Rationalize the denominator and simplify the expression below. Show all steps and calculations to earn full credit. You may want to do this work by hand and upload an image of that written work rather than try to type it all out. \frac{8}{1- \sqrt[]{17} }
Answers
The Solution:
The given expression is
[tex]\frac{8}{1-\sqrt[]{17}}[/tex]Rationalizing the expression with the conjugate of the denominator, we have
[tex]\frac{8}{1-\sqrt[]{17}}\times\frac{1+\sqrt[]{17}}{1+\sqrt[]{17}}[/tex]This becomes
[tex]\frac{8(1+\sqrt[]{17})}{1^2-\sqrt[]{17^2}}[/tex][tex]\frac{8+8\sqrt[]{17}}{1-17}=\frac{8(1+\sqrt[]{17})}{-16}=-\frac{1+\sqrt[]{17}}{2}[/tex]Thus, the correct answer is
[tex]-\frac{1+\sqrt[]{17}}{2}[/tex]Related Questions
-10 is no less than 2 times a number plus 14
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Let the number be x.
Then according to the question,
[tex]\begin{gathered} -10\ge2x+14 \\ -10-14\ge2x \\ -24\ge2x \\ x\ge-12 \end{gathered}[/tex]Thus, the number should be greater than or equal to -12.
pls help no need for no need for long explanations just a summary
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As shown in the figure:
There are two parallel lines of the triangle
Using the ratio and proportional to find the value of x
So,
[tex]\begin{gathered} \frac{x}{6}=\frac{9}{2} \\ \\ x=6\cdot\frac{9}{2}=\frac{54}{2} \\ \\ x=27 \end{gathered}[/tex]So, the answer is: x = 27
I need help I already answered just to make sure
Answers
The height of the tree is 13.82 m
Step - by - Step Explanation
What to find? Height of the tree.
Given:
• Angle of elevation = 62,°
,• Eye-level above the ground =160cm
,• Distance away from the tree = 6.5m
We need to first sketch the problem, to have a clearer picture of the question.
Change 160cm to meter
160 cm = 160/100 = 1.6 m
Height of the tree = 1.6 + x
We need to find the value of x.
From the sketch above;
Opposite =x
Adjacent =6.5
θ= 62°
Using the trigonometric ratio;
[tex]\tan \theta=\frac{opposite\text{ }}{\text{adjacent}}[/tex]Substitute the values.
[tex]\tan 62=\frac{x}{6.5}[/tex]Cross-multiply.
x=6.5tan62°
x = 12.22 m
Height of the tree = 1.6 m + 12.22m
Height of the tree = 13.82 m
OR
Height of the tree = 1382 cm approximately.
Acetaminophen and liver damage. It is believed that large doses of acetaminophen
(the active ingredient in over the counter pain relievers like Tylenol) may cause damage to the
liver. A researcher wants to conduct a study to estimate the proportion of acetaminophen users
who have liver damage. For participating in this study, he will pay each subject $20 and provide
a free medical consultation if the patient has liver damage.
(a) If he wants to limit the margin of error of his 98% confidence interval to 2%, what is the
minimum amount of money he needs to set aside to pay his subjects?
(b) The amount you calculated in part (a) is substantially over his budget so he decides to use
fewer subjects. How will this affect the width of his confidence interval?
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Using proportions we can conclude that the researcher should recruit a minimum of 1509 subjects.
What is proportion?A proportion is an equation that sets two ratios at the same value. For instance, you could express the ratio as follows: 1: 3 if there is 1 boy and 3 girls (for every one boy there are 3 girls).So, a study is being planned to determine the percentage of acetaminophen users who suffer liver injury.
With,
Level of confidence: 98%E=0.03 is the error margin.Then,
The z-value for 98% confidence is known Zₙ = 2.33.Calculation of the sample size: n = p(1 - p)(Zₙ/E)²In order to obtain the most cautious estimate, we should pick p = 0.5 because the researcher has no preconceived notions about what the sample proportion should be:
n = 0.5(1-0.5)(2.33/0.03)²1508.0277778 = 1509Therefore, using proportions we can conclude that the researcher should recruit a minimum of 1509 subjects.
