1. AABBCCDD: The probability of this happening is [tex]1/16[/tex], since each parent would need to contribute a dominant allele for each gene.
2. AABBCcDD: This genotype can be produced in two ways:
a) If both parents are homozygous dominant for A and B, heterozygous for C, and homozygous dominant for D.
The probability of this happening is = 1/128.
b) If one parent is homozygous dominant for A and B, heterozygous for C, and homozygous dominant for D, and the other parent is heterozygous for A and B, homozygous dominant for C, and heterozygous for D.
3. The probability of this happening is 1/32.
AaBbCcDd : The probability of this happening is 1/256.
4. aaBBCcDD - This genotype can be produced in two ways:
a) If both parents are homozygous recessive for A, homozygous dominant for B, heterozygous for C, and homozygous dominant for D. The probability of this happening is 1/128.
b) If one parent is homozygous recessive for A, homozygous dominant for B, heterozygous for C, and homozygous dominant for D, and the other parent is heterozygous for A, homozygous dominant for B, homozygous dominant for C, and heterozygous for D.
The probability of this happening is 1/32.
To solve this problem, we need to use the principles of probability and Punnett squares.
For a tetrahybrid cross, we need to consider the four genes independently and combine the probabilities of each gene's alleles.
Assuming that A, B, C, and D are dominant alleles, and a, b, c, and d are recessive alleles, we can create a Punnett square for each gene, which would look like this:
A | A | a | a
---|-----|-----|----
B | B | b | b
---|-----|-----|----
C | C | c | c
---|-----|-----|----
D | D | d | d
Each box in the Punnett square represents a possible combination of alleles from the two parents.
For example, the top-left box represents offspring that inherit an A allele from the mother and an A allele from the father.
We can use these Punnett squares to calculate the probabilities of each genotype in the F2 offspring.
AABBCCDD - This genotype can only be produced if both parents are homozygous dominant for all four genes.
The probability of this happening is [tex](1/2)^4 = 1/16[/tex] , since each parent would need to contribute a dominant allele for each gene.
AABBCcDD - This genotype can be produced in two ways:
a) If both parents are homozygous dominant for A and B, heterozygous for C, and homozygous dominant for D.
The probability of this happening is[tex](1/2)^4 * 1/2 * (1/2)^3 = 1/128[/tex]
b) If one parent is homozygous dominant for A and B, heterozygous for C, and homozygous dominant for D, and the other parent is heterozygous for A and B, homozygous dominant for C, and heterozygous for D.
The probability of this happening is[tex]2 * (1/2)^4 * 1/2 * 1/2 * 1/2 = 1/32[/tex]
AaBbCcDd - This genotype can be produced in 16 ways, since each gene can be inherited in two different ways (dominant or recessive).
The probability of this happening is [tex](1/2)^8 = 1/256.[/tex]
aaBBCcDD - This genotype can be produced in two ways:
a) If both parents are homozygous recessive for A, homozygous dominant for B, heterozygous for C, and homozygous dominant for D. The probability of this happening is[tex](1/2)^4 * 1/2 * (1/2)^3 = 1/128.[/tex]
b) If one parent is homozygous recessive for A, homozygous dominant for B, heterozygous for C, and homozygous dominant for D, and the other parent is heterozygous for A, homozygous dominant for B, homozygous dominant for C, and heterozygous for D.
The probability of this happening is [tex]2 * (1/2)^4 * 1/2 * 1/2 * 1/2 = 1/32.[/tex]
Note that we have assumed independent assortment of the four genes, which means that the inheritance of one gene does not affect the inheritance of another gene.
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To get system b below the second equation in system a was replaced by the sum of that equation and the first equation and the first equation in system a multiplied by -2
5x-y= -11
The answer of this question is equation [-6x+4y=16].
Define Equation?An equation is a mathematical statement that shows the equality between two expressions, typically separated by an equal sign. It can contain variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division. The goal of solving an equation is to find the value of the variable that makes the equation true.
