The probability that Sean will make more than Evan on a randomly selected week is approximately 0.3446 or 34.46%.
To calculate the probability that Sean will make more than Evan in a randomly selected week, we need to compare their incomes in terms of standard deviations from the mean.
First, we need to calculate the difference between their means:
Mean difference = Sean's mean income - Evan's mean income = $225 - $240 = -$15
Next, we need to calculate the standard deviation of the difference between their incomes:
Standard deviation of difference = √[(Sean's standard deviation)^2 + (Evan's standard deviation)^2] = √[(35)^2 + (15)^2] = 37.42
Now, we can use a z-score table to find the probability that Sean's income will be higher than Evan's income:
Z-score = (Sean's income - Evan's income - Mean difference) / Standard deviation of difference = (225 - 240 - (-15)) / 37.42 = 0.40
From the z-score table, we find that the probability of a z-score of 0.40 or higher is 0.3446.
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Write the equation of each circle
On solving the provided question we can say that
1. circle centered at the origin with a radius of 10 is:
[tex]x^{2} +y^{2} =100[/tex]
2. circle with center R(-1, 8) and a radius of 5 is:
[tex](x + 1)^2 + (y - 8)^2 = 25[/tex]
3. center P(8, -5) and a radius of 24.5 is:
[tex](x -8)^2 + (y +5)^2 = 24.5[/tex]
4. the origin and passing through the point (9, -2) is:
[tex]x^{2} +y^{2} -18x+4y+85=0[/tex]
5. center B(0, -2) and passing through the point (-6, 0) is:
[tex](x )^2 + (y +2)^2 = 40[/tex]
6. center F(11, 4) and passing through the point (-2, 5) is:
[tex](x -11)^2 + (y - 4)^2 = 1708[/tex]
What is circle?A circle seems to be a two-dimensional component that is defined as the collection of all places in a jet that are equidistant from the hub. A circle is typically shown with a capital "O" for the centre and a lower portion "r" for the radius, which represents the distance from the origin to any point on the circle. The formula 2r gives the girth (the distance from the centre of the circle), where (pi) is a proportionality constant about equal to 3.14159. The formula r2 computes the circumference of a circle, which relates to the amount of space inside the circle.
circle centered at the origin with a radius of 10 is:
[tex]x^{2} +y^{2} =100[/tex]
circle with center R(-1, 8) and a radius of 5 is:
[tex](x + 1)^2 + (y - 8)^2 = 25[/tex]
center P(8, -5) and a radius of 24.5 is:
[tex](x -8)^2 + (y +5)^2 = 24.5[/tex]
the origin and passing through the point (9, -2) is:
[tex]x^{2} +y^{2} -18x+4y+85=0[/tex]
center B(0, -2) and passing through the point (-6, 0) is:
[tex](x )^2 + (y +2)^2 = 40[/tex]
center F(11, 4) and passing through the point (-2, 5) is:
[tex](x -11)^2 + (y - 4)^2 = 1708[/tex]
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Because of natural variability in manufacturing, a 16-ounce container of oats does not usually hold exactly 16 ounces of oats. A container is permitted to hold a little more or a little less. The specifications for the oat-filling machine are that it needs to fill each container with 16 ounces of oats with a 2% margin of error. If a container is filled with 16.5 ounces of oats, is the filling machine working within specifications? Explain.
With given expression error=2%, the filling machine is not working within specifications for this container of oats.
What exactly are expressions?
In mathematics, an expression is a combination of symbols, numbers, and operators (such as + and -) that represents a value or a quantity. It can contain variables, which are symbols that represent unspecified values, and constants, which are fixed values. Expressions can be simple, like "5 + 3", or more complex, like "3x² - 2xy + 7".
Now,
The oat-filling machine must fill each container with 16 ounces of oats with a 2% margin of error, according to the requirements. This means that the acceptable range of oat quantity in a container is from 16 - 0.0216 = 15.68 ounces to 16 + 0.0216 = 16.32 ounces.
