Answers
Answer:
A seems to be correct
Step-by-step explanation:
Related Questions
The polynomial 3x² + mx? - nx - 10 has a factor of (x - 1). When divided by x + 2, the remainder is 36. What are
the values of m and n?
Answers
Answer:
[tex]m = 12[/tex]
[tex]n =3[/tex]
Step-by-step explanation:
Given
[tex]P(x) = x^3 + mx^2 - nx - 10[/tex]
Required
The values of m and n
For x - 1;
we have:
[tex]x - 1 = 0[/tex]
[tex]x=1[/tex]
So:
[tex]P(1) = (1)^3 + m*(1)^2 - n*(1) - 10[/tex]
[tex]P(1) = 1 + m*1 - n*1 - 10[/tex]
[tex]P(1) = 1 + m - n - 10[/tex]
Collect like terms
[tex]P(1) = m - n + 1 - 10[/tex]
[tex]P(1) = m - n -9[/tex]
Because x - 1 divides the polynomial, then P(1) = 0;
So, we have:
[tex]m - n -9 = 0[/tex]
Add 9 to both sides
[tex]m - n = 9[/tex] --- (1)
For x + 2;
we have:
[tex]x + 2 = 0[/tex]
[tex]x = -2[/tex]
So:
[tex]P(-2) = (-2)^3 + m*(-2)^2 - n*(-2) - 10[/tex]
[tex]P(-2) = -8 + 4m + 2n - 10[/tex]
Collect like terms
[tex]P(-2) = 4m + 2n - 10 - 8[/tex]
[tex]P(-2) = 4m + 2n - 18[/tex]
x + 2 leaves a remainder of 36, means that P(-2) = 36;
So, we have:
[tex]4m + 2n - 18 = 36[/tex]
Collect like terms
[tex]4m + 2n = 36+18[/tex]
[tex]4m + 2n = 54[/tex]
Divide through by 2
[tex]2m + n=27[/tex] --- (2)
Add (1) and (2)
[tex]m + 2m - n + n = 9 +27[/tex]
[tex]3m =36[/tex]
Divide by 3
[tex]m = 12[/tex]
Substitute [tex]m = 12[/tex] in (1)
[tex]m - n =9[/tex]
Make n the subject
[tex]n = m - 9[/tex]
[tex]n = 12 - 9[/tex]
[tex]n =3[/tex]
What is the length of an arc with a central angle of 2/3pi radians and a radius of 24 centimeters?
Use 3.14 for pi.
Enter your answer, as a decimal, in the box.
Answers
9514 1404 393
Answer:
50.24 cm
Step-by-step explanation:
Fill in the given numbers and do the arithmetic.
s = rθ
s = (24 cm)(2/3π) = (24 cm)(2/3)(3.14) = 50.24 cm
²/₃ + ¹/₃ please answer
Answers
FINAL ANSWER:
1
Step-by-step explanation:
[tex]\frac{2}{3} +\frac{1}{3}[/tex]
the denominators are the same so all we need to do is add.
[tex]\frac{2}{3} + \frac{1}{3} =\frac{3}{3}[/tex]
[tex]\frac{3}{3} =[/tex] 1 whole
final answer: 1
hope this answer helps you :)
have a great day and may God Bless You!
What are the domain and range of the function represented by the set of
ordered pairs?
{(-16, 0), (-8, -11), (0, 12), (12,4)}
Answers
Answer:
domain:-16,-8,0,12
range:0,-11,12,14
The mean of a data set is observed to be very different from its median, representing a strong skewness. However, the 1.5 IQR rule reveals that there are no outliers. Which of the following is correct, if the sample size is 100?
a. A normal quantile plot of the data follows a diagonal line, and the t-procedure is appropriate to use.
b. A normal quantile plot of the data does not follow a diagonal line, and the t- procedure is not appropriate to use.
c. A normal quantile plot of the data follows a diagonal line, and the t-procedure is not appropriate to use.
d. A normal quantile plot of the data does not follow a diagonal line, and the t- procedure is appropriate to use.
