Answer:
r = 90/30
r = 3
T12 = 10 × 3¹¹
T12 = 1771470
How many real roots and how many complex roots exist for the polynomial
F(x) - X4+ x2 - 5x2 + x -- 6?
O A. 2 real roots and 2 complex roots
B. O real roots and 4 complex roots
O c. 3 real roots and 1 complex root
D. 4 real roots and 0 complex roots
Answer:
D. 4 real roots and 0 complex roots
Step-by-step explanation:
If I assume that the function you are saying is
[tex]F(x)=x^4+x^3-5x^2+x-6[/tex]
There should be up to "4 roots," there can't be more or less than 4 total solutions. First, we need to check how many sign changes are there in this function. There are 3 positive real roots. Now lets check for negative roots.
[tex]F(-x)=x^4-x^3-5x^2-x-6[/tex]
There are is only 1 negative real root. Since we basically have 4 real roots, and the max is 4. There should be 4 real roots and 0 complex roots.
the mean monthly income of trainees at a local mill is 1100 with a standard deviation of 150. find rthe probability that a trainee earns less than 900 a month g
Answer:
The probability is [tex]P(X < 900 ) = 0.0918[/tex]
Step-by-step explanation:
From the question we are told that
The sample mean is [tex]\= x = 1100[/tex]
The standard deviation is [tex]\sigma = 150[/tex]
The random number value is x =900
The probability that a trainee earn less than 900 a month is mathematically represented as
[tex]P(X < x) = P(\frac{X -\= x}{\sigma} < \frac{x -\= x}{\sigma} )[/tex]
Generally the z-value for the normal distribution is mathematically represented as
[tex]z = \frac{x -\mu }{\sigma }[/tex]
So From above we have
[tex]P(X < 900 ) = P(Z < \frac{900 -1100}{150} )[/tex]
[tex]P(X < 900 ) = P( Z <-1.33)[/tex]
Now from the z-table
[tex]P(X < 900 ) = 0.0918[/tex]
HELP number 12 pls i do nor have long more
Answer:
Dian has $250 originally.
Step-by-step explanation:
Let the total money Dian has originally = $S
Dian gave [tex]\frac{2}{5}[/tex] of her total money to Justin,
Money given to Justin = [tex]\frac{2}{5}(\text{S})[/tex]
Money left with Dian = S - [tex]\frac{2}{5}(\text{S})[/tex]
= [tex]\frac{\text{5S-2S}}{5}[/tex]
= [tex]\frac{3S}{5}[/tex]
Since Dian has $150 left then the equation will be,
[tex]\frac{3S}{5}=150[/tex]
S = [tex]\frac{150\times 5}{3}[/tex]
S = $250
Therefore, Dian has $250 originally.
How to do this? what is the answer??
Answer:
I think that is the C
Step-by-step explanation:
Answer:
Option B is the correct answer.
Step-by-step explanation:
here, arc RT =162°
as in question given that the value of arc RT is 162° the value of angle RST is 1/2 of 162°.
so, its value must be 81°only.
hope it helps..
What is the value of the expression iºxi1 x 2 x 3 xi4?
a) 1
b) -1
c) i
d) -i
Answer:
Option b.
Step-by-step explanation:
Note: The given expression is not in correct form. Consider the given expression is [tex]i^0\times i^1\times i^2\times i^3\times i^4[/tex].
Let as consider the given expression is
[tex]i^0\times i^1\times i^2\times i^3\times i^4[/tex]
We know that,
[tex]i^0=1,i^2=-1,i^3=-i,i^4=1[/tex]
Using these values, we get
[tex]i^0\times i^1\times i^2\times i^3\times i^4=1\times i\times (-1)\times (-i)\times 1[/tex]
[tex]=i^2[/tex]
[tex]=-1[/tex]
The value of given expression is -1.
Therefore, the correct option is b.
SOMEONE PLEASE HELP ME!!! I REALLY NEED SOME HELP!!!
Which of the following points is a solution of the inequality y < - lxl?
A. (1, -2)
B. (1, -1)
C. (1, 0)
Answer:
A. (1, -2)
Step-by-step explanation:
We can substitute the variables of x and y into the inequality of [tex]y < -|x|[/tex].