What is system?In mathematics, a system refers to a collection of mathematical objects or entities that are related or interconnected in some way.
System A
5x-y=-11
3x-2y=-8
System B
5x-y=-11
-2(3x-2y)=-8×(-2)
5x-y=-11
-6x+4y=16
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How do you find the area of this shaded shape? Thank you!
Answer:
1,760m
Step-by-step explanation:
The side of the smaller triangle is multiplied by 4, which got 44 in the bigger triangle. So you would multiply the base of the smaller by 4 as well, resulting in 80. Now you need to multiply the base and the side of the triangle, and divide that answer by half.
FORMULA FOR A TRIANGLE:
A= 1/2( L x W )
A= 1/2 (44 x 80)
A= 1/2 (3520)
A= 1760
Therefore, the area of the shaded triangle is 1,760m.
SORRY IF THIS DID NOT MAKE SENSE!
1. Find all exact solutions on [0, 2π). (Enter your answers as a comma-separated list. )2 cos2(t) + cos(t) = 1t =2. Find all exact solutions on [0, 2π). (Enter your answers as a comma-separated list. )2tan2(t) = −3 sec(t)t =3. Solve for 0 ≤ θ < π. (Enter your answers as a comma-separated list. )sin(θ) = sin(2θ)θ =4. Find all exact solutions on the interval [0, 2π). (Enter your answers as a comma-separated list. )cos(2t) = −sin(t)t =5. Find all exact solutions on the interval [0, 2π). Look for opportunities to use trigonometric identities. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE. )cos(2x) − cos(x) = 0x =
a) The exact solutions on [0, 2π) are t = π/3, π, and 5π/3. b) The exact solution on the interval [0, π) is t = 2π/3. c) The solutions are θ = π/3 and θ = 5π/3. d) The exact solutions on the interval [0, 2π) are: t = arcsin[(-1 + [tex]\sqrt{41}[/tex])/4] and t = 2π - arcsin[(-1 + [tex]\sqrt{41}[/tex])/4] using trigonometric identities.
a) We can rewrite the equation as:
2[tex]cos^{2}t[/tex] + cos(t) - 1 = 0
Using the quadratic formula, we get:
cos(t) = [-1 ± [tex]\sqrt{1-4(2)(-1)}[/tex] ] / (4)
cos(t) = [-1 ± [tex]\sqrt{9}[/tex]]/4
cos(t) = [-1 ± 3]/4
Thus, we have two solutions:
cos(t) = 1/2, which gives us t = π/3 and t = 5π/3
cos(t) = -1, which gives us t = π
Therefore, the exact solutions on [0, 2π) are t = π/3, π, and 5π/3.
b) We can use the identity [tex]tan^{2}t[/tex] + 1 = [tex]sec^{2}t[/tex] to rewrite the equation as:
[tex]tan^{2}t[/tex] = - [tex](3/2)^{2}[/tex]
Taking the square root of both sides and remembering that tan(t) is negative in the third quadrant, we get:
tan(t) = -3/2
Using the identity tan(t) = sin(t)/cos(t), we can rewrite this as:
sin(t)/cos(t) = -3/2
Multiplying both sides by cos(t) and rearranging, we get:
sin(t) = -3cos(t)/2
Squaring both sides and using the identity [tex]sin^{2}t[/tex] + [tex]cos^{2}t[/tex] = 1, we get:
9[tex]cos^{2}t[/tex]/4 + [tex]cos^{2}t[/tex] = 1
Expanding and simplifying, we get:
13 [tex]cos^{2}t[/tex] /4 = 1
[tex]cos^{2}t[/tex] = 4/13
Taking the square root of both sides and remembering that cos(t) is negative in the third quadrant, we get:
cos(t) = -2[tex]\sqrt{13}[/tex] /13
Using the identity [tex]sin^{2}t[/tex] + [tex]cos^{2}t[/tex] = 1, we can solve for sin(t) as:
sin(t) = -3/2 cos(t) = 3[tex]\sqrt{13}[/tex] /13
Therefore, the exact solution on the interval [0, π) is t = 2π/3.
