Answers
Answer:
Last option
Step-by-step explanation:
Writing \(4^{-2}\) is the same as (to remove a negative power we put it under 1) :
1/4²
\(8^{0}\) = 1 (anything to the power of 0 is 1)
\(5^{6}\) can stay as it is
Now we have 1/4² × 1 × \(5^{6}\) =
\(5^{6}\) / 4²
Which is the last option
Hope this helped and have a good day
Answer:
\(\frac{5^6}{4^2}\)Step-by-step explanation:
First, break the question down into individual parts:
For \(4^{-2}\):
Use the exponent law that states \(a^{-m}=\frac{1}{a^m}\)
For this problem, let a=4 and m=-2
So,
\(4^{-2}=\frac{1}{4^2}\)
For \(8^0\):
Use the exponent rule that states \(a^0=1\)
For this problem, let a=8
So,
\(8^0=1\)
Since the prompt states the solution must have positive exponents and \(5^6\) already has positive exponents, it can be assumed \(5^6\) does not need to be manipulated.
Next, insert the derived values above into the original problem:
\(4^{-2}*8^0*5^6\\(\frac{1}{4^2})(1)(5^6)\\\frac{5^6}{4^2}\)
Related Questions
The temperature cooled by 4° on the first day of the year together on the 1st 2 days of the year the temperature heated up 7°
Answers
The temperature on the second day is 11°.
How to calculate the temperature?Expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both.
Temperature is a unit used to express hotness or coldness on any of a number of scales, including Fahrenheit and Celsius. The direction that heat energy will spontaneously flow depending on temperature.
Let the temperature on the second day be x.
Based on the information, temperature cooled by 4° on the first day of the year together on the 1st 2 days of the year the temperature heated up.
-4 + x = 7
Collect the like terms
x = 7 + 4..
x = 11
The temperature is 11°
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The temperature cooled by 4° on the first day of the year together on the 1st 2 days of the year the temperature heated up 7°. What is the Temperature on tue second day?
Find log0.81 rounded to the nearest tenth.
Answers
The value of the logarithm of 0.81 for logarithm properties is equal to - 0.1.
How to determine the value of a logarithm
Herein we must use logarithm properties to simplify a given logarithm and solve the resulting expression. The properties to be used in this question are described below:
㏒ (a / b) = ㏒ a - ㏒ b
㏒ aᵇ = b · ㏒ a
First, write the logarithmic equation:
㏒ 0.81
㏒ 81 / 100
Second, use the logarithmic property for a division:
㏒ 81 - ㏒ 100
Third, use the logarithmic property for a power:
㏒ 3⁴ - ㏒ 10²
4 · ㏒ 3 - 2 · ㏒ 10
4 · ㏒ 3 - 2
4 · 0.477 - 2
- 0.092
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List the terms of the polynomial. Give the coefficient of the second term. -4y5 + 6x4 +9w³ - 4w - 1 Separate terms using commas. Enter your answer as an expression. Example: 3x^2+1, x/5, (a+b)/c . Make sure your variables match those in the question. Terms Coefficient
Answers
The coefficient of the second term, 6x⁴, is 6.
The terms of the polynomial are:
-4y⁵, 6x⁴, 9w³, -4w, -1
The coefficient of the second term, which is 6x⁴, we look at the number in front of the variable term.
The coefficient is 6.
Therefore, the list of terms is:
-4y⁵, 6x⁴, 9w³, -4w, -1
Each term represents a separate component of the polynomial, where the variable is raised to a certain power and multiplied by its coefficient.
The coefficients indicate the scalar value by which each term is multiplied.
The polynomial's terms are -4y5, 6x4, 9w3, -4w, and -1.
Looking at the number in front of the variable term, we can determine the second term's coefficient, which is 6x4.
There is a 6 coefficient.
As a result, the terms are as follows: -4y5, 6x4, 9w3, -4w, and -1.
Each term represents a different part of the polynomial, where the variable is multiplied by its coefficient and raised to a given power.
The scalar value by which each phrase is multiplied is shown by the coefficients.