Let's start with A, -2 being y and 1 being x.
[tex]-2 < - |1|[/tex]
The absolute value of 1 is 1, and negating that gets us -1.
[tex]-2 < -1[/tex]
Indeed, -2 is less than -1! So A is a solution to the inequality.
Let's test the rest of them, just in case.
For B:
[tex]-1 < -|1|[/tex]
Absolute value of 1 is 1, negating it is -1.
[tex]-1<-1[/tex]
-1 is EQUAL to -1, not less than it, so is not a solution to the inequality.
Let's try C.
[tex]0 < -|1|[/tex]
Absolute value of 1 is 1, negating it is -1.
[tex]0 < -1[/tex]
0 is GREATER than -1, so that is not a solution to the inequality.
Hope this helped!
Find the slope of the line passing through the points (-3, -8) and (4,6).
Answer:
slope = 2Step-by-step explanation:
The formula of a slope:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
We have
[tex](-3;\ -8)\to x_1=-3;\ y_1=-8\\(4;\ 6)\to x_2=4;\ y_2=6[/tex]
Substitute:
[tex]m=\dfrac{6-(-8)}{4-(-3)}=\dfrac{6+8}{4+3}=\dfrac{14}{7}=2[/tex]
The formula for the slope m of the line that passes through two points [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] is the following:
[tex]m=\dfrac{y_1-y_2}{x_1-x_2}[/tex]
We have points (4,6) and (-3,-8). Let's plug these values into the formula for slope:
[tex]m=\dfrac{6-(-8)}{4-(-3)}[/tex]
[tex]=\dfrac{14}{7}=2[/tex]
The slope of the line passing through the two points is 2. Let me know if you need any clarifications, thanks!
Is 3 a solution to the equation 6x – 7 = 12?
Answer:
3 is not a solution
Step-by-step explanation:
6x – 7 = 12?
Substitute 3 in for x and see if the equation is true
6*3 - 7 = 12
18-7 = 12
11 =12
This is false so 3 is not a solution
A circle is centered at CC-1, -3) and has a radius of 6.
Where does the point P(-6, -6) lie?
Choose 1 answer:
Inside the circle
On the circle
Outside the circle
Answer:
outside the circle i think
Step-by-step explanation:
Answer:
inside the circle
Step-by-step explanation:
Tree diagram:
Emily has a box with 4 different colored tiles: one red, one green, one blue and one yellow. If he draws one of the pieces without looking, what is the probability of drawing the green before the red?
Answer: [tex]\dfrac{1}{12}[/tex]
Step-by-step explanation:
Given: Emily has a box with 4 different colored tiles: one red, one green, one blue and one yellow.
We assume that repetition is not allowed
Total number of ways to draw two tiles = [tex]^4P_2=\dfrac{4!}{(4-2)!}[/tex] [By permuattaions]
[tex]=\dfrac{4\times3\times2}{2}=12[/tex]
Favourable outcome = First green then red (only one way)
So, the probability of drawing the green before the red [tex]=\dfrac{\text{favorable outcomes}}{\text{Total outcomes}}[/tex]
[tex]=\dfrac{1}{12}[/tex]
hence, the required probability =[tex]\dfrac{1}{12}[/tex]
Mai invests $20,000 at age 20. She hopes the investment will be worth $500,000 when she turns 40. If the interest compounds continuously, approximately what rate of growth will she need to achieve her goal? Round to the nearest tenth of a percent.
Answer:16.1%
Step-by-step explanation:
Answer:
The investment needs the rate of growth to be approximately 16.1%.
Step-by-step explanation:
3 + 5x, for x = 10
A. 350
B. 120
C. 53
D. 75
Answer:C
Step-by-step explanation:
Pemdas
3+5(10)
5*10=50
3+50=53
aryn needs enough mulch to cover a rectangle flower bed measuring 2 1/4 yd by 3 1/2yd each bag cover 3 square yds and cost $4 how many bags does she need and how much money she need
Answer:
cars are dum
Step-by-step explanation:
Plz help answer a - d 1. Miguel is playing a game in which a box contains four chips with numbers written on them two of the chips have the number one one chip has the number three and the other chip has the number 5 Miguel must choose to chips if both chips have the same number he wants to dollars if the two chipsy chooses have different numbers he loses $1 (-$1) Look at pictures for the questions
Answer:
Step-by-step explanation:
Hello!
