Answer:
Empirical Rule
Step-by-step explanation:
The Empirical Rule is also known as the Sigma rule or the 68-95-99.7% rule. The rule state that for a given data set, 68% of all data values will fall within the first standard deviation from the mean. The rule also states that 95% of all data values would fall within two standard deviations, while almost all the data which amounts to about 99.7% will fall within three standard deviations.
The empirical rule is used in forecasting based on the given datasets because it is a certainty that after obtaining the standard deviation, data values can be assigned to the categories they fall into, under the Empirical rule.
If a 5 ft tall man cast an 8 ft long shadow at the same time a tree cast a 24 ft long shadow, how tall is the tree?
Answer:
15 feet
Step-by-step explanation:
We have 2 similar right triangles with legs height and length of shadows.
height of men : length of shadows of the man = height of tree : length of shadows of the tree
5 : 8 = x : 24
8x = 5* 24
x = 5*24/8 = 15 (feet)
Answer:
15ft
Step-by-step explanation:
5 ft is to 8 ft
A ft is to 24 ft
A = 24*5/8
A = 15ft
15ft
in how many ways cvan 5 people be chosen and arranged in a straight line, if there are 6 people to choose from'
Answer:
720 different waysStep-by-step explanation:
Permutation has to do with arrangement. If r objevt selected from n pool of objects are to be arranged in a straight line, this can be done in nPr number of ways.
nPr = n!/(n-r)!
If 5 people are to be chosen and arranged in a straight line, if there are 6 people to choose from, this can be done in 6P5 numbe of ways.
6P5 = 6!/(6-5)!
6P5 = 6!/1!
6P5 = 6*5*4*3*2*1
6P5 = 720 different ways
The diagram shows the floor plan for Harry's new tree house. The entry terrace on the tree house is shaped like an isosceles trapezoid.
Answer:
what do you need help with its not really clear
Answer
1. 48 2. 308
Step-by-step explanation:
"A motorist wants to determine her gas mileage. At 23,352 miles (on the odometer) the tank is filled. At 23,695 miles the tank is filled again with 14 gal- lons. How many miles per gallon did the car average between the two fillings?"
Answer:
24.5 mpg
Step-by-step explanation:
(23,695 - 23,252) / 14 = 24.5mpg
Answer:
The car averaged a total of 24.5 miles per gallon between the two fillings
Step-by-step explanation:
Firstly, we calculate the difference between the mileages.
This will give us the total distance traveled.
That would be 23,695 - 23,352 = 343 miles
The tank capacity obviously is 14 gallons
So mathematically, miles per gallon averaged between the two fillings = distance traveled by the car/gallon of fuel used = 343/14 = 24.5 miles per gallon
Classify the polynomial 2x^3+6x^2-4 by the number of terms. binomial. trinomial. cubic. quadratic.
Answer:
monomial
Step-by-step explanation:
0.3% of a country has a certain disease. The test for the disease has a sensitivity of 92% (i.e., of those we know have the disease, the test comes back positive 92% of the time.) It has a specificity of 96% (i.e., of those who do NOT have the disease, the test comes back negative 96% of the time.) Determine the ACCURACY of this test (round to 5 decimals) Remember, ACCURACY is correct values (i.e. true positives true negatives)
Answer:
0.95988 (Accuracy of the test )
Step-by-step explanation:
To determine the accuracy of this test we have to list out the given values
Prevalence rate of the disease = 0.3% = 0.003
sensitivity rate of the disease = 92% = 0.92
specificity rate for the test = 96% = 0.96
The accuracy of the test can be found using this equation
Accuracy = sensitivity * prevalence + specificity ( 1 - prevalence )
= 0.92 * 0.003 + 0.96 ( 1 - 0.003 )
= 0.00276 + 0.95712
= 0.95988
Which line has a slope of -? 2 x – y = 0 - x + 2 y = 0 x - 2 y = 0 x + 2 y = 0 NEXT
Answer:
Easiest way to do this is to get the X's on one side of the equals sign and the Y's on the other. Then, you can choose the one with the negative sign in it.
When you do that,
First one is 2x=0+y, or y = 2x
Second one is 2y=0+x, or 2y = x (weird right)
Third one is x=0+2y, or 2y = x (again, weird right)
Final one is 2y=0-x, or 2y = -x
The final one is the answer. Cheers, but don't forget to remember this for next time bro.
