Answer:
990 ways
Step-by-step explanation:
The total number of automobiles we have is 11.
Now, what this means is that for the first position , we shall be selecting 1 out of 11 automobiles, this can be done in 11 ways( 11C1 = 11!/(11-1)!1! = 11!/10!1! = 11 ways)
For the second position, since we have the first position already, the number of ways we can select the second position is selecting 1 out of available 10 and that can be done in 10 ways(10C1 ways = 10!9!1! = 10 ways)
For the third position, we have 9 automobiles and we want to select 1, this can be done in 9 ways(9C1 ways = 9!/8!1! = 9 ways)
Thus, the total number of ways the first three finishers come in = 11 * 10 * 9 = 990 ways
Which is the graph of y = cos(x − π)?
Answer:
Graph 1.
Step-by-step explanation:
Th graph of [tex]y=\cos{(x-\pi)}[/tex] looks exactly like the graph of [tex]y=\cos{x}[/tex] if we shifted the axes [tex]\pi[/tex] units to the left. This has the visual effect of shifting the graph forward [tex]\pit[/tex][tex]\pi[/tex] units (imagine filming someone and panning the camera to the left; the person moves right in the camera frame).
So the point at [tex]x=0[/tex], which used to be [tex](0, \cos{0})=(0,1)[/tex] is now [tex](0,\cos{(0-\pi)})=(0,\cos{(-\pi)})=(0,-1)[/tex], which we can find on the first graph.
The graph of the cosine function is the first graph (counting from the left).
Which is the graph of y = cos(x − π)?This is rather easy to see.
We do know that cos(− π) = cos (π) = -1
In this case, where:
f(x) = y = cos(x − π)
We will have:
f(0) = cos( − π) = -1
So we only need to see which graph has a y-intercept equal to -1. By looking at the graphs we can see that the only one that meets this condition is the first graph (counting from the left). So that is the correct option.
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Patty has a bulletin board on her wall with the
dimensions shown.
How many photos in the shape of a parallelogram will it
take to cover the bulletin board if each photo has a
base of 6 inches and a height of 4 inches?
photos
36 in
24 in.
Intro
Done
DDDDDDD
7
Answer:
36
Step-by-step explanation:
Answer:
36 I did the math
Step-by-step explanation:
EZ
Angles A M Y and Y M B form a line. Angles Y M B and B M X form a line. Angles X M A and A M Y form a line. Choose each angle to complete the linear pairs. ∠AMY and ∠AMX ∠BMY and ∠BMX and ∠AMX and
Answer:
AMY
BMY
BMX
Step-by-step explanation:
I took the assignment
Answer:
The answers are : B, B, A
Step-by-step explanation:
RIGHT ON EDG!
Simplify the following expression. (73×61y)-(45×6y)
Answer:
4183y
Step-by-step explanation:
Multiply 73 and 61
73 × 61y = 4453
4453 - (45 × 6y)
Then multiply 45 by 6
45 × 6 = 270
4453y - 270y
Subtract
4453y - 270y = 4183y
1244.416666666 rounded to the nearest hundred
A sphere and a cylinder have the same radius and height. The volume of the cylinder is 21m. what is the volume of the sphere.
