The probability that a) the sample has a proportion between 0.5 and 0.7 is 0.780. b) The probability that the sample has a proportion within 5% is 0.819. c) The probability that the sample has a proportion less than 0.50 is 0.001. d) The probability that the sample has a proportion greater than 0.80 is 0.000.
a) To calculate this probability, we first need to standardize the interval (0.5, 0.7) using the formula: z = (p - P) / (σ / √(n))
where p is the sample b, P is the population proportion, σ is the standard deviation of sample proportions, and n is the sample size. Substituting the values, we get:
z1 = (0.5 - 0.62) / (0.8 / √(40)) = -2.24
z2 = (0.7 - 0.62) / (0.8 / √(40)) = 1.12
Using the standard normal table or calculator, the area between -2.24 and 1.12 is 0.780. Therefore, the probability that the sample has a proportion between 0.5 and 0.7 is 0.780.
b) The probability that the sample has a proportion within 5% of the population proportion is 0.819. We can find the range of sample proportions within 5% of the population proportion by adding and subtracting 5% of the population proportion from it, which gives: P ± 0.05P = 0.62 ± 0.031
The interval (0.589, 0.651) represents the range of sample proportions within 5% of the population proportion. To calculate the probability that the sample proportion falls within this interval, we standardize it using the formula above and find the area under the standard normal curve between -1.55 and 1.55, which is 0.819.
c) The probability that the sample has a proportion less than 0.50 is 0.001. To calculate this probability, we standardize the value of 0.50 using the formula above and find the area to the left of the resulting z-score, which is: z = (0.50 - 0.62) / (0.8 / √(40)) = -4.46
Using the standard normal table or calculator, the area to the left of -4.46 is 0.001. Therefore, the probability that the sample has a proportion less than 0.50 is 0.001.
d) The probability that the sample has a proportion greater than 0.80 is 0.000. To calculate this probability, we standardize the value of 0.80 using the formula above and find the area to the right of the resulting z-score, which is: z = (0.80 - 0.62) / (0.8 / √(40)) = 5.60
Using the standard normal table or calculator, the area to the right of 5.60 is very close to 0.000. Therefore, the probability that the sample has a proportion greater than 0.80 is 0.000.
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Ariana has 144 peaches. She has to pack 9 boxes with an equal number of peaches. How many peaches should she pack in each box.
Answer:
16 peaches
Step-by-step explanation:
Let's break this down:
Total: 144 peaches
Number of boxes she has to fill evenly: 9
Question: How many peaches are able to fit into each box evenly?
144 peaches/9 boxes = 16 peaches
So, Ariana should pack 16 peaches into each box
Hope this helps :)
QUESTION IN PHOTO I MARK BRAINLIEST
The value of x in the intersecting chord is determined as 18.6.
What is the value of x?The value of x is calculated by applying intersecting chord theorem, which states that the angle at center is equal to the arc angle of the two intersecting chords.
m ∠EDF = arc angle EF
50 = 5x - 43
The value of x is calculated as follows;
5x = 50 + 43
5x = 93
divide both sides by 5;
5x/5 = 93/5
x = 18.6
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Consider the quadratic function: f(x)=x^2-6x+8
Identify the coordinates of the x(intercepts if any
Answer:
x-intercepts (4,0) (2,0)
y-intercepts (0,8)
Step-by-step explanation:
have a good day :)
Evaluate each geometric series described. . 34) a, =-2, a = 256, r=-2 n 33) a=-1, a = 512, r=-2 : A) 397 B) 341 -- B) 149 1 2 A) 3 C) 170 C) - D) 463 D) 156 3 n 71 35) a, = 4, a = 16384, r=4 , , A) 22
(34) the sum of the series is 170. (33) The sum of the series is 341. (35) the sum of the series is 21844
To evaluate a geometric series, we use the formula:
Sn = a(1 - r^n) / (1 - r)
where:
Sn = the sum of the first n terms of the series
a = the first term of the series
r = the common ratio between consecutive terms
n = the number of terms we want to sum
Let's use this formula to evaluate the given geometric series:
34) a1 = -2, a8 = 256, r = -2
To find the sum of this series, we need to know the value of n. We can find it using the formula:
an = a1 * r^(n-1)
a8 = -2 * (-2)^(8-1) = -2 * (-2)^7 = -2 * (-128) = 256
Now we can solve for n:
an = a1 * r^(n-1)
256 = -2 * (-2)^(n-1)
-128 = (-2)^(n-1)
2^7 = 2^(1-n+1)
7 = n-1
n = 8
So this series has 8 terms. Now we can use the formula to find the sum:
Sn = a(1 - r^n) / (1 - r)
S8 = (-2)(1 - (-2)^8) / (1 - (-2))
S8 = (-2)(1 - 256) / 3
S8 = 510 / 3
S8 = 170
Therefore, the sum of the series is 170.
