The probability that a CD player will break down during the guarantee period is about 0.1985 or 19.85%.
To find the probability that a Sunshine CD player will break down during the 3-year guarantee period, we'll use the properties of the normal distribution.
Given a mean life of 4.1 years and a standard deviation of 1.3 years, we can calculate the z-score corresponding to the 3-year guarantee period:
z = (x - μ) / σ = (3 - 4.1) / 1.3 ≈ -0.846
Now, we'll look up the probability associated with this z-score in a standard normal distribution table, or use a calculator or software to find the cumulative probability. The probability corresponding to a z-score of -0.846 is approximately 0.1985.
Therefore, the probability that a CD player will break down during the guarantee period is about 0.1985 or 19.85%.
For the sketch, draw a bell-shaped curve to represent the normal distribution. Mark the x-axis with the mean (4.1 years) in the center, and scale it with the standard deviation (1.3 years).
Place a vertical line at 3 years to represent the end of the guarantee period, and shade the area to the left of this line to represent the probability of breaking down during that period.
To learn more about probability, refer below:
https://brainly.com/question/30034780
#SPJ11
-8
Find the distance, d, of AB.
A = (-7, -7) B = (-3,-1)
-6 -4
A
-2
B -2
-4
-6
-8
d = √x2-x1² + y2 - Y₁|²
d = [?]
Round to the nearest tenth.
Distance
Step-by-step explanation:
Using the distance formula:
d = √[(x2 - x1)² + (y2 - y1)²]
where A = (x1, y1) and B = (x2, y2), we can find the distance between points A and B as follows:
d = √[(-3 - (-7))² + (-1 - (-7))²]
d = √[4² + 6²]
d = √52
d ≈ 7.2
Therefore, the distance between points A and B is approximately 7.2 units, rounded to the nearest tenth.
The Phillips family bought 8 bags of cookies. Each bag had 17 cookies. They have since eaten 29 of the cookies. How many cookies do they have left?
Answer:107
Step-by-step explanation:8*17-29=107 so our answer is 107
Find the absolute maximum and minimum values of f(x,y) = x^2 + 2y^2 on the square [0,1] x [0,1]
Answer:
The maximum is when both X and y = 1.The maximum value of the function is 3.When both X and YY are equal to 0, the minimum value is 0
The absolute maximum value is 3 and the absolute minimum value is 0.
To find the absolute maximum and minimum values of f(x,y) = x^2 + 2y^2 on the square [0,1] x [0,1], we need to consider both the interior and the boundary of the square.
First, check for critical points in the interior by finding the partial derivatives and setting them equal to zero:
fx = 2x and fy = 4y
Setting them equal to zero, we have:
2x = 0 => x = 0
4y = 0 => y = 0
The only critical point in the interior is (0,0).
Next, evaluate f(x,y) on the boundary of the square [0,1] x [0,1]. The boundary consists of four segments: x=0, x=1, y=0, and y=1.
1. x=0: f(0,y) = 2y^2 (for y in [0,1])
2. x=1: f(1,y) = 1 + 2y^2 (for y in [0,1])
3. y=0: f(x,0) = x^2 (for x in [0,1])
4. y=1: f(x,1) = x^2 + 2 (for x in [0,1])
Now, compare the values of f at the critical point and boundary points to find the absolute maximum and minimum:
Absolute minimum: f(0,0) = 0
Absolute maximum: f(1,1) = 3
So the absolute maximum value is 3 and the absolute minimum value is 0.
To learn more about critical points, refer below:
https://brainly.com/question/29144288
#SPJ11
HELP!!!
What is the unit rate of this graph?
BLUE: 200 beats/minute
TEAL: 75 beats/minute
YELLOW: 100 beats/minute
RED: 150 beats/minute
For which values of k would be the pruduct of k/3x12 be greater than 12
The product (k/3) x 12 is greater than 12 for values of k greater than 3.
