Select the simplification that accurately explains the following statement. √9=9 1/2
Answers
The simplification that explains the statement is [tex](9^{\frac{1}{2} })^{2} = (9^{\frac{1}{2} } )(9^{\frac{1}{2} } ) = 9^{\frac{1}{2} + \frac{1}{2} } = 9^{\frac{2}{2} } = 9^{1} = 9[/tex]
How to simplify an expression?The law of indices(exponent) can be used to explain the following statement:
[tex]\sqrt{9} = 9^{\frac{1}{2} }[/tex]
Therefore, using the law of indices.
[tex](a^{x}) (a^{y} ) = a^{x+y}[/tex]
Hence, applying this law of exponents.
Exponents of numbers are added when the numbers are multiplied, subtracted when the numbers are divided, and multiplied when raised by still another exponent:
[tex](9^{\frac{1}{2} })^{2}[/tex]
[tex](9^{\frac{1}{2} } )(9^{\frac{1}{2} } )[/tex]
[tex]9^{\frac{1}{2} + \frac{1}{2} }[/tex]
[tex]9^{1}[/tex]
9
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Related Questions
Mia buys a t-shirt online for $15.. If shipping and
handling are an additional 30% of the price, how
much shipping and handling will Mia pay?
Answers
Mia will pay a total of $4.5 for the shipping and handling of the t-shirt
How to determine the shipping and handling price?From the question, we have the following parameters that can be used in our computation:
Cost of the shirt = $15
shipping and handling = 30%
The amount paid for the shipping and handling of the t-shirt can be calculated using the following equation
Amount paid = original price * + shipping and handling
Substitute the known values in the above equation, so, we have the following representation
Amount paid = 15 * 30%
Evaluate the products
Amount paid = 4.5
Hence, the amount paid is $4.5
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The probability that a marksman will hit a target each time he shoots is 0. 89. If he fires 15 times, what is the probability that he hits the target at most 13 times?.
Answers
The probability that marksman will hits the target at most 13 times is 27.92%.
Explain the term binomial distribution?Let X be the quantity of times that target is hit and be a random variable. 15 rounds are fired, hence the number of trials ("n") is equal to 10 as a result. In a binomial distribution, "p" denotes the likelihood of success, and "q" is the likelihood of failure (where q = 1 - p). Since there is a 0.89 chance of striking the target, p = 0.89 and q = 0.11.The number of successes ("x") is the probability mass function for such binomial distribution.
P(X = x) = ⁿCₓ . pˣ . qⁿ⁻ˣ
We are interested in the likelihood that the target will be struck exactly five times, therefore the desired number of successes is five (i.e., x = 13).
P(X = 13) = ¹⁵C₁₃. (0.89)¹³ (0.11)²
P(X = 13) = 0.2792
P(X = 13) = 27.92%
Thus, the probability that marksman will hits the target at most 13 times is 27.92%.
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Sort the following polygons in order of increasing area.
Answers
The area of the polygons arranged in order of increasing Area is:
Rectangle = 4Triangle = 12Square = 13What is a polygon?A polygon is a planar figure characterized by a limited number of straight line segments joined to create a closed polygonal chain in geometry. A polygon is defined as a bounded planar region, a bounding circuit, or both. A polygonal circuit's segments are known as its edges or sides.
The area of the triangle is given as:
[Ax(By - Cy) + Bx(Cy - Ay) + Cx(Ay - By)]/2
Where Ax and Ay are the x and y coordinates for the vertex of A. The same applies for the x and y notations of the B and C vertices.
Hence given:
A(-4-3), B(1, -3), C(-1,2)
we have
[-4(-3-2) + (1(2-(-3)) + (-1(-2-(-3))]/2
= 24/2
= 12
Hence the area of the triangle is 12.
To calculate the area of the rectangle, we use the distance formula. The equation for this is given as:
d² = (x₂ - x₁)² + (y₂-y₁)²
Where (x₁, x₂) are the coordinates of the first point and
(y₁, y₂) are the coordinates of the second point.