33) a1 = -1, a9 = 512, r = -2
We can use the same method as before to find n:
an = a1 * r^(n-1)
512 = -1 * (-2)^(9-1) = -1 * (-2)^8
512 = 256
This is a contradiction, so there must be an error in the problem statement. Perhaps a9 is meant to be a5, in which case we can find n as:
an = a1 * r^(n-1)
a5 = -1 * (-2)^(5-1) = -1 * (-2)^4
a5 = 16
512 = -1 * (-2)^(n-1)
-512 = (-2)^(n-1)
2^9 = 2^(1-n+1)
9 = n-1
n = 10
So this series has 10 terms. Now we can use the formula to find the sum:
Sn = a(1 - r^n) / (1 - r)
S10 = (-1)(1 - (-2)^10) / (1 - (-2))
S10 = (-1)(1 - 1024) / 3
S10 = 1023 / 3
S10 = 341
Therefore, the sum of the series is 341.
35) a1 = 4, a14 = 16384, r = 4
Again, we can find n using the formula:
an = a1 * r^(n-1)
16384 = 4 * 4^(14-1) = 4 * 4^13 = 4 * 8192 = 32768
This is a contradiction, so there must be an error in the problem statement. Perhaps a14 is meant to be a7, in which case we can find n as:
an = a1 * r^(n-1)
a7 = 4 * 4^(7-1) = 4 * 4^6 = 4 * 4096 = 16384
16384 = 4 * 4^(n-1)
4096 = 4^(n-1)
2^12 = 2^(2n-2)
12 = 2n-2
n = 7
So this series has 7 terms. Now we can use the formula to find the sum:
Sn = a(1 - r^n) / (1 - r)
S7 = (4)(1 - 4^7) / (1 - 4)
S7 = (4)(1 - 16384) / (-3)
S7 = 65532 / 3
S7 = 21844
Therefore, the sum of the series is 21844.
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Lucinda has already earned $30 walking dogs. She earns $3 per dog walked, and she needs at least $80 to buy more leashes. Write and solve an inequality to determine how many more dogs Lucinda will need to walk to have at least $80.
I would say she has to walk 17 dogs, im not sure if that's correct though
Let's assume that Lucinda needs to walk "x" more dogs to have at least $80. Then, the amount of money she will earn from walking those "x" dogs can be calculated by multiplying the number of dogs by the amount of money earned per dog, which is $3:
Amount of money earned from walking "x" dogs = $3x
To determine how many more dogs Lucinda needs to walk to have at least $80, we can write the following inequality:
$30 + $3x ≥ $80
Simplifying the inequality, we get:
$3x ≥ $50
Dividing both sides by 3, we get:
x ≥ 16.67
Since we can't walk a fraction of a dog, we need to round up to the nearest whole number. Therefore, Lucinda needs to walk at least 17 more dogs to have at least $80.
Write a division expression for each fraction 1/2
Answer: 1 ÷ 2
Step-by-step explanation: I think this is what you mean?
what are the outcomes
A 6 sided number cube is rolled 5 times
Answer:
7776 outcomes
Step-by-step explanation:
To get the total number of outcomes we multiply the total number of possibilities for each roll. Since there are 5 rolls, the total number of outcomes will be:
6 x 6 x 6 x 6 x 6 = 7776 outcomes
Help pls! Find the area of the circle
Use π = 3.14 and round your answer to the nearest hundredth.
the area of the circle is 615. 4 m²
How to determine the area
The formula that is used to calculate the area of a circle is expressed with the equation.