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The correct question is given below:
It is believed that large doses of acetaminophen (the active ingredient in over the counter pain relievers like Tylenol) may cause damage to the liver. A researcher wants to conduct a study to estimate the proportion of acetaminophen users who have liver damage. If she wants to limit the margin of error of her 98% confidence interval to be no more than 3%, what is the minimum number of subjects that she needs to recruit? [Note: The researcher has no expectations about what the sample proportion should be ahead of time, so she – and you – should use p = 0.5 to get the most conservative estimate.]
Help - Classifying Quadrilaterals
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A square is all of these combined because each one could be a square, which means a square is each of these.
Answer:
A square is each of these because they may all be squares, hence a square is all of them.
Step-by-step explanation:
A tub of theater popcorn has 247.5 grams of popcorn, which is 275% larger than a regular bag of popcorn. How many grams of popcorn would be in a regular sized bag.
Answers
Let's begin by listing out the information given to us:
A tub has this: 247.5 grams of popcorn = 275%
regular-sized bag: x grams = 100%
We will solve using simple proportion
[tex]\begin{gathered} 247.5g=275 \\ xg=100 \\ \text{Cross Multiply, we have:} \\ 247.5\cdot100\cdot g=275\cdot x\cdot g \\ \text{Make x the subject of formula (divide by 275g)} \\ \frac{247.5\cdot100\cdot g}{275\cdot g}=\frac{275\cdot x\cdot g}{275\cdot g} \\ 0.9\cdot100=x\Rightarrow x=900 \\ x=900g \end{gathered}[/tex]If Allie’s parents are willing to spend $300 for a party, how many people can attend?
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At least 20 people can attend the party
Use the model to solve for x
PLS HELPPP
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Answer:
I think x is -6
Step-by-step explanation:
Side 1:
3x+1
3x-10+1=(-29)
3x-6+1=(-17)
Side 2:
2x-5
2x-10-5=(-25)
2x-6-5=(-17)
A disk is in the form of square and measures 5.25inches on each side. Find the diagonal length of thedisk. I am taking geometry In the 8th grade and I am lost
Answers
Answer:
The diagonal length is 7.42 inches.
Explanation:
The disk with its diagonal is:
Then, we can look at the diagonal as the hypotenuse of a right triangle. Then, if we call D to the diagonal:
[tex]\begin{gathered} D^2=(5.25in)^2+(5.25)^2 \\ D=\sqrt{2(5.25in)^2}\approx7.42in \end{gathered}[/tex]When interest rates are low, some automobile dealers offer loans at 0% APR, as indicated in a 2016 advertisement by a prominent car dealership, offering zero percent financing or cash back deals on some models.Zero percent financing means the obvious thing—that no interest is being charged on the loan. So if we borrow $1,200 at 0% interest and pay it off over 12 months, our monthly payment will be $1,200/12 = $100.Suppose you are buying a new truck at a price of $26,000. You plan to finance your purchase with a loan you will repay over two years. The dealer offers two options: either dealer financing with 0% interest, or a $2,600 rebate on the purchase price. If you take the rebate, you will have to go to the local bank for a loan (of $23,400) at an APR of 6.5%.What would your monthly payment be if you took the rebate? (Round your answer to the nearest cent.)
