The simplified radical form of the equation [tex](x^{4})^{\frac{5}{6} }[/tex] is [tex]x^{\frac{10}{3} }[/tex]
The exponentiation is written as [tex]a^{n}[/tex], where a is the base and n is the exponent or power. We say as "a by n". Exponent means the number of times the base is used as a factor.
The expression = [tex](x^{4})^{\frac{5}{6} }[/tex]
Here we have to apply the exponent rule
We know,
The power rules for the exponent [tex](a^{m})^{n}=a^{mn}[/tex]
Here multiply the exponent times the power.
Simplify it
[tex](x^{4})^{\frac{5}{6} }=(x)^{4(\frac{5}{6}) }[/tex]
=[tex]x^{\frac{20}{6} }[/tex]
Divide both 20 and 6 by 2 to make it to simplest form, then the result
=[tex]x^{\frac{10}{3} }[/tex]
Hence, the simplified radical form of the equation [tex](x^{4})^{\frac{5}{6} }[/tex] is [tex]x^{\frac{10}{3} }[/tex]
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After a person gets a 2% raise in salary, the new salary is $11874. What was the original salary?
Answer:
Original salary was $11641.17Step-by-step explanation:
Let the initial salary be x.
Set equation and solve for x:
x + 2% of x = 11874x + x*2/100 = 11874x + 0.02x = 118741.02x = 11874x = 11874/1.02x = 11641.17 (rounded to the nearest cent)
Answer:
The original salary is $11641.18.
Step-by-step explanation:
The equation will be,
→ x + (x × 2)/100 = 11874
Now the original salary will be,
→ x + (x × 2)/100 = 11874
→ x + 0.02x = 11874
→ 1.02x = 11874
→ x = 11874/1.02
→ x = 11641.1764706
→ [ x = 11641.18 ]
Hence, original salary is $11641.18.
12. Ben and Jerry invest $50 000 and $75 000 respectively in the same bank.
If the rate is 8%, how many whole years will it take for Ben to cross the amount of money that Jerry would have in 2 years?
Solve −3 = x/4 + 5 using the replacement set {−32, 8, 32} .
A. −32
B. 8
C. 32
D. I don't know.
Answer:
A
Step-by-step explanation:
substitute the values from the replacement set into the right side of the equation to find which values of x make the equation true.
x = - 32
[tex]\frac{-32}{4}[/tex] + 5 = - 8 + 5 = - 3 ← True
x = 8
[tex]\frac{8}{4}[/tex] + 5 = 1 + 5 = 6 ≠ - 3 ← False
x = 32
[tex]\frac{32}{4}[/tex] + 5 = 8 + 5 = 13 ≠ - 3 ← False
the solution is therefore x = - 32
Write a polynomial equation with integer coefficients that has the given roots.
x = -1 x=-6
Polynomial equation with integer coefficients that has roots x= -1 and
x = -6 is equal to x² +7x +6=0.
As given in the question,
Given roots for the polynomial equation with integer coefficient are
x = -1 ⇒ x + 1=0
x = -6 ⇒ x + 6 =0
Polynomial equation is
( x + 1) ( x + 6) =0
⇒ x² + 1x + 6x + 6 =0
⇒ x² + 7x + 6 =0
Therefore, polynomial equation with integer coefficients that has roots x= -1 and x = -6 is equal to x² +7x +6=0.
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help i need help i this please
Answer:
-∞ and -∞ both answers
Step-by-step explanation:
From the graph it is clear that as x becomes smaller and smaller, y gets smaller and smaller. So as x → -∞, y → -∞
On the positive x side, as x gets bigger and bigger, y gets smaller and smaller so
as x → +∞, y → -∞
PLEASE HELP!
The data show what an apartment resident paid per month for her electric bill during a calendar year.
$56, $72, $120, $120, $122, $124, $128, $135, $152, $168, $183, $200
Use the data to answer the questions.
What is 1.5 ∙ IQR?
A: 40
B: 60
C: 80
What is the lower boundary?
A: 60
B: 66
C: 120
What is the upper boundary?
A: 160
B: 220
C: 251.5
Which sentence describes the outliers?
A: There are no outliers.
B: The outlier is less than the lower boundary.
C: The outlier is greater than the upper boundary.
Using the median concept and the quartiles, we have that:
1.5 IQR is: B. 60.The lower boundary is: A. 60.The upper boundary is: B. 220.The sentence that describes the outliers is: B: The outlier is less than the lower boundary.What are the median and the quartiles of a data-set?The median of the data-set separates the bottom half from the upper half, that is, it is the 50th percentile.The first quartile is the median of the first half of the data-set.The third quartile is the median of the second half of the data-set.The interquartile range is the difference between the third quartile and the first quartile.Values that are more than 1.5 IQR from either quartile are considered outliers.In this problem, there are 12 elements, hence:
Q1 is the 0.25 x 12 = 3rd element.Q3 is the 0.75 x 12 = 9th element.Thus, Q1 = 120, Q3 = 160 and the IQR is:
IQR = 160 - 120 = 40.
