The probability that randomly selected mechanical component weighs: more than 11.5 lbf is 0.0099, less than 8.7 lbf is 0.3208, less than 5.0 lbf is 0.0228, between 6.2 lbf and 7.0 lbf is 0.1314, between 10.3 lbf and 14.0 lbf is 0.0436, between 6.8 lbf and 8.9 lbf is 0.3464.
We can use the standard normal distribution and z-scores to answer these questions:
P(X > 11.5) = P(Z > (11.5 - 8) / 1.5) = P(Z > 2.33) = 0.0099
Therefore, the probability that a randomly selected mechanical component weighs more than 11.5 lbf is 0.0099, or about 1%.
P(X < 8.7) = P(Z < (8.7 - 8) / 1.5) = P(Z < 0.47) = 0.3208
Therefore, the probability that a randomly selected mechanical component weighs less than 8.7 lbf is 0.3208, or about 32%.
P(X < 5.0) = P(Z < (5 - 8) / 1.5) = P(Z < -2) = 0.0228
Therefore, the probability that a randomly selected mechanical component weighs less than 5.0 lbf is 0.0228, or about 2%.
P(6.2 < X < 7.0) = P((6.2 - 8) / 1.5 < Z < (7 - 8) / 1.5) = P(-1.2 < Z < -0.67) = 0.1314
Therefore, the probability that a randomly selected mechanical component weighs between 6.2 lbf and 7.0 lbf is 0.1314, or about 13%.
P(10.3 < X < 14.0) = P((10.3 - 8) / 1.5 < Z < (14 - 8) / 1.5) = P(1.53 < Z < 2.67) = 0.0436
Therefore, the probability that a randomly selected mechanical component weighs between 10.3 lbf and 14.0 lbf is 0.0436, or about 4%.
P(6.8 < X < 8.9) = P((6.8 - 8) / 1.5 < Z < (8.9 - 8) / 1.5) = P(-0.47 < Z < 0.60) = 0.3464
Therefore, the probability that a randomly selected mechanical component weighs between 6.8 lbf and 8.9 lbf is 0.3464, or about 35%.
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____The given question is incomplete, the complete question is given below:
Suppose that the weight of a mechanical component is normally distributed with mean p = 8.0 Ibf and standard deviation = 1.5 lbf. Answer the following questions: 1. If you randomly select a mechanical component, what is the probability that it weighs more than 11.5 lbf? 2. If you randomly select a mechanical component, what is the probability that it weighs less than 8.7 lbf? 3. If you randomly select a mechanical component, what is the probability that it weighs less than 5.0 lbf? 5. If you randomly select a mechanical component, what is the probability that it weighs between 6.2 lbf and 7.0 lbf? 6. If you randomly select a mechanical component, what is the probability that it weighs between 10.3 lbf and 14.0 lbf? 7. If you randomly select a mechanical component, what is the probability that it weighs between 6.8 lbf and 8.9 lbf?
Calculate the area of a triangle XYZ with
angle X = 90°, XZ = 15 cm and XY = 12 cm
The area of the right triangle with side lengths of 15cm and 12cm is 90 cm².
What is the area of the triangle ?The area of triangle can be determined using the equation;
Area = 1/2 × base × height.
The angle described forms a right-triangle.
Height of the triangle = XZ = 15cmBase of the triangle = XY = 12cmAngle X = 90°Area A = ?Area = 1/2 × base × height
Area = 1/2 × 12cm × 15cm
Area = 6cm × 15cm
Area = 90 cm²
Therefore, the area of the triangle is 90 cm².
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I really need help with this quetion, this would really help
The estimate for the mean book thickness is 3.2 mm.
What is mean?
In arithmetic, mean is the sum of all the added values of all the data in a set divided by the number of data in the set.
To find the mean book thickness, we can use the formula for the mean (also known as the average):
mean = (sum of all data points) / (number of data points)
Since we don't have the exact thickness of each book, but rather intervals of thickness and the number of books in each interval, we can use a weighted mean to estimate the mean thickness.