c) We can use the identity sin(2θ) = 2sin(θ)cos(θ) to rewrite the equation as:
sin(θ) = 2sin(θ)cos(θ)
Dividing both sides by sin(θ) (assuming sin(θ) is non-zero), we get:
1 = 2cos(θ)
cos(θ) = 1/2
Therefore, the solutions are θ = π/3 and θ = 5π/3.
d) We can use the identity cos(2t) = 1 - 2 [tex]sin^{2}t[/tex] and rearrange the equation as:
2 [tex]sin^{2}t[/tex] + sin(t) - 5 = 0
Solving this quadratic equation using the quadratic formula, we get:
sin(t) = [-1 ± [tex]\sqrt{41}[/tex]]/4
Since the sine function has a range of [-1, 1], only the positive solution is possible, so we have:
sin(t) = (-1 + [tex]\sqrt{41}[/tex])/4
Using the identity [tex]cos^{2}t[/tex] = 1 - [tex]sin^{2}t[/tex] , we can solve for cos(t) as:
cos(t) =[tex]\sqrt{1-sin^{2}t}[/tex] = [tex]\sqrt{17-\sqrt{41} }/4[/tex]
Therefore, the exact solutions on the interval [0, 2π) are:
t = arcsin[(-1 + [tex]\sqrt{41}[/tex])/4] and t = 2π - arcsin[(-1 + [tex]\sqrt{41}[/tex])/4]
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a computer retail store has personal computers in stock. a buyer wants to purchase of them. unknown to either the retail store or the buyer, of the computers in stock have defective hard drives. assume that the computers are selected at random. (a) in how many different ways can the computers be chosen?
The probability that exactly one of the computers will be defective is 0.141
To calculate the probability of exactly one defective computer being selected out of four computers, we can use the binomial distribution formula
P(X = k) = (n choose k) × p^k × (1 - p)^(n - k)
where P(X = k) is the probability of exactly k successes (in this case, one defective computer), n is the total number of trials (in this case, four computers being selected), p is the probability of success (in this case, the probability of selecting a defective computer), and (n choose k) is the binomial coefficient, which represents the number of ways to choose k items out of n.
The probability of selecting a defective computer is 4/15, since there are 4 defective computers out of 15 in total. Therefore, the probability of selecting exactly one defective computer out of four is:
P(X = 1) = (4 choose 1) × (4/15)^1 × (11/15)^3
= 4 × 4/15 × 1331/3375
= 0.141
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The given question is incomplete, the complete question is:
A computer retail store has 15 personal computers in stock. A buyer wants to purchase 4 of them. Unknown to either the retail store or the buyer, 4 of the computers in stock have defective hard drives. Assume that the computers are selected at random. What is the probability that exactly one of the computers will be defective?
Please help me i really don't know what to do
Answer:
A 48 pound catfish would be approximately 45 inches long
Step-by-step explanation:
First find the slope of the line, m, using 2 points on the line, (20, 3) and (25, 12)
m = (12-3) / (25-20) = 9/5
Use the point (30, 21) and slope to find the equation (in point-slope form) of the line:
(y - 21) = 9/5(x - 30) = 9/5x - 270/5 = 9/5x - 54
y = 9/5x - 54 + 21 = 9/5x - 33
y = 9/5x - 33 now you have the equation of the line in y = mx + b form
Find x (catfish length) when y = 48 (catfish weight)
48 = 9/5x - 33
9/5x = 48 + 33 = 81
x = 81 · 5/9 = 45
x = 45 inches
Your friend says that the inequalities x ≤ 4/3 and -6x ≤ -8 is your friend correct? Explain
x - 4/3 ≤ 0 is equivalent to x ≥ 4/3, and they both represent the same set of values for x. My friend is correct.
Are the inequalities x ≤ 4/3 and -6x ≤ -8 equivalent?The relationship between two values that are not equal is defined by inequalities.
