Answer:
P =26%
Step-by-step explanation:
In this problem we have the ages of all new employees hired during the last 10 years of normally distributed.
We know that the mean is [tex]\mu = 35[/tex] years and standard deviation is [tex]\sigma = 10[/tex] years
By definition we know that if we take a sample of size n of a population with normal distribution, then the sample will also have a normal distribution with a mean
[tex]\mu_m = \mu[/tex]
And with standard deviation
[tex]\sigma_m = \frac{\sigma}{\sqrt{n}}[/tex]
Then the average of the sample will be
[tex]\mu_m = 35\ years[/tex]
And the standard deviation of the sample will be
[tex]\sigma_m =\frac{10}{\sqrt{10}} = 3.1622[/tex]
Now we look for the probability that the mean of the sample is greater than or equal to 37.
This is
[tex]P({\displaystyle{\overline {x}}}\geq 37)[/tex]
To find this probability we find the Z-score
[tex]Z = \frac{{\displaystyle{\overline{x}}} -\mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
[tex]Z = \frac{37 -35}{\frac{10}{\sqrt{10}}} = 0.63[/tex]
So
[tex]P({\displaystyle{\overline {x}}}\geq 37) = P(\frac{{\displaystyle{\overline {x}}}-\mu}{\frac{\sigma}{\sqrt{n}}}\geq\frac{37-35}{\frac{10}{\sqrt{10}}}) = P(Z\geq0.63)[/tex]
We know that
[tex]P(Z\geq0.63)=1-P(Z<0.63)[/tex]
Looking in the normal table we have:
[tex]P(Z\geq0.63)=1-0.736\\\\P(Z\geq0.63) = 0.264[/tex]
Finally P = 26%
To find the probability that the sample mean age of 10 employees is at least 37, we can use the Central Limit Theorem and standardize the sample mean. The probability is approximately 2.28%.
Explanation:To solve this problem, we need to use the Central Limit Theorem, which states that the sample mean of a large enough sample size will be approximately normally distributed regardless of the shape of the population distribution.
In this case, the mean age of new employees is normally distributed with a mean of 35 and a standard deviation of 10. We want to find the probability that the sample mean age of 10 employees is at least 37.
To find this probability, we first need to standardize the sample mean using the formula z = (x - μ) / (σ / sqrt(n)), where x is the sample mean, μ is the population mean, σ is the population standard deviation, and n is the sample size.
Using this formula, we have z = (37 - 35) / (10 / sqrt(10)) = 2 * sqrt(10).
From a standard normal distribution table, we can find that the probability of getting a z-score less than 2 * sqrt(10) is approximately 1 - 0.0228 = 0.9772. However, we want the probability of getting a sample mean at least 37, so we subtract this probability from 1 to get 1 - 0.9772 ≈ 0.0228.
Therefore, the probability that the sample mean age of 10 employees will be at least 37 is approximately 2.28%.
Solve equation 5(n-4) = -60
Answer:
n = -8
Step-by-step explanation:
The variable has 4 subtracted and that quantity is multiplied by 5. You can find the value of the variable by reversing these operations, in reverse order. That means you first divide both sides of the equation by 5:
5(n-4)/5 = -60/5
n -4 = -12 . . . . . . simplify
Then you undo the subtraction of 4. You accomplish that by adding 4 to both sides of the equation.
n -4 +4 = -12 +4
n = -8 . . . . . . . . . simplify
_____
This equation can also be solved by first eliminating parentheses. Then you have
5n -20 = -60
Now, the variable is multiplied by 5, then 20 is subtracted from the sum. Reversing these operations in reverse order, we first add 20 to both sides of the equation:
5n -20 +20 = -60 +20
5n = -40 . . . . . . . . . . . . . simplify
Then we undo the multiplication by dividing both sides of the equation by 5:
n = -8
_____
The rule to remember is "whatever you do to one side of the equation must also be done to the other side". This is what keeps the equal sign valid.
