Answers
[tex] = \sqrt{25 \times 2 \times y^2 \times y \times x^{14} \times x} [/tex]
[tex] = 5|x^7y|\sqrt{2xy} [/tex]
Related Questions
simple interest = P × r × t
Joe borrowed $900 from Sam for six months. How much will Sam earn if he charges Joe a simple interest rate of 4 percent?
Answers
Answer:
$18.
Step-by-step explanation:
We have been given that Joe borrowed $900 from Sam for six months. The interest rate charged by Sam is 4%.
We will use Simple interest formula to solve our given problem.
[tex]I=PrT[/tex], where,
[tex]I=\text{Simple interest}[/tex],
[tex]P=\text{Principal amount}[/tex],
[tex]r=\text{Interest rate in decimal form}[/tex],
[tex]T=\text{Time in years}[/tex].
Let us convert our given rate in decimal form.
[tex]4\%=\frac{4}{100}=0.04[/tex]
12 months = 1 year.
1 month = 1/12 year.
6 months = 6/12 year = 1/2 year = 0.5 year.
Upon substituting our given values in simple interest formula we will get,
[tex]I=900*0.04*0.5[/tex]
[tex]I=900*0.02[/tex]
[tex]I=18[/tex]
Therefore, Sam will earn $18 if he charge Joe a simple interest rate of 4 percent.
Explain how to find the degree of a polynomial.
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Answer:
The Degree of a Polynomial is the largest of the degrees of the individual terms. Add the degrees of the variables of each term to decide what is the Degree of the Polynomial. Degree of term 1 is 2 (1+1= 2), Degree of term 2 is 6 (2+4 = 6), Degree of term 3 is 7 (5+2 = 7) 7 is the Degree of the Polynomial.
The amplitude of y = -3sin(x) is _____.
Answers
Amplitude: A = 3
For this case what you can do are two methods to find the amplitude.
Method 1:
Graph the function to see the zero-peak behavior of the function.
Method 2:
A = absolute value (-3)
A = 3
Note:
Using method 1 we see that the zero-peak amplitude is 3.
Answer:
A = 3
Bryan is paid $32 per hour and works 8 hours per day. He receives one paid day off for each 16 days that he works. What is his true hourly wage?
A. $40 per hour
B. $34 per hour
C. $32 per hour
D. $48 per hour
Answers
$40 per hour is his true hourly wage, option A is correct.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Bryan works 8 hours per day, so he works 16 x 8 = 128 hours during the 16-day period.
His pay for the 16-day period is 16 x 8 x $32 = $5,120.
He receives one paid day off for each 16 days that he works, so he gets 16/1 = 16 paid days off for every 16 days worked.
Therefore, he actually works for 16 - 16/1 = 0 days during those 16 days.
His true hourly wage is his total pay divided by the actual number of hours he works:
True hourly wage = $5,120 / 128 hours = $40 per hour
Hence, $40 per hour is his true hourly wage, option A is correct.
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John wants to build a corral next to his barn. He has 300 feet of fencing to enclose three sides of his rectangular yard.
a. What is the largest area that can be enclosed?
b. What dimensions will result in the largest yard?
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x = width
300 - 2x = long
The area will be:
A = (x) * (300 - 2x)
A = 300x - 2x²
We look for the maximum area, for this, we derive:
A '= 300 - 4x
We match zero:
0 = 300 - 4x
x = 300/4 = 75
Therefore, the width is:
x = 75 feet
The length is:
300 - 2x = 300 - 2 (75) = 300-150
150 feet
Answer:
Part A:
The maximum area will be:
A = (150) * (75) = 11250 square feet
Part B:
The dimensions are:
Length = 150 feet
width = 75 feet
Arnold's company reimburses his expenses on food, lodging, and conveyance during business trips. The company pays $40 a day for food and lodging and $0.50 for each mile traveled. Arnold drove 400 miles and was reimbursed $2600. Part A: Create an equation that will determine the number of days x on the trip (3 points) Part B: Solve this equation justifying each step with an algebraic property of equality. (6 points) Part C: How many days did Arnold spend on this trip? (1 points)
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Part A. We now know that the total cost of the miles the company have to pay to Arnold is $200. We also know the company pays him $40 a day for food and lodging. So let [tex]x[/tex] represent the number of days of Arnold's business trip:
[tex]y=40x+200[/tex]
where
[tex]y[/tex] is the amount the company will reimburse Arnold after [tex]x[/tex] days.
