It appears that Nolan has met the conditions for constructing a confidence interval for the mean birth weight in Somalia. However, he should also check the skewness and presence of outliers in the sample to ensure that the normal approximation is appropriate.
What is skewed data?In other words, data with a lower bound are frequently skewed right, and data with an upper bound are typically biased left.
Start-up effects can also cause skewness.
To construct a confidence interval for the mean birth weight in Somalia, we need to ensure that the following conditions are met:
Random Sampling: Nolan used a simple random sample of 100 births, which meets the condition of random sampling.
Independence: Each birth weight in the sample should be independent of the other. This condition is met if the sample size is less than 10% of the total population of births in Somalia.
Sample size: In general, a sample size of at least 30 is recommended to use the normal distribution to approximate the sampling distribution of the sample mean. Since Nolan's sample size is 100, this condition is met.
Skewness and outliers: Nolan mentioned that the sample data was slightly skewed with a few outliers.
Therefore, all the required conditions are given above.
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Answer:
the data is a random sample from the population of interest.
the sampling distribution of x is approximately normal.
individual observations can be considered independent.
Step-by-step explanation:
Follow the guided instructions below to rotate the figure 90° clockwise about the point (2, 3).
Answer:
Follow the guided instructions below to rotate the figure 90° clockwise about the point (2, 3).
Step-by-step explanation:
Follow the guided instructions below to rotate the figure 90° clockwise about the point (2, 3).
Answer:15 because it is connected to the line
Step-by-step explanation:
Real World Example 1 - Write and Solve an Inequality
a. Of the students surveyed at Madison High School, fewer than eighty-four said they have
never purchased an item online. This is about one-eighth of all those surveyed. How
many students were surveyed?
X < 84
8x < 84 (8)
The answer is 8x < 672
According to the information, the mathematical expression with which the problem is solved is 8x < 672.
How to find the expression that solves this problem?To find the expression that solves this problem we must take into account that it is an inequality. So we must use the symbols greater than > or less than <. Additionally, we must read the information in the statement to identify how it goes to the inequality.
According to the above, there are less than 84 students who answered that they had never bought online (x). Then the expression would start like this:
x < 84Subsequently, they do not say that x equals one eighth of the total number of students. Then the expression would be modified like this:
8x < 84 (8)Finally, if we simplify this expression, it would look like this:
8x < 672So, that would be the expression of this inequality.
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Use synthetic division an(d)/(o)r factoring to write f(x)=20x^(3)+44x^(2)-17x-5 in completely factored form, given that (-(5)/(2)) is a zero of f(x).
The function f(x) in completely factored form is (4x+1)(5x-1)(x+5).
To write f(x)=20x^(3)+44x^(2)-17x-5 in completely factored form, we can use synthetic division with the given zero of (-(5)/(2)).
Step 1: Set up the synthetic division with the given zero and the coefficients of the polynomial.
(-(5)/(2)) | 20 44 -17 -5
|______________
Step 2: Bring down the first coefficient, 20, and multiply it by the given zero.
(-(5)/(2)) | 20 44 -17 -5
| -50
|______________
| 20
Step 3: Add the result of the multiplication to the next coefficient and repeat the process until all coefficients have been used.
(-(5)/(2)) | 20 44 -17 -5
| -50 3 10
|______________
| 20 -6 -14 5
Step 4: The last number in the bottom row is the remainder. If it is zero, then the given zero is a factor of the polynomial. In this case, the remainder is 5, so (-(5)/(2)) is not a factor of f(x).
Since (-(5)/(2)) is not a factor of f(x), we cannot use synthetic division to write f(x) in completely factored form. Instead, we can use factoring to find the factors of f(x).
f(x) = 20x^(3)+44x^(2)-17x-5
= (4x+1)(5x-1)(x+5)
Therefore, f(x) in completely factored form is (4x+1)(5x-1)(x+5).
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Help needed! Immediately would be very great :)
Answer: 56 inches
Step-by-step explanation:
To find the length of each side, use Pythagorean's Theorem, a² + b² = c²
Note the bottom sides are the same length and the top two are the same length.
Bottom sides:
5² + 12² = c²
25 + 144 = c²
169 = c²
13 = c
Top sides:
9² + 12² = c²
81 + 144 = c²
225 = c²
15 = c
Add it all together
13 + 13 + 15 + 15 = 56
The perimeter is 56 inches.
