PQ and QR are 2 sides of a regular 12 sided polygon. PR is a diagonal of the polygon.
Work out the size of angle PRQ.
You must show your working
Answers
The size of the angle PRQ is approximately 26.565 degrees.
Since PQ and QR are two sides of a regular 12-sided polygon, they are congruent, and the polygon can be divided into 12 congruent isosceles triangles with base PQ and QR.
Let's call the center of the polygon O. Since the polygon is regular, the angle POQ is 360/12 = 30 degrees. Also, since PR is a diagonal of the polygon, it divides angle POQ into two congruent angles, each measuring 15 degrees.
Now, let's consider the triangle PQR. We know that angle PQR is 180 - (15 + 15) = 150 degrees (since the sum of angles in a triangle is 180 degrees).
Using the Law of Cosines, we can find the length of PR:
PR² = PQ² + QR² - 2(PQ)(QR)cos(angle PQR)
PR² = PQ² + QR² - 2(PQ)(QR)cos(150)
PR² = PQ² + QR² + (PQ)(QR)
Since PQ = QR, we can simplify this to:
PR² = 2(PQ²) + PQ²
PR² = 3(PQ²)
Therefore,
PQ² = (1/3)(PR²)
Now, let's consider the triangle PRQ. We know that PQ is a side of the polygon, so it has length 1 (we can choose any unit of length we like). Also, we know that QR is a side of a regular 12-sided polygon, so we can use the formula for the side length of a regular polygon:
QR = 2PQsin(180/12) = PQ√(6 + 2sqrt(3))
Substituting PQ = 1, we get:
QR = √(6 + 2√(3))
Finally, we can use the Law of Cosines again to find the angle PRQ:
cos(angle PRQ) = (PQ² + QR² - PR²) / (2PQQR)
cos(angle PRQ) = (1 + 6 + 2√3) - PR^2) / (2√(6 + 2√(3)))
Substituting PR² = 3(PQ²) = 3, we get:
cos(angle PRQ) = (7 + 2√(3)) / (2√(6 + 2√(3)))
Taking the inverse cosine, we get:
angle PRQ = 26.565 degrees (to 3 decimal places)
Therefore, the size of the angle PRQ is approximately 26.565 degrees.
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Related Questions
Which equation is the easiest to identify the x-intercepts?
a. Factored Form
b. Standard Form
c. Vertex Form
d. None of the above
Please only answer if you actually know which one is right. :)
Answers
The easiest equation to identify the x-intercepts is the factored form of a quadratic equation, or option A.
The equation that is the easiest to identify the x-intercepts is the factored Form.
Option A is the correct answer.
We have,
In factored form, the equation is written as a product of linear factors, and the x-intercepts (or roots) are easily identifiable by setting each factor equal to zero and solving for x.
The x-intercepts correspond to the values of x when the entire expression becomes zero, which happens when at least one of the factors equals zero.
Thus,
The equation that is the easiest to identify the x-intercepts is the factored Form.
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You are given an isosceles trapezoid ABCD with median XY. Complete the following.
Answers
The value of ∠ABD is 120 degrees if given an isosceles trapezoid ABCD with median XY
What is trapezoid ?
A trapezoid is a quadrilateral (a four-sided polygon) with at least one pair of parallel sides. The parallel sides of a trapezoid are called bases, and the non-parallel sides are called legs.
Since ABCD is an isosceles trapezoid, the length of AB is equal to the length of CD. Let's assume that AB = CD = a, and BC = d.
The length of XY is equal to half the sum of the lengths of the non-parallel sides AB and CD. Therefore, XY = (1/2)(AB+CD) = (1/2)(a+a) = a.
So, the length of the median XY is a.
Since ABCD is an isosceles trapezoid, the base angles A and D are congruent. Let's assume that m∠ABD = x.
Since XY is the median of ABCD, it bisects the legs AB and CD at M and N, respectively. Therefore, AM = MB = (AB/2) and DN = NC = (CD/2).
Since AD and BC are parallel, we have ∠AMB = ∠DNC (corresponding angles). Also, ∠AMB + ∠BMD = 180° (linear pair), so ∠BMD = 180° - ∠AMB.
Similarly, we have ∠CND + ∠DNC = 180° (linear pair), so ∠CND = 180° - ∠DNC.
Since AD and BC are parallel, we have ∠ABD + ∠BMD = 180° (co-interior angles), so ∠ABD = 180° - ∠BMD.
