Rationalization of the surd [tex]\frac{(3+\sqrt{2} )}{(\sqrt{5} )+\sqrt{3} }[/tex] gives [tex]\frac{3\sqrt{5} -3\sqrt{3}+\sqrt{10} -\sqrt{6} }{2}[/tex]
What is surd?In mathematics surd refers to the root of numbers that do not have a perfect root. Surds are used to represent irrational numbers in square root, cube root and so on.
How to Rationalize (3+√2)/(√5+√3)The data given the question is
[tex]\frac{(3+\sqrt{2} )}{(\sqrt{5} )+\sqrt{3} }[/tex]
This is solved as follows;
[tex]\frac{(3+\sqrt{2} )}{(\sqrt{5} )+\sqrt{3} }[/tex]
Rationalizing the denominator
[tex]\frac{(3+\sqrt{2} )}{(\sqrt{5} +\sqrt{3} }*\frac{\sqrt{5} -\sqrt{3} }{\sqrt{5} -\sqrt{3} }[/tex]
multiplying out
[tex]\frac{3\sqrt{5}-3\sqrt{3} +\sqrt{10}-\sqrt{6} }{5-\sqrt{15} +\sqrt{15} -3}[/tex]
adding and subtraction when required
[tex]\frac{3\sqrt{5}-3\sqrt{3} +\sqrt{10}-\sqrt{6} }{5-3}[/tex]
[tex]\frac{3\sqrt{5}-3\sqrt{3} +\sqrt{10}-\sqrt{6} }{2}[/tex]
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what is the value of -20 - (-23)?
Given:
[tex]-2-(-23)=[/tex]When two negetive sign comes together it becomes positive.
[tex]\begin{gathered} -2-(-23)=-2+23 \\ =23-2 \\ =21 \end{gathered}[/tex]Thus, the final answer is 21.
Solve negative a minus eight ninths equals one third for a. a equals 5 over 9 a equals negative 5 over 9 a equals 11 over 9 a equals negative 11 over 9
8/9 - 1/3
To subtract these two fractions, first find a common denominator.
The common denominator will be the
least common multiple for the two denominators.
In this case, the least common multiple of 9 and 3 is 9.
So to subtract, a denominator of 9 is needed in each fraction.
8/9 already has 9 in the denominator so it stays the same.
To get a 9 in the denominator of 1/3, multiply top and bottom by 3.
This gives us 3/9.
So we have 8/9 - 3/9 which is 5/9.
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In a survey of a group of men, the heights in the 20-29 age group were normally distributed, with a mean of 68.3
inches and a standard deviation of 4.0 inches. A study participant is randomly selected. Complete parts (a) through (d)
below.
(a) Find the probability that a study participant has a height that is less than 68 inches.
The probability that the study participant selected at random is less than 68 inches tall is
There is a 0.0530 percent probability that the randomly chosen study participant will be shorter than 68 inches.
The standard deviation of a random variable, sample, statistical population, data set, or probability distribution is the square root of its variance. Low standard deviation means data are clustered around the mean, and high standard deviation indicates data are more spread out.
We have been given that
μ = 68.3
σ = 4.0
Find the probability that a study participant has a height that is less than 68 inches.
We are supposed to find P(x<68)
x = 68
z = (x - μ) / σ
z = (68 - 68.3) / 4
z = -0.3 / 4
z = -0.075
Use z table :
So, P(z<-0.0725)=0.0530
So, The probability that the study participant selected at random is less than 68 inches tall is 0.0530
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Could you better explain what the question is asking please ?
Recall that two figures are similar if their corresponding angles have the same measure.
Therefore, if we reduce or increment the measurement of each angle, the resulting figure will not be similar to the original figure.
Now, notice that increasing the length of the sides of a polygon does not necessarily result in a similar figure, for example:
Now, recall that translations, rotations, reflections, and dilations result in similar figures.
Answer: Third and last options.
I need help I’m not sure I did this right and need help on the graphing!! And table next to it please :( !
