Based on the product of powers rule, the missing power in the given calculation is 2/3.
The product of powers rule is used in simplifying exponents. In a given term a^x, a number or variable raised to a power is called the base, while the superscript number is called the exponent, or power. According to the rule, if the bases are the same in the multiplication problem, it can be simplified by adding the exponents. Hence, for any number a and all integers m and n:
a^m * a^n = a^(m+n)
The given calculation is:
5^1/3*5^□ = 5
5^1/3*5^□ = 5^1
Hence, the sum of the powers would be one. Let the missing power be x. Therefore,
1/3 + x = 1
x = 1 - 1/3
x = 2/3
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prove Triangle ACE is an isosceles triangle by completing this proof.
Hint: there are 3 parts to this proof!
An isosceles triangle is a type of triangle which has two of its sides to be equal, viz-a-viz two of its internal angles are equal. The required proof in the given question are stated below:
A triangle is a trigon with just three straight sides, thus three internal angles. Thus, the sum of its internal angles equals [tex]180^{o}[/tex]. Some common examples are. equilateral, isosceles, right angled, scalene, etc.
An isosceles triangle is one which has two of its sides equal, so that the measure of two of its internal angles are also equal.
Therefore, the expected proof in the question are:
STATEMENT REASON
1. AB = BC = CD = DE = EA Similar sides of a regular pentagon
2. AB = DE Congruent of sides of similar triangle
3. BC = CD Congruent of sides of similar triangle
4. <ABC = <EDC Congruent angles of similar triangle
5. AC = CE Congruent sides of an isosceles triangle
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Which one is not criteria of congruence * ASA SAS AAS SSA?
Answer:
Step-by-step explanation:
well this makes no sese is there any pics
Eh I don't know ???
Picture should be shown...
Consider the conversion facts 1 inch = 2.54 centimeters and 1 centimeter = 0.39 inch. PLEASE HELP
a. Write an expression for the exact number of inches in 1 centimeter.
b. Use a calculator to evaluate your expression in part (a). Explain why the measurement conversion may be slightly different when converting between metric units and U.S. custumary units.
The expression for the exact number of inches in 1 centimeter is 1/2.54. Using a calculator to evaluate the expression gives 0.39370074. There may be a slight difference when converting due approximation of figures
How to write an expression for the exact number of inches in 1 centimeter?Given the conversion facts:
1 inch = 2.54 centimeters and 1 centimeter = 0.39 inch
a. The expression for the exact number of inches in 1 centimeter will be:
1 centimeter = 1/2.54 (Since 1 inch = 2.54 centimeters)
b. Using a calculator to evaluate the expression in (a) will give:
1 centimeter = 1/2.54 = 0.39370074
The measurement conversion may be slightly different when converting between metric units and U.S. custumary units because of the approximation of figures when converting from one unit to the other
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find the dimensions of the rectangular corral split into 2 pens of the same size producing the greatest possible enclosed area given 300 feet of fencing.
The dimensions of the rectangular corral:
length = 75 ft and width = 5 ft
Let m be the length of the rectangular corral and n be the width of the rectangular corral.
The perimeter of the rectangular corral,
P = 2m + 2n
The rectangular corral split into 2 pens of the same size.
So, P = 2m + 3n
The 2 pens producing the greatest possible enclosed area given 300 feet of fencing.
300 = 2m + 3n
n = (300 - 2m)/3
Area of the rectangular corral,
A = m * n
A(n) = m * (300 - 2m)/3
A(m) = (300/3)*m - (2/3)*m
Taking derivatives on both sides of the equation:
A'(m) = 100 - (4/3)*m
for A'(m) = 0,
100 - (4/3)*m = 0
m = 100 * (3/4)
m = 75
So, n = (300 - 2(75))/3
n = 50
Therefore, the length of the rectangular corral = 75 ft and width = 5 ft
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Inga is solving 2x2 + 12x – 3 = 0. Which steps could she use to solve the quadratic equation? Select three options.
The steps that she could use to solve the quadratic equation is determined as 2(x² + 6x + 9) = 18 + 3.
How to solve the equation by quadratic equation?x ax2 + bx + c = 0 is a quadratic equation, which is a second-order polynomial equation in a single variable. a 0. It has at least one solution because it is a second-order polynomial equation, which is guaranteed by the algebraic fundamental theorem.
