Answer:
C. 6 nights in Washington, 4 nights in Atlanta, and 12 nights in Dallas
Step-by-step explanation:
Given $f(x) = \frac{\sqrt{2x-6}}{x-3}$, what is the smallest possible integer value for $x$ such that $f(x)$ has a real number value? Please show steps. Thank you!
(I rewrote the question without the symbols, they are the same question)
Given f(x) = {2x-6}/{x-3}, what is the smallest possible integer value for x such that f(x) has a real number value? Thank you!
===========================================================
Explanation:
The given function is
[tex]f(x) = \frac{\sqrt{2x-6}}{x-3}[/tex]
which is the same as writing f(x) = ( sqrt(2x-6) )/(x-3)
The key for now is the square root term. Specifically, the stuff underneath. This stuff is called the radicand.
Recall that the radicand cannot be negative, or else the square root stuff will result in a complex number. Eg: [tex]\sqrt{-4} = 0+2i[/tex]
The question is basically asking: what is the smallest x such that [tex]\sqrt{2x-6}[/tex] is a real number?
Well if we made 2x-6 as small as possible, ie set it equal to 0, then we can find the answer
[tex]2x-6 = 0\\\\2x = 6\\\\x = 6/2\\\\x = 3\\\\[/tex]
I set the radicand equal to 0 because that's as small as the radicand can get (otherwise, we're dipping into negative territory).
So 2x-6 set equal to 0 leads to x = 3.
This means x = 3 produces the smallest radicand (zero) and therefore, it is the smallest allowed x value for that square root term.
But wait, if we tried x = 3 in f(x), then we get...
[tex]f(x) = \frac{\sqrt{2x-6}}{x-3}\\\\f(3) = \frac{\sqrt{2*3-6}}{3-3}\\\\f(3) = \frac{\sqrt{0}}{0}\\\\[/tex]
which isn't good. We cannot have 0 in the denominator. Dividing by zero is not allowed. The result is undefined. It doesn't even lead to a complex number. So we'll need to bump x = 3 up to x = 4. You should find that x = 4 doesn't make the denominator 0.
----------------
In short, we found that x = 3 makes the square root as small as possible while staying a real number, but it causes a division by zero error with f(x) overall. So we bump up to x = 4 instead.
The value of my coins if I have p pennies, n nickels and twice as many quarters as pennies.
Answer:
Total value in cents = 51p+5nTotal value in dollars = (51p+5n)/100The answer varies depending if your teacher wants the answer in cents only, or in dollars only.
====================================================
Explanation:
p = number of penniesn = number of nickels2p = number of quarters, since we have twice as many quarters compared to pennies.Based on that, we know,
p = number of cents from the pennies (1 penny = 1 cent)5n = number of cents from the nickels (5 nickels = 5 cents, multiply both sides by n)25(2p) = 50p = number of cents from the quartersand ultimately
p+5n+50p = 51p+5n
represents the total value of all the coins, and this value is in cents. We would divide by 100 to convert from cents to dollars. So we can say that 51p+5n cents = (51p+5n)/100 dollars
----------------
As an example, let's say
p = 4n = 5So we have
p = 4 penniesn = 5 nickelsq = 2p = 2*4 = 8 quartersThis would mean we have
p = 4 cents from the pennies only5n = 5*5 = 25 cents from the nickels only25q = 25*8 = 200 cents from the quarters onlyOverall we have p+5n+25q = 4+25+200 = 229 cents which converts to 229/100 = $2.29
We can also say 51p+5n = 51*4+5*5 = 204+25 = 229 which is a slight shortcut to get the same result (that result being in cents).
Onetta goes to the food court to get a salad and sandwich for lunch. The Daily Deli has 8 varieties of sandwiches and 3 salads. Better Bites has 2 varieties of sandwiches and 7 salads. The Lunch Spot has 5 varieties of sandwiches and 8 salads. Determine the number of ways Onetta can select a sandwich and a salad.
Answer:
Onetta can salect a sandwich and a salad in 78 different ways.
Step-by-step explanation:
Since Onetta goes to the food court to get a salad and sandwich for lunch, and the Daily Deli has 8 varieties of sandwiches and 3 salads, while Better Bites has 2 varieties of sandwiches and 7 salads, and the Lunch Spot has 5 varieties of sandwiches and 8 salads, to determine the number of ways Onetta can select a sandwich and a salad, the following calculation must be performed:
8 x 3 + 2 x 7 + 5 x 8 = X
24 + 14 + 40 = X
78 = X
Therefore, Onetta can salect a sandwich and a salad in 78 different ways.
