Answer:
The equation of the largest sphere with center (10, 8, 7) that is contained completely in the first octant is [tex](x-10)^{2} + (y - 8)^{2} + (z - 7)^{2} = 49[/tex].
Step-by-step explanation:
A sphere is described by its radius and center, the radius of the largest sphere contained in the first octant are determined by the least distance of the center with respect to an orthogonal axis, that is:
Distance regarding x-axis:
[tex]d_{x} = 10 - 0[/tex]
[tex]d_{x} = 10[/tex]
Distance regarding y-axis:
[tex]d_{y} = 8 - 0[/tex]
[tex]d_{y} = 8[/tex]
Distance regarding z-axis:
[tex]d_{z} = 7 - 0[/tex]
[tex]d_{z} = 7[/tex]
Hence, the radius of the sphere must have a measure of 7. The equation of the sphere is represented by the following geometric locus:
[tex](x-h)^{2} + (y-k)^{2} + (z - j)^{2} = r^{2}[/tex] (1)
Where:
[tex]h, k, j[/tex] - Coordinates of the center.
[tex]r[/tex] - Radius of the sphere.
If we know that [tex](h,k,j) = (10, 8, 7)[/tex] and [tex]r = 7[/tex], then the equation of the largest sphere with center (10, 8, 7) that is contained completely in the first octant is:
[tex](x-10)^{2} + (y - 8)^{2} + (z - 7)^{2} = 49[/tex]
Suppose we want to choose 4 colors, without replacement, from 18 distinct colors.
(a) If the order of the choices is relevant, how many ways can this be done?
(b) If the order of the choices is not relevant, how many ways can this be done?
Answers:
(a) 73440(b) 3060=====================================================
Explanation for part (a)
Consider four slots labeled A,B,C,D.
We have
18 choices for slot A17 choices for slot B16 choices for slot C15 choices for slot DWe started at 18 and counted down until we filled the four slots. The countdown is because we cannot repeat a color. Multiply out those values to get the answer: 18*17*16*15 = 73440
You can use the nPr permutation formula as an alternative method
[tex]_nP_r = \frac{n!}{(n-r)!}[/tex]
in this case n = 18 and r = 4. The exclamation marks indicate factorial.
-----------------------------------
Explanation for part (b)
Let's say we had color labels A,B,C,... all the way up to R which is the 18th letter in the English alphabet. From those 18 letters, we can only pick four. Let's say we pick D,E,F,G.
Focusing solely on the set {D,E,F,G}, we only have one set and the order doesn't matter. So {D,E,F,G} is the same as {D,E,G,F}.
There are 4*3*2*1 = 24 ways to arrange those four items meaning that we'll need to divide the result of part (a) by 24 to get the result of part (b)
73440/24 = 3060
You could use the nCr combination formula to get the same result
[tex]_nC_r = \frac{n!}{r!(n-r)!}[/tex]
where n = 18 and r = 4 are the same from last time.
The connection between nPr and nCr is this
[tex]_nC_r = \frac{_nP_r}{r!}[/tex]
which can be rearranged into
[tex]_nP_r = r!*\left( _nC_r \right)[/tex]
these formulas are handy to help us go back and forth between nCr or nPr.
If the order of the choices is relevant, the number of ways of selecting 4 colors out of 18 distinct colors is 73440.
If the order of the choices is not relevant, the number of ways of selecting 4 colors out of 18 distinct colors is 3060.
What are combination and permutation?Combination is a way of selecting items from a collection where the order of arrangement is not relevant.
It is given by:
[tex]^nC_r[/tex] = n! / r! (n-r)!
Permutation is a way of selecting items from a collection where the order of the arrangement is relevant.
It is given as:
[tex]^nP_r[/tex] = n! / (n-r)1
We have,
Number of distinct colors = 18
Number of colors to be chosen = 4
The number of ways the four colors be chosen when the order is not relevant:
= [tex]^{18}C_4[/tex]
= 18! / 4! 14!