The Following is the determination of the quadratic equation's solution;
2x² + 12x - 3 = 0
2x² + 12x = 3
multiply across by two
x² + 6x = ³/₂
Add the two sides of the equation after squarely multiplying the coefficient of x by half.
(x + 3)² = ³/₂ + 3² + 6x + 9 =
9 + ³/₂ (x² + 6x + 9)
= 18 + 3
Thus, the steps that she could use to solve the quadratic equation is determined as 2(x² + 6x + 9) = 18 + 3.
The complete question is : Inga is solving 2x2 + 12x – 3 = 0. Which steps could she use to solve the quadratic equation? Check all that apply.
2(x2 + 6x + 9) = 3 + 18
2(x2 + 6x) = –3
2(x2 + =6x) = 3
x + 3 = 21/2
2(x2 + 6x + 9) = –3 + 9
(x + 3)2 = 6/2
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What is the value of x?
Answer:
x = 1
Step-by-step explanation:
Note that triangle ABC is congruent to triangle DEF by SAS congruency
Thus, using CPCTC, BC - FE
or
: 13x-12 = 7x-6
: 6x = 6
: x = 1
:]
solve pls brainliest
Answer:
c
Step-by-step explanation:
events x and y are independent of each other. if the probability of event x occurring is 1 in 4, and the probability of event y occurring is 1 in 5, the probability of both events occurring is ____.
The probability of both events occurring is 1/20.
What are examples and probability?
A number between 0 and 1 is the probability of an event, where, broadly speaking, 0 denotes the event's impossibility and 1 denotes its certainty.
The likelihood of an event occurring increases as its probability increases. The flip of a fair (impartial) coin serves as a straightforward illustration.
Events X and Y are independent.
The probability of X occurring is 1/4
The probability of Y occurring is 1/5
Since both events are independent, then we have
P(X and Y ) = P(X) * P(Y)
= 1/4 * 1/5
= 1/20
P( X and Y ) = 1/20
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a partially completed chart shows the hierarchy of a set of polygons. what is missing in box 3?
The hierarchy of a group of polygons is depicted in a half finished chart. In box 3, the parallelogram is missing.
Explain about the parallelogram?According to the parallelogram law, the sum of the squares along the four sides of a parallelogram equals the sum of the squares along the two diagonals. The parallelogram must have equal opposed sides in order to be considered a parallelogram in Euclidean geometry. (AC)2 + (BD)2 is equal to 2(AB)2 + 2(BC)2.
No, a parallelogram's angles are not all equal. A parallelogram's opposed angles are equal, and its successive (adjacent) angles are additional, according to two fundamental theorems concerning angles. There are 4 different kinds of parallelograms, including 3 unique kinds. The four types are rhombuses, squares, parallelograms, and rectangles.
one polygon
Quadrilateral two
parallelogram of three
rectangles four rhombus five
Square six
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Answer:
Parallelogram is missing in box 3 of the hierarchy of a group of polygons is depicted in a half finished chart.
Explain about the parallelogram?
The parallelogram law states that the sum of the squares along a parallelogram's four sides equals the sum of the squares along its two diagonals. In Euclidean geometry, the parallelogram must have equal opposite sides in order to be regarded as such. 2(AB)2 + 2(BC)2 is the same as (AC)2 + (BD)2.
No, the angles of a parallelogram are not all equal. Two fundamental theorems of angles state that the opposed angles of a parallelogram are equal and the succeeding (adjacent) angles are additional. Parallelograms come in 4 varieties, including 3 special varieties. Rhombuses, squares, parallelograms, and rectangles are the four types.
one polygon → Quadrilateral two →
parallelogram of three ⇒
( rectangles four) , ( rhombus five) →
Square six
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#46. Find the slope?
Answer:
Step-by-step explanation:
The answer as I believe is H.
I just used the rise/run method, so you’ll go six up and 5 to the left ( the answer is negative because you’re moving to the left).
Hope this helps
How do you solve 2x+7= −17?
Answer:
x = -12
Step-by-step explanation:
How do you solve 2x+7= −17?