Miguel has four chips, two have the number "1", one has the number "3" and the other has the number "5"
If the experiment is "choosing two chips and looking at their numbers" there are the following possible outcomes:
S= {(1,1)(1,3)(1,5)(3,1)(5,1)(3,5)(5,3)}
The sample space for the experiment has 7 possible combinations.
a)
Be X: the amount of money Miguel will receive or owe.
If two chips with the same number are chosen he will receive $2
If the chips have different number he will owe $1
Looking at the possible outcomes listed above, out of the 7, in only one he will select the same number (1,1)
So the probability of him receiving $2 will be 1/7
Now out of the 7 possible outcomes, 6 will make Miguel owe $1, so you can calculate its probability as: 6/7
xi | $2 | -$1
P(xi) | 1/7 | 6/7
b)
To calculate the expected value or mean you have to use the following formula:
[tex]\frac{}{X}[/tex]= ∑[xi*P(xi)]= (2*1/7)(-1*6/7)= -4/7= $-0.57
c)
The expected value is $-0.57, meaning that Miguel can expect to owe $0.57 at the end of the game.
d)
To make the game fair you have to increase the probability of obtaining two chips with the same number. Any probability close to 50% will make the game easier. For example if you change the experiment so that for earning $2 the probability is 4/7 and for owing $1 the probability is 3/7, the expected earnings will be:
(2*4/7)+(-1*3/7)= $0.71
I hope this helps!
15 points + brainliest if you can figure this out!
Answer:
(H1, T1)
Step-by-step explanation:
Since we know that the only number option is 1, we can cancel out the first 3 options. and obviously, there are only heads, and tails. So, using only the # 1 and heads and tails, we can conclude that the answer is (H1, T1).
Answer:
D. (H1, T1)
Step-by-step explanation:
Since all outcomes require card #1 is chosen, so any answer with 2 or 3 can be rejected, therefore the answer is
D. (H1, T1)
Bart bought a digital camera with a list price of $219 from an online store offering a 6 percent discount. He needs to pay $7.50 for shipping. What was Bart's total cost? A. $205.86 B. $211.50 C. $213.36
Answer:
Barts total cost is (c)213.36
Step-by-step explanation:
First, you subtract 6% from $219
=204.92
add shipping,
+7.50
=213.36
Hope this helps <3
Answer:
C. $213.36
Step-by-step explanation:
The original price is $219 and the discount is 6% which is equal to $13.14
$219 - $13.14 + $7.50 (shipping cost) = $213.36
given g(x)=3/x^2+2x find g^-1(x)
Answer:
A
Step-by-step explanation:
[tex]g(x) = \frac{3}{{x}^{2} + 2x} \\ {x}^{2} + 2x - \frac{3}{g(x)} = 0 \\ x = \frac{1}{2} \Big( - 2 + \sqrt{12 + \frac{12}{g(x)} }\Big) \\ x = - 1 + \sqrt{1 \pm \frac{3}{g(x)} } [/tex]
Now replace $x$ by $g^{-1}(x)$ and $g(x)$ by $x$ and you have your answer.
Nearsightedness: It is believed that nearsightedness affects about 8% of all children. In a random sample of 194 children, 21 are nearsighted.
(a) What proportion of children in this sample are nearsighted?
(b) Construct hypotheses appropriate for the following question: do these data provide evidence that the 8% value is inaccurate?
(c) Given that the standard error of the sample proportion is 0.0195 and the point estimate follows a nearly normal distribution, calculate the test statistic (the Z statistic).
(d) What is the p-value for this hypothesis test?
(e) What is the conclusion of the hypothesis test?
Answer:
a)the proportion of student is 0.1082
b)
H1: p = .08
H2: p not equal to 0.08
H1: p =0 .08
H2: p < .08
H1: p =0 .08
H2: p >0 .08
c)z=1.45
d) the p value is 0.1470
e)null hypothesis cannot be accepted,There is no enough evidence to reject the null hypothesis.