Answer:
The volume of the sphere is 14m³
Step-by-step explanation:
Given
Volume of the cylinder = [tex]21m^3[/tex]
Required
Volume of the sphere
Given that the volume of the cylinder is 21, the first step is to solve for the radius of the cylinder;
Using the volume formula of a cylinder
The formula goes thus
[tex]V = \pi r^2h[/tex]
Substitute 21 for V; this gives
[tex]21 = \pi r^2h[/tex]
Divide both sides by h
[tex]\frac{21}{h} = \frac{\pi r^2h}{h}[/tex]
[tex]\frac{21}{h} = \pi r^2[/tex]
The next step is to solve for the volume of the sphere using the following formula;
[tex]V = \frac{4}{3}\pi r^3[/tex]
Divide both sides by r
[tex]\frac{V}{r} = \frac{4}{3r}\pi r^3[/tex]
Expand Expression
[tex]\frac{V}{r} = \frac{4}{3}\pi r^2[/tex]
Substitute [tex]\frac{21}{h} = \pi r^2[/tex]
[tex]\frac{V}{r} = \frac{4}{3} * \frac{21}{h}[/tex]
[tex]\frac{V}{r} = \frac{84}{3h}[/tex]
[tex]\frac{V}{r} = \frac{28}{h}[/tex]
Multiply both sided by r
[tex]r * \frac{V}{r} = \frac{28}{h} * r[/tex]
[tex]V = \frac{28r}{h}[/tex] ------ equation 1
From the question, we were given that the height of the cylinder and the sphere have equal value;
This implies that the height of the cylinder equals the diameter of the sphere. In other words
[tex]h = D[/tex] , where D represents diameter of the sphere
Recall that [tex]D = 2r[/tex]
So, [tex]h = D = 2r[/tex]
[tex]h = 2r[/tex]
Substitute 2r for h in equation 1
[tex]V = \frac{28r}{2r}[/tex]
[tex]V = \frac{28}{2}[/tex]
[tex]V = 14[/tex]
Hence, the volume of the sphere is 14m³
Answer:
14 m³Step-by-step explanation:
We have:
[tex]Cylinder:\\\R-\text{radius}\\H=2R-\text{height}\\V_C-\text{volume};\ V_C=21m^3\\\\\text{the formula of a volume of a cylinder:}\ V=\pi R^2H\\\\V_C=\pi R^2(2R)=2\pi R^3[/tex]
[tex]Sphere:\\\R-\text{radius}\\V_S-\text{volume}\\\\\text{the formula of a volume of a sphere:}\ V=\dfrac{4}{3}\pi R^3[/tex]
[tex]Let's\ transform\ V_C:\\\\2\pi R^3=21\qquad\text{divide both sides by 2}\\\\\pi R^3=\dfrac{21}{2}\qquad\text{multiply both sides by}\ \dfrac{4}{3}\\\\\dfrac{4}{3}\pi R^3=\dfrac{21}{2}\cdot\dfrac{4}{3}\to V_S=\dfrac{(21:3)\cdot(4:2)}{(2:2)\cdot(3:3)}=\dfrac{7\cdot2}{1\cdot1}=\dfrac{14}{1}=14\ (m^3)[/tex]
Find the 73rd term of the arithmetic sequence -28, -41, -54, ...
Answer:
Find the 73rd term of the arithmetic sequence -28, -41, -54, ...... -964
Step-by-step explanation:
U73 = -28 + (73 - 1)-13
U73 = -28 - 949 + 13
U73 = -964
The 73rd term of the arithmetic sequence -28, -41, -54, ... is -964, calculated using the formula of an arithmetic sequence.
Explanation:The 73rd term of the arithmetic sequence -28, -41, -54, ... can be found by using the formula of arithmetic sequence which is a + (n - 1) * d, where 'a' is the first term of the sequence, 'd' is the common difference, and 'n' is the term number. Here, 'a' is -28 and 'd', the difference between the terms, is -13 because -41 - (-28) = -13.
So, plugging in these values to the formula: a + (n - 1) * d = -28 + (73 - 1) * -13 = -28 - 936 = -964. Therefore, the 73rd term of the sequence is -964.
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A rectangular baking pan is 12 inches long, 6 inches wide, and 2.5 inches tall. If 1 cubic inch of cake mix is approximately 0.55 ounces, how much cake mix can the pan hold?
