Answer:
Options (2), (4) and (6)
Step-by-step explanation:
Option (1)
\(8^{-1}=\frac{1}{8}\)
Not equivalent to \(\frac{1}{81}\).
False.
Option (2)
\(9^{-2}=\frac{1}{9^2}\)
\(=\frac{1}{81}\)
True.
Option (3)
\(\frac{9^{8}}{9^{4}}=9^{(8-4)}\)
\(=9^{4}\)
= 6561
False.
Option (4)
\(\frac{9^8}{9^{10}}=9^{8-10}\)
\(=9^{-2}\)
\(=\frac{1}{81}\)
True.
Option (5)
\(9^{-6}9^{3}\) = \(9^{-6+3}\)
= \(9^{-3}\)
= \(\frac{1}{9^3}\)
= \(\frac{1}{729}\)
False
Option (6)
\(9^{5}9^{-7}=9^{(5-7)}}\)
\(=9^{-2}\)
\(=\frac{1}{9^2}\)
\(=\frac{1}{81}\)
True.
Therefore, Options (2), (4) and (6) are the correct options.
Applying the negative exponent rule of power, the expressions that are equivalent to the given expression, 1/81, are: B, D, and F.
What is the Negative Exponent Rule of Power?The negative exponent rule states that: \(a^{-n} = \frac{1}{a^n}\).
Thus, given the expression, 1/81, it can be rewritten or simplified as follows:
1/81 = \(81^{-1} = 9^{-2}\) = \(\frac{9^8}{9^{10}}\) = \(9^5 \times 9^{-7}\)
The expressions that will be equivalent to 1/81 can be expressed, based on the negative exponent rule of power, as:
\(9^{-2}, \frac{9^8}{9^{10}} , 9^5 \times 9^{-7}\) (option B, D, and F).
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Write an equation in standard form for the line that passes through the given points.
(−4, 9), (2,−9)
Answer:
3x + y = -3
Step-by-step explanation:
(-4, 9), (2, -9)
(x₁, y₁) (x₂, y₂)
y₂ - y₁ -9 - 9 -18 -18
m = ----------- = ----------- = ---------- = ------- = -3
x₂ - x₁ 2 - (-4) 2 + 4 6
y - y₁ = m(x - x₁)
y - 9 = -3(x - (-4)
y - 9 = -3(x + 4)
y - 9 = -3x - 12
+9 +9
---------------------
y = -3x - 3
Standard Form:
-3x + y = -3
I hope this helps!
Rob collects data about how many customers enter and leave a store every hour. He records a positive number for additional customers entering the store each hour and a negative number for customers leaving the store each hour. Drag and drop the correct choices into the boxes to complete the answers to the questions.
1) 3:00 to 4:00
The absolute value of the number of people leaving is greater than the absolute value of the number of people entering.2) 103
From 1:00 to 2:00, a total of 14 more people entered, meaning there were 99 people.From 2:00 to 3:00, a total of 8 more people entered, meaning there were 107 people.From 3:00 to 4:00, a total of 4 people left, meaning there were 103 people.The required solution is 4:00 to 5:00 and 87 customers.
It is required to fill in the blanks.
What is arithmetic?The arithmetic refers to working with numbers by doing addition, subtraction, multiplication, and division. Fractions, decimals, percentages, fractions, square root, exponents, and other arithmetic operations are used to achieve mathematical simplifications.
Given:
According to question , Initially, there were 75 customers.
From 1:00 to 2:00, a total of 30 more people entered, meaning there were
75 + 30 - 12
= 93 people.
From 2:00 to 3:00, a total of 14 more people entered, meaning there were
93 + 14 - 8
= 99 people.
From 3:00 to 4:00, a total of 18 people entered, meaning there were
99 + 18 - 30
= 87 people.
4:00 to 5:00 : If the store does not accept any more customers except those who are already inside then, all 87 must leave between 4:00 to 5:00 in order to left from the store by 5:00.
Therefore, the required solution is 4:00 to 5:00 and 87 customers.
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Simplify the algebraic expression -30y+(-15y)+70
Answer:
\(-45y + 70\)
Step-by-step explanation:
Step 1: Combine like terms
\(-30y + (-15y) + 70\)
\(-30y - 15y + 70\)
\(-45y + 70\)
Answer: \(-45y + 70\)
-30y+(-15y)+70 is the same as
-30y-15y+70
Combine like terms-45y+70
That's the ans.hope helpful ~
Consider the functions below. f(x)=8x^2+x+3, g(x)=4x-1, h(x)=3x+6. Which of the following statements is true?