Similarly, we have ∠DCB + ∠CND = 180° (co-interior angles), so ∠DCB = 180° - ∠CND.
Since ABCD is an isosceles trapezoid, we have AB = CD, so AM + MC = DN + NB. Substituting the values, we get (a/2) + d = (a/2) + d. Therefore, d = d.
Now, we can use the fact that ∠BMD = ∠CND to get an equation in terms of x: x + ∠ABD = 180° - x + ∠DCB. Substituting d = d, we get x + ∠ABD = 180° - x + ∠ABD. Therefore, x = (1/2)*(180° - ∠ABD).
Since ABCD is an isosceles trapezoid, we have ∠ABC = ∠DCB. Also, we know that ∠ABD and ∠CBD are supplementary angles. Therefore, ∠ABD + ∠CBD = 180°. Substituting the value of x, we get (1/2)*(180° - ∠ABD) + ∠ABD = 180°. Simplifying, we get ∠ABD = 120°.
Therefore, The value of ∠ABD is 120 degrees if given an isosceles trapezoid ABCD with median XY
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Write the equation of a line perpendicular to y = 2/7 x - 5 and passing through the point (12,12).
1. y = -7/2 x - 30
2. y = 7/2 x - 30
3. y = -7/2 x + 30
4. y = -7/2 x + 54
Answers
Answer:
To find the equation of a line perpendicular to y = (2/7)x - 5 and passing through the point (12,12), we can use the fact that the slopes of two perpendicular lines are negative reciprocals of each other.
First, find the slope of the given line by identifying the coefficient of x. In this case, the slope is 2/7.
The negative reciprocal of 2/7 is -7/2. This is the slope of the line we are looking for.
Use the point-slope form of the equation of a line, which is y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line. Plugging in the values we have:
y - 12 = (-7/2)(x - 12)
Simplify and rewrite in slope-intercept form (y = mx + b) if desired:
y - 12 = (-7/2)x + 42
y = (-7/2)x + 54
So the equation of the line perpendicular to y = (2/7)x - 5 and passing through the point (12,12) is y = (-7/2)x + 54, which is option 4.
Hope This Helps!
30 is what percentage of 15?
Answers
susan keeps track of the number of tickets sold for each play presented at the community theater. within how many standard deviations of the mean do all the values fall?
Answers
The required mean and the standard deviation of the given data based on number of tickets is equal to 111.2 and 32.84 respectively.
Calculate the mean,
Add up all the values in the set and divide by the total number of values,
Mean
= ( Sum of all the observations ) / ( Total number of observations )
= (135 + 71 + 69 + 80 + 158 + 152 + 161 + 96 + 122 + 118 + 87 + 85) / 12
= 1334 / 12
= 111.2
So the mean number of tickets sold is 111.2.
Standard deviation,
Calculate the standard deviation,
First need to calculate the variance.
The difference between each value and the mean, squaring those differences, adding them up, and dividing by the total number of values,
= ((135 - 111.2)^2 + (71 - 111.2)^2 + (69 - 111.2)^2 + (80 - 111.2)^2 + (158 - 111.2)^2 + (152 - 111.2)^2 + (161 - 111.2)^2 + (96 - 111.2)^2 + (122 - 111.2)^2 + (118 - 111.2)^2 + (87 - 111.2)^2 + (85 - 111.2)^2) / 12
= (566.44 + 1616.04 + 1780.84 + 973.44 + 2190.24 + 1664.64 + 2480.04 + 231.04 + 116.64 + 46.24 + 585.64+ 686.44) / 12
= 12937.68 /12
= 1078.14
Square root of the variance to get the standard deviation,
√1078.14= 32.84
So the standard deviation is approximately 32.84.
Therefore, the mean and the standard deviation is equal to 111.2 and 32.84 respectively.
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The above question is incomplete, the complete question is:
Susan keeps track of the number of tickets sold for each play presented at the community theater. within how many standard deviations of the mean do all the values fall?
135, 71, 69, 80, 158, 152, 161, 96, 122, 118, 87, 85.
what is the probability that maximum speed differs from the mean value by at most 1.5 standard deviations
Answers
The probability that the maximum speed of a randomly selected moped differs from the mean value by at most 1.5 standard deviations is 0.8664
We know that the maximum speed of a moped is normally distributed with mean μ = 46.8 km/h and standard deviation σ = 1.75 km/h. We want to find the probability that the maximum speed differs from the mean value by at most 1.5 standard deviations, i.e., we want to find P(|X - μ| ≤ 1.5σ), where X is the maximum speed of a moped.
