The power expression 1 / 5⁸ is the simplified form by algebra properties of (5⁻⁴)².
How to simplify a power expression
In this problem we find a power expression that must simplified by means of algebra properties. First, write the entire expression introduced in the statement:
(5⁻⁴)²
Second, use the property for the power of a power:
5⁻⁸
Third, use the property for the power of a power once again:
(5⁸)⁻¹
Fourth, apply the definition of a division:
1 / 5⁸
The simplified form of (5⁻⁴)² is equal to 1 / 5⁸.
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A pool manager mixes 234 gallons of water with 114 gallons of a chemical to get a particular cleaning solution for a swimming pool. Part B If the pool manager follows the cleaning solution recipe and makes a medium batch of the solution using a total of 11 gallons of water, how many total gallons of the cleaning solution are in the medium batch?
A pool manager mixes 2 3/4 gallons of water with 1 1/4 gallons of a chemical to get a particular cleaning solution for a swimming pool.
What is gallons?The gallon is a unit of measurement used for liquids such as gasoline, water, and milk in the United States. If your car’s tank is running on empty, then you better pull over and buy at least a few more gallons of gas.A gallon is equivalent to 4 quarts of liquid or 3.785 liters. The United States is one of the last countries to use this term. Though the gallon has roots in the British Imperial Units measurement system, the United Kingdom and most countries around the world have switched to the newer International System of Units.To learn more about gallons refer to:
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Someone help me with the left one please!
Since no equation of the line, or graph is provided in the question statement, considering the line to be [3x +4y = 12], the y-intercept of the line is 3.
Find the solution ?[3x +4y = 12] and then, determine it's y-intercept.
To solve this question, we can use two methods:
The standard equation of line is (y = mx + c), where, "m" is the slope of the line, and "c" is the y-intercept. Converting [3x +4y = 12] to the form of the standard equation, we get,
3x+4y=12\\or,4y=-3x+12\\or,y=\frac{-3x+12}{4}\\ or,[y=(\frac{-3}{4})x+3]...(i)
Now comparing (i) to the standard equation of line, we can identify that
(c = 3), i.e., y-intercept of the line [3x +4y = 12] is 3.
Another way we can determine the y-intercept of a line is by, substituting (x = 0) and then solving the equation for "y".
Y-Intercept: The y-intercept is the point on a cartesian plane, where a graph crosses the y-axis, i.e., the value of y when (x = 0).
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Jessica’s is making $300 less than four times what she was making when she started working. Let s represent her starting salary. Write an expression showing how much Jessica is making now in terms of her starting salary, s. Show work.
Answer:
4s-$300
Step-by-step explanation:
Two pieces of information given describe Jessica's salary in relation to her starting salary. This information is that she makes nearly four times her starting salary (multiplication) and the exact amount she is short of exactly four times is $300 (subtraction). As with the order of mathematical operations, start with multiplication, then put the subtraction into the expression.
s
4s
4s-$300
This final expression shows how much she is making now in terms of her starting. salary
A satellite encircles Mars at a distance above its surface equal to 3 times the radius of Mars. The acceleration of gravity of the satellite, as compared to the acceleration of gravity on the surface of Mars, is A)Zero B)the same C)1/3 D)1/16
The acceleration of gravity of the satellite, as compared to the acceleration of gravity on the surface of Mars is (D) 1/16.
The term Acceleration defined as the gravity at the surface of Mars is given by the formula
Gₙ = GM/R²
where
M refers mass of Mars
R refers radius of Mars
Here we need to find if we take a point which is at height 3 times the radius of Mars from its surface.
While we take the height 3 times the radius of Mars from its surface.
The it can be written as,
=> Gₙ = GM/(3R + R)²
When we expand it then we get.
=> Gₙ = GM/16R²
Therefore, the resulting gravity on the surface of the mars is 1/16.
So, the option (D) is correct.
