The solution of the expression is x = (-1 ± i√3)/2 and the domain of the expression is all values of x l x ≥ 0 (option c).
The given equation is -x² = √x. To solve this equation, we need to isolate x on one side of the equation. We begin by squaring both sides of the equation to eliminate the radical:
(-x²)² = (√x)²
x⁴ = x
Now we have a quartic equation, which we can solve by factoring:
x(x³ - 1) = 0
We can further simplify this equation by factoring the cubic term using the difference of cubes formula:
x(x - 1)(x² + x + 1) = 0
From this factorization, we can see that the solutions are x = 0, x = 1, and the solutions of the quadratic factor x² + x + 1 = 0. To find the solutions of the quadratic, we can use the quadratic formula:
x = (-1 ± √1 - 4(1)(1))/2(1)
x = (-1 ± i√3)/2
Therefore, the solutions to the equation -x² = √x are x = 0, x = 1, and x = (-1 ± i√3)/2.
Now let's consider the domain of the solutions, which is determined by the inequality x ≥ 0. This inequality means that the solutions must be greater than or equal to 0. We can see that x = 0 and x = 1 satisfy this inequality.
For the solution x = (-1 ± i√3)/2, we can see that it does not satisfy the inequality x ≥ 0 because it is negative. Therefore, the solutions to the equation -x² = √x in the domain x ≥ 0 are x = 0 and x = 1.
Finally, let's consider the inequality x ≤ 0. This inequality means that the solutions must be less than or equal to 0. We can see that x = 0 satisfies this inequality. However, x = 1 and x = (-1 ± i√3)/2 do not satisfy this inequality. Therefore, the solutions to the equation -x² = √x in the domain x ≤ 0 are x = 0.
Hence the correct option is (c).
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Complete Question:
Solve the expression -x² = √x . And identify the domain of the expression,
A. all values of x
B. all values of x l x ≥ 1
C. all values of x l x ≥ 0
D. all values of x l x ≤ 0
PLS HELP I WILL GIVE YOU 50 PTS BUT IF FOOL ANSWERS WILL GET REPORTED AND GOOD ANSWERS WILL GET BRAINLYEST
Answer: Ok so first you would take the 86 and multiply it by .2 or 20% and that would get you 17.2 for blank 2
then you would take 86 and subtract 17.2 to get 68.8 for blank 3
sooo... he would pay 68 dollars and 80 cents with the coupon
Step-by-step explanation:
im really smart and good at math : )
72° (x+4)° Write an equation that can be used to find the value of x.
Answer:
In a triangle, the sum of the interior angles is 180 degrees. So, we can set up the following equation:
72° + (x+4)° + A = 180°
where A is the measure of the third angle in the triangle.
Simplifying the equation, we get:
(x+4)° + 72° + A = 180°
x + 76° + A = 180°
Subtracting 76° from both sides, we get:
x + A = 104°
Therefore, an equation that can be used to find the value of x is x + A = 104°, where A is the measure of the third angle in the triangle. Note that we do not have enough information to solve for x or A individually, but we can use this equation to relate the two angles in the triangle.
Which of these is something I can pay for with the money in a savings account?
Answer:
what are the options?
Step-by-step explanation:
Question 1
Find the future value twenty-five years from now of an account in which you have $19,675.13 today and into which you make annual $3,000 deposits. Assume the account earns 9.25%.
The future value of the account after 25 years is $210,595.95.
To find the future value of the accountWe can use the formula for future value of an annuity:
FV = P * (1 + r)^n + PMT * ((1 + r)^n - 1) / r
Where
P is the initial investmentr is the annual interest rate n is the number of years PMT is the annual paymentSubstituting the given values, we get:
FV = 19675.13 * (1 + 0.0925)^25 + 3000 * ((1 + 0.0925)^25 - 1) / 0.0925
Simplifying and evaluating, we get:
FV = $210,595.95
Therefore, the future value of the account after 25 years is $210,595.95.
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A population has a mean μ=135 and a standard deviation Ï=28. Find the mean and standard deviation of the sampling distribution of sample means with sample size n=57.
A population has a mean μ=135 and a standard deviation Ï=28.
The mean of the sampling distribution of sample means is equal to the population mean, that is 135.