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The following information was obtained from matched samples taken from two populations. Assume the population of differences is normally distributed. Individual Method 1 Method 2 1 7 5 2 5 9 3 6 8 4 7 7 5 5 6 The point estimate for the difference between the means of the two populations (Method 1 - Method 2) is:_______a. 0. b. 2. c. -2. d. -1
Answers
Answer:
Step-by-step explanation:
Given the data:
Individual Method 1 Method 2 1 7 5 2 5 9 3 6 8 4 7 7 5 5 6
The point estimate for the difference between the means is the difference between the mean of method one and the mean of method 2
2(x+4)+(x+1)=6(2x) solve for x
Answers
Step-by-step explanation:
\({:}\longrightarrow\)\(\sf 2 (x+4)+(x+1)=6 (2x)\)
\({:}\longrightarrow\)\(\sf 2x+8+(x+1)=12x \)
\({:}\longrightarrow\)\(\sf 2x+8+x+1=12x \)
\({:}\longrightarrow\)\(\sf 2x+x+8+1=12x \)
\({:}\longrightarrow\)\(\sf 3x+9=12x \)
\({:}\longrightarrow\)\(\sf 12x=3x+9 \)
\({:}\longrightarrow\)\(\sf 12x-3x=9 \)
\({:}\longrightarrow\)\(\sf 9x=9 \)
\({:}\longrightarrow\)\(\sf x={\dfrac {9}{9}}\)
\({:}\longrightarrow\)\(\sf x=1 \)
Which is the better buy?
68-inch roll of waxed paper for $2.72
8-foot roll of waxed paper for $4.80
Answers
Answer:
68-inch roll of waxed paper for $2.72
Step-by-step explanation:
68-inch roll of waxed paper for $2.72
2.72 / 68 = $0.04 per inch
8-foot roll of waxed paper for $4.80
8 foot = 96 inches
4.80 / 96 = $0.05 per inch
So, 68-inch roll of waxed paper for $2.72 is a better buy.
Cameron throws a football across the field trip the ball is in the air for 75 seconds and travels 3.5 meters per second.how far did the football travel.
Answers
Is AB congruent to CB?
Answers
Answer:
yes
Step-by-step explanation:
they are congruent
transformed to create the graph of Y3x?
How is the graph of the parent function
O It is horizontally stretched by a factor of 3 and reflected over the y-axis.
It is translated 3 units down and reflected over the x-axis
It is horizontally compressed by a factor of 3 and reflected over the x-axis
It is translated 3 units down and reflected over the y-axis.
Answers
Answer:
The graph of the parent function y = 2^x can be transformed to create the graph of y = 2^(3x) by horizontally compressing by a factor of 3. Therefore, the correct answer is C.
Consider a student loan of $17,500 at a fixed APR of 6% for 15 years.
a) calculate the monthly payment
b) determine the total amount paid over over the term of the loan.
c) of the total amount paid, what percentage is paid toward the principal and what percentage is paid for the interest.
Answers
Answer:
A. $147.67
B. $26,581.49
C. Principal: 65.8352%
C. Interest: 34.1647%
The values:
a) PMT = $147.67.
b) $26580.6
c) Of the total amount paid, 65.84 percentage is paid toward the principal and 34.16 percentage is paid for the interest.
What is a loan calculation formula?The formula:
PV = PMT/i[1 - {1/(1+i)ⁿ]
PV denotes the loan sum.
PMT stands for "monthly payment," I for "interest rate" (interest rate % divided by 12), and "n" for the number of months (term of the loan in months)
Given:
Consider a student loan of $17,500 at a fixed APR of 6% for 15 years.
PV is the loan amount = 17500
PMT is the monthly payment .
i is the interest rate per month in decimal form (interest rate percentage divided by 12)
i = 0.06/12 = 0.005
n is the number of months (term of the loan in months)
n = 180 months.
The monthly payment,
PMT = PV i(1+i)ⁿ/{(1+i)ⁿ-1}
PMT = 17500(0.005)(1.005)⁴⁸/{(1.005)⁴⁸-1}
PMT = $147.67.
The total amount paid over the term of the loan,
= 147.67 x 180 = $26580.6
Of the total amount paid, 65.84 percentage is paid toward the principal and 34.16 percentage is paid for the interest.
Therefore, all the required values are given above.
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A club is choosing 2 members to serve on a committee. The club has
nominated 3 women and 3 men. Based on chance alone, what is the
probability no women are chosen to be on the committee?
Answers
Answer: The probability that no women are chosen to be in the committee is 2/5 or 0.40.