Here is the calculation:
First, we'll find the midpoint of each interval:
Interval 1: [0, 2] -> midpoint: x1 = 1
Interval 2: [2, 4] -> midpoint: x2 = 3
Interval 3: [4, 6] -> midpoint: x3 = 5
Next, we'll find the weight of each interval by multiplying the midpoint by the frequency:
Interval 1: x1 * f1 = 1 * 5 = 5
Interval 2: x2 * f2 = 3 * 8 = 24
Interval 3: x3 * f3 = 5 * 7 = 35
Finally, we'll sum up the weights and divide by the total frequency to find the weighted mean:
Weighted mean = (5 + 24 + 35) / (5 + 8 + 7) = 64 / 20 = 3.2
So, the estimate for the mean book thickness is 3.2 mm.
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A study shows that at the end of a school day teenagers typically have 40% of their cell phone battery left when plugged in phone charge at a rate of 3% per minute when using the newest fast charger.
a: write an inequality to represent how many more minutes are needed to reach at least 80% battery life.
b. use the inequality to determine the how many more minutes it will take to have at least 80% battery life
The inequality that represents the more minutes needed to reach 80% of the battery is 3x + 40 ≤ 80. And the number of minutes will be 13.33 minutes.
What is inequality?Inequality is defined as an equation that does not contain an equal sign.
The linear equation is given as,
y = mx + c
Where m is the slope of the line and c is the y-intercept of the line.
Let 'x' be the number of minutes and 'y' be the total battery percentage. Then the equation is given as,
y = 3x + 40
The inequality that represents the more minutes are needed to reach 80 of battery is given as,
3x + 40 ≤ 80
Simplify the inequality, then we have
3x + 40 ≤ 80
3x ≤ 40
x ≤ 13.33 minutes
The inequality that represents the more minutes needed to reach 80% of the battery is 3x + 40 ≤ 80. And the number of minutes will be 13.33 minutes.
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Please help with this question!!
According to the information, we plan to have cruising speed on for a minimum of 3 hours and a maximum of 4.1 hours.
How to calculate how many hours we are going to have the cruising speed on?To calculate how many hours we are going to have the cruising speed on we must carry out the following process:
To calculate the minimum we must subtract 35 from 215 and then divide by the speed:
215 - 35 = 180180 / 60 = 3So the minimum hours would be 3 hours.
On the other hand, to calculate the maximum we must add 35 to 215 and divide it by the speed:
215 + 35 = 250250 / 60 = 4.1So the maximum time would be 4.1 hours.
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A basketball player plays for 30 out of 48 minutes in a game. She sits on the bench the rest of the game. What percentage of the game did the player sit on the bench?
Answer:5/8
Step-by-step explanation: you put the numbers in a fraction the smallest goes on top and the more enormous number at the bottom you simply by finding the most significant standard number between the 2 numbers which is in this case 6 divide it by that and that is how you get your answer
I have 2 questions. 1.If the Percent of Discount is 80% and the Sale Price is $90 then what is the Original Price? 2. If the Percent of Discount is 15% and the Sale Price is $146.54 then what is the Original Price? HELP ME PLEASE!!???
The requried solutions are as follows,
(1) the original price is $450. (2) the original price is $172.40.
Sale price is defined as the price of a product marked including of various price cut such as discounts.
Here,
If the percent of discount is 80% and the sale price is $90, we can use the following formula to find the original price x (let)
Sale price = Original price - Discount
$90 = x - 0.8x
Simplifying the right-hand side:
$90 = 0.2x
x = $450
Therefore, the original price is $450.
If the percent of discount is 15% and the sale price is $146.54, we can use the same formula:
Sale price = Original price - Discount
$146.54 = x - 0.15x
Simplifying the right-hand side:
$146.54 = 0.85x
x = $172.40
Therefore, the original price is $172.40.
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help me please help help
The equation that can be used to find the number of gardens that Kalisa welds is given as follows:
200 + 5.5w = 260.50.
How to construct the equation?Kalisa's earnings are divided as follows:
Mows 8 lawns for $25 each -> total of 25 x 8 = $200.Welds w gardens for $5.5 each -> total of 5.5w.Hence the equation for the total earnings is constructed follows:
T(w) = 200 + 5.5w.
Her total earnings are of $260.50, hence the number of gardens that Kalisa welds is given as follows:
200 + 5.5w = 260.50.