The standard deviation of the sampling distribution of sample means can be calculated by using the formula
SE = Ï /[tex]\sqrt{n}[/tex]
Where Ï is the population standard deviation and n is the sample size.
By putting the given values we get
SE = 28 / [tex]\sqrt{57}[/tex] = 3.7
Hence, the mean of the sampling distribution of sample means is 135, and the standard deviation is 3.7.
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Laura had 10 shirts she then bought 3 shirts each week for 4 weeks
If Laura had 10 shirts to begin with and then bought 3 shirts each week for 4 weeks, she would have:
10 + (3 x 4) = 22 shirts
After 4 weeks, she would have a total of 22 shirts.
What is the relative minimum of the function?
Enter your answer in the box.
A grid with x axis increments of two increasing from negative ten to ten and y axis increments of two increasing from negative ten to ten. The grid contains a parabola opening up with a vertex at x equals negative three and y equals negative two.
The relative minimum of the function include the following: -2.
What is the vertex form of a quadratic equation?In this exercise, you are required to determine the relative minimum of the function with respect to the vertex form of a quadratic function h(x) that is written in standard form. Mathematically, the vertex form of a quadratic equation is given by this formula:
y = a(x - h)² + k
Where:
h and k represents the vertex of the graph.a represents the leading coefficient.Based on the information provided about this quadratic function, we can reasonably infer and logically deduce that that its vertex is at x equals negative three and y equals negative two.;
Vertex (h, k) = (-3, -2)
Therefore, the relative minimum is equal to -2.
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You are playing a game where a quarter is tossed 4 times. What is the probability that the quarter lands on tails exactly one time?
PLEASE ANSWER FAST!
Solve for x. Round your answer to the nearest tenth, and type it in the blank without units.
The value of x in the triangle is 17.6 m.
How to solve for the value of x in the triangle?
Trigonometry deals with the relationships between the sides and angles of triangles.
The three primary trigonometric functions are sine, cosine, and tangent, which are ratios of the sides of a right triangle. These functions are often abbreviated as sin, cos, and tan.
Using the given triangle:
cos 54° = x/30 (cos = adjacent/hypotenuse)
x = 30 * cos 54°
x = 17.6 m
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ms. todd gives students a project where she gives all students in her class a single set of ordered pairs numbered 1 through 30. they need to graph ordered pairs in order and then connect the dots in the order in which they are graphed to make a picture. this serves as their final unit project on graphing points on the coordinate plane. is this a suitable project?
Yes, the project consists on single set of ordered pairs numbered 1 through 30 on coordinate planes for all class students is a suitable one.
Ordered pair is a composition of the x- coordinate (i.e., abscissa) and the y coordinate (i.e, ordinate), that's two values written in a fixed order within. In mathematics, an ordered pair ( pair means two objects) so, (a, b) is a pair of objects in particular order. The order in the pair is very significant, that is ordered pair (a, b) is different from the ordered pair (b, a). Now, Ms. todd provide a project to students which consists a single set of ordered pairs numbered 1 through 30, for all students in her class. We can easily graph a ordered pair on coordinate plane. Coordinate plane is a 2-D graph made using x-coordinate and y-coordinate. There is two axis x-axis and y-axis. So, first they collect all possible ordered pairs from 1 to 30 like ( 1,1),( 1,2),(1,3),..........(1,30), (30,1),.....,(30,30) ... etc. In this coordinate plane consists 30 numbers value on y-axis and 30 on x-axis. Then, draw on graph. Hence, it is suitable.
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Carbon 14 has a half-life of 5,600 years. If a fossil contains 3 g of radioactive carbon 14, how many grams did it contain 11,200 years ago
Carbon 14 has a half-life of 5,600 years, which means that after 5,600 years, half of the initial amount of Carbon 14 will decay. Therefore, we can use the following formula to find the amount of Carbon 14 that was present 11,200 years ago:
A = A0 * (1/2)^(t/T)
where:
A0 = initial amount of Carbon 14
A = amount of Carbon 14 remaining after time t
t = time elapsed since the initial amount was present
T = half-life of Carbon 14
How many grams did it contain 11,200 years ago?We know that the fossil contains 3 g of Carbon 14, which is the amount remaining after 11,200 years. We want to find the initial amount, A0.