Hope this helps!
Write the first five terms of a sequence. Don't make your sequence too simple. Write both an explicit formula and a recursive formula for a general term in the sequence.
For the arithmetic sequence:
f(n) = f(1) + (n - 1)*4
Where the first term of the sequence is f(1) = 2
are:
f(1) = 2
f(2) = 6
f(3) = 10
f(4) = 14
f(5) = 18
How to write the first five terms of a sequence?We want to write the first five terms of a sequence, so first let's define the sequence.
We can define an arithmetic sequence with the recursive formula:
f(n) = f(n) + 4
And the explicit formula.
f(n) = f(1) + (n - 1)*4
Where we can define the first term of the sequence as f(1) = 2
Then the first five terms are:
f(1) = 2
f(2) = 2 + 4 = 6
f(3) = 6 + 4 = 10
f(4) = 10 + 4 = 14
f(5) = 14 + 4 = 18
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one of the angles of a parallelogram is 36\deg greater than another one. find the angles of the parallelogram.
The value of the angles of the parallelogram are 72 degree and 108 degree.
What are the characteristics of a parallelogram?A quadrilateral with the opposing sides parallel is known as a parallelogram. It has numerous crucial traits, including:
A parallelogram has equal-length opposite sides. A parallelogram has opposite angles that are equally sized. A parallelogram's diagonals cut each other in half. A parallelogram is divided into four equal-sized triangles by its diagonals. A parallelogram's internal angles add up to 360 degrees. A parallelogram is classified as a rectangle if it also contains four right angles, making it a rectangle-shaped parallelogram.
Let us suppose the smaller angle = x.
The other angle is thus x + 36.
In a parallelogram the opposite angles are equal thus:
x + x + x + 36 + x + 36 = 360
4x + 72 = 360
4x = 288
x = 72
The value of x + 36 = 72 + 36 = 108
Hence, the value of the angles of the parallelogram are 72 degree and 108 degree.
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factor x^3 + 1/8
thank you
[tex]\textit{difference and sum of cubes} \\\\ a^3+b^3 = (a+b)(a^2-ab+b^2) ~\hfill a^3-b^3 = (a-b)(a^2+ab+b^2) \\\\[-0.35em] ~\dotfill\\\\ x^3+\cfrac{1}{8}\implies x^3+\cfrac{1^3}{2^3}\implies x^3+\left( \cfrac{1}{2} \right)^3~\hfill \stackrel{\textit{let's just for a second make}}{\cfrac{1}{2}=a} \\\\\\ x^3+a^3\implies (x+a)(x^2-ax+a^2)\implies \left( x+\frac{1}{2} \right)\left( x^2-\frac{x}{2}+\frac{1}{4} \right)[/tex]
Im really confused .
Answer:
Triangle A is not a scale drawing
Triangle B is a scale drawing
Triangle C is not a scale drawing
Which answer choice correctly represents the quotient of 28,134 divided by 71?
A.
B.
C.
D.
Answer:
please give brainliest
Step-by-step explanation:
396.253521127
Prove that any two consecutive terms in the Fibonacci sequence
are relatively prime. (The Fibonacci sequence is given by f1 = 1,
f2 = 1, fn = fn−2 + fn−1.)
They are relatively prime.
Proof: Let fn and fn-1 be any two consecutive terms in the Fibonacci sequence. By definition, fn = fn-2 + fn-1. Since both fn and fn-1 are integers,
they must have no common factors other than 1,
so they are relatively prime.
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27. For which values of k, if any, are u and v orthogonal? (a) u = (k. 1,3), v = (1,7,K) (b) u = (-2,k,k), v = (k. 5, k) 28. Use vectors to find the cosines of the interior angles of the triangle with vertices A(0,-1), B(1,-2), and C(4,1), 29. Use vectors to show that A(3, 0, 2), B(4,3,0), and C(8, 1.-1) are vertices of a right triangle. At which vertex is the right angle? 30. In each part determine whether the given number is a valid ISBN by computing its check digit. (a) 1-56592-170-7 (b) 0-471-05333-5 31. In each part determine whether the given number is a valid ISBN by computing its check digit. (a) 0-471-06368-1 (b) 0-13-947752-3
For two vectors to be orthogonal, their dot product should be zero.