Assuming that the vertices are labeled as follows:
A (7,9), B(6,9), C(6,5), D(7,5), then
AB² = (6-7)² + (9-9)²
AB² = 1 + 0
AB = 1
BC² = (6-6)² + (5-9)²
BC² = 0² + -4²
BC = 4
CD² = (7-6)² +(5-5)²
CD² = 1² + 0²
CD = 1
DA² = (7-7)² + (9-5)²
DA² = 0² +4²
DA = 4
From the above, we can tell as is typical of a rectangle, that AB = CDand BC = DA
Since the Area of the rectangle is AB x CD OR BC x DA
The area of the rectangle =
4 x 1 = 4
Using the distance methods we can also arrive at the length of the sides of the square.
Since the area of a square is given as L² we only need the lenght one one side.
Hence,
AB = 3.60555
Hence the area of the square =
3.60555²
= 12.9999908025
Area of the square [tex]\approx[/tex] 13.
Thus the polygons arranged in order of increasing area are:
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Paula bought a ski jacket on sale for $6 less than a quarter of the original price. She paid $45 for the jacket.
Write an equation that can be used to find the original price of the jacket, then solve you equation to find the
answer.
Answers
Answer:
let price of jacket be xx-6$=$45 as equationx-6$=$45x=45$+$6x=$51 therefore original price of jacket is $51the wall thickness of 21 randomly selected glass 2-liter bottles was measured by a quality-control engineer. the wall thickness of those glass 2-liter bottles follows a normally distribution with unknown variance. the sample mean and the sample standard deviation of those 21 selected bottales was found to 4.15 millimeters and 0.09 millimeter, respectively. which of the following is the correct 90% two-sided confidence interval for the mean wall thickness?
Answers
The 90 % Prediction interval on the wall thickness of next bottle tested is (4.41, 4.99).
What is meant by Prediction Interval?A prediction interval is a form of confidence interval (CI) used with regression analysis predictions; it is a range of values that forecasts the value of a new observation based on your existing model.
Confidence intervals and predictions are frequently used interchangeably. They are not exactly the same thing, though.
A confidence interval is a set of values connected to a population parameter. the population's mean, as an illustration.
Where you anticipate an upcoming number to fall is called a prediction interval.
The Interval Uncertainties
It doesn't imply that you can forecast with confidence where a single number will fall, just like with most things in statistics.
Confidence intervals are usually accompanied with a confidence level, which represents the amount of uncertainty.
How to solve?
X=4.7
s=0.7
n=25
The tabulated value of t at 24 degree of freedom is 2.06
t24=2.064
The 90 % Prediction interval on the wall thickness of next bottle tested is given by:
=(4.7±t24×0.7√25)
=(4.7−2.064×0.75,4.7+2.064×0.75)
=(4.7−0.28896,4.7+0.28896)
=(4.41,4.99)
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The approximate distance from Earth to the moon is 240 thousand miles. The approximate distance from Earth to the sun is 93 million miles. In standard notation, the approximate distance from the sun to Earth is miles greater than the approximate distance from Earth to the moon. In scientific notation, the distance is m × 10n, where m is and n is
Answers
The approximate distance from the sun to Earth is miles greater than the approximate distance from Earth to the moon by 9.276 × 10^7.
What is the scientific notation?Scientific notation is a method of displaying very large or very small numbers in a more simplified format. We know that entire numbers can be extended indefinitely, but such large numbers cannot be written on a piece of paper. Furthermore, the numbers in the millions place after the decimal required to be represented in a simpler format.
In this case, the approximate distance from Earth to the moon is 240 thousand miles. This will be 2.4 × 10^5
The approximate distance from Earth to the sun is 93 million miles. This will be:
= 9.3 × 10^7
The difference will be:
= (9.3 × 10^7) - (2.4 × 10^5)
= 9.276 × 10^7
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11 black balls and 14 white balls are placed in an urn. two balls are then drawn in succession. what is the probability that the second ball drawn is a white ball if the second ball is drawn without replacing the first ball? a) 0.2333 b) 0.5376 c) 0.5600 d) 0.2567 e) 0.3033 f) none of the above.
Answers
The probability for the given condition is, 0.56.
What is probability?
The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.
Given:
11 black balls and 14 white balls are placed in an urn. two balls are then drawn in succession.
We have to find the probability that the second ball drawn is a white ball if the second ball is drawn without replacing the first ball.