Let's plug in the values we have into the formula and solve for A0:
3 g = A0 * (1/2)^(11,200/5,600)
3 g = A0 * (1/2)^2
3 g = A0 * 1/4
A0 = 4 * 3 g
A0 = 12 g
Therefore, the fossil contained 12 g of Carbon 14 11,200 years ago.
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Gabby made a scale drawing of the town library. She used the scale 1 centimeter : 5 meters. The actual width of the parking lot is 80 meters. How wide is the parking lot in the drawing?
The width of the parking lot in the drawing is 16 centimeters
Gabby made a scale drawing of the town library. She used the scale 1 centimeter : 5 meters. The actual width of the parking lot is 80 meters.
If the scale is 1 centimeter : 5 meters, then 1 centimeter on the drawing represents 5 meters in real life.
To find the width of the parking lot in the drawing, we need to set up a proportion
1 cm : 5 m = x cm : 80 m
Where x is the width of the parking lot in the drawing.
To solve for x, we can cross-multiply and simplify
1 cm * 80 m = 5 m * x cm
80 cm = 5x
x = 16 cm
Therefore, the width of the parking lot in the drawing is 16 centimeters.
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Only questions 7, 9, 10, and 11
PLS show how you got the answer and explain
GIVING BRAINLIEST
Answer:
7) .15 + .7 = .85, .1 + .7 = .8
9) Another way to write 44n (44
times n) is 44•n.
Another way to write 44 ÷ n (44
divided by n) is 44/n.
10) $.25 × 7 = $1.75
11) A driver buys d gallons of gas at $3.25 per gallon. How much does the driver spend on gas?
You work in a pharmacy that mixes different concentrations of saline solutions for its customers. The pharmacy has a supply of two concentrations, 0.50% and 2%. The function
100(0.02) + x(0.005)
y=
100 +x
gives the amount x in milliliters of the 0.5% solution you must add to 100 milliliters of the 2% solution to form a new concentration y of saline solution. How
many milliliters of the 0.5% solution must you add for the combined solution to have a concentration of 0.88%?
You must add approximately mL.
(Round to one decimal place as needed)
Answer:
294.7 mL
Step-by-step explanation:
You want to know the volume (x) in mL of 0.5% solution to be added to 100 mL of 2% solution to make a mix that has a concentration of 0.88%.
SetupThe given equations seem to be missing something. We want ...
100(0.02) +x(0.005) = (100 +x)(0.0088)
SolutionWe like to play with larger numbers, so we'll multiply this equation by 100 as we simplify it.
200 +0.5x = 88 +0.88x
112 = 0.38x . . . . . . . . . . . . . subtract 88+0.5x
294.7 = x . . . . . . . . . . . . divide by 0.38
You must add approximately 294.7 mL of 2% solution.
52W high 52W low Name of Stock Symbol High Low Close
37.18 29.39 Zycodec ZYO 39.06 32.73 34.95
11.76 7.89 Unix Co UNX 16.12 12.11 15.78
Last year, a stockholder purchased 40 shares of Zycodec at its lowest price of the year and purchased 95 shares of Unix at its highest price of the year. If the stockholder sold all shares of both stocks at their respective closing price, what was the overall gain or loss?
The overall loss is $604.30.
The overall gain is $604.30.
The overall loss is $660.35.
The overall gain is $660.35.
the overall gain is positive, we can conclude that the stockholder made a profit of $190.10. Therefore, the correct answer is: "The overall gain is $190.10."
How to solve the question?
To calculate the overall gain or loss, we need to first find the total cost of buying the shares and the total revenue from selling them.
For the 40 shares of Zycodec purchased at its lowest price of 29.39, the total cost would be:
40 shares x $29.39/share = $1,175.60
For the 95 shares of Unix purchased at its highest price of 16.12, the total cost would be:
95 shares x $16.12/share = $1,531.40
The total cost of purchasing both stocks would be:
$1,175.60 + $1,531.40 = $2,707
Now, we need to find the total revenue from selling the shares. The closing price of Zycodec is 34.95, so the revenue from selling 40 shares would be:
40 shares x $34.95/share = $1,398
The closing price of Unix is 15.78, so the revenue from selling 95 shares would be:
95 shares x $15.78/share = $1,499.10
The total revenue from selling both stocks would be:
$1,398 + $1,499.10 = $2,897.10
The overall gain or loss would be the difference between the total revenue and total cost:
Overall gain/loss = total revenue - total cost
Overall gain/loss = $2,897.10 - $2,707
Overall gain/loss = $190.10
Since the overall gain is positive, we can conclude that the stockholder made a profit of $190.10. Therefore, the correct answer is: "The overall gain is $190.10."
