Answers
Answer:
Step-by-step explanation:
Given function is,
[tex]r(x)=\frac{3x^3-7}{x^2-6x+9}[/tex]
For x = 0, substitute the value of x in the given function.
[tex]r(0)=\frac{3(0)^3-7}{(0)^2-6(0)+9}[/tex]
[tex]r(0)=\frac{-7}{9}[/tex]
For r = 3,
[tex]r(3)=\frac{3(3)^3-7}{(3)^2-6(3)+9}[/tex]
[tex]r(3)=\frac{81-7}{9-18+9}[/tex]
[tex]=\frac{74}{(9-18+9)}[/tex]
[tex]=\frac{74}{0}[/tex]
Function is undefined at x = 3.
For x = -3,
[tex]r(-3)=\frac{3(-3)^3-7}{(-3)^2-6(-3)+9}[/tex]
[tex]=\frac{-81-7}{9+18+9}[/tex]
[tex]=\frac{-88}{36}[/tex]
[tex]=-\frac{22}{9}[/tex]
Related Questions
Which of the following is not true?
Answers
Answer:
C. m<c = 140°
Step-by-step explanation:
Let's analyse each of the given options:
A. m<a = 140° is TRUE
Rationale: angle a and 140° are vertical angles. Vertical angles are congruent.
B. m<b = 140° is TRUE.
Rationale: angle a and 140° are alternate interior angles. Alternate interior angles are congruent.
C. m<c = 140° is NOT TRUE.
Rationale: angle c and 140° are same side interior angles. Same side interior angles are supplementary.
D. m<d = 140° is TRUE.
Rationale: angle d and 140° are corresponding angles. Corresponding angles are congruent.
Help me find the domain and range please!
Answers
Answer:
Domain: (-∞, 1]
Range: (-∞, 3]
Step-by-step explanation:
The function starts at point (1, 3) and goes to the left and down forever.
Domain: (-∞, 1]
Range: (-∞, 3]
Answer:
Domain: [tex](-\infty, 1][/tex]
Range: [tex](-\infty, 3][/tex]
Step-by-step explanation:
The domain of a function represents the range of x-values that are part of the function, read left to right. We can see that the function goes forever to the left and stops at [tex]x=1[/tex] when we read left to right. Therefore, the domain of this function is [tex]\boxed{(-\infty, 1]}[/tex].
The point at [tex]x=1[/tex] is a filled-in solid dot so it is included as part of the function. Use square brackets to denote inclusive.
The range of a function represents all y-values that are part of the function, read bottom to top. The function continues down forever and stops at [tex]y=3[/tex] when read bottom to top. Therefore, the range of this function is [tex]\boxed{(-\infty, 3]}[/tex]. Similar to the domain, we use a square bracket on the right to indicate that [tex]y=3[/tex] is included in the function. If the dot was not filled-in, then we would use a parenthesis to indicate that [tex]y=3[/tex] would not be part of the function.
Which best describes the function represented by the
table?
Х
-2
2
4
6
Y у
-5
5
10
15
O direct variation; k = 33 를
O direct variation; k = 5
- 를
O inverse variation; k = 10
direct variation; k = 1
10
Answers
Answer:
Direct variation
[tex]k = 2.5[/tex]
Step-by-step explanation:
Given
The attached table
Required
The type of variation
First, we check for direct variation using:
[tex]k = \frac{y}{x}[/tex]
Pick corresponding points on the table
[tex](x,y) = (-2,-5)[/tex]
So:
[tex]k = \frac{-5}{-2} = 2.5[/tex]
[tex](x,y) = (4,10)[/tex]
So:
[tex]k = \frac{10}{4} = 2.5[/tex]
[tex](x,y) = (6,15)[/tex]
So:
[tex]k = \frac{15}{6} = 2.5[/tex]
Hence, the table shows direct variation with [tex]k = 2.5[/tex]
What is the range of the table of values
Answers
Answer:
Range: { 0,3,5,7,9}
Step-by-step explanation:
The range is the values that y takes
Range: { 0,3,5,7,9}
Now we have to find,
The range of the table of values,
→ Range = ?