We have the equation as;
A = πr²
Such that the parameters are given as;
A is the area of the circleπ takes the constant value of 22/7 or 3.14r is the radius of the circleFrom the diagram shown, we have that;
A = unknown
r = 14m
Now, substitute the values, we get;
Area = 3.14 ×14²
Find the square value
Area = 3.14(196)
Multiply the values
Area = 615. 4 m²
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Huang buys 3 shirts that each cost the same amount a pair of pants that cost 12$ and pays with a 100$ bill which expressesion represents the amount of change huang receive
Answer: 64$
Step-by-step explanation:
John has a pepper shaker in the shape of a cylinder. It has a radius of 9 mm and a height of 32 mm. John wants to cover the pepper shaker with tape, How much tape is needed? Round to the hundredths
John needs approximately 1,814.4 mm² of tape to cover the pepper shaker. Rounded to the hundredths, the answer is 1,814.40 mm².
To calculate the amount of tape needed to cover the pepper shaker, we need to find the lateral area of the cylinder. This is given by the formula L = 2πrh, where r is the radius and h is the height.
Substituting the values given, we get L = 2π(9 mm)(32 mm) = 1,814.4 mm².
Therefore, John needs approximately 1,814.40 mm² of tape to cover the pepper shaker.
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Jayden need wood to enclose his garden he measures one side of his garden and finds it is 6 feetlong how many feet of wood does jayden need to enclose his garden
To enclose his garden, Jayden needs 24 feet of wood assuming his rectangular-shaped garden has sides of 6 feet each.
How much wood does Jayden need?Jayden needs wood to enclose his garden. He measured one side of his garden and found that it is 6 feet long.
To calculate how many feet of wood Jayden needs to enclose his garden, we need to know the length of all sides of the garden.
Assuming that the garden is rectangular in shape, we need to know the length of the other side as well.
Let's say the other side is also 6 feet long. In this case, we can calculate the total length of wood required by using the formula for the perimeter of a rectangle, which is:
Perimeter = 2 x (Length + Width)
Here, the length and width of the garden are both 6 feet.
So, we can substitute these values in the formula and get:
Perimeter = 2 x (6 + 6) = 2 x 12 = 24 feet
Therefore, Jayden needs 24 feet of wood to enclose his garden.
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An angle measures 11.4° more than the measure of its complementary angle. What is the measure of each angle?
The measure of the angle is 50.7° and the measure of its complementary angle is 39.3°.
What is the measure of each angle?Let x be the measure of the angle and y be the measure of its complementary angle.
Then we have:
x = y + 11.4 (since the angle measures 11.4° more than its complementary angle)
x + y = 90 (since the two angles are complementary)
Substituting the first equation into the second equation, we get:
(y + 11.4) + y = 90
2y + 11.4 = 90
2y = 78.6
y = 39.3
Substituting y = 39.3 into the first equation, we get:
x = y + 11.4 = 50.7
So, we have
x = 50.7
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Consider the series Σ(1) с (where c is a constant). For which values of c will the series converge, and for which it diverge? Justify your answer, and show all your work. (Hint: Use the root test)
To determine whether the series Σ(1) с converges or diverges, we can use the root test. The root test states that if the limit of the absolute value of the nth root of the terms of the series approaches a value less than 1, then the series converges. If the limit approaches a value greater than 1, the series diverges. If the limit equals 1, the test is inconclusive and another test should be used.
Using the root test, we have:
lim┬(n→∞)〖|1^(1/n) c| = lim┬(n→∞)|c| = |c|〗
If |c| < 1, then the limit approaches a value less than 1 and the series converges. If |c| > 1, then the limit approaches a value greater than 1 and the series diverges. If |c| = 1, then the test is inconclusive.
Therefore, the series Σ(1) с converges if |c| < 1, and diverges if |c| > 1. If |c| = 1, then another test should be used to determine convergence or divergence.
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Find the probability that a point chosen randomly inside the rectangle is in each given shape. Round to the nearest tenth.
1. The probability that the point chosen is in the triangle is 0.1 (nearest tenth)
2. The probability that the point is in the square is 0.2( nearest tenth)
What is probability?A probability is a number that reflects the chance or likelihood that a particular event will occur. The certainty for an event is 1 which is equivalent to 100%.
Probability = sample space / total outcome
total outcome is the area of rectangle , which is
A = l× w
= 12 × 8
= 96
area of the rectangle = 1/2 bh
= 1/2 × 4 × 5
= 2 × 5
= 10
Area of the square = 4×4
= 16
1. Probability the the point will be in the triangle= 10/96 = 5/48
= 0.1( nearest tenth)
2. probability the the point will be in the square =
16/96 = 1/6
= 0.2 ( nearest tenth)
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2. Iwo functions t and g are definea on the set R of real numbers by f: x x² - 2x - 4. g: x → X - 1 Find the value fx for which f(x) = (x) = m - 4.
