The exponents are;
1) x^7/4
2) 2^1/12
3) 81y^8z^20
4) 200x^5y^18
What are exponents?
Exponents, sometimes referred to as powers or indices, are a type of mathematical notation used to indicate the size of a number raised to a specific power or the repeated multiplication of a number by itself. They serve as a condensed form of repeated multiplication.
We can see that;
1) 4√x^3 . x
x^3/4 * x
= x^7/4
2) 3√2 ÷ 4√2
2^1/3 -2^1/4
2^1/12
3) (3y^2z^5)^4
81y^8z^20
4) (5xy^3)^2 . (2xy^4)^3
25x^2y^6 . 8x^3y^12
200x^5y^18
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true or false and explain or show your reasoning
10-⁵=-10⁵
(10²)-³=(10²)³
10³/10¹⁴=10-¹¹
Answer:
a. False : because 10^-5= 1/10^5 where as -10^5=-1 × 10^5
therefore 1/10^5 not equal to -1×10^5
b. False : because (10^2)^-3 = 100^-3=1/100^3 where as (10^2)^3 = 100^3=1000000 there fore 1/100^3 not equal to 1000000
c. True : because 10^3/10^14=10^(3-14)=10^-11 therefore both left side and right side of the equation are equal
What is the volume of this shape
Answer:
volume = 684π m³ or 2148.85 m³
Step-by-step explanation:
volume = (π6² x 11) + (4/3π6³) = 396π + 288π = 684π m³ or 2148.85 m³
If 15 people start a race, in how many different ways can the top 3 finishers be determined?
Hence, 15 people out of 3 people can be chosen in 35 ways.
Combinations:It is a method that helps us to determine the number of possible ways an item can be chosen given that the order of selection does not matter. Hence we are free to select the items in any order.Combinations are often confused with permutations. Permutations are the number of ways the given items can be arranged. Here the order is important.The formula for combinations:If we have 'n' items and we are required to choose 'r' items, the number of ways in which it can be done is calculated as:\(^{n}C_{r} }\) = \(\frac{n!}{(n-r)!r!}\)It is given that:
The total number of people in a race, n = 15
The number of finalists, r = 3.
Hence, the number of ways in which 3 people out of the 15 people can be finishers are:
\(^{15}C_{3} }\) = \(\frac{15!}{(15-3)!3!}\) = \(\frac{15!}{12!3!}\) = 35.
Hence, 15 people out of 3 people can be chosen in 35 ways.
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Which of the following would be the quickest and cheapest way to develop a global strategy? A. fully-owned subsidiaries B. greenfield investments C. strategic alliances D. acquisitions
Considering the factors of time and cost, strategic alliances generally emerge as the quickest and cheapest way to develop a global strategy. (option c)
Strategic alliances involve partnerships or collaborations between companies from different countries, with the goal of leveraging each other's strengths to achieve mutual benefits.
By sharing resources, knowledge, and networks, companies can expand their global presence more efficiently and cost-effectively. Strategic alliances can enable faster market entry and access to new markets by leveraging the partner's existing infrastructure, distribution channels, and customer base.
Moreover, pooling resources can help reduce costs and risks associated with global expansion.
Therefore, strategic alliances can be a relatively quicker and cheaper way to develop a global strategy, as they provide an opportunity to tap into existing capabilities and market presence of the alliance partner.
Hence the correct option is (c).
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Mitch opens up a bank account with an initial deposit of $100. Additionally, each month John adds a fixed
amount of money to his bank account. If after 10 months John has a total of $250 in his bank account, how
much has he been adding to his bank account each month?
The amount that Mitch been adding to his bank account is $15
How much has Mitch been adding to his bank account?An equation is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenario.
In this case, let the amount each month be x
Since Mitch opens up a bank account with an initial deposit of $100. Additionally, each month John adds a fixed amount of money to his bank account. This will be:
100 + 10(x) = 250
100 + 10x = 250
Collect like terms
10x = 250 - 100
10x = 150
Divide
x = 150/10
x = 15
The amount is $15.