Using the properties of the normal distribution, we can standardize X to get a standard normal distribution
Z = (X - μ) / σ
Substituting the values of μ and σ, we get
Z = (X - 46.8) / 1.75
We want to find P(|Z| ≤ 1.5), which is the probability that Z lies between -1.5 and 1.5.
Using a standard normal distribution table or a calculator with a normal distribution function, we can find that P(|Z| ≤ 1.5) = 0.8664.
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The given question is incomplete, the complete question is:
Mopeds (small motorcycles with an engine capacity below 50 cm3) are very popular in Europe because of their mobility, ease of operation, and low cost. Suppose the maximum speed of a moped is normally distributed with mean value 46.8 km/h and standard deviation 1.75 km/h. Consider randomly selecting a single such moped. What is the probability that maximum speed differs from the mean value by at most 1.5 standard deviations?
question a father is color blind, and a mother is homozygous dominant for normal vision. what is the probability that one of their offspring will be color blind? responses 0% 0% 100% 100% 50% 50% 25%
Answers
If a father has a color blindness condition and a mother has a homozygous dominant trait for normal vision, there is a 50% probability that one of their children will inherit color blindness.
The father is color blind, which means he has only one X chromosome, and that chromosome carries the gene for color blindness. The mother is homozygous dominant for normal vision, which means she has two copies of the normal vision gene.
The offspring will inherit one X chromosome from each parent. If a son inherits the X chromosome from the mother that carries the normal vision gene, he will have normal vision because he only needs one copy of the normal vision gene to express it.
However, if a son inherits the X chromosome from the father that carries the gene for color blindness, he will be color blind because he does not have another X chromosome to compensate for the faulty gene.
Since there is a 50% chance that a son will inherit the X chromosome from the father that carries the gene for color blindness and a 50% chance that he will inherit the X chromosome from the mother that carries the normal vision gene, the probability of their offspring being color blind is 50%.
Hence, the correct answer is 50%
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make a number line and mark the points that represent the following, x squared = 16
Answers
Answer:
-4 and 4
Step-by-step explanation:
To solve this, we can take the square root of both sides, which would give us x = -4 and 4.
On the number line, you can label these points.
A cylindrical can of vegetables has a label wrapped around the outside, touching end to end. The only parts of the can not covered by the label are the circular top and bottom of the can. If the area of the label is 66π square inches and the radius of the can is 3 inches, what is the height of the can?
Answers
Answer:
We can begin by finding the total surface area of the can. The area of the label is given as 66π square inches. Since the label is wrapped around the outside of the can, the area covered by it is the lateral surface area of the cylinder. The lateral surface area of a cylinder is given by 2πrh, where r is the radius and h is the height of the cylinder. We can write the equation for the lateral surface area as: 2πrh = 66π Simplifying this equation, we get: rh = 33 We also know that the radius of the can is given as 3 inches. Substituting this value in the above equation, we get: 3h = 33 Solving for h, we get: h = 11 inches Therefore, the height of the can is 11 inches.
Use your knowledge of dot plots to answer the questions below.
2. The height of all 23 students in Mrs. Dani's preschool class are shown in the dot plot below.
a. What is the median height of the preschoolers?
O
00
00
00000
00
00
+111
32 33 34 35 36 37 38 39 40
HEIGHT IN INCHES
b. What is the mode height of the preschoolers?
c. What is the range in student height?
d. About what percent of preschoolers in Mrs. Dani's class were taller than the median height?
e. How does the number of preschoolers who are 38 inches or faller compare to the number of
preschoolers who are 36 inches tall?
Answers
a.The median height of the preschoolers is 36 inches.
b.The mode height is 35 inches.
c.The range in student height is 40 - 32 = 8 inches.
d.Since the median height is 36 inches, about 50% of the preschoolers in Mrs. Dani's class were taller than the median height.
e. There are 4 dots above 38 and 7 dots between 35 and 38.
What is median?The median is the middle value of a dataset when it is arranged in order from least to greatest or greatest to least. If the dataset has an odd number of values, the median is the middle value. If the dataset has an even number of values, the median is the average of the two middle values.
What is range?Range is the difference between the largest and smallest values in a set of data. In statistics, range is a measure of dispersion that indicates the spread or variability of a set of observations.