Answers
Answer:
a. A normal quantile plot of the data follows a diagonal line, and the t-procedure is appropriate to use.
Step-by-step explanation:
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 [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
In this question:
Sample size of 100 > 30, which means that we use the Central Limit Theorem, and thus, the sampling distribution is approximately normal, following a diagonal line, and since the standard deviation of the population is not know, we use the t-procedure. Thus, the correct answer is given by option a.
The solution set of the inequality 1 + 2y
Answers
Answer:
is it four I am not quite sure
Golf Scores In a professional golf tournament the players participate in four rounds of golf and the player with the lowest score after all four rounds is the champion. How well does a player's performance in the first round of the tournament predict the final score
Answers
Answer:
Mean scores.
Step-by-step explanation:
The golf player will score in the first round, according to these scores the golf player scores can be predicted. The golf player can perform high in first round but he may score lesser in the second round due to stress or mental pressure. The scores can be predicted taking mean of the scores and adding standard deviation to it.
Hello!
i need help with question 67 & 68
Answers
Answer:
67. A
68. D
Step-by-step explanation:
I don't remember exactly the explanation, but I recommend you try to learn more about number lines sometime when you aren't under stress from schoolwork, because they're pretty simple questions to answer once you get a better understanding of them!
Find the measure of of RA.
Answers
Answer:
RA = 24
Step-by-step explanation:
Since the triangle is isosceles ( 2 equal sides ) , then LU is a perpendicular bisector , so
AU = RU , that is
4r = 18 - 2r ( add 2r to both sides )
6r = 18 ( divide both sides by 6 )
r = 3
Then
RA = 18 - 2r + 4r = 18 + 2r = 18 + 2(3) = 18 + 6 = 24
Which one is a better deal?
paying $2.88 for a 12 roll package of toilet paper
paying $1.20 for a 6 roll package of toilet paper
Answers
Answer:
paying $1.20 for a 6 roll package of toilet paper
Step-by-step explanation:
to find the answer, double 6 to equal 12 and double the price as well. therefore, it is 2.40. since 2.40 is cheaper than 2.88, it is a better deal.
paying $1.20 for a 6 roll package
Step-by-step explanation:
$2.88 divided by 12 = $0.24
$1.20 divided by 6 = $0.20
Hence, i think the best deal is paying $1.20 for a 6 roll package
the cost of 7 shirts is $63. find the cost of 5 shirts
1. $35
2. $45
3. $52
4. $70
Answers
Explanation:
We know that the cost of 7 shirts is $63. To find the $ to shirt ratio we divide 63 by 7. This makes $9 for every shirt. To find the cost of 5 shirts you multiply 5 by 9 making 45. The cost of five shirts is $45.
I hope this helps. Please mark me the Brainliest, it’s not necessary but I put time and effort into every answer and I would appreciate it greatly. Have a great day, stay safe and stay healthy ! :)
U have to work out the value of a by the way
Answers
Answer:
Step-by-step explanation:
180-90=2b+b
90=3b
90/3=b
30=b
2b=2*30
=60
180-90=a+a
90=2a
a=90/2
a=45
the answer is 45 degrees
hope it helps!!let me know if it does
Answer:
a= 15°
Step-by-step explanation:
> use the fact that the sum of angles in a triangle is 180°
> based on the picture in the small right triangle we have b° +2b° +90° =180°
b +2b +90 =180° , combine like terms
3b +90 = 180, subtract 90 from both sides of the equation
3b = 90, divide by 3 both sides of the equation
b = 30°
> angle b has a ray that continues as a line so it makes an 180° angle and we have the acute triangle so we can write that
a + a+ (180-b) =180, substitute b
2a + 180-30 =180, subtract 180 from both sides, and add 30 to both sides
2a=30, divide by 2 both sides
a= 15°
I want my answer please help
Answers
Answer:
This is pretty simple
Step-by-step explanation:
So the only thing you need to know about negatives and positives is that if your multiplying or dividing a number with 1 negative in the expreession/equation The answer will always result in a negative. If its 2 negatives its always positive. Thats all you need to know and then just solve it from there.