Answer:
We are given that:
- f(x) = x² - 2x - 4
- g(x) = x - 1We want to find fx for which f(x) = g(x) - 4, or in other words:
- f(x) = x - 1 - 4
- f(x) = x - 5
We can solve forTo find the value of x for which f(x) = g(x) - 4 (which is what I assume you meant by "f(x) = (x) = m - 4"), we can set up the following equation:
f(x) = g(x) - 4
Substituting the given expressions for f(x) and g(x), we get:
x² - 2x - 4 = x - 1 - 4
Simplifying, we have:
x² - 3x - 3 = 0
We can solve for x using the quadratic formula:
x = (-(-3) ± sqrt((-3)² - 4(1)(-3))) / (2(1))
x = (3 ± sqrt(21)) / 2
Therefore, the two values of x for which f(x) = g(x) - 4 are:
- x = (3 + sqrt(21)) / 2
- x = (3 - sqrt(21)) / 2
2
How much water will a cone hold that has a diameter of 6 inches and a height of 21 inches.
Use 3. 14 for 7 and round your answer to the nearest whole number.
A 66 cubic inches
B 198 cubic inches
C) 594 cubic inches
D 2374 cubic inches
The volume of water a cone with a diameter of 6 inches and a height of 21 inches can hold is 198 cubic inches. So, the correct answer is B) 198 cubic inches.
To find the volume of water a cone with a diameter of 6 inches and a height of 21 inches can hold, we will use the formula for the volume of a cone: V = (1/3)πr²h.
Given a diameter of 6 inches, the radius (r) is 3 inches. The height (h) is 21 inches, and we will use 3.14 as an approximation for π.
V = (1/3) * 3.14 * (3²) * 21
V = (1/3) * 3.14 * 9 * 21
V = 3.14 * 3 * 21
V = 197.82 cubic inches
Rounding to the nearest whole number, the volume of water the cone can hold is approximately 198 cubic inches. Therefore, the answer is B) 198 cubic inches.
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If the volume of the cube is (4)(4)(4) =
64 cm3, what is the volume of the oblique
prism if it has been tilted at 60°?
The volume of the oblique prism is approximately 55.424 cm³.
The volume of the cube is given as 64 cm³, which means that each side of the cube has a length of 4 cm.
To find the volume of the oblique prism, we need to know the area of the base and the height. The base of the oblique prism is a parallelogram, and we can find its area using the formula:
area = base × height
where the base is the length of one side of the parallelogram, and the height is the perpendicular distance between the base and the opposite side.
Since the parallelogram is tilted at an angle of 60°, we need to find the perpendicular height by using trigonometry. The height of the parallelogram is given by:
height = (side length) × sin(60°)
height = 4 × sin(60°)
height = 4 × 0.866 = 3.464
Therefore, the area of the base is:
area = (side length) × height
area = 4 × 3.464 = 13.856 cm²
To find the volume of the oblique prism, we multiply the area of the base by the height of the prism. Since the height of the prism is also 4 cm (the same as the side length of the cube), we have:
volume = area of base × height
volume = 13.856 × 4 = 55.424 cm³
Therefore, the volume of the oblique prism is approximately 55.424 cm³.
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A rhombus has a perimeter of 88 and
two acute angles that measure 40° each.
Find the length of the shorter diagonal.
PLEASE HELP ME ASAP
The length of the shorter diagonal is approximately 7.07 units.
A rhombus is a four-sided polygon in which all sides are equal in length. It is also called a diamond shape because it is often used for diamond-shaped figures. In this case, we are given that the perimeter of the rhombus is 88. Since all sides of the rhombus are equal, we can divide the perimeter by 4 to find the length of one side.
88 ÷ 4 = 22
Therefore, each side of the rhombus measures 22 units.
We are also given that two of the angles in the rhombus are acute angles measuring 40° each. Since all angles in a rhombus are equal, we can find the measure of the other two angles by subtracting the sum of the acute angles from 360.
360 - 2(40) = 280
Each of the other two angles measures 140°.
To find the length of the shorter diagonal, we can use the formula:
Shorter diagonal = (2 × Area) / Length of longer diagonal
The area of a rhombus can be found by multiplying the length of the longer diagonal by the length of the shorter diagonal and then dividing by 2.