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kevin meal came to 45$ he tipped his sever 20% how much tip did he leave for the sever
Question 3
Terry has a new retirement account. He plans to make deposits of $4,750 per year for the next 40 years. He expects the account to earn 9.1% for the first 25 years, 6.9% for the next ten years, and then 4.5% for the last five years. How much will have have at the end of the forty years based on these assumptions?
With an initial investment of $19,675.13 and yearly deposits of $3,000 at an interest rate of 9.25%, the account will be worth around $336,312.91 in 25 years.
what is unitary method ?The unitary approach is a strategy for problem-solving in which the value of one piece of a quantity is determined, then the cost of an unique number of units associated with that quantity is subsequently determined using that value. In other words, it's a method of proportional used to resolve issues where one unit's value is known but another's value is needed. The unitary method's fundamental premise is to establish a percentage between two quantities, one of which is stated in the form of one unit and the other in terms of a greater number of units.
given
In the following ten years, we have:
P = $4,750 r = 6.9% = 0.069
n = 10
[tex]FV2 = $4,750 * ((1 + 0.069)^10 - 1) / 0.069[/tex]
= $74,894.87
In the previous five years, we have:
P = $4,750
r = 4.5% = 0.045
n = 5
= $127,756.44
Lastly, we can combine the two figures to determine the account's entire future value:
FV is $208,556.47 + $127,756.44 = $336,312.91 (annual deposits + initial investment).
With an initial investment of $19,675.13 and yearly deposits of $3,000 at an interest rate of 9.25%, the account will be worth around $336,312.91 in 25 years.
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HELP FAST PLEASE
Simplify: m5 p8 m6 p10
1) mp¹3. mp¹6
2) m11 p18
3)m18.p11
4)(m. p)29
Answer:
the answer is 2) m11 p18.
Step-by-step explanation:
m5 p8 m6 p10 = (m5 m6) (p8 p10) = m11 p80
Therefore, the answer is 2) m11 p18.
assertion: if p and q are integers and is represented in the form of p/q then it is a rational number
reason: 17/3 is a rational number
The assertion will be correct and the reason provided is also correct.
A rational number is termed as a number which can be represented as the ratio of the two integers, where the denominator (q) will be not equal to zero. In other words, a rational number can be expressed in the form of a p/q, where p and q are the integers and q ≠ 0.
In the given reason, 17/3 is cited as an example of a rational number. Since both 17 and 3 are integers, and 3 ≠ 0, 17/3 can be expressed as the ratio of two integers, making it a rational number.
Therefore, the assertion will be true, and the reason provided is correct.
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Using the explicit formula find the 11th term of the sequence. -4, 8, -16, 32, ...
Answer:
4096.
Step-by-step explanation:
We need to check if it's a geometric or arithmetic sequence (looking for the common ratio, r). The sequence goes -4, 8, -16, 32, so we can multiply the previous number by -2 to get the next number, and so on and so forth. This makes it a geometric sequence.
The formula for finding the nth term of a geometric sequence is [tex]u_{n} = u_{1} r^{n-1}[/tex]. The term we are looking for is the 11th. Let's plug these values in now:
[tex]u_{n} = u_{1}r^{n-1}[/tex]
[tex]u_{11} = -4(-2)^{11-1}[/tex]
[tex]u_{11} = 4096[/tex]
Therefore the 11th term is 4096.
Question 10(Multiple Choice Worth 2 points)
(Circle Graphs MC)
A New York City hotel surveyed its visitors to determine which type of transportation they used to get around the city. The hotel created a table of the data it gathered.
