Engineers must consider the breadths of male heads when designing helmets. The company researchers have determined that the population of potential clientele have head breadths that are normally distributed with a mean of 6.9-in and a standard deviation of 0.8-in.In what range would you expect to find the middle 98% of most head breadths?Between and .If you were to draw samples of size 47 from this population, in what range would you expect to find the middle 98% of most averages for the breadths of male heads in the sample?Between and
Answers
The population of potential clientele have head breadths normally distributed with mean 6.9 in and standard deviation 0.8 in
98% of the breadths must differ from the mean by no more than 2.33 times the standard deviation.
This mean the the range we would expect to find the middle 98% of most head breadths is represented by the interval [6.9 - 2.33*0.8, 6.9 + 2.33*0.8] = [5.04, 8.76] in
If we are considering samples of size 47, the standard deviation for the mean of each sample is given by:
\(\frac{\sigma}{\sqrt[]{n}}=\frac{0.8}{\sqrt[]{47}}=0.117\text{ in}\)In this case, we would expect to find 98% of most averages for the breadths of male heads in the interval [6.9 - 2.33*0.117, 6.9 + 2.33*0.117] = [6.63, 7.17] in
Related Questions
if an item regularly cost d dollars and is discounted 12 percent, which of the following represents the discounted price?
Answers
If an item usually costs d dollars a 12% discount can be represented as 0.88d.
What is a discount?This refers to a deduction in the regular price of a product or service that is usually represented using a percentage.
How can the discounted price be represented?Considering 12% is being deducted from 100% (100-12 = 88). The final price can be represented as 0.88d or 0.88 multiplied by the regular price (d).
For example, if the regular price is $100, 0.88 x 100 = $88.
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Steve wants to buy a new music player.
The player he wants costs $279.95. The city
he lives in charges a 5% sales tax,
SO for
every
$100.00 Steve spends, he has to pay
a sales tax of $5.00. How much
sales tax
will Steve have to
pay
for the music player?
Answers
Answer: $14 for sales tax
Step-by-step explanation:
you're buying a $279.95 item with a sales tax of 5%. Your math would be simply: [cost of the item] x [percentage as a decimal] = [sales tax]. That's $279.95 x 0.05 =$13.9975
but if you round up which is possible in your case its $14
a third grader has a goal of solving 100 math facts in 5 minutes (or 300 seconds). how many seconds can he spend on each math fact? give unit rate in seconds per fact.
Answers
Answer:
1 fact per 3 seconds because you divide 300 by 100
Answer:
3 seconds/per fact
Step-by-step explanation:
300 divided by 100
= 3
plzzz help I picked A already and it was wrong
Answers
Answer:
probably C I'm terrible at math but that look about right
A red bowl, a green bowl, and a blue bowl are on the kitchen table. Alan places one egg into a randomly selected bowl. Then Bethany places one egg into a randomly selected bowl. X = # of eggs placed into the red bowl. Y = # of empty bowls at the end of the experiment. Draw a table describing the joint probability mass function of X and Y. (Advice: start by drawing a tree diagram.) Please show all steps.
Answers
There is insufficient information so the joint probability mass function of X and Y.
given that
there are three bowls they are a red bowl , a green bowl and a blue bowl are on the kitchen table
alan places one egg into a randomly selected bowl.
X = # of eggs placed into the red bowl
Y = # of empty bowls at the end of the experiment.
the joint probability mass function of X and Y
1. Not sufficient
R=5
let us consider when G = 2 , B = 1 => P(G) = 2/8
when G=1, B=2 => P(G) = 1/8
2. Not Sufficient
P(B) = 1/3 = x/3x
But this doesn't tell us anything about B or total because P(B) = 1/3 , but it could also be 2/6 or 3/9 so on..
So we can have different B . Thus we can have different G combinations.
Together - Not Sufficient
P(B) = x/(3x) , R = 5
P(G) = 1- P( not G )
= 1- P(R or B)
But we cannot calculate this with out knowing P(R) and P(B).
we cannot solve this problem because there is no proper information is given.