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Given a2 = 7 and a5 = −56 of a geometric sequence, what is the recursive equation for the nth term? a an = 2(an − 1), a1 = 3.5 b an = 2(an − 1), a1 = −3.5 c an = −2(an − 1), a1 = 3.5 d an = −2(an − 1), a1 = −3.5
Answer: an=-2(an-1), a1=3.5
Step-by-step explanation: took the quiz and got it right
An = -3.5(-2)ⁿ⁻¹ and -3.5 are the Nth and first terms of the above sequence, respectively.
What is Geometric sequence?Every term in a geometric series is obtained by multiplying the term before it by the same number. Aₙ = a₁ rⁿ⁻¹ is the general phrase for it. The common ratio is denoted by the number r.
Given a₂ = 7 and a₅ = −56 for a geometric sequence.
From the general formula of geometric sequence's nth term
Aₙ = a₁ rⁿ⁻¹
Thus
A₂ = 7 = a₁ r²⁻¹ = a₁ r
A₅ = -56 = a₁ r⁵⁻¹ = a₁ r⁴
comparing both equations
A₂/ A₅ = a₁ r / a₁ r⁴
=> -7/56 = 1/r³
=> r³ = -8
=> r = -2
putting this value of r in equation 1
a₁ = -7/2
Hence, for the nth term of the sequence
Aₙ = -7/2(-2)ⁿ⁻¹
Therefore, the Nth term and the first term of the given sequence are Aₙ = -3.5(-2)ⁿ⁻¹ and -3.5 respectively.
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Graph represents the solution set y>5/-2x+2?
The graph of the linear inequality y > 5 / (-2x + 2) shows a solution of (0, 2.5)
Graph of Linear InequalityThe graph of an inequality in two variables is the set of points that represents all solutions to the inequality. A linear inequality divides the coordinate plane into two halves by a boundary line where one half represents the solutions of the inequality. The boundary line is dashed for > and < and solid for ≤ and ≥.
In the given inequality, y > 5 / (-2x + 2) can be represented on a graph using a graphing calculator.
Kindly find the attached graph below
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How could you organize the weighting and grades information differently so that Oscar's and Reagan's final grades are given by WG?
Answer i just need points
Step-by-step explanation: maybe 90
What is the answer for identifying the slope and Y intercept for this graph ?
in a recent survey 70% of the community favored building a health center in their neighborhood. If 14 citizens are chosen find the probability that 8 of them favor building the health center
The probability of those that favors building the health center is 0.196
What is probability?The probability is the measure of the likelihood of an event to happen. It measures the certainty of the event. The formula for probability is given by; P(E) = Number of Favorable Outcomes/Number of total outcomes.
In a recent survey, 70% of the community favored building a health center in their neighborhood. If 14 citizens are chosen, find the probability that exactly 8 of them favor the building of the health center.
According to the scenario, 70% of the community favoured in building a health centre.
Hence , p=0.7.
In order to find the probability, binomial theorem will be used as follows :
= 0.196
Hence, The probability is 0.196
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Find the 15th term in the following
arithmetic sequence:
22, 19, 16, 13, . . .
Hint: Write a formula to help you.
1st term + common difference (desired term - 1)
22+ [?]([ ]-1)
Enter the number that belongs in the green box.
Enter
Is 5x/4-y/3 = 6 linear or non linear
Answer:
linear
Step-by-step explanation:
To tell if a function is linear, simply look at the exponents of the variables "x" and "y". Both of these exponents will have to be one and only one (1), any other exponent will turn the function into non-linear. Radicals also count as exponents different than one, because they are fractional exponents. Since there are no radicals or exponents written in this equation, we can conclude that all variable exponents are one (1), hence it's a linear equation.
What are the coefficients in the following expression x^2+2x-5xy-y+3y^4
Answer:
1,2,-5,-1,3
Step-by-step explanation:
the coefficients are the numbers before the variables (x and y)
if there is nothing infront of the variable then the coefficient is 1
if there is only a negative sign infront of the variable then the coefficient is -1
A line passes through the point (3,2) and has a slope of 6. Write an equation in slope-intercept form for this line.
Answer: y=6x-16
Step-by-step explanation:
Slope-intercept form is y=mx+b, where m is slope and b is y-intercept.
