To solve this problem, we can use the z statistic to find for the probability. The formula for z score is:
z = (x – u) / s
Where,
u = the sample mean = 68
s = standard deviation of the samples = 12
x = sample value = 70
In this case, what is asked is the probability that the sample mean is larger than 70, therefore this corresponds to the right of z on the graph of normal distribution.
z = (70 – 68) / 12
z = 2 / 12
z = 0.17
Therefore finding for P at z ≥ 0.17 using the standard distribution tables:
P (z = 0.17) = 0.5675
But this is not the answer yet since this is the P to the left of z. Therefore the correct one is:
P (z ≥ 0.17) = 1 - 0.5675
P (z ≥ 0.17) = 0.4325 = 43.25%
The probability that the sample mean is larger than 70 is 43.25%
The probability that the sample mean is larger than 70 for a sample size of 40 from a population with a mean of 68 and standard deviation of 12 is approximately 14.69%.
To determine this probability, we can use the Central Limit Theorem (CLT), which states that the distribution of sample means will be approximately normal if the sample size is large enough (n ≥ 30 is a common benchmark).
The standard error of the mean is calculated using the formula:
SE = σ / √n
Where σ is the population standard deviation and n is the sample size.
In this case:
σ = 12
n = 40
Therefore,
SE = 12 / √40 ≈ 1.8974
The z-score is calculated using the formula:
z = (M - μ) / SE
Where M is the sample mean,
μ is the population mean,
SE is the standard error.
Given,
μ = 68
M = 70
Therefore,
z = (70 - 68) / 1.8974 ≈ 1.054
Using the z-table, we find the probability that a z-score is less than 1.054 is approximately 0.8531.
However, we need the probability that the sample mean is greater than 70, so we subtract this from 1,
1 - 0.8531 ≈ 0.1469
Thus, the probability that the sample mean is larger than 70 is approximately 0.1469, or 14.69%.
When determining the number of significant figures in a number, zeroes to the left of the decimal point are never counted.
a. True
b. False?
On a final exam, each multiple-choice question is worth 4 points and each word problem is worth 8 points. Lorenzo needs at least 50 points on the final to earn a "B" in the class. Which inequality represents x, the number of correct multiple-choice questions, and y, the number of correct word problems, he needs to earn a "B"? 4x + 8y < 50 4x + 8y ≤ 50 4x + 8y > 50 4x + 8y ≥ 50
Hence, the inequality that will represent the marks he needs is:
4x+8y≥50
Step-by-step explanation:On a final exam, each multiple-choice question is worth 4 points and each word problem is worth 8 points.
Lorenzo needs at least 50 points on the final to earn a "B" in the class.
Let x be the number of correct multiple-choice questions, and y, the number of correct word problems.
Hence, the inequality that will represent the marks he needs is:
4x+8y≥50
wahts the quotient of 92 and 5
By selling a stool for rupees 67.50,a carpenter loses 10%.how much percent would he gain or lose by selling it for rupees 82.50.?
A rectangular box has dimensions of length = 6, width = 4, and height = 5. the measure of the angle formed by a diagonal of the box with the base of the box is
To find the angle formed by a diagonal of a rectangular box with its base, calculate the base diagonal using the Pythagorean Theorem and then use the inverse tangent function with the height and base diagonal as arguments.
Explanation:The angle formed by a diagonal of the rectangular box with the base of the box can be found using the Pythagorean Theorem. In this case, the box has a length of 6, a width of 4, and a height of 5. The diagonal of the base can be calculated as the hypotenuse of a right triangle formed by the length and the width. According to the Pythagorean theorem, this diagonal (D) is √(6² + 4²) which is √(36 + 16) or √52. To find the angle between the box's base diagonal and the body diagonal (which includes the height), we need to use trigonometry, specifically the inverse tangent function (tan-1). So we have the length of the box's base diagonal (D) and the height (H), forming a right triangle with the body diagonal as the hypotenuse. The angle θ can be calculated using tan-1(H/D), where H is the height of the box and D is the length of the diagonal on the base. This equates to tan-1(5/√52). Evaluating this expression with a calculator gives us the angle θ formed by the body diagonal with the base of the box.
Which transformations can be used to map a triangle with vertices A(2, 2), B(4, 1), C(4, 5) to A’(–2, –2), B’(–1, –4), C’(–5, –4)? a 180 (dagree) rotation about the origin a 90 (dagree) counterclockwise rotation about the origin and a translation down 4 units a 90 (dagree) clockwise rotation about the origin and a reflection over the y-axis a reflection over the y-axis and then a 90(dagree) clockwise rotation about the origin
The triangle ABC is mapped to A'B'C' through a 180-degree rotation about the origin, as all the points' x and y coordinates have changed signs, consistent with this transformation.
To determine which transformations can map the original triangle ABC to the new triangle A'B'C', we must closely examine the coordinates given and analyze the possible transformations.
Looking at the coordinates:
A(2, 2) to A'(-2, -2) suggests a reflection over the origin, which can be considered as a 180-degree rotation around the origin.
