The rationalized expression would be [tex]\sqrt{3}+\frac{\sqrt{9} }{\sqrt{x}}[/tex].
What is a rationalized expression?
A rationalized expression is an expression that has been written in a simplified form which eliminates any radicals (square roots, cube roots, etc.) from the denominator. The denominator is made a rational number, meaning it can be expressed as a fraction with an integer numerator and denominator. This is done by multiplying both the numerator and the denominator by the radical of the denominator. This process is called rationalization.
The given expression is
[tex]=\frac{\sqrt{9}}{\sqrt{3}+ \sqrt{x} } \\\\=\frac{\sqrt{9} }{\sqrt{3} }+ \frac{\sqrt{9} }{\sqrt{x}}\\\\=\frac{3 }{\sqrt{3} }+\frac{\sqrt{9} }{\sqrt{x}}\\\\=\sqrt{3}+\frac{\sqrt{9} }{\sqrt{x}}[/tex]
Hence, the rationalized expression would be [tex]\sqrt{3}+\frac{\sqrt{9} }{\sqrt{x}}[/tex].
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How can I solve this ? What is the angle whose tangent is 456/321?
The angle whose tangent is 456/321 is 54.85°
The tangent of an angle in trigonometry is the ratio of the lengths of the adjacent side to the opposing side. In order for the value of the cosine function to not be 0, it is the ratio of the sine and cosine functions of an acute angle.
The Tangent Formula is given as:
Tan A = Opposite Side/Adjacent side
In terms of sine and cosine, tangent may be represented as:
Tan A = Sin A / Cos A
We know that the sine of an angle is equal to the length of the opposite side divided by the length of the hypotenuse side whereas the cosine of the angle is the ratio of the length of the adjacent side to the ratio of the hypotenuse side.
That is, Sin A = Opposite Side/ Hypotenuse Side
Cos A = Adjacent Side/ Hypotenuse Side
Therefore, tan A = Opposite Side/ Adjacent Side
[tex]tan^{-1} (1.42056)[/tex] =54.85°
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the sample midrange for the data. (ii) explain why the sample midrange might be preferred to the sample mean as an estimator of the population mean.
Answer:
The sample midrange for the data is 559
What is Sample midrange?
Although the sample midrange only uses a small fraction of the data, outliers can have a significant impact on it. It offers details on the distribution's skewness and heavy tails, which are identical to those of the random variable's distribution. Although the structure of this distribution is not obvious, with large sample sizes, the central limit will cause it to resemble a normal distribution.
According to question:
Minimum value: 34
Maximum values: 1084
The sample midrange can be computed as:
(Minimum value + Maximum value) / 2
⇒ (34+1084)/2
⇒ (1118)/2
⇒ 559
Hence, the sample midrange is 559
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The Complete Question is
Can anyone solve these 2 questions they are very easy but i want to double check
Answer:
Corresponding angels:
a,f
h,b
e,d
c,g
y = 80 Vertical angles are congruent
x = 50 Sum of the interior angles of a triangle is 180
180 - 80 -50 = 50
Step-by-step explanation:
The value of x is the equation X + 5 = 12 is
Answer:
x+5=12
or,x=12-5
or,x=7
There were 900 freshwater fish at an aquarium 212 fish are in the large tank there are 16 fish in each smaller tank How many smaller tanks are there
Answer: 43 small tanks
Step-by-step explanation:
First, take 900 - 212 = 688 fish in small tanks
Then take 688 divided by 16 fish in each tank = 43
So there are 43 smaller tanks
1. Noah placed an empty bowl on a scale. He added different amounts of a liquid to the bowl, recording the amount of liquid added, in tablespoons, and the total weight of the bowl and liquid, in grams, each time on a scatter plot. He fit the line
y = 14.75x+861.82 to the data in his scatter plot, where x represents the amount
of the liquid, in tablespoons, and y represents the total weight of the bowl and the
liquid, in grams. Determine the weight, in grams, when 18 tablespoons on the liquid are placed in the bowl. determine the approximate number of tablespoons of the liquid noah needs to add so that the total weight is 1,200 grams
1. The weight for 18 tablespoons is 1127.32 grams.
2. The number of tablespoons of the liquid noah needs to add so that the total weight is 1,200 grams is 23 tablespoon.
What is the weight when 18 tablespoons on the liquid are placed in the bowl?It's vital to note that 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.