Answer:
See explanation and picture below.
Step-by-step explanation:
In both multiplication and division of 2 numbers, different signs give you negative and equal signs give you positive.
In other words, positive & positive or negative and negative give you a positive answer.
Negative and positive or positive and negative give you negative answer.
Roulette is a casino game that involves spinning a ball on a wheel that is marked with numbered squares that are red, black, or green. Half of the numbers 1 - 36 are colored red and half are black and the numbers 0 and 00 are green. Each number occurs only once on the wheel. What is the probability of landing on an even number and a number greater than 17? (A number is even if it is divisible by 2. 0 and 00 are considered even as well.)
Answers
Answer:
the wording (punctuation) of the question can lead to different interpretations....
I assume that the question was >17 & even which is "5/19",
BUT... it can also be read as two questions
first >17 which is "10/19"
and second an even number which is "9/19"
BUT !!! I think that the question answer is 5/19
Step-by-step explanation:
Even Number = 18/38 = 9/19
greater 17 = 20/38 = 10/19
Even & greater 17 = 10/38 = 5/19
After deduction of 4 paisa in a Rupee a sum of Rs 720 is left.What was it originally?
Answers
Given:
After deduction of 4 paisa in a Rupee a sum of Rs 720 is left.
To find:
The original amount.
Solution:
We know that,
1 Rs. = 100 paisa
After deduction of 4 paisa in a Rupee, we get
[tex]100-4=96[/tex]
It means Rs. 720 is the 96% of the original amount.
Let x be the original amount.
[tex]720=\dfrac{96}{100}x[/tex]
[tex]72000=96x[/tex]
[tex]\dfrac{72000}{96}=x[/tex]
[tex]750=x[/tex]
Therefore, the original amount is Rs. 750.
1. Write 3.3.3.3.3 as a power.
Answers
Answer:
3^5
Step-by-step explanation:
On the iPad it looks like that but the five is on the top right smaller
Answer:
3⁵
every 3 has it own power that is 1 however that .3 confused us
You are charged $9.33 total for a meal, assume the 7% sales tax, how much was the menu price of this item?
I have already tried
$8.68
$8.71
$8.67
all were wrong
Answers
Answer:
$8.71.
Step-by-step explanation:
Given that you are charged $ 9.33 total for a meal, assuming the 7% sales tax, to determine how much was the menu price of this item, the following calculation must be performed:
100 + 7 = 107
107 = 9.33
100 = X
100 x 9.33 / 107 = X
933/107 = X
8.71 = X
Therefore, the menu price of this item was $ 8.71.
1-0.4^n>=0.99 howwwwwwwwwwwwwwwwwwwwwwwwww
Answers
Answer:
n>=6
Step-by-step explanation:
1-0.4ⁿ>=0.99
1-0.99>=0.4ⁿ
0.4ⁿ<=0.01
Apply log10:
Log10(0.4ⁿ)<=log10(0.01)
n×log10(0.4)<=log10(0.01)=-2
Because log10(0.4)=-0.39794 is negative we get:
n>=5.028.
Since n is integer, we have n>=6
a bag contain 3 black balls and 2 white balls.
1. A ball is taken from the black and then replaced, a second is taken. what is the probabilities that.
(a) there are both black,
(b)one is black one is white,
(c) at lease one is black,
(d) at most one is one is black.
2. find out if all the balls are chosen without replacement.
please kindly solve with explanation. thank you.