The solution for the given system of equations, y = [tex]\frac{-1}{2}[/tex]x + 5 and y = 3x - 2 is (2,4) and the graph is attached below
What is the system of equations?The system of equations is a set of equations consist the same variables. If the given equation are all linear then, it is the system of linear equation.
To solve such system, it is required to figure out the variable values that can solve all the equations involved in the system.
For the given system of equation the variable value is x.
So, [tex]\frac{-1}{2}[/tex]x + 5 = 3x - 2
2 + 5 = 3x + [tex]\frac{x}{2}[/tex]
7 = x ([tex]\frac{6+1}{2}[/tex]) = [tex]\frac{7x}{2}[/tex]
x = 2
Now apply the obtained value of x in either of the equations:
y = 3x - 2
y = 6 - 2
y = 4
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Convert0.0032% in fraction
STEP-BY-STEP EXPLANATION:
What to do? Convert percentage to fraction
Given parameter
0.0032%
Transform the quadratic equation into a perfect square equation by completing the square.x² + 4x +2=0
Solution:
Given:
[tex]x^2+4x+2=0[/tex]Help Me Please!!
Thank you
Answer: 1/2
Step-by-step explanation:
1) Find the equation of sin of angle K
Sine is opposite/hypotenuse.
Opposite of K = 5.
the hypotenuse of K = 10
You then get 5/10
2) Simplify the fraction
5/10 = 1/2
Which of the following is the correct mathematical expression for:
Double a number and then increase it by five
2x+5
2x-5
1/2x+5
1/2x-5
At Shannon’s hats, 356 out of the 400 hats at the store are baseball caps. What percentage of the hats at the store are baseball caps?
Answer:
89%
Step-by-step explanation:
Answer:
Step-by-step explanation:
Ahmed is 144 miles away from Blake. They are traveling towards each other. If Blake travels 8 mph fasterthan Ahmed and they meet after 4 hours, how fast was each traveling?
Data:
• Distance ( ,D ,)= 144 miles
,• Time ( ,t ,) = 4 hours
,• Speed of Ahmed (,A,): unknown
,• Speed of Blake (,B,): unknown
,• Formula of speed:
[tex]D=\frac{speed}{t}[/tex]Procedure:
• As Blake travels 8 mph faster than Ahmed
[tex]B=8+A[/tex]Since they are traveling towards each other, we can add up their speeds as follows:
[tex]B+A=(8+A)+A=2A+8[/tex]Using the distance formula, we can find the speed:
[tex]D=\frac{2A+8}{t}[/tex][tex]2A+8=D\cdot t[/tex][tex]2A=D\cdot t-8[/tex][tex]A=\frac{D\cdot t-8}{2}=\frac{144\cdot4-8}{2}=284[/tex]To know the speed of Blake:
[tex]B=284+8=292[/tex]Answer:
• Blake = 292 mph
,• Ahmed = 284 mph
Issay's school plans to add one of three new elective classes next year:
teen leadership, fashion design, or robotics. Issay wants to know which
class the students at his school want most. He plans to survey a sample
of the population. Will each approach result in a sample that is
representative of the population? Explain.
Be
Yes, the probability approaches each time will result in getting a sample that is representative of the population of that group class.
Why does the entire sample need to be an absolute representative of the population?If you are going on and properly conducting the specific research on a specific population, you will totally want to make sure that your taken sample of that population is absolutely representative.
If in any case your sample is a kind of representative of your total population, you will be able to confidently take up and generalize the results of your study to that of the population.
How to determine if a sample is absolutely representative of the population?In order to be a representative sample, the sample of the group must represent the total population as a whole.
For instance, if the researcher’s population of absolute interest has 60% of people of total ages 18-25 and 40% of the total people ages from about 26-40, then the representative sample must also absolutely reflect this ratio.
Is there the single one way of ensuring that a sample is absolutely representative of the population?The best way of ensuring a representative sample is to have a complete list (i.e., sampling frame) of all the elements in the present population and know that each and every element (e.g., people or present households) on the list that has a nonzero chance (but then it is not necessarily required to be an equal chance) of being included in the entire sample.