When we subtract 4/3 from both sides; x ≤ 4/3 can be rewritten as:
x - 4/3 ≤ 0
-6x ≤ -8 can be simplified by dividing both sides by -6 and reversing the inequality which gives:
x ≥ 4/3.
Full question "Your friend says that the inequalities x ≤ 4/3 and -6x ≤ -8 is your friend correct? Explain the reason"
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Your boss hands you a memo with a summary of the monthly data. The number of imports is shown as f(x), and the number of exports is shown as g(x). Use the data in the table below, representing both functions, to explain to your boss the solution to the system of equations and what that solution represents. Use complete sentences.
Month f(x) = No. of imports g(x) = No. of exports
January (1) 3 3
February (2) 6 4
March (3) 9 5
April (4) 12 6
The solution to this system of equations can be found by equating f(x) and g(x) and solving for x:
3x = x + 2
2x = 2
x = 1
What is the functions about?Based on the given table data, we can see that the number of imports (f(x)) and the number of exports (g(x)) follow a linear relationship with respect to the month (x). The data shows that as the month progresses, both the number of imports and exports increase.
The system of equations can be represented as follows:
f(x) = 3x
g(x) = x + 2
The first equation f(x) = 3x represents the number of imports, where the coefficient of x is 3, indicating that the number of imports increases by 3 units for every increase of 1 unit in the month.
The second equation g(x) = x + 2 represents the number of exports, where the coefficient of x is 1, indicating that the number of exports increases by 1 unit for every increase of 1 unit in the month. Additionally, there is a constant term of 2, which represents the initial number of exports in the month of January.
The solution to this system of equations can be found by equating f(x) and g(x) and solving for x:
3x = x + 2
2x = 2
x = 1
The solution x = 1 represents the month of January, where both the number of imports and exports are equal to 3. This implies that in the month of January, there were 3 units of imports and 3 units of exports.
In all, the solution to the system of equations indicates that in the month of January (x = 1), the number of imports (f(x)) and the number of exports (g(x)) were both 3 units, as per the given data in the table.
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Following the logic shown in the proof above, describe the missing answer for "Reason 2".
A
Vertical Angles Theorem
B
CPCTC
C
Reflexive Property
D
Given
The reason is 2) Vertical Angles Theorem.
Given is figure in which two triangles are joined,
We need to complete the proof of ΔBCA ≅ ΔDCE,
So,
BC = DC, AC = EC [given]
∠BCA = ∠DCE [Vertical Angles Theorem]
ΔBCA ≅ ΔDCE by SAS rule,
Hence, the reason is 2) Vertical Angles Theorem.
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The highest point of a normal curve occurs at Group of answer choices the mean. two standard deviations to the right of the mean. approximately three standard deviations to the right of the mean. one standard deviation to the right of the mean.
The highest point of a normal curve, also known as a Gaussian distribution or bell curve, always occurs at the mean. This is because the normal curve is symmetrical around the mean, with the same number of values on either side of the mean. Therefore, the peak of the curve must be directly above the mean.
The standard deviation is a measure of how spread out the values in a distribution are. For a normal distribution, approximately 68% of the values fall within one standard deviation of the mean, 95% fall within two standard deviations of the mean, and 99.7% fall within three standard deviations of the mean. Therefore, while the highest point of the normal curve occurs at the mean, the curve does extend out to both sides of the mean, with the height of the curve gradually decreasing as the distance from the mean increases.
Specifically, the point at which the curve begins to flatten out on either side of the peak is approximately one standard deviation away from the mean. At two standard deviations away from the mean, the curve has flattened out significantly, and at three standard deviations away from the mean, the curve is almost entirely flat. This is known as the empirical rule, or the 68-95-99.7 rule.
Understanding the normal curve and its characteristics is important in statistics and data analysis, as many real-world phenomena can be approximated using a normal distribution. By knowing the mean and standard deviation of a distribution, we can make predictions about the likelihood of various outcomes occurring.
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If r = 7 units and x = 5 units, then what is the volume of the cylinder
The cylinder's volume is 245 cubic units as a result.