Answers
Answer:
Step-by-step explanation:
Total number of balls = 3 + 2 = 5
1)
a)
[tex]Probability \ of \ taking \ 2 \ black \ ball \ with \ replacement\\\\ = \frac{3C_1}{5C_1} \times \frac{3C_1}{5C_1} =\frac{3}{5} \times \frac{3}{5} = \frac{9}{25}\\\\[/tex]
b)
[tex]Probability \ of \ one \ black \ and \ one\ white \ with \ replacement \\\\= \frac{3C_1}{5C_1} \times \frac{2C_1}{5C_1} = \frac{3}{5} \times \frac{2}{5} = \frac{6}{25}[/tex]
c)
Probability of at least one black( means BB or BW or WB)
[tex]=\frac{3}{5} \times \frac{3}{5} + \frac{3}{5} \times \frac{2}{5} + \frac{2}{5} \times \frac{3}{5} \\\\= \frac{9}{25} + \frac{6}{25} + \frac{6}{25}\\\\= \frac{21}{25}[/tex]
d)
Probability of at most one black ( means WW or WB or BW)
[tex]=\frac{2}{5} \times \frac{2}{5} + \frac{3}{5} \times \frac{2}{5} \times \frac{2}{5} + \frac{3}{5}\\\\= \frac{4}{25} + \frac{6}{25} + \frac{6}{25}\\\\=\frac{16}{25}[/tex]
2)
a) Probability both black without replacement
[tex]=\frac{3}{5} \times \frac{2}{4}\\\\=\frac{6}{20}\\\\=\frac{3}{10}[/tex]
b) Probability of one black and one white
[tex]=\frac{3}{5} \times \frac{2}{4}\\\\=\frac{6}{20}\\\\=\frac{3}{10}[/tex]
c) Probability of at least one black ( BB or BW or WB)
[tex]=\frac{3}{5} \times \frac{2}{4} + \frac{3}{5} \times \frac{2}{4} + \frac{2}{5} \times \frac{3}{4}\\\\=\frac{6}{20} + \frac{6}{20} + \frac{6}{20} \\\\=\frac{18}{20} \\\\=\frac{9}{10}[/tex]
d) Probability of at most one black ( BW or WW or WB)
[tex]=\frac{3}{5} \times \frac{2}{4} + \frac{2}{5} \times \frac{1}{4} + \frac{2}{5} \times \frac{3}{4}\\\\=\frac{6}{20} + \frac{2}{20} + \frac{6}{20} \\\\=\frac{14}{20}\\\\=\frac{7}{10}[/tex]
In ABC, if CB AC≅ , m∠A = 3x + 18, m∠B = 7x – 58, and m∠C = 2x – 8, find x and the measure of each angle.
Answers
9514 1404 393
Answer:
x = 19
A = 30°
B = C = 75°
Step-by-step explanation:
In an isosceles triangle, the angles opposite the congruent sides have the same measures.
A = B
3x +18 = 7x -58
76 = 4x . . . . . . . . add 58-4x
19 = x . . . . . . . . . divide by 4
Then the equal angles measure ...
A = B = 3(19) +18 = 75
C = 2(19) -8 = 30
Angles A, B, C measure 75°, 75°, 30°, respectively.
_____
Alternate solution
The sum of angles in a triangle is 180°, so you could write ...
(3x +18) +(7x -58) +(2x -8) = 180
12x = 228 . . . . . add 48
x = 19 . . . . . divide by 12
Find a power series representation for the function. (Assume a>0. Give your power series representation centered at x=0 .)
f(x)=x2a7−x7
Answers
Answer:
Step-by-step explanation:
Given that:
[tex]f_x = \dfrac{x^2}{a^7-x^7}[/tex]
[tex]= \dfrac{x^2}{a^7(1-\dfrac{x^7}{a^7})}[/tex]
[tex]= \dfrac{x^2}{a^7}\Big(1-\dfrac{x^7}{a^7} \Big)^{-1}[/tex]
since [tex]\Big((1-x)^{-1}= 1+x+x^2+x^3+...=\sum \limits ^{\infty}_{n=0}x^n\Big)[/tex]
Then, it implies that:
[tex]\implies \dfrac{x^2}{a^7} \sum \limits ^{\infty}_{n=0} \Big(\Big(\dfrac{x}{a} \Big)^{^7} \Big)^n[/tex]
[tex]= \dfrac{x^2}{a^7} \sum \limits ^{\infty}_{n=0} \Big(\dfrac{x}{a} \Big)^{^{7n}}[/tex]
[tex]= \dfrac{x^2}{a^7} \sum \limits ^{\infty}_{n=0} \Big(\dfrac{x^{7n}}{a^{7n}} \Big)}[/tex]
[tex]\mathbf{= \sum \limits ^{\infty}_{n=0} \dfrac{x^{7n+2}}{a^{7n+7}} }}[/tex]
Lightbulbs. A company produces lightbulbs. We know that the lifetimes (in hours) of lightbulbs follow a bell-shaped (symmetric and unimodal) distribution with a mean of 7,161 hours and a standard deviation of 564 hours. Use the Empirical Rule (68-95-99.7 rule) to answer the following question: The shortest lived 2.5% of the lightbulbs burn out before how many hours
Answers
Answer:
Please find the complete question and its solution in the attached file.
