How do you Simplify a4 x a5
The simplification of the given expression by the law of indices will be a⁹.
What is the law of indices?Index (indices) in Maths is the power or exponent which is raised to a number or a variable.
In other words, the mathematics of power or exponent of any number is called indices.
Another example could be 7² = 7³/7 here we divide to obtain power 2.
As per the given expression,
a⁴ × a⁵
By the law of indices that [tex]a^{m} \times a^{n} = a^{m+n}[/tex].
a⁴ × a⁵ = a⁽⁴ ⁺ ⁵⁾ = a⁹
Hence "The simplification of the given expression by the law of indices will be a⁹".
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I Put 45 Points!!
Use what you have learned from this chapter to make a model boat out of a 10-cm square piece of foil. Test your model boat in a tank of water to see how many pennies it can support before sinking. Compare the performance of your boat with those of your classmates. Suggest several design improvements based on your results. Respond to at least one other students posting giving suggestions on how the model of their boat or yours could be improved to increase buoyancy.
The ratio of girls to boys in a classroom is 3:5. Kevin says there must be 8 students in the classroom. Which explains whether Kevin is correct?
Kevin is incorrect because 3:5 may be a simplified ratio.
Kevin is incorrect because 3:5 may be a simplified ratio. Option C is correct.
Given that,
The ratio of girls to boys in a classroom is 3:5. Kevin says there must be 8 students in the classroom. Which explains whether Kevin is correct is to be determined,
The ratio can be defined as the proportion of the fraction of one quantity towards others. e.g.- water in milk.
Here, the ratio of girls to boys is 3:5, Which implies there are 3 girls over 5 boys in the number, This is the simplified ratio of the girls to boys of the students in the class. So, Kevin says there must be 8 students in the classroom which is right, but Kevin does not explain the proportion in his statement,
Thus, Kevin is incorrect because 3:5 may be a simplified ratio. Option C is correct.
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Which quadratic regression equation best fits the data set?
Answer:
D. [tex]y=1.87x^2-5.16x+10.54[/tex]
Step-by-step explanation:
The data set is given by,
x y
1 5.9
2 8.9
3 13.4
4 20.1
5 30.1
6 45.1
7 67.7
Using the regression calculator, we see that,
The quadratic equation that best fits the data is [tex]y=1.87x^2-5.16x+10.54[/tex] as shown below.Thus, option D is correct.
A company is selecting students for interviews at the career fair. The number of students selected from university A is given by f(x) = 4x + 5, where x represents the number of days of the fair. The number of students selected from university B is given by g(x) = 2x + 8. Which function best describes the total number of students selected at the career fair?
a. h(x) = (4x + 5)(2x + 8)
b. h(x) = 2x - 3
c. h(x) = -2x + 3
d. h(x) = 6x + 13
Answer:
B, for plato students that is
Step-by-step explanation:
Which expression can be used to find the number of liters in 15 quarts?
Answer:15 quarts/1 x 0.95 liter/1 quart
Step-by-step explanation:
The histogram represents the distributions of rain amounts in two cities. Which best explains how the histogram is useful for comparing the shapes of the data sets? It is easier to visually compare the means of the data. It is easier to visually compare the standard deviations of the data. It is easier to visually compare the medians of the data. It is easier to visually compare symmetry and skew of the data.
Answer:
It is easier to visually compare symmetry and skew of the data.
Step-by-step explanation:
Given that the histogram represents the distributions of rain amounts in two cities.
Histogram enables us to have a visual idea easily understandable about the pattern of the distribution.
The important points are whether the distribution is symmetrical or right/left skewed.
Mean, median, std deviations cannot be found easily by justing seeing the histograms.
Hence correct answer is
It is easier to visually compare symmetry and skew of the data.
Solve the following automotive-services problem.
Resistance = 0.1 ohm
Current = 60 amps
Voltage = ______ ?
A. 0.6
B. 6 60
C. 600
Arthur buys a zero coupon bond with a face value of $5000 for $4000. The bond has five years until it matures. How much would Arthur earn if he holds this bond to maturity?
Can someone help me with this problem?
On Monday Mrs. Wise bought 3 lbs of apples at $4 per lb. On Tuesday, apples were on sale for 20% off so she bought another 5 lbs. How much money did Mrs. Wise spend on apples on Tuesday?
Pencils sells for 98 cents per dozen. how much more per pencils
Look at the picture below // 99 points // PLEASEE HELPP
Find the value of a in the parallelogram.
Which expression makes the equation true for all values of X? 16 X -16 =4(?)
Round 6541 to the nearest thousand
To round 6541 to the nearest thousand, identify the place value and look at the hundreds place. The answer is 6000.
Rounding 6541 to the nearest thousand:
Identify the place value you are rounding to, which is the nearest thousand.
Look at the hundreds place since we are rounding to the nearest thousand. In 6541, the hundreds digits is 5, so the thousands digit remains 6, and all digits after that become 0. Therefore, 6541 rounded to the nearest thousand is 6000.
A local magazine is offering a $2,500 grand prize to one lucky winner. $1,000 will be paid on the day of the drawing. the remaining $1,500 will be paid in three annual payments of $500 each, starting one year after the drawing. how much would this prize be worth to you if you can earn 9 percent on your money?
How measuring angles could be useful in thge real world?
answer asap, Ill give brainliest, show work
Steve can paint a room three times as fast as Billy. When they work together, Steve and Billy can paint a large room in 4 hours. How many hours would it take Billy to paint it by himself?
