Answer:
Fernando’s response is incorrect because he inappropriately applied the Rational Root Theorem. Dennis’ response is incorrect. According to the Fundamental Theorem of Algebra, the polynomial p(x) cannot have six roots, or zeros, because it is only of degree 3. Emily’s response is correct because she correctly factored the polynomial, and correctly used the definition of zeros to reach her answer.Step-by-step explanation:
The Rational Root Theorem offers a list of possible rational roots. Each needs to be tested to see if it is an actual rational root. Fernando and Dennis made inappropriate assumptions about what the Rational Root Theorem allowed them to conclude.
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Step-by-step explanation:
Joe mama
Blake is going to invest in an account paying an interest rate of 1.5% compounded quarterly. How much would Blake need to invest to the nearest dollar, for the value of the account to reach $910 in 10 years
Answer:
$783.46
Step-by-step explanation:
Compounded interest rate (quarterly) formula: A = P(1 + r/4)^4t
Simply plug in our known variables and solve:
910 = P(1 + 0.015/4)^4(10)
910 = P(1.00375)^40
910 = 1.16151P
P = 783.464
Answer: 783
Step-by-step explanation:
compute an interval estimate with 90% confidence for the mean time to complete an employment test. Assuming a population standard deviation of three hours, what is the required sample size if the error should be less than a half hour
Answer:
The required sample size 'n' = 97 .41 hours
Step-by-step explanation:
Explanation:-
Given standard deviation of the Population 'σ' = 3 hours
Given the Margin of error = [tex]\frac{1}{2} hour[/tex]
The Margin of error is determined by
[tex]M.E = \frac{Z_{\frac{\alpha }{2} S.D} }{\sqrt{n} }[/tex]
Given level of significance ∝ = 0.10 or 0.90
Z₀.₁₀ = 1.645
[tex]\frac{1}{2} =\frac{1.645 X 3}{\sqrt{n} }[/tex]
Cross multiplication , we get
[tex]\sqrt{n} = 2 X 1.645 X 3[/tex]
√n = 9.87
Squaring on both sides, we get
n = 97.41 hours
Final answer:-
The required sample size 'n' = 97.41 hours
HELP!!!!! 70 points I keep help
Answer:
The answer is the last one because if the diagonals of a quadrilateral bisect each other then it's a parallelogram.
Answer:
Last answer choice
Step-by-step explanation:
One of the prerequisites for a quadrilateral to be a parallelogram is for the diagonals to bisect each other. Since K is the midpoint, this means that it is halfway between the ends of each of the diagonals, and that they therefore bisect each other. Hope this helps!
Davon is picking out some movies to rent, and he has narrowed down his selections to 4 children's movies, 3 documentaries, 6 comedies, and 5 mysteries. How many different combinations of 9 movies can he rent if he wants all 6 comedies?
Answer:
220
Step-by-step explanation:
There are 6 comedies and 12 non-comedies. He wants all 6 of the comedies, and 3 of the non-comedies.
The number of ways he can choose 6 comedies from 6 is ₆C₆ = 1.
The number of ways he can choose 3 non-comedies from 12 is ₁₂C₃ = 220.
So the total number of combinations is 1 × 220 = 220.
Explain how to find the coordinates of an endpoint of a line segment, given the
coordinates of the other endpoint and the midpoint.
Answer:
d
Step-by-step explanation:
hope this helps
Which equation represents the line that passes through and left-parenthesis 4, StartFraction 7 Over 2 right-parenthesis.?
Answer:
We want a line that passes through the point (4, 7/2)
and we have no other information of this line, so we can not fully find it, but we can find a general line.
We know that a line can be written as:
y = a*x + b.
Now we want that, when x = 4, we must have y = 7/2.
7/2 = a*4 + b
b = -a*4 + 7/2
Then we can write this line as:
y = a*x - a*4 + 7/2.
Where a can take any value, and it is the slope of our line.
Answer:
A
Step-by-step explanation:
Write down the 3rd term in the sequence given by: T(n) = n2 + 4 pls explain how to do It plsss
Answer:
T(3) = 13
Step-by-step explanation:
If we are trying to find the 3rd term of this specific sequence, then we simply plug in 3 as n.
T(3) = (3)² + 4
T(3) = 9 + 4
T(3) = 13
However, this isn't proper notation for an arithmetic or geometric sequence.
Answer:
13
Step-by-step explanation:
T(n) = n² + 4
Put n as 3 to find the third term.