Define the cylinder's volume?It is possible to determine how much material a cylinder can carry by using its volume, which is known as its capacity in geometry. Cubic measurements for a cylinder's volume include cm³, m³, in³, etc.
The formula V = r²h is used to determine the volume of a cylinder, where r is the radius of its circular base and h is the height between the bases' perpendicular centers.
As a result, if r = 7 units and x = 5 units, we can use the formulas below to get the cylinder's volume:
V = πr²h
V = π(7)²(5)
= 245 cubic units per volt
Consequently, the size of the cylinder 245 cubic units as a result.
Complete question given below:
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If r = 7 units and x = 5 units, then what is the volume of the cylinder(height=x)?
The volume of the cylinder is 245π cubic units.
What is cylinder?The cylinder is a three-dimensional shape having a circular base. A cylinder can be seen as a set of circular disks that are stacked on one another.
The formula for the volume of a cylinder is:
V = πr²h
where r is the radius of the base, h is the height, and π is the mathematical constant pi (approximately equal to 3.14).
Substituting r = 7 units and h = 5 units into the formula, we get:
V = π(7)²(5)
V = π(49)(5)
V = 245π
Therefore, the volume of the cylinder is 245π cubic units. Note that the volume is an exact value in terms of π, and cannot be simplified further without a numerical approximation of π.
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a study timed left-handed and right-handed people to see how long it took them to hit a buzzer. the data is shown below: the forty two right handed people had an average of 1.7 s and a standard deviation of 1.4 s. the forty seven left handed people had an average of 1.1 s and a standard deviation of 0.4 s. the difference is 0.6 s, and the standard deviation of the matched pairs differences is 0.1 s. find an 82% confidence interval for the difference in left-handed or right-handed people. what z or t score should you use?
We can say with 82% confidence that the true difference in mean times for left-handed and right-handed people is between -0.978 s and -0.222 s and t-distribution is used.
To calculate the certainty interim for the contrast between left-handed and right-handed individuals, we are able to utilize the taking-after equation:
CI = (x1 - x2) ± t*SE
where:
x1 = the meantime for left-handed people
x2 = the meantime for right-handed people
t = the critical value for the t-distribution with n1+n2-2 degrees of freedom and the desired confidence level (in this case, 82%)
SE = the standard error of the difference in means, which is calculated as:
[tex]SE = sqrt((s1^2/n1) + (s2^2/n2))[/tex]
where:
s1 = the standard deviation for left-handed people
s2 = the standard deviation for right-handed people
n1 = the sample size for left-handed people
n2 = the sample size for right-handed people
Plugging in the given values, we get:
x1 - x2 = 1.1 - 1.7 = -0.6
s1 = 0.4
s2 = 1.4
n1 = 47
n2 = 42
[tex]SE = sqrt((0.4^2/47) + (1.4^2/42)) = 0.261[/tex]
To find the critical value for the t-distribution, we can use a t-table or a calculator. With n1+n2-2 = 87 degrees of freedom and an 82% confidence level, the critical value is approximately 1.360.
Thus, the 82% confidence interval for the difference in left-handed or right-handed people is:
CI = (-0.6) ± (1.360*0.261) = (-0.978, -0.222)
hence, we can say with 82% confidence that the true difference in mean times for left-handed and right-handed people is between -0.978 s and -0.222 s.
Note that we used the t-distribution because the sample sizes for both groups are relatively small (n1 = 47, n2 = 42).
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jessica purchased a large cookie in the shape of a spring peep. After arriving home, she ate part of the cookie and had 1/4 remaining. She decided to give the rest of her cookie to her three sisters to let them share equally. What fraction of the original cookie will each of her sisters get to eat
3/4
If she ate part of the large cookie and was left with 1/4 of the cookie, that means only 3/4 of the cookie is left.
I need help asap!!! + 35 points
Raquelle bought 34.144 grams of pepper and 34.15 grams of suger. Did Raquelle buy more pepper or sugar?