Since we are given a point and the slope, all we have to do is solve for b.
y=mx+b [plug in point and slope]
2=6(3)+b [multiply]
2=18+b [subtract both sides by 18]
b=-16
With b, we can plug into our equation y=6x-16.
An online streaming service charges a monthly fee as well as a one-time sign-up fee. The cost for this online streaming service is modeled by the following function where m represents the number of months the service is subscribed to and C(m) represents the total cost given that amount of time:
C(m) = 13m + 9
In the above function, what is the slope?
What is the y-intercept?
How do we interpret the slope of this function?
How do we interpret the y-intercept of this function?
The slope of the given line is 13 and the y - intercept of the line is 9.
What is equation of line?
A straight line's general equation is y = mx + c, where m denotes the gradient and y = c denotes the point at which the line crosses the y-axis. On the y-axis, this value c is referred to as the intercept.
Consider, the given equation of line,
C(m) = 13m + 9
We have to find the slope and y - intercept of the given equation.
From the given equation the slope of the equation is 13 and the y - intercept is 9.
Consider, the general equation of line
y = mx + c
where,
m is the slope of line and
c is the y - intercept of the line.
Compare the given equation C(m) = 13m + 9 with, y = mx + c
⇒ m = 13 and c = 9
Hence, the slope of the given line is 13 and the y - intercept of the line is 9.
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10, 12, 11, 13, 14, 12, 13, 14, 13, and 12 find the mean.
The mean of the given data is 12.4
What is mean?The mean can be calculated only for numeric variables, no matter if they are discrete or continuous. It's obtained by simply dividing the sum of all values in a data set by the number of values.
Given that, a data, 10, 12, 11, 13, 14, 12, 13, 14, 13, and 12
Arranging the data in ascending order, 10, 11, 12, 12, 12, 13, 13, 13 14, 14
The sum is = 10+12+11+13+14+12+13+14+13+12 = 124
Total number of data = 10
Mean = sum of the numbers/ total numbers of data
Mean = 124/10
Mean = 12.4
Hence, the required mean is 12.4
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What is the equation, in stanard form, of a parabola that models the values in the table x-3 0 2 f(x) -8 -2 -28
The equation of the parabola is f(x)= 7x²+5x-2 when values of the x are -3,0,2 and the f(x) are -8,-2,-28.
Given that,
The values of the x are -3,0,2 and the f(x) are -8,-2,-28
We have to find the equation of the parabola with the x and f(x) values.
We know that,
The equation of the parabola of the form f(x) = ax²+bx+c
So,
-3a-3b+c=-8 ----->equation(1)
c=-2
2a+2b+c=-28 ------>equation(2)
Substituting c=-2 in equation(1) and equation(2)
-3a-3b-1+8=0
-3a-3b+7=0 ------>equation(3)
2a+2b-2+28=0
2a+2b+26=0 ------>equation(4)
Subtracting 2×equation(3) and 3×equation(4)
b=5
Substituting in equation(1)
a=7
Therefore, The equation of the parabola is f(x)= 7x²+5x-2 when values of the x are -3,0,2 and the f(x) are -8,-2,-28.
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Write the equation of the line that passes through the points (9, -4) and (2, -2).
Put your answer in fully simplified point-slope form, unless it is a vertical or
horizontal line.
Answer:
y +2 = -2/7(x -2)
Step-by-step explanation:
You want the point-slope equation of the line through (9, -4) and (2, -2).
SlopeThe slope is given by ...
m = (y2 -y1)/(x2 -x1)
m = (-2 -(-4))/(2 -9) = 2/-7 = -2/7
Point-slope equationThe point-slope equation of a line with slope m through point (h, k) is ...
y -k = m(x -h)
Using the second point with the found slope, the equation is ...
y +2 = -2/7(x -2)
if an advertisement is placed in 4 different places in vogue magazine and then runs for 5 issues, the number of opportunities to see would be: group of answer choices depends on the gross rating points for vogue. 15 20 10
If an advertisement is placed in 4 different places in vogue magazine and then runs for 5 issues, the number of opportunities to see would be 20
Opportunity to See reveals the typical frequency with which a person has encountered a specific advertising channel.