Type of Transportation Number of Visitors
Walk 120
Bicycle 24
Car Service 45
Bus 30
Subway 81
Which of the following circle graphs correctly represents the data in the table?
circle graph titled New York City visitor's transportation, with five sections labeled walk 80 percent, bus 16 percent, car service 30 percent, bicycle 20 percent, and subway 54 percent
circle graph titled New York City visitor's transportation, with five sections labeled walk 40 percent, bicycle 8 percent, car service 15 percent, bus 10 percent, and subway 27 percent
circle graph titled New York City visitor's transportation, with five sections labeled subway 40 percent, bus 8 percent, car service 15 percent, bicycle 10 percent, and walk 27 percent
circle graph titled New York City visitor's transportation, with five sections labeled subway 80 percent, bicycle 20 percent, car service 30 percent, bus 16 percent, and walk 54 percent
So, the circle graph entitled New York City visitor's transportation with five sections labelled walk 40%, bicycle 8%, car service 15%, bus 10%, and subway 27% is the proper option that displays the data in the circular graphs.
Explain about the circle graphs:A circle represents 360 degrees. A circle can be split up into smaller sections. An arc is a segment of a circle, and arcs are named based on their angles.
To illustrate information and data, use a circle graph or pie chart. Often, a circle graph is used to quickly and proportionately display the findings of an investigation.
Given data:
Type of Transportation Number of Visitors Percentage
Walk 120 120*100/ 300 = 40%
Bicycle 24 24*100/ 300 = 8%
Car Service 45 45*100/ 300 = 15%
Bus 30 30*100/ 300 = 10%
Subway 81 81*100/ 300 = 27%
Total 300
So, the circle graph entitled New York City visitor's transportation with five sections labelled walk 40%, bicycle 8%, car service 15%, bus 10%, and subway 27% is the proper option that displays the data in the circular graphs.
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Follow the rules to create two number sequences that go to the fifth term each. Rule 1: Multiply by 3 starting from 10. Rule 2: Subtract 7 starting from 58. What is the first term that appears in both sequences? (2 points) a 30 b 55 c 60 d 180
the answer is (a) 30.To find the first term that appears in both sequences, we can simply compare the terms in each sequence until we find a match
what is sequence ?
In mathematics, a sequence is a set of numbers, called terms, arranged in a specific order. Each term in the sequence is obtained by applying a certain rule or formula to the preceding term(s) in the sequence.
In the given question,
Using Rule 1, we can create the first sequence:
10, 30, 90, 270, 810
Using Rule 2, we can create the second sequence:
58, 51, 44, 37, 30
To find the first term that appears in both sequences, we can simply compare the terms in each sequence until we find a match.
We see that the number 30 appears in both sequences as the fifth term of the second sequence and the second term of the first sequence.
Therefore, the answer is (a) 30.
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You may need to use the appropriate appendix table or technology to answer this question. The following results come from two independent random samples taken of two populations. Sample 1 Sample 2 ni = 50 n2 = 35 = X1 13.6 x2 = 11.6 0 1 = 2.4 02 3 (a) What is the point estimate of the difference between the two population means? (Use x1 - xz.) 2 (b) Provide a 90% confidence interval for the difference between the two population means. (Use X2 Round your answers to two decimal places.) 0.98 X to 3.02 x - X2. Round your answers to two decimal places.) (C) Provide a 95% confidence interval for the difference between the two population means. (Use X X to 3.21 x 0.79
The appendix table the point estimate of the difference between the two population means is 2
The difference between the two population means, we need to find the standard error of the difference and use the t-distribution with (n1 + n2 - 2) degrees of freedom. The formula for the standard error of the difference is:
SE = sqrt[ (s1 / n1) + (s2 / n2) ]
Substituting the given values, we get:
SE = sqrt[ (2.4 / 50) + (3 / 35) ] = 0.617
Using a t-distribution with 83 degrees of freedom (50 + 35 - 2), and a 90% confidence level, we find the t-value to be 1.66 (from the t-table or calculator). Therefore, the 90% confidence interval is:
x1 - x2 ± t(α/2) * SE
= 2 ± 1.66 * 0.617
= 0.98 to 3.02
So, we can say with 90% confidence that the true difference between the two population means lies between 0.98 and 3.02.
To calculate the 95% confidence interval:
x1 - x2 ± t(α/2) * SE
= 2 ± 2.00 * 0.617
= 0.79 to 3.21
So, we can say with 95% confidence that the true difference between the two population means lies between 0.79 and 3.21.
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Solve for x. Round your answer to the nearest tenth, and type it in the blank without units.
X is the adjacent side and is 50 inches long.