Answer:
sugger
Step-by-step explanation:
because she bought 34.15 super and 34.144 pepper
Derek had 10 2/3 ounce of water in a glass He drank 1/4 of an ounce
After Derek drinks 1/4 ounce of water, he is left with 95/3 ounces of water in his glass.
Derek initially had 10 2/3 ounces of water in his glass. To find out how much water is left after he drinks 1/4 ounce of water, we need to subtract 1/4 from 10 2/3. To do that, we need to convert the mixed number (10 2/3) into an improper fraction.
To convert a mixed number into an improper fraction, we multiply the whole number by the denominator of the fraction and then add the numerator. In this case, we have:
10 x 3 + 2 = 32/3
Therefore, Derek initially had 32/3 ounces of water in his glass.
To subtract 1/4 from 32/3, we need to make sure the denominators are the same. We can convert 1/4 into twelfths by multiplying both the numerator and denominator by 3. This gives us:
1/4 x 3/3 = 3/12
Now that we have a common denominator of 12, we can subtract:
32/3 - 3/12 = 383/12 - 3/12 = 380/12
To simplify, we can divide both the numerator and denominator by 4:
380/12 ÷ 4/4 = 95/3
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Complete question is:
Derek had 10 2/3 ounce of water in a glass He drank 1/4 of an ounce of the water from his glass how much water is left in Derek's glass?
Y is directly proportional to the cube root of x. When x is increased by 700%, find the percentage increase in y
If Y is directly proportional to the cube root of x, the percentage increase in y when x is increased by 700% is 100%.
If y is directly proportional to the cube root of x, we can write this relationship as y = [tex]kx^{(1/3)[/tex], where k is the constant of proportionality.
To find the percentage increase in y when x is increased by 700%, we first need to determine the new value of x. An increase of 700% means that x is multiplied by (1 + 700%) = 8. Therefore, the new value of x is 8 times the original value.
Substituting the new value of x into the equation for y, we get:
y = [tex]k(8x)^{(1/3)[/tex]
Simplifying this expression, we can write:
y = [tex]k(2^{3x)^{(1/3)[/tex]
y = k2x
So, we can see that when x is increased by 700%, y is increased by a factor of 2. This corresponds to a percentage increase of 100%.
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6 Three vertices of a rectangle are (7, 2), (3, 2), and (3, 9).
. What are the coordinates of the fourth vertex?
• What is the perimeter of the rectangle?
the weekly earnings of bus drivers are normally distributed with a mean of $395. if only 1.1 percent of the bus drivers have a weekly income of more than $429.35, what is the value of the standard deviation of the weekly earnings of the bus drivers?
The value of the standard deviation of the weekly earnings of the bus drivers is $14.57.
To solve this problem, we can use the standard normal distribution table or a calculator that provides the inverse of the standard normal distribution. Let X be the weekly earnings of the bus drivers, then we have:
P(X > $429.35) = 0.011
Using the standard normal distribution table or calculator, we can find the z-score that corresponds to a probability of 0.011, which is approximately -2.33. We can then use the formula for standardizing a normal variable:
z = (X - μ) / σ
where μ is the mean and σ is the standard deviation of the distribution. Substituting the given values, we have:
-2.33 = ($429.35 - $395) / σ
Solving for σ, we get:
σ = ($429.35 - $395) / (-2.33) = $14.57
Therefore, the value of the standard deviation of the weekly earnings of the bus drivers is $14.57.
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X2 = 16 what is the anwser?
Answer:
x=4
Step-by-step explanation:
If the equation is:
[tex]x^{2} =16[/tex]
then the answer is 4, because to solve this, you would have to take the square root of both sides to cancel out the square on the left side of the equation:
[tex]\sqrt{x^{2} } =\sqrt{16}\\ x=4[/tex]
Hope this helps :)
Convert the rectangular coordinates (-3√3, 0) into polar form. Express the angle
using radians in terms of over the interval 0 ≤ 0 < 27, with a positive value of r.