The OTS is used to assess the success of advertising campaigns along with the Gross Rating Point (GRP) and other information.
The OPS can be calculated using the formula below: The total number of individuals contacted is known as the net reach. The amount of people reached, regardless of the number, is known as the gross reach.
According to the question,
Number of places advertisement is placed = 4
Number of issues = 5
Therefore , Opportunities to see would be = 4 × 5
=> 20
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WILL MARK BRAINLIEST ‼️‼️
MULTIPLE CHOICE‼️
Which equation illustrates the identity property of multiplication?
Answer:
C
Step-by-step explanation:
Anything multiplied by one is itself...its identity
Find x
NOTE: Angles not necessarily drawn to scale.
Answer:
148 degrees
Step-by-step explanation:
b/c a line is 180 degrees and the angle given is 32 so 180- 32= 148
and the line is bisected at point p so it is 148 because of alternate interior angles.
What is the slope of the line?
-3
3
-1
1
By analyzing the given line mathematically, we get the required slope of the line as 3.
What is Slope ?A line's steepness and direction can be expressed as a value called slope. It is frequently represented in variable format by the letter m. Its gradient or rate of change are other names for a line's slope.
The rise over run or slope formula, often known as the vertical change in y divided by the horizontal change in x, To determine the change in y over the change in x, the slope formula requires two points, (x1, y1) and (x2, y2).
As from the Line,
Two points = (1,2), (2,5)
(x1, y1) = (1,2)
(x2,y2) = (2,5)
Using two point we can calculate slope as
= [tex]\frac{y2-y1}{x2-x1}[/tex]
Putting the points in the formula, we get:
[tex]\frac{5-2}{2-1}[/tex]
= 3
Hence, we get the required slope as 3.
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A line has a slope of -9 and includes the points (2, w) and (1, 7). What is the value of w?
Answer:
-2
Step-by-step explanation:
y=-9x+b
7=-9+b b=16
w=-9*2+16
w=-2
Solve the inequality for x.
2(4x+9) ≤5x+3
4)
Michael runs 0.18 miles a minute. How many minutes will it
take Michael to run 4.23 miles?
per from tuua dagoltz of mastill
By using unitary method, it can be calculated that
Michael runs 4.23 miles in 23.5 minutes
What is unitary method?
Unitary method is the process in which the value of single unit can be calculated from the value of multiple unit and the value of multiple unit can be calculated from the value of single unit. Sometimes Value of single unit can be less than the value of multiple unit. For example - The relation between the cost of a commodity and the quantity of the commodity
Sometimes Value of single unit can be more than the value of multiple unit. For example - The relation between the number of men and the number of days taken by those men to do a certain job.
This problem is based on unitary method
Michael runs 0.18 miles a minute.
Michael runs 1 mile in [tex]\frac{1}{0.18}[/tex] minutes
Michael runs 4.23 miles in [tex]\frac{1}{0.18} \times 4.23[/tex] minutes
Michael runs 4.23 miles in 23.5 minutes
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What is 9/12 in simplest form? A 2/3 B 3/4 C 12/16 D 10/13
3/4 is 9/12 in simplest form.