To determine the values of k for which the product (k/3) x 12 is greater than 12, follow these steps:
Step 1: Set up the inequality:
(k/3) x 12 > 12
Step 2: Simplify the inequality by dividing both sides by 12:
(k/3) > 1
Step 3: Multiply both sides by 3 to solve for k:
k > 3
So, the product (k/3) x 12 is greater than 12 for values of k greater than 3.
Learn more about inequality,
https://brainly.com/question/25944814
#SPJ11
R1 and R2 be relations on a set A represented by the matrices ?
R1 and R2 are relations on a set A, which means they define a set of ordered pairs of elements in A. The matrices that represent R1 and R2 can be thought of as a way to visualize these ordered pairs.
Each row and column of the matrix corresponds to an element in A. If there is a 1 in the ith row and jth column of the matrix for R1, then (i,j) is an ordered pair in R1. Similarly, if there is a 1 in the ith row and jth column of the matrix for R2, then (i,j) is an ordered pair in R2.
If there is a 0 in a particular position in the matrix, then the corresponding pair is not in the relation.
Let R1 and R2 be relations on a set A. These relations can be represented by matrices M1 and M2, respectively, with dimensions |A|x|A|, where |A| is the cardinality of set A. The elements of the matrices M1 and M2 are binary, indicating whether there is a relation between the corresponding elements of set A in R1 and R2, respectively. If there is a relation, the matrix element will be 1, and if there is no relation, the matrix element will be 0.
To know more about set, refer to the link below:
https://brainly.com/question/13088885#
#SPJ11
solve this and I will give u brainlist.
True or false: the lateral surface of cone a is exactly 1/2 the lateral surface area of cylinder b
The lateral surface area of a cone can be less than or greater than half the lateral surface area of a cylinder, depending on the specific dimensions of each shape. The given statement is true.
It depends on the specific dimensions and measurements of cone A and cylinder B. In general, however, it is not true that the lateral surface area of a cone is exactly half the lateral surface area of a cylinder with the same base and height.
The lateral surface area of a cone is given by πrl, where r is the radius of the base and l is the slant height of the cone. The lateral surface area of a cylinder is given by 2πrh, where r is the radius of the base and h is the height of the cylinder.
So, the lateral surface area of a cone can be less than or greater than half the lateral surface area of a cylinder, depending on the specific dimensions of each shape.
To learn more about dimensions visit:
https://brainly.com/question/8286598
#SPJ11
Nate jumped 26 inches. Maria jumped 32 inches.
How much farther did Maria jump than Nate?
Drag numbers and symbols to the lines. Write an equation to represent the problem. Use for the unknown.
26
32
.
+
Maria jumped 6 inches farther than Nate.
To see why, we can subtract Nate's jump height from Maria's jump height:
32 - 26 = 6
So Maria jumped 6 inches farther than Nate did.
To represent this problem mathematically, we can use the equation:
Maria's jump height - Nate's jump height = the difference in their jump heights
Or, using variables:
M - N = D
Where M represents Maria's jump height, N represents Nate's jump height, and D represents the difference between their jump heights. Plugging in the numbers from the problem, we get:
32 - 26 = D
Simplifying, we get:
6 = D
So D, the difference between their jump heights, is 6 inches.
To know more about jump height, refer to the link below:
https://brainly.com/question/29155594#
#SPJ11
find the area of each polygon below b=6 h=9 ft h =10cm b = 8 h=8m b=9m
Pythagorean Theorem help quickly please
Using the Pythagorean theorem, the height of the ramp in the given diagram is 8.9 ft
Pythagorean theorem: Calculating the height of the ramp
From the question, we are to determine how high the ramp is
From the Pythagorean theorem which states that "in a right triangle, the square of the longest side, that is hypotenuse, equals sum of squares of the two other sides".