[tex]x[/tex] is the number of days.
Part B. We know that the amount the company will reimburse Arnold is $2600, so [tex]y=2600[/tex]. Lets replace that value in our equation and solve for [tex]x[/tex] to find the number of days:
[tex]y=40x+200[/tex]
[tex]2600=40x+200[/tex]
The first thing we are going to do to solve our equation is subtract 200 to both sides using the subtraction property of equality:
[tex]2600-200=40x+200-200[/tex]
[tex]2400=40x[/tex]
Next, we are going to divide both sides of the equation by 40, using the division property of equality, to find the value of [tex]x[/tex]:
[tex] \frac{2400}{40} = \frac{40x}{40} [/tex]
[tex]60=x[/tex]
Finally, we can use the reflexive property of equality to get:
[tex]x=60[/tex]
Part C. We can conclude that Arnold spend 60 days in his business trip.
Mrs. McDonnell is making 25 paper cones to fill with popcorn for her daughter's birthday party. 4 inches 7 inches Find the volume of one paper cone if the diameter is 4 inches and the height is 7 inches. Round your answer to the nearest cubic inch.
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The formula for the volume of a cone is V=(1/3)πr²h. Substituting our information we have:
V=(1/3)(3.14)(4/2)²(7)
We divide the diameter by 2 because the radius is half of the diameter. This gives us:
V=1/3(3.14)(28) = 29.306 ≈ 29in³
The volume of one paper cone if the diameter is 4 inches and the height, is 7 inches is equal to 29in³.
We have given that,
Mrs. McDonnell is making 25 paper cones to fill with popcorn for her daughter's birthday party.
The volume of one cone would be 29 in³.
What is the formula for the volume of a cone?The formula for the volume of a cone is V=(1/3)πr²h.
Substituting our information we have:
V=(1/3)(3.14)(4/2)²(7)
We divide the diameter by 2 because the radius is half of the diameter. This gives us:
V=1/3(3.14)(28)
V= 29.306
V≈ 29in³
Therefore the volume of one paper cone if the diameter is 4 inches and the height, is 7 inches is equal to 29in³.
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List the first five terms of each of the following geometric sequence.
A_1 = 10; r = 5
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Find the volume of a cone?
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Hope this helps!
1. Suppose that the amount of algae in a pond triples every 2 hours. If the pond initially contains 80 pounds of algae, how much algae will be in the pond after 8 hours? (1 point)
a) 720
b) 1,280
c) 6,480
d) 320
Answers
It triples every 2 hours
2 hours later = 3(80)
4 hours later = 3(3(80)))
6 hours later = 3(3(3(80)))
8 hours later = 3(3(3(3(3(80)))))
8 hours later = [tex] 3^{4} [/tex] x 80
8 hours later = 6480 (Answer C)
OR
We find the number of 2 hours period in that 8 hours
8 ÷ 2 = 4
It starts at 80 pounds
It tripes every 2 hours
Total algae = [tex] 3^{4} [/tex] x 80 = 6480 (Answer C)
In the figure, TU is tangent to the circle at point U. Use the figure to answer the questions.
(a) Describe the relationship among the lengths of the segments formed by the secant, RT, and the tangent segment, TU. You may used words and/or an equation.
(b) Suppose RT = 9 in. and ST = 4 in. Is it possible to find the length of TU? If so, show how to find the length. If not, explain why not.
Thanks in advance. I appreciate the help. I'm still not that good at questions like this one.