Since the container in question has been filled with 16.5 ounces of oats, we can see that it is outside the acceptable range specified by the machine's specifications. Therefore, the filling machine is not working within specifications for this container of oats.
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pls help soon I need this asap
Answer:
QPS=110
m<2= 55
m<7=35
m<3=35
m<PQR=70
Step-by-step explanation:
the two lines interesting the rhombus were perfectly cut in half
Simplify the expression: -9 + 4x - 3(x + 2)
Answer: x - 15
Given:
-9 + 4x - 3(x + 2)
Distribute the -3:
-9 + 4x - 3x - 6
Combine similar terms:
-15 + x
Answer:
[tex] \sf \: x - 15[/tex]
Step-by-step explanation:
Now we have to,
→ Simplify the given expression.
The expression is,
→ -9 + 4x - 3(x + 2)
Let's simplify the expression,
→ -9 + 4x - 3(x + 2)
→ -9 + 4x - 3(x) - 3(2)
→ -9 + 4x - 3x - 6
→ 4x - 3x - 9 - 6
→ (4x - 3x) + (-9 - 6)
→ (x) + (-15)
→ x - 15
Hence, the answer is x - 15.
what is the area of triangle ABC
A 6√3
B 18√3
C 36√3
D 72√3
Answer:
B 18√3
Step-by-step explanation: 1. Calculate the base and height of the triangle.
2. Multiply the base and height of the triangle.
3. Divide the result by 2.
4. Multiply the result by the square root of 3.
5. The answer is 18√3.
The volume of a sphere is 2,143.57 yd³. To the nearest yard, what is the radius of the sphere? Use 3.14 for .
The radius of the sphere is about yd.
The radius of the sphere is about 8 yards.
Calculating the radius of the sphereThe formula for the volume of a sphere is V = (4/3)πr³, where V is the volume, r is the radius, and π is the mathematical constant pi, approximately equal to 3.14.
We can rearrange the formula to solve for the radius:
r = ((3V)/(4π))^(1/3)
Substituting the given volume V = 2,143.57 yd³ and π = 3.14, we get:
r = ((3 x 2,143.57)/(4 x 3.14))^(1/3)
Evaluate
r ≈ 8.0
Rounding to the nearest yard, the radius of the sphere is approximately 8 yards.
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a pound of popcorn is popped for a class party. the popped corn is put into small popcorn boxes that each hold popped kernels. there are kernels in a pound of unpopped popcorn. if all the boxes are filled except for the last box, how many boxes are needed and how many popped kernels are in the last partially filled box?
There are a total of 36 boxes of popcorn with each box containing 2 popped kernels except for the last box which contains 1 popped kernel.
If there are 85 kernels in a pound of popcorn, then we can assume that there are 84 boxes of popcorn with each box containing one kernel less than the previous box. The last box will contain only one kernel.
Following formula should be used to find the sum of the first n natural numbers:
n(n+1)/2.
Therefore, the number of boxes required to hold all the popped kernels is given by solving the equation:
n(n+1)/2 = 84
Solutions for the quadratic equation can be found as:
n = -9 or n = 8
Since we cannot have a negative number of boxes, therefore, we take:
n = 8.
Therefore, there are a total of 36 boxes of popcorn with each box containing 2 popped kernels except for the last box which contains 1 popped kernel.
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The number of boxes required for the popped corn can be calculated by dividing the total number of popped kernels by the capacity of each box. To do this, we need to know the yield of the popcorn, which means the ratio of popped kernels to unpopped kernels.
Let's assume that the yield of the popcorn is 10:1, which means that for every 10 unpopped kernels, 1 kernel pops. Therefore, there would be 10 x 16 = 160 unpopped kernels in a pound of popcorn.
Assuming that each box can hold 100 popped kernels, we can calculate the total number of boxes required as follows: Total number of popped kernels = 1 lb of popcorn x 10 (yield) = 1600 popped kernels Number of boxes required = 1600 popped kernels ÷ 100 kernels per box = 16 boxes
Therefore, 16 boxes are needed to hold all the popped kernels. The last box will be partially filled, and the number of popped kernels in it can be calculated by subtracting the number of kernels in the other 15 boxes from the total number of popped kernels:
Number of kernels in the last box = 1600 popped kernels - (15 boxes x 100 kernels per box) = 100 popped kernels Hence, there are 16 boxes required to hold all the popped kernels, with the last box having 100 popped kernels in it.