= 18 x 17 x 16 x 15 / 4 x 3 x 2
= 3060
The number of ways the four colors be chosen when the order is relevant:
= [tex]^{18}P_4[/tex]
= 18! / 14!
= 18 x 17 x 16 x 15
= 73440
Thus,
If the order of the choices is relevant, the number of ways of selecting 4 colors out of 18 distinct colors is 73440.
If the order of the choices is not relevant, the number of ways of selecting 4 colors out of 18 distinct colors is 3060.
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Handrail should be mounted 34 inches minimum and 38 inches maximum above ramps. Which inequality represents the required height?
Answer:
[tex]34 \leq x \leq 38[/tex]
Step-by-step explanation:
34 inches minimum
This means that x has to be at least 34, that is:
[tex]x \geq 34[/tex]
38 inches maximum
This means that x can be at most 38, that is:
[tex]x \leq 38[/tex]
Which inequality represents the required height?
The intersection of 34 minimum and 38 maximum is:
[tex]34 \leq x \leq 38[/tex]
QUICK!! GIVING BRAINLIEST TO CORRECT ANSWER QUICK!!
Answer:
Im fairly sure it is 45ft^3
Answer:
[tex]45ft^{2}[/tex]
Step-by-step explanation:
V=L*W*H
The step function f(x) is graphed
What is the value of f(-1)?
0-3
O-1
ОО
0 1
The value of f(-1) in the graph is 1.
What is Function?In mathematics, a function is an expression, rule, or law that establishes a relationship between an independent variable and a dependent variable (the dependent variable). In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences.
The graph leads to the following finding:
The values of f(-1) for x = -1 are -1 and -3.
The function does, however, have a closed circle at f(-1) = 1.
The function has an open circle at f(-1) = -3.
A closed circle represents inclusive principles.
Hence, the graph's value for f(-1) is 1.
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40 POINTS!!!!! Find the value of x in the triangle shown below.
Answer:
a
Step-by-step explanation:
Solve each equation over the interval [0°, 360°). If a decimal approximation is necessary, round to four decimal places. cos 2x -cos x-2 = 0
Answer:earthy
Step-by-step explanation:vuinh
Help please!!!!!!!!!!!!!!!
Answer:
-1, 5
Step-by-step explanation:
no really explanation, but its a graph and when u have agraph x goes before y. and the x in the middle of it is what its talking about and u can see the middle is on a 5 and a -1
If 25 counters are a whole set how many are there in four fifths of the set
Answer:
20
Step-by-step explanation:
25*4/5=5*4=20
Answer:
20
Step-by-step explanation:
25 x 4/5=100/5=20
write an equivalent expression: −12(−2x+4y)
Answer:
24x-48y
hope this helps
have a good day :)
Step-by-step explanation:
Step-by-step explanation:
−12(−2x+4y) = 24x - 48y
______
What is the area, in square units, of the parallelogram shown below?
21 s u
56 s u
63 s u
81 s u
Answer:
Area of parallelogram = 63 square units
Step-by-step explanation:
In the given parallelogram:
Height of parallelogram = 9 units
Base of parallelogram = 7 units
Find:
Area of parallelogram
Computation:
Using area of parallelogram;
Area of parallelogram = Height of parallelogram x Base of parallelogram
Area of parallelogram = 9 x 7
Area of parallelogram = 63 square units
Find the sum and Express it in simplest form. (u^3+3u^2+3) + (-6u^3-8u^2)
Answer:
-5u^3 - 5u^2 + 3.
Step-by-step explanation:
(u^3 + 3u^2 + 3) + (-6u^3 - 8u^2)
= u^3 + 3u^2 + 3 - 6u^3 - 8u^2
= u^3 - 6u^3 + 3u^2 - 8u^2 + 3
= -5u^3 - 5u^2 + 3.
Which of the following are statistical questions? Select all that apply.
A.
How many goals does a high school soccer team score in each game?
B.
How long does it take a high school student to run a mile?
C.
What is the world record for the fastest time to run 1 mile?
D.
How many runs did the Georgetown Giraffes baseball team score last night?