Area = (diagonal1 × diagonal2) / 2
We know that the longer diagonal is twice the length of the shorter diagonal.
Longer diagonal = 2 × Shorter diagonal
Substituting these values into the formula, we get:
Shorter diagonal = (2 × (22 × Shorter diagonal × sin 40°)) / (2 × Longer diagonal)
Simplifying, we get:
Shorter diagonal = (22 × Shorter diagonal × sin 40°) / Longer diagonal
Plugging in the values we know, we get:
Shorter diagonal = (22 × Shorter diagonal × sin 40°) / (2 × Shorter diagonal)
Shorter diagonal = 11 × sin 40°
Using a calculator, we can find that:
Shorter diagonal ≈ 7.07
Therefore, the length of the shorter diagonal is approximately 7.07 units.
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In a school of 580 students, one class was asked which hand they write with.
• “L” means they use their left hand.
• “R” means they use their right hand.
Here are the results:
L, R, R, R, R, R, R, R, R, L, R, R, R, R, R
1) Based on this sample, estimate the proportion of students at the school who write with their left hand.
2) Estimate the number of students at the school who write with their left hand.
3) A different class of `18` students is surveyed. Estimate how many write with their left hand.
1. The proportion of students at the school who write with their left hand is 2/15 OR 13.3%
2. The estimated number of students who write with their left hand is 77 students
3. The estimated number of students in the different class of 18 students who write with their left hand is 2
Estimating the number of students that write with their left handFrom the question, we are to estimate the proportion of students who write with their left hand
To estimate the proportion of students at the school who write with their left hand, we need to count the number of students in the sample who write with their left hand and divide by the total number of students in the sample.
From the given sample, there are 2 students who write with their left hand and 13 students who write with their right hand. So the estimated proportion of students who write with their left hand is:
2/15 = 0.133
OR
13.3%
2.
To estimate the number of students at the school who write with their left hand, we can multiply the proportion by the total number of students in the school
That is,
2/15 x 580 = 77.33
Thus, about 77 students write with their left hand
3.
To estimate how many students in a different class of 18 students write with their left hand, we can apply the proportion to the new sample:
2/15x 18 = 2.4
Hence, about 2 students in the different class write with their left hand.
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The cost of manufacturing a certain type of headphone varies inversely as the number of headphones increases. If 8000 headphones can be manufactured for $8. 00 each, find the cost to manufacture 2000 headphones
The cost to manufacture 2000 headphones as the number of headphones varies inversely with the cost of manufacture is $32
Let x = number of headphones
y = cost of manufacturing headphones
The cost of manufacturing a certain type of headphones is inversely proportional to the number of headphones.
The equation for inversely proportional is
x₁ y₁ = x₂ y₂
x₁ = 8000 , y₁ = 8 , x₂ = 2000 y₂ = ?
Putting the value in the equation we get ,
8000 × 8 = 2000 × y₂
64000/2000 = y₂
y₂ = 32
Cost of manufacturing 2000 headphones is 32 .
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traveling 60 mhp in the car after 3 hours how long would that be
Answer:
Step-by-step explanation:
60 x 3 = 180
180 miles
Un Jardinero usa un total de 61. 5 galones de gasolina en un mes. De la cantidad total
3/5
de gasolina, se usaron en sus cortadoras de césped. ¿Cuántos galones de gasolina usa
el jardinero en sus cortadoras de césped en ese mes? Me ayudan plis
The gardener used 36.9 gallons of gasoline in the lawnmowers in that month.
What are proportions?In mathematics, a proportion is a statement that two ratios are equal. It expresses the relationship between two or more quantities that are directly proportional to each other. A proportion can be represented as an equation of the form:
a/b = c/d
We know that the gardener used a total of 61.5 gallons of gasoline in a month and that 3/5 of that total was used in the lawnmowers.
To find out how much gasoline the gardener used in the lawnmowers, we need to multiply the total amount of gasoline by 3/5:
61.5 gallons x 3/5 = 36.9 gallons
Therefore, the gardener used 36.9 gallons of gasoline in the lawnmowers in that month.
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Decide whether the triangles are similar. If so, determine the appropriate expression to solve for x.
Triangles ABC and EDF; triangle ABC has angle A measuring 53 degrees, angle C measuring 62 degrees, side AC labeled as y, side AB labeled as w, and side BC labeled as x; triangle EDF has angle D measuring 61 degrees, angle F measuring 53 degrees, side DE labeled z, side EF labeled u, and side DF labeled r.