2x + 7 = -17
2x = -17 - 7
2x = -24
x = -12
------------
check
2 × (-12) + 7 = -17
-24 + 7 = -17
-17 = -17
The answer is good
In an analysis of variance problem if SST = 120 and SSTR-80, then SSE is
a. 200
b. 40
c. 80
d. 120
The value of SSE (sum squared error) is 40 in the given analysis of the variance problem if SST = 120 and SSR = 80. Option b is correct.
How to find SSE in an analysis of variance problems with the SST and SSR values?Here the words SSE means Sum Squared Error, SST means Sum of Squares Total and SSR means Sum of Square Regression.
In the SSE accuracy measure, errors are squared and then added. It is used when the data points are similar in magnitude.
The formula is SST = SSR + SSE ⇒ SSE = SST - SSR
Calculation:The given values of the analysis of the variance problem are
SST = 120; SSR = 80
Then, the value of SSE = SST - SSR = 120 - 80 = 40
So, option b is correct.
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The coordinates of the vertices of a rectangle are A (5, 3), B (5,-9), C (-1,-9), and D (-1, 3)
72 square units is the area of rectangle when coordinates of the vertices of a rectangle are A (5, 3), B (5,-9), C (-1,-9), and D (-1, 3
What is Area of Rectangle?The area of Rectangle is length times of width.
The coordinates of the vertices of a rectangle are A (5, 3), B (5,-9), C (-1,-9), and D (-1, 3)
The distance from AB
Distance=√(x₂-x₁)²+(y₂-y₁)²
=√(5-5)²+(-9-3)²=√(-12)²=√144=12
The distance from BC
=√(-1-5)²+(-9+9)²=√36=6
Length is 12 units and width is 6 units
Area of rectangle=Length×Width
=12×6
=72 square units
Hence, 72 square units is the area of rectangle when coordinates of the vertices of a rectangle are A (5, 3), B (5,-9), C (-1,-9), and D (-1, 3)
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2(x+ 5) = 3x +1 solve
Answer:
x= 9
Step-by-step explanation:
2(x + 5 ) = 3x + 1
expand the bracket first
2x + 10 = 3x + 1
then collect like terms
2x-3x = 1 - 10
-1x = - 9
and the last step is divide both side by -1
then x = 9
Tristan has $1.40 worth of nickels and dimes. He has twice as many nickels as dimes. Write a system of equations that could be used to determine the number of nickels and the number of dimes that Tristan has. Define the variables that you use to write the system.
The equation will be d(x+2y) = $1.40,where x = cost of dimes , y = cost of nickels, t = number of dimes.
What is an equation?
In mathematics, equation represent two expressions are equal.
e.g. x + 2y = 3,
Here , x + 2y is one expression and 3 is another, which are equated using equal to symbol.
Let's us consider ,
Number of dimes = t
Then number of nickels = 2t
Cost of one dime = x
Cost of one nickel = y
Then the total cost = xt +2yt
And total cost given = $1.40
So, the final equation = t(x+2y) = 1.40
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What is the volume of the sphere 3,3
Answer: r≈0.89
Step-by-step explanation:
I need help, thanks…
Answer:
1st and 4th are the right answers
Step-by-step explanation:
the rule for the sides of a triangle are that two of the side lengths need to be bigger than the third one. Because of this the 1st and 4th are the only ones that meet this expectation.
Avery had $25.27 in her wallet. If she bought lunch with 10.75% dollars from her wallet, how much money did she have in her wallet after lunch?
Answer:
$22.55
Step-by-step explanation:
Not 100% sure but you can double check...
a flight overbooked by 4 passengers
(Write an integer to represent the equation)
The integer the represent a flight overbooked by 4 passengers is y = x + 4
What is Equation Modelling?
Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.
Given,
A flight overbooked by 4 passengers.
Let, x = Initial capacity of the flight to have passengers
and, y = Total capacity after adding all the passengers
so, the equation is
y = x + 4
Therefore, the integer the represent a flight overbooked by 4 passengers is y = x + 4.
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Emma and Jane were playing soccer in their backyard, and Emma kicked the ball to
Jane. The curve of the ball's path can be represented by
d=-16t² + 32t + 9, where d is the distance of the ball from Emma and t is
the time (in seconds). Find how long it takes the ball to reach Jane.
4
It takes 4 seconds for the ball to reach Jane.
It takes 2.25 seconds for the ball to reach Jane.
It could take 2.25 seconds or 0.25 seconds.
It could take 4 seconds or 3.25 seconds.
