Answer:
0.619 = 61.9% probability of choosing a professor or an instructor.
Step-by-step explanation:
A probability is given by the number of desired outcomes divided by the number of total outcomes.
In this question, we have that:
7 + 4 + 4 + 6 = 21 members
7 + 6 = 13 professors or instructors.
Find the probability of choosing a professor or an instructor.
p = 13/21 = 0.619
0.619 = 61.9% probability of choosing a professor or an instructor.
g(x)=x^2-5x
f(x)=2x+1
Find (g-f)(x)
Answer:
(g-f)(x) = x²-7x -1
Step-by-step explanation:
hello :
g(x)=x²-5x f(x)=2x+1
(g-f)(x) =g(x) - f(x) = x²-5x- ( 2x+1 ) = x²-5x - 2x-1
(g-f)(x) = x²-7x -1
Jason rolls the die 14 times. What is the experimental probability that he will roll a 2
The experimental probability that Jason will roll a 2 is 3/14.
What is the probability?Probability can be defined as the ratio of the number of favourable outcomes to the total number of outcomes of an event.
We know that, probability of an event = Number of favourable outcomes/Total number of outcomes.
Given that, Jason rolls the die 14 times.
From the given table,
Number of favorable outcomes = 3
Total number of outcomes = 14
So, the probability = 3/14
Therefore, the experimental probability that Jason will roll a 2 is 3/14.
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how much greater is 620,000 than 62?
Answer:
10,000
Step-by-step explanation:
620,000/62 = 10,000
A farmer is building a fence to enclose a rectangular area against an existing wall. Three of the sides will require fencing and the fourth side is a wall that already exists. If the farmer has 148 feet of fencing, what is the largest area the farmer can enclose?
Answer:
Step-by-step explanation:
There are several things we need to know to solve this: the perimeter formula of a rectangle, the area formula of a rectangle, and how to complete the square to find the answer. First of all, if the farmer has 148 feet of fencing to enclose 3 sides of a rectangle, the perimeter formula we need will include only 3 sides, the 2 widths and the 1 length:
P = 2w + l; solving for l and filling in our length of fencing gives us:
l = 148 - 2w
The area then for this will be:
A = (148 - 2w)(w) which is the same thing as length times width (area for a rectangle). Multiplying that out gives us:
[tex]A=148w-2w^2[/tex]. Let's rearrange that and put it into descending order so we can complete the square on it:
[tex]A=-2w^2+148w[/tex]
The reason we want to complete the square is because the answer that results from that will give us the dimensions of the rectangle (the width and the length) and also the area. Completing the square maximizes (or minimizes) area.
To complete the square, first factor out the -2 since the leading coefficient when you complete the square has to be a +1. When we do that we get:
[tex]A=-2(w^2-74w)[/tex]. Set it equal to 0 so we can factor it:
[tex]-2(w^2-74w)=0[/tex]
The idea now is to take half the linear term (the term stuck to the w), divide it in half, then square that number. Our linear term is 74. Half of 74 is 37, and 37 squared is 1369. So we add 1369 to both sides, the left side first:
[tex]-2(w^2-74w+1369)=...[/tex]
But we didn't just add in 1369. There's a -2 out front there that refuses to be ignored. It's a multiplier. What we ACTUALLY added in was -2 times 1369 which is -2738; therefore:
[tex]-2(w^w-74w+1369)=-2738[/tex]
The left side can be simplified down to a perfect square binomial:
[tex]-2(w-37)^2=-2738[/tex]
Now we'll add over the -2738:
[tex]-2(w-37)^2+2738=y[/tex] and from there determine our answer. The (w-37) term is the width of the rectangle; therefore, the length is 148 - 2(37) which is 74; the total area if the 2738. Completing the square gives us the vertex form of the parabola; the vertex is (37, 2738) where 37 is the width of the rectangle and 2738 is the max area.