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how do I do this. . I don't know ho2
A linear equation has a constant slope.
For every step increase in x, there needs to be another step increase in y.
From the table,
x decreases by 2 units
y doesn't decrease by the same unit
So, this cannot be linear relationship.
To see whether it is quadratic or exponential, we graph the (x,y) points and see the general shape of the curve by connecting the points in a smooth curve.
The graph is shown below:
From seeing the graph, it is quite evident that the tabular relationship represents a quadratic function.
Thus, the correct answer is:
Bsolve this literal equation for h A=bh
we have the equation
A=bh
solve for h
that means -----> isolate the variable h
so
step 1
Divide both sides by b
A/b=bh/b
simplify
A/b=h
rewrite
h=A/bWhat’s the domain of F(x)=|x|, g(x)=x+9 find domain for f o g
The domain of the functions F(x)=|x|, g(x)=x+9, f o g is x ∈ R the functions exist for all real numbers.
What is a function?
It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
The function f(x):
f(x) = |x|
The domain of the function is:
x ∈ R
g(x) = x + 9
The domain of the function:
x ∈ R
f o g = f(g(x)) = |x + 9|
The domain of the function f o g is x ∈ R
Thus, the domain of the functions F(x)=|x|, g(x)=x+9, f o g is x ∈ R the functions exist for all real numbers.
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The length of a rectangle is 5 in. longer than its width and the rectangle has an area of
50in².
What are the dimensions of the rectangle
The dimensions of the rectangle are L=10in, B=5in
What is rectangle?A rectangle includes everything listed below:
A plane figureA closed formA quadrilateralThe parallelogramYour polygon's four sides must be two congruent pairings in order to have two pairs of parallel sides. The length of the left and right sides, as well as the base and top, will be equal.
let width of rectangle be x, then length will be
B=5+x
given area of rectangle
A=50in²
area = length×width
A=L×B
50 = x×(5+x)
50=5x+x²
x²+5x-50=0
x²+10x-5x-50=0
x(x+10)-5(x+10)=0
x=-10 or x=5
since x=-10 is not possible
therefore, x=5
Length(L)=5+5=10in
Width(B) = 5in
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Max knows that 1/2 stick of butter is enough for 2 batches of cookies how many cookies can he make with 4 sticks of butter
Answer:
16 batches of cookies
Step-by-step explanation:
First, I converted the fraction (1/2) to a decimal (.5). Then I divided 4 by .5 and got 8. Next, multiply 8 by 2 and we get 16, which means we can make 16 batches of cookies.
4 ÷ .5 = 8
8 × 2 = 16
Bro help pls I need this done by tmr or else they take point if I turn it late
Answer:
180
Step-by-step explanation:
So, in the first 4 games, they score 10 points. If this continues to happen in the remaining 18 games, it would be 180.
10 x 18 = 180.
hwlp
Marcus has twice as many CD's as Kristen. Sherry has 12 more than Kristen. Together they have 100 CD's. How many does each person have?
Marcus have 44 CDs, Sherry have 34 CDs and Kristen have 22 CDs.
Let us assume that Kristen has x numbers of CD's.
According to the provided situation,
Marcus have twice the number of CDs as Kristen.
Number of CDs of Marcus = 2x
The number of CDs of Sherry is 12 more than the CDs of Kristen
Number of CDs of of Sherry = 12 + x
Total number of CDs combined are 100.
So, we can write,
x + 2x + (12 + x) = 100
4x + 12 = 100
Any equation with the highest degree of variable as one, just like the above equation is called Linear Equation.
Further solving the Equation,
4x + 12 = 100
4x = 88
x = 22
The number of CDs that Kristen has is 22.
The number of CDs that Marcus have is 2(22).
The number of CDs Marcus gas is 44.
The number of CDs Sherry has is (12 + x) which is equal to 34.
The number of CDs Kristen, Marcus and Sherry have is 22, 44 and 34 respectively.
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Line segments AB and CD arecongruent. Their coordinatesare AC-11, -3), B(-2,5), C(7,1)and D(x, 9). Find the value of x.