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b) Find the value of 2a2 + 5b2 when a = -6 and b = 2
Answer:
-4
Step-by-step explanation:
2a2+5a2
2(-6)2=-24
5(2)2=20
-24+20=-4
Answer: -4
Step-by-step explanation:
(2x-6×2)(5×2×2)
-24+20
-4
Roger is replacing the liner of a chimney. The length of the liner required is 33 ft. Roger has 400 inches of stainless steel pipe for the liner. Is this enough? Justify your answer.
Roger has enough stainless steel pipe to replace the chimney liner, with a slight surplus remaining.
To determine if Roger has enough stainless steel pipe for the chimney liner, we need to convert the given measurements to a consistent unit of measurement. Since the length of the liner required is given in feet, we need to convert the 400 inches of stainless steel pipe to feet.
There are 12 inches in a foot, so 400 inches is equal to 400/12 = 33.33 feet (approximately).
Comparing this converted length of the stainless steel pipe (33.33 feet) with the length of the liner required (33 feet), we can see that Roger does indeed have enough pipe. In fact, he has slightly more than required.
Since the length of the liner required is 33 feet and Roger has 33.33 feet of stainless steel pipe available, there is a surplus of approximately 0.33 feet (about 4 inches) of pipe. This additional length is more than enough to cover any potential measurement errors or adjustments needed during the installation process.
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Find the slope of the line that passes through each pair of points
Answer:
Slope of 2
Step-by-step explanation:
First thing is to look at the change in x and y from the points. You can do this by subtracting the x valie from the other value and the same for the y values. So you would do 2-0=2.
So we know the change in x between the points, so now we find the change in y. 5-1=4.
Now that we know the change in x and y, we use the expression below to solve for the slope.
\( \frac{rise}{run} \: or \: \frac{y}{x} \)
We can insert what we found and then solve for the equation
\( \frac{4}{2} \)
So we solve for that, which is 2. Now we know the slope is 2.
Answer:
given us,
(x1y1)= (2,5)
(x2y2)= (0,1)
here,
(y-y1)= (y2-y1)/ (x2-x1)× (x-x1)
or, (y-5)=(1-5)/(0-2)× (x-2)
or, y-5= -4/-2 ×(x-2)
or,y-5= 2(x-2)
or, y-5/ x-2= 2
or,y-5= 2x-4
or, 2x-y= -4+5
:. 2x-y= 1
Step-by-step explanation:
2x-y= 1
If you use a batch of cake batter for cupcakes and bake them for the time suggested for baking a cake, what will be the result
Baking cupcakes for the time suggested for baking a cake may result in overbaked and dry cupcakes.
This is because cupcakes are smaller and have less volume than cakes, so they require less baking time to cook through. Overbaking can also cause cupcakes to lose their moisture and become tough. It is important to follow the suggested baking time for cupcakes to achieve the desired texture and flavor.
To ensure that cupcakes are baked correctly, it is recommended to test them for doneness using a toothpick or cake tester. Insert the toothpick in the center of the cupcake, and if it comes out clean, the cupcakes are done.
If the toothpick has batter on it, the cupcakes need more time to bake. Adjust the baking time accordingly, and continue checking until the toothpick comes out clean.
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George Garcia wants to purchase a used station wagon. One
used-vehicle guide shows the average retail value of the station
wagon at $13,000. Add $50 for having tinted windows, $100 for
air-conditioning, and $35 for power windows. Deduct $200 for
excessive mileage. What is the average retail price for the
station wagon?
The averages retail price for the station wagon will be $12985.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that one used-vehicle guide shows the average retail value of the station wagon at $13,000. Add $50 for having tinted windows, $100 for air-conditioning, and $35 for power windows. Deduct $200 for excessive mileage.
The average price will be calculated as,
Price = 13000 + 50 + 100 + 35 - 200
Price = 13185 - 200
Price = $12985
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Stuck on this question
Answer:
ABD =30 +45
ABD=75
75°is the answer
a student takes an exam containing 13 true or false questions. if a student randomly guesses on the entire exam, what is the standard deviation of the number of incorrect answers? round your answer to two decimal places.