Step-by-step explanation:
We have two positions, and we have 6 options for those positions, 3 are men, and 3 are women.
If we want to see the probability where no women are chosen, then this means that in the first selection a man is chosen.
If all the 6 nominees have the same probability of being chosen, then the probability that in the first selection a man is chosen is equal to the number of men divided the total number of nominees, this is:
p1 = 3/6 = 1/2.
Now the same happens for the second selection, but now we have 5 total nominees and 2 are men, so the probability now is:
p2 = 2/5
And the joint probability will be the product of the individual probabilities, then we have:
P = p1*p2 = (1/2)*(2/5) = 2/5.
The probability that no women are chosen to be in the committee is 2/5 or 0.40.
The probability that no woman is chosen to be on the committee is 0.40.
GivenA club is choosing 2 members to serve on a committee.
The club has nominated 3 women and 3 men.
The number of ways to select two persons from 6 will be:
\(\rm = ^6C_2\)
Therefore,
The probability that no woman is chosen to be on the committee is;
\(= \dfrac{1}{2} \times \dfrac{2}{5}\\\\= \dfrac{1}{5}\\\\=0.40\)
Hence, the probability that no woman is chosen to be on the committee is 0.40.
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What’s the correct answer answer asap for brainlist
Answers
Answer:
your answer is B
Step-by-step explanation:
Germany, Austria-Hungary, Bulgaria, and the Ottoman Empire
show how 4 x 3/4
can be solved using multiplication and division.
Answers
Answer:
3
Step-by-step explanation:
4/1 x 3/4
12/4=3
Twice the sum of a number and 7 is equal to three times the difference of the number and 8. Find the number.
Answers
Answer:
the number is 10.
Step-by-step explanation:
2(x + 7) = 3(x - 8)
2x + 14 = 3x - 24
2x = 3x -10
x = 10
In each blank below a single digit is inserted such that the following six three-digit numbers, in this order, form an arithmetic sequence: 1_ _, _ _ 9, 2 _ 2, _ 6 _, 2 _ _, _ 3 _What is the value of the next number in the sequence?
Answers
The series appears to be 166, 199, 232, 265, 298, 331
With examples, define sequence?
A list of numbers in a certain order is known as a sequence. A term is the name given to each number in a sequence.
In a series, each term has a place (first, second, third and so on). Take the sequence 5, 15, 25, 35, as an example. Each number is referred to as a word in the sequence.
The last number of the common difference must end in 3
And this must be a 2 digit number
So....the first number must end in 6
The the 4th number must be 265
So..... the 5th number must end in 8
And the last digit of the last term must end in 1 [ and begin with 3 ]
Putting all this together we have that
265 + 2d = 331
2d = 66 ⇒ d = 33
So the first term must be 265 - 3 (66) = 166
the series appears to be 166, 199, 232, 265, 298, 331
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1) Which is the slope in the following linear equation?
y= 7x + 3
A. 3
B. 11
C. 7
D. 4
Answers
Answer:
C. 7
General Formulas and Concepts:
Algebra I
Slope-Intercept Form: y = mx + b
m - slope b - y-interceptStep-by-step explanation:
Step 1: Define
y = 7x + 3
Step 2: Break Function
Identify Parts
Slope m = 7
y-intercept b = 3
What is the minimum unit cost of C(x)=0.7^2-210x+27,464?
Answers
What is the median of the following Systolic Blood Pressure in mmHg: 121, 110, 114, 100 160, 130 130?
Answers
Answer:
121
Step-by-step explanation:
firstly you arrange the numbers in ascending order the number in the middle is considered to be the median
Write in slope intercept form: slope= 7, y intercept =3
Answers
where m = slope and b = y-intercept
y = 7x + 3
\( \rm\int_{0}^{2021} \frac{ \sqrt{x + \sqrt{x + \sqrt{x + \sqrt{x} + \cdots } } } }{1 + \sqrt{x - \sqrt{x - \sqrt{x - \sqrt{x - \cdots} } } } } dx \\ \)
Answers
We have the identity
\((a + b)^2 = a^2 + 2ab + b^2 = a^2 + ab + b (a + b) \\\\ ~~~~ \implies a + b = \sqrt{a^2 + ab + b (a + b)} \\\\ ~~~~ \implies a + b = \sqrt{a^2 + ab + b \sqrt{a^2 + ab + b \sqrt{a^2 + ab + b \sqrt{\cdots}}}}\)
assuming \(a+b\ge0\).