The polar form of the rectangular coordinates (-3√3, 0) is r = 3√3 and θ = 0
To convert the rectangular coordinates (-3√3, 0) into polar form, we can use the following equations:
r = √(x² + y²)
θ = tan⁻¹(y/x)
In this case, x = -3√3 and y = 0, so we have:
r = √((-3√3)² + 0²) = 3√3
θ = tan⁻¹(0/(-3√3)) = tan⁻¹(0) = 0
Since the angle is given in radians over the interval 0 ≤ θ < 2π (which is equivalent to 0 ≤ θ < 6.28318), we need to add 2π to θ if it is negative, to ensure that θ is in the specified interval.
However, in this case, θ is already equal to 0, which is within the specified interval.
Therefore, the polar form of the rectangular coordinates (-3√3, 0) is:
r = 3√3
θ = 0 (in radians, over the interval 0 ≤ θ < 2π)
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To pass an online class a student must answer 75% of questions correcrtly on a final exam. If there are 60 quesrtions on the exam, how many questions must a student answer correctly to pass
Answer: If there are 60 questions and the student has to answer 75% of questions then the number of questions the student must answer is 45
Step-by-step explanation:
No of questions= 60,
Answers to be given= 75%
then no of questions to pass the exam= No of questions*Answers to be given in percentage
=60*75/100\
=45
joseph earned a score of 516 on exam a that had a mean of 600 and a standard deviation of 40. he is about to take exam b that has a mean of 76 and a standard deviation of 20. how well must joseph score on exam b in order to do equivalently well as he did on exam a? assume that scores on each exam are normally distributed.
Joseph must score at least 32 on exam B to do equivalently well as he did on exam A.
To determine how well Joseph must score on exam B in order to do equivalently well as he did on exam A, we need to find the equivalent z-score for his exam A score and then use it to find the corresponding score on exam B.
First, we find the z-score for Joseph's exam A score:
z = (x - mu) / sigma
z = (516 - 600) / 40
z = -2.1
The z-score of -2.1 indicates that Joseph's exam A score is 2.1 standard deviations below the mean.
To find the equivalent score on exam B, we use the formula:
z = (x - mu) / sigma
Solving for x, we get:
x = z * sigma + mu
x = -2.1 * 20 + 76
x = 32
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You have been asked to build a scale model of your school out of toothpicks. Imagine your school is 30 feet tall. Your scale is 1 ft:1.47 cm.
If a toothpick is 6.3 cm tall, how many toothpicks tall will your model be?
The transportation department is resurfacing 12. 75 miles of roadways in Collin County. The crew completes work on ¼ - mile section of roadway each hour. How many hours will it take to complete the resurfacing project?
The number of hours it will take to complete the resurfacing project is:
51 hours
How to divide fractions?We are told that the department of transportation is resurfacing 12. 75 miles of roadways in Collin County.
Now, we are also given that:
Number of miles completed each hour = 1/4 mile in section = 0.25 mile per hour
Thus, the number of hours it will take to complete the resurfacing project is:
That would be 12.75 divided by 0.25 hours
= 12.75/0.25
= 51 hours
Thus, we conclude that is the total time it will take to complete the project
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if an arugmetn is invalid, then whever the premises are all false, the conlucison must also be flase
An argument can be invalid even if the premises are true and the conclusion is false.This statement is actually false.
Invalidity refers to the structure of the argument, not the truth value of the premises or conclusion. An invalid argument fails to establish the truth of its conclusion even if its premises are true. In contrast, a valid argument guarantees that the conclusion follows from the premises, regardless of the truth or falsity of the premises. Therefore, an argument can be valid with false premises, and an argument can be invalid with true premises.
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Conclude that there is no guarantee that the conclusion will be false when all the premises are false in an invalid
argument.
If an argument is invalid, then whenever the premises are all false, the conclusion must also be false.
An invalid argument is one where the conclusion does not necessarily follow from the premises, even if the premises
are all true.