Answer:
n = - 8
Step-by-step explanation:
There are 2 possible approaches to solving this question
method 1
5(n - 4) = - 60 ( divide both sides by 5 )
n - 4 = - 12 ( add 4 to both sides )
n = - 8
method 2
5(n - 4) = - 60 ( distribute left side )
5n - 20 = - 60 ( add 20 to both sides )
5n = - 40 ( divide both sides by 5 )
n = - 8
what is angle COD????
Given a straight line segment AB with points A, O, and B, and angle measures <COA, <COD, and <DOB, we find <COD to be 45 degrees using angle sum properties.
In the given scenario, we have a straight line segment AB, and points O, A, and B lying on it. We are required to find the measure of angle COD, denoted as <COD. According to the information provided, <COA is (3x + 94), <COD is (x + 36), and <DOB is (2x - 4).
Since A, O, and B are collinear, the sum of the angles around point O must be 180 degrees. Therefore, <COA + <COD + <DOB = 180 degrees. Substituting the given angle measures into the equation, we get:
(3x + 94) + (x + 36) + (2x - 4) = 180.
Combining like terms and solving for x:
6x + 126 = 180,
6x = 54,
x = 9.
Now that we have the value for x, we can find <COD by substituting it into the expression (x + 36):
<COD = 9 + 36 = 45 degrees.
Therefore, the measure of angle COD is 45 degrees.
Given: The measure of arc EY = The measure of arc YI, m∠EXY = 80°, and m∠K = 25°.
Find: The measure of arc EI.
PLEASE HELP ME WITH A PROBLEM FROM MY GEOMETRY HOMEWORK AS SOON AS POSSIBLE THANK YOU SO MUCH!!!
Kyle.
Let [tex]x=m\widehat{EY}=m\widehat{YI}[/tex]. By the inscribed angle theorem, we have
[tex]m\angle EJI=\dfrac12m\angle EOI=\dfrac12m\widehat{EI}=\dfrac{m\widehat{EY}+m\widehat{YI}}2=x^\circ[/tex]
Then
[tex]m\angle KJE=(180-x)^\circ[/tex]
Also by the inscribed angle theorem, we have
[tex]m\angle ELY=\dfrac12m\angle EOY=\dfrac12m\widehat{EY}=\left(\dfrac x2\right)^\circ[/tex]
so that
[tex]m\angle KLX=\left(180-\dfrac x2\right)^\circ[/tex]
Angles EXY and LXJ form a vertical pair so they are congruent and both have measure [tex]80^\circ[/tex].
The sum of the interior angles to any quadrilateral is [tex]360^\circ[/tex], so for quadrilateral KLXJ we get
[tex]25^\circ+\left(180-\dfrac x2\right)^\circ+(180-x)^\circ+80^\circ=360^\circ\implies x^\circ=70^\circ[/tex]
So,
[tex]m\widehat{EI}=2x^\circ=\boxed{140^\circ}[/tex]
Answer:
Step-by-step explanation:
Let . By the inscribed angle theorem, we have
Then
Also by the inscribed angle theorem, we have
so that
Angles EXY and LXJ form a vertical pair so they are congruent and both have measure .
The sum of the interior angles to any quadrilateral is , so for quadrilateral KLXJ we get
So,
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Find the length of AB. Leave your answer in terms of pi
Answer:
14.7π
Step-by-step explanation:
The length of the arc is calculated as
arc AB = circumference × fraction of circle
= 2π × 6 × [tex]\frac{140}{360}[/tex]
= [tex]\frac{12(140)\pi }{360}[/tex] = 14.7 π
HURRY!!!!!!
I neeeed helpif you help ill put you on my stream maybe!!!
Answer:
Q1. is 628 cm
Q2 18.84 cm
Step-by-step explanation:
Q1. 400 / 2 = 200 to get the radius
3.14 * 200 = 628
Q2. 12 / 2 = 6 to get the radius
31.4 * 6 = 18.84
What did cicero mean by delivery
cicero meant to transfer something to someone .
Answer:
Body language and vocal technique
Step-by-step explanation:
Which description best fits the distribution of the data
shown in the histogram?
A. The mean is greater than the median.
B. The mean and median are approximately the same
C. The mean is less than the median
Answer:
The correct option is A.
Step-by-step explanation:
From the given histogram it is clear that it is right skewed or positive skewed distribution because the tail is stretched toward right.
Negative skewed: Mean < Median < Mode
No skewed: Mean = Median = Mode
Positive skewed: Mean > Median > Mode
Since the given histogram is positive skewed distribution, therefore mean is greater than the median.
Hence the correct option is A.
What is the LCD of 3/4 and 7/10
the LCD is 20
[tex] \frac{3}{4} \times \frac{5}{5} = \frac{15}{20} \\ \\ \frac{7}{10} \times \frac{2}{2} = \frac{14}{20} [/tex]
ABCD is a square.
What is the length of line segment DC?
5 units
7 units
11 units
13 units
It can be any of these. We cannot actually say without knowing the length of any of the other sides.
Answer:
D. 13 units
Step-by-step explanation:
Which table represents a linear function
It is the first one because the X side is going up at a steady rate and the Y is also going up at a steady rate
From the given table, table 1 represents the linear function.
Rate of change can be used to detect a linear function.
We can calculate rate of change to check whether the given coordinates represent linear relationship or not.
Formula used to calculate rate of change, m
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex].......................................................1
For table 1:
Calculating value of m using eq 1 for points (2,7) and (4,9)
[tex]m=\dfrac{9-7}{4-2}\\\\m=1[/tex]
Similarly,
Calculating value of m using eq 1 for points (6,8) and (11,13)
m=1
Slope remains same. So, it shows linear relationship.
For table 2:
Calculating value of m using eq 1 for points (1,7) and (2,9)
[tex]m=\dfrac{9-7}{2-1}\\\\m=2[/tex]
Similarly,
Calculating value of m using eq 1 for points (3,12) and (4,15)
m=3
Value of slope changes from 2 to 3. Thus, it does not show linear relationship.
For table 3:
Calculating value of m using eq 1 for points (1,7) and (2,11)
[tex]m=\dfrac{11-7}{2-1}\\\\m=4[/tex]
Calculating value of m using eq 1 for points (3,12) and (4,13)
m=1
Value of slope changes from 4 to 1. Thus, it does not show linear relationship.
For table 4:
Calculating value of m using eq 1 for points (2,7) and (4,9)
[tex]m=\dfrac{9-7}{4-2}\\\\m=1[/tex]
Calculating value of m using eq 1 for points (6,12) and (8,15)
m=3/2
Value of slope changes from 1 to 3/2. Thus, it does not show linear relationship.
So, the Slope of table 1 is the same for all the coordinates. Thus, table 1 represents a linear function.
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PLZZZ HELP ASAP!!!!!!!!!!!!!!!!It is a 75 mile trip to your grandparent's house. Which divisibility rule proves that 75 is an odd number? A) divisibility by 1 B) divisibility by 2 C) divisibility by 3 D) divisibility by 5
Divisibility by 2 would be the correct answer. Two is an even number, and the only listed at that. Odd numbers are only divisible by another odd number. Hope I helped you !
Answer:
the answer is B) divisibility by 2
Step-by-step explanation:
I got the answer on the USA test prep.
thanks for your help with brainly
which two numbers are solutions of 2n - 15≤ = -3
×║thank you║×
Answer:
n ≤ 6
Step-by-step explanation:
2n - 15 ≤ -3
Add 15 to both sides.
2n ≤ 12
Divide both sides by 2.
n ≤ 6
The solution of this inequality is any number less than or equal to 6. There is an infinite number of solutions. Since you are asked to pick two numbers that are solutions, I assume you have choices that were given. Look at the choices, and pick any number less than 6 and 6 itself if it is a choice.
The answer for which two numbers are solutions of 2n - 15≤ = -3
Is n≤ 6
Evaluate the expression.
8^7/8^7
The value of the expression (8^7)/(8^7) is 1.
The expression (8^7)/(8^7) can be simplified using the properties of exponents. According to the quotient rule of exponents, when dividing two numbers with the same base, the exponents are subtracted. In this case:
(8^7)/(8^7) = 8^(7-7) = 8^0
Any non-zero number raised to the power of 0 is equal to 1, according to the fundamental property of exponentiation. Therefore, the value of the expression (8^7)/(8^7) is 1.
Hence, the value of the expression (8^7)/(8^7) is 1.
By applying the quotient rule of exponents, we simplify the expression to 1, reflecting the property of exponentiation where any non-zero number raised to the power of 0 equals 1.
A recipe requires 1/4 cup of oil for every 2/3 cup of water. How much oil (in cups) is needed per cup of water?
Answer:
[tex]\frac{3}{8}[/tex] cups of oil
Step-by-step explanation:
Given : A recipe requires 1/4 cup of oil for every 2/3 cup of water.
To Find: How much oil (in cups) is needed per cup of water?
Solution:
Oil required by [tex]\frac{2}{3}[/tex] cup of water = [tex]\frac{1}{4}[/tex]
Oil required by 1 cup of water = [tex]\frac{\frac{1}{4}}{\frac{2}{3}}[/tex]
= [tex]\frac{3}{8}[/tex]
Hence [tex]\frac{3}{8}[/tex] cups of oil is needed for per cup of water.
The oil required for one cup of water is 3/8 cup.
How do you calculate the quantity of oil?Given that a recipe requires 1/4 cup of oil for every 2/3 cup of water.
The quantities of oil and water are given in fractions. We can write as,
[tex]\dfrac {1}{4}cup \; oil = \dfrac {2}{3} cup\;water[/tex]
[tex]1 cup\;water = \dfrac {\dfrac {1}{4}cup\;oil}{\dfrac{2}{3}}[/tex]
[tex]1cup\;water = \dfrac {3}{8}cup\;oil[/tex]
Hence we can conclude that the oil required for one cup of water is 3/8 cup.
To know more about fractions, folow the link given below.
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{Answer the question below.}
Answer:
16÷25=0.64
0.64x2 =1.28
Step-by-step explanation:
Twelve students earned A's. This was 3/8 of the students in the class. What percent of the students did not earn A's?
Answer:
62.5% of the class
Step-by-step explanation:
If 12 students is 3/8 of the class, the ones who earned A's, then 5/8 did not earn A's.
Let c represent the total number of students in the class.
Then (3/8)c = 12, and c = (8/3)(12) = 32.
5/8 of these 32 students did not earn A's: (5/8)(32) = 20.
These 20 students constitute 20/32 of the class, or 0.625 of the class, or 62.5% of the class.
twice the difference of a number and 7 equals 2.
Hello there!
An equation to model the number is: n - 7 x 2 = 2
To find the equation, break apart the question.
twice the difference of a number and 7 equals 2. - "Twice" means we are multiplying by 2, or x 2
twice the difference of a number and 7 equals 2. "The difference of a number and 7" means we are subtracting n - 7, and this is being multiplied by 2 so we have n - 7 x 2 so far.
twice the difference of a number and 7 equals 2. "Equals two" means the equation is equal to 2, or = 2, so our equation is n - 7 x 2 = 2.
The value of the number based on the information given is 8.
Let the number be represented by x.
Since we are given the equation that twice the difference of a number and 7 equals 2, the equation to solve this will be:
2(x - 7) = 2
2x - 14 = 2
2x = 2 + 14
2x = 16
x = 16/2
x = 8
The value of the number is 8
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Given T(2,5,4) and M(3,1,0) find The ordered triple that represents TM. Then find the magnitude of TM?