The standard deviation of the number of incorrect answers is approximately 1.28.
Let X be the number of incorrect answers on the exam. Since each question is a true or false question, the probability of guessing correctly is 0.5 and the probability of guessing incorrectly is also 0.5.
The expected value of X is given by:
E(X) = np = 13(0.5) = 6.5
The variance of X is given by:
Var(X) = np(1-p) = 13(0.5)(0.5) = 1.625
The standard deviation of X is the square root of the variance:
SD(X) = sqrt(Var(X)) = sqrt(1.625) ≈ 1.2
Therefore, the standard deviation of the number of incorrect answers is approximately 1.28.
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HELP ASAP !!!!
Write and graph linear equations
Answer:
first graph the y-intercept start at 0 and go up 2 plot that. Then, go up 7 from 2 and to the right 1
Step-by-step explanation:
what is the quotient of the expression
\( \frac{21a {}^{3} b - 14ab {}^{2} + 7ab}{7ab} \)
The length of a picture frame is inches more than the width. For what values of x is the perimeter of the picture frame greater than inches?
9514 1404 393
Answer:
x > 35
Step-by-step explanation:
The perimeter is twice the sum of length and width. You want x such that ...
P > 156
2(x +(x+8)) > 156
4x +16 > 156 . . . . . simplify
x +4 > 39 . . . . . . . . divide by 4
x > 35 . . . . . . . . . . . subtract 4
The perimeter of the frame will be greater than 156 inches for x > 35.
A hyperbola has its foci at (1, 7) and (1, –13). A directrix of the hyperbola is y = 16/5. What is the equation of the hyperbola?
Which criteria can be used to prove triangles are congruent select all that apply?
The four criteria that can be used to prove triangles are congruent and can be used to prove the triangles are congruent.
Triangle congruence: Two triangles are said to be congruent if all three of their corresponding sides and all three of their corresponding angles have the same measurements. These triangles can be moved around, rotated, flipped, and turned to have a same appearance. They match up with one another when moved.
The four criteria that can be used to prove triangles are congruent are SAS (Side-Angle-Side), ASA (Angle-Side-Angle), AAS (Angle-Angle-Side), and SSS (Side-Side-Side). Additionally, CPCTC (Corresponding Parts of Congruent Triangles are Congruent) can be used to prove the triangles are congruent.
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Solve 3x2−3x=0 by factoring.
Answer:
3x(x-1) = 0
x= 1
Step-by-step explanation:
is 3x2 supposed to mean 3x^2 i dont know
Two points on the circumference of a circle of radius $r$ are selected independently and at random. From each point a chord of length $r$ is drawn in a clockwise direction. What is the probability that the two chords intersect?
$\textbf{(A)}\ \frac{1}{6}\qquad\textbf{(B)}\ \frac{1}{5}\qquad\textbf{(C)}\ \frac{1}{4}\qquad\textbf{(D)}\ \frac{1}{3}\qquad\textbf{(E)}\ \frac{1}{2}$
If two points are drawn in a clockwise direction, the probability that the two chords intersect is 1/3.
Option D is the correct answer.
We have,
Imagine having a circle with a point A marked inside it.
Now, draw a chord (a straight line segment) starting from point A, going in a clockwise direction until it reaches the circle again.
Now,
Draw a chord from point B in a clockwise direction.
To find the probability, we first need to consider how far apart points A and B can be for their chords to intersect.
Let's call this distance "r."
If A and B are more than r units apart, their chords won't intersect.
To understand where point B can be located, imagine the perimeter of the circle as a whole circle divided into 360 equal parts.
(since there are 360 degrees in a circle).
Now, focus on the clockwise chord from point A.
It spans an arc or a portion of the circle.
If we divide the circle into 360 parts, the chord from point A covers 120 of those parts.
