ANSWER
[tex]\frac{5( \sqrt{11} + \sqrt{3} )} {8} [/tex]
EXPLANATION
The given rational function is
[tex] \frac{5}{ \sqrt{11} - \sqrt{3}} [/tex]
We need to rationalize the denominator by multiplying both the numerator and the denominator by the conjugate of
[tex] \sqrt{11} - \sqrt{3} [/tex]
which is
[tex]\sqrt{11} + \sqrt{3} [/tex]
When we rationalize we obtain:
[tex] \frac{5( \sqrt{11} + \sqrt{3} )}{(\sqrt{11} - \sqrt{3} )( \sqrt{11} + \sqrt{3} )} [/tex]
The denominator is now a difference of two squares:
[tex](a - b)(a + b) = {a}^{2} - {b}^{2} [/tex]
We apply this property to get
[tex]\frac{5( \sqrt{11} + \sqrt{3} )}{( \sqrt{11}) ^{2} - ( \sqrt{3}) ^{2} )} [/tex]
[tex]\frac{5( \sqrt{11} + \sqrt{3} )}{11 - 3} [/tex]
This simplifies to
[tex]\frac{5( \sqrt{11} + \sqrt{3} )} {8} [/tex]
Or
[tex]\frac{5 } {8}\sqrt{11} + \frac{5 } {8}\sqrt{3} [/tex]
Answer:
B
Step-by-step explanation:
A study is created in which the participants were randomly assigned to groups for different treatments. Which best describes the reason this was done?
A. It allows us to see the true nature of any effects of different treatments.
B. It allows us to determine if the treatment effect is significantly different from the placebo effect.
C. It allows us to distinguish among the effects of different factors.
D. It allows us to use chance as a way to create groups that are similar to the population.
Answer:
D) it allows us to use chance to create groups that are similar to the population.
Step-by-step explanation:
A study is created in which the participants were randomly assigned to groups for different treatments. This was done as it allows us to use chance to create groups that are similar to the population.
Random assignment is the use of chance, to make sure that every participant has the same chance to be selected in groups. These divided groups can be experimental groups or treatment groups.
Please help. I’ll give brainliest
Answer:
4/15
Step-by-step explanation:
Multiples of 4: 4, 8, 12, 16, 20, 24, 28 (there are 7)
19: There is 1
Total: 7+1=8
8/30=4/15
Write y=(-5/8)x+3 in standard form using integers
the stem and leaf plot below shows the number of points scored in each basketball game a team played during a season in how many games were more than 40 points scored?
|Stem | Leaf|
| 6 | 1 6 7|
| 5 |2 2 8|
| 4 |4 5 8 9|
| 3 |0 2 6 6 6|
| 2 | 0 8 |
A. 4
B. 6
C. 7
D. 10
Sam intends to roll a six sided cube 100 times. What is the probability model he can use to predict whether or not each roll will give a result that is not a prime number?
The outcomes of rolling fair six sided die is [tex] \{1,2,3,4,5,6\} [/tex]. The prime numbers in the above outcomes are [tex] \{2,3,5\} [/tex]. The probability of not rolling a prime number is [tex] p=\frac{3}{6}= 0.5 [/tex].
Each trial is independent.
In the given experiment of 100 trials, the binomial probability model can be used to predict the number of occurrence of non-prime numbers (X). The probability mass function is
[tex] P(X=x)=C(100,x)p^x(1-p)^{100-x},x=0,1,2,3,...,100 [/tex]. Since [tex] p=0.5,1-p=0.5 [/tex]
[tex] P(X=x)=C(100,x)0.5^x(0.5)^{100-x},x=0,1,2,3,...,100 \\
P(X=x)=C(100,x)(0.5)^{100},x=0,1,2,3,...,100 [/tex]
Three out of 4 students made an A on the last arithmetic test. If there are 32 students how many students made an A
24 students made an A in the last arithmetic test.
What is the ratio?An ordered pair of numbers a and b, represented as a / b, is a ratio if b is not equal to 0. An equation with two ratios set equal to one another is called a percentage.
Given, Three out of 4 students made an A on the last arithmetic test.
out of 4 students, the student gets an A = 3
out of 1 student get A = 3/4
Since there are 32 students in total
out of 32 students, the student gets A = 3/4 * 32
out of 4 students, the student gets an A = 24
therefore, out of 32 students, there are 24 students who got A's.
