Answer:
50.24
Step-by-step explanation:
The formula for the area of a circle is
Area = 3.14 (π) x radius squared [tex]4^{2[/tex]
Area = 3.14 (π) x (4 x 4)
Area = 3.14 (π) x 16
Area = 50.24
is 3.14159 a rational or irrational number?
Answer:
Irrational
Step-by-step explanation:
It would be a irrational number because it’s a crazy decimal/pi and you can’t determine what number comes next.
Grear Tire Company has produced a new tire with an estimated mean lifetime mileage of 36,500 miles. Management also believes that the standard deviation is 5,000 miles and that tire mileage is normally distributed. To promote the new tire, Grear has offered to refund some money if the tire fails to reach 30,000 miles before the tire needs to be replaced. Specifically, for tires with a lifetime below 30,000 miles, Grear will refund a customer $1 per 100 miles short of 30,000.
a) For each tire sold, what is the expected cost of the promotion?
b) Please perform the simulation for 1000 times, what is the probability that Grear will refund more than $50 for a tire?
Answer:
Step-by-step explanation:
standard deviation σ =5000
Mean μ = 36500
X = 30000
Probability that tire fails to reach 30000 miles
P(< 30000) = P( z < (30000-36500) / 5000 )
= P ( z < - 1.3 )
= .0968 ( from z table )
refund per mile = .01
refund for 30000 mile = .01 x 30000 = 300
expected cost of promotion
= 300 x .0968
= 29.04
b )
refund of $50 is equivalent to shortage of milage by 50 / .01 = 5000 miles
Probability of miles less than 30000 - 5000 = 25000
P ( X < 25000 ) = P ( z < (25000 - 36500) / 5000 )
P ( z < - 2.3 )
= 0.0107 Answer .
Ali is sledding down a hill the graph shows her elevation as she sleds down the hill.
Answer:
The steepness of the hill is a function of the speed of the sled.
Hope this helps :)
Find the reciprocal.
- 1/5 and 2 3/8
Answer:
The reciprocal is simply the opposite, so flip it. For te first one, since its a negative, flip it to make it positive, and flip 1/5 to 5/1. I hope this helps
Step-by-step explanation:
Use the distributive to remove the parentheses: x(c-4)
Answer:
xc + -4x
Step-by-step explanation:
The distributive property allows the multiplication of a sum by multiplying each addend separately and then sum those products.
With this in mind, let's apply the distributive property to the expression:
x (c - 4)
= x * c + x * (-4)
= xc + -4x
Cheers.
The identification code on a bank card consists of 1 digit followed by 2 letters. The code must meet the following conditions: The digit must be odd. The letters A, E, I, O, and U cannot be used. Letters cannot be used more than once.
Answer:
For the code we have 3 selections.
The first selection is a digit that must be odd, so the options are {1, 3, 5, 7 ,9}
So we have 5 options.
The second selection is a letter from the set of all the letters (27) minus the set of the vowels (5)
So here we have 27 - 5 = 22 options
The third selection is also a letter from the previous set, but because each letter can be used only one time, and in the previous selection we already selected one of the letters, in this selection we have a letter less than in the previous selection.
Here we have 22 - 1 = 21 options.
The total number of combinations (of possible codes) is equal to the product of the number of options for each selection:
C = 5*22*21 = 2310.
There are 2310 different possible codes
1. Twelve years ago, your grandma put money into a savings account for you that earns 7.5% interest annually and is
continuously compounded. How much money is currently in your account if she initially deposited $10,000 and you
have not taken any money out?
Answer:
23,817$
Step-by-step explanation:
And you will have earned 13,817 in interest.
The final amount of money $10000 of 7.5% compound interest for 12 years is $23817.79.
What is compound interest?
Compound interest is applicable when there will be a change in principal amount after the given time period.
If you give anyone $500 at the rate of 10% annually then $500 is your principle amount.
Given that,
Principle amount P = $10000
Rate of interset R = 7.5% = 0.075
Time period T = 12 years
Compound interest formula ;
A = P[1+R]^T
A = 10000[1+0.075]¹²
A = $23817.79
Hence "The final amount of money $10000 of 7.5% compound interest for 12 years is $23817.79".
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Find the standard form of the equation of the ellipse with the given characteristics. Center: (1, 2); vertex: (−7, 2); minor axis of length 12
Answer:
(x-1)²/64 + (y-2)²/144 = 1
Step-by-step explanation:
The standard equation of an ellipse is expressed as (x-h)²/a² + (y-k)²/b² = 1
Where the coordinate (h,k) is the centre of the ellipse.
a is the the difference of the x coordinates of the centre and the vertex.
b is the minor axis.