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An airplane's velocity with respect to the air is 530 miles per hour, and it is flying a bearing of 55 degrees.The wind, at an altitude of the plane, is blowing southeast with a velocity of 35
milles per hour. What is the true direction of the plane, and what is its groundspeed? Round to the nearest thousandths.
Answers
The groundspeed of the plane is 531.8 mph, rounded to the nearest thousandth.
We will use vector addition to find the true direction and groundspeed of the plane. We can break down the velocity of the plane and the velocity of the wind into their north-south and east-west components.
Next, we can find the north-south and east-west components of the plane's velocity.
cos(55°) = 0.5736
sin(55°) = 0.8192
North-south component: 530 × 0.8192 = 433.1 mph
East-west component: 530 × 0.5736 = 304.8 mph
So the velocity vector of the plane can be represented as:
P = 433.1 mph north + 304.8 mph east
Similarly, we can find the north-south and east-west components of the wind velocity:
cos(135°) = -0.7071
sin(135°) = 0.7071
North-south component: 35 × 0.7071 = 24.75 mph (south)
East-west component: 35 × -0.7071 = -24.75 mph (west)
So the velocity vector of the wind can be represented as:
W = 24.75 mph south - 24.75 mph west
Now we can add the velocity vectors of the plane and the wind to find the true velocity vector:
T = P + W
T = (433.1 mph north + 304.8 mph east) + (24.75 mph south - 24.75 mph west)
T = 433.1 mph north + 280.05 mph east - 24.75 mph south
The direction of the true velocity vector can be found using the arctan function:
arctan(280.05 / 433.1) = 33.16° east of north
So the true direction of the plane is 33.16° east of north.
To find the groundspeed, we can use the Pythagorean theorem:
\(|T| = \sqrt{((433.1)^2 + (280.05)^2 + (-24.75)^2) } = 531.8\)mph
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one of the acute angles of a right triangle is 36° find the other acute angles
Answers
Step-by-step explanation:
An acute angle is an angle less or equal to 90 degrees.
let the other angle be x.
x + 36 = 90
grouping like terms
X = 90 - 36
X = 54 degrees
Answer:
54
Step-by-step explanation:
= ∠A + ∠B + ∠C = 180o … [∵sum of the angles of a triangle is 180]
or 180 = 36 + 90 + ∠C
C=54
Write the phrase as an expression. Two less than a number t.
Answers
Answer:
t-2
Step-by-step explanation:
"less than a number t" read backwards
t-2
Number A is 4.576. Number 3 10.043 greater than a. Number Cis 2.510 less than 8. What is the total
walue of numbers A. B, and ?
Answers
Answer:
14.619
Step-by-step explanation:
10.043 + 4.576 = 14.619
7. A quadratic function has the form y-ax' for
some nonzero value of a and (4, 48) is on the
graph. What is the value of a?
Answers
Diana is going to roll a 6-sided die. What's the probability she will role a 4 or
a 5? *
Answers
The probability of rolling any one number on a 6 sided die is 1/6
The probability of rolling a 4 is 1/6
The probability of rolling a 5 is 1/6
The probability of rolling a 4 or a 5 is the probability of rolling a 4 plus the probability of rolling a 5:
1/6 + 1/6 = 2/6 = 1/3
The answer is 1/3
all muntiple of 5 is an odd number true proposition?
Answers
a of 5 is 2.5 b of 5 is 2.5 although 5+5=10 = 2.5×4 =10 (even) x of 5 is odd and y of 5 is even
Therefore, its false;)
6x−3(6−5x)+3x=10−4(2−x)
Answers
Answer:
x =1
Step-by-step explanation:
\(6x-3\left(6-5x\right)+3x=10-4\left(2-x\right)\\\\Group\:like\terms\\6x+3x-3\left(-5x+6\right)=10-4\left(2-x\right)\\\\Add\:similar\:elements:\:6x+3x=9x\\9x-3\left(-5x+6\right)=10-4\left(2-x\right)\\\\Expand\:-3\left(-5x+6\right):\quad 15x-18\\9x+15x-18=10-4\left(2-x\right)\\\\\mathrm{Add\:similar\:elements:}\:9x+15x=24x\\24x-18=10-4\left(2-x\right)\\\\Expand\:10-4(2-x):4x+2\\24x-18=4x+2\\\\Add\:18\:to\:both\:sides\\24x-18+18=4x+2+18\\\\Simplify\\24x=4x+20\\\)
\(\mathrm{Subtract\:}4x\mathrm{\:from\:both\:sides}\\24x-4x=4x+20-4x\\\\Simplify\\20x=20\\\\\mathrm{Divide\:both\:sides\:by\:}20\\\frac{20x}{20}=\frac{20}{20}\\\\Simplify\\x=1\)
Three-fourths of the yard is covered with grass and one-fourth is used as a garden. The sprinkler could only water 1/5 of the yard, so the rest died. Use the model to find out how much of the grass died.
Answers
3/5 or 60% of the grass died because the sprinkler could only water 1/5 of the yard.
Let's start by breaking down the information given:
- Three-fourths of the yard is covered with grass.
- One-fourth of the yard is used as a garden.
- The sprinkler could only water 1/5 of the yard.
To find out how much of the grass died, we need to determine the portion of the grass that was not watered by the sprinkler.
Let's assume the total area of the yard is represented by the value 1. Therefore, we can calculate the area of the grass as 3/4 of the total yard, which is (3/4) * 1 = 3/4.
The sprinkler can only water 1/5 of the yard, so the portion of the grass that was watered is (1/5) * (3/4) = 3/20.
To find the portion of the grass that died, we subtract the watered portion from the total grass area:
Portion of grass that died = (3/4) - (3/20) = 15/20 - 3/20 = 12/20.
Simplifying, we get:
Portion of grass that died = 3/5.
Therefore, 3/5 or 60% of the grass died because the sprinkler could only water 1/5 of the yard.
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In the given equation, b is a positive constant.
The sum of the solutions of the equation is 5.
What is the value of b?
x²(x+3)(x - b) = 0
Answers
Answer: b = 8
Step-by-step explanation:
From the equation, we can see that x = 0 is one of the solutions. This means that the remaining solutions must add up to 5.
Let's factor the equation and set each factor equal to zero:
x²(x+3)(x - b) = 0
x = 0 or x + 3 = 0 or x - b = 0
Solving for x in each case, we get:
x = 0 or x = -3 or x = b
Since the sum of the solutions is 5, we can write:
0 + (-3) + b = 5
Simplifying, we get:
b - 3 = 5
Adding 3 to both sides, we get:
b = 8
Therefore, the value of b is 8.
b = 8.
Step by step solved:
Since the equation is equal to zero, it can be factored into three parts: x²=0, x+3=0, and x-b=0.
The solutions for x²=0 are x=0 and x=0 (a double root).
The solution for x+3=0 is x=-3.
The solution for x-b=0 is x=b.
Therefore, the sum of the solutions is 0 + 0 + (-3) + b = 5.
Simplifying the equation, we get b = 8.
So the value of b is 8.
Evaluate the expression when c=9 and d=8. 4c+d
please help
Answers
Answer:
44
Step-by-step explanation
4c + d
this is an expression and since they provided c and d it is easy to solve
c = 9 and d = 8. You need to plug in c and d into the expression to solve the problem.
4(9) + (8)
4 times 9 is 36 so it leaves you with 36 + 8
36 + 8 = 44
I hope this helps but basically the concept is just plugging in the numbers in place of the variables. For future problems plug in the numbers given where the variables are.
Shaikha sold 10 packages of sugar cookies and 2 packages of oatmeal cookies for $56. Khalid sold 9 packages of sugar cookies and 3 packages of oatmeal cookies for $60. What system of equations can be used to find the price of a package of sugar cookies and a package of oatmeal cookies? (sugar cookies: x and oatmeal cookies: y )
Answers
Answer:
The system that can be used is:
\(10x + 2y = 56\)
\(9x + 3y = 60\)
Step-by-step explanation:
We have that:
x is the price of a package of sugar cookies, y is the price of a package of oatmeal cookies.
Shaikha sold 10 packages of sugar cookies and 2 packages of oatmeal cookies for $56.
This means that:
\(10x + 2y = 56\)
Khalid sold 9 packages of sugar cookies and 3 packages of oatmeal cookies for $60.
This means that \(9x + 3y = 60\)
System that can be used:
The system that can be used is:
\(10x + 2y = 56\)
\(9x + 3y = 60\)
A
-2+
Which graph represents the
function y = tan x?
B
2T
2T
D
-2+1
21
4+
ㅠ
2T
2πT
Answers
The graph that represents the function y= tanx is Option A.
What is the description of the above function?The graph of y =tan (x) is a periodic function that has vertical asymptotes at x = (n + 1/2)π, where n is an integer.
It oscillates between positive and negative infinity, creating a wave- like pattern.
It has a repeating pattern of sharp peaks and valleys, exhibiting both positive and negative slopes.
Thus, option A is the correct answer.
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can someone please help me with this question
Answers
Answer:
1.9.75x> 195
2.9.75x> 195
9.75/9.75x>195/9.75
x>20hrs
Determine if the given ordered pairs are solution of x+ 4y = 7.
1. (3,1)
Solutions:
Answers
Answer:
True
Step-by-step explanation:
3 X 1 = 3
4 X 1 = 4
3 + 4 = 7
Hope this helps!
Answer:
(3, 1) is a solution
Step-by-step explanation:
If the coordinates are solutions of the equation, you should be able to solve the equation to get the y-value when you input the x-value;
So in the case of (3, 1), input x = 3 and solve for y:
(3) + 4y = 7
4y = 4
y = 1
Solving the equation gives y = 1, which is the same as the given coordinates, hence it is a solution or, in other words, this point falls on the line graphed by the equation
GIVING BRAINLIEST IF U ANSWER
Answers
Answer:
3/10
Step-by-step explanation:
There are a total of three people. 1/2 of the blueberry pie plus 2/5 of the apple pie is equal to 9/10 of a whole pie. Divide that by 3 and each person gets 3/10 of pie.
Find x. Round to the nearest tenth if necessary.
Answers
Answer:
5
Step-by-step explanation:
3+x
Answer:
Is there any picture? If there isn't, it cannot be solved.
Step-by-step explanation:
Help I will award brainliest help asap! Uwu: If a man can run p miles in x minutes, how long will it take him to run q miles at the same rate?
Answers
Answer:
Speed= Dist/time= p/x miles per minute
Time to run q miles=q divided by p/x= qx/p minutes
Step-by-step explanation:
If f(x) = − 5, what is f(8.6)?
1.) 3
2.) 4
3.) 8
4.) 9
Answers
Answer: It's 2.) 4 is the answer
QUESTION ON PIC BRAINLIEST THANK YOU!
Answers
2: Neither
3: Parallel
4: Pretty sure it’s neither but could be perpendicular
2x² + 10 factorización
Answers
Answer:
2(x² + 5)
Step-by-step explanation:
To factor 2x² + 10, we can first factor out the greatest common factor of the terms, which is 2:
2x² + 10 = 2(x² + 5)
We can't factor anymore, so the answer is:
2(x² + 5)
Answer:
2(x² + 5)
Step-by-step explanation:
To factorise this, do the distributive property backwards. In other words:
2x² + 10
2x² ÷ 2 + 10 ÷ 2
x² + 5
2(x² + 5)
∴ 2(x² + 5) is the answer
What is -9 as a fraction?
Answers
Answer:
\(-\frac{9}{1}\)
Step-by-step explanation:
Its just the same way as making positive 9
a fraction, but just add the negative sign.
Hope this helps :))
The perimeter of the rectangle below is 76 units. Find the value of y.
Answers
The solution is : the value of y is 7.
Here, we have,
The perimeter of a rectangle is found by
P = 2 (l+w)
P = 2( 3y+3+2y)
Combine like terms
P = 2(5y+3)
We know the perimeter is 76
76 = 2(5y+3)
Divide each side by 2
76/2 = 2/2(5y+3)
38 = 5y+3
Subtract 3 from each side
38-3 = 5y+3-3
35 = 5y
Divide each side by 5
35/5 = 5y/5
7 =y
We want the length of AD = BC = 2y
AD = 2y=2*y = 14
Hence, The solution is : the value of y is 7.
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Let S be a set. Consider the algebraic structure (℘(S),∪,∩). Taking union to be the additive operation and intersection to be the multiplicative operation, investigate whether or not this algebraic structure is a commutative ring. That is, either prove or provide a counterexample for each property of a commutative ring.
Bonus: Does this structure have zero divisors?
Answers
The algebraic structure (℘(S),∪,∩) is a commutative ring.
To prove that the algebraic structure (℘(S),∪,∩) is a commutative ring, we need to show that it satisfies the following properties:
Addition is commutative: A ∪ B = B ∪ A for any A, B ∈ ℘(S)
Addition is associative: (A ∪ B) ∪ C = A ∪ (B ∪ C) for any A, B, C ∈ ℘(S)
There exists an additive identity: there exists a set 0 ∈ ℘(S) such that A ∪ 0 = A for any A ∈ ℘(S)
There exists an additive inverse: for any A ∈ ℘(S), there exists a set -A ∈ ℘(S) such that A ∪ -A = 0
Multiplication is commutative: A ∩ B = B ∩ A for any A, B ∈ ℘(S)
Multiplication is associative: (A ∩ B) ∩ C = A ∩ (B ∩ C) for any A, B, C ∈ ℘(S)
There exists a multiplicative identity: there exists a set 1 ∈ ℘(S) such that A ∩ 1 = A for any A ∈ ℘(S)
Distribution property: A ∩ (B ∪ C) = (A ∩ B) ∪ (A ∩ C) for any A, B, C ∈ ℘(S)
Addition is commutative: This property is true, as the union operation is commutative. Therefore, A ∪ B = B ∪ A for any A, B ∈ ℘(S).
Addition is associative: This property is also true, as the union operation is associative. Therefore, (A ∪ B) ∪ C = A ∪ (B ∪ C) for any A, B, C ∈ ℘(S).
There exists an additive identity: The empty set ∅ is the additive identity, as A ∪ ∅ = A for any A ∈ ℘(S).
There exists an additive inverse: The additive inverse of any set A is its complement -A, as A ∪ -A = ∅ for any A ∈ ℘(S).
Multiplication is commutative: This property is true, as the intersection operation is commutative. Therefore, A ∩ B = B ∩ A for any A, B ∈ ℘(S).
Multiplication is associative: This property is also true, as the intersection operation is associative. Therefore, (A ∩ B) ∩ C = A ∩ (B ∩ C) for any A, B, C ∈ ℘(S).
There exists a multiplicative identity: The set S is the multiplicative identity, as A ∩ S = A for any A ∈ ℘(S).
Distribution property: This property is also true, as the intersection operation distributes over the union operation. Therefore, A ∩ (B ∪ C) = (A ∩ B) ∪ (A ∩ C) for any A, B, C ∈ ℘(S).
Therefore, we have shown that the algebraic structure (℘(S),∪,∩) is a commutative ring.
Bonus: This structure does not have zero divisors. A zero divisor is an element a of a ring that is not zero and that has a product with some nonzero element b that is equal to zero. However, in
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Marie spends $450.00 at a department store. She has two coupons: one for a 15% discount and one for $50 off any purchase above $300. The store allows the coupons to be combined. Which coupon should be applied first, and what is the final purchase price?
Answers
Answer:
Apply the 15% discount first, and the final purchase price is $332.50.
Step-by-step explanation:
The 15% discount of the two coupons should be applied first so that the final price is cheaper.
The final purchase price at the department store is $332.5.
What is a percentage?The percentage is calculated by dividing the required value by the total value and multiplying by 100.
Example:
Required percentage value = a
total value = b
Percentage = a/b x 100
Example:
50% = 50/100 = 1/2
25% = 25/100 = 1/4
20% = 20/100 = 1/5
10% = 10/100 = 1/10
We have,
Cost = $450
Two coupons.
Offer = 15% discount
off = $50
Now,
15% discount first and then $50 off.
(450 - 15/100 x 450) - 50
= (450 - 67.5) - 50
= $332.5
Now,
$50 off first and then the 15% discount.
(450 - 50) = 400
400 - 15/100 x 400
= 400 - 60
= $340
We see that,
When the 15% discount is applied first the final price is cheaper.
Thus,
15% discount should be applied first.
The final purchase price is $332.5.
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