Then the range will be the numbers that is in the Y column.
→ Range = ?
→ Range = (value that Y takes)
→ Range = 0,3,5,7,9
Therefore, the range is 0,3,5,7,9.
Integration of [(x+1)/(x-1)]dx
Answers
Hello!
∫[(x+1)/(x-1)dx
∫t+2/t dt
∫t/t + 2/t dt
∫1 + 2/t dt
∫1dt + ∫2/t dt
∫t + 2In (|t|)
x - 1 + 2In (|x-1|)
x + 2In (|x-1|) + C, C ∈ R
Good luck! :)
HELPPPPPPP PLEASEEEEEEE
Answers
Answer:
150 dollars. if I am wrong correct me
Answer:
C and D
Step-by-step explanation:
15 to 30 galons at $9.95 to $21.00
the minimum amount can be found by calculating the minimum amount sold at a minimum price 15*9.95 = $149.25
the maximum amount can be found by calculating the maximum amount sold at a maximum price 30*21 = $630
there are 2 choices that are between 149.25 and 630, C, and D
Craig made a mobile using geometric shapes including triangles shaped as shown. For what value of X and Y can you use a triangle congruence theorem to show that the triangles are congruent? Which triangle congruence theorem can you use? Explain.
.
.
.
May you also show the work? Please help. Thank you.
Answers
Answer:
x = 3
y = 8
Step-by-step explanation:
In the given triangle FGH,
m∠F + m∠G + m∠H = 180° [Triangle sum theorem]
60° + 90° + m∠H = 180°
m∠H = 30°
If the given triangles FGH and TUV are congruent, their corresponding sides will be equal in measure.
m∠F = m∠T
7y + 4 = 60°
7y = 56
y = 8
GH ≅ UV
8x - 12 = 12
8x = 24
x = 3
Using the AAS congruence theorem, the values of x and y that show that both triangles are congruent are: x = 3 and y = 8.
What is the AAS Congruence Theorem?According to the angle-angle-side congruence theorem (AAS), two triangles are congruent if they have two corresponding congruent angles and one pair of corresponding non-included sides that are congruent.
Thus, by the AAS theorem, we have:
8x - 12 = 12
8x = 12 + 12
8x = 24
x = 3
Also,
7y + 4 = 60
7y = 60 - 4
7y = 56
y = 8
Therefore, using the AAS congruence theorem, the values of x and y that show that both triangles are congruent are: x = 3 and y = 8.
Learn more about AAS congruence theorem on:
https://brainly.com/question/3168048
Which of the following is a polynomial?
Answers
Answer:
(D.) 3x^2 + 6x
Step-by-step explanation:
the other options aren't complete and some don't even create a parabola.
how to solve for
LN and what are the variables
Answers
Answer:
v See below. v
Step-by-step explanation:
LM = MN
11x - 21 = 8x + 15
[tex]3x-21=15\\3x=36\\[/tex]
x = 12
LM = 11(12) - 21 = 132 - 21 = 111
MN = 8(12) + 15 = 96 + 15 = 111
LN = 111 + 111 = 222
A line that passes through the origin also passes through the point (6,2). What is the slope of the line?
please answer with an explanation
Answers
9514 1404 393
Answer:
1/3
Step-by-step explanation:
The slope of a line is the ratio of its "rise" to its "run." The "rise" is the change in vertical distance, and the "run" is the corresponding change in horizontal distance between two points on the line. The formula for the slope is ...
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}\qquad\text{where $(x_1,y_1)$ and $(x_2,y_2)$ are points on the line}[/tex]
In this problem, you are told the line passes through the origin, which is point (x, y) = (0, 0), and through point (6, 2). Using these coordinates in the slope formula gives ...
[tex]m=\dfrac{2-0}{6-0}=\dfrac{2}{6}=\boxed{\dfrac{1}{3}}[/tex]
__
You may notice that when the line passes through the origin, the slope is simply the ratio y/x of any point on the line. Here, that ratio is 2/6 = 1/3.
