Answer:3√(p/q)3
Step-by-step explanation: Find the cube root .
The law used to simplify the expression [tex]( (p/q)^3 \)[/tex] is the "Power of a Quotient" rule.
The correct option is (b).
The "Power of a Quotient" rule states that when a fraction is raised to a power, we can raise both the numerator and denominator to that power individually. Mathematically, it is represented as:
[tex]\[ \left(\frac{a}{b}\right)^n = \frac{a^n}{b^n} \][/tex]
Applied to the expression [tex]\( (p/q)^3 \)[/tex], we raise both[tex]\( p \) and \( q \)[/tex] to the power of 3:
[tex]\[ \left(\frac{p}{q}\right)^3 = \frac{p^3}{q^3} \][/tex]
This simplification allows us to express the original expression in terms of powers of the numerator and denominator separately. In other words, the exponent 3 is distributed to both [tex]\( p \) and \( q \), resulting in \( p^3 \)[/tex]in the numerator and [tex]\( q^3 \)[/tex] in the denominator.
Using this rule, we can handle expressions involving powers of fractions efficiently, breaking them down into simpler terms that are easier to work with or evaluate. It's particularly useful when dealing with algebraic expressions or equations where fractions with powers are involved, providing a systematic approach to simplification.
complete question given below:
Which law would you use to simplify the expression
[tex](p\q)^3[/tex]?
a.power of a power
b.power of a quotient
c.quotient of powers
d.power of a product
change the decimal to a fraction and reduce .62
Answer:
31/50
Step-by-step explanation:
0.62 = 62/100 = 31/50
Solve x^5 - 8x^4 + 22x^3 - 26x^2 + 21x - 18 -0.
Answer:
= x^5 - 8x^4 + 22x^3 - 26x^2 + 21x - 18
Step-by-step explanation:
x^5 - 8x^4 + 22x^3 - 26x^2 + 21x - 18 - 0
Since all the exponents have different bases, the only thing we can do is subtract 18 from 0, which gives us an answer of:
= x^5 - 8x^4 + 22x^3 - 26x^2 + 21x - 18
What is the following product? (5 square root 2-4 square root 3) (5 square root 2-4 square root 3)
Answer:
(5 square root 2-4 square root 3) (5 square root 2-4 square root 3)
= 98 - 40[tex]\sqrt{6}[/tex]
Step-by-step explanation:
i) (5[tex]\sqrt{2}[/tex] - 4[tex]\sqrt{3}[/tex]) × (5√2 - 4√3)
=(5[tex]\sqrt{2}[/tex] × 5[tex]\sqrt{2}[/tex]) - (5[tex]\sqrt{2}[/tex] × 4[tex]\sqrt{3}[/tex]) - (4[tex]\sqrt{3}[/tex] × 5[tex]\sqrt{2}[/tex]) + (4[tex]\sqrt{3}[/tex] × 4[tex]\sqrt{3}[/tex])
= 50 - 20[tex]\sqrt{6}[/tex] - 20[tex]\sqrt{6}[/tex] + 48
= 98 - 40[tex]\sqrt{6}[/tex]
Answer:
98 - 40√6
Step-by-step explanation:
The words expression can be represented as follows:
(5√2 - 4√3) (5√2 - 4√3)
The question is to find the products .
(5√2 - 4√3) (5√2 - 4√3)
Multiply through to open the bracket
25 × 2 - 20√6- 20√6 + 16 × 3
50 - 20√6 - 20√6 + 48
50 - 40√6 + 48
50 + 48 - 40√6
98 - 40√6
What is the experimental probability of drawing a red marble, given the following results?
Marble Color Blue Green Red
Times Drawn 8
Answer:
7/20..i hope its correct
Step-by-step explanation:
all = 8+5+7
=20
red marbles / all = 7/20
Answer:
7/20
Step-by-step explanation:
Use a calculator to find the approximate value of cos-1(0.55).
Answer:
The approximate value is [tex]56.63^o[/tex]
Step-by-step explanation:
Let
[tex]\theta[/tex] ----> the measure of angle in degrees
we have that
[tex]cos(\theta)=0.55[/tex]
Using a calculator
Find the measure of angle [tex]\theta[/tex]
[tex]\theta=cos^{-1}(0.55)[/tex]
[tex]\theta=56.63^o[/tex]
Ethan buys a new phone. It cost 75$. He will pay for this on his 1st bill.