How many games are played in a 4 team round robin tournament? (Each team
plays every other team only once.)
Answer: 6
Step-by-step explanation:
If we call each team, A, B, C and D, each team has to play each other team once. Let's call each pairing between 2 teams the 2 teams' letters next to each other, e.g. AB is A playing against B. A has to play against B, C and D so we have AB, AC and AD. So we have 3 so far.
We have already counted that B is playing A but we haven't counted B playing C and D yet so we also have BC and BD. So we have 5 in total
Lastly, C needs to play D, we have already counted C playing B and C playing A so we have CD left. In total that gives 6.
Now we have already included D playing every other team so we don't include any other pairings.
In total, now every team has played every other team giving a total of 6.
(another way of solving this is doing "3!2 but if you haven't learnt factorials yet stick to the first method.
Answer:
6 games.
Step-by-step explanation:
The answer is the number of combinations of 2 from 4
= 4*3 / 2*1
= 6.
What is the inverse of the logarithmic function
f(x) = log2x?
f –1(x) = x2
f –1(x) = 2x
f –1(x) = logx2
f –1(x) = StartFraction 1 Over log Subscript 2 Baseline x EndFraction
Answer:
B. edge 2021
B. is correct for the next one too.
Step-by-step explanation:
B. is the correct answer for the first one
B. is also the correct answer for the second one
Find the volume o the sphere.
Answer:
The volume of sphere is 267.95 units³.
Step-by-step explanation:
Given that the formula of volume of sphere is V = 4/3×π×r³ where r represents radius. Then, you have to substitute the values into the formula :
[tex]v = \frac{4}{3} \times \pi \times {r}^{3} [/tex]
[tex]let \: r = 4[/tex]
[tex]v = \frac{4}{3} \times \pi \times {4}^{3} [/tex]
[tex]v = \frac{4}{3} \times \pi \times 64[/tex]
[tex]v = \frac{256}{3} \times 3.14[/tex]
[tex]v = 267.95 \: {units}^{ 3} [/tex]
Is (-1, -1) a solution of y = 3x + 2?
Answer:
Yes
Step-by-step explanation:
Well the integer (-1, -1) means x = -1 and y = -1
So we can plug this into the equation
-1 = 3(-1) + 2
-1 = -3 + 2
-1 = -1
So yes (-1, -1) is a solution.
Hi Folks, l have this Rearranging difficult formulae exercise, l have the answer but l dont understand at all the procedure, the method applied, if someone can explain it to me please will be appreciatted thanks 1/a = 1/b+1/c the procedure is: 1= a/b + a/c (x a) b= a+ ab/c (x b) bc= ac +ab ( x c) b (c-a) = ac b= ac/c-a OR b= - ac /a - c Def l dont understand the method thanks for your help
Step-by-step explanation:
1/a = 1/b + 1/c
Multiply both sides by a.
1 = a/b + a/c
Multiply both sides by b.
b = a + ab/c
Multiply both sides by c.
bc = ac + ab
Subtract ab from both sides.
bc − ab = ac
Factor b.
b (c − a) = ac
Divide both sides by c − a.
b = ac / (c − a)
Answer:
see below
Step-by-step explanation:
1/a = 1/b+1/c
Multiply each side of the equation by a
a( 1/a) =a( 1/b+1/c)
1 = a/b + a/c
Then multiply each side of the equation by b
b*1 =b( a/b + a/c)
b = a + ab/c
Then multiply each side of the equation by c
cb = c( a+ ab/c)
bc = ac + ab
We have gotten rid of the fractions
Now we can solve for a
Factor out a on the right side
bc = a( c+b)
Then divide by c+b on each side
bc / ( c+b) = a ( c+b) / ( c+b)
bc / ( c+b) = a
Now we can solve for b
bc = ac + ab
Subtract ab from each side
bc -ab = ac + ab-ab
bc -ab = ac
Factor out b on the left side side
b( c-a) = ac
Then divide by c-a on each side
b( c-a) / ( c-a) = ac / ( c-a)
b = ac/ ( c-a)
We can factor out -1
b = -ac/( a-c)
Plz help asap!!!!!!!!!!!!!
Answer:
6.64 ft²
Step-by-step explanation:
Given the above triangle with 2 sides of lengths 3.2 ft and 4.7 ft respectively, and angle 62° in between, the following formula can be used to calculate the area: ½*a*b*sin(θ).