Right angle triangleUsing the trigonometric ratio of cosine:
cos(60 degrees) = adjacent / hypotenuse
cos(60 degrees) = 1/2 (cosine of 60 degrees is 1/2)
So, we can solve for the X, the adjacent:
adjacent = cos(60 degrees) x hypotenuse
adjacent = (1/2) x 100 inches
adjacent = 50 inches
Therefore, the length of the adjacent is 50 inches.
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A store sells pajamas in two sizes.
• The child size is for people less than `60` inches tall.
• The adult size is for people `60` inches tall or more.
Juan’s height is `145` centimeters.
Would he fit the child or adult size
What is the answer
he would fit the child size
his height is 145cm and we want to convert it into inches so the formula is
length/2.54=
145cm/2.54=57.08in
so juan is 57.08 inches, so he fits the child size.
Rewrite the equation in slope-intercept form: 5x + 9y = 30
Answer:
y = (-5/9)x + 30/9
Step-by-step explanation:
To rewrite the equation 5x + 9y = 30 in slope-intercept form, we need to isolate y on one side of the equation.
5x + 9y = 30
Subtract 5x from both sides of the equation to isolate 9y:
5x - 5x + 9y = -5x + 30
9y = -5x + 30
Divide both sides of the equation by 9 to solve for y:
9y/9 = (-5x + 30)/9
y = (-5/9)x + 30/9
Between which values on the df = 3 line does your calculated χ^2 value lie?- between 1.42 and 2.19- between 1.42 and 2.37- between 1.65 and 2.19- between 2.37 and 3.66
The x² value lie between 1.42 and 2.37
The formula to calculate the x² value is:
χ² = Σ (Observed frequency - Expected frequency)² / Expected frequency
Here, Σ represents the sum of all the values in the calculation. The observed frequency is the actual frequency of a category in the sample, while the expected frequency is the theoretical frequency based on the null hypothesis.
The x² value is compared to a chi-squared distribution table to determine its significance level. The table shows the probability of obtaining a certain x² value under the null hypothesis for different degrees of freedom. Degrees of freedom (df) are calculated as the number of categories minus 1.
If the calculated x² value is greater than the critical value from the table for a given significance level, the null hypothesis is rejected, and the alternative hypothesis is accepted. This means that there is a significant relationship between the variables. If the calculated x² value is less than the critical value, the null hypothesis is accepted, and no significant relationship is found.
In the context of the problem given, the x² value is used to test the hypothesis that the genes are unlinked. The significance level used is 0.05, which means that there is a 5% chance of rejecting the null hypothesis when it is actually true. If the probability corresponding to the x² value is less than or equal to 0.05, the hypothesis should be rejected. If it is greater than 0.05, the results are not statistically significant, and the hypothesis is accepted.
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Complete Question:
The x² value means nothing on its own- it is used to find the probability that, assuming the hypothesis is true, the observed data set could have resulted from random fluctuations. A low probability suggests that the observed data are consistent with the hypothesis, and thus the hypothesis should be rejected, A standard cutoff point used by biologists is a probability of 0.05(5%). If the probability corresponding to the x² value is 0.05or considered statistically significant, the hypothesis (that the genes are unlinked) should be rejected. If the probability is above 0.05, the results are not statistically significant: the observed data are consistent with the hypothesis.
Determines which values on the df =3 line of the table your calculated x² value lies between.
Quiz Active
Does anyone know the answer
Answer:c the third one
Step-by-step explanation: because i did it!
What are the measures of ∠1 and ∠2?
The measure of angle 1 is 67.4°. The measure of angle 2 is 104.5°.
What is angle?An angle is the measure of the amount of rotation between two lines or two planes that meet at a point. It is typically measured in degrees or radians. An angle can be acute, meaning it is less than 90 degrees, right, meaning it is exactly 90 degrees, obtuse, meaning it is greater than 90 degrees but less than 180 degrees, or straight, meaning it is exactly 180 degrees. An angle can also be positive or negative, depending on the direction of rotation between the lines or planes. Angles are used in various fields such as mathematics, engineering, physics, and geometry.
Here,
180-121.8=58.2°
180-(58.2+17.3)=104.5°
180-104.5=75.5°
180-(75.5+37.1)=67.4°
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1. the general term of a sequence is 4n - 1 which time is a. 15 b. 83
Answer:
the answer of the sequence is a