I can't figure this out
9514 1404 393
Answer:
143 in²
Step-by-step explanation:
The figure is dimensioned in such a way that it can be divided easily into three rectangular areas. The top rectangle is 10 in wide and 7 in high. The vertical rectangle below that is 4 in wide and 12 in high, and the square appendage on the right is 5 in square.
Then the total area is the sum of products of length and width:
A = (10 in)(7 in) + (4 in)(12 in) + (5 in)(5 in) = (70 +48 +25) in²
A = 143 in²
The area of the irregular figure is 143 in².
Simplify
8(10 m)
80 + m
18 m
80 m
810 m
80m, you kind of distribute so 8 times 10m is 80m
Name the postulate or theorem
Answer:
pythagoras theorem
Step-by-step explanation:
Pythagoras theorem states that “In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides“.
WILL MARK BRAINLIEST
Solve for x.
60
10
20
120
Answer:
x = 10
Step-by-step explanation:
Let's draw the center of the circle S and the segments SE and SD.
SE is perpendicular to EF (as EF is tangent to circle).
That means FED + DES = 90deg
We also know that DSE = 120deg
And because the SED is an isosceles triangle, we know that angle measures for DES and SDE are equal.
DES = (180deg - 120deg) / 2 = 30deg
FED = 90deg - DES = 90deg - 30deg = 60deg
7x - 10 = 60
7x = 70
x = 10
Which of these shows the complete factorization of 6x^2y^2-9xy-42
Answer:
3 • (2xy - 7) • (xy + 2)
Step-by-step explanation:
(((2•3x2) • y2) - 9xy) - 42
6x2y2 - 9xy - 42 = 3 • (2x2y2 - 3xy - 14)
The complete factorization of 6x^2y^2-9xy-42 is 3 (2x^2y^2 - 3xy - 14).
What is factorization?factorization is the method of breaking a number into smaller numbers that multiplied together will give that original form.
The given expression is
[tex]6x^2y^2-9xy-42[/tex]
= [tex](((2\times3x^ 2) \times y^2) - 9xy) - 42[/tex]
The factorized form will be
= [tex]3 (2x^2y^2 - 3xy - 14)[/tex]
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13
What is the inverse of when
15
multiplying fractions?
13
A
15
15
B
13
13
C с
13
15
D
15
Answer:
Step-by-step explanation:
15x13=?
15+15+1=31
so the answer is 31
Help me I need this really bad and I need a good grade I’m behind on school
Answer:
If you share 7 apples equally with 3 people, then there are 2 1/3 apples per person.
The number 2 represents the number of whole apples each individual gets.
The denominatior, 3, represents how many times an apple will have to be split to divide equally
The numerator, 1, represents how many 3rds each person gets.
I’m not sure and please explain how you got the answer pleaseee
Answer:
A
Step-by-step explanation:
Because 30+18=48, and 3(10+6)=48
10+6=16
3•16=48
Plz help me the question is in the picture
Find the area of the trapezoid.
22.2 cm
9.86 cm
8.52 cm
[? ]cm2
Enter the exact answer. Do not round
Answer:
151.4496
Step-by-step explanation:
it has not been rounded or anything that is the exact answer
Answer: 151.45 (151.4496)
Step-by-step explanation:
Formula: A = (a+b)/2 * h
Base = 22.2
Base = 8.52
Height = 9.86
Do the following:
(22.2+8.52)/2 * 9.86 = 151.4496
An apartment complex stretched a string of decorative floats diagonally across a
rectangular pool. The width of the pool is 15 ft and the length of the pool is 20 ft.
What is the length of the a diagonal that the floats are stretched across ?
Answer:
25 feet
Step-by-step explanation:
Use the pythagorean theorem, where the width and length of the pool are the legs of the triangle.