From the information, Noah placed an empty bowl on a scale and the equation is given as:.
y = 14.75x + 861.82
x = the amount of the liquid, in tablespoons
y = the total weight
The weight for 18 tablespoons will be:
y = 14.75x + 861.82
y = 14.75(18) + 861.82
y = 1127.32
The liquid that Noah needs to add so that the total weight is 1,200 gram will be:
y = 14.75x + 861.82
14.75x + 861.82 = 1200
Collect like terms
14.75x = 1200 - 861.82
14.75x = 338.18
Divide
x = 138.18 / 14.75
x = 23
The tablespoons is 23.
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Question 9 Which of the following distributions has a mean that varies? I. The population distribution II. The distribution of sample data III. The sampling distribution of the sample mean
O ll only
O IIl only
O I only
O all three distributions
O II and III
II and III only distributions has a mean that varies
The mean of a distribution is a measure of the central tendency of the data, and it can vary depending on the sample being analyzed.
For the population distribution, the mean is a fixed value that is calculated using all of the data in the population. The mean of the population distribution does not vary.
For the distribution of sample data, the mean is calculated using the data in the sample. If you take different samples from the same population, the mean of each sample will be different, so the mean of the distribution of sample data varies.
For the sampling distribution of the sample mean, the mean is calculated using the means of multiple samples. The mean of the sampling distribution is known as the population mean. As with the distribution of sample data, the mean of the sampling distribution varies depending on the samples that are used to calculate it.
Therefore, the mean of the distribution of sample data and the sampling distribution of the sample mean both vary, while the mean of the population distribution does not vary.
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a recent study of minimum wage earners found that 55% of them are 16 to 24 years old. suppose a random sample of 12 minimum wage earners is selected. what is the probability that exactly 7 of them are 16 to 24 years old.
The probability that exactly 7 of them are 16 to 24 years old is 0.222
In this question we have been given a recent study of minimum wage earners found that 55% of them are 16 to 24 years old.
A random sample of 12 minimum wage earners is selected. we need to find the probability that exactly 7 of them are 16 to 24 years old.
Here, n = 12
p = 0.55
1 - p = 0.45
x = 7
Using binomial distrubution the required probability would be,
P = 12C7 * (0.55)^7 * (0.45)^(12 - 7)
P = 792 * 0.01522 * (0.45)^5
P = 792 * 0.01522 * 0.01845
P = 0.2224
Therefore, the required probability is 0.222
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Find the Amount (A) (Principal Rs 50000 Time = 7 years interest = 3%.
Answer: Rs 60500
Step-by-step explanation:
Principal = Rs 50000 = p
Time = 7 years = t
Simple interest rate = 3% = r
Interest = p*t*r/100
using above formula,
50000*7*3/100=10500
So, final amount = principal + interest = 50000+10500 = Rs 60500
Translate the phrase into an algebraic expression.
The sum 9 of C and.
WHAT IS THE ANSWER.
Which of the following system of equations has no solution?
O 3x - y = 2,9x - 3y = 6
O 4x - 7y + 28 = 0,5y - 7x + 9 = 0
O 3x - 5y - 11 = 0,6x - 10y - 7 = 0
O None of these
4x - 7y + 28 = 0,5y - 7x + 9 = 0 is the system of equation that has no solution.
What is meant by system of equation?A group of equations comprising one or more variables is known as a system of equations. The variable mappings that satisfy each component equation, or the points where all of these equations cross, are the solutions of systems of equations.
Name three types of system of equation.Dependent, Independent and inconsistent are the three types of system of equation.
If we solve this system of equation we will get complex roots that means it has no solution.
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a better understanding of how I can solve for 1/2d-3/4d+3f-2f
The simplified form of the given expression is, 1/4d + f.
What is simplified form of the expression?
To simplify an expression, create an equivalent expression without any terms that are similar.
The expression will then be rewritten using the fewest terms possible.
Mathematical operations can be made much simpler by using the right order of operations. Exponents, terms in parentheses, multiplication, division, addition, and finally subtraction are the correct order of operations.