In the given diagram,
We have a right triangle
The measure of the hypotenuse is 21 ft
One of of the side measures 19 ft
Now, we will calculate x
By the Pythagorean theorem, we can write that
h² + 19² = 21²
h² = 21² - 19²
h² = 441 - 361
h² = 80
h = √80
h = 8.94427 ft
h ≈ 8.9 ft
Hence, the ramp is 8.9 ft high
Learn more on Pythagorean theorem here: https://brainly.com/question/27165976
#SPJ1
A company had a profit of $4,758 in January and a profit of -$3,642 in February. The company's profits for the months of March through May
were the same in each of these months. By the end of May, the company's total profits for the year were -$1,275.
What were the company's profits each month from March through May? Enter the answer in the box.
The company's profits for March through May were each -$797.
What was the company's profits for March through May?Let's start by adding the profits for January and February:
Profit for January + Profit for February = $4,758 + (-$3,642) = $1,116
We know that the company's profits for March through May were the same in each of these months, so let's call this common profit "X". Therefore, the total profit for these three months would be:
3 * X = 3X
Adding up the profits for all five months gives us the total profit for the year:
$1,116 + 3X = -$1,275
Subtracting $1,116 from both sides gives us:
3X = -$2,391
Dividing both sides by 3 gives us:
X = -$797
Therefore, the company's profits for March through May were each -$797.
Learn more about profits
brainly.com/question/15036999
#SPJ11
solve the equation |4x +9|=|6-5x|
|4x +9|=|6-5x|
4x+5x=6-9
9x=-3
x=-3/9
x=-1/3
Answer:
x = 15
x = - ⅓
Step-by-step explanation:
|4x+9| = |6-5x|
4x+9=6-5x or 4x+9=-6+5x
Lets do the first one first
4x+9=6-5x
9x=-3
x= -3/9 = -1/3
4x+9=-6+5x
15=x
So the two solutions are x = 15 and x = -⅓
This is my math hw someone help pls ?
2. Rectangle WXYZ with vertices W(-3,-4), X(0,-5), Y(-2,-11),
and Z(-5, -10); 180° rotation about N(2,-3)
The rectangle WXYZ after a 180° rotation about the point N(2,-3) is W(3,-2), X(0,-1), Y(2,5), and Z(5,4).
To perform a 180° rotation about the point N(2,-3), we can follow these steps:
1. Translate the rectangle and the point N to the origin by subtracting their respective coordinates from each vertex and point.
2. Perform the rotation by multiplying the coordinates of each vertex and point by the 2x2 rotation matrix:
[cos(180°) -sin(180°)]
[sin(180°) cos(180°)]
which simplifies to:
[-1 0]
[ 0 -1]
3. Translate the rectangle and the point N back to their original positions by adding their respective coordinates to each vertex and point.
Let's apply these steps to rectangle WXYZ and point N:
1. Translate the rectangle and point N to the origin:
W' = (-3 - 2, -4 + 3) = (-5, -1)
X' = (0 - 2, -5 + 3) = (-2, -2)
Y' = (-2 - 2, -11 + 3) = (-4, -8)
Z' = (-5 - 2, -10 + 3) = (-7, -7)
N' = (2 - 2, -3 + 3) = (0, 0)
2. Perform the rotation using the matrix:
[-1 0]
[ 0 -1]
W'' = [-1 0] * [-5, -1] = [5, 1]
[0 -1]
X'' = [-1 0] * [-2, -2] = [2, 2]
[0 -1]
Y'' = [-1 0] * [-4, -8] = [4, 8]
[0 -1]
Z'' = [-1 0] * [-7, -7] = [7, 7]
[0 -1]
N'' = [-1 0] * [0, 0] = [0, 0]
[0 -1]
3. Translate the rectangle and point N back to their original positions:
W = [5 - 2, 1 - 3] = (3, -2)
X = [2 - 2, 2 - 3] = (0, -1)
Y = [4 - 2, 8 - 3] = (2, 5)
Z = [7 - 2, 7 - 3] = (5, 4)
N = [0 + 2, 0 + 3] = (2, 3)
Therefore, the rectangle WXYZ after a 180° rotation about the point N(2,-3) is W(3,-2), X(0,-1), Y(2,5), and Z(5,4).
