,000
Arranging the Company B salaries in ascending order: 39,000, 44,000, 48,000, 51,000, 52,000, 54,000
Median of Company B salaries = (48,000 + 51,000) / 2 = 49,500
Mode of Company B salaries = There are no repeating values, so there is no mode.
To summarize:
- Mean of Company A salaries: $49,167
- Median of Company A salaries: $50,000
- Mode of Company A salaries: No mode
- Mean of Company B salaries: $48,000
- Median of Company B salaries: $49,500
- Mode of Company B salaries: No mode
Based on these measures of center, we can see that the mean and median salaries of Company A are slightly higher than those of Company B. However, since there is no mode in either dataset, we cannot consider the mode as a determining factor in this case.
Out of a pool of 26 men and 29 women what is the probability that 6 men and 6 women will be selected?
Let's evaluate the probability based on the given information.
The number of ways to choose 6 men from 26 can be calculated as:
C(26, 6) = 26! / (6! * (26-6)!) = 26! / (6! * 20!) = 230,230.
The number of ways to choose 6 women from 29 can be calculated as:
C(29, 6) = 29! / (6! * (29-6)!) = 29! / (6! * 23!) = 177,100.
The total number of possible outcomes is the combination of selecting 6 men and 6 women from the given pool of 26 men and 29 women:
Total outcomes = C(26, 6) * C(29, 6) = 230,230 * 177,100 = 40,795,315,300.
Therefore, the probability of selecting exactly 6 men and 6 women from the given pool is:
Probability = 1 / Total outcomes = 1 / 40,795,315,300 ≈ 2.45 x 10^-11.
Hence, the probability is approximately 2.45 x 10^-11.
what is 3 to power of 2 -4 to the power of 5=
Step-by-step explanation:
Unclear what you are asking
here is one possibility
3^2 - 4^5
9 - 1024 = - 1015
Here is another possibility
(3^(2-4) )^5 = = (3^(-2))^5 = 3 ^-10 = 1/59049
help it’s past due and i have a test on it tomorrow
Reflect on what led to this situation and identify strategies to prevent it from happening again. This way, you can develop better time management skills and study habits for future assignments and tests.
Stay calm: It's important to remain calm and composed to think clearly and make the best use of your time.
Prioritize: Assess the situation and determine the importance of each task. Focus on completing the task that is past due first.
Communicate: If possible, reach out to your teacher or professor and explain the situation. Apologize for the delay and request an extension or an opportunity to make up the assignment or test.
Allocate time: Allocate dedicated time to work on the overdue task. Break it down into smaller, manageable parts to make it less overwhelming.
Seek help: If you're struggling with the task or need clarification, reach out to classmates, friends, or online resources for assistance. Don't hesitate to ask for help when you need it.
Plan your study time: Make a study schedule for the test that you have tomorrow. Allocate sufficient time for each subject or topic, focusing on areas that require more attention.
Review efficiently: Prioritize the key concepts, formulas, or theories that are likely to be covered in the test. Use active studying techniques such as summarizing, creating flashcards, or teaching the material to someone else.
Take breaks: While it's important to work efficiently, don't forget to take short breaks to rest and recharge. Breaks can help improve focus and prevent burnout.
positive: Maintain a positive mindset and believe in your ability to overcome challenges. Negative thoughts can hinder your productivity and performance.
Learn from the experience: Reflect on what led to this situation and identify strategies to prevent it from happening again. This way, you can develop better time management skills and study habits for future assignments and tests.
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There is a math oriented pizza restaurant that advertises their slices based on arc measurement and pie radius . Recently they had a lunch special for a Personal Pie with a radius of 4 inches . What would the area of a 135 slice of pizza be? Round your answer to the nearest hundredth.
The area of a 135 slice of pizza be,
⇒ 6,782.41 inches²
We have to given that;
Recently they had a lunch special for a Personal Pie with a radius of 4 inches .
Since, WE know that;
Area of circle is,
A = πr²
Where, r is radius of circle
Here, Radius of circle = 4 inches
Hence, Area of pizza is,
⇒ A = 3.14 x 4²
⇒ A = 50.24 inches²
Hence, the area of a 135 slice of pizza be,
⇒ 50.24 × 135
⇒ 6,782.41 inches²
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Use the remainder theorem to find P(2) for P(x)=-x^3+3x^2+6.
Specifically, give the quotient and the remainder for the associated division and the value of P(2).
Answer: The value of P(2) is equal to 26
Step-by-step explanation:
To find P(2) for the given polynomial P(x) = -x^3 + 3x^2 + 6, we can use the remainder theorem by dividing the polynomial by (x - 2).
-x^2 + 5x - 4
__________________________
x - 2 | -x^3 + 3x^2 + 0x + 6
(x^3 - 2x^2)
___________
5x^2 + 0x
(5x^2 - 10x)
____________
10x + 6
(10x - 20)
__________
26
The quotient is -x^2 + 5x - 4, and the remainder is 26.
Therefore, the value of P(2) is equal to the remainder, which is 26.
A square garden has a length of (x+3) ft and a width of (x+2) ft. what is the perimeter and area of the garden?
Answer:
Perimeter:[tex]4x+10[/tex] feet
Area:[tex]x^{2}+5x+6[/tex] feet
Step-by-step explanation:
The perimeter is equal to 2*width +2*length. The width is x+2 and the length is x+3, therefore the perimeter is equal to 2x+4+2x+6 which equals 4x+10.