His phone plan charges 0.06 dollars per minute on the phone.
'He has $90 to spend on his 1st bill. How long can he be on his phone to not go over his budget?
A)80 minutes
B)250 minutes
C) 1050 minutes
D)1250 minutes
Answer:250
Step-by-step explanation: Subtract 90 from 75 which is 15 then divide 15 by .06 which is 250
Answer:a
Step-by-step explanation:
a
two positive improper fractions are multiplied. Is the product sometimes, always, or never less than 1? Explain
10. Find the equation of a line with a slope of O and that passes through
the point (-2,5).
Answer:
Y=5
Step-by-step explanation:
If the slope is 0 it will be a line parallel to the x axis with a constant value of y and since we know it passes through a point with y coordinate of 5 we know that the constant value of y is 5
Which number means the same as 7,000,000,000 + 900,000,000 + 20,000,000 + 7,000,000 + 100,000 + 70,000 + 3,000 + 800 + 60? A. 7,927,137,860 B. 7,972,173,860 C. 7,927,173,806 D. 7,927,173,860
Answer:
d
Step-by-step explanation:
Answer:
D. 7,927,173,860
Step-by-step explanation:
Because math
2 pluse 2 what does that equal
Answer:
The answer is 4. as 2 plus 2 is equal to 4
Step-by-step explanation:
2+2=4
What is the solution for x in the equation?
9x - 20 - 4x = 40
Answer:
Step-by-step explanation:
X=12
Answer:
x= 12
Step-by-step explanation:
9x-20-4x=40
add 20 on both sides
40+20=60
combine like terms
9x-4x=5x
divide 60 by 5
=12
Which statement describes whether a right triangle can be formed using one side length from each of these squares? 3 squares have areas of 64 inches squared, 225 inches squared, and 289 inches squared.
A: Yes, a right triangle can be formed because the sum of the areas of the two smaller squares does not equal the area of the largest square.
B:Yes, a right triangle can be formed because the sum of the areas of the two smaller squares equals the area of the largest square.
C:No, a right triangle cannot be formed because the sum of the areas of the two smaller squares does not equal the area of the largest square.
D:No, a right triangle cannot be formed because the sum of the areas of the two smaller squares equals the area of the largest square.
Answer:
the correct answer is B
"yes, a right triangle can be formed because the sum of the areas of the two smaller squares equals the area of the largest square."
Step-by-step explanation:
took the test, got it right. nice day folks. amos @kay_flores575
Right triangle can be formed because the sum of the areas of the two smaller squares equals the area of the largest square.
What is area?
" Area is the space occupied by any two dimensional object on the flat surface."
What is right angled triangle?"Right angled triangle is a two dimensional figure with three sides and three vertices . Any one of the interior angle should be equals to 90°."
Formula applied
Pythagoras theorem
a² = b² +c²
According to the question,,
Three square with areas 64inches , 225 inches and 289 inches.
We can write this areas as
289 = 225 + 64
⇒(17)² = (15)² + (8)²
Applying formula we can say that a right triangle can be formed.
Hence, we conclude that Option B is correct.
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Which statement describes the graph of the system of equations below? 1.5x+0.2y=2.68
1.6+0.3y=2.98
Answer:
( 1.17 3 , 4.6 )
Step-by-step explanation:
Maureen bought a coat. She was excited because it was on sale, so she paid $15.25 less than the original price. She paid $48.75 for the coat. Write and solve an equation to determine the original price. Let p represent the original price. It's getting cold outside! The temperature dropped steadily at a rate of about 4 degrees every hour. If the temperature dropped a total of 22 degrees, how many hours have passed? Let h represent the number of hours
Answer:
$33.50 for coat, 5.5 hours
Step-by-step explanation:
For the coat, since it was on sale, then it would be $48.75-$15.25=p=$33.50.
If the temperature drops 4 degrees every hour, if t dropped 22 degrees, then you would do 22 divided by 4, to find out how many hours it had dropped for. 22 divided by 4=h=5.5 or 5 1/2.