Answer:
Amount of cake mix baking pan can hold is 99 ounces
Step-by-step explanation:
Here we have the size of the baking pan is given by the following relation
Volume of baking pan = Length × Width × Height
Volume of baking pan = 12 in. × 6 in. × 2.5 in. = 180 in.³
Mass of 1 cubic inch of cake mix = 0.55 ounces, therefore, the mass of cake mix that the 180 in.³ baking pan can hold is found as follows;
Amount of cake mix baking pan can hold = Volume of baking pan × Mass per cubic inch of cake mix
Amount of cake mix baking pan can hold = 180 in.³ × 0.55 ounce/in.³ = 99 ounces.
THow much will fencing cost to enclose a field that is 725 feet by 1,021 feet if fencing costs $13.57 per foot? $47,386.44 $23,693.22 $10,044.85 $10,044,853.25
Answer:
$47,386.44
Step-by-step explanation:
Given;
Dimension of the field = 725 feet by 1,021 feet
Length = 1021 ft
Breadth = 725 ft
Cost per foot = $13.57 per foot
Perimeter of the field = 2 × (length + breadth)
Perimeter = 2 × ( 1021 + 725) = 3492 ft
The cost of fencing the field is;
Cost per feet × perimeter
= $13.57 × 3492
= $47,386.44
What is the explicit formula for this geometric sequence -6,-18,-54,-162,…
Answer: an= -6(3)^(n-1)
(B)
Step by step explanation: a1 is -6 and a2 is -18, only B would match the sequence. The only other answer that comes close is -6(-3)^(n-1) but if you multiply -6 by -3 you get 18 instead of -18
A committee consisting of 3 boys and 4 girls is to be formed from a group of 10 boys and 12 girls. How many different committees can be formed from the group?
Answer:
3 different committees
Step-by-step explanation:
after 3 committees are formed there will be one extra boy however without any more girls another committee cannot be formed.hope this helps!!!
Number of committees of 3 boys and 4 girls formed from the group of 10 boys and 12 girls = 59400
What is combination?The combination is defined as “An arrangement of objects where the order in which the objects are selected does not matter.” The combination means “Selection of things”, where the order of things has no importance.
Number of combinations of taking x items out of total n items
ⁿCₓ = n!/x!(n-x)!
Given,
Number of girls in group = 12
Number of boys in group = 10
Selecting 3 boys from the group
= ¹⁰C₃
= ¹⁰C₃
= 10!/3!(10 - 3)!
= 10!/3!×7!
= (10 × 9 × 8 × 7!)/(3 × 2 × 1 × 7!)
= 10 × 3 × 4
= 120
Selecting 4 girls from group
= ¹²C₄
= 12!/4!(12 - 4)!
= 12!/4!×8!
= (12 × 11 × 10 × 9 × 8!)/(4 × 3 × 2 × 1 × 8!)
= 3 × 11 × 5 × 3
= 495
Total number of committees of 3 boys and 4 girls formed from the group
= ¹⁰C₃ × ¹²C₄
= 120 × 495
= 59400
Hence, 59400 different committees can be formed from the group.
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What is the volume of the following cylinder?
43.96 in.3
12.56 in.3
21.98 in.3
87.92 in.3
Answer:
d) 87.92
Step-by-step explanation:
V = A(base)* height= πr² * h= 3.14*2²*7=87.92
Evaluate the expression when x=-7.
x² + 4x-5
Answer:
72
Step-by-step explanation:
In triangle ABC, angle A measures 50 degrees, angle B measures 30 degrees. Find the measure of angle C.
A.100 degrees
B.50 degrees
C.110 degrees
Answer:
100 degrees
Step-by-step explanation:
You are running late, but still have a chance to make it to that important meeting on time. It normally takes 24 seconds to get from the first floor to your normal third floor, but you have to get to the fourteenth floor. You have 3 minutes to get there. Will you get there on time? How many minutes early or late will you be? (Round to the nearest hundredth if necessary.)
Answer:
3+11+ 14
24x11=264
264sec=4.4 minutes
youll be late by 1min 40 sec
Given that it takes 12 seconds to reach each floor, you will reach the 14th floor in 156 seconds. Compared to the total time available (180 seconds), you will be 24 seconds (or 0.4 minutes) early to your meeting.