Step-by-step explanation:
CHECK THE ATTACHMENT FOR DETAILED EXPLANATION
Write 21/7 as a whole number
Answer: 3
Step-by-step explanation:
7x=21 21/7=3
Find the area of the figure. Round to the nearest tenth if necessary. 386.3m^2 194.3m^2 193.1m^2 201.9m^2
Add the top and bottom numbers together, divide that by 2 then multiply by the height.
15.3 + 19.5 = 34.8
34.8/2 = 17.4
17.4 x 11.1 = 193.14
Answer is 193.1 m^2
Which sequence of transformations on preimage Triangle ABC will NOT produce the image A’B’C’
Answer:
b
Step-by-step explanation:
Which correlation coefficient could represent the relationship in the scatterpot. Beach visitors
Answer:
A. 0.89.
Step-by-step explanation:
The value of correlation coefficient ranges from -1 to 1. Any value outside this range cannot possibly be correlation coefficient of a scatter plot representing relationship between two variables.
The scatter plot given shows a positive correlation between average daily temperatures and number of visitors, as the trend shows the two variables are moving in the same direction. As daily temperature increases, visitors also increases.
From the options given, the only plausible correlation that can represent this positive relationship is A. 0.89.
Find the surface area of the attached figure and round your answer to the nearest tenth, if necessary.
Answer:
[tex] S.A = 246.6 in^2 [/tex]
Step-by-step explanation:
The figure given above is a square pyramid, having a square base and 4 triangular faces on the sides that are of the same dimensions.
Surface area of the square pyramid is given as: [tex] B.A + \frac{1}{2}*P*L [/tex]
Where,
B.A = Base Area of the pyramid = 9*9 = 81 in²
P = perimeter of the base = 4(9) = 36 in
L = slant height of pyramid = 9.2 in
Plug in the values into the given formula to find the surface area
[tex] S.A = 81 + \frac{1}{2}*36*9.2 [/tex]
[tex] = 81 + 18*9.2 [/tex]
[tex] = 81 + 165.6 [/tex]
[tex] S.A = 246.6 in^2 [/tex]
Assume production time per unit is normally distributed with a mean 40 minutes and standard deviation 8 minutes. Using the empirical rule, what percent of the units are produced in MORE than 32 minutes?
Answer:
84%
Step-by-step explanation:
We find the z-score here
z= x-mean/SD = 32-40/8 = -1
So the probability we want to find is;
P(z>-1)
This can be obtained using the standard score table
P(z>-1) = 0.84 = 84%
Luke is organising a camping trip for the youth club. He is looking at the temperature and rainfall charts for Brighton and Newquay. What is the probability of it raining in July in Brighton? Give your answer as a fraction.
Answer:
The answer is 15.6/31 or 1/2
Step-by-step explanation:
The data in the question is sufficient to find an answer for it.
1. I look at the temperature and rainfall chart for Brighton, United Kingdom.
2. Check for rainy season and dry season.
3. The rainy season lasts approximately 5 months while the dry season (which still has some rainfall) lasts approximately 7 months. All together, 12 months of the calendar year.
4. July happens to fall within the dry season. The temperature and rainfall statistics are observed.
The number of rainfall days is 15.6 and we know there are 31 days in July.
If the approximate number of days it rains in Brighton, in July, is 15.6 then the probability of rainfall in the month is 15.6/31 which is = 0.503 or 0.5
Therefore, there's a 50% chance of having rainfall in Brighton, on any day in the month of July.
In fraction, 0.5 = 1/2
Which of the following are solutions to the equation below?
Check all that apply.
x2 - 6x + 9 = 11
Answer:
x = 3 ± sqrt(11)
Step-by-step explanation:
x^2 - 6x + 9 = 11
Recognizing that this is a perfect square trinomial
(x-3) ^2 =11
Taking the square root of each side
sqrt((x-3) ^2) = ± sqrt(11)
x-3 =± sqrt(11)
Add 3 to each side
x = 3 ± sqrt(11)
Answer:
[tex]\large\boxed{\sf \ \ x = 3+\sqrt{11} \ \ or \ \ x = 3-\sqrt{11} \ \ }[/tex]
Step-by-step explanation:
Hello,
[tex]x^2-6x+9=11\\<=> x^2-2*3*x+3^2=11\\<=>(x-3)^2=11\\<=> x-3=\sqrt{11} \ or \ x-3=-\sqrt{11}\\<=> x = 3+\sqrt{11} \ or \ x = 3-\sqrt{11}[/tex]
Do not hesitate if you have any question
Hope this helps
All sides of the building shown above meet at right angles. If three of the sides measure 2 meters, 7 meters, and 11 meters as shown, then what is the perimeter of the building in meters?