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The price of a plane ticket from a certain city to another increased from 700 to 840. Find the percent of increase
The percent of increase in price is 20 %
A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100. The proportion therefore refers to a component per hundred. Per 100 is what the word percent means. The letter "%" stands for it.
Percentage formula = (Value/Total value) × 100
increase 700 to 840
old price is 700
new price is 840
price increase is 840 - 700
=140
percentage increase in price is
= 140*100/700= 20 percentage
Percentage formula = (Value/Total value) × 100
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Katya sold
46 books at £1.40 each
32 bracelets at £1.50 each
some badges at 90p each
She got a total of £134
Work out how many badges Katya sold.
Answer:
This is a math problem. To solve it, you need to use algebra. Let me show you how.
Let x be the number of badges Katya sold. Then we can write an equation using the given information:
46 × 1.40 + 32 × 1.50 + 0.90 × x = 134
Simplifying the equation, we get:
64.4 + 48 + 0.9x = 134
Subtracting 64.4 and 48 from both sides, we get:
0.9x = 21.6
Dividing both sides by 0.9, we get:
x = 24
Therefore, Katya sold 24 badges.
Step-by-step explanation:
what fraction is equivalent to 3/5
Answer:15/25
Step-by-step explanation:
In any set of positive integers the replacement of a set of three 2s with a set of two threes will not change the sum
The statement is incorrect. The replacement of three 2s with two threes will change the sum.
For example, consider the set {2, 2, 2}. The sum of this set is 6. However, if we replace three 2s with two threes, the new set becomes {3, 3}, and its sum is 6, which is different from the original sum. Hence, replacing a set of three 2s with a set of two threes does change the sum. An integer is a whole number that can be positive, negative, or zero. Integers are numbers that don't have any fractional or decimal component. Some examples of integers are: -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, and so on. The set of integers is denoted by the symbol "Z", which stands for Zahlen, the German word for "numbers". Integers are an important mathematical concept used in many branches of mathematics and science, including algebra, number theory, and computer science.
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Complete Question
In any set of positive integers the replacement of a set of three 2s with a set of two threes will not change the sum" State whether the statement was correct or incorrect.
Which equations are true for the values of x, y, and z? Select three options.
2 lines intersect to form 4 angles. Clockwise, from top, the angles are: 65 degrees, x, y, z.
The equations that are true of the values x, y, and z are :
x degrees + 65 degrees = 180 degreesx degrees = z degreesy degrees = 65 degreesHow to find the equations ?The line that x degrees and 65 degrees is on, is a straight line which means that they will both add up to 180 degrees :
x degrees + 65 degrees = 180 degrees
x and z are congruent angles which means they are both the same angle measure.
y would be equal to 65 degrees because, just like x and z, y and 65 degrees are congruent.
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Options include:
x degrees + 65 degrees = 180 degreesx degrees = z degreesy degrees = 65 degreesx degrees= 65 degreesx degrees + y degrees + z degrees = 115 degreesLog_6 x + log_6 3 = log_6 (x+1)
The solution to the equation log_6 x + log_6 3 = log_6 (x+1) is x = 1/2.
Explain:
We can reduce the complexity of the left side of the equation by using the logarithmic identity log a + log b = log (ab):
Log6 x plus Log6 3 equals Log6 (3x)
When we add this to the initial equation, we obtain:
Log6 (3x) equals Log6 (x+1).
Because logarithms have the one-to-one property, we can drop the logarithm on both sides to get the following results:
3x = x + 1
When we simplify this equation, we obtain:
2x = 1
x = 1/2
As a result, x = 1/2 is the answer to the equation log 6 x + log 6 3 = log 6 (x+1).
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Find the value of x =
Answer:
360-137+x+y
Step-by-step explanation:
at this point of contact, is the number of field lines per unit of balloon surface area equal to the number of field lines per unit of box surface area?
a) The electric field magnitude on the balloon surface will be different from the electric field magnitude on the box surface.
b) the electric field lines intersect with the planar surface of the box, the field lines will be compressed or spread out depending on the angle of incidence.