A.
As x approaches infinity, the value of g(x) eventually exceeds the values of both f(x) and h(x).
B.
Over the interval [3, 5], the average rate of change of g and h is more than the average rate of change of f.
C.
Over the interval [0, 2], the average rate of change of f and h is less than the average rate of change of g.
D.
As x approaches infinity, the values of g(x) and h(x) eventually exceed the value of f(x).
The functions f(x)=8x^2+x+3, g(x)=4x-1, h(x)=3x+6 C.Over the interval [0, 2], the average rate of change of f and h is less than the average rate of change of g is true.
What is increasing function?
⇒ The function is said to be increasing if the y value increases as the x value increase over a given range
What is average rate of change?
⇒An average rate of change function is a process that calculates the amount of change in one item divided by the corresponding amount of change in another
As x approaches infinity the value of f(x) eventually exceeds the value of both g(x) and h(x)
And it is true for the interval [0,2]
The faster the growth rate higher the average rate of change
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Answer:
C.
Over the interval [0, 2], the average rate of change of f and h is less than the average rate of change of g.
Dr. Rasp selects four students at random from the students in STAT 301. What is the probability that at least two of the students were born on the same day of the week? [HINT: it’s easier to begin with the probability that they all four were born on different days. Why?]
The answer is 0.650, but I don`t understand how this number was gotten
The probability that at least two of the students were born on the same day of the week is 0.6501.
What is Probability?Probability refers to potential. A random event's occurrence is the subject of this area of mathematics.
The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events.
The degree to which something is likely to happen is basically what probability means.
Given:
Total students = 4
So, Total number of possible outcomes = 7 x 7 x 7 x 7
Number of ways of choosing 4 from 7 = C(7, 4) = 35
So, number of outcomes in which no day is repeated
= 4! x 35 = 840
P(girls all born on different days) = 840/(2401) = 0.3498
P(at least two born on same day) = 1 - 0.3498
= 0.6501
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You model your investment account using the formula y = 20000(1.035)x where x represents the
number of years and y represents the account balance after x years. What is the growth rate of your
investment?
Answer:
Step-by-step explanation:
The growth rate of the investment is represented by the constant multiplier in the exponential term of the formula y = 20000(1.035)x. In this case, the constant multiplier is 1.035, which represents the annual growth rate of the investment account.
To calculate the growth rate as a percentage, we can subtract 1 from the constant multiplier, and then multiply the result by 100.
So, the growth rate of the investment is:
1.035 - 1 = 0.035
0.035 * 100 = 3.5%
Therefore, the growth rate of the investment is 3.5%.
You are conducting research for a popular blog to find out the proportion of readers who are satisfied with the site's newly designed navigation. You want to make sure that you increase your chances for capturing the true proportion of readers who are satisfied, but the margin of error is too large.
Which of the following would you do?
A. Use a larger confidence level, but choose a smaller margin of error
B. To increase your confidence, you must be willing to accept a smaller margin of error
C. To get a smaller margin of error, you must be willing to accept lower confidence
D. All of the above
Answer: Option(C) is correct option
Explanation:
Margin of error is the factor that occurs in survey for determining random sampling error. It indicates about confidence interval (CI) through describing difference occurring in poll result and actual population value.If there is high margin of error, then confidence is low because poll result will not reflect the actual population result collected through survey.
According to the question, researcher would try to get small margin of error so that lower confidence interval can be acceptable because large confidence interval(CI) will indicate more margin of error.
Other options are incorrect because small margin of error cannot produce increment in confidence or usage of large confidence.Large confidence interval will result in large margin of error. Thus, the correct option is option(c).
The EXACT value of 2 divided (0.01)2
Answer:
Find the exact value using trigonometric identities.
100
Step-by-step explanation:
The exact value of 2 divided by (0.01) 2 is 20000.
We are given that;
2 divided (0.01)2
Now,
To find the exact value of 2 divided by (0.01) 2, we can use the following steps:
Rewrite 0.01 as a fraction: 0.01 = 1/100
Square both the numerator and the denominator: (0.01) 2 = (1/100) 2 = 1/10000
Flip the fraction and multiply by 2: 2 / (0.01) 2 = 2 x 10000/1 = 20000
Therefore, by algebra the answer will be 20000.