Given the centre to be (1,2), on comparing with the coordinate (h,k),
h = 1 and k = 2
The difference of the x coordinates of the centre and the vertex = -7-1 = -8
The minor axis as given in the equation is b = 12
Substituting the given parameters into the equation of an ellipse above we will have;
(x-1)²/(-8)² + (y-2)²/12² = 1
(x-1)²/64 + (y-2)²/144 = 1
The final equation gives the required standard form of the equation of the ellipse.
Which equation has a constant of proportionality equal to 3?
Answer:
Step-by-step explanation:
y = 3x is an example of such an equation.
Answer:
D for Khan Academy. :p
Hope it helps :)
Step-by-step explanation:
Evaluate each expression. (Simplify your answers completely.)
Answer:
b- 6
c- 72 square root 2
Step-by-step explanation:
Find valve of X of a vertical angle with 5x+4 degrees and 8x- 71 degrees
Answer: The value of x in a vertical angle is 25.
Step-by-step explanation:
So far the givens are:
a vertical angle with 5x + 4 degrees and 8x - 71 degrees
We know that all vertical angles are congruent. Therefore, we also know that the two given equations are equal. So knowing that, we can do:
5x + 4 = 8x - 71
Group like terms:
71 + 4 = 8x - 5x
75 = 3x
25 = x
Hence your answer.
Auto racing is a sport enjoyed by many people. In each race, there may be up to 25 cars on the racetrack. Which of the following is NOT an example of a quantitative variable you might use to describe a car in a race?
A. the brand of car
B. the number of tires used
C. the number of laps completed
D. the average speed (in mpg)
Answer:
A. the brand of car
Step-by-step explanation:
quantitative variable are those variable whose value can be represented by any number. The number may be fractional, decimal or discrete. But it should have some value like 2, 8, 1000 , 3.555, 4/5 ETC.
______________________________
Given
A. the brand of car
The brand cannot have numerical value. Brand has value like ferrari, mercedes, SKODA , JEEP etc.
Hence,
A. the brand of car is an example of a quantitative variable that might not be used to describe a car in a race. (Answer)
___________________________
Other three
can have numerical values
as
the number of tires can have value 1,2,3,4,5
the number of laps completed can have value from 0, 1, 2, ...to n laps as decided for thr race
average speed can have value 40 km.hr, 45.666 km/hr ...etc
Answer:
the brand of car
This is the answer edge 2020
Step-by-step explanation:
Can someone help & explain. I don’t understand!!
Answer:
{2, 3, 4, 5, 6}
Step-by-step explanation:
You are expected to determine the digits of the given number, then list them between curly brackets. Even if a digit appears in the number more than once, you need list it only once. It is helpful to sort the elements of a set, but not necessary.
__
The digits are 5, 3, 2, 6, 4, 6.
In sequence, the unique digits are 2, 3, 4, 5, 6.
The set of digits in the number is ...
{2, 3, 4, 5, 6}
_____
"Roster notation" means you simply list the elements of the set.
Points A, B, and C are collinear and AB. AC at (n, q) and point C is located at (-3,-4). What are the values of n and q?
Answer:
the answer is -4
Step-by-step explanation:
whats 16*2-3(2^6+12)*5
Answer:
- 328
Explanation:
16*2-3(2*6+12)*5 = 32 - 3(12+12)*5 = 32-3*24*5 = 32-360 = - 328
Answer: The answer is 11,020.
Step-by-step explanation:
Do the equation one step at a time:
1. 16 times 2 = 32
2. 32 - 3 = 29
3. (2 ^ 6 + 12) = 64 + 12 = 76
4. (29)(76) = 2,204
5. (2,204) times 5 = 11,020.
Hence, your answer.
the absolute value of twice a number increased by 11
Answer: I2*N + 11I
Step-by-step explanation:
Let's break the sentence so it is easier to understand:
First, "the absolute value of a number N" is:
INI.
"twice a number increaced by 11"
is:
2*N + 11
Then; "the absolute value of twice a number increased by 11" is:
I2*N + 11I
Which of the following units is commensurable with miles?
• acres
• kilograms
• hours
• centimeter
Answer:
centimeter
Step-by-step explanation:
Miles is a measure of distance, so the commensurable measure will also be a distance measure.
acres - area measure
kilograms - mass measure
hours - time measure
centimeter - distance measure
Using the commensurable units concept, it is found that centimetres is commensurable with miles.
-------------------
Two units of measurement are said to be commensurable if they represent the same thing.-------------------
Miles is a measurement of distance.Acres is a measurement of area, thus, it is incommensurable with miles.Kilograms is a measurement of mass, thus, it is incommensurable with miles.Hours is a measurement of time, thus, it is incommensurable with miles.Centimetres is a measurement of distance, thus, it is commensurable with miles, being the correct option.A similar problem is given at https://brainly.com/question/17387584
Solve the following linear equation and please explain how you did it 6y+8=6(y+4)−16
Answer:
infinite solutions, true for all y
Step-by-step explanation:
6y+8=6(y+4)−16
Distribute
6y+8 = 6y+ 24 - 16
Combine like terms
6y+8 = 6y+8
Subtract 6y from each side
8=8
Since this is always true, the equation is true for all real y
Answer:
True of all values of 'y'.