In other words, it is possible for the premises to be true, but the conclusion to be false. However, in the scenario you
described, all the premises are false. In an invalid argument, there is no guarantee that the conclusion will also be false.
Identify the argument as invalid.
Recognize that all the premises are false.
Understand that in an invalid argument, the conclusion does not necessarily follow from the premises.
Conclude that there is no guarantee that the conclusion will be false when all the premises are false in an invalid
argument.
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Please help this is the last question I can't get it wrong
Answer:10g-3
Step-by-step explanation:
Answer:
g=0.5
Step-by-step explanation:
2(5—1)=3
10g—2=3
10g—2+2=3+2
10g=5
10g/10=5/10
g=0.5
In 2010, Haiti was hit by a devastating earthquake, which registered at 7.0 on the Richter scale. The largest recorded earthquake since 1900 occurred in 1960 in Valdivia, Chile, and registered at 9.5 on the Richter scale. About how many times greater was the intensity of the Chilean earthquake? a. 2.5 b. 25 c. 150 d. 316
In 2010, Haiti was hit by a devastating earthquake, which registered at 7.0 on the Richter scale. The largest recorded earthquake since 1900 occurred in 1960 in Valdivia, Chile, and registered at 9.5 on the Richter scale. About 316 times greater was the intensity of the Chilean earthquake.
Hence, the correct option is D.
The Richter scale is a logarithmic scale that measures the magnitude of an earthquake. Each increase of one on the Richter scale represents a tenfold increase in the amplitude of the seismic waves.
To find out how many times greater the intensity of the Chilean earthquake was compared to the Haitian earthquake, we will have to find the difference in magnitude between the two earthquakes.
9.5 - 7.0 = 2.5
Since each increase of one on the Richter scale represents a tenfold increase in the amplitude of the seismic waves, a 2.5 increase represents
10^(2.5) = 316.2
Hence, the intensity of the Chilean earthquake was about 316 times greater than the intensity of the Haitian earthquake.
Hence, the correct option is D.
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Answer:d
Step-by-step explanation:
its d
Jenae wants to buy a fuel-efficient car. She finds one that can travel 500 miles on one tank of gas. If the gas tank holds 16 gallons, calculate the miles per gallon.
The table shows the free throw statistics for four players on Kent Middle School’s basketball team. Who had the best free throw statistics?
Using percentages we know that Terrel has the best free throw statistics which is 70.83%.
What is the percentage?In mathematics, a quantity or ratio known as A% stands for a percentage of 100.
There are several different ways to depict a dimensionless connection between two numbers, including ratios, fractions, and decimals.
To represent percentages, the symbol "%" is typically written after the number.
In mathematics, a percentage is a number or ratio that is expressed as a fraction of 100.
So, in the given situation where we need to get whose statistics are the best.
We need to calculate the percentages in all cases as follows:
Jack: 18/39*100 = 46.15%
Henry: 54%
Terrel: 17/24*100 = 70.83%
Riley: 9/23*100 = 39.13%
Since Terrel has the highest %, so he has the best free throw statistics.
Therefore, using percentages we know that Terrel has the best free throw statistics which is 70.83%.
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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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I WILL GIVE 10 POINTS
Divide 15x5 − 3x3 − 9x2 by −3x2.
12x3 − 6x − 12
−5x3 − 6x + 3
−5x3 + x + 3
−5x3 + x − 3
The option (3) is correct the quotient is −5x³ + x + 3.
What is factorization method in quadratic equation ?To solve quadratic equations by factoring, we first express the quadratic polynomial into a product of factors by using middle term splitting or different identities and then set each factor equal to 0. The equation a x 2 + b x + c = 0 ( a ≠ 0 ) can be written as.
According to given question
To divide[tex]15x^5[/tex] − 3x³ − 9x² by −3x² using the factorization method, we can factor out −3x² from the expression and simplify to get:
[tex]15x^5[/tex]− 3x³ − 9x²= −3x²(−5x³ + x + 3)
Therefore, the quotient is −5x³ + x + 3.
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