_____
Additional comment
A line through the origin is the graph of a proportional relationship. That is, y is proportional to x. The slope of the line is the constant of proportionality. The equation of the line is ...
y = kx . . . . . . where k is the constant of proportionality.
The line in this problem statement will have the equation ...
y = (1/3)x
(a) The heights of male students in a college are thought to be normally distributed with mean 170 cm and standard deviation 7.
The heights of 5 male students from this college are measured and the sample mean was 174 cm.
Determine, at 5% level of significance, whether there is evidence that the mean height of the male students of this college is higher than 170 cm.
[6]
(b) (i) The result of a fitness trial is a random variable X which is normally distributed with mean μ and standard deviation 2.4 . A researcher uses the results from a random sample of 90 trials to calculate a
98% confidence interval for μ . What is the width of this interval?
[4]
(ii) Packets of fish food have weights that are distributed with standard deviation 2.3 g. A random sample of 200 packets is taken. The mean weight of this sample is found to be 99.2 g. Calculate a 99% confidence interval for the population mean weight.
[4]
(c) (i) Explain the difference between a point estimate and an interval
Estimate. [2]
(ii) The daily takings, $ x, for a shop were noted on 30 randomly chosen days. The takings are summarized by Σ x=31 500 and
Σ x2=33 141 816 .
Calculate unbiased estimates of the population mean and variance of the shop’s daily taking. [4
Answers
Answer:
the answer is 50 but I don't know if
Problem: The height, X, of all 3-year-old females is approximately normally distributed with mean 38.72
inches and standard deviation 3.17 inches. Compute the probability that a simple random sample of size n=
10 results in a sample mean greater than 40 inches. That is, compute P(mean >40).
Gestation period The length of human pregnancies is approximately normally distributed with mean u = 266
days and standard deviation o = 16 days.
Tagged
Math
1. What is the probability a randomly selected pregnancy lasts less than 260 days?
2. What is the probability that a random sample of 20 pregnancies has a mean gestation period of 260 days
or less?
3. What is the probability that a random sample of 50 pregnancies has a mean gestation period of 260 days
or less?
4. What is the probability a random sample of size 15 will have a mean gestation period within 10 days of
the mean?
Know
Learn
Booste
V See
Answers
Answer:
0.1003 = 10.03% probability that a simple random sample of size n= 10 results in a sample mean greater than 40 inches.
Gestation periods:
1) 0.3539 = 35.39% probability a randomly selected pregnancy lasts less than 260 days.
2) 0.0465 = 4.65% probability that a random sample of 20 pregnancies has a mean gestation period of 260 days or less.
3) 0.004 = 0.4% probability that a random sample of 50 pregnancies has a mean gestation period of 260 days or less.
4) 0.9844 = 98.44% probability a random sample of size 15 will have a mean gestation period within 10 days of the mean.
Step-by-step explanation:
To solve these questions, we need to understand the normal probability distribution and the central limit theorem.
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
The height, X, of all 3-year-old females is approximately normally distributed with mean 38.72 inches and standard deviation 3.17 inches.
This means that [tex]\mu = 38.72, \sigma = 3.17[/tex]
Sample of 10:
This means that [tex]n = 10, s = \frac{3.17}{\sqrt{10}}[/tex]
Compute the probability that a simple random sample of size n= 10 results in a sample mean greater than 40 inches.
This is 1 subtracted by the p-value of Z when X = 40. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{40 - 38.72}{\frac{3.17}{\sqrt{10}}}[/tex]
[tex]Z = 1.28[/tex]
[tex]Z = 1.28[/tex] has a p-value of 0.8997
1 - 0.8997 = 0.1003
0.1003 = 10.03% probability that a simple random sample of size n= 10 results in a sample mean greater than 40 inches.
Gestation periods:
[tex]\mu = 266, \sigma = 16[/tex]
1. What is the probability a randomly selected pregnancy lasts less than 260 days?
This is the p-value of Z when X = 260. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{260 - 266}{16}[/tex]
[tex]Z = -0.375[/tex]
[tex]Z = -0.375[/tex] has a p-value of 0.3539.