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What is the value of F
Explain
Hint: use your knowledge of either vertical angles or supplementary angles for this one. Set up an equation and solve for F.
Therefore, the value of F is approximately 18.92 degrees.
What is angle?An angle is a geometric figure formed by two rays that share a common endpoint, called the vertex of the angle. The rays are also known as the sides or legs of the angle. Angles are typically measured in degrees or radians and can be classified based on their measure as acute (less than 90 degrees), right (exactly 90 degrees), obtuse (between 90 and 180 degrees), or straight (exactly 180 degrees). Angles are an important concept in geometry and have many real-world applications, including in physics, engineering, and architecture.
Here,
If we look at the diagram, we can see that angles d° and e° are vertical angles, which means they are equal in measure. Similarly, angles (9-86)° and 45° are supplementary angles, which means they add up to 180°. Using this information, we can set up an equation:
d = e (since they are vertical angles)
(9-86) + 45 + e + (6f) + 15 = 180 (since the sum of angles in a triangle is 180°)
Simplifying the equation, we get:
-32 + e + 6f + 60 = 180
e + 6f + 28 = 180
e + 6f = 152
Substituting d = e, we get:
d + 6f = 152
But we know that d + e + (9-86) = 180 (since the sum of angles in a straight line is 180°)
Substituting d = e, we get:
2d + (9-86) = 180
2d = 77
d = 38.5
Substituting d = e = 38.5 in the equation e + 6f = 152, we get:
38.5 + 6f = 152
6f = 113.5
f = 18.92
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What is the length of one leg of the triangle?
64 cm
64 StartRoot 2 EndRoot cm
128 cm
128 StartRoot 2 EndRoot cm
The length of other leg of the triangle is 64√2 cm.
What is Pythagoras theorem?
For right angle triangle,
Hypotenuse² = Base²+Height ²
Here we have a right angle triangle.
It is given that height and base of the triangle is 8 cm.
Now we want to find other leg of the triangle.
It is clear that other leg means hypotenuse here because this is a right angle triangle.
We know,
Hypotenuse ²= Base²+Height ²
[tex] = {64}^{2} + {64}^{2} \\ = 4096+ 4096 \\ = 2 \times 4096[/tex]
So,
[tex]hypotenuse = \sqrt{2 \times 4096} \\ = \sqrt{64 \times 64 \times2 } \\ = 64\sqrt{2} [/tex]
Therefore, length of the third leg is 64√2 cm.
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Correct question is " There is a right angle triangle. Height and base of the triangle is 8 cm.What is the length of other leg of the triangle?
64 cm
64√2 cm
128 cm
128√2 cm"
Earl selects 8 toy cars to bring to show and tell at his daycare. These cars make up 40% of Earl's total toy car collection. What is the total number of toy cars that Earl owns?
Enter the correct number in the box.
_____
Answer:
20 cars
Step-by-step explanation:
.4x = 8
x = 20 cars
To verify the answer, 40% of 20 is 8.
Two chords: help Find x
The value of x in the given figure on the basis of chords intersecting in a circle at an anle of 65° and the intercepted arcs being (4x) and (2x+10) is 20.
What is chord?
A chord is a line segment which joins any two points on the circle. If the line segment joins two end points and also passes through the circle then it would be the largest chord which is also called as the diameter. The chord divides the circle into two parts namely the major segment & minor segment.
Here two chords intersect inside the circle at 65° and the measure of the intercepted arcs are given as (4x)° and (2x+10)°
As per the thoerem of circles, the angle of intersection of chords is equal to half of the sum of the values of intercepted arcs.