B(4, 1) to B'(-1, -4) also suggests a similar transformation, as the x and y values are negated and swapped in position.
C(4, 5) to C'(-5, -4) follows the same pattern.
All these transformations indicate that the original triangle has been rotated 180 degrees about the origin. This can also be observed by noting that the x and y coordinates have simply changed their signs, an effect of 180-degree rotation about the origin. This satisfies the claim of the classical geometry theorem which states that such transformations can be expressed as either a translation or a rotation. In this case, it's purely a rotation as there's no translation component.
the least common multiple of 2/3 5/6 and 9/4
The least common multiple of 2/3 5/6 and 9/4 is 12.
What is a fraction?A fraction represents a part of a number or any number of equal parts.
A fraction consisting of a quotient and remainder is a mixed fraction. we can convert the mixed fraction to improper fraction by first dividing the numerator by denominator and then taking the quotient as whole number and remainder as the numerator of proper fraction keeping the denominator same.
We are given that;
The numbers 2/3 5/6 and 9/4
Now,
To find the least common multiple of fractions, we need to find the least common multiple of their denominators and divide it by the greatest common factor of their numerators. The steps are:
Multiples of 3: 3, 6, 9, 12, 15, 18,
Multiples of 6: 6, 12, 18,
Multiples of 4: 4, 8, 12,
Find the greatest common factor of 2, 5 and 9. This is the largest number that can divide all three numbers without leaving a remainder. One way to do this is to list the factors of each number and find the largest one that they have in common. For example:
Factors of 2: 1 and 2
Factors of 5: 1 and 5
Factors of 9: 1,3 and9
The only common factor is 1, so this is the greatest common factor of the numerators.
Divide the least common multiple of the denominators by the greatest common factor of the numerators. This gives us:
12 /1 =12
Therefore, the LCM of given fraction will be 12.
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How long does it take a plane, traveling at a speed of 110 m/s, to fly once around a circle whose radius is 2850 m?
Answer:
It takes to the plane [tex]162.792[/tex] seconds to fly once around a circle whose radius is 2850 m at a speed of [tex](110)\frac{m}{s}[/tex]
Step-by-step explanation:
The first step in this exercise is to find the total distance that the plane will fly.
This distance is equal to the perimeter of a circle whose radius is 2850 m.
Given a circle of radius R, the perimeter ''P'' can be calculated as :
[tex]P=\pi .d=\pi .2.R[/tex]
Where ''d'' is the diameter of the circle that is equal to 2.R
The distance that the plane will fly in the exercise is :
[tex]P=\pi .2.R=\pi .2.(2850m)=17907.078m[/tex]
Now, the speed is equal to distance divided by time.
[tex]speed=\frac{distance}{time}[/tex]
We have the speed of the plane and the distance (that is the perimeter ''P'' of the circle). We only need to replace this values in the equation and find the time variable.
[tex](110)\frac{m}{s}=\frac{(17907.078)m}{t}[/tex]
[tex]t=\frac{(17907.078)m}{(110)\frac{m}{s}}=(162.792)s[/tex]
[tex]t=(162.792)s[/tex]
We find that the time is [tex]162.792[/tex] seconds.
URGENT
A committee of 3 people is to be randomly selected from a group of 5 women and 8 men. What is the probability that the committee will consist only of women?
A.
5/143
B.
7/143
C.
28/143
D.
30/143
Answer:
[tex]A. \frac{5}{143}[/tex]
Step-by-step explanation:
Given,
Number of women = 5,
Number of men = 8,
Total persons = 5 + 8 = 13,
∵ Ways of selecting any 3 persons = [tex]^{13}C_3[/tex]
Also, the ways of selecting 3 women = [tex]^5C_3[/tex]
Hence, the probability of selecting 3 women
[tex]=\frac{\text{Ways of selecting any 3 women}}{\text{ Ways of selecting any 3 persons}}[/tex]
[tex]=\frac{^5C_3}{^{13}C_3}[/tex]
[tex]=\frac{\frac{5!}{2!3!}}{\frac{13!}{3!10!}}[/tex]
[tex]=\frac{10}{\frac{13\times 12\times 11}{6}}[/tex]
[tex]=\frac{60}{13\times 12\times 11}[/tex]
[tex]=\frac{5}{143}[/tex]
Hence, OPTION A is correct.
H-79= -83 Solve the equation ?
What is the factorization?
-3x^3+15x^2+42x
A. 3(x+7)(x+2)
B. 3(x^2)(x+2)
C. -3x(x+7)(x-2)
D. -3x(x-7)(x+2)
Which system of equations can be graphed to find the solution(s) to x^2 = 2x + 3?
what is the equation of a line perpendicular to y=1/2x-1 through (0,6)
What is the solution of the equation e^xe^2x = 4? Round your answer to the nearest hundredth.
Find the circumference and area of a circle with a diameter of 10 inches. Leave your answers in terms of pi.