In this questions,
a. The median height is the middle value of the data when arranged in order. Since there are 23 students in the class, the median will be the average of the 12th and 13th tallest students. Looking at the dot plot, we can see that the 12th and 13th tallest students both have a height of 36 inches. Therefore, the median height of the preschoolers is 36 inches.
b. The mode height is the most common height among the students. Looking at the dot plot, we can see that the mode height is 35 inches, as there are more dots above 35 than any other value.
c. The range is the difference between the highest and lowest values in the data set. Looking at the dot plot, we can see that the shortest student is 32 inches tall and the tallest student is 40 inches tall. Therefore, the range in student height is 40 - 32 = 8 inches.
d. Since the median height is 36 inches, about 50% of the preschoolers in Mrs. Dani's class were taller than the median height.
e. There are fewer preschoolers who are 38 inches or shorter than preschoolers who are 36 inches tall. From the dot plot, we can see that there are 4 dots above 38 and 7 dots between 35 and 38.
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The lengths and corresponding weights for 15 different-
sized bluegill fish were measured and recorded. A
regression analysis was completed and the computer
output is given.
Regression Analysis: In (Weight) versus in (Length)
Predictor
SE Coef
T
P
Constant
0.54
0.036
R-Sq=0.99
in (Length)
s=0.0443
Coef
-5.28
3.44
-9.777
95.113
R-Sq (adj)-0.995
0.000
0.000
What is the equation of the least-squares regression
line?
Weight = 3.44 - 5.28 In(Length)
Length = -5.28+3.44 In(Weight)
In(Weight) = 3.44 - 5.28 In(Length)
In(Weight) = -5.28+3.44 In(Length)
Answers
The least-squares regression line has the equation In(Weight) = -5.28 + 3.44 In (Length)
A statistical tool for establishing the relationship between two variables is the equation of the least-squares regression line. The length and weight of bluegill fish are the variables under investigation in this case.
The regression analysis produced the equation In(Weight) = -5.28 + 3.44 In (Length).
The weight's natural logarithm as a function of length is represented in this equation. The equation can be changed in order to calculate a bluegill fish's weight based on its length.
The equation Weight = [tex]0.0054 * e(3.44 In(Length))[/tex] is the end result. Based on their length, bluegill fish can be estimated to weigh a certain amount using this calculation.
The coefficient of determination demonstrates that 99% of the variability in weight can be explained by the variable in length and that the high R-squared value of 0.99 suggests that the equation is a good fit for the data. The management of fisheries can benefit from this knowledge, which can help determine the weight of bluegill fish depending on their length.
The relationship between the weight and length of bluegill fish can be seen in this equation. The equation can be adjusted to solve for Weight in order to provide an estimate of weight for a given length:
Weight = [tex]e^(In(Weight))[/tex] (where e: base of natural logarithm)
Weight = [tex]e^(-5.28+3.44 In(Length))[/tex]
Weight = [tex]e^(-5.28) * e^(3.44 In(Length))[/tex]
Weight = [tex]0.0054 * e^(3.44 In(Length))[/tex]
So, using this equation, one may determine a bluegill fish's weight if they knew its length.
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Complete the condition statements that must be met in order for three side lengths—a, b, and c—to create a triangle(fill in the blanks)
a__b+c and a __b−c
AND
Apply the Triangle Inequality Theorem to determine which three side lengths form a triangle.
A.10, 20, 15
B.8, 4, 12
C.8, 8,20
D.20, 10, 30
Answers
Part A: To create a triangle: a ≤ b+c and a ≥ b−c.
Part B: Three side lengths form a triangle: A.10, 20, 15 ; B.8, 4, 12 and D.20, 10, 30.
Explain about the Triangle Inequality Theorem?The triangle inequality, written as a + b c, states that any two triangle sides added together must be greater than or equal to the third side a + b ≥ c. The basic tenet of the theorem is that a straight line connects any two places.
Some metric spaces, especially spaces that have a way to measure distances, have analogues for the triangle inequality. Norms, also known as measurements, are commonly denoted by enclosing an entity as from space in two single or the double vertical lines, such as | | or || ||.Part A: a__b+c and a __b−c.
By using the triangle inequality,
The longest side is less than equal to the other sum of other two sides:
Thus,
a ≤ b+c and a ≥ b−c.
Part B: Three side lengths form a triangle.
A.10, 20, 15
10 + 15 ≥ 20 (longest side) (correct option.)
B.8, 4, 12
8 + 4 ≥ 12 (longest side) (correct option.)
C.8, 8,20
8 + 8 ≥ 20 (longest side) (incorrect option.)
But 16 < 20 (incorrect option.)
D.20, 10, 30
10 + 20 ≥ 30 (longest side) (correct option.)