0.3539 = 35.39% probability a randomly selected pregnancy lasts less than 260 days.
2. What is the probability that a random sample of 20 pregnancies has a mean gestation period of 260 days or less?
Now [tex]n = 20[/tex], so:
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{260 - 266}{\frac{16}{\sqrt{20}}}[/tex]
[tex]Z = -1.68[/tex]
[tex]Z = -1.68[/tex] has a p-value of 0.0465.
0.0465 = 4.65% probability that a random sample of 20 pregnancies has a mean gestation period of 260 days or less.
3. What is the probability that a random sample of 50 pregnancies has a mean gestation period of 260 days or less?
Now [tex]n = 50[/tex], so:
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{260 - 266}{\frac{16}{\sqrt{50}}}[/tex]
[tex]Z = -2.65[/tex]
[tex]Z = -2.65[/tex] has a p-value of 0.0040.
0.004 = 0.4% probability that a random sample of 50 pregnancies has a mean gestation period of 260 days or less.
4. What is the probability a random sample of size 15 will have a mean gestation period within 10 days of the mean?
Sample of size 15 means that [tex]n = 15[/tex]. This probability is the p-value of Z when X = 276 subtracted by the p-value of Z when X = 256.
X = 276
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{276 - 266}{\frac{16}{\sqrt{15}}}[/tex]
[tex]Z = 2.42[/tex]
[tex]Z = 2.42[/tex] has a p-value of 0.9922.
X = 256
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{256 - 266}{\frac{16}{\sqrt{15}}}[/tex]
[tex]Z = -2.42[/tex]
[tex]Z = -2.42[/tex] has a p-value of 0.0078.
0.9922 - 0.0078 = 0.9844
0.9844 = 98.44% probability a random sample of size 15 will have a mean gestation period within 10 days of the mean.
Entering 38.00 into the Price of Sneakers field Entering 6.00 into the Price field Entering 3.00 into the Price of Leather field True or False: You will no
Answers
Answer:
This question seems incorrect.
Kindly take a look again and re-state it properly to enable me give the most accurate answer.
Thank you
To make a salad dressing you mix vinegar and olive oil in the ratio 2:5 how much olive oil is needed with 20 ml of vinegar
Answers
Answer:
Step-by-step explanation:
Set this up as a proportion with the ratios being
[tex]\frac{vinegar}{oil}[/tex] If there is a 2:5 ratio of vinegar to oil, that ratio looks like this:
[tex]\frac{v}{o}:\frac{2}{5}[/tex] and if we are looking for how much oil, x, is needed for 20 ml of vinegar, then that ratio completes the proportion:
[tex]\frac{v}{o}:\frac{2}{5}=\frac{20}{x}[/tex] and cross multiply.
2x = 100 so
x = 50 ml of oil
Which function represents the graph below?
Answers
Answer:
The answer is the third one below
is perpendicular to line segment
. If the length of is a units, then the length of is
units.
Answers
Answer:
AB is perpendicular to [GH] and GH is [A]
Step-by-step explanation:
Which of the following statements provides the correct freezing and boiling points of water on the Celsius and Fahrenheit temperature scales?
Answers
The freezing point of water is 0°C or 32°F while the boiling point of water is 100°C or 212°F.
TemperatureTemperature is the measure of the degree of hotness or coldness of a substance or place. It is usually expressed Fahrenheit and Celsius scale. Temperature indicates the direction of heat flow.
The freezing point of water is 0°C or 32°F while the boiling point of water is 100°C or 212°F.