At the point of contact between the spherical balloon and the wall of the cubical box, the electric field magnitude will not be the same on both surfaces. This is because the surface of the balloon is spherical, while the surface of the box is planar. The electric field lines emanating from the charged ball will be spherically symmetric around the ball and perpendicular to the surface of the balloon. However, when the electric field lines intersect with the planar surface of the box, the field lines will be distorted due to the change in direction of the surface. As a result, the electric field magnitude on the balloon surface will be different from the electric field magnitude on the box surface.
At the point of contact, the number of field lines per unit area will also be different for the balloon surface and the box surface. The electric field lines from the charged ball will be distributed uniformly over the surface of the spherical balloon, so the number of field lines per unit area will be constant over the entire surface. However, when the electric field lines intersect with the planar surface of the box, the field lines will be compressed or spread out depending on the angle of incidence. Therefore, the number of field lines per unit area on the box surface will not be the same as the number of field lines per unit area on the balloon surface.
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Question:
A small charged ball is suspended at the center of a spherical balloon that is nestled snugly inside a cubical cardboard box. On one side, the balloon touches the wall of the box. (a) At this point of contact, is the electric field magnitude on the balloon surface equal to the electric field magnitude on the box surface? Assume neither object is polarized. (b) At this point of contact, is the number of field lines per unit of balloon surface area equal to the number of field lines per unit of box surface area?
A rectangle that has an area of 357 square inches is 17 inches wide. Using the formula for area ( A = lw), how long is the rectangle?
a. 21 inches
b. 340 inches
c. 20 inches
d. 15 inches
The length of the rectangle given the area and width is 21 inches
What is the length of the rectangle:Area of the rectangle = 357 square inches
Width of the rectangle = 17 inches
Length of the rectangle= l
Area of a rectangle = Length × width
357 = l × 17
357 = 17l
divide both sides by 17
l = 357 / 17
l = 21 inches
In conclusion, 21 inches is the length of the rectangle.
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33.3% and 0.3 as a fraction
0.3 as a fraction would be 3/10
33.3 would be 333/10
To check it so 3 ÷ 10 and 333 ÷ 10
It will give you the decimal again.
Step-by-step explanation:You're welcome.
Answer: the answer is 33.3 is 33 3/10 and 0.3 is 3/10
Step-by-step explanation:
you welcome (ﾉ◕ヮ◕)ﾉ*:･ﾟ✧
ime taken by a randomly selected applicant for a mortgage to fill out a certain form has a normal distribution with mean value 10 min and standard deviation 3 min. if five individuals fill out a form on one day and six on another, what is the probability that the sample average amount of time taken on each day is at most 11 min? (round your answer to four decimal places.)
The probability that the sample average amount of time taken on each day is at most 11 min:
P([tex]\bar{X_1}[/tex] < 11) = 0.8682
P([tex]\bar{X_2}[/tex] < 11) = 0.8897
We know that the formula for the z-score is:
[tex]z=\frac{x-\mu}{\sigma}[/tex]
Let X be the time taken by a randomly selected applicant for a mortgage to fill out a certain form
[tex]\mu_x[/tex] = 10
[tex]\sigma_x[/tex] = 2
Here, five individuals fill out a form on one day and six on another.
This means that the population is the same on both days, but the samples of different sizes.
On Day 1 the average[tex]\bar{X_1}[/tex] ∼Norm(10, 2/[tex]\sqrt{5}[/tex])
We find the probability using z-score.
The probability that the sample average amount of time taken on day 1 is at most 11 min:
P([tex]\bar{X_1}[/tex] < 11)
=[tex]P(\frac{\bar{X_1}-10}{(\frac{2}{\sqrt{5} } )} < \frac{11-10}{(\frac{2}{\sqrt{5} } )})[/tex]
= P(z < 1.118)
= 0.8682
Similarly, on Day 2 the average[tex]\bar{X_1}[/tex] ∼Norm(10, 2/[tex]\sqrt{6}[/tex])
So the probability that the sample average amount of time taken on day 1 is at most 11 min:
P([tex]\bar{X_2}[/tex] < 11)
=[tex]P(\frac{\bar{X_2}-10}{(\frac{2}{\sqrt{6} } )} < \frac{11-10}{(\frac{2}{\sqrt{6} } )})[/tex]
= 0.8897
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The complete question is:
The time taken by a randomly selected applicant for a mortgage to fill out a certain form has a normal distribution with mean value 10 min and standard deviation 2 min. If five individuals fill out a form on one day and six on another, what is the probability that the sample average amount of time taken on each day is at most 11 min?