We have the following points:
A(-11, -3) and B(-2,5)
The distance between AB is:
[tex]\left(|-11--2|,|-3-5|\right)=(9,8)[/tex]C(7,1) and D(x, 9)
[tex]\begin{gathered} 7-x=9 \\ x=-9+7 \\ x=-2 \end{gathered}[/tex]the value of x is -2
1. When a number is divided by 5, the result is 50 less than if the number had been divided by 6. What is the number?
2. I have two turtles. Today, the older turtle's age is 11 times that of the younger turtle. In 24 years, the older turtle's age will only be 7 times that of the younger turtle. If both turtles survive until then, how many years from today will the older turtle's age be 3 times that of the younger turtle?
1) A number that is divided by 5, with the result as 50 less than if the number had been divided by 6 is; -1500
2) If both turtles survive until then, the number of years from today that the older turtle's age would be 3 times that of the younger turtle is; 146 years
How to solve Algebra Word Problems?1) Let the number be x. We are told that it is divided by 5, and the result is 50 less than if the number had been divided by 6. Thus, we have;
(x/6) - (x/5) = 50
Multiply through by 30 to get;
5x - 6x = 1500
-x = 1500
x = -1500
2) Let the older turtle be x and the younger one be y.
Today, the older turtle's age is 11 times that of the younger turtle. Thus;
Todays age;
Older turtle = 11y years
Younger turtle = y years
In 24 years, the older turtle's age will only be 7 times that of the younger turtle. Thus;
11y + 24 = 7(y + 24)
11y + 24 = 7y + 168
11y - 7y = 168 - 24
4y = 144
y = 144/4
y = 36
Thus;
Age of older turtle today = 11 * 36 = 396 years
Age of younger turtle today = 36 years
Thus, for older turtle to be thrice the age of younger turtle, then;
3(36 + t) = 396 + t
108 + 3t = 396 + t
2t = 292
t = 292/2
t = 146 years
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Find all value of x for which:
a. f(x) > g(x)
b.f(x) < g(x)
Answer: a. (-10, 0) u(12, infinity)
b. (negative infinity, -10) u(0, 12)
All of this is assuming that the ends of both functions are continuing in the direction it's going shown in the graph.
Step-by-step explanation:
f(x) and g(x) basically means the y value. So when f(x) is greater than g(x), it's saying the y value for the f(x) line is greater than the y value for g(x). This happens when x = -10 till x = 0 and x = 12 till forever going right.
Side note: (-10, 0) is a way to write the domain, with the first number meaning the start and the second number meaning the end.
Can you please help me
Area of Sector.
The area of a sector is given by the formula below:
[tex]\begin{gathered} \text{Area =}\frac{\theta}{360}\times\pi r^2 \\ \text{where }\theta=148\text{ ; r=6m ; }\pi=\frac{22}{7} \end{gathered}[/tex]Substituting these values into the formula above, we get
[tex]\begin{gathered} \text{Area of the shaded sector = }\frac{148}{360}\times\frac{22}{7}\times6^2 \\ \text{ } \\ \text{ = }\frac{148\times22}{70}\text{ = }46.514\text{ }\approx46.5m^2 \end{gathered}[/tex]Thus, the correct answer is 46.5 square meters.
HELPPPPPPPPPPPPPPPPPPPPPPPPPPPPP
Answer:
It would be, Yes, No, Yes, Yes.
Hope this helps!
If f(x) = 1/x which equation describes the graphed function?
y = f(x+2) -1 is the equation which describes the graphed function.
What is translation?Translation is the act of moving a shape or a figure from one location to another. A figure can move in translation up, down, right, left, or anywhere else in the coordinate system. Only the object's position changes during translation; its size stays the same. In mathematics, a translation is the up, down, left, or right movement of a shape. Because the translated shapes appear to be exactly the same size as the original ones, they are consistent with one another. Just one or more directions have been altered.
Given,
When F crosses the x-axis when it is negative.