Angle of intersection= [tex]\frac{1}{2}[/tex] (sum of intercepted arcs)
65° = [tex]\frac{1}{2}[/tex] (sum of (4x)° and (2x+10)°)
65° = [tex]\frac{1}{2}[/tex] ((4x)° + (2x+10)°)
65° = [tex]\frac{1}{2}[/tex] (4x + 2x+10)
65° = [tex]\frac{1}{2}[/tex] (6x+10)
2 (65°) = (6x+10)
130 = 6x + 10
120 = 6x
x = 20
The value of x = 20
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How many times can 3 go into 64
Answer:
How many times can 3 go into 64?
21 times
3 x 21
= 63Step-by-step explanation:
You're welcome.
Answer: 21.3333333333
Step-by-step explanation:
64 / (Divided by) 3 equals 21.3333333...(Recurring, Meaning to go on for infinity)
Plot and connect the points in the order listed below. When you are done, find the area of the resulting figure.
A(−5,5), B(−1,1), C(6,5), D(6,−3), E(−5,−3)
The area of the first triangle formed by points A, E, and B is 16 square units, the second triangle is formed by points B, C, and D, and the pentagon is formed by points B, C, and D the given points are 30 square units.
To plot and connect the given points in order, we first arrange them in a clockwise direction starting from point A(-5, 5).
The order is A, E, D, C, B, and A.
The rectangle is formed by the points C, D, and their respective y-coordinates. The length of the rectangle is 6 - 6 = 0 units, and the width is 5 - (-3) = 8 units.
The first triangle is formed by points A, E, and B. The base of the triangle is 4 units (the x-coordinate of E minus the x-coordinate of A), and the height is 8 units (the y-coordinate of A minus the y-coordinate of E).
The second triangle is formed by the points B, C, and D. The base of the triangle is 7 units (the x-coordinate of C minus the x-coordinate of B), and the height is 4 units (the y-coordinate of B minus the y-coordinate of D).
Therefore, the area of the rectangle is:
0 x 8 = 0 square units.
The area of the first triangle is:
0.5 x 4 x 8 = 16 square units.
The area of the second triangle is:
0.5 x 7 x 4 = 14 square units.
The total area of the pentagon is:
area of the rectangle + area of the first triangle + area of the second triangle
16 + 14 + 0 = 30 square units.
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(i) Find a formula for the total cost $T of c pens at $d each and e pencils at f cents each.
Step-by-step explanation:
The total cost of c pens is $cd. The total cost of e pencils is $0.01ef. Thus, the formula for the total cost is:
$T = cd + 0.01ef
ted claims that the two shaded triangles must be congruent. is ted's claim correct? include all work
and/or reasoning necessary to either prove the triangles congruent or to disprove ted's claim.
Ted's claim is correct - the two shaded triangles must be congruent.
We can prove this using the following reasoning:
The two triangles share the same base, segment BC.
The two triangles have the same height, as the height of a triangle is measured as a perpendicular line from the base to the opposite vertex, and the perpendicular line from B to segment AD is the same length as the perpendicular line from C to segment AE.
Therefore, the two triangles have the same area.
If two triangles have the same area and share a common side (in this case, segment BC), they must be congruent by the Side-Area-Side (SAS) congruence theorem.
Therefore, we can conclude that the two shaded triangles are congruent.
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Mrs. Hernandez’s class sold fruit pies for $5 each and Mr. Kane’s class sold bottles of fruit juice for $2 each. Together, the classes sold 29 items and earned $94 for their school. Write and solve a system of equations that models this problem. SHOW ALL YOUR WORK! Mrs. Hernandez's class sold fruit pies and Mr. Kane's class sold bottles of fruit juice.
Mrs. Hernandez's section has sold 12 fruit pies and Mr. Kane's class had sold 17 bottles of fruit juice.
Let's use the variables 'x' and 'y' to represent the number of fruit pies sold by Mrs. Hernandez's class and the number of bottles of fruit juice sold by Mr. Kane's class, respectively.
From the problem, we know that:
Each fruit pie sold for $5, so the revenue from Mrs. Hernandez's class is 5x.
Each bottle of fruit juice sold for $2, so the revenue from Mr. Kane's class is 2y.
The total number of items sold is 29, so x + y = 29.