(a) The dot product of u and v is k+21k=22k. For u and v to be orthogonal, 22k=0, which means k=0.
(b) The dot product of u and v is -2k^2+5k^2+k^2=4k^2. For u and v to be orthogonal, 4k^2=0, which means k=0.
Therefore, in both cases, the vectors are orthogonal when k=0.
Let AB and AC be vectors joining the points A(0,-1), B(1,-2), and C(4,1), respectively. Then,
AB = (1-0, -2-(-1)) = (1,-1)
AC = (4-0, 1-(-1)) = (4,2)
The cosine of the angle between two vectors u and v is given by the dot product of u and v divided by the product of their magnitudes, i.e., cos(theta) = (u.v)/(|u||v|).
(a) Cosine of angle A = cos(BAC) = (AB.AC)/(|AB||AC|) = (1(4) + (-1)(2))/sqrt(2^2+1^2 * 4^2+2^2) = 2/3
Cosine of angle B = cos(CAB) = (AC.AB)/(|AC||AB|) = (4(1) + 2(-1))/sqrt(4^2+2^2 * 2^2+1^2) = 1/3
Cosine of angle C = cos(ABC) = (AB.BC)/(|AB||BC|) = ((1)(3) + (-1)(-1))/sqrt(2^2+1^2 * 2^2+1^2) = 5/9
(b) Let AB and BC be vectors joining the points A(3,0,2), B(4,3,0), and C(8,1,-1), respectively. Then,
AB = (4-3, 3-0, 0-2) = (1, 3, -2)
BC = (8-4, 1-3, -1-0) = (4, -2, -1)
AC = (8-3, 1-0, -1-2) = (5, 1, -3)
The cosine of the angle between two vectors u and v is given by the dot product of u and v divided by the product of their magnitudes, i.e., cos(theta) = (u.v)/(|u||v|).
Cosine of angle A = cos(BAC) = (AB.AC)/(|AB||AC|) = (1(5) + 3(1) + (-2)(-3))/sqrt(1^2+3^2+(-2)^2 * 5^2+1^2+(-3)^2) = 0
Cosine of angle B = cos(CAB) = (AC.AB)/(|AC||AB|) = (5(1) + 1(3) + (-3)(-2))/sqrt(5^2+1^2+(-3)^2 * 1^2+3^2+(-2)^2) = -7/9
Cosine of angle C = cos(ABC) = (AB.BC)/(|AB||BC|) = ((1)(4) + (
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I NEED HELPP ASAP!!!!!!!!!!!!!!!!!
The measure of center that would best summarize the plot is given as follows: Median of 11.
The measure of variability is given as follows: IQR of 1.5.
What does a box-and-whisker plot shows?A box and whisker plots shows these five features from a data-set, listed as follows:
The minimum non-outlier value.The 25th percentile, which is the median of the bottom 50%.The median, which splits the entire data-set into two halfs, the bottom 50% and the upper 50%.The 75th percentile, which is the median of the upper 50%.The maximum non-outlier value.From the plot, these features are given as follows:
Minimum non-outliter value of 6.Q1 of 10.Median of 11.Q2 of 11.5.Maximum non-outlier value of 16.The median is the best measure of center of the data-set.
There is an outlier at 16, hence the best measure of variability is the IQR, given by the difference between the Q3 and the Q1, hence:
IQR = 11.5 - 10
IQR = 1.5.
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Find the missing degrees in the circle
The missing degrees in the circle are 260 degrees.
What is circle ?
A circle is a geometrical shape that represents a set of points in a plane that are equidistant from a fixed point called the center. The distance from the center to any point on the circle is called the radius, and the diameter of the circle is the distance across its widest point, passing through the center.
To find the missing degrees in the circle, we need to use the fact that the sum of the central angles in a circle is equal to 360 degrees.
In this circle, we have two central angles: one measuring 100 degrees and the other measuring x degrees. We also know that the sum of these two central angles is equal to 360 degrees.
Therefore, we can set up the following equation:
100 + x = 360
To solve for x, we can subtract 100 from both sides:
x = 260
Therefore, the missing degrees in the circle are 260 degrees.
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There are 1,000 grams in 1 kilogram. Lucas has a bucket with 2 kilograms of sand. Mac has a bucket with 4 kilograms of sand. How many grams of sand do they have in all?