The number of seconds to reach Jane will be 2.25 seconds. Then the correct option is B.
What is a function?A function is an assertion, concept, or principle that establishes an association between two variables. Functions may be found throughout mathematics and are essential for the development of significant links.
The curve of the ball's path is given below.
d = -16t² + 32t + 9
The number of seconds to reach Jane is given as,
0 = -16t² + 32t + 9
16t² - 32t - 9 = 0
16t² - 36t + 4t - 9 = 0
4t(4t - 9) + 1(4t - 9) = 0
(4t - 9)(4t + 1) = 0
t = 9/4, -1/4
t = 2.25, -0.25
The number of seconds to reach Jane will be 2.25 seconds. Then the correct option is B.
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Arrange the investments in order from the highest risk and return potential to the lowest risk and return potential.
the stock of a large company with a long history of stable returns and dividends
rental real estate in a stable city with average economic growth
a US Treasury bond that matures in 6 months and pays 1.5% interest
the stock of a small company with a wide range of price swings
The arrangement is as follows;
The stock of a small company with wide range of price swing.The stock of a large company with long history of stable returns and dividends .Rental real estate in a sable city with average economic growth US treasury bond that matures in 6 months and pays 1.5% in Teresa.What is stock?
A stock is a colloquial phrase for any company's ownership certificates. On the other hand, a share alludes to a certain company's stock certificate. You become a shareholder if you possess shares of a specific corporation.
The given data about stock and investment can be arranged in order from the highest risk and return potential to the lowest risk and return potential as mentioned above in the answer.
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pollsters are concerned about declining levels of cooperation among persons contacted in surveys. a pollster contacts 77 people in the 18-21 age bracket and finds that 65 of them respond and 12 refuse to respond. when 294 people in the 22-29 age bracket are contacted, 259 respond and 35 refuse to respond. assume that 1 of the 371 people is randomly selected. find the probability of getting someone in the 22-29 age bracket or someone who agreed to respond.
The probability of getting someone in the 22-29 age group to respond or someone who agreed to respond is 259/371
Let X be the event of contacting the 18-21 age group
Let Y be the event of contacting 22-29 age group
Let A be th event that the pollster responded
Let B be the event that they did not respond
Here,
Probability no. of favorable outcomes/total no. of outcomes/
Hence,
n(A) = 65 + 259
= 324
P(A) = 324/371
Similarly, P(Y) = 294/371
Now,
P(A∩Y) = 259/371
We know that P(C ∪ D) = P(C) + P(D) - P(C∩D)
Therefore, P(A∪Y) = P(A) + P(Y) - P(A ∩ Y)
= 324/371 + 294/371 - 259/371
= 359/371
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two less than the product of a number and three
Evaluate when f = 4.5.
A 2-column table with 5 rows. Column 1 is labeled Key Words with entries two, less than, product, a number, three. Column 2 is labeled Replace with entries 2, minus, times, f, 3.
Write and evaluate the expression shown on the left. Then, check all that apply.
Write the expression as 2 – 3f.
Write the expression as 3f – 2.
Write the expression as 2f – 3.
The value when f = 4.5 is 6.75.
The value when f = 4.5 is 6.
The value when f = 4.5 is 11.5.
The expression as 3f – 2.
The value when f = 4.5 is 11.5.
How to illustrate the equation?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
Two less than the product of a number and three will be:
(3 × f) - 2
= 3f - 2
When f = 4.5
(3 × 4.5) - 2
= 11.5
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Jacob makes lemonade to sell at a carnival. He makes 20 cups of lemonade in 120 minutes. Working at this rate, how many cups of lemonade can Jacob make in 1 hour?
Answer:
10 cups
Step-by-step explanation:
120minutes divided into 60minutes = 2 hours
20 divided by 2 = 10 cups
a contractor is considering a sale that promises a profit of 240000.0 dollars with a probability of 0.76 or a loss (due to bad weather, strikes, and such) of 20000.0 with a probability of 0.24. what is the expected profit?
The expected profit that the contractor will earn from the sale is equal to $177600.
Whenever a contactor does sale of a certain commodities, he expects that whatever he does he earns a profit from the sales. Profit is earned when the selling price of the commodity is more than the price at which the commodity was brought by the contractor.