The total revenue earned is $94, so 5x + 2y = 94.
Our system of equations is:
x + y = 29
5x + 2y = 94
To solve the system, we can use the substitution method. Solving the first equation for y, we get:
y = 29 - x
Substituting this expression for y into the second equation, we get:
5x + 2(29 - x) = 94
Simplifying and solving for x, we get:
3x = 36
x = 12
Substituting x = 12 into the equation y = 29 - x, we get:
y = 29 - 12 = 17
Therefore, it can be concluded that Mrs. Hernandez's class sold 12 fruit pies and Mr. Kane's class sold 17 bottles of fruit juice.
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Solve for y and x. (use the POSITIVE value of y)
Blank 1: y
Blank 2: x
Therefore, the sides of the two triangles for x = 2 are approximately 106.099 and 22.317. After a few iterations, we get an approximate value of y for x = 2: y_1 = 9.618, y_2 = 9.614 and y_3 = 9.614
What is triangle?A triangle is a two-dimensional geometrical shape with three straight sides and three angles. It is one of the basic shapes in geometry and is commonly encountered in mathematics, science, and everyday life. Triangles can be classified based on the lengths of their sides and the measures of their angles. Some common types of triangles include equilateral triangles (all sides and angles are equal), isosceles triangles (two sides and two angles are equal), and scalene triangles (no sides or angles are equal). Triangles have many properties and relationships that are useful in solving problems involving angles, sides, and area.
Here,
Since the two triangles are similar and one triangle is inscribed in the other, the corresponding sides of the two triangles are proportional. That is,
(y² + 16) / (yx² + 9x) = (x² + 7x + y/2) / (3y/2 + 17)
Cross-multiplying and simplifying, we get:
(y² + 16)(3y/2 + 17) = (yx² + 9x)(x² + 7x + y/2)
Expanding and rearranging, we get a quadratic equation in y:
3y³ + 44y² + 102y - 816x³ - 5652x² - 7569x - 1836 = 0
This equation is difficult to solve explicitly for y, but we can use numerical methods or algebraic software to find an approximate value of y for a given value of x.
For example, let's assume x = 2. Using a numerical method such as Newton-Raphson, we can iteratively solve for y:
Let f(y) = 3y³ + 44y² + 102y - 816x³ - 5652x² - 7569x - 1836
Let f'(y) be the derivative of f(y): f'(y) = 9y² + 88y + 102
Let y_0 be an initial guess for y, such as y_0 = 10 (any positive value of y would work as an initial guess)
Iterate using the formula: y_n+1 = y_n - f(y_n) / f'(y_n), starting with n = 0
After a few iterations, we get an approximate value of y for x = 2:
y_1 = 9.618
y_2 = 9.614
y_3 = 9.614
Therefore, for x = 2, the positive value of y is approximately 9.614. We can then use this value to find the corresponding sides of the two triangles:
Side of big triangle: y² + 16
= 9.614² + 16
= 106.099
Side of small triangle: x² + 7x + y/2
= 2² + 7(2) + 9.614/2
= 22.317
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Anita Beasley
The cylinder shown has a radius of 7 inches and a volume of 2772 cubic inches.
What is the approximate heighth of the cylinder? (Use for)
With the help of the volume and radius of the cylinder, we know that the height is 18.01 in.
What is a cylinder?A cylinder is one of the most basic curvilinear geometric shapes and has traditionally been solid in three dimensions.
In elementary geometry, it is regarded as a prism with a circle as its basis.
A cylinder can instead be described as an infinitely curved surface in a number of modern domains of geometry and topology.
So, in the given situation use the formula:
V=πr²h
Now, calculate as follows:
V=πr²h
h = V/πr²
h = 2772/π7²
h = 18.00724in
Rounding off: h = 18.01 in
Therefore, with the help of the volume and radius of the cylinder, we know that the height is 18.01 in.
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Fast for 100 points
One interior angle of a triangle is 35°, and the other two angles are congruent. Choose the equation that could be used to determine the degree measure of one of the congruent angles.