= 360 * 1/3
= 120
Since the chord from point A covers 120 parts out of 360, we can say that point B can be located in those 120 parts (or 120/360 of the perimeter) in order for the chords to intersect.
Now,
The probability that the two chords intersect.
= 120/360
= 1/3
Thus,
The probability that the two chords intersect is 1/3.
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In the given diagram, the points A, B, and C lie on a circle whose center is O. BOC is a diameter of the circle.
The following set of premises is relevant to the investigation of the given geometric diagram:
I. The radii of a circle are of equal length.
II. Angles opposite to equal sides of a triangle are equal.
III. The sum of the angles of a triangle is 180°.
With reference to the diagram, which conclusion can be drawn correctly from the premises?
Answer:
m∠BAC = 90°
Option B
Step-by-step explanation:
From premise 1 we get AO = AC and AO = OB
From premise 1 and 2 we get
m∠OAC = m∠OCA = x say and
m∠OAB = m∠OBA = y say
But m∠OCA = m∠ACB =x
m∠OBC = m∠ABC = y
From all three premises we get in triangle ABC:
m∠BAC + m∠ABC+ m∠ACB = 180
Knowing
m∠BAC = m∠OAC + m∠OAB = x + y
m∠ACB = x
m∠ABC = y
So we get
(x + y) + x + y = 180
2x + 2y = 180
x + y = 180/2 = 90°
Since x + y = m∠BAC,
m∠BAC = 90°
solve by factoring 2x^2 + 10x - 28 = 0
Answer:
x = 2, x = -7
Step-by-step explanation:
Hello!
First, let's factor the equation by grouping.
Factor2x² + 10x - 28 = 02(x² + 5x - 14) = 02(x² + 7x - 2x - 14) = 02(x(x + 7) - 2(x + 7)) = 02(x - 2)(x + 7) = 0Set each factor with x equal to 0, and solve for x.
(x - 2) = 0The solutions for x are 2 and -7.
The average weight of an adult one horned male rhinoceros found in Nepal is about 21 quintal.
The average weight of an adult one-horned male rhinoceros found in Nepal is about 21 quintals. The scientific name for the one-horned rhinoceros is Rhinoceros unicorn is.
One-horned rhinoceroses are found in India, Nepal, Bhutan, and Indonesia. The one-horned rhinoceros is the largest animal in Nepal.
It can weigh up to 2,300 kg. Its body is covered in skin that looks like plates of armor. The one-horned rhinoceros is a herbivore, meaning it eats only plants.
They live in swamps, marshes, and forested areas near rivers, and they are excellent swimmers.
The one-horned rhinoceros has been endangered for many years due to poaching, habitat loss, and hunting.
The numbers of these animals have been increasing due to conservation efforts and strict laws in Nepal. The average weight of an adult one-horned male rhinoceros found in Nepal is about 21 quintals.
They are a protected species in Nepal, and there are several parks and conservation areas where they can be seen.
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Here is the complete question below:
The average weight of an adult one-horned male rhinoceros found in Nepal is about 21 quintal. Can you provide more information about the size, habitat, or any other relevant details regarding these rhinoceroses?
Simplify 6(x + 3). i suck at math pls help
Answer:
6x +18
Step-by-step explanation:
6(x + 3)
Distribute
6*x + 6*3
6x +18
Answer:
6x + 18
Step-by-step explanation:
Given
6(x + 3) ← multiply each term in the parenthesis by 6
= 6x + 18
QUICKK
Solve systems by substitution Find the solution
SHOW ALL WORK
Y = 2
3x + 4y = 20
( , )
Write the following as an algebraic expression. Simplify if possible.
Add 8y − 6 to 2y + 3.
The answer is ____.
Answer: 10y - 3
Step-by-step explanation:
We just add the "+" sign between the two.
So we get:
8y - 6 + 2y + 3
The y terms are like, so we do :
(8y + 2y) - 6 + 3
Which is:
10y - 6 + 3
The integers are like (common), so we do:
10y (-6 + 3)
Which is :
10y - 3
It is - 3 because -6 + 3 = -3, and we also add the "-" with the integer
So our final answer is=
10y - 3
Make my answer the brainliest!