Step-by-step explanation:
Shortest had survived after 6741 hours [tex]2.5\%[/tex] of the lights burnt.
[tex]\to 0.15\% + 2.35\% = 2.50\%[/tex]
Which of the following is the minimum value of the equation y = 2x2 + 5?
5
0
−5
2
Answers
Find the axis of symmetry by plugging the respective variables into -b/2a
-5/2(0) = 0
There is no b-value in our equation, or rather, the value of b is 0. To see this, y = 2x^2 + 5 can be written as
y = 2x^2 + 0x + 5
We plug 0 into f(x), establishing every x-value as 0.
f(0) = 2(0)^2 + 5
f(0) = 0 + 5
f(0) = 5
5 is now your vertex’s y-value. Plot the two values together.
(0, 5)
We know that this is a minimum because the leading coefficient is positive, meaning the the graph’s parabola will open down.
Given right angle ABC, what the value of tan(A)?
5/13
12/13
12/5
13/12
need answer asap
Answers
Hi there!
[tex]\large\boxed{12/5}}[/tex]
tan (angle) = Opposite side / Adjacent side, so:
Tan (A) = opposite side / adjacent side
= 24 / 10
Simplify:
= 12 / 5
write the equation of the line shown in the graph above in slope-intercept form
Answers
y= -2/3x + 1
1= c
Step 1: Write slope-intercept form equation
To start answering this question, it helps to write out the example equation for slope-intercept form. Let’s do this now.
y=mx+b
Keep in mine that the y represents the answer, the m represents the slope, the x represents the variable, and the b represents the y-intercept.
Step 2: Determine the y-intercept
I find that it is easiest to determine the y-intercept first. This is the b in the equation. The y-intercept can be find by looking at the y-axis, and seeing where the line intersects with the axis. In this case, it seems to be at 1. Let’s substitute this into our equation now.
y=mx+b
y=mx+1
Step 3: Determine slope
For the final thing that we need to fill in, we need to find the slope. The slope is the m in the equation, and can be found by the formula of rise/run. Choose any two points, and see how far they are from each other up and down (rise), as well as left and right (run).
For the sake of this problem, we will work with (0,1) and (-3,3). There is a difference in the rise of 2 and in the run of 3. This makes the rise/ run be 2/3. Let’s substitute this now.
y=mx+1
y= 2/3x+1
The slope will also need to be negative since the line on the graph descends. Let’s change this to a negative now.
y= -2/3x+1
This is your answer. Hope this helps! Comment below for more questions.
rotation 180 degrees about the origin.
Answers
Answer:
Take the picture you uploaded.
Click the rotate button twice.
Done
Use the arithmetic progression formula to find the sum of integers from 75 to 100.75,76,77....99,100.
Answers
Answer:
The sum is 2275
Step-by-step explanation:
Given
[tex]75,76,77....99,100[/tex]
Required
The sum
Using arithmetic progression, we have:
[tex]S_n = \frac{n}{2}(T_1 + T_n)[/tex]
Where:
[tex]T_1 = 75[/tex] --- first term
[tex]T_n = 100[/tex] --- last term
[tex]n = T_n - T_1 + 1[/tex]
[tex]n = 100 - 75 + 1 = 26[/tex]
So, we have:
[tex]S_n = \frac{n}{2}(T_1 + T_n)[/tex]
[tex]S_n = \frac{26}{2}*(75 + 100)[/tex]
[tex]S_n = 13*175[/tex]
[tex]S_n = 2275[/tex]
A public opinion survey is administered to determine how different age groups feel about an increase in the minimum wage. Some of the results are shown in the table below.
