Final answer:
To calculate the arc length of a circle with a radius of 5 feet and a central angle of 42 degrees, convert the angle to radians and multiply by the radius to get the arc length, which is 7π/6 feet or approximately 3.665 feet.
Explanation:
To find the arc length s subtended by a central angle of 42 degrees in a circle with a radius of 5 feet, first convert the angle from degrees to radians. Since there are 2π radians in 360 degrees, you multiply the angle in degrees by π/180 to get radians. Therefore, the central angle in radians is 42 * (π/180) = 7π/30 radians. The arc length s is then found by multiplying the central angle in radians by the radius of the circle (s = rθ).
Using the formula s = rθ, you have:
s = 5 * (7π/30) = 35π/30 = 7π/6 feet.
Therefore, the arc length s is 7π/6 feet, or approximately 3.665 feet.
If the point (4,-1) is a point on the graph of f, then f( )=?
What is the value of the digit 8 in Alaska's population
express $15 for 10 gallons a unit rate
A washer and dryer cost $815 combined. The washer cost $85 less than the dryer. What is the cost of the dryer?
How do you rename 5400 as hundred
A garden table and a bench cost $786 combined. The garden table costs $36 more than the bench. What is the cost of the bench?
Dr. Black is standing 15 feet from a streetlamp. The lamp is making his shadow 8 feet long. He estimates that the angle of elevation from the tip of his shadow to the top of the street lamp 50 degrees. To the nearest foot, the streetlamp is about
The area of a rectangular wall of a barn is 42 ft. Its length is 8 feet longer. Than twice its width. Find the length and width of the wall of the barn.
six sevenths 6/7
of an estate is to be divided among relatives. Of the remaining estate,
one fifth 1/5
goes to the American Cancer Society. What fraction of the estate goes to the American Cancer Society?
The fraction of the estate that goes to the American Cancer Society is
The American Cancer Society receives 1/35 of the total estate after it has been divided among relatives and other beneficiaries. This is determined by multiplying the fraction of the estate remaining (1/7) by the fraction of that remaining estate going to the Cancer Society (1/5).
Explanation:The question states that six-sevenths, or 6/7, of the estate has been divided among relatives, which leaves one-seventh, or 1/7, of the estate remaining. It is this remaining fraction that is further divided, with one fifth, or 1/5, going to the American Cancer Society. To determine the fraction of the total estate that this represents, we multiply these two fractions together: [tex]1/7 * 1/5 = 1/35.[/tex] Therefore, the American Cancer Society receives one-thirty-fifth of the total estate.
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For football tryouts, 12 coaches and 42 players will split into groups. Each group will have the same numbers of coaches and players. What is the greatest number of groups that can be formed?
gratest common factor for 12 and 42 is 6
so 6 groups can be formed
12/6 = 2
42/6 = 7
6 groups with 2 coaches and 7 palers
what is the complete factorization of the polynomial below. x^3-3x^2+x-3
Answer:
(x-3)(x+i)(x-i)
Step-by-step explanation:
[tex]x^3-3x^2+x-3[/tex]
We apply grouping method
We group first two terms and last two terms
[tex](x^3-3x^2)+(x-3)[/tex]
Take out GCF x^2 from first group. Also take out 1 from second group
[tex]x^2(x-3)+1(x-3)[/tex]
[tex](x-3) (x^2+1)[/tex]
Now we factor x^2 + 1
We use difference of square formula
a^2 - b^2 = (a+b)(a-b)
x^1 + 1 can be written as [tex]x^2 - (-1)[/tex], the value of -1 is i^2
[tex]x^2 +1 = x^2 -(-1) = x^2 - i^2[/tex]
x^2 - i^2 = (x+i)(x-i)
Final answer is (x-3)(x+i)(x-i)
The complete factorization of the polynomial x^3 - 3x^2 + x - 3 is (x - 3)(x^2 + 1). The process involves grouping and factoring out common terms.
The question asks for the complete factorization of the polynomial x^3 - 3x^2 + x - 3. To factor this polynomial, we are looking for factors of the lowest possible order that will multiply together to give us the original polynomial. Let's first look for a common factor in all the terms. In this case, there isn't a common factor except for 1, so we move on to finding factors through other means such as grouping.