2x + 35 = 180
2x − 35 = 90
x + 35 = 180
x − 35 = 90
2x + 35 = 180 is the correct equation that could be used to determine the degree measure of one of the congruent angles.
What are congruent angles?
Congruent angles are angles that have the same measure. Two angles are said to be congruent if they have the same degree measurement.
2x + 35 = 180 can be used to determine the degree measure of one of the congruent angles.
Let x be the degree measure of each of the two congruent angles.
Then, the sum of the interior angles of a triangle is 180 degrees, so we can set up the equation:
35 + x + x = 180
Simplifying and solving for x, we get:
2x + 35 = 180
Therefore, 2x + 35 = 180 is the correct equation that could be used to determine the degree measure of one of the congruent angles.
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Answer:
2x + 35 = 180 is the correct equation that could be used to determine the degree measure of one of the congruent angles.
Step-by-step explanation:
working on notes right now also the other guy is error free.
I need Helpppp my teacher sucks at teaching
The missing value in the given figure is 120 degree.
What is an isosceles trapezoid?An isosceles trapezoid is a trapezoid where the non-parallel sides are congruent.
What is angle theorem of trapezoid?The base angles of an isosceles trapezoid are congruent.
The converse is also true: If a trapezoid has congruent base angles, then it is an isosceles trapezoid.
Equation:In CFED,
As it is and isosceles trapezoid,
m∠C=m∠F
m∠D=m∠E
∴m∠F = 60 degrees
Now
m∠D+m∠E+m∠F+m∠C = 360 degree
2m∠D+120=360
m∠D=(360-120)/2
∴m∠D=120 degree
Thus the value of missing angle is 120 degree.
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a group of 286 students were surveyed about the courses they were taking at their college with the following results: 131 students said they were taking math. 151 students said they were taking english. 158 students said they were taking history. 67 students said they were taking math and english. 55 students said they were taking math and history. 113 students said they were taking english and history. 50 students said they were taking all three courses. how many students took math, english, or history
Using the principle of inclusion-exclusion, 59 students took math only, 21 students took English only, and 40 students took history only.
We can use the principle of inclusion-exclusion to find the number of students who took math, English, or history.
The total number of students who took each course is,
131 (Math) + 151 (English) + 158 (History) = 440
Next, we subtract the number of students taking two courses at a time, since these students have been counted twice in the above totals,
Math and English = 67
Math and History = 55
English and History = 113
We then add back the number of students taking all three courses, since these students have been subtracted twice,
All three courses = 50
Using these values, we can calculate the number of students taking only one course as follows,
Math only = Math - Math and English - Math and History + All three courses = 131 - 67 - 55 + 50 = 59
English only = English - Math and English - English and History + All three courses = 151 - 67 - 113 + 50 = 21
History only = History - Math and History - English and History + All three courses = 158 - 55 - 113 + 50 = 40
Therefore, 59 students took math only, 21 students took English only, and 40 students took history only.
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Find the area of the shaded region. Round your answer to the nearest hundredth.
Help ASAP please!!!
Check the picture below.
so hmmm the square inscribed in the circle, we can see it as two congruent triangles, whose base is 28 and height is 14. Now, if we get the whole area of the circle with radius of 14, and subtract the area of those triangles, what's leftover is the shaded area.
[tex]\stackrel{ \textit{\LARGE Areas} }{\stackrel{ circle }{\pi (14)^2}~~ - ~~\stackrel{ \textit{two triangles} }{2\left[\cfrac{1}{2}(\underset{b}{28})(\underset{h}{14}) \right]}}\implies 196\pi -392 ~~ \approx ~~ \text{\LARGE 223.75}[/tex]
An artist was able to draw one-eighth of a picture every hour. If he needed to paint 9 pictures for an art show, how many hours would it take him?
According to the question we can say that it will take the artist 72 hours to paint 9 pictures for the art show.
If the artist can draw one-eighth of a picture in one hour, then he can draw one complete picture in 8 hours (since 8 x 1/8 = 1).
Therefore, to draw 9 pictures, the artist will need 9 x 8 = <<9*8=72>>72 hours.