P(white ball) = 14 / (11 + 14) = 14 / 25
P(2nd ball is white) = P(first ball is white)*P(2nd ball is white) + P(first ball is black)*P(2nd ball is white)
= (14 / 25) * (13 / 24) + (11 / 25) * (14 / 24)
=0.56
Hence, the probability for the given condition is, 0.56.
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what is the difference between a convex set and a convex function with respect to linear programming?
Answers
A linear problem is always convex, because anything linear is convex.
What is linear programming?
A mathematical model whose requirements are expressed by linear connections can be optimized using a technique known as linear programming. A particular type of mathematical programming is linear programming.
A convex function is a real-valued function defined on an interval with the property that its epigraph (the set of points on or above the graph of the function) is a convex set. Convex minimization is a subfield of optimization that studies the problem of minimizing convex functions over convex sets.
Every linear function has a concave shape. However, only convex polygons (possible sets of linear programs) exist.
A linear problem is always convex, because anything linear is convex.
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when conducting a one-way independent anova with three levels on the independent variable, an f-ratio that is large enough to be statistically significant tells us:
Answers
One or more of the mean differences are statistically significant, but not the precise location of the group differences.
In mathematical modeling, statistical modeling, and experimental sciences, there are dependent and independent variables. A variable that is independent is precisely what it sounds like. It is a stand-alone variable that is unaffected by the other variables you are attempting to assess. Age, for instance, might be an independent variable.
Dependent variables are so-called because, during an experiment, their values are examined on the assumption or presumption that they are governed by the values of other variables.
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The area of a rectangle is given by 2x-x-7x+9x+6cm
Answers
Answer: =3x+6
Step-by-step explanation:
1. Which method would be the simplest way to solve the system?
7x + 5y = 19
-7x - 2y = -16
Ographing
substitution
elimination
Odistributive
(1 point)
Answers
Answer: a
Step-by-step explanation:
a magazine provided results from a poll of adults who were asked to identify their favorite pie. among the respondents, % chose chocolate pie, and the margin of error was given as percentage points. given specific sample data, which confidence interval is wider: the % confidence interval or the % confidence interval? why is it wider?
Answers
To be more certain that it captures the true value of the population proportion, a 95 % confidence interval must be larger than an 80 % confidence interval.
What is confidence interval?An area created using fixed-size samples of data from a population (sample space) that follows a certain probability distribution is known as a confidence interval. A selected population statistic is built into the interval with a specified probability. An estimate's level of uncertainty is described by a confidence interval, which is a range of numbers. You have a 5% probability of being incorrect with a 95% confidence interval. You have a 10% chance of being incorrect with a 90% confidence interval. A 95% confidence interval is narrower than a 99% confidence interval.
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if the expression $(12-x)\div(3x)$ represents a non-negative integer, what is the largest possible integer value of $x$?
Answers
The largest possible value of the expression (12 - x)/3x is 3.
Expression
In algebra, expression is the combination of variables, numbers and constants.
Given,
Here we have the expression (12 - x)/3x.
Now we have to find the largest possible integer value.
As we have given in the question that the x takes only the non negative integer, then the values must be 1, 2, 3, ….
So, we have to apply the values on the given expression ,
Then we get the values,
=> x = 1 = > (12 - 1)/3(1) = 11/3 = 3.6
=> x = 2 => (12 - 2) / 3(2) = 10/6 = 1.6
=> x = 3 => (12 - 3) / 3(3) = 9/9 = 1
Therefore, the resulting value is 3.
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PLSSSS help I will mark brainliest
The total distance a freely falling body covers in time, t, is given by the equation d(t)=1/2 gt 2 , where g is constant at 10 m/s 2 . Show, in terms of n, the distance a falling body covers in t = n seconds of movement.
Show, in terms of n, the distance a falling body covers in t = n - 1 seconds of movement.
The distance a freely falling body covers in the nth second is given by s (n) =d (n) -d(n-1). Show s (n)in terms of g, in simplified form.
Answers
What is an equation of the line that passes through the point (8, 0) and is parallel to
the line x + y = 5?
Answers
Answer:
y = -x + 8
Step-by-step explanation:
x + y = 5
y = -x + 5
y = -x + b
0 = -(8) + b
b = 8
y = -x + 8
Could you please give me brainliest for this? Thank you!