We can attempt to group terms to facilitate the factoring process:
First, consider the polynomial in two parts (x^3 - 3x^2) and (x - 3).Within the first group (x^3 - 3x^2), we can factor out an x^2, which gives us x^2(x - 3).The second group is already in the form (x - 3), mirroring the (x - 3) factor we found in the first group.We then combine these to get the full expression x^2(x - 3) + (x - 3).Next, we can factor out the common (x - 3) term from both groups, obtaining (x - 3)(x^2 + 1).The polynomial x^3 - 3x^2 + x - 3 can now be expressed as the product of (x - 3) and (x^2 + 1). This represents the polynomial in its factored form using real coefficients.
Gina wants to ship 3 books that weigh 2 7/16 pounds 1 7/8 pounds and 1/2 pound the max weight she can ship is 6 pounds estimate to see if Gina can ship all 3 books.
Answer:
→Weight of First book
[tex]=2\frac{7}{16}\\\\=\frac{39}{16}[/tex]
→ Weight of Second book
[tex]=1\frac{7}{8}\\\\=\frac{15}{8}[/tex]
→Weight of Third book
[tex]=\frac{1}{2}[/tex]
→Total weight of three books
[tex]=\frac{39}{16}+\frac{15}{8}+\frac{1}{2}\\\\=\frac{39+30+8}{16}\\\\=\frac{77}{16}\\\\=4\frac{13}{16}[/tex]
→Maximum Weight of 3 books that Gina Can Ship =6 Pounds
[tex]\rightarrow 6 >4\frac{13}{16}[/tex]
Yes, Gina Can ship all 3 Books.
Size of U.S. States The total surface area (in square miles) for each of six selected eastern states is listed here.
28,995 PA
37,534 FL
31,361 NY
27,087 VA
20,966 ME
37,741 GA
The total surface area for each of six selected western states is listed (in square miles).
72,964 AZ
70,763 NV
101,510 CA
62,161 OR
66,625 CO
54,339 UT
Find the standard deviation for each data set. Which set is more variable?
Answer:
Second set.
Step-by-step explanation:
I put the formula of standart deviation in the image below.
x is each data of the list
μ is the data average
N is the amount of elements.
So, for the first list we have:
μ= [tex]\frac{28995+37534+31361+27087+20966+37741}{6}= \frac{183684}{6}=30614[/tex]
DE= [tex]\sqrt{\frac{|28995-30614|^{2}+|37534-30614|^{2}+|31361-30614|^{2}+|27087-30614|^{2}+|20966-30614|^{2}+|37741-30614|^{2}}{6} }[/tex]
= [tex]\sqrt{\frac{2621161+47886400+558009+12439729+93083904+50794129}{6} }[/tex]
= [tex]\sqrt{\frac{207383332}{6} }[/tex]
= [tex]\sqrt{ 34563888.6667 }[/tex]
= 5879.1061.
For the other list of elements:
μ= [tex]\frac{72964+70763+101510+62161+66625+54339}{6}= \frac{428362}{6}=71393.66[/tex]
DE=[tex]\sqrt{\frac{|72964-71393.66|^{2}+|70763-71393.66|^{2}+|101510-71393.66|^{2}+|62161-71393.66|^{2}+|66625-71393.66|^{2}+|54339-71393.66|^{2}}{6} }[/tex]
= [tex]\sqrt{\frac{2465967.71+397732.03+906993934.99+85242010.67+22740118.19+290861427.71}{6} }[/tex]
= [tex]\sqrt{\frac{1308701191.3}{6} }[/tex]
= [tex]\sqrt{218116865.21 }[/tex]
= 6029.32
Then, the second set is more variable.
Joanne buys a rug with an areas of 35/4 square meters. The length of the rug is 7/2 meters, What is the width , in meters, of the rug?
A grocery store has a shelf with half-gallon containers of milk. What type of number best represents the total number of gallons? Complete the statement.
Answer:
Step-by-step explanation: The half gallon milk combination is considered A Rational Number
Arrange the values according to magnitude. What is the easiest way to tackle this?
Simplify. −3i √-40
Enter your answer, in simplest radical form, in the box.
HURRY!
i have the answer here
6√10
-3i√-40
-3i^2√40
^
4 * 10
2*2 5*2
-3i^2√2*2*2*5
-6i^2√10
-6(-1)=6
6√10
☺
Over a 6 week period, the price of an MP3 player dropped steadily, from $82 to $34. What is the average weekly change in the price of the MP3 player over this period?
what is 22.62 rounded to the nearest tenth
the number of science books checked out at the school library is directly proportional to the number of students in Physics class. If 42 books were checked out when 6 students were in physics class, how many books were checked out when 11 students were in the class. A. 66 books B. 47 books C. 53 books D. 77 books E. none of the above
The waitress and the hostess at a restaurant share the tips at the end of the shift the average amount earned in tips between the two of them is 50$ the waitress gets $30 and the hostess gets $20 if they countine to earn money at this rate how many dollars will the waitress receive if they earn 200 at the end of the shift
What kind of transformation is illustrated in this figure?
dilation
translation
rotation
reflection
Triangle D E F and another triangle D-prime E-prime F-prime is of the same size, shape but turned a different angle
Solve the problem. Round to the nearest cent.