Thus, a and b are the 2 given sides and θ is the included angle in between both sides.
Therefore,
Area = ½*3.2*4.7*sin(62)
Area = ½*15.04*0.88295
Area = ½*13.279568
Area = 6.639784
Area = 6.64 ft² (to the nearest hundredth)
Help thank you!!!!!!!
[tex] v = \sqrt{4900} + \sqrt{8100} = 70 + 90 = 160[/tex]
Answer: D. 160
The function h(t) = –16t2 + 28t + 500 represents the height of a rock t seconds after it is propelled by a slingshot. What does h(3.2) represent? the height of the rock 3.2 seconds before it reaches the ground the time it takes the rock to reach the ground, or 3.2 seconds the time it takes the rock to reach a height of 3.2 meters the height of the rock 3.2 seconds after it is propelled
Answer:
The answer is d
Step-by-step explanation:
h(3.2) represents the height of the rock 3.2 seconds after it is propelled.
What is Function?A function is a relation from a set A to a set B where the elements in set A only maps to one and only one image in set B. No elements in set A has more than one image in set B.
Given a function,
h(t) = -16t² + 28t + 500
Here t represents the time after it is propelled.
h(t) represents the height of the rock t seconds after it is propelled.
So, h(3.2) represents the height of the rock 3.2 seconds after it is propelled.
Hence the correct option is D.
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20 points + brainliest = 30 points!
Answer:
see below
Step-by-step explanation:
Addition and subtraction are both closed under polynomials.
That means that when we add and subtract polynomials, we will end up with a polynomial
f(x) + g(x) will = always be a polynomial when we start with polynomials
f(x) - g(x) will = always be a polynomial when we start with polynomials
Answer:
[tex]\boxed{\mathrm{view \: explanation}}[/tex]
Step-by-step explanation:
A polynomial is an expression consisting of variables and coefficients.
[tex]f(x)[/tex] and [tex]g(x)[/tex] are polynomial functions.
Adding polynomials and subtracting polynomials is essentially combining like terms of polynomial expressions.
[tex]f(x)+g(x)[/tex] is always a polynomial
[tex]f(x)-g(x)[/tex] is always a polynomial
If you add, subtract or multiply any two polynomials then the result will be always a polynomial.
Which value of x would make NO IKI
?
K
(x + 2) in
o 1
N
(x - 3) in
06
o 8
x-4) in 0
x in
o 10
Save and Exit
Next
Submit
Answer:
[tex]\boxed{x = 8}[/tex]
Step-by-step explanation:
For NO ║ KJ, The two triangles must be similar and their sides must be proportional.
So, the proportion of their sides is:
=> [tex]\frac{x-4}{x} = \frac{x-3}{x+2}[/tex]
Cross Multiplying
[tex]\sf x (x-3)= (x-4)(x+2)\\Multiplying\\x^2-3x = x^2+2x-4x-8\\x^2-3x = x^2-2x-8\\Subtracting\ x^2\ to \ both \ sides\\ -3x = -2x -8\\Adding \ 2x\ to\ both\ sides\\-3x+2x = -8\\-x = -8\\[/tex]
x = 8
So, For x = 8, NO will be parallel to KJ.
6 2/9 - 5 - 8/9 = ?
Which of the following is the slope-intercept form of 6x + 2y = 28
a) y= 3x-4
b) y= 3x +4
c) y= -3x+4
d) y= -3x-4
Set up a rational equation and then solve the following problems. A positive integer is twice another. The difference of the reciprocals of the two positive integers is 1/18. Find the two integers.
Answer:
9 and 18
Step-by-step explanation:
2x and x are the numbers
1/x-1/2x=1/18
2/2x-1/2x=1/18
1/2x=1/18
2x=18X=9,
2x=18
The two integers are 9 and 18
Dr. Gongol, a sleep specialist, predicts that the proportion of snoring events compared to other events during a sleep study is more than 35%. To test this prediction, he evaluates 200 random sleep studies and found that 140 studies showed that more than 35% events were snores. The following is the setup for this hypothesis test: H0:p=0.35 Ha:p>0.35 The p-value for this hypothesis test is 0.03. At the 5% significance level, should he reject or fail to reject the null hypothesis?
