Answer: A fifth degree polynomial could have 5 linear factors. But the factors do not have to be be distinct.
Step-by-step explanation:
The fundamental theorem of algebra tells that every non-constant single-variable polynomial with complex coefficients has at least one complex root.Corollary to the fundamental theorem tells that every polynomial of m>0 degree has exactly m zeroes.Thus by corollary to fundamental theorem of algebra, a fifth degree polynomial must have 5 zeroes . But A fifth degree polynomial could have 5 linear factors if all zeroes are real numbers.
The factors could be distinct or similar.
Thus , The factors do not have to be distinct .
Ms. Johnson uses a statistics program to analyze all the data collected by her students during a lab experiment about the acceleration due to gravity. The program reports a mean of 31.5 and a standard deviation of 2.5.
What is the variance of the data? Round to the nearest tenth.
1.6
2.5
5.6
6.3
Since the variance is the square of the standard deviation, the variance here is 6.3.
What is variance?In statistics, the variance shows how much the values spread out around the mean. The standard deviation is obtained as the square root of the variance of a given value.
Now;
[tex]s = \sqrt{v}[/tex]
s = 2.5
[tex]v = s^2[/tex]
[tex]s = (2.5)^2 =[/tex]6.3
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Which two super powers engaged in the cold war?
The Cold War was a prolonged period of geopolitical tension between the United States and the Soviet Union, involving an arms race, proxy wars, and a race for technological superiority, but avoiding direct military conflict due to the threat of nuclear annihilation.
Explanation:The two superpowers that engaged in the Cold War were the United States and the Soviet Union. The Cold War was a period of geopolitical tension between these two countries that began shortly after the end of World War II and lasted until the collapse of the USSR in 1991. This era was characterized by political and ideological conflicts that were expressed through proxy wars, the arms race, propaganda, and competition in technological advancements such as the space race.
While it was called a 'war', the Cold War did not result in direct military conflict between the two nations. Instead, the struggle for global supremacy was played out through indirect means, including support for opposing sides in regional conflicts such as the Korean War, the Vietnam War, and the Soviet-Afghan War. The fear of Mutually Assured Destruction (M.A.D.) due to both nations possessing extensive nuclear arsenals was a deterrent against a 'hot' war.
The Cold War impacted almost every aspect of international relations and domestic policies within the superpower nations and their allies, with each side attempting to limit the influence and spread of the other's ideology. The United States followed a policy of containment to prevent the spread of communism, and the Soviet Union tried to expand its socialist model and create a buffer zone against the West.
Data set 1: 0, 25, 50, 75, 100
Data set 2: 30, 40, 50, 60, 70
Data set 3: 40, 45, 50, 55, 60
Note that all three data sets have a median of 50. Notice how spread out the points are in each data set and compare this to the standard deviations for the data sets. Describe the relationship you see between the amount of spread and the size of the standard deviation and explain why this connection exists.
am going to assume you know how to calculate standard deviation, as it is long and tedious to type up. If you really don't understand how to calculate them, I will explain it. The standard deviation is larger in data set 1 than 2, because the spread is larger. The larger the spread, the larger the deviation of the numbers in the set are from the mean (average) number. The standard deviation in 1 is greatest. 2 is in the middle, and 3 is the lowest standard deviation. Hope this helps, good luck.
Answer:
Larger the standard deviation larger the spread present in data.
Step-by-step explanation:
Standard Deviation is the square root of sum of square of the distance of observation from the mean.
[tex]Standard deviation(\sigma) = \sqrt{\frac{1}{n}\sum_{i=1}^{n}{(x_{i}-\bar{x})^{2}}}[/tex]
where, [tex]\bar{x}[/tex] is mean of the distribution.
It is used to measure dispersion (spread) of the data. Larger the standard deviation larger the dispersion (spread) present in data.