Explanation:To solve this problem, we need to determine how long it takes for you to reach each floor. If it takes you 24 seconds to reach the 3rd floor from the 1st floor, we can infer that it takes you 12 seconds to reach each floor (24 seconds/2 floors). Therefore, to reach the 14th floor from the first, it would take 12 seconds times 13 floors which equals 156 seconds.
Then, we need to convert the time given to get to the meeting, which is 3 minutes, into seconds (3 minutes * 60 seconds/minute = 180 seconds).
Subtract the required time to reach the 14th floor (156 seconds) from the total time available (180 seconds), and you will be 24 seconds early for your meeting (or 0.4 minutes, rounding to the nearest hundredth, if the time is converted back into minutes).
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Which property is illustrated by the statement 6 • 4 = 4 • 6? *
Answer:
Commutative Property of Multiplication
Step-by-step explanation:
put the fractions in order starting with the smallest to the largest
21/40, 29/40, 17/20, 3/4, 4/5
Answer:
21/40, 17/20, 29/40, 3/4, 4/5
Step-by-step explanation:
21/40 = 10.5/20
29/40 = 14.5/20
17/20 = 13.5/20
3/4 = 15/20
4/5 = 16/20
Find the elapsed time between 5:25 pm and 11:11 pm
Answer:
5 hours 46 minutes
Step-by-step explanation:
Which describes an investment in which all of the money to be invested is deposited at one time
Answer: lump sum investment
Step-by-step explanation:
Answer:
It is lump-sum payments.
Step-by-step explanation:
What is lump-sum payment?
A lump-sum payment is an amount paid all at once, as opposed to an amount that is divvied up and paid in installments.
What is investment?
Investment is the dedication of an asset to attain an increase in value over a period of time.
An investment in which all of the money to bee invested is deposited at one time is called lump-sum payment.
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135% of what number is 81
Answer:
60
Step-by-step explanation:
Of means multiply and is means equals
Let n be the unknown number
135% * n = 81
Change to decimal form
1.35 n = 81
Divide each side by 1.35
1.35n/1.35 = 81/1.35
n =60
I need help!!
I don’t get it!!
Answer:
170
Step-by-step explanation:
Sebastian has 3 whole apples. He cuts each whole into fourths. Sebastian gives away 4 4 of the apples. Which is the number of fourths Sebastian has left as a fraction?
Answer: He now has eight-fourths of the apples left.
Step-by-step explanation: If Sebastian has three whole apples and now decides to cut each apple into fourths, that is four parts, then the total number of fourths he has left can be derived as follows;
1 apple = 4 parts
3 apples = 3 x (4 parts)
3 apples = 12 parts
If Sebastian gives away four of the apples, we can now express this as;
Remainder = 12 parts - 4 parts
Remainder = 8 parts
What Sebastian had was fourths and no longer whole apples, hence from our calculation, Sebastian has eight-fourths (8 quarters, or 8 fourths) left as a fraction of his apples.
Final answer:
Sebastian cuts 3 apples into fourths, giving him 12 pieces. He gives away 4 pieces, leaving him with 8 fourths of an apple. The number of fourths left expressed as a fraction is 8/4.
Explanation:
Sebastian starts with 3 whole apples and cuts each into fourths, resulting in 3 x 4 = 12 pieces. After giving away 4 fourths of the apples, we subtract 4 from the original 12 pieces to answer the question: Which is the number of fourths Sebastian has left as a fraction?
To find out how many fourths are left, we compute 12 - 4 = 8 fourths. This can be simplified to the fraction 8/4, which equals 2 whole apples. However, since the question asks for the answer in the form of a fraction representing the fourths, we should write our final answer as 8/4.
If we were to simplify the fraction to show the number of whole apples instead of fourths, we would say that Sebastian has 2 whole apples left.
Find the student’s error in solving the following inequality.