Stan’s savings account has a balance of $1986. After 23 years, what will the amount of interest be at 4% compounded annually?
a.
$2908.93
c.
$2913.93
b.
$2899.93
d.
$794.40
1986*1.04^(23) = 4894.93
4894.93-1986 = 2908.93
Answer is A
Answer:
a. $2908.93
Step-by-step explanation:
We have been given that Stan’s savings account has a balance of $1986. The amount of interest be at 4% compounded annually.
To find the final amount after 23 years we will use compound interest formula.
[tex]A=P(1+\frac{r}{n})^{nT}[/tex], where,
A = Final amount,
P= Principal amount,
r = Annual interest rate in decimal form,
n = Number of times interest in compounded per year,
t = Time in years.
Let us convert our given rate in decimal form.
[tex]4\%=\frac{4}{100}=0.04[/tex]
Upon substituting our given values in above formula we will get,
[tex]A=\$1986(1+\frac{0.04}{1})^{1*23}[/tex]
[tex]A=\$1986(1+0.04)^{23}[/tex]
[tex]A=\$1986(1.04)^{23}[/tex]
[tex]A=\$1986*2.4647155431651442[/tex]
[tex]A=\$4894.9250687259763812[/tex]
To find the amount of interest we will subtract principal amount from final amount.
[tex]\text{Amount of interest}=\$4894.9250687259763812-\$1986[/tex]
[tex]\text{Amount of interest}=\$2908.925068725976\approx 2908.93[/tex]
Therefore, the amount of interest after 23 years will be $2908.93 and option a is the correct choice.
How many packages of diapers can you buy with $36 when on package costs $9?
Based on the calculations, the number of diapers which can be bought with $36 is equal to $4.
Given the following data:
Cost of diaper = $9.Amount for packages = $36.How to calculate the number of diapers?In order to determine the number of diapers that can be bought with $36, we would set up a direct proportion equation as follows:
$9 = 1 diaper
$36 = X diapers.
Cross-multiplying, we have:
9X = 1 × 36
9X = 36
X = 36/9
X = $4.
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cookies are sold singly or in packages of 12 or 36.With this packaging how many ways can you buy 72 cookies?
Danika is making necklaces.she has 512 silver beads and 278 blue.About how many more silver than beads does Danika have?
Answer:
234 more silver beads.
Step-by-step explanation:
We have been given that Danika is making necklaces. She has 512 silver beads and 278 blue.
To find the number of silver beads is how much more than blue beads, we will subtract number of blue beads from silver beads.
[tex]\text{Number of more silver beads}=512-278[/tex]
[tex]\text{Number of more silver beads}=234[/tex]
Therefore, Danika has 234 more silver beads than blue beds.
Kate Alexander worked 40 hours last week. Her pay rate is $8.50 per hour. Assuming 7.65% social security withholding, how much should her employer withhold from her check for social security?
0.65
6.50
2.60
26.01
There are 48 students going on a field trip. Each van holds 10 students. If every van but the last one is full, how many students will be in the last van?
All of the following are true statements except _____. |56| = 56 -|56| = 56 |-56| = 56 -|56| = -56
The arcade has 3 pinball machines and 5 video games. If a person wants to play one pinball machine and one video game, how many different combinations of games could that person play?
The number of possible combinations of playing one pinball game and one video game, given there are 3 pinball machines and 5 video games available, is 15.
Explanation:The subject of this question is combinatorics, a part of Mathematics that deals with combination and arrangement of objects. The question in essence is asking about the number of combinations one can play on a pinball machine and a video game in an arcade.
In the given context, there are 3 pinball machines and 5 video games. If a person wants to play one of each (one pinball game and one video game), we can calculate the number of combinations by simply multiplying the number of options for each game. That is, 3 pinball machines multiplied by 5 video games equals 15 different combinations.
So, there are 15 different combinations of games a person can play when selecting one pinball and one video game from the given sets.
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