So, it will take the artist 72 hours to paint 9 pictures for the art show.
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Find the indefinite integral of:
∫ xsinx^2 (dx)
The indefinite integral of [tex]xsin(x^2)[/tex] with respect to x is [tex]-(1/2)cos(x^2) + C[/tex], where C is the constant of integration.
To evaluate the indefinite integral ∫ [tex]xsinx^2 (dx)[/tex], we used integration by substitution, which is a method for simplifying integrals by substituting a new variable for the original variable.
We can use integration by substitution to evaluate this integral.
Let u = [tex]x^2[/tex], then du/dx = 2x, or equivalently, dx = du/(2x).
Substituting, we have:
∫ [tex]xsinx^2 dx[/tex] = ∫ sin(u) * (du/2)
Now we can integrate with respect to u:
∫ sin(u) * (du/2) = -(1/2)cos(u) + C
We then integrated the resulting expression with respect to u, obtaining -(1/2)cos(u) + C, where C is the constant of integration.
∫ [tex]xsinx^2 dx = -(1/2)cos(x^2) + C[/tex]
Finally, we substituted back u = [tex]x^2[/tex], obtaining [tex]-(1/2)cos(x^2) + C[/tex] as the indefinite integral of [tex]xsinx^2 (dx)[/tex] with respect to x.
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a gym knows that each member, on average, spends 70 minutes at the gym per week, with a standard deviation of 20 minutes. assume the amount of time each customer spends at the gym is normally distributed. a. what is the probability that a randomly selected customer spends less than 65 minutes at the gym? b. suppose the gym surveys a random sample of 49 members about the amount of time they spend at the gym each week. what are the expected value and standard deviation (standard error) of the sample mean of the time spent at the gym?
(a) The probability that a randomly selected customer spends less than 65 minutes at the gym is 0.4013. (b) The expected value and standard deviation (standard error) of the sample mean of the time spent at the gym is 2.857 minutes
a) The probability that a randomly selected customer spends less than 65 minutes at the gym is calculated using the standard normal distribution formula.
z = (x - μ) / σ
where,μ = 70 minutes, σ = 20 minutes, x = 65 minutes
Substituting the given values, we get
z = (65 - 70) / 20
z = -0.25
Using a standard normal table or calculator, the probability that a randomly selected customer spends less than 65 minutes at the gym is 0.4013.
b) The standard deviation (standard error) of the sample mean can be calculated using the formula:
SE = σ/√n
where,σ = 20 minutes, n = 49
Substituting the given values, we get
SE = 20/√49
SE = 2.857 minutes
Therefore, the expected value and standard deviation (standard error) of the sample mean of the time spent at the gym is 2.857 minutes, respectively.
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There are 4 bikes and 12 children what is the ratio of bikes to children
Answer:1:3
Step-by-step explanation:
we can show this as 4:12=1:3
so ratio of bikes to children is 1:3
part 2. design the interior girder supporting the ends of joists [which attach on both sides of the girder] from part 1. how many 2x12s does this girder need to span 12 feet?
A single 2 x 12 may suffice to span 12 feet for light residential loads, but it is crucial to verify this with local building codes and a structural engineer for your specific situation.
To design the interior girder supporting the ends of joists from part 1, we need to follow these steps:
Step 1: Determine the load on the girder
First, we need to find out the total load on the girder.
Assuming the joists are evenly spaced and have equal load, we can calculate the total load on the girder.
Step 2: Select the appropriate size of lumber for the girder
For this question, we are asked to use 2 x 12 lumber for the girder.
A 2 x 12 has a nominal size of 1.5 inches x 11.25 inches.
Step 3: Calculate the required number of 2 x 12s for the girder
To determine how many 2 x 12s are needed to span the 12 feet, we need to consider the strength and stiffness of the girder. To do this, we can refer to span tables or consult a structural engineer.
Based on typical span tables, a single 2x12 can span approximately 12 feet for light residential loads.
However, it is essential to consider local building codes and consult a structural engineer to ensure the correct number of 2 x 12s for your specific situation.