Learn more about "rectangle": https://brainly.com/question/25292087
#SPJ11
solve for the value of x .
80(x+15)
=60
Answer:
x = [tex]\frac{-57}{4}[/tex]
Step-by-step explanation:
solve for the value of x .
80(x+15)=60
80(x + 15) = 60
80x + 1200 - 60 = 0
80x + 1140 = 0
80x = -1140
x = -1140/80
x = [tex]\frac{-57}{4}[/tex]
Answer:
-14.25
Step-by-step explanation:
Given: 80 (x+15) = 60
Solution: On opening the brackets, we get
> 80x + 80 * 15 = 60
> 80x + 1200 = 60
Then, taking 1200 to the other side of the equation,
80x = 60 - 1200
Therefore, 80x = -1140
Now, dividing both sides by 80, we get:
80x/80 = -1140/80
So, x= -14.25
Hope this helps!
PLS HLEP AND SHOW WORK I WILL MATK BRAINLYEST
Answer:
38. (A) True
39. (B) False
Step-by-step explanation:
The set of people working in the summer consists of both female an male since there is no determiner to show that the 80% of students are a specific gender. Therefore, the answer to the first question is True (A).
My expression for finding the probability of being female and working part time in summer only is:
[tex]\frac{84}{100} \\\\ \\ \\ \\[/tex][tex](\frac{1}{2} *\frac{80}{100})\\[/tex][tex]=\frac{42}{125}[/tex] which is also equal to 0.336. Therefore the second question is false.
Please forgive me if I'm wrong but I'm open to any correction or criticisms.
Clara's class is preparing for a field trip. Her teacher purchased bottled water for the trip and asked Clara to stock a cooler with 2 bottles for every student who is going. 5 of the students didn't turn in permission slips and aren't going on the trip. So, Clara stocks the cooler with 38 bottles of water.
Which equation can you use to find the total number of students, n, in Clara's class?
The equation that can be used to find the total number of students would be n = 19 + 5.
How to find the equation ?It is acknowledged that Clara provided 2 bottles per each pupil joining her on the excursion. Denote, by using ‘x’, the quantity of learners present; we can then inscribe the succeeding formula:
2x = 38
By resolving this mathematical principal, the total number of students attending the event is revealed.
x = 38 / 2
x = 19
Currently, 19 individuals are confirmed to embark upon the outing, due to five individuals failing to furnish required consent forms and will be absent. Subsequently, we may deduce the quantity of pupils (designated as ‘n’) in Clara’s class:
n = 19 (students going on the trip ) + 5 ( students not going )
n = 19 + 5
Find out more on equations at https://brainly.com/question/25976025
#SPJ1
PLEASE HURRY DUE IN 2 HOURS
Explain how the shapes shown have been sorted.
Two groups of shapes. In group A, one shape has four equal side lengths of three, and no right angles. The opposite sides are parallel. Two shapes have two pairs of opposite equal side lengths. One shape has side lengths of four and eight. The other side lengths are three and two. Opposite sides are parallel, and there are no right angles. In group B there are three four sided shapes. One has opposite equal side lengths of seven and four and four right angles. One shape has four equal side lengths of three and four right angles. One shape has one set of opposite parallel sides and one right angle. None of the side lengths in the last shape are equal.
The image is below if you don't want to read all that, And PLEASE actually answer the question.
The figure with opposite sides are parallel and equal is parallelogram.
From the group A:
In first image opposite sides are parallel and equal.
One pair of parallel sides = 4 units and the another pair of parallel sides = 8 units
So, it is parallelogram.
In second image opposite sides are parallel and all the sides are equal.
So, it is rhombus.
In third image opposite sides are parallel and equal.
One pair of parallel sides = 3 units and the another pair of parallel sides = 2 units
So, it is parallelogram.
From the group B:
In first image opposite sides are parallel and equal.
One pair of parallel sides = 4 units and the another pair of parallel sides = 7 units and all angles measures equal to 90°.