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please please help me super quick
Answers
The statement AB corresponds to GH is not true.
What is trapezoid?
A trapezoid, also known as a trapezium, is a quadrilateral with at least one pair of parallel sides. The parallel sides are called the bases of the trapezoid, and the other two sides are called the legs or the lateral sides. A trapezoid can be either right or oblique. In a right trapezoid, one of the angles between the bases is a right angle, while in an oblique trapezoid, none of the angles between the bases is a right angle. The height of a trapezoid is the perpendicular distance between the bases.
Which given statement is not true?
The statement that is NOT true is AB corresponds to GH.
Since the trapezoids are congruent, their corresponding sides are equal in length. Therefore, AD corresponds to EH, BC corresponds to FG, and AB corresponds to EF. However, AB does not correspond to GH because they are not parallel sides in the trapezoids.
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Find the perimeter of a square with a diagonal of length of 12 cm. Please help !!!math help
Answers
Step-by-step explanation:
Let's use the Pythagorean Theorem to find the length of one side of the square.
The Pythagorean Theorem states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.
In this case, the diagonal of the square is the hypotenuse of a right triangle, and the two sides are the sides of the square. Let's call the length of one side of the square "s".
Using the Pythagorean Theorem, we get:
s^2 + s^2 = 12^2
2s^2 = 144
s^2 = 72
s = √72
s ≈ 8.49
Now that we know the length of one side of the square, we can find the perimeter by multiplying by 4 (since all four sides of a square have the same length):
Perimeter = 4s
Perimeter = 4(√72)
Perimeter ≈ 33.96 cm
Therefore, the perimeter of the square with a diagonal of length 12 cm is approximately 33.96 cm.
Due tonight please help!
The pool at the local YMCA needs to be emptied for maintenance work.
The table at the left shows how fast water is being pumped out of the pool at certain times.
Find the average rate of change from time t=1 to t=8. Include units on your final answer.
Answers
The average rate of change from time t=1 to t=8 will be -17.57 gallons/hour.
How to calculate the average rate of changeIt should be noted that to find the average rate of change of R(t) from t = 1 to t = 8, we need to calculate the total change in R(t) over that time interval and divide by the duration of the interval.
The total change in R(t) from t = 1 to t = 8 is R(8) - R(1), which is:
R(8) - R(1) = 175 - 298 = -123
The negative sign indicates that the rate of pumping is decreasing over this time interval.
The duration of the interval is 8 - 1 = 7 hours.
Therefore, the average rate of change from t = 1 to t = 8 is:
(-123 gallons/hour) / (7 hours) = -17.57 gallons/hour
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continuing with problem 1, calculate the probability that the average sample weight is greater than 185 lbs when 15 participants are randomly selected for the sample? enter your answer rounded to two decimal places. do not enter % in the answer box. for example, if your answer is 0.12345 or 12.345% then enter as 12.35 in the answer box.
Answers
Answer:more context?
Step-by-step explanation:
according to the world health organization (who) child growth standards, the head circumference for boys at birth has a normal probability distribution with a mean of 34.5cm and a standard deviation of 1.3cm. what is the head circumference of a newborn boy who marks the start of the 75th percentile? enter a number without units.
Answers
The head circumference of a newborn boy who marks the start of the 75th percentile is approximately 35.38 cm.
To find the head circumference of a newborn boy who marks the start of the 75th percentile, we need to first find the z-score corresponding to the 75th percentile using the standard normal distribution.
The z-score formula is
z = (x - μ) / σ
where x is the observed value, μ is the mean, and σ is the standard deviation.
To find the z-score that corresponds to the 75th percentile, we need to look up the z-score associated with a cumulative area of 0.75 under the standard normal distribution curve. This value can be found using a table or calculator and is approximately 0.674.
Now we can use the formula for the z-score to solve for the head circumference of a newborn boy at the 75th percentile
z = (x - μ) / σ
0.674 = (x - 34.5) / 1.3
0.674 × 1.3 = x - 34.5
0.8762 + 34.5 = x
x = 35.3762
x ≈ 35.38 cm
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Solve 8x + 6 < 18 - 2x
Answers
8x + 6 < 18 - 2x
Adding 2x to both sides:
8x + 2x + 6 < 18
Combining like terms:
10x + 6 < 18
Subtracting 6 from both sides:
10x < 12
Dividing both sides by 10:
x < 1.2
Therefore, the solution for x is x < 1.2.