Addie saved more than $36. Which inequality represents the amount she saved
Answer:
S>36
where S is saving
Maria has 15 dollars that she can spend at the movies. A movie ticket costs 7 dollars. Which inequality represents the greatest amount of money, f, Maria can spend on food and drinks?
The inequality which represents the greatest amount of money, f, Maria can spend on food and drinks is f < 8.
What is Linear Inequalities?Linear inequalities are defined as those expressions which are connected by inequality signs like >, <, ≤, ≥ and ≠ and the value of the exponent of the variable is 1.
Given that,
Maria has 15 dollars that she can spend at the movies.
Total amount Maria has = $15
Cost of a movie ticket = $7
Let f be the amount that she can spend maximum on food and drinks.
f < remaining amount
f < 15 - 7
f < 8
Hence the inequality is f < 8.
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what does 3 over 4 times 2 equal?
Answer: 1.5
Da maths: Bruh ask google
approximate
[tex] log_{3}14 + 1 [/tex]
Answer:
log(14) / log(3) + 1 OR 3.40217350
Step-by-step explanation:
How do I rotate a point by 180 degrees clockwise?
180 degrees is half of a circle, and clockwise means turning in the direction a clock does - right.
So a point would be turned right halfway around.
483.6 is what percent of 180
Answer:
We assume, that the number 180 is 100% - because it's the output value of the task.
2. We assume, that x is the value we are looking for.
3. If 100% equals 180, so we can write it down as 100%=180.
4. We know, that x% equals 483.6 of the output value, so we can write it down as x%=483.6.
5. Now we have two simple equations:
1) 100%=180
2) x%=483.6
where left sides of both of them have the same units, and both right sides have the same units, so we can do something like that:
100%/x%=180/483.6
6. Now we just have to solve the simple equation, and we will get the solution we are looking for.
7. Solution for 483.6 is what percent of 180
100%/x%=180/483.6
(100/x)*x=(180/483.6)*x - we multiply both sides of the equation by x
100=0.37220843672457*x - we divide both sides of the equation by (0.37220843672457) to get x
100/0.37220843672457=x
268.66666666667=x
x=268.66666666667
now we have:
483.6 is 268.66666666667% of 180
Select all of the following that are ordered pairs of the given function.
f(x)=3-2x
Answer:
(-1,5), (0,3), (2,-1)
Step-by-step explanation:
We can just test out each of the answers as follows:
Let's start with (-2,-1). We see that f(-2) = 3 - 2x(-2) = 3+4 = 7, so this is not a solution.
Now let's work out the rest:
f(-1) = 3 - 2x(-1) = 3 + 2 = 5. So yes (-1,5) is a solution
f(0) = 3-2x0 = 3 so yes, (0,3) is a solution
f(1) = 3 - 2x1 = 1 so (1,0) is not a solution
f(2) = 3 -2x2 = -1, so yes (2,-1) is a solution
the perimeter of a rectangle is 32 centimeters. The length is 1 cm more than twice the width. Find the dimensions of the rectangle.
Answer: length = 11cm , width = 5cm
Step-by-step explanation:
The formula for calculating the perimeter of a rectangle is given by :
P = 2 ( L + w )
The length is 1 cm more than twice the width implies:
L = 1 + 2w
substituting into the formula , we have
32 = 2 ( 1 + 2w + w )
32 = 2 ( 1 + 3w)
32 = 2 + 6w
32 - 2 = 6w
30 = 6w
Therefore :
w = 5
then
L = 1 + 2w
L = 1 + 2 ( 5 )
L = 1 + 10
L = 11
Therefore , the length is 11 cm and the width is 5cm
LN is tangent to circle o at point M and QM is a diameter. Determine the measure of the following angles.
The measure of QML is degrees
The measure of ZPMN is degrees.