1.5 IQR is: 1.5 x 40 = 60.
The boundaries are:
120 - 60 = 60. (lower).160 + 60 = 220(upper).There is a value less than 60 in the data set, hence the sentence that describes the outliers is: B: The outlier is less than the lower boundary.
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Answer:
Use the data to answer the questions.
What is 1.5 ∙ IQR? ✔ 60
What is the lower boundary? ✔ 60
What is the upper boundary? ✔ 220
Which sentence describes the outliers? ✔ The outlier is less than the lower boundary.
Step-by-step explanation:
edge 2023
Amy paid $66.94 for a pair of running shoes during a 15%-off sale. What was the regular price?
...
if you add all the prime numbers between 2 and 33 and then multiply it by itself y
Answer:
24964
Step-by-step explanation:
hope this works - btw this is not including 2 and 33
Lucy paid $120 for an item at the store that was 20 percent off the original price. what was the original price?
Answer:
$150
Step-by-step explanation:
Given the following question:
Lucy paid 120 dollars for an item
The item was 20% off
What was the original price? To find the original price we will need to use the formula to calculate percentages.
20% of 150
[tex]\frac{p\times n}{100}[/tex]
[tex]\frac{20\times150}{100}[/tex]
[tex]20\times150=3000[/tex]
[tex]3000\div100=30[/tex]
[tex]150-30=120[/tex]
[tex]=120[/tex]
Which means our original price is "$150."
Hope this helps.
Does anyone know where the a in front of the parentheses for the LCD : a(a+5)(a-6) came from?
Thank you!
Answer:
See below
Step-by-step explanation:
If you factor [tex]a^2-a-30[/tex] you get [tex]\left(a^2+5a\right)+\left(-6a-30\right)[/tex]
= [tex]a(a+5)-6(a+5)[/tex]
= [tex]a(a+5)(a-6)[/tex]
That's where the a comes in
Not sure if that answers your question
Question 5
A swimming pool has a length of 30 ft, a width of 12 ft, and a uniform depth of 8 ft. How many gallons of water does it hold?
(Hint: Find the volume in cubic ft and then use dimensional analysis to convert to gallons. 7.5 gal - 1 cubic ft.)
Round your answer to the nearest whole gallon, but do not include a unit of measure with your response.
V = 4 + at, solve for a.
Answer: a=(V-4)/t
Step-by-step explanation:
V = 4 + at
V-4=at
a=(V-4)/t
add 1/2 + 1/4 + 1 1/4
Answer:
Final answer is 2
Step-by-step explanation:
4. Randall's monthly water bill from April to July is listed in the table below. What was the percent
increase in his bill from May to July?
The percent increase in his bill from May to July is 32.29%.
What is the percent increase in the bill?
Percentage can be described as a fraction out of an amount that is usually expressed as a number out of hundred. Percentages are a measure of frequency. The sign used to represent percentages is %.
The percent increase in his bill from May to July = (bill in July / bill in May)^(1/number of months) - 1
(136.50 / 78)^(1/2) - 1 = 32.29%
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Homework 4.3 Partial Derivatives
If Partial Derivatives f(x,y) -8e^4x sin(7y) is 32 e^(4 x) sin(7 y) and
56 e^(4 x) cos(7 y)
Partial Derivatives
d/dx(8 e^(4 x) sin(7 y))
Factor out constants:
= 8 (d/dx(e^(4 x))) sin(7 y)
Using the chain rule, d/dx(e^(4 x)) = (d e^u)/(du) (du)/(dx), where u = 4 x and d/(du) (e^u) = e^u:
= e^(4 x) (d/dx(4 x)) 8 sin(7 y)
Factor out constants:
= 4 (d/dx(x)) 8 e^(4 x) sin(7 y)
Simplify the expression:
= 32 e^(4 x) (d/dx(x)) sin(7 y)
The derivative of x is 1:
= 32 e^(4 x) sin(7 y)
Simplify the expression:
32 e^(4 x) sin(7 y)
Part 2:
Partial Derivatives
d/dy(8 e^(4 x) sin(7 y))
Factor out constants:
= 8 e^(4 x) (d/dy(sin(7 y)))
Using the chain rule, d/dy(sin(7 y)) = (dsin(u))/(du). (du)/(dy), where u = 7 y and d/(du) (sin(u)) = cos(u):
= cos(7 y) (d/dy(7 y)) 8 e^(4 x)
Factor out constants:
= 7 (d/dy(y)) 8 e^(4 x) cos(7 y)
Simplify the expression:
= 56 e^(4 x) cos(7 y) (d/dy(y))
The derivative of y is 1:
= 56 e^(4 x) cos(7 y)
Simplify the expression:
56 e^(4 x) cos(7 y)
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Write the coordinates of the vertices after a rotation 90° counterclockwise around the origin.