In total, they have 6000 grams of sand.
What are basic arithmetic operations?
The basic arithmetic operations are the four fundamental mathematical operations used to manipulate numerical values. They are addition, subtraction, multiplication, and division.
To solve the problem, we need to know the conversion factor between kilograms and grams, which is 1 kilogram = 1000 grams.
First, we can find out how many grams of sand Lucas has in his bucket. We are given that he has 2 kilograms of sand, so we can use the conversion factor to convert kilograms to grams:
2 kilograms x 1000 grams/kilogram = 2000 grams
Therefore, Lucas has 2000 grams of sand in his bucket.
Next, we can find out how many grams of sand Mac has in his bucket. We are given that he has 4 kilograms of sand, so we can use the conversion factor again:
4 kilograms x 1000 grams/kilogram = 4000 grams
Therefore, Mac has 4000 grams of sand in his bucket.
To find out the total amount of sand they have in grams, we can add the amount of sand each of them has:
2000 grams + 4000 grams = 6000 grams
Therefore, in total, they have 6000 grams of sand.
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On a piece of paper, graph this system of inequalities. Then determine which
region contains the solution to the system.
y≤x-2
y²-x-4
OA. Region A
B. Region B
OC. Region C
OD. Region D
A
D
10
8
6
4
2
-10-8-04-2 01
2
-8
-8
-10
N
4
'В'
B
C
B
10
The region that contains the solution to the system is region B
How to determine the region with the solutionGiven the following system of inequalities
y ≤ x - 2
y ≥ 1/4x - 4
Next, we analyze each of the inequalities expressions
Inequality 1: y ≤ x - 2
This is a less than or equal to inequalitySo, the bottom part is shadedInequality 2: y ≥ 1/4x - 4
This is a greater than or equal to inequalitySo, the upper part is shadedUsing the above as a guide, we have the following:
This means that the intersection regionn contains the solution
This is represented by the region (b)
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Marcus found these three ordered pairs for the equation y = 52x + 150: (0, 150), (10,670), and (20,1190).
When he graphs these, what is the best range for the y-axis?
0 to 150
0 to 670
0 to 20
0 to 1190
Which ordered pair is NOT a solution of y > 3x + 4? Responses (2, 12) (2, 12) (0, 5) (0, 5) (–2, 1) (–2, 1) (1, 7)
The ordered pair that is NOT a solution of y > 3x + 4 is (-2, 1). Hence, the answer is (E) (-2, 1).
What is inequality?A relationship between two expressions or values that are not equal to each other is called 'inequality. ' So, a lack of balance results in inequality.
The given inequality is y > 3x + 4. To check which ordered pair is not a solution of this inequality, we need to substitute the values of x and y from each ordered pair into the inequality and check whether the inequality holds or not.
Checking the ordered pairs one by one, we have:
(2, 12): y = 12 and x = 2, so 12 > 3(2) + 4 is true. Therefore, (2, 12) is a solution of the inequality.
(0, 5): y = 5 and x = 0, so 5 > 3(0) + 4 is true. Therefore, (0, 5) is a solution of the inequality.
(-2, 1): y = 1 and x = -2, so 1 > 3(-2) + 4 is false. Therefore, (-2, 1) is not a solution of the inequality.
(1, 7): y = 7 and x = 1, so 7 > 3(1) + 4 is true. Therefore, (1, 7) is a solution of the inequality.
Therefore, the ordered pair that is NOT a solution of y > 3x + 4 is (-2, 1). Hence, the answer is (E) (-2, 1).
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Fatoumata kicks a football. Its height in feet is given by ℎ ( � ) = − 16 � 2 + 96 � h(t)=−16t 2 +96t where � t represents the time in seconds after kick. What is the appropriate domain for this situation?
For the given equation of the height the appropriate domain for this situation is 0 ≤ t ≤ 6.
What role does the domain play?The collection of all feasible input values that are appropriate for the circumstance being represented is known as the domain. In this instance, the domain stands for the range of time values relevant to the height of the football following a kick. The domain helps to avoid absurd or impossible outcomes by ensuring that the function is only evaluated for legitimate inputs.
The ball with follow a parabolic path, thus the maximum height is attained at:
t = -b/2a
Substituting the values we have:
t = -96/(-32) = 3 seconds.