The triangles are not similar; no expression for x can be found.
ΔABC ~ ΔDEF; x equals r times w over u
ΔABC ~ ΔEFD; x equals r times w over u
ΔABC ~ ΔEFD; x equals r times w over z
The triangles ABC and EDF are similar, and x = r × w/u.
As per the question, we have angle A in triangle ABC congruent to angle F in triangle EDF, angle C in triangle ABC congruent to angle D in triangle EDF, and angle B in triangle ABC congruent to angle E in triangle EDF.
Therefore, the triangles are similar by the Angle-Angle (AA) similarity theorem.
To find the expression for x, we can use the fact that the corresponding sides of similar triangles are proportional.
In this case, we have:
x/w = u/r (corresponding sides of similar triangles)
Solving for x, we get:
x = r × w/u
Therefore, x = r × w/u, and it can use this expression to solve for x in triangle ABC and EDF.
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Describe and correct the error in finding the circumference of ⊙C
Step-by-step explanation:
C= 2πr
Given,
Diameter= 9
so, radius = 9÷2 = 4.5
C= 2 x π x 4.5
= 28.3 (3.s.f)
In the united states, the number of children under age 18 per family is skewed right with a mean of 1.9 children and a standard deviation of 1.1 children.
analyst 1 wants to calculate the probability that a randomly selected family from the united states has at least 2 children.
analyst 2 wants to calculate the probability that if 40 families from the united states are randomly selected, the mean number of children per family is at least 2 children.
what sample size does analyst 1 plan to use?
enter an integer. what sample size does analyst 2 plan to use?
enter an integer.
The probability of a randomly selected family from the United States having at least 2 children is 0.2734. The probability that if 40 families from the United States are randomly selected, the mean number of children per family is at least 2 children is 0.1884. Analyst 1 plans to use a sample size of 1 and analyst 2 plans to use a sample size of 40.
Analyst 1 wants to calculate the probability that a randomly selected family from the United States has at least 2 children. Since the number of children under age 18 per family is skewed right with a mean of 1.9 children and a standard deviation of 1.1 children, we can use the normal distribution to solve this problem.
To calculate the probability of a randomly selected family having at least 2 children, we need to find the area under the normal curve to the right of 2.
Using a standard normal distribution table or calculator, we can find that the area to the right of 2 is approximately 0.2734. Therefore, the probability of a randomly selected family from the United States having at least 2 children is 0.2734.
Analyst 2 wants to calculate the probability that if 40 families from the United States are randomly selected, the mean number of children per family is at least 2 children. Since we know that the mean number of children per family in the population is 1.9 children and the standard deviation is 1.1 children, we can use the central limit theorem to approximate the sampling distribution of the sample means.
The central limit theorem tells us that the sampling distribution of the sample means will be approximately normal with a mean of 1.9 children and a standard error of the mean equal to the population standard deviation divided by the square root of the sample size.
We want to find the probability that the mean number of children per family is at least 2, so we need to standardize the sample mean using the formula:
z = (sample mean - population mean) / (standard error of the mean)
Plugging in the values, we get:
z = (2 - 1.9) / (1.1 / sqrt(40)) = 0.889
Using a standard normal distribution table or calculator, we can find that the area to the right of 0.889 is approximately 0.1884. Therefore, the probability that if 40 families from the United States are randomly selected, the mean number of children per family is at least 2 children is 0.1884.
So, analyst 1 plans to use a sample size of 1 and analyst 2 plans to use a sample size of 40.
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In rhombus YZAB, if YZ=12, find AB.
The length of side AB is also 12 units.
What is a rhombus?
A rhombus is a four-sided quadrilateral with all sides of equal length. It is also known as a diamond or a lozenge. In a rhombus, opposite sides are parallel, and opposite angles are equal. Additionally, the diagonals of a rhombus bisect each other at right angles, meaning they intersect at a 90-degree angle and divide each other into two equal segments.
Since a rhombus has all sides of equal length, we know that YZ = AB. Therefore, if YZ = 12, we have:
AB = YZ = 12
So the length of side AB is also 12 units.
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PLEASE HELP THIS IS MY LAST QUESTION PLEASEEEEEE
Given PQR with angle P = 42°, angle R = 26°, and PQ = 19, solve the triangle. Round all answers to the nearest tenth.