Solve for c, the hypotenuse/diagonal
a² + b² = c²
15² + 20² = c²
225 + 400 = c²
625 = c²
25 = c
So, the length of the diagonal is 25 feet
25. Which two conversions are correct?
A. 7 mm = 70 cm
B. 7 cm = 0.07 m
C. 7,000 m = 7 km
D. 0.7 cm = 70 mm
E. 7 m = 7,000 km
Answer:
The answer is B and C
Step-by-step explanation:
1 Meter is equal to 0.001 Kilometer
1 Centimeter is equal to 0.01 Meters
The unit conversions which has the true measurements are
a) 7 cm = 0.07 m
b) 7,000 m = 7 km
What is unit conversion?In order to translate measurements of a particular amount between different units, a mathematical conversion factor is usually used. This modifies the measurement of the quantity without altering its effects.
The particular circumstances or the intended result control the conversion process. This may be governed by law, a contract, a list of technical specifications, or other publicly available standards.
A precise conversion from one system to another is necessary for some measures in order to maintain the precision of both the original measurement and the conversion.
Based on the connection between a particular pair of original units and a particular pair of target units, each conversion factor is chosen.
Given data ,
Let the unit conversion be represented as A
Let the first measurement be p
where the value of p is
p = 7 cm
From the unit conversion , 1 m = 100 cm
So , 7 cm = 0.07 m
And , let the second measurement be q = 7,000 m
From the unit conversion , 1 km = 1,000 m
7,000 m = 7 km
Hence , the unit conversions are solved
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Anyone know this? Answer for cookie!
Answer:
no solution
Step-by-step explanation:
the value of 3x+2y can't be two different things at once
Answer: no solutions
Step-by-step explanation:
when the two equations have the same x and y values but a different y intercept they can not have any solutions because they are parallel
In the year 1986 reg Morris ate 30 hotdogs in 64 seconds how many seconds per hotdog is this
Answer:
Step-by-step explanation:
Time taken to eat 30 hot dogs = 64 seconds
Time taken to eat 1 hot hot dog = 64 ÷ 30
≈ 2 seconds
Calculus helpppppppppppppppp
Answer:
[tex]\displaystyle y' = \frac{5x^2 + 3}{3(1 + x^2)^\bigg{\frac{2}{3}}}[/tex]
General Formulas and Concepts:
Pre-Algebra
Equality PropertiesAlgebra I
FunctionsFunction NotationExponential Rule [Root Rewrite]: [tex]\displaystyle \sqrt[n]{x} = x^{\frac{1}{n}}[/tex]Algebra II
Logarithms and Natural LogsLogarithmic Property [Multiplying]: [tex]\displaystyle log(ab) = log(a) + log(b)[/tex]Logarithmic Property [Exponential]: [tex]\displaystyle log(a^b) = b \cdot log(a)[/tex]Calculus
Derivatives
Derivative Notation
Derivative Property [Multiplied Constant]: [tex]\displaystyle \frac{d}{dx} [cf(x)] = c \cdot f'(x)[/tex]
Derivative Property [Addition/Subtraction]: [tex]\displaystyle \frac{d}{dx}[f(x) + g(x)] = \frac{d}{dx}[f(x)] + \frac{d}{dx}[g(x)][/tex]
Basic Power Rule:
f(x) = cxⁿ f’(x) = c·nxⁿ⁻¹Derivative Rule [Chain Rule]: [tex]\displaystyle \frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)[/tex]
Logarithmic Derivative: [tex]\displaystyle \frac{d}{dx} [lnu] = \frac{u'}{u}[/tex]
Implicit Differentiation
Step-by-step explanation:
Step 1: Define
Identify
[tex]\displaystyle y = x\sqrt[3]{1 + x^2}[/tex]
Step 2: Rewrite