Answer:
c. [tex]\:<\:1,-4,-4\:>\:,\sqrt{33[/tex]
Step-by-step explanation:
Given T(2,5,4) and M(3,1,0);
[tex]^{\to}_{TM}=^{\to}_{OM}-^{\to}_{OT}[/tex]
[tex]^{\to}_{TM}=\:<\:3,1,0\:>\:-\:<\:2,5,4\:>\:[/tex]
[tex]^{\to}_{TM}=\:<\:3-2,1-5,0-4\:>\:[/tex]
[tex]^{\to}_{TM}=\:<\:1,-4,-4\:>\:[/tex]
The magnitude of this vector is :
[tex]|^{\to}_{TM}|=\sqrt{1^2+(-4)^2+(-4)^2[/tex]
[tex]|^{\to}_{TM}|=\sqrt{1+16+16[/tex]
[tex]|^{\to}_{TM}|=\sqrt{33[/tex]
Answer:
C
Step-by-step explanation:
Edge 2020 :)
PLZ HELP GIVING AS MANY POINTS AS I CAN
7 and trinomial i believe !
What is the value of x?
A. 20
B. 35
C. 60
D. 70
Answer:
A. 20
Step-by-step explanation:
Since they both reflect each other, you would set (3x)° equal to (x + 40)°. Then move -x to the other side of the equivalence symbol to get 40 = 2x. This is how x is defined. You immediately divide by 20 to get your result above.
I am joyous to assist you anytime.
7 times the sum of a number and 4 is the same as 8 decreased by 3 times the number. Find the number
Answer:
7(x4) = 8-x
Step-by-step explanation:
Answer:
x= -2
Step-by-step explanation:
7(4+x)=8-3x would be your equation
your first step would be to move your 3x to the other side of the equation by adding 3x to both sides after this your equation should look as follows: 7(4+x)+3x=8 2nd: you should distribute your 7 to the numbers inside of the parenthsis and combine like terms to get 10x+28=8 then you move your 28 to the other side by subracting 28 and you will get 10x=-20 divide by ten to get the answer which is x=-2
Help for the two questions shown.
(1) the answer for this question is 33 metre square
rectangle is 4*7 that is 28meter square +5 m^2
33m^2
(2) answer for this question is 19 yard square
area of square is 3*3 that is 9m^2+10m^2
19m^2
hope it helps you !!!!!!!
what is the area of parallelogram abcd? HELP THIS IS TIMED
Answer:
13.04 square units
Step-by-step explanation:
Since this is a parallelogram, we only need to solve for the sides of 2 sides.
We can use the distance formula.
The distance from A --> D :
A(3,6) and D(2,2)
2 - 3 = -1
-1^2 = 1
2 - 6 = -4
-4^2 = 16
1 + 16 = 17
[tex]\sqrt{17}[/tex]
The distance from A --> B :
A(3,6) and B(6,5)
6 - 3 = 3
3^2 = 9
5 - 6 = -1
-1^2 = 1
9 + 1 = 10
[tex]\sqrt{10}[/tex]
Multiply.
[tex]\sqrt{10}*\sqrt{17}=13.04[/tex]
*Rounded to the nearest hundreth
What is the surface area of this cylinder? Please show steps!
Answer:
251.33
Step-by-step explanation:
the formula is π r-squared h
so the formula for this question is π (2 squared)(20)
you will square 2 to get 4 then multiply that by π then lastly multiply by 20
Answer:
area = (exact) 88pi ft^2 or (approximate) 276 ft^2
Step-by-step explanation:
The surface area of a cylinder is the sum of the areas of the bases, two circles, and the lateral area which is a rectangle.
Each base is a circle, and the two bases are congruent, so find the area of one base and multiply by 2.
The lateral area is a rectangle. You need to find the length and width of the rectangle. Think of a can of food with a label wrapped around. If you make a vertical cut from one base to the other, and you unwrap the label, you will see that the lateral surface of a cylinder is a rectangle that has the height of the cylinder as its length, and the circumference of the base are its width.
area of circle = pi *r^2
area of rectangle = length * width
length of rectangle: length = 2(pi)r
width of rectangle: width = height = h
total area of cylinder = area of bases + lateral area
total area of cylinder = 2 * pi *r^2 + 2(pi)r * h
total area of cylinder = 2 * pi * (2 ft)^2 + 2 * pi * 2 ft * 20 ft
total area of cylinder = 8pi ft^2 + 80pi ft^2
total area of cylinder = 88pi ft^2
The exact area is 88pi ft^2.
If you need an approximate area, then use 3.14 for pi.
area = 88 * 3.14 ft^2
area = 276 ft^2
Which letter could represent sin -135°?
A. a
B. b
C. c
D. d
Answer:
Option D.
Step-by-step explanation:
we know that
Angle -135° is equal to
360°-135°=225°
The angle belong to the III quadrant
225°-180°=45°
sin(45°)=d/1=d
therefore
sin(-135°)=-sin(45°)=d ---> the value is negative
I’m stuck on this question can some help me ?????
Answer:
plant B would recycle 60 more red bottle and plant c would recycle 38 more bottles
Step-by-step explanation:
Identify the rule for function table
Answer:
i think that it is y=12-x
Step-by-step explanation:
Answer:
Y = x÷2
Step-by-step explanation:
For this purpose, we have to examine all the x and y values.
Looking at the first x value which is 24, the output is 12 which is half of the input.
Then for second input x=12, the output is y=6, which again is half of the output.
Then for the last value of x, the same rule applies.
So we can conclude that y=x/2 or y=x÷2.
So option C is the right answer..
Find the total area of the solid figure.
90 sq. ft.
126 sq.ft
150 sq.ft
Answer:
90 sq. ft.
Step-by-step explanation:
The formula you need to use is length*width*height. If you plug the numbers given into the equation, you get 5*3*6. Multiply this for the answer.
Answer: The correct option is (B) 126 sq. feet.
Step-by-step explanation: We are given to find the total area of the solid figure.
We can see that the given solid figure is a cuboid.
The total area of a cuboid with length l units, breadth b units and height w units is given by
[tex]A=2(lb+bh+hl).[/tex]
For the given cuboid, we have
length, l = 5 feet,
breadth, b = 3 feet and
height, h = 6 feet.
Therefore, the total area of the given cuboid will be
[tex]A=2(5\times 3+3\times6+6\times 5)=2(15+18+30)=2\times63=126~\textup{sq. feet}.[/tex]
Thus, the total area of teh solid figure is 126 sq. feet.
Option (B) is CORRECT.
a textbook has a length of 6 inches, a height of y inches, and a width of x inches. if the length of the diagonal of the front cover is 8 inches and the length of the diagonal of the width is 7 inches, find the values of x and y.
Answer:
Part 1) The value of x is [tex]2\sqrt{7}\ in[/tex]
Part 2) The value of y is [tex]\sqrt{21}\ in[/tex]
Step-by-step explanation:
Part 1
Find the value of x
Applying Pythagoras Theorem
[tex]8^{2}=x^{2} +6^{2}[/tex]
[tex]x^{2}=8^{2}-6^{2}[/tex]
[tex]x^{2}=28[/tex]
[tex]x=2\sqrt{7}\ in[/tex]
Part 2
Find the value of y
Applying Pythagoras Theorem
[tex]7^{2}=x^{2} +y^{2}[/tex]
substitute the value of x
[tex]7^{2}=28 +y^{2}[/tex]
[tex]y^{2}=7^{2}-28[/tex]
[tex]y^{2}=21[/tex]
[tex]y=\sqrt{21}\ in[/tex]
Explain why a semi-truck will accelerate more slowly than a motorcycle?
the semi truck has more weight than a motorcycle. the truck will have to go slow with it carring the passangers and the cargo, alonf with the weight of the trailer and and the weight of the cab itself. the motorcycle will only carry the passanger and the cycle its self. theres a big weight difference. anorher thinf is the motors are both a different size. the motorcycles motor is alot smaller than the trucks so the bikes motor will get ready faster. the same goes with alot of pick up trucks. some trucks have a weight to start signal because they are trying to get the motor ready.
I hope this helps.
Answer:
The semi-truck has more weight than the motorcycle.
Step-by-step explanation:
Obviously a truck is heavier than a motorcycle, so it will have more inertia. Hope this helps!