Consider the given expression,
1/2d - 3/4d + 3f - 2f
Here the like terms are '1/2d and 3/4d' and '3f and 2f'.
To simplify the expression,
1/4d + f
Hence, the simplified form of the given expression is, 1/4d + f.
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Question
Find the range of the function represented by the list of ordered pairs below.
((-9, 4). (-0,3). (-8,0). (-2, -4))
Answer: {4,3,0,-4}
Step-by-step explanation:
The range is the set of all the values of y
Range {4,3,0,-4}
What is 16/64 simplified?
Answer:
1/2
Step-by-step explanation:
16/64 (divide the numerator and denominator by 4)
-> 4/8 (divide the numerator and denominator by 4)
-> 1/2
Please help, giving thanks and brainliest:) (Please give an explanation if possible and please dont give a fake answer)
Answer: h = 92
Step-by-step explanation:
148 - 180 = 32
32 + 56 = 88
88 - 180 = 92
Which of the following is not a piece of required information in order to determine sample size? a. estimated population standard deviation b. estimated population median c. acceptable level of sampling error d. desired level of confidence e. All are necessarv to determine sample size.
E. All are necessary to determine sample size is not a piece of required information in order to determine sample size.
Determining an appropriate sample size is an important step in the research process as it helps to ensure that the results from the sample will be representative of the population as a whole. In order to accurately determine the appropriate sample size, you need to have an estimated population standard deviation, an estimated population median, an acceptable level of sampling error, and a desired level of confidence. The population standard deviation and median will help you determine the central tendency and variability of the population, while the acceptable level of sampling error and desired level of confidence will help you determine the margin of error you are willing to accept in your results. All four of these pieces of information must be taken into consideration in order to accurately determine the appropriate sample size.
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Geometry- Can someone break this down for me in a simple way?
Answer:
z = 22
Step-by-step explanation:
Because we are given that angle measures TUW and VUW are the same, we can assume that both triangles are the same since they also have 90 degree angles and both their third angles are equal to 54. (I found that out by taking 180 degrees which is the total angle measure of all triangles, and subtracted it by 90 and 36).
Since they are the same, that means that side TW is the same length as side VW. With this information we can set up an expression:
2z = z + 22
Now, all we have to do is solve for z
2z = z + 22
-z - z
z = 22
Complete the table of values below: x -2 -1 0 1 2 3 f(x)=(1/3)^x -2 ANSWER
-1 ANSWER
0 ANSWER
1 ANSWER
2 ANSWER
9, 3, and 1 are the values of a, b, and c using the exponential function g(x)=(1/3)∧x.
What are exponential functions?A mathematical function with the formula f (x) = an x is an exponential function.
Where x is a variable, and an is a constant called the basis of the function.
The most typically seen exponential-function base is the transcendental number e, which is equivalent to about 2.71828.
So, the exponential function:
g(x) = (1/3)∧x
From the table, we are also to find out the value of a, b and c
If x = -2
g(-2) = a = (1/3)⁻²
a = 1/3⁻²
a = 9
Accordingly,
If x = -1
g(-1) = b = (1/3)⁻¹
a = 1/3⁻¹
b = 3
Hence,
If x = 0
If x = -1
g(0) = c = (1/3)⁰
c = 1
Therefore, 9, 3, and 1 are the values of a, b and c using the exponential function g(x) = (1/3)∧x.
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Complete question:
Complete the table of values for the function.
f(x) = ( 1/3) ^x
a=
b=
c=
Ashley is going to invest in an account paying an interest rate of 5.6% compounded continuously. How much would Ashley need to invest, to the nearest dollar, for the value of the account to reach $2,080 in 16 years?
Rounding to the nearest dollar, Ashley would need to invest $1,062 to reach $2,080 in 16 years at an interest rate of 5.6% compounded continuously.
How can you figure out compound interest in mathematics?Compound interest (CI) is calculated as CI = P(1 + r/100)n - P. To calculate the compound interest value, first compute the amount and then deduct the principal from it.