The ball will then follow the downward path and will take an additional 3 seconds to reach the ground.
Thus, the total time taken will be 3 + 3 = 6 seconds.
Also, the ball initially starts from rest at 0 seconds.
Hence, the domain of the situation will be represented as 0 ≤ t ≤ 6.
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i need helpp pp pp p
Answer:
I CAN NOT SEE THAT OML
Step-by-step explanation:
Aliza needs to run at a rate faster than 8.2 feet per second in order to exceed her fastest time in a race. After running for 15 minutes, her coach determines that she is running at an average rate of 5.8 miles per hour. He converts the average rate to feet per second as shown below:
Answer:
8.50667 or approximately 8.51 feet per second
Step-by-step explanation:
The most approximate way to get the feet per second is to multiply the miles per hour by 1.467.
DUE TODAY HELP!!!!!!!!!!!!
The image shows a circle with radius 5 units. Use the arc length and the radius to calculate the radian measure of 180 degrees.
The radian measure of 180 degrees is [tex]\pi \\[/tex] radians.
How to find the relation between angle subtended by the arc, the radius and the arc length?[tex]2\pi^c = 360^\circ = \text{Full circumference}[/tex]
The superscript 'c' shows angle measured is in radians.
If radius of the circle is of r units, then:
[tex]1^c \: \rm covers \: \dfrac{circumference}{2\pi} = \dfrac{2\pi r}{2\pi} = r\\\\or\\\\\theta^c \: covers \:\:\: r \times \theta \: \rm \text{units of arc}[/tex]
We are given that;
Radius=5units
Radian=180 degrees
Now,
The arc length of a circle is given by the formula:
arc length = (r * theta)
where r is the radius of the circle and theta is the angle in radians subtended by the arc at the center of the circle.
We know that the radius of the circle is 5 units, and we want to find the radian measure of an arc that subtends an angle of 180 degrees.
Since 180 degrees is half of a full circle, the arc length of this arc will be half of the circumference of the circle:
arc length = (1/2) * 2 * pi * r
= pi * r
Plugging in r = 5, we get:
arc length = pi * 5 = 5pi
Now we can use the formula for arc length to find the radian measure of the arc:
arc length = r * theta
5pi = 5 * theta
theta = pi
Therefore, by the arc length the answer will be [tex]\pi[/tex] radians.
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Answer this easy geometry question. And no links, please.
Answer:
Yes, they are equal.
Step-by-step explanation:
Because these are both right triangles, we know that one angle is similar. And seeing that side MO is the hypotenuse of both triangles, by the SA theorem we know that the two are equal. Or because we know that this is a reactangle or square by the four equal angles, we know that because this triangle is split in half, the triangle have to be equal.
-Hope this
A factory manufactures a metal peice in 32 minutes new technology allowed the factory to cut that time by 8% then another improvement cut the time by 5% how long does it take to manufacture the peice now round your answer to nearest minute
The time is takes to manufacture the piece after two improvements is 28 minutes
Calculating how long it takes to manufacture a pieceFrom the question, we are to calculate how long it takes to manufacture a metal piece
First, we need to find the new time taken to manufacture the metal piece after the two improvements.
The first improvement reduces the time by 8%. This means that the new time is:
32 - (8% of 32)
= 32 - 2.56
= 29.44 minutes
The second improvement reduces the time by 5%. This means that the new time is:
29.44 - (5% of 29)
= 29.44 - 1.45
= 27.99 minutes
We can round this to the nearest minute, which gives us 28 minutes.
Hence, it takes 28 minutes to manufacture the metal piece.
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Find the area of the right triangle in simplest radical form that has a hypotenuse of 8 ft and a leg of 4 ft. (No decimals)
In its simplest radical form, the area of the right triangle is 8sqrt(3) square feet.
How is area determined?
The length of the other leg of the right triangle can be determined using the Pythagorean theorem:
[tex]a^2 + b^2 = c^2[/tex]
where the hypotenuse is c and the triangle's legs are a and b.