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HOW MANY GALLONS OF GASOLINE THAT IS 9% ETHANOL MUST BE ADDED TO 2,000 GALLONS OF GASOLINE WITH NO ETHANOL TO GET A MIXTURE THAT IS 7% ETHANOL.
The required 7,000 gallons of gasoline which are 9% ethanol must be added to 2,000 gallons of gasoline with no ethanol to get a mixture that is 7% ethanol.
What is the Ratio?The ratio can be defined as the proportion of the fraction of one quantity towards others. e.g.- water in milk.
Here,
To solve the problem, we can use the following formula:
(amount of ethanol in the final mixture) / (total amount of gasoline in the final mixture) = 7%
To find the amount of ethanol in the 2,000 gallons of gasoline with no ethanol:
ethanol in 2,000 gallons of gasoline with no ethanol = 0 × 2,000 = 0 gallons
Then, find the amount of ethanol in the final mixture:
ethanol in final mixture = (0.09x + 0 * 2,000) / (x + 2,000)
Notice that we use 0 gallons for the ethanol in the 2,000 gallons of gasoline with no ethanol, since it contains no ethanol.
Ethanol in the final mixture / total amount of gasoline in the final mixture = 7%
(0.09x + 0) / (x + 2,000) = 0.07
0.09x + 0 = 0.07(x + 2,000)
0.09x = 0.07x + 140
0.02x = 140
x = 7,000
Therefore, 7,000 gallons of gasoline which is 9% ethanol must be added to 2,000 gallons of gasoline with no ethanol to get a mixture that is 7% ethanol.
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\(\frac{2}{2+\sqrt{7} }\)
Answer:
\(\huge\boxed{\sf \frac{2\sqrt{7}-4 }{3}}\)
Step-by-step explanation:
This is a rationalizing denominator question.
Given expression:\(= \displaystyle \frac{2}{2+\sqrt{7} } \\\\Multiply \ and \ divide \ by \ conjugate \ 2 - \sqrt{7} \\\\= \frac{2}{2+\sqrt{7} } \times \frac{2-\sqrt{7} }{2-\sqrt{7} } \\\\\underline{\sf Using \ formula:}(a+b)(a-b)=a^2-b^2\\\\= \frac{2(2-\sqrt{7}) }{(2)^2-(\sqrt{7})^2 } \\\\= \frac{4-2\sqrt{7} }{4-7} \\\\= \frac{4-2\sqrt{7} }{-3} \\\\= \frac{-(4-2\sqrt{7}) }{3} \\\\= \frac{2\sqrt{7}-4 }{3} \\\\\rule[225]{225}{2}\)
El Servicio Sismológico del Instituto Geofísico del Perú detectó un sismo cuya coordenada de localización es, 5 km al este y 3 km al norte, del centro de la ciudad de Arequipa. Si el sismo tuvo un radio de expansión de 4 km a la redonda. ¿Cuál es la ecuación de la circunferencia del área afectada? ¿La onda expansiva del sismo afectó a la ciudad de Arequipa? Justifique su respuesta
Answer:
ajoskne kksiebndk hbsmoirvx abpdhr redaodona been be beef be nedid jso jd jdmt odoen
I’ll give a brainliest to whoever answers this ::::Find the equation of the line through the point A(4,6) and with a slope m=3
hi
line equation is : mx+p
so if a line goes throught A(4;6) and with m = 3 so you have 3 *(4) +P = 6
so : 12 +P = 6
P = 6-12
P = -6
line equation is : 3m -6
If you put two straight angles together, you get an angle that is 360°. You can think of this
angle as turning all the way around so that you are facing the same direction as when you
started the turn.
380
Answer:
what is your question?
Step-by-step explanation:
what is the inverse f(x)=1/5x
Answer:
F = 1/5
Step-by-step explanation:
if you take away 25 from a number you will be left with two and halftimes 30. what is the number?
Question 6 of 19 Step 1 of 1 Suppose that quiz scores in a beginning statistics class have a mean of 7.1 with a standard deviation of 0.4. Using Chebyshev's Theorem, state the range in which at least 75% of the data will reside. Please do not round your answers. Answer(How to Enter) 4 Points to
Suppose that quiz scores in a beginning statistics class have a mean of 7.1 with a standard deviation of 0.4, the range in which at least 75% of the data will reside is from 6.3 to 7.9.
Chebyshev's Theorem is a statistical tool that provides a range for how much data is likely to fall within a certain number of standard deviations from the mean.
Specifically, it tells us that, for any set of data, no matter how it is distributed, at least 1 - (1/k^2) of the data will fall within k standard deviations from the mean, where k is any positive number greater than 1.
In this case, we want to find the range in which at least 75% of the data will reside. We can use Chebyshev's Theorem to determine the minimum value of k that will give us this range. We know that at least 75% of the data should fall within two standard deviations from the mean, so we can set k = 2.
Using Chebyshev's Theorem, we can say that at least 1 - (1/2^2) = 75% of the data will fall within 2 standard deviations from the mean. The standard deviation is 0.4, so two standard deviations would be 2 * 0.4 = 0.8.
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If f(x) = -x³ + x² + x, find f(-3).
Answer:
33
Step-by-step explanation:
Substitute f(-3) in the problem and you'll get f(-3) = -x³ + x² + x.
Substitute the given value into the function and evaluate.
Answer:
33.
Step-by-step explanation:
f(x) = -x³ + x² + x.
f(-3) = -(-3)³ + (-3)² + (-3)
= -(-27) + (9) - 3
= 27 + 9 - 3
= 36 - 3
= 33.
Hope this helps!
? Question
Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar.
What is a value of √7 inches to the nearest hundredth?
The value of √7 to the nearest hundredth is 2.65.
What is Square root?
A square root of a number x is a number y such that y² = x; in other words, a number y whose square is x.
Here, given number;
y = \(\sqrt{7}\)
y = 2.64575....
y = 2.65
Thus, the value of √7 to the nearest hundredth is 2.65.
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To maintain essential electricity, a gasoline generator at a Puerto Rico hospital uses 3 gallons of gasoline per hour. a) How many gallons of gas are needed to fuel the generator for 1 full day? 72 2 points b) How much co2 will be produced by running the generator for 1 full day? 2 points
The mass of the CO2 produced IS 630 Kg
What is gasoline?Gasoline is a kind of fuel that is composed mostly of isooctane. In most engines, gasoline is widely used hence the demand for the product is high. We know that the combustion of an alkane (of which gasoline is one) would produce carbon dioxide and water according to a balanced reaction equation.
The balanced reaction equation for the combustion of gasoline is shown in the image attached to this answer.
Since a Puerto Rico hospital uses 3 gallons of gasoline per hour, and there are 24 hours in a day, it the follows that 72 gallons of gasoline are used per day. This 72 gallons is the equivalent of 272.88 L
Now;
Given that the density of gasoline = 748.9 g/L
Mass of gasoline = 748.9 g/L * 272.88 L = 204 Kg
Number of moles of gasoline = 204 * 10^3/114 g/mol = 1789.5 moles
If 2 moles of gasoline produces 16 moles of CO2
1789.5 moles produces 1789.5 moles * 16 moles/2 moles = 14316 moles
Mass of CO2 = 14316 moles * 44 g/mol = 630 Kg
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f(x)= −2x^2 + 8x − 10
{Find } f(-4)
Answer:
simply you have to substitute (-4) for all the (x) terms-2x²+8x -10-2(-4)²+8×(-4)-10-2(16) - 32 -10-32 -32 - 10-74
What are the outputs of the function below?
-6, -3, 1, 5
-6, -3, 4, 6
-8, 2, 4, 6
-8, 2, 1, 5
Answer:
\(5 { \times 54}^{2} \)
Anna is buying school supplies. She spends $3 for a pack of 4 fancy pencils and $2 for a pencil case. Then, she buys a notebook for $2. She has a $10 bill. How much change will she receive?
Answer:
3 not including tax, if it needs to include tax i dont know
Write each quadratic equation in standard form.
With solution please, thank you!