To find the amount Ashley needs to invest, we can use the formula for continuously compounded interest:
A = P * e^(rt)
where A is the final amount, P is the principal (the initial investment), r is the interest rate, and t is the time in years.
We know that A = $2,080 and r = 5.6% = 0.056, and we want to solve for P. We can rearrange the formula to solve for P:
P = A / e^(rt)
Plugging in the values, we get:
P = $2,080 / e^(0.056 * 16)
The value of e^(0.056 * 16) can be calculated using a calculator or computer, and it is approximately 1.96. Plugging this in, we get:
P = $2,080 / 1.96 = $1062.24
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Vladmir sketches the graph of the function f(x)=12(x+6)2−3
as shown below
He then translates this function 11 units to the right and 4 units down to obtain the new function g(x)=12(x−h)2+k
. Which function correctly shows integer values for h and k?
The function that correctly shows the value of k and h is g(x) = 12(x - 5)² - 7
How to determine the function correctly?From the question, we have the following parameters that can be used in our computation:
f(x) = 12(x + 6)² - 3
The transformation is given as
11 units to the right and 4 units down
This is represented as
(x - 11, y - 4)
So, we have the following representation
g(x) = 12(x + 6 - 11)² - 3 - 4
Evaluate
g(x) = 12(x - 5)² - 7
Hence, the function is g(x) = 12(x - 5)² - 7
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ix different books will be displayed from left to right in the library window. how many different arrangements are there?
The total number of different arrangements possible for the books in the library window are 362880.
The total number of books that has to be arranged is 9.
The books has to be arranged in a pattern of left to right in the library window.
So here by we have a total possible 9 positions for 9 book because we have to create different arrangements every time.
Now, the total possible arrangement of the books can be given as,
= 9x8x7x6x5x4x3x2x1
= 362880
So the total number of possible different arrangements are 362880.
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decide whether enough information is given to prove that $\triangle abc\cong\triangle dbe$ using the sss congruence theorem. explain. two triangles, triangle a c b and triangle d e b that share a common vertex b. point b is on the segment a d. in triangle a c b, side a c is marked with single tick, side b c is marked with double ticks and side a b is marked with three ticks. in triangle d e b, side d e is marked with single tick, side b e is marked with double ticks and side b d is marked with three ticks.put responses in the correct input to answer the question. select a response, navigate to the desired input and insert the response. responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. responses can also be moved by dragging with a mouse.you are given that $\overline{ab}\cong$ response area, $\overline{bc}\cong$ response area, and $\overline{ac}\cong$ response area. so, the triangles response area be proven congruent using the sss congruence theorem.
No, enough information is not given to prove that triangles are congruent using the SSS congruence theorem.
The SSS congruence theorem expresses that assuming in two triangles, three sides of one are consistent to three sides of the other, then, at that point, the two triangles are said to be congruent.
Now, we are given that triangle ACB and triangle DEB that share a common vertex b. So, both triangles share a common side. So, one side is same for both of triangles.
From the diagram, we can see that both triangles opposite side are equal. So, second side is equal for both of triangles.
Now, from the diagram, we can see that both triangles vertically opposite angles are equal. So, we have two sides equal and one angle is equal.
So, given triangle is proved to congruent by SAS congruency not by SSS congruency.
Hence, enough information is not given.
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for 86 points, Stewart loves playing Genshin Impact so much that he “forgets” to do his schoolwork. It’s really starting to impact his grades and he has 36 overdue assignments. The semester is almost over, and he really needs to improve his grades. He can realistically complete 4 overdue assignments each day.
Draw a graph to represent this situation.
Answer:
it will take him 9 days to complete 36 assignments
Step-by-step explanation:
1. In a party for 30 young children, 12 were served Coca-Cola drink, while 14 were served pepsi-cola. If 9 children were served Coca- Cola but not with pepsi-cola, find a. the number of children served both drink. b. the number of children served at least one type of drink. C.the number of children not served any of the drinks.
solve with showing equations
The number of children served both Coca-Cola and Pepsi-Cola is 3, the number of children served at least one type of drink is 9, and the number of children not served any of the drinks is 9.