270
Answer:
Part 1) [tex]m\angle QML=90^o[/tex]
Part 2) [tex]m\angle PMN=63^o[/tex]
Step-by-step explanation:
The complete question in the attached figure
Part 1) Find the measure of angle QML
we know that
According to the Perpendicular Tangent Theorem, tangent lines are always perpendicular to a circle's radius at the point of intersection
so
radius OM is perpendicular to LN at point M
therefore
[tex]m\angle QML=90^o[/tex]
Part 2) Find the measure of angle PMN
we know that
[tex]m\angle QMN=m\angle QMP+m\angle PMN[/tex] ---> by angle addition postulate
we have
[tex]m\angle QMN=90^o[/tex]
[tex]m\angle QMP=27^o[/tex]
substitute
[tex]90^o=27^o+m\angle PMN[/tex]
[tex]m\angle PMN=90^o-27^o=63^o[/tex]
Applying the perpendicular tangent theorem, the missing angles are:
m∠QML = 90°
m∠PMN = 63°
What is the Perpendicular Tangent Theorem?The Perpendicular Tangent Theorem states that tangent lines are perpendicular to the radius of a circle at the point where they intersect, forming a right angle.
Thus:Based on the perpendicular tangent theorem,
m∠QML = m∠QMN = 90°
Thus:m∠QML = 90°
m∠PMN = 90° - 27°
m∠PMN = 63°
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A circular path 3 feet wide has an inner diameter of 350 feet. How much farther is it around the outer edge of the path than around the inner edge? Round to nearest hundredth. Use 3.14 for π.
Answer:
18.84 feet farther is it around the outer edge of the path than around the inner edge.
Step-by-step explanation:
Given:
A circular path 3 feet wide has an inner diameter of 350 feet.
Use 3.14 for π.
Now, to find how much farther is it around the outer edge of the path than around the inner edge.
Width of the circular path = 3 feet.
Inner diameter of circular path = 350 feet.
So, to get the inner radius we divide the inner diameter of circular path by width of circular path:
[tex]350\div 3[/tex]
[tex]=116.67\ feet.[/tex]
r = 116.67 feet.
Now,
Thus, the outer radius is:
[tex]116.67+3[/tex]
[tex]=119.67\ feet.[/tex]
R = 119.67 feet.
Now, we get the circumference of inner edge and outer edge:
Circumference of inner edge = 2πr.
[tex]Circumference\ of\ inner\ edge=2\times 3.14\times 116.67[/tex]
[tex]=732.69\ feet.[/tex]
Circumference of outer edge = 2πR.
[tex]Circumference\ of\ outer\ edge=2\times 3.14\times 119.67[/tex]
[tex]Circumference\ of\ outer\ edge=751.53\ feet.[/tex]
Now, to get how much farther is it around the outer edge of the path than around the inner edge:
Circumference of outer edge - circumference of inner edge.
[tex]751.53-732.69[/tex]
[tex]=18.84\ feet.[/tex]
Therefore, 18.84 feet farther is it around the outer edge of the path than around the inner edge.
The difference in distance around the outer edge of the path compared to the inner edge is 18.84 feet.
To find how much farther it is around the outer edge of the circular path compared to the inner edge, we need to calculate the circumferences of both the inner and outer edges and find the difference.
1. First, calculate the inner circumference using the inner diameter of 350 feet:
Inner Circumference = π × inner diameter = 3.14 × 350 = 1099 feet.
2. Next, calculate the outer diameter by adding the width of the path to each side of the inner diameter:
Outer Diameter = inner diameter + 2 × width of the path = 350 + 2 × 3 = 356 feet.
3. Then, calculate the outer circumference using the outer diameter:
Outer Circumference = π × outer diameter = 3.14 × 356 = 1117.84 feet.
4. Finally, find the difference between the outer and inner circumferences:
Difference = Outer Circumference - Inner Circumference = 1117.84 - 1099 = 18.84 feet.
Therefore, it is 18.84 feet farther around the outer edge of the path than around the inner edge.
find the greatest common divisor for 22/34 then simplify the fraction
Step-by-step explanation:
[tex]22=\boxed{2}\times11\\\\34=\boxed2\times17\\\\GCD(22,\ 34)=\boxed2\\\\\dfrac{22}{34}=\dfrac{22:2}{34:2}=\dfrac{11}{17}[/tex]
Answer:
11/17
Step-by-step explanation:
22 and 34
22: 1, 2, 11, 22
34: 1, 2, 17, 34
22/34 ÷ 2/2 = 11/17
In a two-digit number the tens digit is four less than the units digit. Seven times the tens digit plus five times the units digit is equal to 56. Find the digits.