PLEASE HELP!!!!!!!!!
1. y=-x^2+2 what is the
Domain:
Range:
Vertex:
Axis of symmetry:
y intercepts:
2. y=x^2-6x+3 What is the:
Domain:
Range:
Vertex:
Axis of symmetry:
y intercepts:
3: y=-2x^2-8x-5 What is the:
Domain:
Range:
Vertex:
Axis of symmetry:
y intercepts:
4. f(x)=-x^2+1 What’s the:
Domain:
Range:
Vertex:
Axis of symmetry:
y intercepts:
5. f(x)=-2x^2+8x-3 What’s the:
Domain:
Range:
Vertex:
Axis of symmetry:
y intercepts:
6. f(x)=2x^2+8x+1 what’s the:
Domain:
Range:
Vertex:
Axis of symmetry:
y intercepts:
A pole 6 feet tall is used to support a guy wire for a tower, which runs from the tower to a metal stake in the ground. After placing the pole, Ian measures the distance from the pole to the stake and from the pole to the tower, as shown in the diagram below. Find the length of the guy wire, to the nearest foot.
Answer:
here you go
Step-by-step explanation:
A guy wire runs from the top of a cell tower to a metal stake in the ground. Emily places a 10-foot tall pole to support the guy wire. After placing the pole, Emily measures the distance from the stake to the pole to be 11 ft: She then measures the distance from the pole to the tower to be 23 ft: Find the length of the guy wire, to the nearest foot.
The two triangles are congruent. Solve for x. Then find all missing angles.
(I found x but I don’t know how to figure out y)
Using the definition of congruent triangles, the missing values are:
x = 35
y = 30°
What are Congruent Triangles?Given that the two triangles in the image above are congruent, it implies that all its corresponding angles and corresponding side lengths have equal measure.
Therefore, we have:
2x - 10 = x + 25
Solve for x:
2x - x = 10 + 25
x = 35
Plug in the value of x to find the missing angles:
y + 90 + (2x - 10) = 180 [triangle sum theorem]
y + 90 + (2(35) - 10) = 180
y + 90 + 60 = 180
y = 30°
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for each pair of number, determine by what percent the second number is greater than the first. also determined by what percent the first number is less than the second 5 and 10
To get by what percent the second number (10) is greater than the first number (5), we can use the following formula:
percent increase = ((new value - old value) / old value) x 100%
So, for the pair of numbers 5 and 10:
percent increase = ((10 - 5) / 5) x 100% = 100%
This means that 10 is 100% greater than 5.
To determine by what percent the first number (5) is less than the second number (10), we can use the following formula:
percent decrease = ((old value - new value) / old value) x 100%
So, for the pair of numbers 5 and 10:
percent decrease = ((10 - 5) / 10) x 100% = 50%
This means that 5 is 50% less than 10.
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Is -y/4 = 2x -5 linear
trinomio cuadrado perfecto
[tex]\alpha^{3} -10\alpha ^{\frac{3}{2} } +25[/tex]
61. Detecting a Speeder A policewoman has positioned herself
500 ft from the intersection of two roads. She has carefully
measured the angles of the lines of sight to points A and B as
shown in the drawing. If a car passes from A to B in 1.75 sec
and the speed limit is 55 mph, is the car speeding?
HINT Find the distance from B to A and use R = D/T.
The Distance between A, B based on the information will be 28.705 feet
How to calculate the distanceFrom the information, the policewoman has positioned herself 500 ft from the intersection of two roads and she has carefully measured the angles of the lines of sight to the points.
Distance between A, B will be:
= 500 tan(15.4) - 500 tan(12.3)
= 500 (tan 15.4 - tan 12.3)
= 500(0.0574)
= 28.705 feet
The speed will be:
= 28.705 / 1.75
= 16.403 ft/s
= 12.3 mph
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The expression 2.2x + 8 represents the number of miles Trent jogged during a race and 5x represents the number of miles that Ling jogged during the same race in x hours. Write and expression to show how many more miles did Ling Jog than Trent?