What is 9/12 in simplest form?The simplest form of 9/12 is 3/4.To reduce a fraction to its simplest form, you need to divide the numerator and denominator by the same number until it cannot be divided further.In this case, both 9 and 12 can be divided by 3, which results in the fraction 3/4.To divide a fraction by a number, you need to divide the numerator by the number and divide the denominator by the same number. For example, if you divide 9/12 by 3, you would get 3/4.This is because when you divide 9 by 3, you get 3, and when you divide 12 by 3, you get 4.The other fractions given (2/3, 12/16, and 10/13) are not the simplest form of 9/12 and therefore are not the answer.The simplest form of 9/12 is 3/4.To learn more about simplifying fractions refer to:
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The variation in temperature (in Celsius) of the kinematic viscosity (in m? /s) of some synthetic oil was found to be as follows: T = 10 20 40 60 80 100 120 M = 2.5 X 10-: 5.1 X 10-4 0.95 X 10-4 4.98 X 10-5 2.12 X 10-5 1.05 10-s 5.87 X 10-6 1 We will develop best fit of this data to the exponential function / = exp (~b/T): (a) Use a linear regression analysis to determine the parameters and b Hint: yOu will need to transform the data as preliminary step. See the table in the notes regarding the details of this. Additionally you will need to transform the T data because of the -1/T in the fit function_ (b) Plot the transformed data and linear regression curve on the same graph:
a) Using a linear regression analysis, the parameters a and b can be found by transforming the data as follows:
log(M) = log(a) - b/T
log(M) log(2.5 x 10-4) log(5.1 x 10-4) log(0.95 x 10-4) log(4.98 x 10-5) log(2.12 x 10-5) log(1.05 x 10-5) log(5.87 x 10-6)
T 10 20 40 60 80 100 120
1.3979 0.6989 -0.0041 -1.2998 -2.1245 -2.9594 -3.7697
Using the transformed data, a linear regression analysis can be used to find the parameters a and b.
b) Plotting the transformed data and the linear regression curve on the same graph:
c) Using the same graph to plot the data and the best fit exponential curve:
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The table and grab below shows the distance travel between two different objects which statement is correct about the speed of the two objects
The statement which is correct about the speed of the two objects is both travel at steadily increasing speed.
What is meant by direct relation?A direct relation exists when the two variables rise or fall together. In a straight link, as X rises, Y rises as well. A straight relationship will always have a positive slope on a graph.
What is speed?Speed is the pace at which an object's position changes in any direction. The distance travelled in relation to the time it took to travel that distance is how speed is defined. Since speed simply has a direction and no magnitude, it is a scalar quantity.
The graph shows the direct relation that means with increasing time and distance speed will increase. Moreover, the table also shows direct and increasing relation about the speed of two objects so the statement both travel at steadily increasing speed is correct.
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using the least-squares regression line, calculate the predicted value and residual value for the data point where the non-native grass biomass is equal to 35 and the coastal sage scrub biomass is equal to 20. give your answers precise to three decimal places.
By using the least-squares regression line the equation will be y = 1.518x + 0.305.
Let us find the value of slope and y-intercept that suits the data y = mx + b
And then , we have to find the value of x² ,∑x,∑y,∑x²,∑xy also N
Then, we have to calculate the slope m
m = n∑(xy) - ∑x ∑y / n ∑(x²) - (∑x)²
= 5 X 236 -26 X 41 / 40 - 676
= 249 / 164
= 1.5183
Then , we hace to calculate the intercept b
b = ∑y - m∑x / n
= 41 - 1.5183 X 26 / 5
= 0.3049
After this we have to assemble it in the equation of line
y =mx + b
Therefore ,
y = 1.518x + 0.305
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The proportion of households that own mutual funds but not individual stocks or individual stocks but not mutual funds is a. 40%. b. 60%. c. 80%. d. 100%
The proportion of households that own mutual funds but not individual stocks or individual stocks but not mutual funds is in option (b) 60%.
Proportion: Two ratios are said to be proportional if they express the same relationship.
Given that:
P (households owning mutual funds) = 60% = 0.6
P (households owning individual stocks) = 40% = 0.4
P (households owning both mutual funds and individual stocks) = 20% = 0.2
P (households that own mutual funds but not individual stocks or individual stocks but not mutual funds)
= P(A) only + P(B) only = [P(A) - P(A∩B)] + [P(B) - P(A∩B)]
= 0.4 + 0.2 = 0.6 = 60%.
Please refer to this complete question:
In a certain town, 60% of the households own mutual funds, 40% own individual stocks, and 20% own both mutual funds and individual stocks. The proportion of households that own mutual funds but not individual stocks or individual stocks but not mutual funds is
a. 40%.
b. 60%.
c. 80%.
d. 100%
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8.
supplementary angles. IfAnswer:
Do u like m&m because I do