What is the domain of the function shown on the graph?
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Answer:
all real numbers
Step-by-step explanation:
The arrows on the ends of the curve indicate that the graph extends to infinity horizontally. The domain is the horizontal extent, so is all real numbers.
__
Additional comment
Apparently, y=-7 is a horizontal asymptote, so the range is y > -7.
What is 9,000,000 + 8,000 + 90,000,000 + 100 + 2 + 90,000 + 90 in standard form?
Answer:
i thank its 4000
Step-by-step explanation:
please mark this answer as brainlist
You need to design a rectangle with a perimeter of 14.2 cm. The length must be 2.4 cm. What is the width of the
rectangle? (You might want to draw a picture.)
a) Let w = the width of the rectangle. Write the equation you would use to solve this problem.
b) Now solve your equation
* cm.
The width of the rectangle must be. Cm
Part (a)
Answer: 2(2.4+w) = 14.2--------------
Explanation:
L = 2.4 = length
W = unknown width
The perimeter of any rectangle is P = 2(L+W)
We replace L with 2.4, and replace P with 14.2 to get 14.2 = 2(2.4+w) which is equivalent to 2(2.4+w) = 14.2
========================================================
Part (b)
Answer: w = 4.7--------------
Explanation:
We'll solve the equation we set up in part (a)
2(2.4+w) = 14.2
2(2.4)+2(w) = 14.2
4.8+2w = 14.2
2w = 14.2-4.8
2w = 9.4
w = 9.4/2
w = 4.7
The width must be 4.7 cm.
Trevor is studying a polynomial function f(x). Three given roots of f(x) are -7, 2i, and 7. Trevor concludes that f(x) must
be polynomial with degree 3. Which statement is true?
Answer:
B Trevor isn't correct because -2i must also be a root
Step-by-step explanation:
A Trevor is correct.
B Trevor is not correct because –2i must also be a root.
C Trevor is not correct there cannot be an odd number of roots.
D Trevor is not correct because there cannot be both rational and complex roots.
statements^^^^^^
The statement that f(x) must be a polynomial with degree 3 is not necessarily true based on the given roots.
What is a function?A function has an input and an output.
A function can be one-to-one or onto one.
It simply indicated the relationships between the input and the output.
Example:
f(x) = 2x + 1
f(1) = 2 + 1 = 3
f(2) = 2 x 2 + 1 = 4 + 1 = 5
The outputs of the functions are 3 and 5
The inputs of the function are 1 and 2.
We have,
Since one of the roots is complex (2i), it follows that the coefficients of f(x) must be complex as well, and therefore f(x) must be a polynomial with complex coefficients.
However, it is possible for f(x) to have a higher degree than 3.
For example,
The polynomial (x + 7)(x - 2i)(x + 2i)(x - 7) has degree 4 and has the given roots of -7, 2i, and 7. Therefore, f(x) could be a polynomial with degree 4 or higher.
Thus,
The statement that f(x) must be a polynomial with degree 3 is not necessarily true based on the given roots.
Learn more about functions here:
https://brainly.com/question/28533782
#SPJ2
The dotplots below display the scores for two classes on a 30-point statistics quiz. Class A has 26 students and Class B has 25 students.
2 dot plots. For Class A, the dots are spread out more. For Class B, the dots are more grouped together.
Which statement best compares the variability of the quiz scores for Class A and Class B?
The scores on the quiz for Class A have more variability than the scores for Class B.
The scores on the quiz for Class B have more variability than the scores for Class A.
The scores on the quiz for Class A have less variability than the scores for Class B.
The scores on the quiz for Class B have about the same variability as the scores for Class A.
I think its (A), The scores on the quiz for Class A have more variability than the scores for Class B. Can someone check me?
The statement that best compares the variability of the quiz scores for Class A and Class B is A; The scores on the quiz for Class A have more variability than the scores for Class B.
How does the dot plot work?Suppose we're measuring something whose values are numeric. For each value of that thing we observe, we plot a dot above that value in the number line. Thus, the total number of dots in the dot plot tells us the total number of observations of the values of that thing we did.