1. What is the constant of variation for the relationship f(x) = 40x?
2. Which equation is the direct variation equation if f(x) varies directly with x and f(x) = -12 when x=6
Solve x2 + 10x = 24 by completing the square. Which is the solution set of the equation?
Answer:
-12 and 2
Step-by-step explanation:
[tex]x^2+10x=24\\[/tex]
[tex]x^2+2*5*x=24[/tex]
[tex]x^2+2*5*x+5^2-5^2=24[/tex]
[tex](x^2+2*5*x+5^2)-5^2=24[/tex]
Using the identity
[tex]a^2+2*a*b+b^2 = (a+b)^2[/tex]
we get
[tex](x+5)^2-5^2=24[/tex]
[tex](x+5)^2-25=24\\[/tex]
[tex](x+5)^2=24+25\\(x+5)^2=49\\(x+5)=+7 \\or (x+5)=-7\\[/tex]
Solving both of them we get
x=-12 or x=2
3500 calories for 6 servings of pie how many calories per serving
What is 59.69 written in expanded form
Final answer:
The expanded form of 59.69 is 50 + 9 + 0.6 + 0.09.
Explanation:
59.69 written in expanded form can be expressed as:
50 + 9 + 0.6 + 0.09
5 * 10 + 9 * 1 + 0.6 * 0.1 + 0.09 * 0.01
5 * 10 + 9 * 1 + 6 * 0.1 + 9 * 0.01
50 + 9 + 0.6 + 0.09
Therefore, the expanded form of 59.69 is 50 + 9 + 0.6 + 0.09.
Final answer:
The number 59.69 written in expanded form is 50 + 9 + 0.6 + 0.09. Each term represents a digit according to its place value, with tens, ones, tenths, and hundredths places accounted for respectively.
Explanation:
Writing the number 59.69 in expanded form means expressing each digit according to its place value. Expanded form is a way of writing numbers to see the math value of individual digits. The number 59.69 would be broken down as follows:
50 + 9 + 0.6 + 0.09
Each term represents a digit in the number: '5' is in the tens place, so it is represented as 50; '9' is in the ones place, so it is simply 9; '6' is in the tenths place, so it is represented as 0.6; '9' is in the hundredths place, so it is represented as 0.09.
When performing calculations, particularly in subjects such as chemistry, scientific notation is often used to express large or tiny numbers efficiently. For example, to enter a number in scientific notation into a calculator, you must know the correct process, which can vary based on the calculator model. Consulting the instructor or the calculator's manual is advisable if there are any doubts.
Furthermore, working with scientific notation involves understanding how to properly write and interpret the exponents, which indicate how many places the decimal point has been moved.
Using the information given, select the statement that can deduce the line segments to be parallel. If there are none, then select none. please help asap
Answer:
option C
Step-by-step explanation:
In the figure attached, the given quadrilateral will be parallelogram if the given angles ∠7 = ∠3 and ∠8 = ∠4 ( alternate angles ) or ∠1 = ∠5 and ∠2 = ∠6 ( alternate angle )
But the given angles are ∠7 and ∠8 which represent a big angle A when combined.
Therefore, option C none will be the answer.
laissez faire is the term used to describe a capitalist economy without any regulations
Information about Laissez-faire's economy is given.
What is a Laissez-faire economy?Laissez-faire is a free-market, capitalist economic theory that rejects government interference. The French Physiocrats, who lived in the 18th century, created the laissez-faire ideology. According to proponents of laissez-faire, government involvement in industry and markets hinders economic progress.
Laissez-Faire capitalism allowed businesses to pursue just their financial goals without having to worry about restrictions from the state or taxes. Naturally, this might induce unfavorable externalities and knowledge asymmetries that could enable producers to act badly and get away with it. Laissez-Faire proponents contend that since the market would eliminate such undesirable actors, extensive and expensive regulation is not necessary. However, in practice, negative actors might carry on their operations for a very long time. Without government testing and regulatory oversight to safeguard consumers, for instance, it could not be known if a vitamin manufacturer is putting sawdust in place of herb powder in their capsules.
Therefore, In real world the laissez-faire is a capitalist economy have regulations.
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Write and solve an equation to answer the question. "18 is 32% of what number w"
The value of 32% of 18 is equal to 56.25.
The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that 18 is 32% of the number w. The value of w will be calculated as:-
18 x 32/100 = w
Solve the above equation by mathematical operations to get the value of w,
18 x 32/100 = w
w = 56.25
Therefore, the value of w will be 56.25.
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Suppose that an individual has a body fat percentage of 18.9% and weighs 149 pounds. How many pounds of her weight is made up of fat? Round your answer to the nearest tenth.
Fifty students in the third-grade class listed their hair and eye colors in the table below: Brown hair Blonde hair Total Blue eyes 14 8 22 Brown eyes 16 12 28 30 20 50 Are the events "blonde hair" and "blue eyes" independent?
A) Yes, P(blonde hair) • P(blue eyes) = P(blonde hair ∩ blue eyes)
B) Yes, P(blonde hair) • P(blue eyes) ≠ P(blonde hair ∩ blue eyes)
C) No, P(blonde hair) • P(blue eyes) = P(blonde hair ∩ blue eyes)
D) No, P(blonde hair) • P(blue eyes) ≠ P(blonde hair ∩ blue eyes)
Answer: the answer is D
Step-by-step explanation:
What’s one way we can check our answer to 2x10=20
Find m<A. Round to the nearest tenth.
A.
49.5°
B.
53.1°
C.
63.4°
D.
66.4°