-1 indicates a 1 unit down translation.
So, the equation will be y = f(x+2) -1.
y = f(x+2) -1 is the equation which describes the graphed function.
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Greta offers to buy a team photo for 15 of her teammates, but 6 of them don't want one. If a team photo costs $2, how much will Greta spend on her teammates? Choose the correct expression and solution to this problem. O A. The expression is 2(15 + 6). Greta will spend $42. OB. The expression is 2(15 - 6). Greta will spend $18. C. The expression is 15(6 - 2). PREVIOUS
The teammates are 15 but 6 of them do not want the photo, so the number of the teammates who wants the photo is 15 - 6.
Now, each photo cost $2 adn the number of photo is equal to the number of teammates who wants the photo which is (15-6), so the expression for the total cost is:
[tex]2\cdot(15-6)_{}[/tex]We have to multiply the cost of each photo for the number of photo Greta will buy.
Assume that a sample is used to estimate a population mean μ . Find the 99.5% confidence interval for a sample of size 867 with a mean of 60.2 and a standard deviation of 21.9. Enter your answer as a tri-linear inequality accurate to 3 decimal places.
Population means μ as a tri-linear inequality is given as 58.852< m<61.548 with a confidence interval of 99.5%.
What is a confidence interval?
Add & deduct the error margin from the sample mean to get this confidence interval.The confidence interval's top and lower limits are represented by this result.Mean, x= 60.2
sample size, n= 867
standard deviation=21.9
population mean m as a tri-linear inequality is given by,
The t value for a 99.5% Confidence interval because the sigma is unknown.
From Inverse t Distribution Calculator, the Confidence interval is 0.995 and the degree of freedom is 867-1=866
One-sided t-Score: 1.8125
We can now determine the standard error E:
E=1.8125(21.9/√867)=1.348
We can now create the confidence interval by:
x - E < m< x + E
60.2-1.348< m <60.2+1.348
58.852< m<61.548
Population means μ as a tri-linear inequality is given as 58.852< m<61.548 with a confidence interval of 99.5%.
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Find the area of the figure given to the right. Round to the nearest whole number.
Looking at the figure, we can tell that the top is a triangle and the base is a trapezium. To find the area of the figure, we would find the sum of the triangle and the trapezium.
Recall, the formula for finding the area of a triangle is expressed as
Area = 1/2 x base x height
Looking at the triangle,
base = 9 + 9 = 18
height = 3
Thus, Area = 1/2 x 18 x 3 = 27
Again, the formula for finding the area of a trapezium is expressed as
Area = 1/2(a + b)h
where
h is the height of the trapezium
a and b are the lengths of the parallel sides
Looking at the trapezium,
a = 9 + 9 = 18
b = 13.4 + 13.4 = 26.8
h = 12
Area = 1/2(18 + 26.8)12
Area = 268.8
rounding to the nearest whole number,
Area = 269 squared ft
Don is 6 feet tall. At a given time of day, he measures his shadow to be 13 feet long. At the same time, he measures the shadow length of a nearby tree to be 52 feet. How tall is the tree?
Answer:
24
Step-by-step explanation:
We will use the proportional concept to solve it.
So, 6/13 = x/52
x = 6*4
x = 24
So, height of tree is 24 feet
8. The length, width, and a height of a box are different integer lengths. If the volume is 125
cubic centimetres, then which of the following could be the length of the height in
centimetres?
(a) 1
(b) 5
(c) 25
(d)125
(e) 50
The length , width and height of a box with volume 125 cubic centimeters will be
1, 5 and 25.
Explanation:
The volume of a box can be calculated by multiplying its length, width, and height.
here given volume = 125
V = l x w x h
125 = l x w x h
l, w, h is the factors of 125
To find the common factors, we must first list the factors of each of the given numbers.
since 125 is composite number, it will have more than two factors.
125 → 1, 5, 25 and 125.
The factors of 125 is 1, 5, 25,125
here 125 cannot consider as length since volume is 125 other sides cannot be 0.
so the length, width, height can be 1 , 5, 25.
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