The digits of the number are 7 and 3
Step-by-step explanation:
In a two-digit number:
The tens digit is four less than the units digitSeven times the tens digit plus five times the units digit is equal to 56We need to find the digits
Assume that the unit digit is x and the ten digit is y
∵ x represents the unit digit
∵ y represents the ten digit
∵ The ten digit is four less than the unit digit
- That means subtract 4 from the unit digit to get the ten digit
∴ y = x - 4 ⇒ (1)
∵ Seven times the tens digit plus five times the units digit is
equal to 56
- That means multiply the ten digit by 7 and the unit digit by
5 and add the two products and equate the sum by 56
∴ 7y + 5x = 56 ⇒ (2)
Now we have a system of equations to solve it
Substitute y in equation (2) by equation (1)
∵ 7(x - 4) + 5x = 56
- Simplify the left hand side
∴ 7x - 28 + 5x = 56
- Add the like terms in the left hand side
∴ 12x - 28 = 56
- Add 28 to both sides
∴ 12x = 84
- Divide both sides by 12
∴ x = 7
- Substitute the value of x in equation (1) to find y
∵ y = 7 - 4
∴ y = 3
∴ The number is 37
The digits of the number are 7 and 3
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Maggie found the area of the irregular figure by dividing it into a triangle and a rectangle.
Answer:
33cm^2
Step-by-step explanation:
Rectangle:
5 x 6 = 30
Triangle:
1 side 6 - 3 = 3
2 side 7- 5 = 2
area of right triangle:
A = (ab) / 2
A = (3 * 2) / 2
A = 3
sum:
30 + 3 = 33
Answer:
swallla swalla swalla swalla drake swalla drake swalla swalla swalla freaky freaky gurlll
Step-by-step explanation:
A restaurant offers hamburgers with one, two, or three patties. Let X represent the number of patties a randomly chosen customer orders on their hamburger. Based on previous data, here's the probability distribution of X along with summary statistics:
X=# of patties 1 2 3
P(X) 0.40 0.50 0.10
Mean: μX=1.7
Standard deviation: σX≈0.67
The total price of each burger is set at $2 per patty. Let T represent the total price a randomly chosen customer pays for their burger. Find the mean of T
Answer:
The mean price a randomly chosen customer pays for her or his burger is US$ 3.40
Step-by-step explanation:
Let's find out the mean of T (total price a randomly chosen customer pays for their burger), this way:
Mean of T = 0.4 * $ 2 + 0.5 * $ 4 + 0.1 * $ 6
Mean of T = 0.8 + 2 + 0.6
Mean of T = US$ 3.40
The mean price a randomly chosen customer pays for her or his burger is US$ 3.40
In the given case, the mean of T is [tex]\[ \boxed{3.4} \text{ dollars} \][/tex]
To find the mean of T, which represents the total price a randomly chosen customer pays for their burger, we can use the relationship between T and X.
Given that the price per patty is $2, the total price T can be expressed as:
T = 2X
We are given the mean number of patties [tex]\( \mu_X = 1.7 \).[/tex]
The mean of a transformed variable can be found using the linear transformation properties of the mean.
Specifically, if [tex]\( T = aX + b \),[/tex] then:
In this case, since T = 2X , we have a = 2 and b = 0.