E (-8,9)
F(-4,9)
G(-4,2)
D(2,-8)
The coordinates of the vertices E (-8,9), F(-4,9), G(-4,2), and D(2,-8) when rotated 90° counterclockwise around the origin of the new coordinates will be E'( - 9, - 8 ), F'( - 9, - 4 ), G'( - 2, - 4 ), and D'( 8, 2 ).
A point A( x, y ) becomes A' when a point is rotated 90 degrees counterclockwise about the origin ( - y, x ). To put it another way, flip x and y, and make y negative.
Therefore, when point E( - 8, 9 ) is rotated 90° counterclockwise around the origin will be:
E'( - 9, - 8 )
When point F( - 4, 9 ) is rotated 90° counterclockwise around the origin the new point will be:
F'( - 9, - 4 )
When point G( - 4, 2 ) is rotated 90° counterclockwise around the origin the new point will be:
G'( - 2, - 4 )
When point D( 2, - 8 ) is rotated 90° counterclockwise around the origin the new point will be:
D'( 8, 2 )
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3. Write the number: three hundred
seven thousand, fifty-nine and six
tenths
S
At a certain company, the average starting salary s for a new worker is $25,000. The actual salary has an absolute deviation of at most $1800. Write and solve an inequality to find the range of the starting salaries.
The range of the salary will be the closed interval [23,200, 26,800].
What is an absolute function?The absolute function is also known as the mode function. The value of the absolute function is always positive.
The absolute function is given as
f(x) = | x |
A new hire at one organization may expect to get an average beginning pay of $25,000 per year. The absolute divergence from the real compensation is no more than $1800.
Let 'x' represent the actual salary. Then the inequality is given as,
|x - 25,000| ≤ 1800
- 1,800 ≤ x - 25,000 ≤ 1,800
25,000 - 1,800 ≤ x ≤ 25,000 + 1,800
23,200 ≤ x ≤ 26,800
The range of the salary will be the closed interval [23,200, 26,800].
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if angle 2=6x+8 and angle 4=4x+11 what is the value of angle 2?
Answer:
17
Step-by-step explanation:
Angle 2 and angle 4 are alternate exterior angles so they congruent angles which means they have same angle measurement.
To find the measure of angle 2 we first need to find the value of x.
And to do that we can write the following equation based on the information we have in hand:
6x + 8 = 4x + 11 transfer like terms to the same side of the equation
6x - 4x = 11 - 8 add/subtract like terms
2x = 3 divide both sides by 2
x = 1.5 now to find the measure of angle 2 replace x with 1.5
6×(1.5)+8 = 17
a map has a scale of 1:1000.
i)
What distance on the ground (in meters) is represented on the map as
(a) 2cm (b) 7.6cm?
ii)
What distance on the map represents
(a) 100m (b) 2.6km?
(a) The distance on the ground represented 2 cm on the map is 2000 cm.
(b) The distance on the ground represented 7.6 cm on the map is 7600 cm
It is a technique wherever we discover worth|the worth} of one unit from the worth of multiple units and also the value of multiple units from the worth of one unitIt is given that a map has a scale of 1:1000 which means that 1 cm of the map represents 1000 cm on the ground .
i) (a) Using unitary method , we get
1 cm on map is equivalent to = 1000 cm on the ground
2 cm on map is equivalent to = 2 × 1000
= 2000 cm on the ground
(b) Using unitary method , we get
1 cm on map is equivalent to = 1000 cm on the ground
7.6 cm on map is equivalent to = 7.6 × 1000
= 7600 cm on the ground
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Which measurement is closest to 270 cm: 9ft, 680in. or 270 in.?
The measurement 9 feet is closest to 270 centimeters.
What measure is equivalent to another measure?
In this problem we have a case of unit conversions, in which we must find what measure in a unit offers the best approximation to other represented in other unit. Please notice that a centimeter equals 25 / 762 feet and 50 / 127 inches. Now we proceed to calculate the equivalent quantities in feet and inches by simple rule of three:
x = 270 cm × (25 / 762 feet / cm)
x ≈ 8.858 feet
x = 270 cm × (50 / 127 inches / cm)
x ≈ 106.299 inches
The measurement 9 feet is closest to 270 centimeters.
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Draw AABC with vertices at A(1,6), B(1, 1) and C(5, 1). In this triangle, AB²+ BC² = AC².
Next, use the GeoGebra tools to draw ADEF such that AB = DE, m/E = 90°, and
EF = BC.