The Standard deviation of 1st data set is 39.53
The Standard deviation of 2nd data set is 15.81
The Standard deviation of 3rd data set is 7.91
Hence,
(Spread of 1st data set) > (Spread of 2nd data set) > (Spread of 3rd data set)
What is the sum of the first 18 terms of the arithmetic series 11+15+19+23+...?
Bob has some 10 lb weights and some 3 lb weights. Together, all his weights add up to 50 lbs. If x represents the number of 3 lb weights and y represents the number of 10 lb weights, which equation can be used to find the number of each type of weight Bob has?
A)3x – 10y = 50
B)3x = 50 – 10y
C)50 + 10y = 3y
D)50 + 3y = 10y
3. What is another name for plane VTL?
Plane T
Plane Z
Plane ZXV
Plane LTX
Answer:
Plane Z
Step-by-step explanation:
You and three friends earn money by painting houses. You agree to split the profits equally. You buy brushes, tape, and paint for $750. If your total income is $2,600, how much is your share of the profit?
linear differential equation question:
y"'-6y"+12y' -8y = 0
To solve this linear differential equation, we can use the method of characteristic equation. The general solution is y = (c1 + c2x + c3x^2)e^(2x), where c1, c2, and c3 are constants.
Explanation:To solve this linear differential equation, we can use the method of characteristic equation. Let's assume that the solution is of the form y = e^(rx). Substituting this in the given equation, we get the characteristic equation as r^3 - 6r^2 + 12r - 8 = 0. This can be factored as (r - 2)^3 = 0. So, the characteristic roots are r = 2, 2, and 2.
Since we have repeated roots, the general solution is given by y = (c1 + c2x + c3x^2)e^(2x), where c1, c2, and c3 are constants.
Therefore, the general solution to the linear differential equation y''' - 6y'' + 12y' - 8y = 0 is y = (c1 + c2x + c3x^2)e^(2x), where c1, c2, and c3 are constants.
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According to Professor Robinson, which of the following aspects of A Streetcar Named Desire can be said to reflect elements of Tennessee Williams's life?
a. hunger for love
b. feelings of unworthiness
c. feelings of guilt
d. using alcohol for its mood-altering affects
e. all of the above
The time of year at the beginning (May) and ending (October) of A Streetcar Named Desire symbolize:
a. rebirth and the coming death
b. life c. death
d. joy and laughter
e. good luck and bad luck
Ms. Wilson draws a model of the factorization of a polynomial with integer factors. Her model is partially complete.
Answer:
b
Step-by-step explanation:
When solving negative one over eight (x + 35) = −7, what is the correct sequence of operations?
Multiply each side by negative one over eight , add 35 to each side
Multiply each side by negative one over eight , subtract 35 from each side
Multiply each side by −8, subtract 35 from each side
Multiply each side by −8, add 35 to each side
Answer:
3
Step-by-step explanation:
i have done this test before
Senator Snortsalot is campaigning for reelection. During his visit to Patheticville, he plans to have 17,500 brochures distributed. His schedule is very tight, and he will only be in Patheticville for 4 hours. How many volunteers will he need if each volunteer can distribute 225 brochures in one hour?
write the negation of the statement:
No vans have three wheels
Your current schedule only lets you take two 1-credit courses every six months. You need 12 credits to get the degree you want. How long will it take you to get the degree?
Solve the quadratic equation: 2x2 + 11x − 6 = 0 ...?
Which choice is equivalent to the expression below?
What is a1 in the sequence?
−4, −2, −12, −14, ...
−4
−2
−12
−14
Simplify. (–8x) ÷ (–4)
Line r is parallel to line t. Find the measurement of Angle 6. The diagram is not to scale.
A.32
B.138
C.42
D.142
Using the completing-the-square method, find the vertex of the function f(x) = 5x2 + 10x + 8 and indicate whether it is a minimum or a maximum and at what point.