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[tex]rs \times st = tu {}^{2} [/tex]
(b)
yes it is possible the formula is in part a, but we're given just the side rt and st, not rs, but not to worry we can get rs with subtraction. we can do 9-4=5 for rs. now we can plug in our values to find tu
[tex]5 \times 4 = tu {}^{2} [/tex]
simplify with algebra
[tex] \sqrt{20} = tu[/tex]
FINAL ANSWER
[tex]2 \sqrt{5} = tu[/tex]
The lengths of segments in the circle are determined by the tangent-secant theorem. Given RT = 9 inches and ST = 4 inches, we can use this theorem to find that TU will be approximately 8.06 inches.
Explanation:In this complex geometry problem involving circles and tangents, there are several relationships at play. You're looking at a circle that has a secant, RT, and a tangent, TU, creating several segments within the figure.
(a) According to the tangent-secant theorem, the squared length of the tangent segment is equal to the difference in the squared lengths of the entire secant and its external part. This can be expressed mathematically as TU² = RT² - ST².
(b) We can use this theorem with the given lengths for RT and ST to find the length of TU. Plugging in, we get TU² = 9² - 4² = 65. The length of TU is the square root of this, which is approximately 8.06 inches.
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Which rigid transformation does NOT result in a reversed orientation of the original image? Justify your answer
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Hope that helped :)
D) T(x,y) = (x, y - 2); The transformation slides the original image a given distance in a given direction. Is the CORRECT answer
What Is The Value Of n So That The Expression
X² + 12 x + n Is A Perfect Square Trinomial ?
( 1 Point )
A . 36
B . 36
C . 72
D . 144,
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Given is the expression, x² + 12x + n
It says to find value of 'n' that converts it into a Perfect Square Trinomial.
A perfect square trinomial is a quadratic expression which has a single root with multiplicity 2. i.e. it is of the form :- x² + 2bx + b² = (x + b)²
On comparing it with the given expression, we get :-
So 2b = 12 and n = b²
b = 6
and so b² = 6² = 36.
⇒ n = 36
Hence, x² + 12x + 36 = (x + 6)² i.e. n = 36 is the final answer.
A cell phone plan charges $15$15 per month for 300300 text messages. The plan charges $0.08$0.08 for each additional text message. You use 6060 additional texts this month. What is your bill for the month?
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The company charges 15 dollars per month for first 300 text messages and thereafter 0.08 dollars for any additional text message.
It says that we used additional 60 text messages (after fair usage of first 300 messages in the plan).
Our bill for this month would be sum of charges for 300 messages and charges for additional 60 messages.
Total bill = 15 dollars + 60x0.08 dollars = (15 + 4.80) dollars.
Total bill = 19.80 dollars.
Hence, our bill this month would be 19.80 dollars.
how is the graph of y=-1/2(5)^x-3 translated from the graph of y=1/2(5)^x
Answers
The transformation of [tex]y = -\frac12(5)^{x-3[/tex] to [tex]y = \frac12(5)^{x[/tex] is reflection across the x-axis followed by a shift to the left by 3 units
Describing the transformation of f(x) to g(x).
From the question, we have the following parameters that can be used in our computation:
[tex]y = -\frac12(5)^{x-3[/tex]
[tex]y = \frac12(5)^{x[/tex]
Rewrite them as
[tex]f(x) = -\frac12(5)^{x-3[/tex]
[tex]g(x) = \frac12(5)^{x[/tex]
From the above, we have that
f(x) is first reflected across the x-axis
This is represented by the loss of negative factor in g(x)
Then f(x) is shifted left by 3 units
This is represented by the loss of -3 in g(x)
Hence, the transformation of f(x) to g(x) is reflection across the x-axis followed by a shift to the left by 3 units
Help Please
Tamara needs to buy motor oil to fill the 3 empty cylindrical barrels at her oil service center each barrel is 7 ft deep and has a radius of 4 ft what is the volume of oil needed use 3.14 for the radius.
Answers
Answer:
1055.04 volume
Step-by-step explanation:
Sam cut a flat wooden board into fourths. He used three of the pieces as backgrounds for posters. He used equal pieces of the leftover board as backgrounds for 5 photos. What fraction of the original board did he use for each photo background? Enter your answer in the boxes.
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If you used 3 of these, you are left with 1/4.
Out of the 1/4 leftover, you create 5 equal-sized pieces.