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Which answer choice below is a solution to this equation?7x + 5 – 2x = 2x – 7A. 2B. 0C. -4D. 8
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SOLUTION:
Step 1:
In this question, we are given the following:
[tex]7x\text{ + 5 - 2 x = 2 x- 7}[/tex]Step 2:
The details of the solution are as follows:
[tex]\begin{gathered} 7\text{ x - 5 - 2 x = 2 x - 7} \\ 5x\text{ - 5 = 2x - 7} \\ collecting\text{ like terms, we have that:} \\ 5\text{ x - 2x = - 7 - 5} \\ 3\text{ x = - 12} \\ Divide\text{ both sides by 3, we have that:} \\ x\text{ =}\frac{-12}{3} \\ x\text{ = - 4 \lparen OPTION C \rparen} \end{gathered}[/tex]CONCLUSION:
The final answer is:
[tex]x\text{ = - 4 \lparen OPTION C\rparen}[/tex]
4. A survey explored the relationship between gender and video game play. Which is not a reasonable interpretation of the data? Play Daily Do Not Play Daily Total Boys 45 5 50 Girls 12 38 50 Total 57 43 100 O A) More boys surveyed play video game daily than girls. TO B) Ignoring gender, a little more than half of the students surveyed play video games daily. Of the boys surveyed, 5% do not play video games daily. OD) Of the girls surveyed, exactly 24% play video games daily.
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Answer:
C.
Explanation:
Let's analyze each answer option:
Option A.
Taking into account the table, we can say that 45 boys play video games daily and 12 girls play video games daily, so more boys play video games daily than girls because 45 is greater than 12.
Option B.
In the same way, there is a total of 57 students that play video games daily and 43 that don't. Since 57 is a little higher than 50 (half of the 100 students surveyed), we can say that a little more than a half of the students surveyed play video games daily.
Option C.
There are 50 boys surveyed and from them 5 do not play video games daily, so the percentage of boys that don't play video games daily is:
[tex]\frac{5}{50}\times100=0.1\times100=10\text{ \%}[/tex]Option D.
In the same way, there are 50 girls surveyed, and 12 play video games daily, so the percentage of girls that play video games daily is:
[tex]\frac{12}{50}\times100=0.24\times100=24\text{ \%}[/tex]Therefore, the only option that is not a reasonable interpretation of the data is C. because the percentage of boys that don't play video games daily is 10% instead of 5%
HELP PLEASEEEEE!!!!!!
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Answer: D=2/7 R=4/7
Step-by-step explanation: there are 7 parts and D is the 2nd part R is the 4th part.
Write the rate as fraction in simplest form 22 gallons of pest rifles for 8 acres of crops
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Since the given rate is 22 gallons of pest for 8 acres of crops, then
We need to find how many acres per gallon
Then we will divide 22 acres by 8 gallons to find the rate
[tex]rate=\frac{22}{8}[/tex]Divide up and down by 2 to simplify
[tex]\begin{gathered} rate=\frac{\frac{22}{2}}{\frac{8}{2}} \\ \\ rate=\frac{11}{4} \end{gathered}[/tex]The answer is:
The rate is 11/4 gallon per acre (2 3/4)
By noon, the temperature in Nome had risen by 13 degrees. What was the temperature there at noon (Nome is -27 currently)
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If there will be an increase of 13 degrees, the temperature will be -14 degrees.
What was the temperature there at noon?We know that by noon, the temperature had risen by 13 degrees, and currently the temperature is -27 degrees.
A "rise" in temperature means that the temperature increases, so the temperature at noon will be 13 degrees more than now, and now it is -27 degrees, so we will get:
-27° + 13° = -14°
The temperature at noon will be -14°.
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solve for y please and thank uou
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Similar triangles are triangles that maintain the same ratio even though they are of different scales. Their angles are however equal.