Answer:
I think A and B
Step-by-step explanation:
• A statistical question is a question that has more than one possible answer ( and can be answered by collecting data) where there will be variability in the data. for instance an example would be " How old are the students in this room?"
• However a non statical question has only one answer for instance "How old are you?"
both a and b dont have specific answers because it's not talking about a specific high school students or a specific soccer team. i would guess those are correct, but using the information from above you can also see what you think! hope this helps :)
what is 12.92÷10 to the power of five
than you
Answer:
0.0001292
Step-by-step explanation:
a raised to the power -m is 1/a raised to power m
Melissa has two coupons for shoes. Coupon A: Coupon B: 15% off of S41 shoes $10 rebate on S41 shoes Choose the coupon that gives the lower price. Then fill in the blank with the correct value.
Answer:22
Step-by-step explanation:
The complete sentence is
The price with coupon B is $10 less than the price with coupon A.
It depends on the original price of the S41 shoes.
Coupon A offers a 15% discount on S41 shoes, while Coupon B provides a $10 rebate on S41 shoes.
Let's assume the original price of the S41 shoes is P dollars.
Using Coupon A, the discounted price would be 85% of the original price = (0.85 * P) dollars.
Using Coupon B, the price after the $10 rebate = (P - $10) dollars.
Now, compare (0.85 * P) with (P - $10).
simplify the expression (0.85 * P) < (P - $10) as
0.85P < P - $10
0.85P - P < - $10
-0.15P < - $10
P > (- $10) / (-0.15)
P > $66.67
Therefore, if the original price of the S41 shoes is greater than $66.67, Coupon A (15% off) will give a lower price. If the original price is lower than $66.67, Coupon B ($10 rebate) will give a lower price.
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True or False
More than one phylum of animals are invertebrates
Answer:
True
Step-by-step explanation:
The largest animal phylum is also included within invertebrates
HELP ME WITH THIS PLEASEEEEE? IM STUGGLING
Answer:
(x-5)(x+5)
Step-by-step explanation:
x^2 -25
We can rewrite this as the difference of squares
x^2 - 5^2
(x-5)(x+5)
Kate's dog was learning to balance a ball on his nose. The
first day he balanced the ball 6 out of 20 times; the second
day, 8 out of 25 times. Which day did he do better?
Answer:
The answer is the first day
Mark has a six-sided number cube. Each side is numbered from1 to 6. What is the probability, expressed as a ratio that Mark will roll a 3?
Answer:
1 : 6
Step-by-step explanation:
21 x 5/7 anybody know please?
Answer:
15
Step-by-step explanation:
Answer:
15
Step-by-step explanation:
EEE
What is the solution to the equation -3(h+5)+2 = 4(h+6)-9?
Oh=-4
Oh = -2
Oh = 2
Oh= 4
Hi plz help, if you can ill mark you 5 starz! :)
Answer:
Step-by-step explanation:
Part A= 59.11
Part B: i think is B
I hope this helps :))
Answer:
Step-by-step explanation:
Part A : 59.11
Part B: the answer is B. You keep the same amount of decimal places in the problem in your product. we had 2 so we have 2 decimal places in 5911 ---> 591.1 --->59.11
ilang metro ang 1300 sentimetro?
a. 1metro
b. 13 metro
c. 130 metro
Answer:
1300 cm = 13 m
Step-by-step explanation:
We need to find meters in 1300 cm.
We know that,
1 m = 100 cm
1 cm = (1/100) m
It means,
[tex]1300\ cm=\dfrac{1300}{100}\ m\\\\=13\ m[/tex]
Hence, there are 13 m in 1300 cm.
YALL PLEASE HELP ME ASAP
Answer:
B
Step-by-step explanation:
Depreciates 14% per year so 100% - 14% is 86% or 0.86. Formula is (principal)(rate)^ years
Please look at the image
Answer:
2) <TWN and <SWM
Step-by-step explanation:
2) <TWN and <SWM
Answer:
(2)
Step-by-step explanation:
This is because they are both vertical to one another!
Hope this helps!
I need the answer. Please help.
===========================================================
Work Shown:
Use the tangent ratio
tan(angle) = opposite/adjacent
tan(B) = AC/AB
tan(61) = AC/1
tan(61) = AC
AC = tan(61)
AC = 1.80404775527142
AC = 1.8
The river is about 1.8 miles wide between points A and C.
Make sure your calculator is in degree mode. One way to check is to type in tan(45) and you should get 1.
The graph shows Micah’s pay for working different numbers of hours. Graph of a diagonal line on a coordinate plane with ALTDCTime worked in hoursALTDC on x-axis and ALTDCPay in dollarsALTDC on y-axis. The diagonal line is going up and to the right. Line passes through points (0, 0), (2, 30), (4, 60), A and (14, 210). A is at (8, 120) Part A What are the coordinates of Point A on the graph? Enter your answer in the boxes. ( , ) LIVE Part B What does the ordered pair for Point A represent? Use the drop-down menus to show your answer. When Micah works hours, he makes $ .
Answer:
Step-by-step explanation:
The coordinates for point A is (8,120)
(k+1)x^2-8kx+(3k+5) calculate the value for k
Answer:
Step-by-step explanation:
Let's simplify step-by-step.
(k+1)(x2)−8kx+3k+5
Distribute:
=(k)(x2)+(1)(x2)+−8kx+3k+5
=kx2+x2+−8kx+3k+5
Answer:
=kx2−8kx+x2+3k+5
A local pizza parlor is selling two different shapes of cheese pizza for the same price. You can get two small square pizza that have sides of 7 inches or a large round pizza with a diameter of 12 inches. Which choice gives you more pizza
Answer:
It is a good idea to buy the round pizza, since it has a total of 113.04 square inches of pizza, while the two square slices together bring together 98 square inches.
Step-by-step explanation:
Since a local pizza parlor is selling two different shapes of cheese pizza for the same price, and you can get two small square pizza that have sides of 7 inches or a large round pizza with a diameter of 12 inches, to determine which choice gives you more pizza the following calculations must be carried out, knowing that the area of a square is equal to pi multiplied by the radius squared, and that the area of a square is equal to its side squared:
Round pizza:
Radius = Half the diameter
3.14 x 6 ^ 2 = X
3.14 x 36 = X
113.04 = X
Square pizzas:
(7x7) x 2 = X
49 x 2 = X
98 = X
Therefore, it is a good idea to buy the round pizza, since it has a total of 113.04 square inches of pizza, while the two square slices together bring together 98 square inches.
A bookmark is shaped like a rectangle with a semicircle attached at both ends. The rectangle is 17 cm
long and 4 cm wide. The diameter of each circle is the width of the rectangle. What is the area of the
bookmark? Use 3.14 for it.
The area of the bookmark is
cm?
Answer:
80.56
Step-by-step explanation:
To find the rectangle area you just multiply its length by its width:
17 * 4 = 68
You have to sum two semicircles on top of that. Since it is 2 semicircles you can just calculate one circle. Using the circle area formula: [tex]\pi*r^2[/tex]
Since the radius (r) is 2 and [tex]\pi[/tex] is 3.14, you have the following equation:
A = 3.14 * 2² ==> A = 3.14 * 4 ==> A = 12.56 (A is Area)
Sum the rectangle's area with the circle's area:
12.56 + 68 = 80.56
And vuoila! there's your answer.
Antonio is planning a birthday party for his daughter. SkateWorld charges a flat fee of $50 plus $3 per child. Roller Land charges $5 per child. If Antonio's daughter wants to invite 21 friends from school and five friends from her basketball team, which rink should Antonio use and how much would he save by doing so?
Answer:
skateworld
Step-by-step explanation:
26x3+50=128 aka skate worlds price
26x5=130 aka roller land price
Antionio should use skateworld and he would save 2$
Answer: SkateWorld. He saves $2
Step-by-step explanation:
SkateWorld:
21 *3 =63
5*3=15
63+15=78
78+50= 128
Roller Land:
21*5= 105
5*5=25
105+25=130
130-128= 2