Answer:
Perimeter= 40 units
Step-by-step explanation:
Ok
We are asked to look for the perimeter.
We have some clue given.
All at right angle and some sides are given it's full length.
We have the bae to be 11 unit
The height to be 7 unit.
What this mean is that taking either the base or the height should sum up to either 11 or 7 respectively.
Let's go for the other side of the height.
Let's take all the vertical height and sum it up to 7 because the right side is equal to 7.
So we have 7+7+11
But it's not complete yet.
We are given a dimension 2.
And the 2 is in two places so it's total 2*2= 4
The two is for a small base .
The base is actually an extra to the 11 of the other base.
So summing up
We have 2*11 + 2*7 + 2*2
Perimeter= 22+14+4
Perimeter= 40 units
A manufacturing process that produces electron tubes is known to have a 10% defective rate. Suppose a random sample of 15 tubes is selected from the manufacturing process. a) Find the probability that no more than two defectives are found?
Answer:
Probability of obtaining no more than two defective tubes = 0.816
Step-by-step explanation:
The Probability of obtaining no more than two defective tubes in a randomly selected sample of 15 tubes is obtained using the binomial distribution formula: nCr × p^r × q^(n -r).
Where n is number of samples;
r is maximum number of defective tubes, r ≤ 2;
p is probability of defective tubes = 10% or 0.1
q is probability of non-defective tubes, q = 1 - p
Further explanations and calculations are given in the attachment below:
please I need help with this question!
The weight of adult males in Boston are normally distributed with mean 69 kilograms and variance 25 kilograms.
I. what percentage of adult male in Boston weigh more than 72 kilograms?
ii. what must an adult male weigh in order to be among the heaviest 10% of the population?
Thank you in advance!
Answer:
lmkjhvjgcfnhjkhbmgnc gfghh
Step-by-step explanation:
Make a decision about the given claim. Use only the rare event rule, and make subjective estimates to determine whether events are likely. For example, if the claim is that a coin favors heads and sample results consist of 11 heads in 20 flips, conclude that there is not sufficient evidence to support the claim that the coin favors heads (because it is easy to get 11 heads in 20 flips by chance with a fair coin).
Claim: The mean pulse rate (in beats per minute) of students in a large math class is greater than 71. A simple random sample of the students has a mean pulse rate of 71.7. Choose the correct answer below.
A. The sample is unusual if the claim is true. The sample is unusual if the claim is false. Therefore, there is not sufficient evidence to support the claim.
B. The sample is unusual if the claim is true. The sample is unusual if the claim is false. Therefore, there is sufficient evidence to support the claim.
C. The sample is not unusual if the claim is true. The sample is not unusual if the claim is false. Therefore, there is sufficient evidence to support the claim.
D. The sample is not unusual if the claim is true. The sample is not unusual if the claim is false. Therefore, there is not sufficient evidence to support the claim.
Answer:
The correct option is (D).
Step-by-step explanation:
In this case, we need to test whether the mean pulse rate (in beats per minute) of students in a large math class is greater than 71.
The hypothesis can be defined as follows:
H₀: The mean pulse rate of students in a large math class is not greater than 71, i.e. μ ≤ 71.
Hₐ: The mean pulse rate of students in a large math class is greater than 71, i.e. μ > 71.
It is provided that the sample mean pulse rate, of a simple random sample of the students is 71.7.
The sample mean is not very different from the population mean.
So, it cannot be said in confidence that the sample is unusual.
Thus, the correct option is (D).
"The sample is not unusual if the claim is true. The sample is not unusual if the claim is false. Therefore, there is not sufficient evidence to support the claim."