T(3) = (3)² + 4
Solve for the powers.
T(3) = 9 + 4
Add the terms.
T(3) = 13
The displacement (in centimeters) of a particle moving back and forth along a straight line is given by the equation of motion s = 2 sin(πt) + 5 cos(πt), where t is measured in seconds.
A) Find the average velocity during each time period.
1) [1, 2]
2) [1, 1.1]
3) [1, 1.01]
4) [1, 1.001]
B) Estimate the instantaneous velocity of the particle when t = 1. cm/s
Answer:
A) 10, -3.73, -6.035, -6.259 . . . cm/s
B) -6.2832 cm/s
Step-by-step explanation:
A) For problems like this, where repeated evaluation of a function is required, I find a graphing calculator or spreadsheet to be an appropriate tool. The attached shows that we defined the position function ...
p(t) = 2sin(πt) +5cos(πt)
and a function for computing the average velocity from t=1. For some time interval ending at t2, the average velocity is ...
Va(t2) = Δp/Δt = (p(t2) -p(1))/(t2 -1)
Then, for example, for t2 = 2, the average velocity on the interval [1, 2] is ...
Va(2) = (p(2) -p(1))/(2 -1) = ((2sin(2π) +5cos(2π)) -(2sin(π) +5cos(π)))/(1)
= (2·0+5·1 -(2·0 +5·(-1)) = 10 . . . . matches the table value for x1 = 2.
Then the average velocity values for the intervals of interest are ...
1) [1, 2] Va = 10
2) [1, 1.1] Va = -3.73
3) [1, 1.01] Va = -6.035
4) [1, 1.001] Va = -6.259
__
B) Sometimes a better estimate is obtained when the interval is centered on the point of interest. Here, we can compute the average velocity on the interval [0.999, 1.001] as a better approximation of the instantaneous velocity at t=1. That value is ...
[0.999, 1.001] Va = -6.283175*
Our estimate of V(1) is -6.2832 cm/s.
The exact value is -2π ≈ -6.2831853... cm/s
__
* This is the average of the Va(0.999) and Va(1.001) values in the table.
Use the given probability value to determine whether the sample results could easily occur by chance, then form a conclusion. A study of the effect of seatbelt use in head-on passenger car collisions found that drivers using a seatbelt had a 64.1% survival rate, while drivers not using a seatbelt had a 41.5% survival rate. If seatbelts have no effect on survival rate, there is less than a 0.0001 chance of getting these results. What do you conclude?
Answer:
As the P-value is very low, we can conclude that there is enough evidence to support the claim that the survival rate is significantly higher when the seatbelt is used.
Step-by-step explanation:
We have a hypothesis test that compares the survival rate using the seatbelt versus the survival rate not using it.
The claim is that the survival rate (proportion) is significantly higher when the seatbelt is used.
Then, the null hypothesis is that the seatbelts have no effect (both survival rates are not significantly different).
The P-value is the probabilty of the sample we have, given that the null hypothesis is true. In this case, this value is 0.0001.
This is very low, what gives enough evidence to claim that the survival rate is significantly higher when the seatbelt is used.
The measurement of the circumference of a circle is found to be 64 centimeters, with a possible error of 0.9 centimeter. (a) Approximate the percent error in computing the area of the circle. (Round your answer to two decimal places.) 2.81 Correct: Your answer is correct. % (b) Estimate the maximum allowable percent error in measuring the circumference if the error in computing the area cannot exceed 1%. (Round your answer to one decimal place.)
Answer:
(a) 2.81%
(b) 0.5%
Step-by-step explanation:
We have the following information from the statement:
P = 64 + - 0.9
(a) We know that the perimeter is:
P = 2 * pi * r
if we solve for r, we have to:
r = P / 2 * pi
We have that the formula of the area is:
A = pi * r ^ 2
we replace r and we are left with:
A = pi * (P / 2 * pi) ^ 2
A = (P ^ 2) / (4 * pi)
We derive with respect to P, and we are left with:
dA = 2 * P / 4 * pi * dP
We know that P = 64 and dP = 0.9, we replace:
dA = 2 * 64/4 * 3.14 * 0.9
dA = 9.17
The error would come being:
dA / A = 9.17 / (64 ^ 2/4 * 3.14) = 0.02811
In other words, the error would be 2.81%
(b) tell us that dA / A <= 0.01
we replace:
[P * dP / 2 * pi] / [P ^ 2/4 * pi] <= 0.01
solving we have:
2 * dP / P <= 0.01
dP / P <= 0.01 / 2
dP / P <= 0.005
Which means that the answer is 0.5%
Pleassssssseeeeee hhheeelllppp
A= -2+(-3)×(-8+4)
-2+(-3)×(-4)
-2+12=10
B=-9+8×7+(-12)
-9+56-12=35
C=8-2= -4
D=8÷2=4
E= -4-35= -39
F=153
Graph g(x)=-2|x-5|-4
Answer:
Step-by-step explanation:
triangles DEF and D'E'F' are shown on the coordinate plane below:
Answer:
Option B
Step-by-step explanation:
Triangle DEF was rotated 90 degrees counter clockwise to create Triangle D'E'F'.