Answer:
[tex]x=\frac{6}{5}[/tex]
Step-by-step explanation:
Solve for x:
[tex]8x+6 < 18-2x[/tex]
Add 2x to both sides
[tex]10x+6 < 18[/tex]
Subtract 6 on both sides
[tex]10x < 12[/tex]
Divide by 10
[tex]x=\frac{12}{10}[/tex]
Simplify fraction
[tex]x=\frac{6}{5}[/tex]
Ben finished 3/5 of an assignment in 2/3 of an hour. How much of the assignment will Ben have finished in 1 hour?
(use visual model to solve to get the answer)
Answers
In one hour, Ben would have completed 9/10 or 90% of his assignment.
How to obtain the amount of completed workLet us assume that the total assignment stands as x. Ben finished 3/5x in 2/3 of 60 minutes. 2/3 of 60 minutes is 40 minutes. So, 3/5x was finished in 40 minutes.
If 3.5x was finished in 40 minutes, in 60 minutes, Ben would have completed 90% of his assignment. This can be represented thus:
3/5x = 40 min
? = 60 min
3/5x × 60 min/40 min
36xmin/40 min
x = 9/10
In summary, we can conclude that Ben would have completed 90% of his assignment in one hour. The same result will be obtained with visual models like the Tape diagram.
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Money Magic
Describe your budgeting process and how you chose to split the money among the different categories. How did that process evolve as you became more experienced playing the game?
Answers
As I became more experienced playing the game, I began to adjust my budgeting process to account for my changing needs.
What is budgeting?Budgeting is a financial planning process that involves creating a plan to manage your income and expenses over a specific period of time.
My budgeting process involved taking the total amount of money I had to spend and splitting it up into different categories based on my needs.
I allocated a portion of the money for food, transportation, entertainment, and other expenses.
As I became more experienced playing the game, I began to adjust my budgeting process to account for my changing needs.
For example, I started to prioritize saving for a larger expense, such as a trip, over smaller items like eating out or entertainment.
I also re-evaluated my spending habits regularly to see if I could be saving money in any area or if I could be spending it more efficiently.
This process helped me to become more mindful and intentional with my spending and allowed me to make smart decisions with my money.
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a researcher believes a new diet should improve weight gain in laboratory mice. if ten control mice on the old diet gain an average of 4 ounces with a standard deviation of 0.3 ounces, while the average gain for ten mice on the new diet is 4.8 ounces with a standard deviation of 0.2 ounces, where is the p-value?
Answers
The p-value is [tex]p(t < \frac{4-4.8}{\sqrt{\frac{0.3^2}{10}+\frac{0.2^2}{10}}})[/tex] .
What is p-value?
The P value is the likelihood, for a particular statistical model, that the statistical summary would be either equal to or more extreme than the actual observed results if the null hypothesis were to hold.
Here Average of 10 mice on old diet = 4 ounces and Standard deviation = 0.3 ounces.
Average of 10 mice on new diet = 4.8 ounces and standard deviation = 0.2 ounces.
With unknown population standard deviations, the t-distribution must be used,
[tex]\sigma_{\overline x_1-\overline x_2} = \sqrt{\frac{s_1^2}{n_1}+\frac{s_2^2}{n_2}}[/tex]
=> [tex]\sigma_{\overline x_1-\overline x_2} = \sqrt{\frac{0.3^2}{10}+\frac{0.2^2}{10}}[/tex]
Now the p-value is ,
=> [tex]p(t < \frac{4-4.8}{\sqrt{\frac{0.3^2}{10}+\frac{0.2^2}{10}}})[/tex]
Hence the p-value is [tex]p(t < \frac{4-4.8}{\sqrt{\frac{0.3^2}{10}+\frac{0.2^2}{10}}})[/tex] .
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Help me me me helppppp
Answers
Step-by-step explanation:
A. To find the equation of a line parallel to line f (y = 2) and passing through point P(-2, -1), we need to understand that parallel lines have the same slope. Since line f is a horizontal line with a slope of 0, the line we are looking for will also have a slope of 0. The equation for a horizontal line with the same y-intercept as point P is simply y = -1.