So, it is rectangle.
In second image one pair of opposite sides are parallel.
So it is trapezium.
In third image opposite sides are parallel and all sides equal.
All angles measures equal to 90°.
So it is square.
Therefore, the figure with opposite sides are parallel and equal is parallelogram.
Learn more about the parallelogram here:
https://brainly.com/question/19187448.
#SPJ1
What kind of triangle has angles that measure 47, 70, and 63 degrees
Answer:
Acute triangle
Step-by-step explanation:
angles that are less than 90° are called acute
This triangle has 3 acute angles, so it is an acute triangle
Luis tiene una mochila de ruedas que mide 3.5 pies de alto cuando se extiende el mango. Al hacer rodar su mochila, la mano de Luis se encuentra a 3 pies del suelo. ?Qué ángulo forma su mochila con el suelo? Aproxima al grado más cercano.
The backpack forms an angle of approximately 15 degrees with the ground.
What is Pythagorean theorem?
The Pythagorean theorem is a fundamental concept in mathematics that relates to the lengths of the sides of a right triangle.
To find the angle that Luis's backpack forms with the ground, we can use the inverse tangent function.
The height of the backpack when the handle is extended is 3.5 feet, and the distance from the ground to Luis's hand is 3 feet. So the opposite side of the triangle is 3.5 - 3 = 0.5 feet, and the adjacent side is the distance from Luis's hand to the backpack, which we can call x.
Using the tangent function, we have:
tan(theta) = opposite/adjacent
tan(theta) = 0.5/x
To solve for x, we can use the Pythagorean theorem:
x² + 3² = (3.5)²
x² = 3.5² - 3²
x² = 3.25
x = sqrt(3.25)
x ≈ 1.8 feet
Now we can substitute x into our tangent equation and solve for theta:
tan(theta) = 0.5/1.8
theta = arctan(0.5/1.8)
theta ≈ 15 degrees
Therefore, the backpack forms an angle of approximately 15 degrees with the ground.
To learn more about Pythagorean theorem from the given link:
https://brainly.com/question/14930619
#SPJ1
5 points
You need to change a blown outdoor lightbulb on your house. The bulb is 5m up, but you have a 1m reach when you are on the top rung of the ladder. If you need 3m of
space off the house for the ladder's base for stability, what is the minimum height of the ladder in meters?
The minimum height of the ladder needed to change the blown outdoor lightbulb is 5 meters.
To determine the minimum height of the ladder needed to change a blown outdoor lightbulb that is 5m up, we need to consider the following terms:
1. The bulb's height (5m)
2. Your reach when on the top rung of the ladder (1m)
3. The required space off the house for the ladder's base for stability (3m)
First, subtract your reach from the bulb's height: 5m - 1m = 4m. This means the ladder needs to reach at least 4 meters up the wall.
Next, we need to use the Pythagorean theorem to find the ladder's minimum height. The theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the ladder) is equal to the sum of the squares of the lengths of the other two sides (the distance from the house and the height up the wall).
Let's denote the ladder's height as L, the distance from the house as A (3m), and the height up the wall as B (4m).
According to the Pythagorean theorem, we have:
L² = A² + B²
Substitute the values for A and B:
L² = (3m)² + (4m)²
L² = 9m² + 16m²
L² = 25m²
Now, find the square root to get the minimum height of the ladder:
L = √25m²
L = 5m
So, the minimum height of the ladder needed to change the blown outdoor lightbulb is 5 meters.
To know more about minimum height refer here:
https://brainly.com/question/15240079
#SPJ11
Which expressions are equivalent to 6\cdot6\cdot6\cdot6\cdot66⋅6⋅6⋅6⋅66, dot, 6, dot, 6, dot, 6, dot, 6 ?
The expressions equivalent to 6\cdot6\cdot6\cdot6\cdot66\cdot6\cdot6\cdot6\cdot66 are 1296\cdot396\cdot2376 and 839808\cdot36.