Answer:
Reject the null hypothesis
Step-by-step explanation:
The claim is H0:p=0.35 Ha:p>0.35
At a significance level of 0.05, if the p value observed is less than 0.05, then we reject the null hypothesis, but if the p value observed is greater than the null hypothesis, then we fail to reject the null hypothesis.
In this case study: the p value is 0.03 which is less than the significance level, this we will reject the null hypothesis and conclude that there is enough statistical evidence to prove that the proportion of snoring events compared to other events during a sleep study is more than 35%.
A contractor originally estimated the total cost of a job including labor and materials at $ 57,000. In reviewing the costs, a new estimate of $ 48,000 is made, reducing the labor cost by 15% and the material cost by 18%. What is each cost, labor and material, of the new estimate?
Answer:
shadow cow
Step-by-step explanation:
In new estimate cost of labor and material is 35,700 and 12,300 respectively.
What is reducing factor?Reduction Factor means the percentage obtained by dividing the Net Worth Shortfall Amount by the Required Net Worth Amount.
According to the question
A contractor originally estimated the total cost of a job including labor and materials at $ 57,000.
let Labor cost = l
Material cost = m
Now ,
l + m = 57000 ----------(1)
A new estimate of $ 48,000 is made, reducing the labor cost by 15% and the material cost by 18%.
i.e,
[tex]\frac{(100-15)}{100} l + \frac{(100-18)}{100} m = 48000[/tex]
[tex]\frac{(85)}{100} l + \frac{(82)}{100} m = 48000[/tex]
0.85l + 0.82m = 48000 --------------------------------(2)
multiplying equation (1) from 0.85
0.85l + 0.85m = 48450 -------------------------------(3)
subtracting equation (1) and (3)
0.85l + 0.85m = 48450
-0.85l -0.82m = -48000
0.03m=450
m = 15000 (old cost )
new cost of m is = 0.82 * 15000 =12,300
putting value of m in equation (1)
l + m = 57000
l + 15000 = 57000
l = 42000 (old cost)
new cost of l is = 0.85l = 0.85*42000
new cost of l is = 35,700
Hence, The new cost of labor is 35,700 and new cost of material is 12,300 .
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Shane has a bag of marbles with 4 blue marbles, 3 white marbles, and 1 red marbles. Find the following probabilities of Shane drawing the given marbles from the bag if the first marble(s) is(are) not returned to the bag after they are drawn. (Give your answer as a fraction)
Answer: A). A Blue, then a Red.
= 4/8 * 1/7
= 1/14
B). A Red, then a White.
= 1/7 * 3/8
= 3/56
C). A Blue, then a Blue, then another Blue.
= 4/8 * 3/7 * 2/6
= 1/14
Step-by-step explanation:
had to complete the question first.
Find the following probabilities of Derek drawing the given marbles from the bag if the first marble(s) is(are) not returned to the bag after they are drawn.
(a) A Blue, then a Red =
(b) A Red, then a White =
(c) A Blue, then a Blue, then a Blue =
given data:
blue marble = 4
white marble = 3
red marble = 1
total marble = 8
solution:
probability of drawing
A). A Blue, then a Red.
= 4/8 * 1/7
= 1/14
B). A Red, then a White.
= 1/7 * 3/8
= 3/56
C). A Blue, then a Blue, then another Blue.
= 4/8 * 3/7 * 2/6
= 1/14
WHOEVER ANSWERS FIRST GETS BRAINLIEST:) Which expression represents the surface area of the cone? A cone with diameter 12 inches, height 8 inches, and slant height 10 inches. S A = pi r l + pi r squared (pi) (6) (10) + (pi) (6 squared) (pi) (8) (10) + (pi) (8 squared) (pi) (12) (10) + (pi) (12 squared) (pi) (10) (12) + (pi) (10 squared)
Answer:
Step-by-step explanation:
The surface area of a cone is:
● Sa = Pi*r^2 +Pi*r*l
r is the radius and l is the slant heigth
The diameter of this cone is 12 inches so the radius is 6 (12/2=6).
●Sa = Pi*36 +Pi*6*10
●Sa = 301.59 in^2
Answer:
pi (6) * 10+ pi ( 6)^2
Step-by-step explanation:
The surface area of a cone is given by
SA = pi rl +pi r^2 where r is the radius and l is the slant height
We know the diameter is 12 so the radius is 12/2 = 6
SA = pi (6) * 10+ pi ( 6)^2
how many pairs of matching surfaces does a cereal box have
Answer:
3 pairs
Step-by-step explanation:
Top and Bottom
Front and Back
Side and Side.