B. To find the equation of a line parallel to line g (y = 2x - 1) and passing through point P(-2, -1), we need to consider that parallel lines have the same slope. The slope of line g is 2. Using the point-slope form (y - y1 = m(x - x1)), where m is the slope and (x1, y1) is the given point P(-2, -1):
y - (-1) = 2(x - (-2))
y + 1 = 2(x + 2)
Now, we can convert this to slope-intercept form (y = mx + b):
y = 2x + 4 - 1
y = 2x + 3
C. To find the equation of a line perpendicular to line f (y = 2) and passing through point Q(3, -2), we need to know that perpendicular lines have slopes that are negative reciprocals of each other. Since line f is a horizontal line with a slope of 0, the line perpendicular to it will be a vertical line. The equation for a vertical line passing through point Q with the same x-coordinate is simply x = 3.
D. To find the equation of a line perpendicular to line g (y = 2x - 1) and passing through point Q(3, -2), we need to find the negative reciprocal of the slope of line g. The slope of line g is 2, so the negative reciprocal is -1/2. Using the point-slope form (y - y1 = m(x - x1)), where m is the new slope and (x1, y1) is the given point Q(3, -2):y - (-2) = -1/2(x - 3)
y + 2 = -1/2(x - 3)
Now, we can convert this to slope-intercept form (y = mx + b):
y = -1/2x + 3/2 - 2
y = -1/2x - 1/2
Freshman and sophomores were surveyed during lunch about their favorite professional football team.
A bar graph with the first bar labeled Jaguars, divided into freshmen from 0 to 40 percent and sophomores from 40 to 100 percent. The second bar is labeled Dolphins, with freshman from 0 to 45 percent and sophomores from 45 to 100 percent, and the third bar is labeled Buccaneers, with freshmen from 0 to 45 percent and sophomores from 45 to 100 percent.
If 140 students selected Jaguars, how many of those students are freshman?
56 students
63 students
77 students
84 students
Answers
Answer:
56 students
Step-by-step explanation:
If 40% of students who picked Jaguars are freshmen, and the total who picked it is 140 means [tex]140\times0.4 = 56[/tex]
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(Subject Algebra)
Answers
The best ordered pair for the solution of the equations is x and y = 7.5 and 1.17 respectively
What is simultaneous equation?Recall that Simultaneous Equations are sets of algebraic equations that share common variables and are solved at the same time (that is, simultaneously
The given equations are
y = -1/3x + 4 and
y = 1/3x -1
This implies that
y+ x/3 = 4 ................1
y -x/3 = -1 ................11
Eliminating y we have
2x/3 = 5
This implies that 2x = 15 Making x the subject of the relation we have
x = 7.5
Put x = 7.5 in equation 1 to have
y= x/3 = 4 ................1
y +7.5/3 = 4
Collecting like terms to have
y = 4-2.83
y = 1.17
Therefore the best options are x and y = 7.50 and 1.17
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Opal makes $12 per hour working for a photographer. She also coaches a competitive soccer team for $7 per hour. Opal needs to earn at least $150 per week, but she does not want to work more than 20 hours per week. A. Create a systems of inequalities to represent this situation. B. Give 2 possible solutions to describe how opal might meet her goals. C. Is (10,6) a solution? Explain.
Answers
Answer: A. Let's use x to represent the number of hours Opal works for the photographer, and y to represent the number of hours she coaches soccer. Then we can create the following system of inequalities to represent the situation:
12x + 7y ≥ 150 (Opal needs to earn at least $150 per week)
x + y ≤ 20 (Opal cannot work more than 20 hours per week)
B. There are different ways Opal can meet her goals, but here are two possible solutions:
Solution 1: Opal works for the photographer for 10 hours and coaches soccer for 10 hours. Then her total earnings for the week would be:
12(10) + 7(10) = 120 + 70 = $190
This meets her goal of earning at least $150 per week, and it also satisfies the constraint that she cannot work more than 20 hours per week.
Solution 2: Opal works for the photographer for 15 hours and coaches soccer for 5 hours. Then her total earnings for the week would be:
12(15) + 7(5) = 180 + 35 = $215
This also meets her goal of earning at least $150 per week, and it satisfies the constraint that she cannot work more than 20 hours per week.
C. To check if (10,6) is a solution to the system of inequalities, we need to substitute x = 10 and y = 6 into both inequalities and see if they are true:
12(10) + 7(6) ≥ 150
120 + 42 ≥ 150
162 ≥ 150 (true)
10 + 6 ≤ 20 (true)
Since both inequalities are true, (10,6) is a solution to the system. However, this solution does not meet Opal's goal of earning at least $150 per week, as her total earnings would be:
12(10) + 7(6) = 120 + 42 = $162
So, while (10,6) satisfies the constraints of the system, it is not a valid solution to the problem.