Answer:
it was b
Step-by-step explanation:
The numbers of beans in some cocoa pods
are 30, 28, 30, 35, 40, 25, 32, 36, 38 and 40.
a Calculate the mean number of beans per
cocoa pod.
b Calculate the standard deviation of the
distribution.
Answer:
a) Mean number of beans = 33.4 per coco pad
b) Standard deviation of the beans = 5.2 per coco pad
Step-by-step explanation:
Step(i):-
a)
Given data 30, 28, 30, 35, 40, 25, 32, 36, 38 and 40.
mean of beans
x⁻ = ∑x/n
[tex]x^{-} = \frac{30+ 28+30+35+40+25+32+36+38 + 40.}{10} = 33.4[/tex]
Mean number of beans per coco pad = 33.4
step(ii):-
b)
standard deviation
∑(xi - x⁻)² = (30-33.4)²+ (28-33.4)²+(30-33.4)²+(35-33.4)²+(40-33.4)²+(25-33.4)²+(32-33.4)²+(36-33.4)²+ (38-33.4)²+(40-33.4)²
On calculation , we get
∑(xi - x⁻)² = 242.4
standard deviation
= [tex]\sqrt{\frac{sum((x-x^{-} )^{2} }{n-1} } = \sqrt{\frac{242.4}{10-1} } = 5.189[/tex]
Standard deviation of the beans (σ) = 5.2 per coco pad
Please answer this correctly
Answer:
Pillows:
Blankets:
Pet Beds:
Step-by-step explanation:
18 + 45 + 27 = 90 (there are 90 students)
18 out of 90 = 20%
45 out of 90 = 50%
27 out of 90 = 30%
Hope this helps!
What is the equation of the line that goes through (1,-1) and is parallel to y=
3x - 3?
Answer:
y+1=3(x-1), D.
Step-by-step explanation:
Parallel lines have the same slope: Slope should be 3.
y+1=3(x-1)
Cars enter a car wash at a mean rate of 4 cars per half an hour. What is the probability that, in any hour, exactly 5 cars will enter the car wash? Round your answer to four decimal places.
Answer:
The probability that, in any hour, exactly 5 cars will enter the car wash is P(x=5)=0.0920.
Step-by-step explanation:
This can be modeled as a Poisson random variable.
The mean rate is the parameter of the Poisson distribution:
[tex]\lambda=4\;\text{cars/half an hour}=8\;\text{cars/hour}[/tex]
The probability that exactly k cars will enter the car wash can be calculated as:
[tex]P(x=k)=8^{k} \cdot e^{-8}/k![/tex]
Then, the probability that exactly 5 cars will enter the car wash is:
[tex]P(5)=8^{5} \cdot e^{-8}/5!=32768*0.0003/120=0.0920\\\\[/tex]
The probability that, in an hour, exactly 5 cars will enter the car wash will be 0.0920.
What is probability?Probability means possibility. It deals with the occurrence of a random event. The value of probability can only be from 0 to 1.
Its basic meaning is something is likely to happen. It is the ratio of the favorable event to the total number of events.
The mean rate is found as;
[tex]\rm \lambda =4 \ cars / half \ an \ hour = 8 car / hour[/tex]
The probability that exactly k cars will enter the car wash
[tex]P(x=K) = \frac{8^k e^{-8}}{k\!}\\\\P(x=5) = \frac{8^5 e^{-8}}{5\!}\\\\ P(x=5)=0.0920[/tex]
Hence the probability that, in an hour, exactly 5 cars will enter the car wash will be 0.0920.