[Equality Property] ln both sides: [tex]\displaystyle lny = ln(x\sqrt[3]{1 + x^2})[/tex]Logarithmic Property [Multiplying]: [tex]\displaystyle lny = ln(x) + ln(\sqrt[3]{1 + x^2})[/tex]Exponential Rule [Root Rewrite]: [tex]\displaystyle lny = ln(x) + ln \bigg[ (1 + x^2)^\bigg{\frac{1}{3}} \bigg][/tex]Logarithmic Property [Exponential]: [tex]\displaystyle lny = ln(x) + \frac{1}{3}ln(1 + x^2)[/tex]Step 3: Differentiate
ln Derivative [Implicit Differentiation]: [tex]\displaystyle \frac{d}{dx}[lny] = \frac{d}{dx} \bigg[ ln(x) + \frac{1}{3}ln(1 + x^2) \bigg][/tex]Rewrite [Derivative Property - Addition]: [tex]\displaystyle \frac{d}{dx}[lny] = \frac{d}{dx}[ln(x)] + \frac{d}{dx} \bigg[ \frac{1}{3}ln(1 + x^2) \bigg][/tex]Rewrite [Derivative Property - Multiplied Constant]: [tex]\displaystyle \frac{d}{dx}[lny] = \frac{d}{dx}[ln(x)] + \frac{1}{3}\frac{d}{dx}[ln(1 + x^2)][/tex]ln Derivative [Chain Rule]: [tex]\displaystyle \frac{y'}{y} = \frac{1}{x} + \frac{1}{3} \bigg( \frac{1}{1 + x^2} \bigg) \cdot \frac{d}{dx}[(1 + x^2)][/tex]Rewrite [Derivative Property - Addition]: [tex]\displaystyle \frac{y'}{y} = \frac{1}{x} + \frac{1}{3} \bigg( \frac{1}{1 + x^2} \bigg) \cdot \bigg( \frac{d}{dx}[1] + \frac{d}{dx}[x^2] \bigg)[/tex]Basic Power Rule]: [tex]\displaystyle \frac{y'}{y} = \frac{1}{x} + \frac{1}{3} \bigg( \frac{1}{1 + x^2} \bigg) \cdot (2x^{2 - 1})[/tex]Simplify: [tex]\displaystyle \frac{y'}{y} = \frac{1}{x} + \frac{1}{3} \bigg( \frac{1}{1 + x^2} \bigg) \cdot 2x[/tex]Multiply: [tex]\displaystyle \frac{y'}{y} = \frac{1}{x} + \frac{2x}{3(1 + x^2)}[/tex][Multiplication Property of Equality] Isolate y': [tex]\displaystyle y' = y \bigg[ \frac{1}{x} + \frac{2x}{3(1 + x^2)} \bigg][/tex]Substitute in y: [tex]\displaystyle y' = x\sqrt[3]{1 + x^2} \bigg[ \frac{1}{x} + \frac{2x}{3(1 + x^2)} \bigg][/tex][Brackets] Add: [tex]\displaystyle y' = x\sqrt[3]{1 + x^2} \bigg[ \frac{5x^2 + 3}{3x(1 + x^2)} \bigg][/tex]Multiply: [tex]\displaystyle y' = \frac{(5x^2 + 3)\sqrt[3]{1 + x^2}}{3(1 + x^2)}[/tex]Simplify [Exponential Rule - Root Rewrite]: [tex]\displaystyle y' = \frac{5x^2 + 3}{3(1 + x^2)^\bigg{\frac{2}{3}}}[/tex]Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Implicit Differentiation
Book: College Calculus 10e
Mr. Thorbes bought a new journal for his poetry. If the journal normally cost $22 but was on sale for 20% off, how much did Mr. Thorbes save?
Answer:
He would save $4.40
Step-by-step explanation:
And in total he would pay 17.60
"A driving instructor is investigating whether the time a driver spends in a driverâs education course improves their score on the driverâs test. The instructor randomly selected 10 drivers from a driverâs education course and recorded the number of hours each driver attended the driverâs education course and their corresponding score on the driverâs test. Assuming all conditions for inference are met, which of the following significance tests should be used for the investigation?"
a. A chi-square test of independence
b. A two-sample t-test for a difference between means
c. A two-sample z-test for a difference between proportions
d. A linear regression t-test for slope
e. A matched pairs t-test for a mean difference
Answer:
e. A matched pairs t-test for a mean difference
Step-by-step explanation:
When the observations from two samples are paired either naturally or by design we find the differences between the two observations of each pair.Treating the differences as a random sample from a normal population with mean ud= u1-u2 and unknwn standard deviation σd we perform one sample t- test on them. This is called the paired difference t- test or a paired t- test.