1/4 divided by 5.
1/4 x 1/5 = 1/20 of the original board for each.
Which of the following represents a physical change to matter?
A. combustion of carbon to form carbon dioxide B. rusting C. melting a stick of butter D. separating hydrogen gas from water,
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the hoop rotates through qan angle of 3/2 pie radian in 1 second how many revolutions does the hoop make in 1 minute
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so, we know it does 3/2 π in 1 second, how many π does it do in 60 seconds(1 minute) ?
[tex]\bf \begin{array}{ccll} radians&seconds\\ \text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\ \frac{3\pi }{2}&1\\\\ r&60 \end{array}\implies \cfrac{\frac{3\pi }{2}}{r}=\cfrac{1}{60}\implies \cfrac{\frac{3\pi }{2}}{\frac{r}{1}}=\cfrac{1}{60}[/tex]
[tex]\bf \cfrac{3\pi }{2}\cdot \cfrac{1}{r}=\cfrac{1}{60}\implies \cfrac{3\pi }{2r}=\cfrac{1}{60}\implies \cfrac{3\pi \cdot 60}{2}=r\implies 90\pi =r\\\\ -------------------------------\\\\ \textit{how many times }2\pi \textit{ goes into }90\pi ?\qquad \cfrac{90\pi }{2\pi }\implies 45[/tex]
Jenna is a professional typist.she can type 22,500 words in 5 hours of typing.in one hour how many words can she type?in one minute how many words can she types?
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If dewayne answered 38 items correctly on a test, and received a score of 76%, How Many items were on the test?
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A bowl of fruit contains 3 apples, 4 bananas, 2 pears and 1 orange.Aminata chooses one piece of fruit at random.What is the probability that she chooses.
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The probability of Aminata choosing a specific type of fruit is calculated by dividing the number of that fruit by the total number of fruits in the bowl. Different fruit types have different probabilities due to their varying quantities.
Explanation:The question asks about the probability of Aminata choosing a specific type of fruit from a bowl containing 3 apples, 4 bananas, 2 pears, and 1 orange. To find the probability of Aminata choosing any one type of fruit, we first need to determine the total number of fruit pieces in the bowl, which is 3 apples + 4 bananas + 2 pears + 1 orange = 10 pieces of fruit.
The probability of selecting any specific type of fruit is then calculated by dividing the number of that fruit type by the total number of pieces.
The probability of choosing an apple is 3/10.The probability of choosing a banana is 4/10 or simplified to 2/5.The probability of choosing a pear is 2/10 or simplified to 1/5.The probability of choosing an orange is 1/10.Each fruit type has a different probability of being chosen based on its quantity in the total mix of fruits.
Please help me out! :)
Answers
if you round it, you get 110.9
Medal to correct answer!!
A game of "Doubles-Doubles" is played with two dice. If a player rolls doubles, the player earns 3 points and gets another roll. If the player rolls doubles again, the player earns 9 more points. How many points should the player lose for not rolling doubles in order to make this a fair game?
3/5
27/35
9/10
1
Answers
The probabilities are the following:
one double= 5/36
two doubles =1/36
no doubles = 1/6
The formula will be,
12/36 + 5[(3-x)/36] - (5)(x/6) = 0
x=27/35
The answer will be 27/35
Step-by-step explanation:Probability is the number of outcomes out of total outcomes present or the extent to which something is likely to happen. In the given problem there are two dices which means there are total 36 outcomes because each dice has 6 sides. So the probability of the given case will be
Probability of getting two doubles on both dice = 1/36
Probability of getting just one double = 5/36
Similarly
Probability of getting no doubles on both dice is = 5/6.
So in order to find the probability we add the products of the probabilities and solve:
12/36 + 5*(3-x)/36 - 5*x/6 = 0
x = 27/35
Which simply means the player should lose 27/35 points for not rolling a double.
HELP!!! Which of the following completes the statements of proof?