To learn more about the probability link is given below.
https://brainly.com/question/795909
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X + 5/7 is less than 1/7
Answer:
x < -4/7
Step-by-step explanation:
X + 5/7 < 1/7
Subtract 5/7 from each side
X + 5/7 -5/7 <1/7-5/7
x < -4/7
Multiply or divide as indicated
x^4•x^-2
Answer:
x^2
Step-by-step explanation:
[tex]x^4\cdot x^{-2}= \\\\x^{4-2}= \\\\x^2[/tex]
Hope this helps!
Answer:
[tex]x^{2}[/tex]
Step-by-step explanation:
[tex]x^4 \times x^{-2}[/tex]
[tex]x^{4+-2}[/tex]
[tex]x^{4-2}[/tex]
[tex]x^{2}[/tex]
Construct a stem-and-leaf plot of the test scores 67 comma 72 comma 86 comma 75 comma 89 comma 89 comma 87 comma 90 comma 99 comma 100. How does the stem-and-leaf plot show the distribution of these data?
Answer:
Given the values: 67,72,86,75,89,89,87 ,90 ,99 and 100.
To create a stem and leaf plot
We place the first digit in the Stem Column and the Second digit in the plot column.
Stem-and-leaf plot of the test scores
[tex]\left|\begin{array}{c|ccccccc}Stem&Leaf\\---&--&--&--&--\\6&7&\\7&2&5\\8&6&7&9&9\\9&0&9\\10&0\end{array}\right|[/tex]
The stem and leaf plot enables us at a glance to see the values or range of the values that are most prevalent.
From the above stem and leaf plot, we can see that values in the range of 80-89 are most prevalent.
We have five samples of data: sample A with 30 successes of 50 cases, sample B with 600 successes of 1000 cases, sample C with 3000 successes of 5000 cases, sample D with 60 successes of 100 cases and sample E with 300 successes of 500 cases. We want to test if the proportion of successes is greater than 0.5. Which sample gives the strongest evidence for the alternative hypothesis?A. AB. BC. CD. DE. E
Answer:
C. with 3000 successes of 5000 cases sample
Step-by-step explanation:
Given that we need to test if the proportion of success is greater than 0.5.
From the given options, we can see that they all have the same proportion which equals to;
Proportion p = 30/50 = 600/1000 = 0.6
p = 0.6
But we can notice that the number of samples in each case is different.
Test statistic z score can be calculated with the formula below;
z = (p^−po)/√{po(1−po)/n}
Where,
z= Test statistics
n = Sample size
po = Null hypothesized value
p^ = Observed proportion
Since all other variables are the same for all the cases except sample size, from the formula for the test statistics we can see that the higher the value of sample size (n) the higher the test statistics (z) and the highest z gives the strongest evidence for the alternative hypothesis. So the option with the highest sample size gives the strongest evidence for the alternative hypothesis.
Therefore, option C with sample size 5000 and proportion 0.6 has the highest sample size. Hence, option C gives the strongest evidence for the alternative hypothesis
Sam plays basketball and last season he made 104 total shots, scoring 200 total points. If the number of two-point shots he made is two less than
five times the number of three-point shots made, how many foul shots (one point) did he make?
The solution is
Answer: he made 22 foul shots
Step-by-step explanation:
Let x represent the number of one point shot that he made.
Let y represent the number of two point shots that he made.
Let z represent the number of three point shots that he made.
If the number of two-point shots he made is two less than five times the number of three-point shots made, it means that
y = 5z - 2
he made 104 total shots. It means that
x + y + z = 104- - - - - - - - - - 1
Substituting y = 5z - 2 into equation 1, it becomes
x + 5z - 2 + z = 104
x + 6z = 106- - - - - - - - - - -2
Total number of points scored is 200. It means that
x + 2y + 3z = 200- - - - - - - - - - 3
Substituting y = 5z - 2 into equation 3, it becomes
x + 2(5z - 2) + 3z = 200
x + 10z - 4 + 3z = 200
x + 13z = 204- - - - - - - - - - 4
Subtracting equation 4 from equation 2, it becomes
- 7z = - 98
z = - 98/ - 7
z = 14
Substituting z = 14 into equation 2, it becomes
x + 6 × 14 = 106
x + 84 = 106
x = 106 - 84
x = 22
In the triangle, not drawn to scale, angle
BAC = 30° and AB = 40 m. The length. BC,
in metres, is
Question Correction
In the right triangle, not drawn to scale, angle BAC = 30° and AB = 40 m. The length. BC, in metres, is
Answer:
23.09 metres
Step-by-step explanation:
The triangle is a right triangle with :
[tex]A=30^\circ \\B=90^\circ\\AB=40$ metres[/tex]
We are required to find the length of the side BC.