In this case, y is the longest side in triangle 2 as 37.5 is the longest side in triangle 1
The ratio is thus:
[tex]\frac{y}{37.5}=\frac{16.5}{27.5}[/tex]Cross multiplying, we have:
[tex]\begin{gathered} 27.5y\text{ =37.5 x 16.5} \\ to\text{ get y, we divide both sides by 27.5} \\ \frac{27.5y}{27.5}\text{ = }\frac{\text{37.5 x 16.5}}{27.5} \end{gathered}[/tex]y = 22.5
34 Sat purchased some art supplies and cord stock in order to make greeting cards. The graphbelow shows the relationship between the number of cards Sat makes and the total cost etthe materials used te make the cardsCost of Noking Greeting CardsTotal Cost(dollars)2 4 6 8 10Number of Cards MadeBased on the graph what will be the total cost of making 25 greeting cards?*2.50G$50.00N $52.50$15.00
Answers
step 1
Find the slope
we have the points
(3,4) and (7,6)
m=(6-4)/(7-3)
m=2/4
m=$0.5 per card
the equation of the line in slope intercept form is equal to
y=mx+b
we have
m=0.50
b=?
point (3,4)
substitute
4=0.5(3)+b
b=4-1.50
b=2.50
y=0.50x+2.5
so
For x=25 cards
substitute
y=0.50(25)+2.50
y=15.00
answer is the option JLine segment AB is on square ABCD. Segment EF on equilateral triangle EFG is 12 units longer than AB. Square ABCD and triangle EFG have equal perimeters. What is the length of AB?
Answers
The length of segment AB when the line segment AB is on square ABCD is 36 units.
What is the length of segment AB?From the task content, the length of the line segment AB which is a side of the square ABCD is to be determined.
In this case, since the perimeters of triangle EFG and square ABCD are equal as given;
Let the length of segment AB = x.
Therefore, EF = x + 12.
Therefore, the perimeter of the equilateral triangle = 3(x +12).
While the perimeter of square ABCD is; 4x.
Therefore, since the perimeters are equal, we equate them and this will be:
3(x + 12) = 4x
3x + 36 = 4x
36 = x.
Therefore, the length is 36 units.
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y = 2x divided by 6?
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Answer: I'm not sure if you're trying to find x or y, but y = x/3 and x = 3y
Step-by-step explanation:
the mean is 5.8the variance is 2.4We have to find the standard deviation and round it to one decimal place.
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To calculate the standard deviation given the variance, we just take the square root.
That because the variance is:
[tex]v=\sigma^2[/tex]And the standard deviation is:
[tex]\sigma[/tex]So, calculating the standard deviation:
[tex]\sigma=\sqrt[]{\sigma^2}=\sqrt[]{v}=\sqrt[]{2.4}=1.54919\ldots\approx1.5[/tex]Thus, the standard deviation is 1.5.
True or False? The end behaviors of each end of any quadratic function are always inthe same direction.
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In general, given a quadratic function,
[tex]\begin{gathered} f(x)=ax^2+bx+c \\ a,b,c\rightarrow\text{ constants} \end{gathered}[/tex]The end behaviors of each end of the function are given by the limits of f(x) when x approaches +/-infinite.
Therefore,
[tex]\lim_{x\to\infty}f(x)=\lim_{x\to\infty}ax^2=a\lim_{x\to\infty}x^2=a*\infty[/tex]and
[tex]\lim_{x\to-\infty}f(x)=\lim_{x\to-\infty}ax^2=a\lim_{x\to-\infty}x^2=a*\infty[/tex]Thus, the two limits are the same and depend on the sign of a.
Hence, the answer is True, the statement is True.A gumball machine contains orange, yellow, and purple gum balls. The probability of getting an orange gumball is 3/4. The probability of getting a yellow gumball is 1/6. If there are 36 gumballs in the machine, how many are there of each color number of purple marbles _______ number of yellow marbles_____ number of orange marbles______
Answers
Given:
Probability of getting orange gumball is, p(o) = 3/4.
Probability of getting yellow gumball is, p(y) = 1/6.
The objective is to find the number of each colored gumballs.
Since, the sum of the events of probability is always 1.
Then, the probability of purple ball p(p) can be calculated as,
[tex]\begin{gathered} \frac{3}{4}+\frac{1}{6}+p(p)=1 \\ p(p)=1-\frac{3}{4}-\frac{1}{6} \\ p(p)=\frac{12-3(3)-1(2)}{12} \\ p(p)=\frac{1}{12} \end{gathered}[/tex]Since, it is given that the total number of gumball is N = 36.