Suppose 10 young recruits are given a physical training by the Army . Their weights are recorded before and after the training. These observations constitutes natural pairing .
When we eliminate the undesireable sources of variation to take observations in pairs , this is called pairing by design.
PLEASE HELP:):):):):):):):)
Answer:
[tex]Area = 8[/tex]
Step-by-step explanation:
Given
The attached figure
Required
Determine the area
The shape is a trapezium. So, the area is:
[tex]Area = \frac{1}{2} *(Sum\ of\ parallel\ sides) * Height[/tex]
From the attached,
The height is 2
The parallel sides are: 2 and 6
So, the area is:
[tex]Area = \frac{1}{2} *(2 + 6) * 2[/tex]
[tex]Area = \frac{1}{2} *8 * 2[/tex]
[tex]Area = 8[/tex]
Hence, the area is 8 units square
doivhrghfufvh - 10 points!
Answer:
I'm sure it's already all the way simplified since there are no common terms
I could he wrong but I dont think theres anything more you can do since they are all their own different term
Step-by-step explanation:
for example if it was 7x-2x-1 then you would subtract 7x and 2x and then it would come put to be 5x-1
hope this helped at all
someone pls help I'm genuinely confused
I've literally been trying to figure out all three of these for like two hours now but I can't figure it out
Answer:
the area is 50
Step-by-step explanation:
Answer:
its 0.09637 but round it by urself . please like my answer and brainliest me hshsshhs
Simplify.
Remove all perfect squares from inside the square root. Assume x is positive.
√ 20x^8
Please help me I really need it
Answer:
Angle C
Step-by-step explanation:
By applying sine rule in the given triangle,
[tex]\frac{\text{sinB}}{CD}=\frac{\text{sinC}}{BD}=\frac{\text{sinD}}{BC}[/tex]
[tex]\frac{\text{sinB}}{\text{sinC}}=\frac{\text{CD}}{\text{BD}}[/tex]
Therefore, sides of the given triangle will be in the same ratio as the sine of the angles.
Since, BD > BC > CD
Therefore, Opposite angles of these sides will be in the same ratio.
∠C > ∠D > ∠B
Largest angle of the triangle is angle C.
Evaluate the polynomial for x=1
Answer:
2
Step-by-step explanation:
Hi there,
In order to solve this expression, you need to substitute x for 1.
You will end up with this expression:
3([tex]1^{2}[/tex]) - 2(1) + 1
Now, simplify the expression.
⇒ 3 - 2 + 1
⇒ 1 + 1
⇒ 2
Therefore, the answer when we evaluate the polynomial for x = 1 is 2.
Which algebraic expression represents the phrase "the quotient of negative eight and the sum of a number and three"
-8
Og+3
8
9+3
-8+g
3
+3
Answer:
[tex]\dfrac{-8}{x+3}[/tex]
Step-by-step explanation:
We need to find an algebraic expression for the given statement i.e. "the quotient of negative eight and the sum of a number and three".
Let the number be x. Quotient means to divide. It means we need to divide -8 and the sum of x and 3.
So, we can write it as follows :
[tex]\dfrac{-8}{x+3}[/tex]
Hence, this is the required solution.
Hannah signs on a $148,500 mortgage at a 4.5% annual interest rate for 20 years. This results in a monthly payment is
$938.48. If only the minimum payment is made in month one, how much of the first payment goes toward reducing her
balance?
First let's find the amount of interest she paid in month 1, then find the amount toward reducing the balance.
Round to the nearest cent.
Answer:
Interest in one month= 556.88
Her balance is reduced by= 381.6
Step-by-step explanation:
How many gallons are in of a 7-gallon container of milk?
Answer:
7
Step-by-step explanation:
Uhh 7 divided by 1 is 7?
Answer:
7
Step-by-step explanation:
There are 7 gallons in a 7-gallon container of milk.