Find out which expression is equivalent to the given expressions?We can use the associative property of multiplication to group the factors in different ways while preserving their product. For example, we can group the first four 6's together and then multiply by the remaining 6 and 66:
6\cdot6\cdot6\cdot6\cdot66\cdot6\cdot6\cdot6\cdot66 = (6\cdot6\cdot6\cdot6)\cdot(6\cdot66)\cdot(6\cdot6\cdot66)
= 1296\cdot396\cdot2376
Alternatively, we can group the last two 6's together and then multiply by the remaining factors:
6\cdot6\cdot6\cdot6\cdot66\cdot6\cdot6\cdot6\cdot66 = (6\cdot6\cdot6\cdot6\cdot66)\cdot(6\cdot6)
= 839808\cdot36 is the equivalent expression.
Learn more about Equivalent
https://brainly.com/question/14323743
#SPJ11
Triangle PQR has vertices at the following coordinates: P(0, 1), Q(3, 2), and R(5, -4). Determine whether or not triangle PQR is a right triangle. Show all calculations for full credit.
Will give Brainliest! No links! Will report
Triangle PQR is not a right triangle.
To determine whether triangle PQR is a right triangle, we need to check if any of its angles is a right angle (90 degrees). We can use the slope formula to find the slopes of the sides of the triangle and check if any of the slopes are negative reciprocals (perpendicular) to each other.
Let's calculate the slopes of the sides PQ, QR, and RP:
Slope of PQ = (y₂ - y₁) / (x₂ - x₁)
= (2 - 1) / (3 - 0)
= 1 / 3
Slope of QR = (y₂ - y₁) / (x₂ - x₁)
= (-4 - 2) / (5 - 3)
= -6 / 2
= -3
Slope of RP = (y₂ - y₁) / (x₂ - x₁)
= (1 - (-4)) / (0 - 5)
= 5 / (-5)
= -1
Now, let's check if any of the slopes are negative reciprocals of each other. We can compare the products of the slopes:
Product of PQ slope and QR slope = (1/3) * (-3) = -1
Product of QR slope and RP slope = (-3) * (-1) = 3
Product of RP slope and PQ slope = (-1) * (1/3) = -1/3
Since the product of the slopes of QR and RP is not equal to -1, triangle PQR is not a right triangle.
Therefore, triangle PQR is not a right triangle.
Learn more about right triangle,
https://brainly.com/question/2217700
#SPJ11
PLEASE HELP MEH
A 1,700-foot support wire is attached to
the top of an 800-foot radio tower.
1,700 ft
800 ft
А
B
A scale drawing of the tower and wire is
drawn using the scale 1 inch: 250 feet.
On the scale drawing, what is the length,
in inches, of AB? (8. 1B, 8. 1F)
F
15 in.
Make sure to
use the scale.
G 7. 5 in.
H
6 in.
J 18 in.
We know that the length of AB on the scale drawing is 10 inches
Using the scale of 1 inch: 250 feet, we can find the length of AB on the scale drawing by multiplying the actual length of AB by the scale factor.
The actual length of AB is the sum of the height of the tower (800 ft) and the length of the support wire (1,700 ft), which is 2,500 ft.
Multiplying 2,500 ft by the scale factor of 1 inch: 250 feet, we get:
2,500 ft ÷ 250 ft/inch = 10 inches
Therefore, the length of AB on the scale drawing is 10 inches.
To know more about length refer here
https://brainly.com/question/9842733#
#SPJ11
Pls help, answer both of the questions with explanation.
(1) Begin with a 1-by-1 square, J. Attach squares which are half as wide (and half as tall) to the middle of each side of Jį to form J2. Attach squares half as wide as those squares to every . outer edge of J2 in order to make J3. Repeat. F F2 F3 (a) Find the area of Jg. (b) If we continue in this way forever, does the area of Joo converge? If so, what does it converge to?
Previous question
Starting with a 1-by-1 square, a sequence of squares J1, J2, J3, ... is created by attaching squares half as wide as the previous squares to the outer edges of each successive square. The area of J∞, the limit of this sequence, is 4/3.