The expected profit from the sale is calculated as the sum of the profits multiplied by their respective probabilities. In this case, the expected profit is given by:
Expected profit = (240000.0 * 0.76) + (-20000.0 * 0.24) = 182400.0 + (-4800.0) = $177,600
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a _______ is a single value used to approximate a population parameter. : a. critical valueb. margin of errorc. confidence intervald. point estimate
A single value that is used to approximate a population parameter is a point estimate (D).
What exactly is a point estimate?A point estimate is frequently in the form of the mean or a proportion calculated from a sample. It can be used to estimate a population parameter. In a random sample of a population, a point estimate is used to discover an approximate value of a population parameter.
In conclusion, the answer is D.
Meanwhile, the margin of error is part of the confidence interval. It is calculated by multiplying the critical value by the sample proportion's standard deviation. Then, a confidence interval in the population denotes a range within which the point estimate value is expected to decrease by a specific percentage. Last, the critical value is contrasted to the acquired statistical test in hypothesis testing to decide whether or not the null hypothesis must be rejected.
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what is the relationship between the variance and the standard deviation? a) variance is twice the standard deviation. b) variance is the square root of the standard deviation. c) there is no constant relationship between the variance and the standard deviation. d) variance is the square of the standard deviation.
The relationship between the variance and standard deviation is: option a)The standard deviation is the square root of the variance.
What is variance?The variance of a random variable from its true population or sample mean is expected in probability theory and statistics. The term "variance" refers to a measurement of how widely apart a group of numbers are from one another.
Here,
Variance and standard deviation are both measures of spread. They calculate the deviation of each data point from the mean. The range of data increases with increasing variation. Using the original unit of measurement, the standard deviation measures the same thing as the variance (whereas variance is the original unit squared).
Therefore ,The relationship between the variance and standard deviation is: option a)The standard deviation is the square root of the variance.
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How many inches is there in 1/8th of a yard?
Answer:
4.5
Step-by-step explanation:
You calculate it. look 1 yard is 36 inches. so 1/8 of a yard is 36 divided by 8. 4.5!
The total distance d, in meters, traveled by an object moving in a straight line can be modeled by a quadratic function that is defined in terms of t, where t is the time in seconds. At a time of 10.0 seconds, the total distance traveled by the object is 50.0 meters, and at a time of 20.0 seconds, the total distance traveled by the object is 200.0 meters. If the object was at a distance of 0 meters when t=0 then what is the total distance traveled, in meters, by the object after 30.0 seconds?
The total distance traveled by the object after 30.0 seconds is 450 meters.
Explain the term quadratic function?f(x) = ax2 + bx + c, for which a, b, and c represent constants and a = 0 represents a quadratic function. The function is known as the quadratic term (abbreviated as ax2), the linear term (abbreviated as bx), and the constant term (abbreviated as c).For the stated function;
Time = 10.0 seconds, distance = 50.0 meters.Time = 20.0 seconds, distance = 200.0 meters.Time = 0.0 seconds, distance = 0.0 meters.As, the total distance is modelled by the quadratic equation-
Let the quadratic equation be-
d = at² + bt + c
For (10, 50)
d = a(10)² + (10)b + c ....eq 1
For (20, 200)
d = a(20)² + (200)b + c ....eq 2
For (0, 0)
d = a(0)² + (0)b + c ....eq 3
Solving eq 1, 2 and 3
a = 1/2 ; b = 0 and c =0
Thus, equation for the distance travelled by the object is-
d = 1/2 t²
For t = 30. sec
d = 1/2 (30)²
d = 450 m
Thus, the total distance traveled by the object after 30.0 seconds is 450 meters.
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suppose that a person with seven friends invites a different subset of three friends to dinner every night for one week (seven days). how many ways can this be done so that all friends are included at least once?
We need to select different combinations of friends for a week and include every friend at least once. The possible number of ways is 72.
What do you mean by Combination?Combinations are mathematical operations that count the number of potential configurations for a set of elements when the order of the selection is irrelevant.
What is the formula to calculate Combination?The formula for combination is as follows:
[tex]C(n,r) = \frac {n!}{r!(n-r)!}[/tex]
Number of for first 5 days = C(7,3)+C(6,3)+C(5,3)+C(4,3)+C(3,3)
=70
2 friends are remaining for last two days and we can assign them in any group of 3.
Total number of ways = 70 +2
=72
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