We are aware that the hypotenuse c is 8 feet long and that leg an is 4 feet long. Let's work out the answer for the opposite leg's length, b:
[tex]b^2 = c^2 - a^2\sb^2 = 8^2 - 4^2\sb^2 = 64 - 16\sb[/tex]
[tex]sqrt(48) = 4sqrt(3) foot where 2 = 48 b[/tex]
Given that we know the lengths of both legs, we can use the following formula to get the triangle's area:
[tex](1/2) * Base * Height = Area[/tex]
We may use the 4 ft leg as the base and the 4sqrt(3) ft leg as the height since one leg is 4 ft and the other is 4sqrt(3) ft:
Area: (1/2) * 4 feet * 4 square feet (3)
= 8sqrt(3) square feet
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rio drew two similar rectangles. one rectangle was 9 inches long and 6 inches wide. the second rectangle was 15 inches wide. how long was the second rectangle?
As a result, the length of the second rectangle is 22.5 inches.
Are rectangles always squares?Every square is also a rectangle because a square is a parallelogram with all particular corners at right angles. Yet not all rectangles are squares; for a rectangle to be a square, all of its sides must be the same length.
We can infer that the two rectangles may have a similar shape but differ in size because we can see how similar they are to one another.
By using the fact that the ratio of the adjacent angles of two comparable rectangles is the same, we can determine the length of the following rectangle.
Let x be the second rectangle's length. Then we can establish a ratio:
9/6 = x/15
We can cross-multiply to find x:
9 x 15 = 6 × x
135 = 6x
x = 22.5
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Solving a rational equation that simplifies to linear: Denominat Solve for v. 6=(5)/(v-8)
The value of v is 8.83.
What is rational equation?A rational equation is an equation that includes one or more fractions with polynomials. It can be solved by cancelling common factors between the numerator and the denominator, and then solving the resulting equation. It is important to note that when cancelling common factors, one must always check that the original equation is still satisfied.
To solve this rational equation that simplifies to linear, you need to solve for v. To do this, first multiply both sides by the denominator:
6(v-8) = 5
Then add 8 to both sides to get rid of the variable in the denominator:
6v - 48 = 5
Finally, add 48 to both sides to isolate the variable v:
6v = 53
Finally, divide both sides by 6 to solve for v:
v = 53/6 = 8.83
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After solving an equation the answer is x=3. What can you say about the solution?
The solution to the equation is x=3, which means that when x is equal to 3, the equation is true.
The solution of an equation is the value of the variable that satisfies the equation.
In this case, the solution is x=3, which means that when x is substituted with 3, the equation is true.
We can say that the solution is unique, as there is only one value of x that satisfies the equation. It is also a real solution, as the value of x is a real number.
Additionally, we can say that the solution is finite, as there is a specific value for x that satisfies the equation.
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find the surface area of each figure. round answers to the nearest hundredth, if necessary
The surface area of the prism is 224 ft².
What is a prism?Having identical endpoints in three dimensions, a prism is a solid object. This combination consists of flat faces, identical bases, and equal cross-sections.
We are given a figure of a prism having a square base.
We know that
Surface Area of Prism (A) = 2a² + 4ah
We are given the following information:
a = 4 ft
h = 12 ft
On substituting these values in the formula, we get
⇒A = 2(4)² + 4(4)(12)
⇒A = 2(16) + (16)(12)
⇒A = 32 + 192
⇒A = 224 ft²
Hence, the surface area of the prism is 224 ft².
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Since there are multiple questions so the question answered above is attached below
PLEASE SOLVE FOR ME NEED ANSWER ASAP PLEASE
Using the leg rule and the Pythagorean theorem, we have:
x = 4
y ≈ 4.5
How to Apply the Leg Rule?The leg rule that can be use to solve the missing measures of the right triangle is given as:
hypotenuse/leg = leg/part
We have the following:
Hypotenuse = 9
Leg = 6
Part = x
Plug in the values:
9/6 = 6/x
9x = 36
x = 36/9
x = 4
Use the Pythagorean theorem to find y:
y = √(6² - 4²)
y ≈ 4.5
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25-9x² can be expressed in factor form as (5+3x)(5-3x)
What is Expression?An expression is combination of variables, numbers and operators.
The given expression is 25-9x²
We have to factor it completely
We have an identity that a²-b²=(a+b)(a-b)
25-9x² can be written as 5²-(3x)²
Now apply the identity
(5+3x)(5-3x)
Hence, 25-9x² can be expressed in factor form as (5+3x)(5-3x)
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