To find the area of J1, we simply calculate the area of the original 1-by-1 square, which is 1.
To find the area of J2, we need to attach squares half as wide (and half as tall) to the middle of each side of J1. The area of each attached square is (1/2)² = 1/4, so the total area added to J1 is 4(1/4) = 1. Thus, the area of J2 is 1 + 4(1/4) = 2.
To find the area of J3, we need to attach squares half as wide as the squares added in the previous step to every outer edge of J2. The area of each attached square is (1/4)² = 1/16, so the total area added to J2 is 4(1/16) = 1/4. Thus, the area of J3 is 2 + 4(1/4) = 3.
We can continue this process to find the areas of J4, J5, and so on. In general, the area of Jn is equal to the area of the previous square plus the area added by the attached squares, which is 4(1/2^(n-1))^2 = 1/2^(2n-2). Therefore, the area of Jn is 1 + 1/4 + 1/16 + ... + 1/4^(n-1) = (4/3)(1 - 1/4^n).
As n approaches infinity, the area of Jn approaches the limit of (4/3)(1 - 0) = 4/3. Therefore, the area of J∞, the limit of the sequence, is 4/3.
For more questions like Limit click the link below:
https://brainly.com/question/12207539
#SPJ11
Let X be the number of screws delivered to a box by an automatic filling device.
Assume = 1000 and
2 = 25. There are problems with too many screws going
into the box or too few screws going into the box.
a. How many units to the right of is 1009? (5 marks)
b. What X value is 2. 6 units to the left of ? (4 marks
There are approximately 0.1480 standard deviations (or 3.7 screws) to the right of the mean when there are 1009 screws in the box. When the automatic filling device delivers 1065 screws to the box, there are approximately 2.6 standard deviations (or 65 screws) to the left of the mean.
To answer this question, we need to use the normal distribution formula.
a. To find how many units to the right of 1000 is 1009, we need to calculate the z-score:
z = (X - μ) / σ
where X = 1009, μ = 1000, and σ = 25.
z = (1009 - 1000) / 25 = 0.36
Using a standard normal distribution table or calculator, we can find that the probability of getting a z-score of 0.36 or higher is 0.3520.
To convert this probability to units to the right of the mean, we subtract it from 0.5 (which represents the area to the left of the mean):
units to the right = 0.5 - 0.3520 = 0.1480
Therefore, there are approximately 0.1480 standard deviations (or 3.7 screws) to the right of the mean when there are 1009 screws in the box.
b. To find the X value that is 2.6 units to the left of the mean, we can rearrange the formula:
X = μ - zσ
where z = -2.6 (since we want units to the left of the mean) and μ and σ are the same as before.
X = 1000 - (-2.6) * 25 = 1065
Therefore, when the automatic filling device delivers 1065 screws to the box, there are approximately 2.6 standard deviations (or 65 screws) to the left of the mean.
To know more about standard deviations refer here:
https://brainly.com/question/23907081
#SPJ11
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.
To learn more about rhombus visit the link:
https://brainly.com/question/26154016
#SPJ9
Each letter in these following problems will be transformed into a number based on their number in the alphabet. Solve these following problems based on this information.
1) n + e
2) t-j
3) d x e
4) p/b
The solution to the problems are given below:
n + e = 14 + 5 = 19t - j = 20 - 10 = 10d x e = 4 x 5 = 20p / b = 16 / 2 = 8How to solveGiving each of the letters numbers based on their numerical position on the English alphabet, we can solve below:
n (14) + e (5) = 14 + 5 = 19
t (20) - j (10) = 20 - 10 = 10
d (4) x e (5) = 4 x 5 = 20
p (16) / b (2) = 16 / 2 = 8
It can be seen that with the letter e for example is the 5th letter of the alphabet and the value is used to compute the addition of the problem.
Read more about addition here:
https://brainly.com/question/778086
#SPJ1