Based on the stock price model, what is the best prediction of what the price will do next? a. hold value b. keep increasing c. start decreasing d. no way to predict
Answers
The best prediction the price will do next is keep increasing.
What is stock price?
The price at which one share of a company would be purchased is known as the share price or stock price. A share's price is not constant; rather, it changes over time in response to market factors. It is likely to rise if the business is thought to be doing well or fall if it isn't living up to expectations.
A company's price rising more quickly indicates that investors are supporting the rally and that the stock will rise further.
On the other hand, a declining price trend with high volume suggests a possible downward trajectory. A high trade volume could also indicate a change in trend.
Hence, the best prediction the price will do next is keep increasing.
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Question 1-4
A punch bowl contained 4 liters of soda, 5 liters of orange juice, and 2 liters of raspberry juice.
Select the statements that are true.
The ratio of the entire punch bowl to the juices is 9: 11.
The ratio of the entire punch bowl to the orange juice is 11 to 5.
The ratio of orange juice to soda is 4 to 5.
4
The ratio of soda to the entire punch bowl is
11
The ratio of orange juice to raspberry juice is 5 : 2.
Answers
Answer:
Its the second one
Step-by-step explanation:
.
design a rectangular milk carton box of width w, length l, and height h which holds 512 cm3 of milk. the sides of the box cost 1 cent/cm2 and the top and bottom cost 2 cent/cm2. find the dimensions of the box that minimize the total cost of materials used.
Answers
The dimensions of the box that minimize the total cost of materials used are:
L = W = 16 cm
H = 32 cm
What is the rectangular dimension?
Two dimensions make up a rectangle: the length and, perpendicular to that, the breadth. A triangle's or an oval's interior likewise has two dimensions.
We have,
volume L* W * H = 512 cm³
sides of the box cost = 1 cent/cm²
top and bottom cost 2 cent/cm²
to find out
dimensions of the box that minimize the total cost of material use
we know here,
L* W * H = 512 cm³
where,
L is length and W is width and H is the height
so when we minimize the cost function
C( L, W, H ) = (1) 1 H ( L + W ) + (2) 1 L W
so put here H
substitute [tex]H = \frac{512}{LW}[/tex] we get,
C(L, W) = 512([tex]\frac{1}{l}, \frac{1}{W}[/tex]) + 2LW
so
minimum cost will be when the two partial derivatives is 0
dC/dL = 2W - 512/L² = 0
so
dC/dW = 2L - 512/W² = 0
L = 256/W²
so
by solving the above equation we get
L = W = (256)⁻³ = 16cm
and
H = 512/16 = 32
H = 32 cm
Hence, the dimensions of the box that minimize the total cost of materials used are:
L = W = 16 cm
H = 32 cm
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please hurry im about to run out of time
Answers
Answer: Quadrant 1, y-axis
Step-by-step explanation:
Factor polynomials
9x^2 - 3x - 2
Many thanks for someone to lend a helping hand!
Answers
Answer:
Step-by-step explanation:
(3x-2)(3x+1)
Answer:
(3x - 2)(3x + 1)
Step-by-step explanation:
9x^2 - 3x - 2 = 9x^ 2 - 6x + 3x - 2 =
=3x(3x - 2) + (3x - 2) = (3x - 2)(3x + 1)
A single die is rolled twice. Find the probability of rolling a 6 the first time and a 1 the second time.
Answers
Answer: I believe it is 2/12. tell me if I am wrong.
Step-by-step explanation: Hope this helps!
How many times does the rotation R(120°, P) need to be applied to a figure to map the figure to itself?
Answers
The number of times the point R ( 120° , P ) needs to be rotated so that the figure is mapped to itself is 3 times
What is Rotation?
The measure of the amount a figure is rotated about the center of rotation is called the angle of rotation. The angle of rotation is usually measured in degrees. We specify the degree measure and direction of a rotation.