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Means-to-MAD question. Pretty easy.
Answer:
Multiply ,Add , divide
Step-by-step explanation:
The following table shows the data collected from four random samples of 50 students from a small middle school regarding their reading preferences
Based on the results in the table, what type of reading is preferred by the majority of students in the samples? (1 point)
A. Novels
B. Short Stories
C. Classics
D. Comic Book
Answer:
A. Novels Hope this helps!
Step-by-step explanation:
Simon has 20 quarters and 12 dimes.He wants to purchase ice cream for his friends.An ice cream cone cost $1.00.How many cones can Simon by for his friends?
What is the surface area of this triangular prism rounded to the nearest tenth? A) 63.3 cm2 B) 75.6 cm2 C) 85.7 cm2 D) 97.2 cm2
Which word best describes 8(2x +4)
Final answer:
The word that best describes 8(2x + 4) is multiplication. When we multiply a number by an expression, we distribute the multiplication to each term in the expression. Simplifying further, 8(2x + 4) becomes 16x + 32.
Explanation:
The word that best describes 8(2x + 4) is multiplication. In this expression, the number 8 is being multiplied by the expression 2x + 4. When we multiply a number by an expression, we distribute the multiplication to each term in the expression. Therefore, the expression becomes 8 * 2x + 8 * 4.
Simplifying further, we get 16x + 32. So, the word that best describes 8(2x + 4) is multiplication.
what is the sum of the polynomials
(-x^2+9)+(-3x^2-11x+4).
• -4x^2-2x+4
• -4x^2-11x+13
• 2x^2+20x+4
• 2x^2+11x+5
The sum of the given polynomials is -4x²-11x+13. Therefore, option B is the correct answer.
What is addition of algebraic expression?Addition of Algebraic Expressions is the process of collecting like terms and adding them. Identify and add the coefficients of like terms and sum them to find the final expression of given problems.
Given that, (-x²+9)+(-3x²-11x+4).
Here, -x²+9-3x²-11x+4
= (-x²-3x²)-11x+9+4
= -4x²-11x+13
Therefore, option B is the correct answer.
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LAST QUESTION HELP A GIRL OUT
Which system of equation can represent the equation?
Answer:
A on edge 2021
Step-by-step explanation:
You spin the spinner and flip a coin find the probability of the compound event only number 3 and 4
To the nearest tenth, find the approximate distance between points A and C. Graph with coordinates A negative 4, negative 4. B negative 2, 5. C 2, 1. D 2, negative 4.
A. 3.3 units
B. 7.8 units
C. 5.2 units
D. 3.6 units
PLEASE HELP!!!!!
how would you solve x^2 -6x +7=0 to complete the square and solve the quadratic equation?
The solution to the quadratic equation x² - 6x + 7 = 0 is found by modifying the equation to the form (x - h)² = k, adding 9 to each side, and then taking the square root of each side to solve for x, resulting in x = 3 ± √2.
Explanation:To complete the square and solve the quadratic equation x² - 6x + 7 = 0, we need to perform a few steps.
First, we need to modify the equation to the form (x - h)² = k by manipulating the x² - 6x part of the equation. By taking half of the coefficient of x (which is -6) and squaring it, we will get 9. Adding 9 to both sides of the equation will give us (x - 3)² = 2. Finally, to solve for x, we take the square root of each side, resulting in x - 3 = ±√2. Solving for x, we find that the solutions of the quadratic equation are x = 3 ± √2. Learn more about Solving Quadratic Equation here:
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the larger of two numbers is 1 more than 3 times the smaller. the diffrence is between 8 time the smaller and 2 tmies the larger is 10 find the numbers
please help and hurry
it’s not the one i picked
11499 round to the nearest thousand
which recursive formula can be used to reresent the sequence 2,6,10,14,18
1. a = 0
1
a = a + 4
n n-1
2. a = 2
1
a = a +4
n-1 n
3. a = 2
1
a = a -4
n n-1
4. a = 2
1
a = a +4
n n-1
Answer:
[tex] 4.\\\left\{\begin{array}{ccc}a_1=2\\a_n=a_{n-1}+4\end{array}\right\\\\check\\\\a_2=a_1+4\to a_2=2+4=6\\\\a_3=a_2+4\to a_3=6+4=10\\\\a_4=a_3+4\to a_4=10+4=14\\\\a_5=a_4+4\to a_5=14+4=18 [/tex]
the sum of 2 consecutive even integers is 234, what is the larger integer
A function describes a proportional relationship for a set of discrete data. What is true about the graph of that function?