Angle Q =__
QR =__
PR =__
To solve the triangle, we have;
Angle Q = [tex]112^{o}[/tex]
QR = 30.0
PR = 40.2
What is a sine rule?A sine rule is a trigonometric function that can be applied to determined the unknown side, or angle of a none right triangle.
From the information given in the question, to solve the triangle;
P + R + Q = 180
42 + 26 + Q = 180
Q = 180 - 68
= 112
Q = [tex]112^{o}[/tex]
Applying the sine rule,
QR/Sin P = PR/Sin Q = PQ/Sin R
PR/Sin Q = PQ/Sin R
PR/Sin 112 = 19/ Sin 26
PRSin 26 = 19*Sin 112
= 17.6165
PR = 17.6165/ 0.4384
= 40.1836
PR = 40.2
Also,
QR/Sin P = PQ/Sin R
QR/Sin 42 = 19/ Sin 26
QRSin 26 = 19*Sin 42
= 12.7135
QR = 12.7135/ 0.4384
= 28.9998
QR = 30
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f(x, y) = ex sin y do first and second order partial derivatives. f(x, y) = e^x sin y. do first and second order partial derivatives
The first order partial derivatives of f(x, y) = ex cos y and the second order partial derivatives are ex sin y = ex cos y.
The given function is f(x, y) = ex sin y. We need to find the first and second order partial derivatives of this function with respect to x and y.
First order partial derivatives:
To find the partial derivative of f(x, y) with respect to x, we treat y as a constant and differentiate ex with respect to x. This gives:
∂f/∂x = ex sin y
To find the partial derivative of f(x, y) with respect to y, we treat x as a constant and differentiate sin y with respect to y. This gives:
∂f/∂y = ex cos y
Second order partial derivatives:
To find the second order partial derivatives, we differentiate the first order partial derivatives we found above. That is, we differentiate ∂f/∂x and ∂f/∂y with respect to x and y, respectively.
∂/∂x (ex sin y) = ex sin y
∂/∂y (ex cos y) = -ex sin y
To find the mixed partial derivatives, we differentiate one of the first order partial derivatives with respect to the other variable. That is,
∂/∂y (ex sin y) = ex cos y
We can also find the mixed partial derivative by differentiating ∂f/∂y with respect to x, which gives the same result:
∂/∂x (ex cos y) = ex cos y
The first order partial derivatives of f(x, y) = ex sin y are ∂f/∂x = ex sin y and ∂f/∂y = ex cos y and the second order partial derivatives are ex sin y, ∂f/∂[tex]y^2[/tex] = -ex sin y, and ∂f/∂x∂y = ∂f/∂y∂x = ex cos y.
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If the circumference of a circle is 50. 4 ft, what is its area? (Use π = 3. 14) *
2 points
50. 24 sq ft
113. 04 sq ft
202. 24 sq ft
314 sq ft
The area of the circle is approximately 202.03 square feet
If the circumference of a circle is 50.4 ft, we can use the formula for the circumference of a circle to find its radius:
C = 2πr
C = circumference
r = radius
r = C / (2π)
Substituting C = 50.4 ft, we get:
r = 50.4 / (2π)
Using a calculator, we can approximate this value to be:
r =25.2/π ft
A circle's area can be calculated using the following formula:
A = πr²
Substituting r = 25.2/π ft, we get:
A = π(25.2/π)²
= 635.04/3.14
= 202.03
Therefore, the area of the circle is approximately 202.03 square feet.
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At a real estate agency, an agent sold a house for $315000. the commission rate is %6.5 for the real estate agency and the commission rate for the agent is %20 of the amount the real estate agency gets. how much did the agency make on the house? how much did the agent earn in commission?
part 2
the agent earned $ in commission.
If the commission rate is %6.5 for the real estate agency, the real estate agency made $20,475 on the house. The agent earned $4,095 in commission.
First, let's determine the commission earned by the real estate agency. To do this, we'll multiply the house price ($315,000) by the commission rate (6.5%).
$315,000 * 6.5% = $20,475
The real estate agency made $20,475 on the house.
Next, let's determine the commission earned by the agent. We'll multiply the commission earned by the real estate agency ($20,475) by the agent's commission rate (20%).
$20,475 * 20% = $4,095
The agent earned $4,095 in commission.
So, the real estate agency made $20,475 on the house, and the agent earned $4,095 in commission.
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