Step-by-step explanation:
[tex]6y+8=6(y+4)-16\\\\6y+8=6y+24-16\\\\6y+8=6y+8\\\\6y+8-8=6y+8-8\\\\6y=6y\\\\6y-6y=6y-6y\\\\\boxed{0=0}[/tex]
Hope this helps.
Ms. Rangtonsmith make $25 dollars an hour. Her boss will be giving him a raise that is 1/5 of her current salary. How much money will Ms. Rangtonsmith be making AFTER he gets a raise?
Answer:
Ms. Rangtonsmith will get $30 after raise
Step-by-step explanation:
Current salary = $25
raise = 1/5 of current salary
substituting current salary with $25
raise in dollar value = 1/5 of $25 = 1/5 *$25 = $5
Thus, raise is $5
total salary after raise will be sum of current salary and raise
total salary after raise = $25 + $5 = $30
Thus, Ms. Rangtonsmith will get $30 after raise
Find the slope of the line passing through the points (-2,5) and (3/2, 2).
Answer:
The answer is
[tex] - \frac{6}{7} [/tex]Step-by-step explanation:
The slope of the line passing through two points can be found by using the formula
[tex]m = \frac{y2 - y1}{x2 - x1} [/tex]where
(x1 , y1) and (x2 , y2) are the points
From the question
The points are (-2,5) and (3/2, 2)
The slope is
[tex]m = \frac{2 - 5}{ \frac{3}{2} + 2} \\ = - \frac{3}{ \frac{7}{2} } \\ = - 3 \div \frac{7}{2} \\ = - 3 \times \frac{2}{7} [/tex]We have the final answer as
[tex] - \frac{6}{7} [/tex]Hope this helps you
Simplify the following expression: [tex]\sqrt{x} 48a^{8}[/tex]
Answer:
[tex]48\sqrt{x}a^{8}[/tex]
Step-by-step explanation:
[tex]\sqrt{x}48a^{8}[/tex]
rewrite using communitive property of multiplication:
[tex]48\sqrt{x}a^{8}[/tex]
[tex]\framebox{\parbox[t][1.0cm]{4.50cm}{\addvspace{0.2cm} \centering $ \;\sqrt[48]{xa^8} \; \, \dfra\;\ \;\; \dfrac{}{} $ } }\\[/tex]
Step-by-step explanation:
[tex]\sqrt{x48a^8}[/tex]
There are no variables we will just rewrite this as:
[tex]\sqrt[48]{xa^8}[/tex]
Hope this helps!
In a manufactory, there are two types of spoilages. It is found that 5% of spoilages are due to transformer spoilage, 8% are due to line spoilage and 3% involve both problems. (a) Are the two types of spoilages independent or not? Justify your answer. (b) What is the probability that: i- line spoilage given that there is transformer spoilage ii- Transformer spoilage but not line spoilage. iii- Transformer spoilage given that there is no line spoilage iv- Neither transformer spoilage nor there is no line spoilage v- Either transformer spoilage or there is no line spoilage
Answer:
Step-by-step explanation:
Let us denote probability of spoilage as follows
Transformer spoilage = P( T ) ; line spoilage P ( L )
Both P ( T ∩ L ) .
Given
P( T ) = .05
P ( L ) = .08
P ( T ∩ L ) = .03
a )
For independent events
P ( T ∩ L ) = P( T ) x P ( L )
But .03 ≠ .05 x .08
So they are not independent of each other .
b )
i )
Probability of line spoilage given that there is transformer spoilage
P L/ T ) = P ( T ∩ L ) / P( T )
= .03 / .05
= 3 / 5 .
ii )
Probability of transformer spoilage but not line spoilage.
P( T ) - P ( T ∩ L )
.05 - .03
= .02
iii )Probability of transformer spoilage given that there is no line spoilage
[ P( T ) - P ( T ∩ L ) ] / 1 - P ( L )
= .02 / 1 - .08
= .02 / .92
= 1 / 49.
i v )
Neither transformer spoilage nor there is no line spoilage
= 1 - P ( T ∪ L )
1 - [ P( T ) + P ( L ) - P ( T ∩ L ]
= 1 - ( .05 + .08 - .03 )
= 0 .9
Are 95/- 5, - 95/5, - 95/5 the same?
Answer:
Step-by-step explanation:
Yes, 95/-5, -95/5, -95/5 are the same.
They are all equal to -19
Answer:
Yes, 95/-5, -95/5, -95/5 are the same.