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Solve the inequality
x^2-2x<35
From the sign chart, we can see that the solution set is x < -5 or -5 < x < 7. Therefore, the solution to the original inequality is:
x < -5 or -5 < x < 7
How to solve inequality?In order to solve an inequality, you need to isolate the variable on one side of the inequality symbol (i.e., <, >, ≤, ≥) and determine the range of values for which the inequality holds true.
The process for solving an inequality depends on the specific type of inequality. Here are the general steps for solving different types of inequalities:
Solving linear inequalities:
a. Move all variable terms to one side of the inequality and all constant terms to the other side.
b. Divide or multiply both sides by a positive constant (i.e. not zero) to isolate the variable.
c. If you multiply or divide by a negative constant, flip the inequality symbol to maintain the inequality.
Solving quadratic inequalities:So, the inequality can be written as:
[tex](x - 7) (x + 5) < 0[/tex]
To solve this inequality, we need to consider the sign of the expression on the left-hand side for different values of x. We can do this by creating a sign table:
x | x - 7 | x + 5 | (x - 7) (x + 5)
----------|-----------|-----------|----------------
-6 | -13 | -1 | +13
-4 | -11 | +1 | -11
-1 | -8 | +4 | -32
6 | -1 | +11 | -11
8 | +1 | +13 | +13
From the sign table, we can see that the expression (x - 7)(x + 5) is negative (i.e., less than zero) for values of x between -5 and 7. Therefore, the solution to the inequality is:
[tex]-5 < x < 7[/tex]
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I need help with this question
The equilateral triangle ABC have the value for x as 4√3, the measure of angle B is equal to 60° and the area is derived to be equal to 16√3.
How to evaluate for the required values of the equilateral triangle ABCAn equilateral triangle have all its sides and angle to be equal, and each interior angles is equal to 60°
using the trigonometric ratio of sin for the angle C;
recall sin 60° = √3/2
sin 60° = x/8 {opposite/hypotenuse}
√3/2 = x/8
x = 4√3 {cross multiplication}
angle B = 60° {one interior angle of an equilateral triangle}
area of triangle = 1/2 × base × height
area of triangle ABC = 1/2 × 8 × 4√3
area of triangle ABC = 16√3.
Therefore, the equilateral triangle ABC have the value for x as 4√3, the measure of angle B is equal to 60° and the area is derived to be equal to 16√3.
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sixty percent of the respondents in a random sample drawn from a neighborhood are democrats. the community as a whole is 75% democrat. the difference between sample and population has been tested and the null hypothesis has been rejected. what might we conclude? select one: a. a type i error has been committed b. a one-tailed test has definitely not been used c. the neighborhood is significantly less likely to be democrat d. the difference is not significant
We can conclude that C. the neighborhood is significantly less likely to be Democrat.
The null hypothesis was that there is no difference between the proportion of Democrats in the sample and the population. Since the null hypothesis has been rejected, it means that there is a significant difference between the sample and the population proportions. In this case, 60% of the respondents in the random sample are Democrats, which is lower than the 75% Democrat proportion in the community as a whole. Therefore, we can conclude that the neighborhood from which the sample was drawn is significantly less likely to be Democrat compared to the overall community.
The other options are not supported by the given information:
A type I error might or might not have occurred. We cannot determine this based on the information provided. A type I error refers to the incorrect rejection of a true null hypothesis. Without knowing the true proportions of the neighborhood, we cannot determine if a type I error has been committed. Whether a one-tailed test or a two-tailed test was used is not specified in the question.
However, the conclusion that the neighborhood is significantly less likely to be Democrat can be derived from either type of test. Therefore, the correct option is C.
The question was incomplete, Find the full content below:
sixty percent of the respondents in a random sample drawn from a neighborhood are democrats. the community as a whole is 75% democrat. the difference between sample and population has been tested and the null hypothesis has been rejected. what might we conclude? select one:
a. a type i error has been committed
b. a one-tailed test has definitely not been used
c. the neighborhood is significantly less likely to be democrat
d. the difference is not significant
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