It is a line connecting a series of points.
It is a line drawn only in the first quadrant.
It is a series of points that cannot be connected by a straight line.
It is a series of points that fall in a straight line but are unconnected.
Answer:
It is a series of points that fall in a straight line but are unconnected.
Step-by-step explanation:
An artist was able to draw one seventh of a picture every hour. If he needed to paint 8 pictures for an art show, how many hours would it take him
The artist 56 hours to complete 8 pictures for the art show.
Question: An artist was able to draw one seventh of a picture every hour. If he needed to paint 8 pictures for an art show, how many hours would it take him?
To find out how many hours it would take the artist to paint 8 pictures, we can use the information given.
The artist can draw one seventh of a picture every hour. This means that in one hour, the artist can complete 1/7 of apicture.
To find out how many hours it would take to complete one picture, we can divide 1 by 1/7.
1 ÷ 1/7 = 7/1
So, it would take the artist 7 hours to complete one picture.
Since the artist needs to paint 8 pictures, we can multiply 7 hours by 8.
7 hours × 8 = 56 hours
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Find the unknown. 1,025 = ( × 9) + 17
Justin is exchanging dollars for rolls of quarters and rolls of dimes at a bank. Each roll of quarters has a value of $10 and each roll of dimes has a value of $5. He exchanges $90 and receives 11 rolls of coins. How many of each type of roll of coins did he receive?
Answer:
Justin got 7 rolls of quarters and 4 rolls of dimes.
Step-by-step explanation:
Let the roll of quarters be x
Let the rolls of dimes be y
As total money received is $90, the equation becomes;
[tex]10x+5y=90[/tex] .....(1)
And he got 11 roll of coins, so equation becomes;
[tex]x+y=11[/tex] or [tex]x=11-y[/tex] .... (2)
Substituting the value of x from (2) in (1)
[tex]10(11-y)+5y=90[/tex]
[tex]=> 110-10y+5y=90[/tex]
[tex]=> -5y=-110+90[/tex]
[tex]=> -5y=-20[/tex]
So, y = 4
As [tex]x=11-y[/tex]
So, [tex]x=11-4[/tex]
x = 7
Hence, Justin got 7 rolls of quarters and 4 rolls of dimes.
The weather report says there is an 85% chance it will be very hot tomorrow. Should you get ready to use the air conditioner? Explain.
Based on the 85% chance of very hot weather, it is reasonable to prepare to use the air conditioner. Weather forecasts with high probabilities can guide us in making practical preparation decisions for comfort and safety.
The weather report indicates there is an 85% chance that it will be very hot tomorrow. Given this high probability, it would be reasonable for you to prepare to use the air conditioner. Decisions based on weather forecasts often involve considering the likelihood of different outcomes and planning accordingly.
Weather is the atmospheric conditions at a particular place over a short period of time, and preparing for it helps us manage daily activities and comfort levels. When the probability of a specific weather event, such as extreme heat, is high, it is generally wise to prepare for that scenario. By planning to use the air conditioner, you can ensure you're able to maintain a comfortable environment during the hot weather.
A container of 8 metal beams weighed one fourth of a ton. If every beam weighed the same amount, how heavy was each?
24 3/8 inches
- 12 3/4 inches
= ?
Correct gets brainliest
Julie has two formal events to go to--one for her work and one for her partner's work. She has six formal dresses--two blue ones, one black, one red, and two white. Since the same people will not be at the two events she is okay wearing the same dress. She finds the probabilty that she wears a blue and a red dress as p(blue and red) = 2 6 · 1 6 . What do you know about the two events
Answer:
The two events are independent.
She used the multiplication rule to calculate the probability. Since she is okay wearing the same dress to the two events they are independent.
Step-by-step explanation: