Using the normal distribution, we have that:
A.
The middle 95% of the wires from Company A tested between 420 and 580 psi.The middle 50% of the wires of Company A tested between 473 psi and 527 psi.B. Due to the higher coefficient of variation, Company A has the larger dispersion.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.For Company A, the mean and the standard deviation are given as follows:
[tex]\mu = 500, \sigma = 40[/tex]
The Empirical Rule is applicable for a normal variable, meaning that 95% of the measures are within 2 standard deviations of the mean, hence:
500 - 2 x 40 = 420.500 + 2 x 40 = 580.The middle 95% of the wires from Company A tested between 420 and 580 psi.
The middle 50% is the measures between the 25th percentile(X when Z = -0.675) and and the 75th percentile(X when Z = 0.675), hence:
25th percentile:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
-0.675 = (X - 500)/40
X - 500 = -0.675(40)
X = 473.
75th percentile:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
0.675 = (X - 500)/40
X - 500 = 0.675(40)
X = 527.
The middle 50% of the wires of Company A tested between 473 psi and 527 psi.
Which Company had the larger dispersion?The company with the larger dispersion has the highest coefficient of variation, given by the standard deviation divided by the mean.
Hence:
Company A: 40/500 = 0.08.Company B: 20/600 = 0.033.Hence Company A has the larger dispersion.
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Which graph is a parabola?
Step-by-step explanation:
THE THIRD GRAPH IS THE PARABOLA!
HOPE THIS HELPS!
complete the table of values.
(please actually answer it, I really need it)
-5-3x
-5-3(-2)=1
-5-3(-1)= -2
-5-3(0)= -5
-5-3(1)= -8
-5-3(2)= 11
solve for y -2(x + 3y) = 18
Answer:
[tex] \sf\large \: y = \frac{ - 1}{3} x - 3[/tex]
Step-by-step explanation:
Let's solve for y.
−2(x+3y)=18
Step 1: Add 2x to both sides.
−2x−6y+2x=18+2x
−6y=2x+18
Step 2: Divide both sides by -6.
−6y/−6 = 2x+18/−6
y= −1/3x−3
Just 16 and 17 please!
Answer:
1(7-6)1/6
Step-by-step explanation:
One number is six less than three times another number. If the sum of the numbers is 38, find the numbers
Answer:
consider the two number as x and y
first given condition
x-6 = 3y
i.e. x= 3y + 6 eqn 1
second given condition
x+ y = 38
i.e. x= 38-y eqn 2
solving eqn 1 and 2
3y + 6 = 38-y
3y + y = 38-6
4y = 32
y = 8
substituting the value of y in eqn 2
x = 38 - y
x= 38-8
x= 30
hence the required numbers are 8 and 30
K
Monica's car will go 455 miles on 17.5 gallons of gasoline in highway driving.
a) How many gallons will it take to drive 2629 miles from her house to a friend's house?
b) How far can the car be driven on 139 gallons of gasoline?
***
please help i have a timer
Answer: 56.25 of 70% and 93.75pints of 90%
Step-by-step explanation: First find the ratios. One juice is 70% and the other is 95%. Your goal is 85%. This is 15% from 70 and 10% from 95. This means you need (15)/(15+10) of 95, which is 3/5 of all the juice to be 95. This means you will need more of the 95% juice, which makes sense because 85 is closer to 95. So 3:5 and total 150=56.25 of 70% and 93.75pints of 90%
can anyone write out step-by-step directions and end up with the solution for this equation
2(3b - 2) = 2(2b + 12)
One way to solve is to follow these steps
2(3b - 2) = 2(2b + 12)
2*3b - 2*2 = 2*2b + 2*12
6b - 4 = 4b + 24
6b-4b = 24+4
2b = 28
b = 28/2
b = 14
Final answer: b = 14What must be subtracted from x² + 2x - 3 to get 2x² - 4
The term (- x² + 2x + 1 ) must be subtracted from (x² + 2x - 3) to get
(2x² - 4).
Here,
We have to find the number which must be subtracted from x² + 2x - 3 to get 2x² - 4.
What is Number system?
A system of writing to express the number is called number system.
Now,
Let 'a' must be subtracted from x² + 2x - 3 to get 2x² - 4.
It can be written as;
(x² + 2x - 3) - a = 2x² - 4
a = (x² + 2x - 3) - (2x² - 4)
a = x² + 2x - 3 - 2x² + 4
a = - x² + 2x + 1
Therefore, The term (- x² + 2x + 1 ) must be subtracted from x² + 2x - 3 to get 2x² - 4.
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The first three terms of a sequence are given. Round to the nearest thousandth (if necessary). 310, 304,298,... 310,304,298,... \text{Find the 47th term.} Find the 47th term.
The 47th term in the given arithmetic sequence is 34.
Given,
The arithmetic sequence = 310, 304, 298,......