90° clockwise rotation: (x,y) becomes (y,-x)
90° counterclockwise rotation: (x,y) becomes (-y,x)
180° clockwise and counterclockwise rotation: (x, y) becomes (-x,-y)
270° clockwise rotation: (x,y) becomes (-y,x)
270° counterclockwise rotation: (x,y) becomes (y,-x)
Given data ,
Let the number of rotation be = n
Let the point be R
Now , the coordinates of the point R is
R ( 120° , P )
Now , to map the figure onto itself it needs to rotate 360°
So ,the number of times 120° needs to rotate to reach 360° is calculated as
n x 120° = 360°
Divide by 120 on both sides , we get
n = 360 / 3
n = 3 times
Therefore , the value of n is 3
Hence , The number of times the point R ( 120° , P ) needs to be rotated so that the figure is mapped to itself is 3 times
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The Wood family bought 6 crates of eggs last week. Each crate had 12 eggs. Since then, they have eaten 27 of the eggs. How many eggs are left?
Answers
Answer:
45 eggs
Step-by-step explanation:
You want to know the number of eggs left after 27 have been eaten from a supply of 6 crates having 12 eggs each.
Egg purchaseIf each of 6 crates had 12 eggs, the number of eggs bought was ...
(6 crates) × (12 eggs/crate) = 72 eggs
Eggs remainingIf 27 of those 72 were eaten, the number remaining is ...
72 -27 = 45
45 eggs are left.
-2x² + 3y² + 4x - 5y-11=0
x+3y-1=0
Answers
(Answer in the image because I couldn't type it here)
Given that the function graphed is f(x), what is f(3)?
Answers
Answer:
c. -24
Step-by-step explanation:
f(3) means the y value where x = 3, therefore f(3) = -24
7+8=8+7 identity property
Answers
Answer:The property used in 7 + 8 = 8 + 7 is Commutative property under addition
Step-by-step explanation:
Answer:
The identity property is a=a, so it is identity property
Step-by-step explanation:
???
if the cost of 1kg of apples is $12 what is the cost of 500g of apples
Answers
Answer:
the answer is $6
Step-by-step explanation:
This is because there are 1000g in 1kg, so 500g is half of that and half of 12 is 6.
this chart shows the changes in value of one share of a stock at the end of each day. the value of stock on mondag morning was 28.42$ a share. sam owns 12 shares a stock what is the total value of sams stocksl at the end of Friday
Answers
Using mathematical operation, the value of stock on Friday is $341.04
The value of Share on FridayTo find the value of the stock on Friday, the value of the stock on Monday is $24.42. Since he own 12 shares, we can multiply 12 by $24.42.
This can be done using a mathematical operation called multiplication.
Multiplication is an operation that represents the basic idea of repeated addition of the same number. The numbers that are multiplied are called the factors and the result that is obtained after the multiplication of two or more numbers is known as the product of those numbers.
The value of the stock is 12 * 28.42 = 341.04
The stock value on Friday will $341.04
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A survey of factories in five northeastern states found that 10% of the 300 workers surveyed were satisfied with the benefits offered by their employers. the margin of error for the population proportion, rounded to the nearest hundredth of a percent, is ±___%.
Answers
The margin of error for the population proportion is ± 3.39%
What is Error?Error is the difference between a genuine value and an estimate, or approximate, representation of that value in practical mathematics. The discrepancy between the mean of the complete population and the mean of a sample taken from that population is a frequent example in statistics.
Given that A survey of factories in five northeastern states found that 10% of the 300 workers surveyed were satisfied with the benefits offered by their employers
i.e. sample size n =300
Sample proportion p = 0.10
q=1-p=0.9
[tex]\sqrt{} \frac{pq}{n}[/tex] = [tex]\sqrt{\frac{0.1*0.9}{300} }[/tex]
Standard error ≈ 0.01732
Margin of error at 95% would be
1.96*std error
= 0.0339=3.39%
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Amelia thinks of a number. Her number is a factor of both 18 and 12. Her number is odd. What is the largest number she could be thinking of?
Answers
Answer:
Step-by-step explanation:
First, Amelia thinks of a number that is a factor of both 18 and 12. This number is odd, so it can't be a whole number. Next, Amelia has to find the largest number that is a factor of both 18 and her chosen number. This number is 36.
Answer:
3
Step-by-step explanation:
You want the largest odd factor of both 18 and 12.
GCDThe greatest common divisor of both 18 and 12 is 6:
18 = 3·6
12 = 2·6
This is an even factor, which has two factors: 2 and 3. Only 3 is an odd factor of both 18 and 12.
The largest odd factor of both 18 and 12 is 3.
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