They are all equal to -19
Step-by-step explanation:
one third of a number less than 9 equal to 7
solve the quadratic equation by completing the square x^2+8x+11=0
Answer:
[tex]x=-4\pm\sqrt5[/tex]
Step-by-step explanation:
So we have the equation:
[tex]x^2+8x+11=0[/tex]
First, subtract 11 from both sides:
[tex]x^2+8x=-11[/tex]
Now, add the c term. Divide 8 by 2 and then square it:
[tex](x^2+8x+16)=-11[/tex]
What we do to one side we must also do to the other. Thus:
[tex](x^2+8x+16)=-11+16[/tex]
Simplify:
[tex](x^2+8x+16)=5[/tex]
Perfect Square Trinomial:
[tex](x+4)^2=5[/tex]
Take the square root:
[tex]x+4=\pm\sqrt5[/tex]
Subtract 4:
[tex]x=-4\pm\sqrt5[/tex]
And that's our answer :)
which of the following statements is not true concerning the equation x^2 - C = 0 for C > 0
A. the left hand side of the equation is called a difference of two squares
B. quadratic equation in this form can always be solved using the square root property
C. a quadratic equation in this form can always be solved by factoring
D. this equation is not considered to be a quadratic equation because it's not at the farm of ax^2 + BX + C = 0
Answer:
it is the quadratic equations to sole your questions
WILL MARK BRAINLIEST An architect is drafting a scale drawing of a house for an upcoming project. The customer wants the front of the house to measure 60 feet long. The architect's sketch shows that the front of the house has a length of 15 inches. Determine the factor of dilation used by the architect as he created the scale drawing for his customer. In your final answer, include all of your calculations.
Answer:
The scale factor is 1/48
Step-by-step explanation:
First, we need to convert 60 feet to inches.
60 feet = 720 inches
Then, we divide 720 by 15
720/15= 48.
The scale factor is 1/48.
The scale factor of dilation is given by the proportion and A = 48
What is Proportion?The proportion formula is used to depict if two ratios or fractions are equal. The proportion formula can be given as a: b::c : d = a/b = c/d where a and d are the extreme terms and b and c are the mean terms.
The proportional equation is given as y ∝ x
And , y = kx where k is the proportionality constant
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Given data ,
Let the proportion be represented as A
Now , the value of A is
We can use the ratio of the lengths of the corresponding sides to find the scale factor or dilation factor used by the architect.
Let A be the factor of dilation used by the architect. Then we can set up the following proportion:
60 feet / A = 15 inches / 1
We can solve for x by cross-multiplying:
60 feet x 1 = A x 15 inches
A = (60 feet) / (15 inches)
We need to convert feet to inches to get the units to match:
A = (60 feet) / (15 inches) x (12 inches / 1 foot)
Simplifying, we get:
A = 720 / 15
A = 48
Hence , the architect used a scale factor of 48 when creating the scale drawing of the house
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4(x+2) = x-4 ALGEBRA TILES ALGEBRA Solution:
Answer:
x = 4
Step-by-step explanation:
Order of Operations: BPEMDAS
Step 1: Write equation
4(x + 2) = x - 4
Step 2: Distribute
4x + 8 = x - 4
Step 3: Subtract 8 on both sides
4x + 8 - 8 = x - 4 - 8
4x = x - 12
Step 4: Subtract x on both sides
4x - x = x - x - 12
3x = 12
Step 5: Divide both sides by 3
3x/3 = 12/3
x = 4
Final Answer:
x = -4
Step-by-step explanation:
step 1 Simplify both sides of the equation:
4(x + 2) = x - 4
(4)(x) + (4)(2) = x + (-4)
4x + 8 = x + (-4)
step 2 Subtract x from both sides:
4x + 8 - x = x - 4 - x
3x + 8 = -4
step 3 Subtract 8 from both sides:
3x + 8 - 8 = -4 - 8
3x = -12
last step Divide both sides by 3:
3x -12
___ = ___
3 3
x = -12/3
x = -4
:)
Solve for x: |3x + 12| = 18
Answer:
X = 2 or X = -10
Step-by-step explanation:
We know either3x+12=18or3x+12=−18
3x+12=18(Possibility 1)
3x+12−12=18−12(Subtract 12 from both sides)
3x=6
3x
3
=
6
3
(Divide both sides by 3)
x=2
3x+12=−18(Possibility 2)
3x+12−12=−18−12(Subtract 12 from both sides)
3x=−30
3x
3
=
−30
3
(Divide both sides by 3)
x=−10
Answer:
x=2 or x=−10
x^3 - 2y^2 - 3x^3 + z^4
Answer:
-2x³ - 2y² + z⁴
Step-by-step explanation:
Step 1: Write out expression
x³ - 2y² - 3x³ + z⁴
Step 2: Combine like terms (x³)
-2x³ - 2y² + z⁴