The number of miles Ling Jog than Trent can be written as the expression 2.8x - 8
How many more miles did Ling Jog than Trent?Trent's expression:
2.2x + 8
Ling's expression:
5x
Where,
Number of hours= x
Number of hours Ling Jog than Trent =Ling's expression - Trent's expression
= 5x - (2.2x + 8)
= 5x - 2.2x - 8
= 2.8x - 8
Therefore, Ling jog 2.8x - 8 miles than Trent.
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{y=−2x+1
{4x+y=9
i need help
Based on the given simultaneous equation, the value of x=-4 whereas the value of y=-7
What is meant by simultaneous equations?Two or more algebraic equations that share variables, such as x and y, are referred to as simultaneous equations.
Because the equations are solved simultaneously, they are referred to as simultaneous equations.
Here are some examples of simultaneous equations:
2x + 4y = 14
4x 4y = 4
6a + b = 18
4a + b = 14
3h + 2i = 8
2h + 5i =10
Each of these equations could have an infinite number of solutions.
However, if we have at least as many equations as variables, we may be able to solve them using simultaneous equations methods.
So, given
{y=−2x+1
{4x+y=9
-4x+y=9 get y alone
add 4x both sides
y=4x+9
insert into y=2x+1
2x+1=4x+9
subtract 1 both sides
2x=4x+8
subtract 4x both sides
-2x=8
divide by -2
x=-4
y=2x+1
y=2(-4)+1
y=-8+1
y=-7
check
-4(-4)+(-7)=9
16+(-7)=9
9=9
x=-4
y=-7
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For which pair of functions f(x) and g(x) below will the limit as x goes to infinity of the quotient of f of x and g of x equals 0 ?
f(x) = ex; g(x) = x2
f(x) = ex; g(x) = ln(x)
f(x) = ln(x); g(x) = ex
f(x) = x; g(x) = ln(x)
The pair of functions f(x) and g(x) below that equals 0 as the limit as x goes to infinity of the quotient of f of x and g of x will be C. f(x) = ln(x); g(x) = ex
How to explain the informationFor the limit of the quotient of f(x) and g(x) to equal 0 as x approaches infinity, it is necessary for f(x) to grow more slowly than g(x).
Out of the options given, the only pair of functions where this is true is f(x) = ln(x) and g(x) = ex. As x approaches infinity, ex grows much faster than ln(x), so the limit of the quotient of these two functions as x approaches infinity is 0.
In conclusion, the correct option is C.
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Leanne's Nursery buys crates of firewood to deliver to customers over the winter. Each crate
measures 4 feet long, 3.5 feet wide, and 4 feet high. How much storage space does the nursery
need for the wood if 60 crates are delivered in an order?
OA 675 cubic feet
OB 3,375 cubic feet
OC 3,937.5 cubic feet
OD 3,360 cubic feet
The volume of storage space that the nursery needs for the wood if 60 crates are delivered in an order is; D: 3360 cubic feet
How to find the total volume of a cuboid?The formula for volume of a cuboid is;
Volume = Length * width * height
We are given;
Length = 4 feet
Width = 3.5 ft
Height = 4 ft
Thus;
Volume of one crate = 4 * 3.5 * 4
= 56 cubic ft
We need a total of 60 crates. Thus;
Total Volume = 60 * 56
Total volume = 3,360 cubic feet
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A quilter created the following shape to use in a block for a new quilt. What is the area of the shape for the quilt block?
The area of the shape for the quilt block is 166.5 in²
What is an area?The area is the region bounded by the shape of an object. The space covered by the figure or any two-dimensional geometric shape, in a plane, is the area of the shape
Given that, a quilt has blocks of design on it, we need to find the area of the block,
To find the area of the block = sum of the areas of the right triangle and the rectangle,
Area of the block = 16 × 9 + 6 × 7.5 × 1/2 = 166.5 in²
Hence, the area of the shape for the quilt block is 166.5 in²
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The figure is unavailable is the question is solved for the figure attached