Paste a picture of your drawing in the answer box.
The picture of the triangle ΔDEF is attached below.
A triangle can be defined as a basic polygon which has 3 sides.
The sum of all the interior angles of a triangle is given by 180°.The area of any triangle is calculated by [tex]\frac{1}{2}[/tex] × base × height.In a right-angled triangle the side opposite the largest angle which is 90° is called the hypotenuse.Pythagoras' theorem states that the sum of the squares of the legs of aright-angles triangle is equal to the square of the hypotenuse of the triangle.In the given ΔABC we see that AC is the hypotenuse and the two sides AB and AC are the legs of the triangle.
m∠B=90°
The ΔDEF is drawn such that m∠E=90° and AB=DE and EF=BC .
Therefore we can say that the two triangles are congruent by SAS axiom of congruency.
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Write a function g whose graph represents the indicated transformation of the graph of f.
f(x) = 3x ; translation 5 units up
the translated function is g(x) =
Answer:
g(x) = 3x +5
Step-by-step explanation:
You want the function that results from translating f(x) = 3x upward by 5 units.
TranslationThe y-coordinate of a point tells how far above the x-axis it is. Adding 5 to the y-coordinate will move that point 5 units farther above the x-axis, which is to say 5 units upward.
The y-coordinate of a point on a graph is the value of the function of the x-coordinate of that point. That is, each point is (x, f(x)). If we want to translate that point 5 units upward, we add 5 to the function value:
(x, f(x) +5) . . . . . graph translated 5 units up
Using the given definition of f(x), this becomes ...
(x, 3x +5)
The translated function is defined as g(x), so we have ...
(x, g(x)) = (x, 3x +5)
or ...
g(x) = 3x +5
Can you please help with this
The fraction 24/56 can be simplified to 3/7, and we can't keep simplifying this.
How to simplify the given fraction?Here we want to simplify the fraction 24/56. To do so, we need to find the greatest common factor between 24 and 56, to find that, we need to write both of these numbers as a product of their prime factors.
We will get:
24 = 2*2*2*3
56 = 2*2*2*7
We can identify the greatest common factor between parenthesis:
24 = (2*2*2)*3
56 = (2*2*2)*7
So the greatest common factor is 2*2*2 = 8, then we can divide both numerator and denominator by 8, we will get:
24/8 = 3
56/8 = 7
Then the fraction 24/56 can be simplified to 3/7, and we can't keep simplifying this.
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Explain how to do -12 - (-98) + 7 - 3
The sum of
5
9
and six times a number is equal to
2
subtracted from seven times the number. Find the number.
ANSWER:
x=61
STEPS FOR SOLVING LINEAR EQUATION :
59+6x=7x−2Subtract 7x from both sides.
59+6x−7x=−2Combine 6x and −7x to get −x.
59−x=−2Subtract 59 from both sides.
−x=−2−59Subtract 59 from −2 to get −61.
−x=−61Multiply both sides by −1.
x=61Hope it helps!!!
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Answer:
answer to the question is x=61
84x7 complete the equation
Answer:
The answer to your question is 588
Answer:
588
Hope this helps
convert into power notation (-2197)
A survey of 541 adults aged 18-24 year olds was conducted in which they
were asked what they did last Friday night. It found:
181 watched TV
• 180 hung out with friends
• 150 ate pizza
• 46 watched TV and ate pizza, but did not hang out with friends
• 36 watched TV and hung out with friends, but did not eat pizza
• 29 hung out with friends and ate pizza, but did not watch TV
• 25 watched TV, hung out with friends, and ate pizza
How may 18-24 year olds did not do any of these three activities last Friday
Answer: 30
Step-by-step explanation:
181+180+150=
361+150=511
541-511=30 18-24 year olds
**46 of 181 students that watched TV ate pizza and the same 46 students of the 150 students that ate pizza watched TV.
What is the slope of a line that passes through the ordered pairs (0,1) and (3,5)?
The slope of a line that passes through the ordered pairs (0,1) and (3,5) would be m = 4/3.
What is the slope of a line which passes through points ( p,q) and (x,y)?Slope tells how vertical a line is.
The more the slope is, the more the line is vertical. When slope is zero, the line is horizontal. Slope of parallel lines are same. Slopes of perpendicular lines are negative reciprocal of each other.
Its slope would be:
[tex]m = \dfrac{y-q}{x-p}[/tex]
WE have been given line that passes through the ordered pairs (0,1) and (3,5).
Slope = m
Therefore,
[tex]m = \dfrac{y-q}{x-p}\\\\m = \dfrac{5 -1}{3-0}\\\\m = \dfrac{4}{3}[/tex]
Hence, the slope of a line that passes through the ordered pairs (0,1) and (3,5) would be [tex]m = \dfrac{4}{3}[/tex].
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