Then, the number of orange ball can be calculated as,
[tex]\begin{gathered} p(o)=\frac{n(o)}{N} \\ \frac{3}{4}=\frac{n(o)}{36} \\ n(o)=36\cdot\frac{3}{4} \\ n(o)=27\text{ balls.} \end{gathered}[/tex]Similarly, the number of yellow ball can be calculated as,
[tex]\begin{gathered} p(y)=\frac{n(y)}{N} \\ \frac{1}{6}=\frac{n(y)}{36} \\ n(y)=\frac{36}{6} \\ n(y)=6 \end{gathered}[/tex]And the number of purple ball can be calculated as,
[tex]\begin{gathered} p(p)=\frac{n(p)_{}}{N} \\ \frac{1}{12}=\frac{n(p)}{36} \\ n(p)=\frac{36}{12} \\ n(p)=3 \end{gathered}[/tex]Hence, the number of orange ball is 27, number yellow ball is 6 and number of purple ball is 3.
For each equation in the table, give the slope of the graph.
Answers
Solving the Question
Linear equations are typically organized like this: [tex]y=mx+b[/tex] where m is the slope and b is the y-intercept.
When the equation is like [tex]y=b[/tex], it means that it is a horizontal line and the slope is 0.
When the equation is like [tex]x=d[/tex], it is a vertical line and the slope is undefined.
AnswerFirst equation: 0
Second equation: undefined
Third equation: [tex]\dfrac{4}{5}[/tex]
The round off errors when measuring the distance that a long jumper has jumped is uniformly distributed between 0 and 5.3 mm. Round values to 4 decimal places when possible.
The mean of this distribution is _____
The standard deviation is _____
The probability that the round off error for a jumper's distance is exactly 0.4 is P(x = 0.4) = ____-
The probability that the round off error for the distance that a long jumper has jumped is between 0 and 5.3 mm is P(1.2 < x < 3.4) = ____
The probability that the jump's round off error is greater than 4.16 is P(x > 4.16) = ____
P(x > 4.2 | x > 1.8) = ___
Find the 85th percentile____
Find the maximum for the lower quartile. ____
Answers
Using the uniform distribution, it is found that:
The mean is of 2.65 mm.The standard deviation is of 1.53 mm.P(X = 0.4) = 0.P(1.2 < x < 3.4) = 0.4151 = 41.51%.P(X > 4.16) = 0.2121 = 21.51%.P(X > 4.2|x > 1.8) = 0.3257 = 32.57%.85th percentile: 4.505 mm.Lower quartile: 1.325 mm.Uniform probability distributionThe uniform distribution has two bounds, a and b, and all outcomes in the distribution are equally as likely.
In this problem, the bounds are as follows:
a = 0, b = 5.3.
Hence the mean is:
M = (a + b)/2 = (0 + 5.3)/2 = 2.65 mm.
The standard deviation is of:
[tex]S = \sqrt{\frac{(b - a)^2}{12}} = \sqrt{\frac{5.3^2}{12}} = 1.53[/tex]
The uniform distribution is continuous, hence the probability of an exact value is of 0.
The probability of finding a value between c and d is:
[tex]P(c \leq X \leq d) = \frac{d - c}{b - a}[/tex]
Hence:
P(1.2 < x < 3.4) = (3.4 - 1.2)/(5.3 - 0) = 0.4151 = 41.51%.
The probability of finding a value above x is:
[tex]P(X > x) = \frac{b - x}{b - a}[/tex]
Hence:
P(X > 4.16) = (5.3 - 4.16)/(5.3 - 0) = 0.2121 = 21.51%.
P(x > 4.2 | x > 1.8) makes the lower bound 1.8, hence:
P(X > 4.2|x > 1.8) = (5.3 - 4.16)/(5.3 - 1.8) = 0.3257 = 32.57%.