Find out more on Temperature at: https://brainly.com/question/24746268
Consider the proportion
8
k
=
5
2.7
Answers
Answer:
4.32 = k
Step-by-step explanation:
8/k = 5/2.7
We can solve using cross products
8* 2.7 = 5k
21.6 = 5k
Divide each side by 5
21.6/5 = k
4.32 = k
Answer: 5k = 21.6 and k = 4.32
there you go have a good day bye
Step-by-step explanation:
The measure of each interior angle of reglar convex polygon is 150 How many sides it does have
Answers
Step-by-step explanation:
Since an interior angle is 150 degrees, its adjacent exterior angle is 30 degrees. Exterior angles of any polygon always add up to 360 degrees. With the polygon being regular, we can just divide 360 by 30 to get 12 sides.
Evaluate x2 + 4x + 1 when x = -3
Answers
Answer:
[tex]-2[/tex]
Step-by-step explanation:
Just substitute -3 for all instances of x.
[tex](-3)^{2} + 4(-3) + 1\\\\[/tex]
[tex]9 - 12 + 1[/tex]
[tex]-2[/tex]
Please help. I'm stuck on this problem
Answers
Answer:
Step-by-step explanation:
[tex]h(t)=-16t^2+96t\\\\h(t)=-t(16t-96)[/tex]
[tex]96=2^5*3\\\\16=2^4\\\\h(t)=-t(2^5*3*t-2^4)=-2^4t(2^1*3*t-1)\\\\h(t)=-16t(6t-1)[/tex]
the b) part is easy do it!
I pleased anyone to help me please
Answers
Answer:
The first one (90, 90) is supplimentary, the next two (54, 36. and 45, 45) are complimentary, and the last two are supplimentary.
Step-by-step explanation:
A complimentary angle is two angles that add up to 90, and supplimentary is two angles that add up to 180! :)
Answer:
1st picture at the top would be a supplementary angle because a supplementary angles always add to 180 degrees.
the 54 and 36 one is a complementary angle
the 45 and 45 would be complementary angle
the last two on the bottom would both be supplementary angles.
High hopes-
Barry
What is the next term of the geometric sequence? 3, -12, 48
Answers
Answer:
-192
Step-by-step explanation:
it is a geometric progression
r=-4
3. The size of a red blood cell is 0.000007 m and the size of a plant
cell is 0.0000127 m. Compare these two.
Answers
Given:
Size of a red blood cell = 0.000007 m
Size of a plant cell = 0.0000127 m
To find:
The comparison of these two values.
Solution:
We have,
Size of a red blood cell = 0.000007 m
Size of a plant cell = 0.0000127 m
Clearly, [tex]0.0000127>0.000007[/tex]. Now, the difference between these two values is:
[tex]0.0000127-0.000007=0.0000057[/tex]
Therefore, the size of a plant cell is 0.0000057 m more than the size of a red blood cell.
Translate the sentence into an inequality. The product of w and 2 is less than 23.
Answers
Answer:
2w<23
Step-by-step explanation:
The product of w and 2 mean that w multiplied by 2
someone please help!!<3
Question 4 of 10
If f(x) = 5x – 2 and g(x) = 2x + 1, find (f - g)(x).
A. 3 - 3x
B. 7x-3
O C. 7x-1
D. 3x - 3
Answers
Answer:
the answer is c
Step-by-step explanation:
the answer is c
find the measures of m and n.
Answers
Answer:
m = 4
n = 5
Step-by-step explanation:
[tex]m + 8 = 3m\\\\m - 3m = - 8\\\\-2m = - 8\\\\m = 4[/tex]
[tex]2n - 1 = 9 \\\\2n = 9 + 1\\\\2n = 10\\\\n = 5[/tex]
What angles can you construct using just a pair of compasses and a ruler?
Answers
Answer:
By using a pair of compasses and a ruler you can draw all angles
What is the solution set of the equation x2+3*-4=6
Answers
Answer:
x=9
Step-by-step explanation:
Can someone help me out here? Not sure how to solve this problem or where to start either?
Answers
Answer:
19.3 miles per gallon
Step-by-step explanation:
First, subtract 54,042.8-53,737.7. The answer is 305.1
Then, find the unit rate. 305.1/15.8
You get 19.31012658. The prompt says to round to the nearest tenth, so round, and you get 19.3.
That's your answer!