Maximum at (1, 8)
Minimum at (1, 8)
Maximum at (−1, 3)
Minimum at (−1, 3)
The vertex of the function f(x) = 5x²+ 10x + 8 and indicate Minimum at (-1, 3)
To find the vertex of the function f(x) = 5x² + 10x + 8 using the completing-the-square method, follow these steps:
Step 1: Write the function in the form (ax² + bx + c).
f(x) = 5x² + 10x + 8
Step 2: Identify the coefficient of x² and divide it by 2. This gives us (b/2a).
In this case, a = 5, b = 10, so (b/2a) = 10 / (2 * 5) = 1.
Step 3: Square the result from Step 2 [(b/2a)²].
(1)² = 1.
Step 4: Add and subtract the result from Step 3 to the function inside the parentheses.
f(x) = 5x² + 10x + 1 - 1 + 8
Step 5: Group the terms.
f(x) = (5x² + 10x + 1 - 1) + 8
Step 6: Factor the quadratic expression inside the parentheses and simplify.
f(x) = 5(x² + 2x + 1) + -5 + 8
f(x) = 5(x + 1)² + 3
Now the function is in the form f(x) = a(x - h)² + k, where (h, k) represents the vertex of the parabola.
Comparing the function with this standard form, we can see that the vertex is at (-1, 3). The value of 'h' represents the x-coordinate of the vertex, and 'k' represents the y-coordinate of the vertex.
Therefore, the correct answer is:
Minimum at (−1, 3)
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A math teacher is trying to analyze her test grades. She surveys the students to find out how many minutes they studied. She then makes a scatterplot of time studying and test grades. What is the domain?
Answer:
Step-by-step explanation:
The correct answer is the number of minutes the students studied. The student's grades is dependent on how long they studied. The domain is the independent variable or the amount of time.
Final answer:
The domain in a scatterplot of study time versus test grades represents all the reported study times of the students. It is visualized by plotting this data on a dot plot or analyzing the distribution to see the correlation between study time and grades.
Explanation:
The domain of a function in mathematics represents the set of all possible input values it can accept, typically the x-values on a graph. In the context of a scatterplot of time studying versus test grades created by a math teacher, the domain would consist of the various amounts of time that students reported studying. Analyzing the distribution of these values can showcase how study time correlates to test performance, assuming that this is a function with a one-to-one correspondence between study time and grade received, passing the vertical-line test.
To create a dot plot, as suggested in a collaborative classroom exercise, you would align a number line with the possible amounts of study time and place a dot above the corresponding value for each student's reported study time. Through this process, you could visualize the amount of study time on the x-axis and gain insights into the study habits of the class.
In a given scenario like the one described for Ms. Phan studying for an economics exam, the total benefit and the expected total gain in her score could be plotted to visualize the marginal benefits of additional study hours. This helps to understand the concept of diminishing returns in relation to study time and test score improvement.
A set of cards contains cards numbered 1 – 8. Mrs. Jacob’s class is conducting an experiment in which a card is drawn from the pile, the number is recorded, and then the card is returned to the set. The class will conduct 1,000 trials. Based on the theoretical probability, which is the best prediction for the number of times a 4 will be drawn from the pile?
Answer:
125
Step-by-step explanation:
Answer:
The best prediction for the number of times a 4 will be drawn from the pile is:
125
Step-by-step explanation:
It is given that:
A set of cards contains cards numbered 1 – 8.
So, the theoretical probability that 4 comes up is:
Ratio of Number of favorable outcome( outcome of 4) to the total umber outcome(i.e. 8 )
Hence, Theoretical Probability that 4 is drawn=1/8
Now, out of 1000 trials the best prediction of number of times 4 is drawn is:
(The probability of drawing 4)×(Number of experiments or trials)
=(1/8)×1000
=125
Quick Geometry Question:
1. A trapezoid has a 60-degree angle and a 45-degree angle. What are the other angles?
2. A trapezoid has a 60-degree angle and a 120-degree angle. What are the other angles?
Answer:
For trapezoids, we have some rules:
The angles always need to ad up to 360°
We also have that the base angles are suplementary, so they need to ad to 180°. (one smaller or equal than 90° and the other greater or equal than 90°)
Then, if the angles are one equal to 60° and the other 45°.