Determine if the two triangles are congruent. If they are, state how you know.
Answer:
hl
Step-by-step explanation:
hl is the hypotenuse and leg of a right triangle
triangle jkl with vertices j (1,-1) k(2,3) and l(3,2): in graphing
The reflection of the triangle JKL across the line x = 4 is equivalent to flipping the preimage across the line x = 4.
The correct coordinates are;
⇒ J' = (7, - 1)
⇒ K' = (6, 3)
⇒ L' = (5, - 2)
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Here, The given transformation is a reflection about the line x = 4
And, The points of triangle JKL are J(1, -1), K(2, 3), and L(3, -2), in the line x = 4
We know that;
The coordinates of the triangle JKL following a reflection across the line x = 4, have the same y-coordinates , while the x-coordinates have the same distance magnitude to the line x = 4, but opposite sign.
Hence, Distance between x-coordinate of the point J and the line x = 4 is 4 - 1 = 3
Which gives;
Distance between x-coordinate of the point J' and the line x = 4 is 4 + 3 = 7
Therefore, the coordinate of the point J' is (7, - 1)
Similarly, we have;
Distance between x-coordinate of the point K and the line x = 4 is
4 - 2 = 2
Distance between x-coordinate of the point K' and the line x = 4 is
4 + 2 = 6
Hence, The coordinate of the point K' is (6, 3)
And, Distance between x-coordinate of the point L and the line x = 4 is
4 - 2 = 2
Distance between x-coordinate of the point L' and the line x = 4 is
4 + 2 = 6
Hence, The coordinate of the point L' is (5, - 2)
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b) If the joint probability distribution of three discrete random variables X, Y, and Z is given by, f(x, y, z)=. (x+y)z 63 for x = 1,2; y=1,2,3; z = 1,2 find P(X=2, Y + Z ≤3).
The probability P(X=2, Y+Z ≤ 3) is 13. Random variables are variables in probability theory that represent the outcomes of a random experiment or event.
To find the probability P(X=2, Y+Z ≤ 3), we need to sum up the joint probabilities of all possible combinations of X=2, Y, and Z that satisfy the condition Y+Z ≤ 3.
Step 1: List all the possible combinations of X=2, Y, and Z that satisfy Y+Z ≤ 3:
X=2, Y=1, Z=1
X=2, Y=1, Z=2
X=2, Y=2, Z=1
Step 2: Calculate the joint probability for each combination:
For X=2, Y=1, Z=1:
f(2, 1, 1) = (2+1) * 1 = 3
For X=2, Y=1, Z=2:
f(2, 1, 2) = (2+1) * 2 = 6
For X=2, Y=2, Z=1:
f(2, 2, 1) = (2+2) * 1 = 4
Step 3: Sum up the joint probabilities:
P(X=2, Y+Z ≤ 3) = f(2, 1, 1) + f(2, 1, 2) + f(2, 2, 1) = 3 + 6 + 4 = 13
They assign numerical values to the possible outcomes of an experiment, allowing us to analyze and quantify the probabilities associated with different outcomes.
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The distance from home plate to the center field fence on the baseball field at Bruce's school is 370 feet. Which golf club (or clubs) could Bruce use to hit a golf ball over the center field fence from home plate? Use the table in part a to answer this question.
The required golf clubs would be those with a feet distance beyond 370 feets. Hence, the golf clubs include :
5 iron, 3 iron, 3 wood and Driver.The distance between home field and center field at Bruce's school is 370 feets.
Therefore, the required golf clubs are those whose distance exceeds 370 feets. Hence, all the golf clubs excluding 9 iron and 7 iron golf clubs.
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Answer:
Bruce could hit a golf ball over the center field fence from home plate using the 5 iron, the 3 iron, the 3 wood, and the driver.
Which value of y would make O P is parallel to L N?
16
24
32
36
Answer:
D. 36 units
Step-by-step explanation:
credit to user calculista