LEt suppose if we observed the value 'x', then we will make a dot above 'x'. If there is already a dot over 'x', then we will make a new dot over that dot.
The dot plot is skewed to the right due to majority of the data occur to the right of the dot plot.
An outlier is a number that is way smaller or way larger than that of other numbers in a data set. Outliers usually occur with a frequency of one.
For Class A the dots are spread out more.
For Class B, the dots are more grouped together.
Here, Looking at the dot plot, it can be seen that the numbers that range from 16 to 21 have only one dot.
The statement that best compares the variability of the quiz scores for Class A and Class B is A; The scores on the quiz for Class A have more variability than the scores for Class B.
To learn more about outliers, please check: brainly.com/question/27197311
SPJ2
Can’t find answers online to check mine.
Answer:
3. 100% = 1
3/4 = 0.75
Now, 0.75 is halfway between 0.5 and 1, so Chris is correct.
4. 10% = 10/100 = 0.1
3/5 = 0.6
Now, 0.2 is not halfway between 0.1 and 0.6, so Emily is wrong.
Answer:
3 đúng 4 wrong
Step-by-step explanation:
100%=1
giữa 0, 5 và 1 =(0,5+1)/2=3/4
10%= 0,1
giữa 0,1 và 3/5 =(0,1+3/5)/2= 0,35 #0,2
At the end of 2 years, P dollars invested at an interest rater compounded annually increases to an amount, A dollars, given by the following formula.
A = P(1+r)?
Find the interest rate if $192 increased to $363 in 2 years. Write your answer as a percent..
-
Annual compound interest rate = % (Type an integer or a decimal.)
Answer:
37.5%
Step-by-step explanation:
A=P(1+r)^t
363=192*(1+r)^2
1.375=1+r, r=0.375=37.5%
27. Which statement is true about the system x+3y=11 y=r-7 a. (8,-1) is a solution to both equations, so it is a solution to the system b. (8,-1) is a solution to one equation but not the other, so it is a solution to the system C. (8,-1) is a solution to one equation but not the other so it is not the solution to the system d. (8,-1) is not a solution to either equation, so it is not a solution to the system
Answer:b. (8,-1) is a solution to one equation but not the other, so it is a solution to the system
Step-by-step explanation:
27. Which statement is true about the system
x+3y=11
y=r-7
a. (8,-1) is a solution to both equations, so it is a solution to the system
b. (8,-1) is a solution to one equation but not the other, so it is a solution to the system
C. (8,-1) is a solution to one equation but not the other so it is not the solution to the system
d. (8,-1) is not a solution to either equation, so it is not a solution to the system
Simplify: (-2)^-3
a) 8
b) 1/8
c) -8
d) -1/8
Answer:
-1/8
Step-by-step explanation:
(-2)^-3
We know that a^-b = 1/a^b
1/(-2)^3
We know (-2)^3 = -8
1/(-8)
-1/8
Mr. Thomas invested an amount of ₱13,900 divided in two different schemes A and B at the simple interest rate of 14% p.a. and 11% p.a. respectively. If the total amount of simple interest earned in 2 years be ₱3508, what was the amount invested in Scheme B?
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Answer:
₱6400
Step-by-step explanation:
Let 'b' represent the amount invested in scheme B. Then 13900-b is the amount invested in scheme A. The total interest for 2 years is then ...
14%(13900-b)(2) +11%(b)(2) = 3508
1946 -0.03b = 1754 . . . . . . divide by 2, simplify
-0.03b = -192 . . . . . . . . . subtract 1946
b = 6400 . . . . . . . . . . . divide by -0.03
The amount invested in scheme B was ₱6400.
$17,818 is invested, part at 11% and the rest at 6%. If the interest earned from the amount invested at 11% exceeds the interest earned from the amount invested at 6% by $490.33, how much is invested at each rate? (Round to two decimal places if necessary.)
Answer:We know the total amount of money invested. $17818
x+y=17818,
We know that the difference in interest earned by the two accounts is $490.33
0.11*x-0.06*y=490.33
x=17818-y
We substitute for x
0.11*(17818-y)-0.06*y=490.33
We multiply out
1959.98-0.11y-0.06*y=490.33
We combine like terms.