Using Trigonometry ratios
[tex]\tan \theta =\dfrac{BC}{AB}\\\tan 30^\circ =\dfrac{x}{40} \\BC, x =40 \times \tan 30^\circ\\BC=23.09$ metres[/tex]
The length BC, in metres, is 23.09 metres.
Choose the ratio that you would use to convert 1.5 feet to miles. Remember
that there are 5,280 feet in one mile.
Answer: B, 1 mile / 5280 ft.
Step-by-step explanation: If you need to convert feet to miles the unit multiplier (ratio) that you use should have miles on top and feet on the bottom so that the feet cancel when you multiply, leaving miles as the unit. B is the only answer that has miles on top and feet on the bottom as well as the correct amounts (1 mile and 5280 ft).
Someone help please!!
Answer:
Step-by-step explanation:
Volume of rectangular prism = length * width * height
= 11 * 8 * 4
= 352 in³
Solve the equation.
5x + 8 - 3x = -10
x = -1
x=1
x=9
Answer:
x=-9solution,
[tex]5x + 8 - 3x = - 10 \\ or \: 5x - 3x + 8 = -10 \\ or \: 2x + 8 = -10 \\ or \: 2x = -10 - 8 \\ or \: 2x = -18\\ or \: x = \frac{-18}{2 } \\ x = -9[/tex]
hope this helps..
Good luck on your assignment
Answer:
x = -9
Step-by-step explanation:
5x + 8 - 3x = -10
Rearrange.
5x - 3x + 8 = -10
Subtract like terms.
2x + 8 = -10
Subtract 8 on both sides.
2x = -10 - 8
2x = -18
Divide 2 into both sides.
x = -18/2
x = -9
A machine produces a part for the automotive industry. 4% of the parts produced were defective in the past, and we believe that the current percentage is not higher. What is the needed sample size for estimating the current percentage of defective parts with the 90% confidence and the 3% margin of error
Answer:
[tex]n=\frac{0.04(1-0.04)}{(\frac{0.03}{1.64})^2}=114.76[/tex]
And rounded up we have that n=115
Step-by-step explanation:
In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 90% of confidence, our significance level would be given by [tex]\alpha=1-0.90=0.1[/tex] and [tex]\alpha/2 =0.05[/tex]. And the critical value would be given by:
[tex]z_{\alpha/2}=-1.64, z_{1-\alpha/2}=1.64[/tex]
Solution to the problem
The margin of error for the proportion interval is given by this formula:
[tex] ME=z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}[/tex] (a)
The proportion of defectives is estimated as: [tex]\hat p=0.04[/tex]. And on this case we have that the margin of error is [tex]ME =\pm 0.03[/tex] and we are interested in order to find the value of n, if we solve n from equation (a) we got:
[tex]n=\frac{\hat p (1-\hat p)}{(\frac{ME}{z})^2}[/tex] (b)
And replacing into equation (b) the values from part a we got:
[tex]n=\frac{0.04(1-0.04)}{(\frac{0.03}{1.64})^2}=114.76[/tex]
And rounded up we have that n=115
Which of the following are solutions to the quadratic equation below?
Check all that apply.
X^2+ 8x=9
A. -3
B. 1
C. -9
D. -1
E. 3
Answer:
1 and -9
Step-by-step explanation:
[tex]x^2+8x-9=0\\<=> x^2-x+9x-9=0\\<=> x(x-1)+9(x-1)=0\\<=> (x+9)(x-1)=0\\<=> x = -9 \ \ or \ \ x =1\\[/tex]
hope this helps
If you spin the spinner 11 times, what is the best prediction possible for the number of times it will land on pink?
If we spin the spinner 11 times, 4 is the best prediction possible for the number of times it will land on pink.
To calculate the expected value of a random variable, simply multiply it with the respective probability and sum the respective products.
Given, total number of outcomes=11.
Total number of pink colored spin= 4
Probability of a spin resulting pink color=4/11
Expected number of spins of pink color= [tex]\sum xp(x)[/tex]
=(1×4/11)+(2×4/11)+(3×4/11)+(4×4/11)
=4/11(1+2+3+4)
=40/11
=3.63 ≈ 4
Thus, the best prediction possible for the number of times it will land on pink is 4.
Learn more about expected value, here:
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Incomplete:
Image of spinner is missing in the question, Therefore attaching it below: