[tex]\boxed{\sf (a+b)^2=a^2+b^2+2ab}[/tex]
Now
[tex]\\ \sf\longmapsto x+\dfrac{1}{x}=12[/tex]
[tex]\\ \sf\longmapsto \left(x+\dfrac{1}{x}\right)^2=12^2[/tex]
[tex]\\ \sf\longmapsto x^2+2\times x\times \dfrac{1}{x}+\left(\dfrac{1}{x}\right)^2=144[/tex]
[tex]\\ \sf\longmapsto x^2+\dfrac{1}{x^2}+2=144[/tex]
[tex]\\ \sf\longmapsto x^2+\dfrac{1}{x^2}=144-2=142[/tex]
Answer:
122
Step-by-step explanation:
x+1/x = 12
x + 1 = 12x
x = 1/11
（1/11）² + 1 / （1/11）² = 1/121 +1 /1/121 = 122
I need some help! thank you!
Answer:
The 1st,Thrid, Fifth Option
Step-by-step explanation:
The first option is true. We can move the orginal square root function to get g(x).
The second option is false. Function g(x) which equals
[tex] \sqrt{x - 3} - 1[/tex]
Domain is all real numbers greater than or equal to 3.
The third option is true. Since minimum point we can get is 0 in a square root function. We have a vertical shift so our new minimum point is
[tex]0 - 1 = - 1[/tex]
We can take the sqr root of 0 so
So all real numbers that are greater than or equal to -1 is true.
The fourth option is false, we need to add 3 instead of subtract 3.
The fifth option is true, we can do that to get back to our original function
A recent study of the relationship between social activity and education for a sample of corporate executives showed the following results. Social Activity Education Above Average Average Below Average College 30 20 10 High School 20 40 90 Grade School 10 50 130 The appropriate test statistic for the analysis is a(n) ______.a. F-statistic.b. t-statistic.c. Chi-square statistic.d. z-statistic.
Answer:
Chisquare statistic
Step-by-step explanation:
The most appropriate test to use here is the Chisquare test as it isemployed when testing the relationship between two variables. Both the T statistic and z statistics are the used for testing difference in means. However, in the analysis above, we are given two variables with each having its own levels. Hence, the Chisquare test is the most appropriate in this kind of situation a it measures if a difference exists between the two variables. It tests if they are related or independent of on one another
A soft drink manufacturer wishes to know how many soft drinks adults drink each week. They want to construct a 95% confidence interval with an error of no more than 0.08. A consultant has informed them that a previous study found the mean to be 3.1 soft drinks per week and found the variance to be 0.49. What is the minimum sample size required to create the specified confidence interval? Round your answer up to the next integer.
Answer:
The minimum sample size required to create the specified confidence interval is 295.
Step-by-step explanation:
We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1 - 0.95}{2} = 0.025[/tex]
Now, we have to find z in the Z-table as such z has a p-value of [tex]1 - \alpha[/tex].
That is z with a pvalue of [tex]1 - 0.025 = 0.975[/tex], so Z = 1.96.
Now, find the margin of error M as such
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
Variance of 0.49:
This means that [tex]\sigma = \sqrt{0.49} = 0.7[/tex]
They want to construct a 95% confidence interval with an error of no more than 0.08. What is the minimum sample size required to create the specified confidence interval?
The minimum sample size is n for which M = 0.08. So
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
[tex]0.08 = 1.96\frac{0.7}{\sqrt{n}}[/tex]
[tex]0.08\sqrt{n} = 1.96*0.7[/tex]
[tex]\sqrt{n} = \frac{1.96*0.7}{0.08}[/tex]
[tex](\sqrt{n})^2 = (\frac{1.96*0.7}{0.08})^2[/tex]
[tex]n = 294.1[/tex]
Rounding up:
The minimum sample size required to create the specified confidence interval is 295.
The concentration of carbon monoxide (CO) in a gas sample is measured by a spectrophotometer and found to be 85 ppm. Through long experience with this instrument, it is believed that its measurements are unbiased and normally distributed, with an uncertainty (standard deviation) of 9 ppm. Find a 95% confidence interval for the concentration of CO in this sample. Round the answers to two decimal places. The 95% confidence interval is
Answer:
The confidence interval is [tex](85 - \frac{14.81}{\sqrt{n}},85 + \frac{14.81}{\sqrt{n}})[/tex], in which n is the size of the sample.
Step-by-step explanation:
We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1 - 0.95}{2} = 0.025[/tex]
Now, we have to find z in the Z-table as such z has a p-value of [tex]1 - \alpha[/tex].
That is z with a pvalue of [tex]1 - 0.025 = 0.975[/tex], so Z = 1.96.
Now, find the margin of error M as such
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
[tex]M = 1.645\frac{9}{\sqrt{n}} = \frac{14.81}{\sqrt{n}}[/tex]
The lower end of the interval is the sample mean subtracted by M. So it is [tex]85 - \frac{14.81}{\sqrt{n}}[/tex]
The upper end of the interval is the sample mean added to M. So it is [tex]85 + \frac{14.81}{\sqrt{n}}[/tex]
The confidence interval is [tex](85 - \frac{14.81}{\sqrt{n}},85 + \frac{14.81}{\sqrt{n}})[/tex], in which n is the size of the sample.
If he is correct, what is the probability that the mean of a sample of 68 computers would differ from the population mean by less than 2.08 months
Complete Question
The quality control manager at a computer manufacturing company believes that the mean life of a computer is 91 months with a standard deviation of 10 months if he is correct. what is the probability that the mean of a sample of 68 computers would differ from the population mean by less than 2.08 months? Round your answer to four decimal places. Answer How to enter your answer Tables Keypad
Answer:
[tex]P(-1.72<Z<1.72)=0.9146[/tex]
Step-by-step explanation:
From the question we are told that:
Population mean \mu=91
Sample Mean \=x =2.08
Standard Deviation \sigma=10
Sample size n=68
Generally the Probability that The sample mean would differ from the population mean
P(|\=x-\mu|<2.08)
From Table
[tex]P(|\=x-\mu|<2.08)=P(|z|<1.72)[/tex]
T Test
[tex]Z=\frac{\=x-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex]
[tex]Z=\frac{2.08}{\frac{10}{\sqrt{68} } }[/tex]
[tex]Z=1.72[/tex]
[tex]P(|\=x-\mu|<2.08)=P(|z|<1.72)[/tex]
[tex]P(-1.72<Z<1.72)[/tex]
Therefore From Table
[tex]P(-1.72<Z<1.72)=0.9146[/tex]
write your answer in simplest radical form
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Answer:
f = 3 units
Step-by-step explanation:
The ratios of side lengths in this 30°-60°-90° triangle are ...
1 : √3 : 2
So, the ratio of interest is ...
1 : √3 = √3 : f
We can see that the numbers in the second ratio are √3 times the numbers in the first ratio, so
f = √3 × √3 = 3
f = 3 units
What is the simplified expression for the
expression below? 4(x+8)+5(x-3)
In the case of normally distributed classes, discriminant functions are linear (straight lines, planes, and hyperplanes for two-, three-, and n-dimensional feature vectors, respectively) when the covariances matrices of corresponding classes are equal.
a. True
b. False
Answer:
True
Step-by-step explanation:
When covariance matrices of corresponding class are identical and diagonal matrix and their class probability is same then the class is normally distributed and its discriminant functions are linear.
identify the angles relationship
Hiiii can u please pls pls pls
Answer:
x | y
0 | 0
6 | 2
12 | 4
Step-by-step explanation:
Multiply each x value in the table by 1/3 to get 0, 2, and 4 for your y values.
Answer:
x y
0 0
6 2
12 4
Step-by-step explanation:
Is means equals
The equation is
y = 1/3 x
Let x = 0
y = 1/3 (0) = 0
Let x = 6
y = 1/3 (6) = 2
Let x = 12
y = 1/3 (12) = 4
Suppose f(x)=x^2. What is the graph of g(x)=1/2f(x)?
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Answer:
see attached
Step-by-step explanation:
The graph of g(x) is a vertically scaled version of the graph of f(x). The scale factor is 1/2, so vertical height at a given value of x is 1/2 what it is for f(x). This will make the graph appear shorter and fatter than for f(x).
The graph of g(x) is attached.
You want to walk from home to a clothing store that is 1/4 miles away you stop for a rest after 1/8 miles how much farther do you have to walk
Answer:
1/8
Step-by-step explanation:
Answer: 1/8
Step-by-step explanation:
1/8 + 1/8 = 2/8 = 1/4
The regression analysis can be summarized as follows: Multiple Choice No significant relationship exists between the variables. A significant negative relationship exists between the variables. For every unit increase in x, y decreases by 12.8094. A significant positive relationship exists between the variables
Answer:
A significant negative relationship exists between the variables
Step-by-step explanation:
Base on the information given in the question which goes thus : For every unit increase in x, y decreases by 12.8094. The value 12.8094 is the slope which is the rate of change in y variable per unit change in the independent variable. The sign or nature of the slope Coefficient gives an hint about the relationship between the x and y variables. The slope Coefficient in this case is negative and thus we'll have a negative relationship between the x and y variables (an increase in x leads to a corresponding decrease in y). This is a negative association.
Let f(x) = 5 + 12x − x^3. Find (a) the x- coordinate of all inflection points, (b)
the open intervals on which f is concave up, (c) the open intervals on which
f is concave down.
Answer:
A) x = 0.
B) f is concave up for (-∞, 0).
C) f is concave down for (0, ∞).
Step-by-step explanation:
We are given the function:
[tex]f(x)=5+12x-x^3[/tex]
A)
We want to find the x-coordinates of all inflection points.
Recall that inflections points (may) occur when the second derivative equals zero. Hence, find the second derivative. The first derivative is given by:
[tex]f'(x) = 12-3x^2[/tex]
And the second:
[tex]f''(x) = -6x[/tex]
Set the second derivative equal to zero:
[tex]0=-6x[/tex]
And solve for x. Hence:
[tex]x=0[/tex]
We must test the solution. In order for it to be an inflection point, the second derivative must change signs before and after. Testing x = -1:
[tex]f''(-1) = 6>0[/tex]
And testing x = 1:
[tex]f''(1) = -6<0[/tex]
Since the signs change for x = 0, x = 0 is indeed an inflection point.
B)
Recall that f is concave up when f''(x) is positive, and f is concave down when f''(x) is negative.
From the testing in Part A, we know that f''(x) is positive for all values less than zero. Hence, f is concave up for all values less than zero. Our interval is:
[tex](-\infty, 0)[/tex]
C)
From Part A, we know that f''(x) is negative for all values greater than zero. So, f is concave down for that interval:
[tex](0, \infty)[/tex]
A ball is thrown from an initial height of 7 feet with an initial upward velocity of 23 ft/s. The ball's height h (in feet) after 1 seconds is given by the following.
h = 7+23t-16t^2
Find all values of 1 for which the ball's height is 15 feet.
Answer:
Step-by-step explanation:
If we are looking for the time(s) that the ball is at a height of 15, we simply sub in a 15 for the height in the position equation and solve for t:
[tex]15=-16t^2+23t+7[/tex] and
[tex]0=-16t^2+23t-8[/tex]
Factor this however you factor a quadratic in class to get
t = .59 seconds and t = .85 seconds.
This means that .59 seconds after the ball was thrown into the air it was 15 feet off the ground. Then the ball reached its max height, gravity took over, and began pulling it back down to earth. The ball passes the height of 15 feet again on its way down after .85 seconds.
Lisa reads an equal number of pages of a book every week. The graph below shows the number of pages of the book left to read, y, after x weeks:
A graph titled Lisas Book Reading shows Number of Weeks on the x-axis and Number of Pages Left on the y-axis. The scale on the x-axis shows numbers from 0 to 6 at increments of 1, and the scale on the y-axis shows numbers from 0 to 350 at increments of 50. A straight line joins the ordered pairs 0, 250 and 1, 200 and 2, 150 and 3, 100 and 4, 50 and 5, 0.
Which equation best models the relationship between x and y?
y = −50x + 250
y = −5x + 50
y = −50x + 350
y = −5x + 250
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Answer:
(a) y = −50x + 250
Step-by-step explanation:
In case you don't realize that the graph starts at 250 and decreases by 50 for each increase of 1 in x, you can see if any of the equations match the given points. The only one that does is the first one:
y = -50x +250
Answer:
(a) y = −50x + 250
Step-by-step explanation:
Evaluate − x 2 −5 y 3 when x = 4 and y =−1
Answer:
-11
Step-by-step explanation:
I am going to assume that it is -x^2-5y^3.
-(4^2)-5(-1^3)
-16-5(-1)
-16+5
-11
Answer:
- 11
Step-by-step explanation:
If x = 4, y = -1
then,
- x^2 - 5y^3 = - (4)^2 - 5(-1)^3
= - 16 + 5
= - 11
A sporting goods store manager was selling a ski set for a certain price. The manager offered the markdowns shown, making the one-day sale price of the ski set $324. Find the original selling price of the ski set.
Answer:
$520.632
Step-by-step explanation:
Factor 12x-40 using the gcf
Answer:
4(3x-10)
Step-by-step explanation:
12x-40 = (4*3)x-(4*10) = 4(3x-10). The GCF is 4.
I need help with this it is very confusing.
Answer:
Part A: 90 + 6x = 108
Part B: 3
Step-by-step explanation:
Part A:
Variable x = number of movie tickets purchased
18 × 5 + 6x = 108
90 + 6x = 108
Part B:
Variable y = number of people
18y + 1(7) = 61
18y + 7 = 61
18y = 54
y = 3
There were 3 people in this group.
The population of the world in 1987 was 5 billion and the annual growth rate was estimated at 2 percent per year. Assuming that the world population follows an exponential growth model, find the projected world population in 2015
Answer:
The projected world population in 2015 was 8,705,121,030 people.
Step-by-step explanation:
Given that the population of the world in 1987 was 5 billion and the annual growth rate was estimated at 2 percent per year, assuming that the world population follows an exponential growth model, to find the projected world population in 2015 the following calculation must be performed :
5,000,000,000 x 1.02 ^ (2015-1987) = X
5,000,000,000 x 1.02 ^ 28 = X
5,000,000,000 x 1.741024 = X
8,705,121,030 = X
Therefore, the projected world population in 2015 was 8,705,121,030 people.
5(u-3)-3=-3(-6u+4)-3u
Answer:
u = -3/5
Step-by-step explanation:
5(u-3) - 3 = -3(-6u + 4) - 3u
(5u - 15) - 3 = (18u - 12) - 3u
5u - 18 = 15u - 12
-18 = 10u - 12
-6 = 10u
u = -6/10
u = -3/5
Write the sentence as an inequality. The temperature t is at least 82 F
Answer:
t ≥ 82
Step-by-step explanation:
at least means that it could be 82 but it could be more
t ≥ 82
Which statement is true about the net and the solid it can form?
A. The length of side a will be 5 m.
B. The length of side b will be 2 m.
C. The length of side c will be 7 m.
D. The length of side c will be 2 m.
Step-by-step explanation:
Option B
The length of side will be 2m...
hope it helps
Use the functions below to complete Parts 1 and 2.
f(x)= |x| g(x)= |x+2| - 3
Part 1: Graph f(x) and g(x) on the grid below. Label each graph.
HINT: Making a table of values for each function may help you to graph them.
Part 2: describe how the graph of g(x) relates to the graph of its parent function, f(x).
HINT: Think about how f(x) was shifted to get g(x).
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Answer:
1. see below
2. g(x) is f(x) translated left 2 and down 3
Step-by-step explanation:
1. The graphs are attached. F(x) is in red; g(x) is in blue.
__
2. The graph of g(x) = f(x -h) +k is the parent function translated by (h, k). Here we have (h, k) = (-2, -3), so g(x) is f(x) translated left 2 and down 3.
A research team is testing a product that will minimize wrinkles among older adults. Volunteers in the age group of 40 to 45 are included in the research. The research team gives a cream to be applied on the face to one group and a placebo cream to the other group.
In factons you divide the numerator and the whole number .. then denominator
Correct?
Answer:
Step-by-step explanation:
yes
(2/3)^x-1=27/8, Find x
Which is heavier, 4- kilograms
or
4
4 kilograms?
Answer:
i think 4 4 kilograms if im wrong sorry
Step-by-step explanation:
4. A typical smartphone battery (yes that includes iphones) degrades at approximately 1%
battery capacity per month with typical use.
a. Construct an equation using f(t) and t that represents the relationship between
"f(t)" the battery capacity of a typical smartphone after "t" months and "L" the
number of months the smartphone has been in normal use.
b. What does the horizontal intercept represent in context? (The x-intercept)
c. What does the vertical intercept represent in context? (The y-intercept)
Answer:
a. [tex]f(t) = (0.99)^{t} 100%\\[/tex]
b. The x - intercept represents the time at which the battery life drops to 0 %.
c. The y - intercept represents the initial battery life.
Step-by-step explanation:
a. Construct an equation using f(t) and t that represents the relationship between
"f(t)" the battery capacity of a typical smartphone after "t" months and "L" the
number of months the smartphone has been in normal use.
Let the initial battery life be I.
After one month, it decreases by 1%. So, our new value, I' = initial value - decrease = I - 1%I = 99%I.
After two months, it decreases by 1% to our new value I". So, our new value, I" = initial value - decrease = I' - 1%I' = 99%I' = 99%(99%)I = (99%)²I
After three months, it decreases by 1% to our new value I'". So, our new value, I"' = initial value - decrease = I" - 1%I" = 99%I" = 99%(99%)²I = (99%)³I
We see a pattern here.
After t months, f(t)
[tex]f(t) = (0.99)^{t} 100%\\[/tex]
b. What does the horizontal intercept represent in context? (The x-intercept)
The x - intercept represents the time at which the battery life drops to 0 %.
c. What does the vertical intercept represent in context? (The y-intercept)
The y - intercept represents the initial battery life.