1469.65=0.17*y
Isolate y
y=1469.65/0.17
y=8645 at 6%
Calculate x
x=17818-8645
x=9173 at 11%
Check
0.11*9173-0.06*8645=490.33
interest earned at 11%=1009.03
interest earned at 6%=518.70
1009.03-518.7=490.33
490.33=490.33
Since this statement is TRUE and neither amount is negative then all is well.We know the total amount of money invested. $17818
x+y=17818,
We know that the difference in interest earned by the two accounts is $490.33
0.11*x-0.06*y=490.33
x=17818-y
We substitute for x
0.11*(17818-y)-0.06*y=490.33
We multiply out
1959.98-0.11y-0.06*y=490.33
We combine like terms.
1469.65=0.17*y
Isolate y
y=1469.65/0.17
y=8645 at 6%
Calculate x
x=17818-8645
x=9173 at 11%
Check
0.11*9173-0.06*8645=490.33
interest earned at 11%=1009.03
interest earned at 6%=518.70
1009.03-518.7=490.33
490.33=490.33
Since this statement is TRUE and neither amount is negative then all is well.
write fifty and two hundreds eight thousandths as a mixed decimal
Answer:
Pretty sure it's 0.528
1. The lease common multiple of 3, 4, 6, and 8 is
OA. 8.
OB. 24.
O C.72.
OD.96.
Answer:
B. 24.
Step-by-step explanation:
3
4 = 2*2
6 = 2*3
8 = 2*2*2
LCM = 2*2*2*3 = 24
In a class of 40 statistics majors, each one constructs a 90% confidence interval for the unknown probability p of a weighted coin landing heads. About how many of the 40 intervals will capture the value of the unknown parameter p? About how many will miss it?
Answer:
36 intervals will capture the value of the unknown parameter p, and 4 will miss it.
Step-by-step explanation:
x% confidence interval:
A confidence interval is built from a sample, has bounds a and b, and has a confidence level of x%. It means that we are x% confident that the population mean is between a and b. x% of confidence intervals capture the unknown parameter.
About how many of the 40 intervals will capture the value of the unknown parameter p?
90% of them will capture, so:
0.9*40 = 36
0.1*40 = 4
36 intervals will capture the value of the unknown parameter p, and 4 will miss it.
5404 buttons are produced by a factory in Jebel Ali in a week. If the factory produced same number of buttons every day of the week, buttons produced in a day is _________________
We need to find the number of buttons the company produced per day
The company produced 772 buttons per day
Total bottons produced in a week = 5404
There are 7 days in a week
If the factory produced same number of buttons every day of the week
Then,
Buttons produced per day = Total bottons produced in a week / Total number of days in a week
= 5404 / 7
= 772 buttons
The company produced 772 buttons per day
Read more: https://brainly.com/question/24368335
Fill the blank with a number to make the expression a perfect square v^2-10v+
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Answer:
25
Step-by-step explanation:
To make this expression into a perfect square trinomial, we must add the square of half the coefficient of the linear term.
v^2 -10v +(-10/2)^2 = v^2 -10v +25
The missing constant is 25.
Evaluate 3x ^ 2 + 3x - 9 , when x = 2
A=-3
B=3
C=9
D=27
Answer:
C. 9
Step-by-step explanation:
Start plugging in the number 2
3(2)^2+3(2)-9
6^2+6-9
12+6-9
18-9
9
Help with question b please
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Answer:
(a) 5.82 cm (correctly shown)
(b) 10.53 cm
Step-by-step explanation:
a) The length BC can be found from the law of sines:
BD/sin(C) = BC/sin(D)
BC = BC·sin(C)/sin(D) = (6 cm)sin(48°)/sin(50°) ≈ 5.82 cm
__
b) The angle ABD is the sum of the angles shown:
angle ABD = 50° +48° = 98°
We know the lengths BA and BD and the included angle ABD, so we can use the law of cosines to find AD.
AD² = BA² +BD² -2·BA·BD·cos(98°)
AD² ≈ 8² +5.82² -2(8)(5.82)(-0.139173) ≈ 110.8411
AD ≈ √110.8411 ≈ 10.53 . . . . cm
g Jack is polling New Yorkers to determine what proportion of them want to legalize recreational marijuana. How many New Yorkers should the sample to ens
Answer:
1006
Step-by-step explanation:
Take proportion, p = 62%
n = (Z² * pq) / M.E²
Margin error = 0.03
p = 62% = 0.62
q = 1 - p = 1 - 0.62 = 0.38
Zcritical at 95% = 1.96
n = (1.96² * (0.62*0.38)) / 0.03²
n = 0.90508096 / 0.0009
n = 1005.6455
n = 1006
Sample size = 1006
Workbook
WB-21
38. What is the circumference of a circle that has a diameter of 12 inches? (Use
3.14 for 1.)
a. 15.14 inches
b. 37.68 inches
c. 376.8 inches
d. 9.42 inches
Answer:
37.68
Step-by-step explanation:
Formula for finding the circumference of a circle is C = 2πr
If you substitute the numbers in you should get 37.68.