The 85th percentile is found as follows:
0.85 x (5.3 - 0) = 4.505 mm.
The lower quartile is the 25th percentile, hence:
0.25 x (5.3 - 0) = 1.325 mm.
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Question 1 1. Which of the following is NOT a true statement? 1 point 21 22 23 24 25 26 27 28 O A. Angle 1 and Angle 5 are corresponding angles. w B. Angle 2 and Angle 7 are alternate interior angles. C. Angle 5 and Angle 8 are vertical angles. D. Angle 3 and Angle 7 are corresponding angles. O I e Type here to searchwhats the answer
Answers
Note:
Corresponding agles are angles on corresponding (the same) side of the two lines intersected by the transversal
Alternate angles are angles on the opposite sides of the transversal
Find the point slope Slope= 7Passing through (6,1)
Answers
The point-slope form of a line always has the form:
[tex]y-y_0=m\cdot(x-x_0)[/tex]"m" represents the slope of the line; in our case, the statement of the problem says that
[tex]m=7[/tex]Besides, (x_0, y_0) is a point of the line. By the statement of the problem (again), we can choose:
[tex]x_0=6,y_0=1[/tex]Then, the point-slope form becomes:
[tex]y-1=7\cdot(x-6)[/tex]Dr. Hughes instructs her students to solve the equation, 2x - 5y = -20, for y. What is the correct first step?Add +5y to both sides of the equation.O Add -2x to both sides of the equation.Add +2x to both sides of the equation.Divide each term in the equation by -5.
Answers
We have the following expression given:
2x -5y = -20
For this case the correct set in order to begin is add 5y in both sides
Add +5y to both sides of the equation.
The next model of a sports car will cost 3.4% more than the current model. The current model costs $36,000. How much will the price increase in dollars? What will be the price of the next model?
Answers
ANSWER
[tex]\begin{gathered} 1224 \\ 37224 \end{gathered}[/tex]EXPLANATION
Given;
Current model costs $36000
$36000 is 100% of current price.
Next model will be 100% plus 3.4%;
[tex]\begin{gathered} 100+3.4=103.4 \\ =\frac{103.4}{100} \\ =1.034 \end{gathered}[/tex]t
[tex]\begin{gathered} 1.034\times36000 \\ =37224 \end{gathered}[/tex]Therefore, the increase in price;
[tex]\begin{gathered} 37224-36000 \\ =1224 \end{gathered}[/tex]Hence, the price increase in dollars is $1224 while the price of the next model is $37224
Parallelogram ABCD was transformed to form parallelogram A'B'C'D'.У.101864D2-10-8-616 8 10a245-6881-101Which rule describes the transformation that was used to form parallelogram A'B'C'D'?O (x + 10, y + 3)0 (-x, y-3)O (x - 10.y-3)(x + 10. y-3)
Answers
Explanation
Step 1
to find the transformation, count the units moved in each axis
for x, (red line)
for y( green line)
[tex]\begin{gathered} \text{for x}\Rightarrow horizontal\Rightarrow from\text{ 2 to -8=-8-(2)=-}10 \\ \text{for y }\Rightarrow vertical\text{ }\Rightarrow\text{from 5 to 2, =2-5=-3} \\ so,\text{ the transformation is} \\ (x-10,y-3) \end{gathered}[/tex]A veterinarian is visited by many pets and their owners each day. Before the doctor attends to each pet, an assistant records information including the type, age, weight, and height of each pet. What are the individuals in the data set?
Answers
Since all the information in the study, such as the type, the age and the weight are related to the pet, individuals in each data-set are the pets.
Who are the individuals on a data-set or on a study?The individual of a data-set is the object which is being analyzed in the study, the object that has it's characteristics analyzed.
In the context of this problem, these following information are analyzed, at the register when the doctor attends each pet and registers the information.
Type of the pet.Age of the pet.Weight of the pet.Height of the pet.All these information belong to the pet that visits the veterinary, hence the individuals in each data-set are the pets.
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