For Against No Opinion
21-40 years 20 5
41-60 years 20 20
Over 60 years 55 15 5
The survey showed that 40% of the 21 - 40 year-olds surveyed are against an increase, and 15% of the entire sample surveyed has no opinion. How many 21 - 40 year-olds surveyed are for an increase? How many 41 - 60 year-olds are against an increase?
Answers
Answer:
25 ; 35
Step-by-step explanation:
Given :
____________For __ Against __ No Opinion
21-40 years _________20 _______5
41-60 years ___20 ______________20
Over 60 years _55____ 15________ 5
Given that :
40% of 21-40 are against
Then :
40% = 20
To a obtain 100% of 21 - 40
40% = 20
100% = x
Cross multiply
0.4x = 20
x = 20/0.4
x = 50
100% of 21 - 40 = 50 people
For = 50 - (20 + 5)
= 50 - 25
= 25
2.)
Total who have no opinion :
(5 + 20 + 5) = 30
30 = 15%
Total number surveyed will be , x :
30 = 15%
x = 100%
Cross multiply :
0.15x = 30
x = 30/0.15
x = 200
Number of 41 - 60 against an increase, y:
(25 + 20 + 5 + 20 + y + 20 + 55 + 15 + 5) = 200
165 + y = 200
y = 200 - 165
y = 35
09:30 am - 4:30 pm minus 30 minutes?
Answers
Answer:
4:30
because 9:30 minus 4:30 = 5:00 and 5:00 minus 30 =4:30
NEED HELP
The average amount of money spent for lunch per person in the college cafeteria is $6.75 and the standard deviation is $2.28. Suppose that 18 randomly selected lunch patrons are observed. Assume the distribution of money spent is normal, and round all answers to 4 decimal places where possible.
C. For a single randomly selected lunch patron, find the probability that this
patron's lunch cost is between $7.0039 and $7.8026.
D. For the group of 18 patrons, find the probability that the average lunch cost is between $7.0039 and $7.8026.
Answers
Answer:
C.[tex]P(7.0039<x<7.8026)=0.1334[/tex]
D.[tex]P(7.0039<\bar{x}<7.8026)\approx 0.2942[/tex]
Step-by-step explanation:
We are given that
n=18
Mean, [tex]\mu=6.75[/tex]
Standard deviation, [tex]\sigma=2.28[/tex]
c.
[tex]P(7.0039<x<7.8026)=P(\frac{7.0039-6.75}{2.28}<\frac{x-\mu}{\sigma}<\frac{7.8026-6.75}{2.28})[/tex]
[tex]P(7.0039<x<7.8026)=P(0.11<Z<0.46)[/tex]
[tex]P(a<z<b)=P(z<b)-P(z<a)[/tex]
Using the formula
[tex]P(7.0039<x<7.8026)=P(Z<0.46)-P(Z<0.11)[/tex]
[tex]P(7.0039<x<7.8026)=0.67724-0.54380[/tex]
[tex]P(7.0039<x<7.8026)=0.1334[/tex]
D.[tex]P(7.0039<\bar{x}<7.8026)=P(\frac{7.0039-6.75}{2.28/\sqrt{18}}<\frac{x-\mu}{\frac{\sigma}{\sqrt{n}}})<\frac{7.8026-6.75}{2.28/\sqrt{18}})[/tex]
[tex]P(7.0039<\bar{x}<7.8026)=P(0.47<Z<1.96)[/tex]
[tex]P(7.0039<\bar{x}<7.8026)=P(Z<1.96)-P(Z<0.47)[/tex]
[tex]P(7.0039<\bar{x}<7.8026)=0.97500-0.68082[/tex]
[tex]P(7.0039<\bar{x}<7.8026)=0.29418\approx 0.2942[/tex]