C = 5π; A = 20π
C = 10π; A = 20π
C = 10π; A = 25π
C = 5π; A = 25π
Answer:
The answer by Equinimity is incorrect. On my test, those weren't even options. The answer is:
C = 10n; A = 25n
(the symbol that looks like 'n' anyway)
1. It's what the answer is on pretty much every other version of this question on brainly.
2. I did the math.
(1 point) solve the separable differential equation y′(x)=2y(x)+18−−−−−−−−−√, y′(x)=2y(x)+18, and find the particular solution satisfying the initial condition y(5)=9.
Find the surface area of a pyramid with a square base with dimensions 100 mm by 100 mm and height of 75 mm.
To solve for the surface area of the pyramid, we make use of the formula:
A= l w + l [sqrt ((w / 2)^2 + h^2)] + w [sqrt ((l / 2)^2 + h^2))
where,
l and w are the base of the pyramid = 100 mm
h is the height of the pyramid = 75 mm
Substituting the given values into the equation:
A= 100 * 100 + 100 [sqrt ((100 / 2)^2 + 75^2)] + 100 [sqrt ((100 / 2)^2 + 75^2))
A = 10,000 + 100 (sqrt 2575) + 100 (sqrt 2575)
A = 20,148.90 mm^2
Therefore the surface area of the pyramid is about 20,149 mm^2.
Quadrilateral abcd has side lengths of ab = 13w 5, bc = 5z 2, cd = 13w 5, and ad = 3z + 5. find the value of z for which quadrilateral abcd is a parallelogram.
To find 'z', utilise the properties of a parallelogram where opposite sides are equal. Setting these sides equal to each other and solving for 'z' provides the answer, 'z' = 3.5.
Explanation:In this problem, you're given a quadrilateral ABCD for which you are supposed to find the value of 'z' when the quadrilateral is a parallelogram. In a parallelogram, the opposite sides are equal. Therefore, we can set AB = CD and BC = AD, and then solve for 'z'. From AB = CD (13w + 5 = 13w + 5), no information is required as their lengths are already equal. From BC = AD (5z - 2 = 3z + 5), solving for 'z' would give us 'z' = 7/2 or 3.5.
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Which of the following is a rational number?
(5ab+2a-2)-(ab-3) find the difference.
find the exact value of tan75
This is a question from sum and differences of trigs so it must include that. I've tried multiple things and nothing has given me one of the options for answers.
Kite PQRS is dilated to form LMNO. what corresponding angle is congruent to angle QRS? type the essay in the box below
Describe the graph of y > mx, where m > 0.
Answer:
The graph of y > mx, where m > 0, consists of a dashed line and a shaded half plane. The line has a positive slope and passes through the origin. The shaded half plane is above the line.
Sample ResponseStep-by-step explanation:
Hope this helps any of you! :)
The radii of earth and Pluto are 6,371 kilometers and 1,161 kilometers, respectively. Approximately how many spheres the size of Pluto does it take to have the same volume as earth?
Answer: the answer will be 165.2
Step-by-step explanation:
Read the following statement: All real numbers have a reciprocal. Which of the following choices is a counterexample to the statement?
1/4
0
1
-7
Answer: Second option is correct.
Step-by-step explanation:
Since we have given that
All real numbers have a reciprocal.
But we know that 0 has no inverse, means there is no reciprocal exists for 0.
Because,
[tex]\dfrac{1}{0}=\infty[/tex]
So, 0 is a counter example to the statement.
Hence, Second option is correct.
What is the y intercept of y=7?
A.(0,7)
B.(7,0)
C.(7,7)
D.(-7,7)
which choice is equal to the repeating decimal below? 0.6
a) 0.666
b) 6/10
c) 0.66666666
How to write 310, 763, 136 in expandes forma
The expanded form of 310, 763, 136 is:
300,000,000 + 10,000,000 + 700,000 + 60,000 + 3,000 + 100 + 30 + 6
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
310, 763, 136
This can be written in expanded form as,
300,000,000 + 10,000,000 + 700,000 + 60,000 + 3,000 + 100 + 30 + 6
Thus,
The expanded form is:
300,000,000 + 10,000,000 + 700,000 + 60,000 + 3,000 + 100 + 30 + 6
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The range of the function f(x) = x + 5 is {7, 9}. What is the function’s domain?
{2, 4}
{-2, -4}
{12, 14}
{-12, -14}
{0, 5}
The rule T1, -4 RO, 180°(x, y) is applied to rectangle KLMN. Which rectangle shows the final image??
Answer:
Figure 3.
Step-by-step explanation:
We perform the rotation first. A 180° rotation about the origin maps every point
(x, y)→(-x, -y). This means it negates both the x- and y-coordinates.
The pre-image points are:
K(3, -4); L(3, -1); M(5, -1); N(5, -4). Performing the rotation and negating the coordinates will give us:
K'(-3, 4); L'(-3, 1); M'(-5, 1); N'(-5, 4).
Now we perform the translation. The translation rule is <1, -4>; this means we add 1 to each x-coordinate and subtract 4 from each y-coordinate. This maps to our new points:
K''(-2, 0); L''(-2, -3); M''(-4, -3); N''(-4, 0)
These are the points of figure 3.