First term of the sequence, t₁ = 310
Common difference of the sequence, d = t₂ - t₁ = 304 - 310 = -6
nth term of an arithmetic sequence, tₙ = t₁ + ( n - 1) d
We have to find the 47th term of the arithmetic sequence.
That is, n = 47
So,
t₄₇ = 310 + (47 - 1) -6
t₄₇ = 310 + (46 x (-6) )
t₄₇ = 310 - 276
t₄₇ = 34
Therefore, the 47th term in the given arithmetic sequence is 34.
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Find the amount if $500 was invested at 8% which compounded quarterly after a period of 2½ years. (please show workings)
The amount generated by the invested amount of $500 which is compounded quarterly will be $610.
What is compound interest?A loan or deposit's interest is computed using the starting principle and the interest payments from the ago decade as compound interest.
We know that the compound interest is given as
[tex]\rm A = P \left (1 + \dfrac{r}{n} \right ) ^{nt}[/tex]
Where A is the amount, P is the initial amount, r is the rate of interest, and t is the number of years.
If $500 had been invested at an annualized rate of 8%, the money would have after 2.5 years. For the quarterly, the value of n will be 4. Then the amount will be
[tex]\rm A = 500 \left (1 + \dfrac{0.08}{4} \right)^{4 \times 2.5}[/tex]
Simplify the equation, then the amount is given as,
A = 500 (1 + 0.02)¹⁰
A = 500 (1.02)¹⁰
A = 500 x 1.22
A = $610
The amount generated by the invested amount of $500 which is compounded quarterly will be $610.
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What fraction is equivalent to 0.16?
will give brainliest, really struggling with probability questions. any type of help would be appreciated
Please see the attached image for your answer. Hope this helps!
Determine whether the relation is a function. Explain. x y 4 –5 –1 –10 0 –9 1 –7 9 1 Multiple choice question. cross out A) Yes; for each element of the domain, there is only one element of the range. cross out B) Yes; for each element of the range, there is only one element of the domain. cross out C) No; the element 1 is in both the domain and the range. cross out D) No; for each element of the domain, there is not only one element of the range.
It is not a function because: C) the element 1 is in both the domain and the range.
What makes a Relation a Function?A relation can be defined as a function if each of the domain values each has exactly one corresponding range value. This means that an element of the domain must not have two different elements from the range that it is related or corresponded to.
In the given function, 1 as an element of the domain is related to two different range elements, 10 and 7. This doesn't satisfy a function property.
Therefore, we can state that: it is not a function because: C) the element 1 is in both the domain and the range.
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Given 4x=12x+22 prove x=-4
the required simplified value of given expression 4x = 12x + 32 is x = -4 (hence proved).
Given that,
An expression is given 4x = 12x + 32,
We have to prove x = -4 as of simplified solution.
The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Here,
4x = 12x + 32
Taking 12x to the left side of the equal sign and it becomes -12x
4x - 12x = 32
Applying subtraction property between 4x and 12
- 8x = 32
Dividing both sides by -6
x = -4
Thus, the required simplified value of the given expression is x = -4 (hence proved).
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PLEASE ANSWER
Simplify the expression -4 1/6 - -6 1/3 Explain your solution using the additive inverse property.
The Additive Inverse is -32/6
Additive Inverse of Real Numbers:
The given number can be whole number, a natural number, an integer, a fraction, a decimal, or any real number. The additive inverse of real numbers is just the negative of the given number.
What is Additive Inverse?
Additive Inverse simply means changing the sign of the number and adding it to original number to get an answer is equal to 0.
Now, Come to the question:
Expression is : [tex]-4\frac{1}{6} -(-6)\frac{1}{3}[/tex]
Solve it : [tex]\frac{-25}{6}-\frac{(-19)}{3}[/tex]
Taking the L.C.M
=[tex]\frac{-25+57}{6}[/tex]
=32/6
Additive inverse of 32/6 is -32/6
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find the median 2.5,2.3,2.3,1.8,2.3,1.5
Answer:2.1
Step-by-step explanation:
i added them then divided by 7
Divide using synthetic division. (4x² + 3x³ + 9x− -20) + (x + 2)
The synthetic division solution of (4x² + 3x³ + 9x− -20) / (x + 2) is mathematically given as
3x^2-2x+13-(6/x+2)
This is further explained below.
What is synthetic division?Generally, Synthetic division is a technique that may be used to manually conduct Euclidean division of polynomials.
Compared to long division, the synthetic division requires less writing and fewer calculations to complete. The approach is most often taught for dividing by linear monic polynomials; however, it may be extended to divide by any polynomial.
In conclusion, The synthetic division solution is mathematically given as
3x^2-2x+13-(6/x+2)
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through: (-2,-4), perp. to y= -1/2x
Answer:
y = 2x
Step-by-step explanation:
The slopes of two perpendicular lines are negative reciprocals of each other. So the slope is 2
m = 2, y = -4, x = -2
y = mx + b
-4 = 2(-2) + b
b = -4 + 4
b = 0
y = 2x
7. Find the perimeter of a regular
pentagon with a side measure of
57 centimeters.