The area is equal to width*length
(x+3)(x+2)=[tex]x^{2}+2x+3x+6=x^{2}+5x+6[/tex]
Write the equation for a parabola that opens down, translated to the right 3, and translated down 2
Answer:
The equation for a parabola that opens down, translated to the right 3, and translated down 2 can be written in the standard form as:
y = a(x - h)^2 + k
where (h,k) represents the vertex of the parabola. Since the parabola opens down, the value of 'a' must be negative. The vertex is translated to the right 3 and down 2, so we have:
h = -3 and k = -2
Substituting these values in the standard form equation, we get:
y = a(x + 3)^2 - 2
This is the equation for a parabola that opens down, translated to the right 3, and translated down 2.
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Calculate the area of the composite figure
Answer:
Step-by-step explanation:
See image below
Find the volume of the solid generated by rotating the figure around the given axis. If
necessary, use 3.14 for and round your answer to the nearest hundredth.
TU
2
5
The volume of the solid generated by rotating the figure is 62.8 cubic units
How to find the volume of the solid generated by rotating the figureFrom the question, we have the following parameters that can be used in our computation:
The figure
The figure is a rectangle with the following dimensions
Length = 5
Width = 2
When rotated around the given axis, we have a cylinder with the following dimensions
Height = 5
Radius = 2
So, we have
Volume = πr²h
This gives
Volume = 3.14 * 2² * 5
Evaluate
Volume = 62.8
Hence, the volume of the solid generated by rotating the figure is 62.8 cubic units
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Graph the relation shown in the table. Is the relation a function? Why or why not?
x:y
-1:3
-1:2
0:-4
4:2
No; a horizontal line passes through two graphed points.
Yes; no vertical line passes through two graphed points.
No; a vertical line passes through two graphed points.
Yes; no horizontal line passes through two graphed points.
The graph of this relation is four points on the coordinate plane (see attached diagram).
Hence option D is true.
Since we know that,
A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output.
And a function is a special relation,
where each input x has a single output y.
This relation is not a function, because for one x (x=-1),
Here are two different possible y (y=3 or y=2).
If you consider the graph, you can see that there will be vertical line passing through the points (-1,3) and (-1,2).
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Based on the supply graph and the demand graph shown above, what is the price at the point of equilibrium?
Hint: Think about the point where they both meet. For example, if you were to place the graphs on top of each other, what would be the point of intersection?
Type the correct number below without the dollar sign.
Based on the supply graph and demand graph shown above, the price at the point of equilibrium is $ 30.
Demand refers to quantity of a commodity that the consumers are willing to, able to purchase at a given price during a given period of time. Supply refers to quantity of a commodity that the producers are willing to, able to offer for sale at a given price during a given period of time.
Demand curve slopes downward due to inverse relationship between price and quantity demanded whereas supply curve slopes upward due to direct relationship between quantity supplied and price. When both demand and supply curve intersect with each other balance is achieved. Intersection point between demand and supply curve is known as equilibrium.
At this point when prices are equal is known as equilibrium price and when quantiy demanded or supplied are equal it is known as equilibrium quantity. When we combine the given graph. Equilibrium is achieved at a point when price is equal to $ 30 and quantity is equal to 20 units.
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Find the area of a circle with radius,
r
= 46cm.
Give your answer rounded to 3 SF.
Answer:
6650 cm³
Step-by-step explanation:
area of a circle = π r², where r is the radius
area = π (46)²
= 2116 π
= 6650 cm³ to 3 significant figures
Camila has 6 bags of candy. She can pour 1/3 of a bag of candy into a bowl. How many bowls of candy can Camila make in all?
Answer:
18 Bowls of Candy
Step-by-step explanation:
Camila has 6 bags of candy, and she can pour 1/3 of a bag into a bowl. To determine how many bowls of candy she can make in total, we need to divide the total amount of candy by the amount of candy per bowl.
Since Camila can pour 1/3 of a bag into a bowl, it means she can make 3 bowls of candy with a full bag.
Now, we can calculate the total number of bowls of candy:
Total bowls of candy = (Number of bags) x (Bowls per bag)
Total bowls of candy = 6 bags x 3 bowls per bag
Total bowls of candy = 18 bowls
Therefore, Camila can make a total of 18 bowls of candy with her 6 bags of candy.
QUESTION 1 1.1 Convert the following to the appropriate units. 1.1.1 1765m to cm 1.1.2 9.4 km to cm 1.1.3 4.2 tons to grams
Answer:
1. 176,500 centimeters
2. 940,000 centimeters
3.42,000,000 grams
Step-by-step explanation:
Convertion:
1.1.1
1765m to cm
1 meter = 100 centimeters
Therefore, 1765 meters =1765*100 centimeters = 176,500 centimeters
1.1.2
9.4 km to cm
1 kilometer = 1000 meters
First convert it into m.
9.4 kilometers = 9.4*1000 meters = 9400 meters
then in cm
1 meter = 100 centimeters
Therefore, 9400 meters = 9400*100 centimeters = 940,000 centimeters
1.1.3
4.2 tons to grams
1 ton = 1000 kilograms
First convert it into kilogram
1 kilogram = 1000 grams
Therefore, 4.2 tons = 4.2*1000 kilograms = 4200 kilograms
then in grams
4200 kilograms = 4200*1000 grams = 42,000,000 grams
I hope this helps! Let me know if you have any other questions.
Question 3 Consider the input numbers: 3; 5; 7:9; 11 3.1.1 Write all the output numbers if the rule 2x is applied. (2)
The required outputs of the given rule are 6, 10, 14, 18, 22.
Given inputs are 3, 5, 7, 9, 11 and the rule is 2x.
To find the outputs by applying the given rule to the inputs.
Let x be the input, then the output is 2x.
That implies,
x = 3 then output = 2× 3 = 6.
x = 5 then output = 2× 5 = 10.
x = 7 then output = 2× 7 = 14.
x = 9 then output = 2× 9 = 18.
x = 11 then output = 2× 11 = 22.
Hence. the required outputs of the given rule are 6, 10, 14, 18, 22.
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