. Tachycardia means ...................heart rate a) fast b) slow c) irregular d) arrhythmic
Answer:
no entiendo inglés........,
Hi,
Answer:
Tachycardia is a fast heart rate
A quality-conscious disk manufacturer wishes to know the fraction of disks his company makes which are defective.
a. Suppose a sample of 865 floppy disks is drawn. Of these disks, 112 were defective. Using the data, estimate the proportion of disks which are defective.
b. Suppose a sample of 865 floppy disks is drawn. Of these disks, 112 were defective. Using the data, construct the 95% confidence interval for the population proportion of disks which are defective.
Answer:
a) 0.1295
b) The 95% confidence interval for the population proportion of disks which are defective is (0.1071, 0.1519).
Step-by-step explanation:
Question a:
112 out of 865, so:
[tex]\pi = \frac{112}{865} = 0.1295[/tex]
Question b:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the z-score that has a p-value of [tex]1 - \frac{\alpha}{2}[/tex].
For this problem, we have that:
[tex]n = 865, \pi = 0.1295[/tex]
95% confidence level
So [tex]\alpha = 0.05[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].
The lower limit of this interval is:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.1295 - 1.96\sqrt{\frac{0.1295*0.8705}{865}} = 0.1071[/tex]
The upper limit of this interval is:
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.1295 + 1.96\sqrt{\frac{0.1295*0.8705}{865}} = 0.1519[/tex]
The 95% confidence interval for the population proportion of disks which are defective is (0.1071, 0.1519).
Reflect figure E across the x-axis and then reflect across the y-axis. What is the resulting figure?
rectangle D
B
rectangle B
9
rectangle C
10
rectangle A
Answer:
2nd option, rectangle B
Step-by-step explanation:
After reflexion, the figure will be at the left side of x=-5
In the picture below, which lines are lines of symmetry for the figure?
A. 1 and 3
B. only 1
C. only 3
D. 2 and 4
Answer:
It's option C. only 3
Step-by-step explanation:
A line of symmetry is a line which will cut any shape in exactly half. In your given picture, only line 3 is symmetrical because if you were to fold the shape after you cut it in half, both halves would match and be equal.
Tìm GTLN và GTNN của
M=x+2y biết x^2 + 4y^2
Answer:
saya tidak tahu !)!(!)!(!)!(!)!(!)!(!)!(!)!(!)!(!)!(!)!(!)!(!)!(!qjjjjbugg7yhhuhhhuhgy fundes per grallahegeuebevhehehnjķßùèò395oìùýþŕèwqàďhĺ
NO LINKS OR ANSWERING WHAT YOU DON'T KNOW. THIS NOT A TEST OR AN ASSESSMENT. PLEASE HELP ME WITH THESE MATH QUESTIONS FOR AN ASSIGNMENT!!! Chapter 10 part 1
1. What is an extraneous solution and what type of functions might they occur in?
2. Given a vertical asymptote and horizontal asymptote, how would you begin to find an expression for a rational function?
Answer:
1.
An extraneous solution is a root of a transformed equation that is not a root of the original equation as it was excluded from the domain of the original equation.
It emerges from the process of solving the problem as a equation.
2.I begin like:
The vertical asymptotes will occur at those values of x for which the denominator is equal to zero:
for example:
x² − 4=0
x²= 4
doing square root on both side
x = ±2
Thus, the graph will have vertical asymptotes at x = 2 and x = −2.
To find the horizontal asymptote, the degree of the numerator is one and the degree of the denominator is two.
The lines shown below are parallel. If the green line has a slope of -2, what is
the slope of the red line?
Answer:
Hi! There's no picture, but we don't need that to find the answer. Parallel lines always have the same slope. I suppose you're saying that the green and red line are parallel -- so, the red line's slope is also -2.
-2 <--
Hope this helps!! Have a nice day & please mark brainliest if you don't mind!