The other two angles are:
a1 = 180° - 60° = 120°
a2 = 180° - 45° = 135°
and now we have: 120° + 60° + 45° + 135° = 360°
for the other we have an angle of 60° and other of 120°.
This two angles can be one next to the other, so may be suplementary.
this mens that the other two angles may be any angles that add to 180° (again, one is less or equal than 90° and the other is greater or equal than 90°)
So we can have:
a1 = 110°
a2 = 70°
for example.
Factor completely 5x2 + 30x + 50
Answer: Complete factorization would be
[tex]5(x^2+6x+10)[/tex]
Step-by-step explanation:
Since we have given that
[tex]5x^2+30x+50[/tex]
We need to find the factors:
Since the terms of above expression is a factor of 5.
So, it becomes,
[tex]5x^2+30x+50\\\\=5(x^2+6x+10)[/tex]
Hence, complete factorization would be
[tex]5(x^2+6x+10)[/tex]
Ann picks a 4-digit number.
The first digit is not zero.
The 4-digit number is a multiple of 5
How many different 4-digit numbers could she pick?
Ann could pick from 1800 different 4-digit numbers that are multiples of 5, considering the range of possible digits for each position and the requirement that it must be a multiple of 5.
To determine how many different 4-digit numbers that are multiples of 5 Ann could pick, we need to consider three things:
The first digit can be anything from 1 to 9 (since the number cannot start with zero).
The second and third digits can be anything from 0 to 9.
The fourth digit must be either 0 or 5 (since the number is a multiple of 5).
For each of the first three digits, we have 9 possible choices (1-9 for the first digit, 0-9 for both the second and third digits), and for the last digit, we have 2 possible choices (0 or 5). Using the counting principle, we multiply the number of choices for each digit together to find the total number of possible 4-digit multiples of 5 Ann can pick:
9 (first digit) × 10 (second digit) × 10 (third digit) × 2 (fourth digit) = 1800 different 4-digit multiples of 5.
So, Ann could pick from 1800 different 4-digit numbers that are multiples of 5.
How do I simplify 8x+10x-4+2x+20
18 players and 3 coaches. this year, 162 players signed up to play soccer. how many coaches are needed?
Can you verify my answer?
I believe it's reflection.
if it rains tomorrow, the probability is 0.8 that john will practice the piano. if it does not rain tomorrow, there is only a .4 chance that john will practice. if there is a 60% that it will rain tomorrow, what is the probability that John will practice his piano lesson? i'm supposed to use a tree diagram to solve this ...?
Answer:64 %
Step-by-step explanation:
Given if it rains John Plays piano is 0.8
i.e. if it rains probability that john will not play is 0.2
If it not rain Then probability that john will play piano is 0.4
he will not play is 0.6
Given if there is 60 % chance that it will rain tomorrow
Thus Pobability that john will play is
[tex]=Probability\ that\ it\ will \times Probability\ john\ will\ play+Probability\ it\ will\ not\ rain\times Probability john will play[/tex]
[tex]=0.6\times 0.8+0.4\times 0.4=0.48+0.16=0.64[/tex]
Find the discriminant of the following equation.
4x2 + 16x + 16 = 0 ...?
Answer:
The discriminant is 0.
Step-by-step explanation:
Since, the discriminant of a quadratic equation [tex]ax^2+bx+c=0[/tex] is,
[tex]D=b^2-4ac[/tex]
Here, the given equation is,
[tex]4x^2+16x+16=0[/tex]
By comparing,
a = 4, b = 16 and c = 16,
Hence, the discriminant of the given equation is,
[tex]16^2-4\times 4\times 16[/tex]
[tex]=256 - 256[/tex]
[tex]=0[/tex]