For the numerator, let \(b=1\), so \(a\ge-1\), which means
\(a^2 + a = x \implies a = \dfrac{-1 + \sqrt{1 + 4x}}2\)
and so
\(\sqrt{x + \sqrt{x + \sqrt{x + \sqrt{\cdots}}}} = \dfrac{-1 + \sqrt{1 + 4x}}2 + 1 = \dfrac{1 + \sqrt{1 + 4x}}2\)
For the denominator, let \(b=-1\) so that \(a\ge1\). Now
\(a^2 - a = x \implies a = \dfrac{1 + \sqrt{1 + 4x}}2\)
so that
\(\sqrt{x - \sqrt{x - \sqrt{x - \sqrt{\cdots}}}} = \dfrac{1 + \sqrt{1 + 4x}}2 - 1 = \dfrac{-1 + \sqrt{1 + 4x}}2\)
So, in the integral we can simplify and evaluate it to
\(\displaystyle \int_0^{2021} \frac{\sqrt{x + \sqrt{x + \sqrt{x + \sqrt{\cdots}}}}}{1 + \sqrt{x - \sqrt{x - \sqrt{x - \sqrt{\cdots}}}}} \, dx \\\\ ~~~~~~~~ = \int_0^{2021} \frac{\frac{1 + \sqrt{1 + 4x}}2}{1 - \frac{1 - \sqrt{1+4x}}2} \, dx \\\\ ~~~~~~~~ = \int_0^{2021} \frac{1 + \sqrt{1 + 4x}}{1 + \sqrt{1 + 4x}} \, dx \\\\ ~~~~~~~~ = \int_0^{2021} dx = \boxed{2021}\)
what is 1/5 x 5 1/3? help please
Answers
Answer:
1 1/15
Step-by-step explanation:
(I think)
And I am not a very good explainer
(sorry)
2. How many radians are in 27"?
Answers
The answer is 0.471 radians.
FORMULA:
Just do 27° × π/180 = 0.4712rad but then cut off the two.
!!!!! Due today !!!!!!!
Answers
Answers:
5)
a.Highest- 96
Lowest-52
b.74
c. 70-80
d. 13
e. 7
6)
a. 89%
b. 51%
c. In the morning(89%)
(GIVING BRAINLIYEST)
7. what is the volume of these 2 objects
Answers
(3 x 6 x 7) + (1 x 2 x 7) = 126 + 14 = 140
4. 216 in^3
(4 x 4 x 9) + (3 x 4 x 6) = 144 + 72 = 216
figure #1
smaller part
4x7x2= 56m
larger part
4x3x7= 84m
84+56= 140m³
figure #2
smaller part
2x4x3= 24m
larger part
4x4x12= 192m
192+24= 216in³
will mark brainleist pls help
Answers
Answer:
x = 31°
Step-by-step explanation:
the sum of the 3 angles in a triangle = 180° , that is
x + 54° + 95° = 180°
x + 149° = 180° ( subtract 149° from both sides )
x = 31°
The maximum and minimum values of a quadratic function are called as_______of the function.
Answers
PLEASE HELP! I’m struggling with each part any help will be amazing
Answers
Answer:
slope: -5/2
y-intercept: (0, 2)
Linear function: y = -5/2x + 2
Step-by-step explanation:
Given points (-2, 7) and (2, -3):
Use these points to solve for the slope of the line using the formula:
m = (y2 - y1)/(x2 - x1)
Let (x1, y1) = (-2, 7)
(x2, y2) = (2, -3)
Substitute these values into the equation:
m = (y2 - y1)/(x2 - x1)
m = (-3 - 7) / [2 - (-2)]
m = -10/ (2 + 2)
m = -10/4 = -5/2
Therefore, the slope of the line in reduced form is m = -5/2.
The y-intercept is the y-coordinate of the point (0, b) where the graph of the linear equation crosses the y-axis of the Cartesian grid. The y-intercept is also the value of y when x = 0.
To solve for the y-intercept, use one of the given points (2, -3) and the slope (m = -5/2), and substitute their values into the slope-intercept form:
y = mx + b
-3 = -5/2(2) + b
-3 = -5 + b
Add 5 to both sides to solve for the y-intercept, b:
-3 + 5 = -5 + 5 + b
2 = b
Given the value of b = 2, it means that the y-intercept is (0, 2).
Therefore, given the slope of -5/2, and the y-intercept, b = 2:
The linear equation in slope-intercept form is: y = -5/2x + 2
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Brooklyn is going to invest in an account paying an interest rate of 3.5% compounded continuously. How much would Brooklyn need to invest, to the nearest ten dollars, for the value of the account to reach $64o in 9 years?
Answers
Brooklyn needs to invest $432.43, rounded to the nearest ten dollars.
To determine how much Brooklyn needs to invest in an account that pays a continuously compounded interest rate, we can use the formula:
A = \(Pe^(^r^t^)\)
where A is the future value of the account, P is the principal investment, e is the mathematical constant approximately equal to 2.71828, r is the interest rate, and t is the time in years.
In this case, we want the future value of the account to be $640, the interest rate is 3.5% (or 0.035 as a decimal), and the time is 9 years. We can substitute these values into the formula and solve for P:
640 = \(Pe^(^0^.^0^3^5^*^9^)\)
640 = Pe^0.315
P =\(640/e^0^.^3^1^5\)
P = 432.43
Therefore, to have a future value of $640 in 9 years with a continuously compounded interest rate of 3.5%.
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6x²-7x=20 solve the following quadratic equation
Answers
Answer:
x = -4/3 and x = 5/2.
Step-by-step explanation:
6x² - 7x = 20
6x² - 7x - 20 = 0
To solve this, we can use the quadratic formula to solve this.
[please ignore the A-hat; that is a bug]
\(\frac{-b±\sqrt{b^2 - 4ac} }{2a}\)
In this case, a = 6, b = -7, and c = -20.
\(\frac{-(-7)±\sqrt{(-7)^2 - 4 * 6 * (-20)} }{2(6)}\)
= \(\frac{7±\sqrt{49 + 80 * 6} }{12}\)
= \(\frac{7±\sqrt{49 + 480} }{12}\)
= \(\frac{7±\sqrt{529} }{12}\)
= \(\frac{7±23 }{12}\)
\(\frac{7 - 23 }{12}\) = \(\frac{-16 }{12}\) = -8 / 6 = -4 / 3
\(\frac{7 + 23 }{12}\) = \(\frac{30}{12}\) = 15 / 6 = 5 / 2
So, x = -4/3 and x = 5/2.
Hope this helps!
Answer:
\(x1 = - \frac{4}{3} \)\(x2 = \frac{5}{2} \)Step-by-step explanation:
\(6 {x}^{2} - 7x = 20\)
Move constant to the left and change its sign
\( {6x}^{2} - 7x - 20 = 0\)
Write -7x as a difference
\(6 {x}^{2} + 8x - 15x - 20 = 0\)
Factor out 2x from the expression
\(2x(3x + 4) - 15x - 20 = 0\)
Factor out -5 from the expression
\(2x(3x + 4) - 5(3x + 4) = 0\)
Factor out 3x + 4 from the expression
\((3x + 4)(2x - 5) = 0\)
When the product of factors equals 0 , at least one factor is 0
\(3x + 4 = 0\)
\(2x - 5 = 0\)
Solve the equation for X1
\(3x + 4 = 0\)
Move constant to right side and change its sign
\( 3x = 0 - 4\)
Calculate the difference
\(3x = - 4\)
Divide both sides of the equation by 3
\( \frac{3x}{3} = \frac{ - 4}{3} \)
Calculate
\(x = - \frac{4}{3} \)
Again,
Solve for x2
\(2x - 5 = 0\)
Move constant to right side and change its sign
\(2x = 0 + 5\)
Calculate the sum
\(2x = 5\)
Divide both sides of the equation by 2
\( \frac{2x}{2} = \frac{5}{2} \)
Calculate
\(x = \frac{5}{2} \)
\(x1 = - \frac{4}{3} \)
\(x2 = \frac{5}{2} \)
Hope this helps...
Best regards!!
Which graph represents an exponential function?
Answers
Answer:
A simple exponential function to graph is y=2x . Notice that the graph has the x -axis as an asymptote on the left, and increases very fast on the right. Changing the base changes the shape of the graph. Replacing x with −x reflects the graph across the y -axis; replacing y with −y reflects it across the x -axis.