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Also:
angle 3=angle 1
angle 3+angle 4 = 180 degrees
angle 1+angle 4 = 180 degrees
Triangle ABC has vertices at A(3, 8) , B(11, 8) , and C(7, 12) . Triangle FGH has vertices at F(8, 4) , G(16, 4) , and H(12, 8) . Which sequence of transformations shows that triangle ABC and triangle FGH are congruent? Select each correct answer. Translate triangle ABC down 4 units, and then translate triangle ABC right 5 units. Translate triangle FGH down 4 units, and then translate triangle FGH left 5 units. Translate triangle FGH up 4 units, and then translate triangle FGH left 5 units. Translate triangle ABC down 4 units, and then translate triangle ABC left 5 units.
Answers
A - (3, 8)
B - (11, 8)
C - (7, 12)
vertices of ΔFGH
F - (8, 4)
G - (16, 4)
H - (12, 8)
after a translation the size nor shape of the triangle changes, every point of the triangle moves the same distance in the same direction.
if we take point A and F
x coordinates of A = 3 and F = 8
the change that has happened can be noted as 'm'
3 + m = 8
m = 5
this means that the point has moved 5 units to the right
y coordinates of A = 8 and F = 4
change that happened is 'n'
8 + n = 4
n = -4
this means that point has moved 4 units downwards
Therefore the correct answer is Translate triangle ABC down 4 units, and then translate triangle ABC right 5 units
This the answer hope it helps!!
The length of a rectangle is 2 ft longer than its width. if the perimeter of the rectangle is 32 ft , find its area.
Answers
Final answer:
To find the area of the rectangle, first solve for the width using the perimeter formula. The width is found to be 7 ft. Then calculate the length as w + 2, which is 9 ft. The area is the product of length and width, resulting in 63 square feet.
Explanation:
To solve this problem, we need to set up equations based on the information given about the rectangle's dimensions and the perimeter.
Step 1: Define Variables
Let w be the width of the rectangle in feet. Consequently, the length l will be w + 2 feet, since the length is 2 feet longer than the width.
Step 2: Perimeter Equation
The perimeter (P) of a rectangle is given by 2(l + w). We can use the perimeter given (32 ft) to create an equation: 2(w + w + 2) = 32.
Step 3: Solve for w
Combine like terms and divide both sides by 2 to find w:
4w + 4 = 32
w = 7 ft.
Step 4: Find l
The length is w + 2, which is 7 ft + 2 ft = 9 ft.
Step 5: Calculate Area
The area of a rectangle is l × w. Therefore, the area is 9 ft × 7 ft = 63 square feet.
Megan predicts she will sell 42 glasses of lemonade this weekend. If Megan actually sold 58 glasses of lemonade, what was Megan's percent error? Round your answer to the nearest tenth of a percent.
Answers
Megan's percent error is approximately 27.6%.
Megan's percent error can be calculated by finding the absolute difference between her predicted value and actual value, dividing that by the actual value, and then multiplying by 100 to get a percentage.
Calculate the absolute difference:
|58 - 42| = 16.
Find the percent error:
(16 / 58) × 100 ≈ 27.6%.
to compute how one currency compared to another you must use the
1. negotiated rate
2.exchange rate
3. agreement rate
or 4.bartered rate
im guessing its the exchange rate right ?,
Answers
The histogram below shows the age distribution of Elizabeth’s grandchildren.
The box-and-whisker plot below shows the same data.
Which of the following best explains why one graph appears skewed and one graph appears symmetric?
A. The intervals on the x-adis of the histogram are too large
B. The interval on the y-axis of the histogram is too small
C. The interval on the x-axis of the histogram is inconsistent
D. The interval in the box-and-whisker plot is too small
Answers
I hope helped`` ^-^
Answer:
Option: C is the correct answer.
C. The interval on the x-axis of the histogram is inconsistent
Step-by-step explanation:
Clearly after looking at the histogram we see that the interval on the x-axis are inconsistent.
Since, the intervals given are:
0-4 ( length of interval is 4)
5-9 ( length of interval is 4)
10-14 ( length of interval is 4)
But the intervals:
(15-19) is missing in the given histogram.
And then a interval of length 4 is given i.e. (20-24)
Hence, option: C is the correct answer.