A: 228 cm
O B: 342 cm
O C: 649 cm
OD: 285 cm
Answer:
D. 285 cm
Step-by-step explanation:
Answer: D: 285 CM
Step-by-step explanation:
To find the perimeter you need to multiply its sides by its measure. It gives you in this case 57x5: 285
The Taj Mahal is an enormous ivory-white marble monument in India that is known for
its architecture. More than 2 x 104 workers were involved in building the Taj Mahal.
Which number shows another way to express 2 x 10¹?
Answer:the iconic Indian building named Taj Mahal
Step-by-step explanation:
write the function whose graph is the graph of y=x^2 but is translated 9 units to thre left
Answer:
y= (x+9)^2
Step-by-step explanation:
If h<0 ( negative) then it shifts to the right, if it is is h>0 ( positive number) then it shift to the left!
y = x2
Shift 2 units left: y = (x+2)2
Then, shift up 9 units: y = (x+2)2 + 9
Then, reflect in the x-axis: y = -(x+2)2 - 9
The width of a rectangle measures (10p - 9p) centimeters, and it’s length measures (7p + 8p) centimeters. Which expression represents the perimeter, in centimeters, of the rectangle?
Answer:
c
Step-by-step explanation:
A recipe for oatmeal cookies calls for 5 cups of flour for every 8 cups of oatmeal. How much flour is needed for a big batch of cookies that used 16 cups of oatmeal?
Answer:
10 cups
Step-by-step explanation:
Since 16 cups is twice 8 cups, it needs twice 5 cups of flour which is 10 cups.
We can also use a proportion.
5/8 = x/16
8x = 5 × 16
x = 5 × 2
x = 10
Answer: 10 cups
On a map , 1 inch represents 50 miles. You measure the distance on the map between two towns as 3 1 2 inches. How many miles apart are the towns?
The towns are 15600 miles apart.
WHAT IS MAP SCALE ?The term "map scale" refers to the proportion between a distance on a map and its corresponding distance on the ground. Lets see an example like, On a map with a scale of 1:100,000, one kilometer on the ground is equivalent to one centimeter. The scale of a map refers to the proportion between a distance on a map and its actual distance on the ground. This simple concept is complicated by the fact that scale must vary across a map due to the curvature of the Earth's surface. The concept of size is now important in two different ways as a result of this development.
The size of the producing globe is compared to the size of the Earth in the first technique. a theoretical globe known as the generating globe, upon which the map is projected and the Earth is compressed. The ratio of the size of the Earth to that of the generating globe is known as the nominal scale, also known as the major scale or representative fraction.
CALCULATION∵ 1 inch = 50 miles on the map
∴ 312 inches = 312 * 50 = 15600 miles .
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someone help me please its for a practice
Answer:
5a,3a
Step-by-step explanation:
(Please someone help me!)
The ordered pair we are looking for is the values of the variables [tex]x[/tex] and [tex]y[/tex], or [tex](x, y).[/tex] We are given that [tex]x=2[/tex], and that the formula to evaluate [tex]y[/tex] is [tex]y = 5^x[/tex]. Note we are given [tex]x[/tex] so we can evaluate [tex]y[/tex] as [tex]y = 5^2 = 25[/tex]. Now, we have both the values of [tex]x[/tex] and [tex]y[/tex], so our ordered pair is thus [tex](x,y) = (2,25).[/tex]
Rick is going to buy donuts for his family. Each donut costs $1.25. If the number of donuts Rick buys is represented using the letter r, which expression represents the total cost?
The algebraic expression that represents the total cost would be: A. 1.25r.
How to Write an Algebraic Expression?Given that the number of donuts Rick buys for his family is represented by letter "r", and we also know that:
cost of each donut = $1.25.
Using an algebraic expression, we can create a mathematical expression that shows the total cost for Rick to by a given number of donuts for his family.
Thus:
1 donut = 1.25
r donuts would cost: 1.25 × r = 1.25r.
Therefore, the algebraic expression that represents the total cost would be: A. 1.25r.
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Select all the correct answers.
If a figure is a square, its diagonals divide it into isosceles triangles.
p: A figure is a square.
q: A figure's diagonals divide into isosceles triangles.
Which represents the converse of this statement? Is the converse true?
0
0
0
The converse of the statement is sometimes true and sometimes false.
q+p
The converse of the statement is false.
The converse of the statement is true.
9-P
P-9
O ~p~9
Answer:
q arrow p, and p arrow q
Step-by-step explanation:
edmentum
Given the equation x(x - 1)²(x + 5)³, the degree is
07
0 3
05
6
Answer:
Dear Friend
the answer is 6
Step-by-step explanation:
Just see the highest possible degree x in each term being multiplied and add the degree
that is
x has a degree 1
(x-1)² has a highest possible x degree as 2
for (x+5)³ it is 3
1+2+3=6