Cereal Boxes have 6 sides
nineteen multiplied by twenty five
Answer:
19*25= 475
Step-by-step explanation:
You can either use a calculator or use the standard operation
Which number is an integer? Negative three-fourths 0 2.3 Pi
Answer:
0
Step-by-step explanation:
An integer is colloquially defined as a number that can be written without a fractional component.
-3/4 ---- It is a fraction itself, so it is a fractional component
0 ---- Has no fractional component
2.3 Pi ---- Pi is irrational and is a decimal, so is 2.3. Most of this is a fractional component already.
The only one we can't eliminate using just the definition is 0.
Hope that helps, tell me if you need a further explanation
From the given numbers the number that is an integer is 0. The correct option is B.
What is an integer?An integer is a whole number that can be positive, negative, or zero and is not a fraction. Integer examples include: -5, 1, 5, 8, 97, and 3,043. The following numbers are examples of non-integer numbers: -1.43, 1 3/4, 3.14,.09, and 5,643.1.
Given the following numbers -(3/4), 0, 2.3, and π. Therefore, from the given numbers the number that is an integer is 0.
Hence, From the given numbers the number that is an integer is 0.
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Write an algebraic expression that represents The quotient of a number squared and eight
Answer:
[tex]\boxed{\frac{x^2 }{8} }[/tex]
Step-by-step explanation:
The quotient is the result from division.
Let x be that number.
Division between x² and 8.
[tex]\frac{x^2 }{8}[/tex]
The algebraic expression representing the quotient of a number squared and eight is x²/8.
What is an algebraic expression?An algebraic expression is a combination of terms formed using mathematical operators (+, -, *, /). The terms are made by the combination of variables and constants.
How to solve the given question?In the question, we are asked to write an algebraic expression that represents the quotient of a number squared and eight.
We know that an algebraic expression constitutes both variables and constants.
We assume the number in the expression to be x.
The number squared is then represented by x².
The quotient of the number squared and eight can be represented as x²/8.
Therefore, the algebraic expression representing the quotient of a number squared and eight is x²/8.
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Find the dimensions of a right circular cylinder of maximum volume that can be inscribed in a sphere of radius 7.
Answer:
The height of the right circular cylinder is 14/√3 and its radius is 7√6/3.
Step-by-step explanation:
Check the attachment for the diagram.
The volume of a right circular cylinder = πr²h
r is the radius of the cylinder
h is the height of the cylinder
V = πr²h... 1
From the diagram, we can use Pythagoras theorem on the right angled triangle to get r². From the triangle P² = r²+(h/2)²
P is the radius of the sphere.
P = 7
7² = r²+(h/2)²
r² = 49-(h/2)²... 2
Substituting equation 2 into 1:
V = π(49-(h/2)²)h
V = π(49h-h³/4)...3
To get the height h of the cylinder, we need to differentiate the volume of the cylinder with respect to h and equate to zero. i.e dV/dh = 0 since it's the maximum volume.
dV/dh = π(49-3h²/4)
0 = π(49-3h²/4)
Dividing both sides by π
0/π = π(49-3h²/4)/π
49-3h²/4 = 0
49 = 3h²/4
3h² = 49×4
3h² = 196
h² = 196/3
h = √196/√3
h = 14/√3
To get the radius of the cylinder, we will substitute h = 14/√3 into equation 2
r² = 49-(h/2)²
r² = 49-{(14/√3)/2}²
r² = 49-{14/2√3}²
r² = 49-(7/√3)²
r² = 49 - 49/3
r² = (147-49)/3
r² = 98/3
r = √98/√3
r = √49× √2/√3
r = 7√2/√3
r = 7√2/√3 × √3/√3
r = 7√6/3
The height of the right circular cylinders is 14/√3 and its radius is 7√6/3.
Suppose that the relation T is defined as follows. =T, , p9, , 0m, , 9p, 66 Give the domain and range of T. Write your answers using set notation.
domain=
range =
Answer:
Step-by-step explanation:
Set notation { } is used in this case, to represent the domain and the range.
The values that go into T are the domain while the values that come out of T are the range.
The domain comprises all x (independent) values while the range comprises all y (dependent) values.
This should be applied in the clear definition of the relation T.