Answer:
\( \frac{6}{x} = 7 - 2x \\ 6 = 7x - 2 {x}^{2} \\ 2{x}^{2} - 7x + 6 = 0\)
Solve the following
8903=e
\(\huge\text{Hey there!}\)
\(\huge\textbf{Equation:}\)
\(\mathsf{8,903 = e^{5x}}}\)
\(\huge\textbf{Simplify:}\)
\(\mathsf{8,903 = e^{5x}}}\)
\(\mathsf{e^{5x} = 8,903}}\)
\(\huge\textbf{Solve for the exponent:}\)
\(\large\textsf{We get: }\downarrow\\\\\mathsf{2.718282^{5x}=8903}\)
\(\huge\textbf{Take the logarithm from both sides:}\)
\(\mathsf{log(2.718282^{5x}) = log(8,903x)}\)
\(\large\textsf{We get:}\\\\\mathsf{5x \times log(2.718282)=log(8903)}\)
\(\huge\textbf{Simplify it:}\)
\(\mathsf{5x = \dfrac{log(8903)}{log(2.718282)}}\)
\(\large\textsf{We get: }\\\\\mathsf{5x = 9.094143}\)
\(\huge\textbf{Divide 5 to both sides:}\)
\(\mathsf{\dfrac{5x}{5} = \dfrac{9.094143}{5}}\)
\(\huge\textbf{Simplify it:}\)
\(\mathsf{x= \dfrac{9.094143}{5}}\)
\(\mathsf{x = 1.818829}\)
\(\mathsf{x \approx 2}\)
\(\huge\textbf{Therefore, your answer should be:}\)
\(\huge\boxed{\mathsf{x =}\frak{\ 1.818829}}\huge\checkmark\)
\(\large\textbf{Or if you're estimating your answer}\downarrow\)
\(\huge\boxed{\mathsf{x \approx }\frak{\ 2}}\huge\checkmark\)
\(\huge\text{Good luck on your assignment \& enjoy your day!}\)
~\(\frak{Amphitrite1040:)}\)
Select all the properties of a right triangle.
A. Has a right angle
B. Has one obtuse angle
C. Has parallel lines
D. Has perpendicular lines
E. Has three acute angles
no links!! help please!!
Answer:
A. has a right angle
thats one
Answer:
I think it is A and D. Not 100% sure tho.
0.3 - 0.04 = i need it ASAP
Fred and George share some money. If Fred gets 3/11 of the money,in what ratio did they share it?
Answer:
Step-by-step explanation:
If they had $11: Fred gets $3, George gets $8.
So the ratio is: 3:8
Which fraction is equivalent to -6 -(-9)/8
Answer:
2/8 = 1/4 = 0.25
Step-by-step explanation:
Consider the function f(x)=x−5ln(x), 1/5≤x≤10.
The absolute maximum value is =
and this occurs at x equals =
The absolute minimum value is =
and this occurs at x equals =
f(x) = x - 5 ln(x)
Get the derivative:
f'(x) = 1 - 5/x
Find the critical points:
• f'(x) = 1 - 5/x = 0 -> 5/x = 1 -> x = 5
• f'(x) is undefined for x = 0, but that's outside the domain of f(x)
Get the second derivative:
f''(x) = 5/x ^2
Check the sign of the second derivative at the critical point x = 5:
f'' (5) = 5/5^2 = 5/25 = 1/5 > 0
Since the second derivative is positive at this point, this means x = 5 is a local minimum.
Check the value of f(x) at the critical point as well as the endpoints of the given domain:
f (5) = 5 - 5 ln(5) ≈ -3.407
f (1/5) = 1/5 - 5 ln(1/5) ≈ 1.809
f (10) = 10 - 5 ln(10) ≈ -1.513
So we have
• absolute maximum = 1/5 - 5 ln(1/5) at x = 1/5
• absolute minimum = 5 - 5 ln(5) at x = 5
The absolute maximum value is f(5)=5−5ln(5), and this occurs at x equals 5
The absolute minimum value is f(1/5)= 1/5−5ln(1/5), and this occurs at x equals 1/5
Given the function f(x)=x−5ln(x),
We are to find the absolute minimum and maximum value of the function
At the turning point f'(x) = x - 5ln(x)
f'(x) = 1 - 5/x
0 = 1 - 5/x
-5/x = -1
-x = -5
x = 5
Find the second derivative of the function;
f''(x) = -5/x²
Substitute the value of x = 5 into the second derivative function to have:
f''(5) = -5/5² = 1/5
Since f''(5) = 1/5 < 0, this is the local maximum and the point x = 5 is the absolute minimum
The absolute maximum value is f(5)=5−5ln(5), and this occurs at x equals 5
The absolute minimum value is f(1/5)= 1/5−5ln(1/5), and this occurs at x equals 1/5
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See the attached photo
-2+14+17 ??
like in row 2, its 12-10=2 and 20-18=2
row 3, 10+14=24 and 18+14+32
row 4, 24+17=41 and 32+17=49
might be wrong so sorry if its wrong
good luck !
also -2+14+17=29
12+29=41
20+29=49
all connects... might work