Step-by-step explanation:
From the observation deck of a seaside building 200m high, Jagan sees two
fishing boats. The angle of depression to the nearest boat is 60° while for
the boat farther away the angle is 45°
(a) How far out to the sea is the nearest boat?
(b) How far apart are the two boats?
Answers
Answer:
(a) 115.47 meters
(b) 261.5 meters
Step-by-step explanation:
Let's label the points as follows: the top of the seaside building is point A, the location of the nearest boat is point B, and the location of the farther boat is point C. We know that AB = 200 m (the height of the building) and that angle BAD = 60° and angle CAD = 45°. We want to find the distance BC (part a) and the distance AC (part b).
(a) To find BC, we can use trigonometry. Let x be the distance from point B to the foot of the perpendicular dropped from point A to the sea (point D). Then, we have:
tan 60° = AB/BD
tan 60° = 200/x
x = 200/tan 60°
x = 200/√3
x ≈ 115.47
So the distance from the building to the nearest boat (BC) is approximately 115.47 meters.
(b) To find AC, we can use the fact that triangle ABC is a right triangle, with angle ABC = 180° - 60° - 45° = 75°. Then we have:
sin 75° = BC/AC
AC = BC/sin 75°
AC ≈ 261.5
So the distance between the two boats is approximately 261.5 meters.
Answer:
Step-by-step explanation:
Let's denote the distance from the observation deck to the nearest boat as x, and the distance from the observation deck to the farther boat as y. We can use trigonometry to solve for x and y.
(a) To find x, we can use the tangent function:
tan(60°) = x/200
Solving for x, we get:
x = 200 tan(60°)
x ≈ 346.4 meters
Therefore, the nearest boat is about 346.4 meters away from the observation deck.
(b) To find y, we can use the tangent function again:
tan(45°) = y/200
Solving for y, we get:
y = 200 tan(45°)
y ≈ 200 meters
Therefore, the farther boat is about 200 meters away from the observation deck.
To find the distance between the two boats, we can simply subtract x from y:
y - x ≈ 200 - 346.4 ≈ -146.4 meters
This result is negative, which means that the two boats are actually closer than the observation deck. This could be due to a few reasons, such as the boats being located behind a cliff or a harbor wall. Alternatively, there could be an error in the measurements or calculations.
What is the formula for the circumference of a circle? c = pi r squared c = 2 pi r c = 2 pi r squared c = pi r cubed
Answers
The formula for the circumference of a circle is "c = 2 pi r", where "c" represents the circumference, "pi" represents the mathematical constant pi (approximately equal to 3.14159), and "r" represents the radius of the circle.
This formula relates the distance around a circle to its size, and is useful for calculating various measurements related to circles, such as arc length and sector area. It is important to note that the formula for the circumference of a circle assumes the circle is a perfect, unbroken curve, and thus may not be accurate for circles that are not perfectly round.
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Find a fraction that is equivalent to 5/7 and the product of its numerator and denominator is 140. Pls help
Answers
Answer:
10 / 14
Step-by-step explanation:
10 × 14 = 140
When 10 / 14 is simplified, you'll get 5 / 7 because 2 will go into 10 five( 5 ) times and 2 will go into 14 seven ( 7 ) times.
The graph of p(x) is shown below. What is the remainder when p(x) is divided by x + 4?
And explain why.
Choices:
1) x-4
2) -4
3) 0
4) 4
Answers
The remainder when the function p(x) is divided by x + 4 as required in the task content is; -0.5.
The remainder from graphs?It follows from the task content that the remainder when a function p(x) is divided by (x + 4).
However, it is important to note that the value of the function at x = -4 represents the remainder of the function when the function p(x) is divided by (x + 4).
Therefore, by checking the value of p (-4) as required, the remainder when the function p(x) is divided by x + 4 as required in the task content is; -0.5.
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200 ft long 125 ft long how many feet of fancing he will need to surround the entire lot
Answers
The required fencing feet. for the right triangle lot, is given as 560.84.
How do we calculate the required fencing feet?Perimeter is the measure of the figure on its circumference. Here, the two sides of the lot is known, we have to evaluate the third side before calculating the perimeter.
Measure of the third side = √[200² + 125²]
The measure of the third side = 235.84
Now, the total fencing required = Perimeter of the triangle
= 200 + 125 + 235.84
= 560.84 ft
Thus, the required fencing for the right triangle lot is 560.84.
Full question "David must install fencing around a lot that is shaped like a right triangle. The side of the lot that runs east-west is 200 ft long. The side of the lot that runs north-south is 125 ft long."
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