To solve this problem, we can use the following equations:
a. The number of children served both drinks = 9 (served Coca-Cola but not Pepsi-Cola) + X (served both Coca-Cola and Pepsi-Cola)
b. The number of children served at least one type of drink = 12 (served Coca-Cola) + 14 (served Pepsi-Cola) - X (served both Coca-Cola and Pepsi-Cola)
c. The number of children not served any of the drinks = 30 (total number of children) - (number of children served at least one type of drink)
Substituting the values given in the problem into the equations above, we get:
a. The number of children served both drinks = 9 + X
b. The number of children served at least one type of drink = 12 + 14 - X
c. The number of children not served any of the drinks = 30 - (12 + 14 - X)
Solving for X in each equation, we get:
a. X = 3 (children served both Coca-Cola and Pepsi-Cola)
b. X = 9 (children served at least one type of drink)
c. X = 9 (children not served any of the drinks)
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If m<1=55, then find the value of m<3
The measure of angle 3 is given as follows:
m < 3 = 55º.
What are vertical angles?Vertical angles are angles that are opposite by the same vertex on crossing segments, hence they share a common vertex, thus being congruent, meaning that they end up having the same angle measure.
The vertical angles in this problem are listed as follows:
1 and 3.2 and 4.The measure of angle 1 is given as follows:
m < 1 = 55º.
Angle 1 and angle 3 are vertical angles, hence the measure of angle 3 is obtained as follows:
m < 3 = 55º.
As angle 3 is congruent to angle 1.
Angles 2 and 4 are also supplementary to angles 1 and 3, meaning that the sum of their measures is of 180º, hence m<2 = m<4 = 125º.
Missing InformationThe diagram is given by the image shown at the end of the answer.
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If f(7) = 22, then f^-1(22) = [?]
The required value of the given inverse function f⁻¹(22) will be 7.
What is an inverse function?The inverse function is defined as a function obtained by reversing the given function.
Given that f(7) = 22
To determine the value of the given inverse function f⁻¹(22)
An inverse function's main objective is to show the value that occurs in a specific function value. Which means :
If we have f(x) and f⁻¹(x), then
if f(a) = b then f⁻¹(b) = a
As per the given question, we have
⇒ f(7) = 22 then f⁻¹(22) = 7
Therefore, the required value of the given inverse function f⁻¹(22) will be 7.
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if you use a different experimental photo-missive material, what would be the same on the graph? (5 points) the y-intercept the intercept the slope
The slope would be the same on the graph.
What is a slope?
A line's steepness is determined by its slope. In mathematics, slope is determined by "rise over run" (change in y divided by change in x).
The slope-intercept form of an equation is used to represent each time the equation of a line is stated as y = mx + b.
M represents the line's slope. Additionally, b is the b in the y-intercepting point (0, b). For instance, the y-intercept is at (0, 7) and the slope is 3 in the equation y = 3x - 7.
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When archeologists excavate a site, they mark it off with a coordinate grid so that they can easily
identify where artefacts are found and keep a record of the site forever. At the West Kennet Long
Barrow in England, a grave site back to 3600 BCE was found. There are three chambers at the
coordinates (7,9), (17, 33) and (-36,41). It has been said that they form an isosceles triangle with
height twice the length of its base.
Determine whether the statement is true. Justify your answer. Hint: An isosceles triangle has at
least two sides of equal side lengths.
The variables x and y vary directly. Use the values to find the constant of proportionality, k. Then write an equation that relates x and y. Write any fractions in simplest form.
y=20; x=12
Step-by-step explanation:
x =ky
x=12,y=20
12 =20k
divide both sides by 20
k=12/20
= 6/5
X=6/5y
Help please! Two angles are complementary. One is three times the measure of the other. What are the measures if each angle?
Answer: 22.5 and 67.5
Step-by-step explanation:
A complementary angle means that two angles add up to 90°
If one angle is 3 times the other,
let x be the value of the other angle.
The bigger angle would be 3x.
Therefore,
3x+x=90°
4x=90°
x=22.5
22.5 is the measure of the smaller angle
and 22.5x3=67.5 would be the other (larger) angle.
Answer:
22.5 degrees and 67.5 degrees
Step-by-step explanation:
3x + x = 90
4x=90
x=90/4
x=22.5
other angle is 3x which is 67.5