Therefore:
[tex]\[ \mu_T = 2\mu_X + 0 = 2 \times 1.7 = 3.4 \][/tex]
So, the mean of T is- [tex]\[ \boxed{3.4} \text{ dollars} \][/tex]
Marilyn has 7/8 yard of ribbon. What is the maximum number of 1/16 yard long pieces Marilyn can cut from this ribbon
Marilyn can cut 14 equal pieces
Solution:
Given that, Marilyn has 7/8 yard of ribbon
To find: Maximum number of 1/16 yard long pieces Marilyn can cut from this ribbon
From given information,
[tex]\text{Total length of ribbon } = \frac{7}{8} \text{ yard }[/tex]
[tex]\text{Length of 1 piece } = \frac{1}{16} \text{ yard }[/tex]
Number of pieces that can be cut from total length of ribbon is found by dividing the total length of ribbon by length of 1 piece
Therefore,
[tex]\text{Number of pieces } = \frac{\text{Total length of ribbon}}{\text{Length of 1 piece }}[/tex]
Substituting the values, we get
[tex]\text{Number of pieces } = \frac{\frac{7}{8}}{\frac{1}{16}}\\\\\text{Number of pieces } = \frac{7}{8} \times \frac{16}{1}\\\\\text{Number of pieces } = 14[/tex]
Thus 14 pieces of ribbon can be cut
I need help simplifying #6
Answer:
The simplified expression is [tex]\frac{12x^8y^5}{5z^4}[/tex]
Therefore [tex]\frac{24x^5y^9z^{-8}}{10x^{-3}y^4z^{-4}}=\frac{12x^8y^5}{5z^4}[/tex]
Step-by-step explanation:
Given expression is [tex]\frac{24x^5y^9z^{-8}}{10x^{-3}y^4z^{-4}}[/tex]
To simplify the given expression as below :
[tex]\frac{24x^5y^9z^{-8}}{10x^{-3}y^4z^{-4}}[/tex]
[tex]=\frac{12x^5y^9z^{-8}}{5x^{-3}y^4z^{-4}}[/tex]
[tex]=\frac{12x^5y^9z^{-8}x^3y^{-4}z^4}{5}[/tex] ( by using the property [tex]a^{m}=\frac{1}{a^{-m}}[/tex] )
[tex]=\frac{12x^5.x^3.y^9.y^{-4}z^{-8}z^4}{5}[/tex]
[tex]=\frac{12}{5}x^{5+3}.y^{9-4}.z^{-8+4}[/tex] ( by using the property [tex]a^m.a^n=a^{m+n}[/tex] )
[tex]=\frac{12}{5}x^8y^5z^{-4}[/tex]
[tex]=\frac{12x^8y^5}{5z^4}[/tex] ( by using the property [tex]a^{-m}=\frac{1}{a^m}[/tex] )
[tex]\frac{24x^5y^9z^{-8}}{10x^{-3}y^4z^{-4}}=\frac{12x^8y^5}{5z^4}[/tex]
The simplified expression is [tex]\frac{12x^8y^5}{5z^4}[/tex]
Therefore [tex]\frac{24x^5y^9z^{-8}}{10x^{-3}y^4z^{-4}}=\frac{12x^8y^5}{5z^4}[/tex]
Answer:
Therefore,
[tex]\dfrac{24x^{5}y^{9}z^{-8}}{10x^{-3}y^{4}z^{-4}}=\dfrac{12x^{8}y^{5}}{5z^{4}}[/tex]
Step-by-step explanation:
Simplify
[tex]\dfrac{24x^{5}y^{9}z^{-8}}{10x^{-3}y^{4}z^{-4}}[/tex]
Solution:
Using the Identities
[tex]1.\ x^{-a}=\dfrac{1}{x^{a}}[/tex]
[tex]2.\ \dfrac{1}{x^{-a}}=x^{a}[/tex]
[tex]3.\ \dfrac{x^{a}}{x^{b}}=x^{(a-b)}[/tex]
Therefore,
[tex]\dfrac{24x^{5}y^{9}z^{-8}}{10x^{-3}y^{4}z^{-4}}=\dfrac{24x^{(5+3)}y^{(9-4)}z^{(-8+4)}}{10}[/tex]
[tex]\dfrac{24x^{5}y^{9}z^{-8}}{10x^{-3}y^{4}z^{-4}}=\dfrac{2\times 12x^{8}y^{5}z^{-4}}{2\times 5}[/tex]
[tex]\dfrac{24x^{5}y^{9}z^{-8}}{10x^{-3}y^{4}z^{-4}}=\dfrac{12x^{8}y^{5}}{5z^{4}}[/tex]
Therefore,
[tex]\dfrac{24x^{5}y^{9}z^{-8}}{10x^{-3}y^{4}z^{-4}}=\dfrac{12x^{8}y^{5}}{5z^{4}}[/tex]