31 < –5x + 6
25 < –5x
–5 < x
A.) The student should have added 6 to both sides instead of subtracting it.
B.) The student divided 25/–5 incorrectly.
C.) The student should have switched the direction of the inequality sign to get –5> x for a final answer.
Answer:
The correct option is:
The student should have switched the direction of the inequality sign to get –5> x for a final answer
Step-by-step explanation:
The students has made a mistake in the 3rd step.
We know that when we multiply or divide any negative number on both sides of the inequality, the sign of inequality reverse its direction.
In step 3 the student divided 25 by -5 but did not switch direction of the inequality sign.
Therefore the correct option is: The student should have switched the direction of the inequality sign to get –5> x for a final answer
Answer:
C
Step-by-step explanation:
Just did it
Factor -6x^2+26x+20 completely.
P.s. Need answers soon!
Answer:
-2(3x+2)(x-5)
Step-by-step explanation:
escribir dos ejemplos numeros decimales y conviertelos a fraccion?
Answer:
0.25
0.5
Step-by-step explanation:
[tex]\frac{1}{4}[/tex]
[tex]\frac{1}{2}[/tex]
.25 = 25/100 = 1/4
.50 = 50 /100 = 1/2
In a certain population of 1000 fruit flies, 640 have red eyes while the remainder has sepia eyes. The sepia eye trait is recessive to red eyes.
a. Calculate the number of homozygous recessive alleles for sepia eyes
b. Determine the number of homozygous dominant alleles for red eyes
c. Convert your answer for (b) into percent
Answer:
b. Determine the number of homozygous dominant alleles for red eyes
Step-by-step explanation:
Find the monthly payment needed to amortize a typical 100,000 mortgage loan over 30 years at annual interest rate of 4.7%, compounded monthly. Find the total interest paid on the loan after 30 years
Answer:
Monthly amortization paid is $1,135
Amount of interest paid is $308,469
Step-by-step explanation:
Here, we are interested in calculating the monthly payment paid and the total value of this interest.
Firstly, we calculate the amount which this loan would be at the end of the 30 years.
To calculate this amount, we make use of the compound interest amount formula
A = P(1 + r/n)^nt
where A is the amount we want to calculate
P is the amount borrowed which is $100,000
r is the interest rate which is 4.7% or simply 4.7/100 = 0.047
n is the number of times yearly which the interest is compounded which is 12 since it is compounded monthly
t is the total time taken to repay the loan which is 30 years
Plugging these values, we have
A = 100,000( 1 + 0.047/12)^(12 * 30)
A = 100,000( 1+ 0.00392)^360
A = 100,000(1 .00392)^360
A = $408,469
The monthly payment needed to amortize the loan will be the amount after 30 years divided by the number of months in 30 years
The number of months in 30 years is 30 * 12 = 360 months
The monthly payment amount is thus 408,469/360 = 1,134.6 approximately $1,135
The total interest paid will be the amount minus the principal
This is $408,469 - $100,000 = $308,469
What are the roots of the function?
0 -8 and 20
O _40 and -8
O-8 and 8
O _40 and 20
Answer:
0
−
8
=
−
8
0-8=-8
20
=
−
8
20=-8
O
⋅
40
=
40
O
O⋅40=40O
−
8
=
40
O
-8=40O
O
−
8
=
40
O
O-8=40O
8
=
40
O
8=40O
O
⋅
40
=
40
O
O⋅40=40O
20
=
40
O
20=40O
Jennas employer deducts 0.2 times her wages for payroll taxes.How much is her net income when her gross income is $580?
Answer:
Net income = $464
Step-by-step explanation:
The tax paid = 580 *2/10 = $116
The gross income = $580
Net income = gross income - tax
= $580 - $116 = $464
what is the outlier of 1,148 ,10 ,43 ,14
Answer:
148
Step-by-step explanation:
an outlier is somthin that stands out
Answer:
148
Step-by-step explanation:
Its farther away from all the other numbers