Answer:
125 : 216
Step-by-step explanation:
Let the volumes of the spheres be V₁ and V₂ respectively.
Volume (Sphere radius = 5) :
V₁ = 4/3π(5)³V₁ = 4/3π x 125V₁ = 500/3πVolume (Sphere radius = 6) :
V₂ = 4/3π(6)³V₂ = 4/3π x 216V₂ = 864/3πTaking the ratio of V₁ and V₂ :
V₁/V₂500/3π x 3π/864500/864125 : 216Given ratio: [tex](\text{Radius of Sphere}_1 : \text{Radius of Sphere}_2) = (5 :6)[/tex]
Step-1) Multiply both sides of the ratio by x:
[tex]\implies (\text{Radius of Sphere}_1 : \text{Radius of Sphere}_2) = (5x :6x)[/tex]
[tex]\implies \text{Radius of Sphere}_1 = 5x;\ \text{Radius of Sphere}_2 = 6x[/tex]
Step-2) Substitute the radiuses of each sphere into the "Volume formula"
Volume of sphere₁ Volume of sphere₂
[tex]\implies \ \ \ \ \ \ \ \ \dfrac{4}{3} \pi r^{3} \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \dfrac{4}{3} \pi r^{3}[/tex]
[tex]\implies \ \ \ \ \ \ \ \ \dfrac{4}{3} \pi (5x)^{3} \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \dfrac{4}{3} \pi (6x)^{3}[/tex]
[tex]\implies \ \ \ \ \ \ \ \ \dfrac{4}{3} \pi (5x)(5x)(5x) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \dfrac{4}{3} \pi (6x)(6x)(6x)[/tex]
[tex]\implies \ \ \ \ \ \ \ \ \dfrac{4}{3} \pi (125x^{3} ) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 4 \pi (2x)(6x)(6x)[/tex]
[tex]\implies \ \ \ \ \ \ \ \ \dfrac{500x^{3} }{3} \pi \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 288x^{3} \pi[/tex]
Step-3) Plug the volume of both spheres in ratio form:
The ratio for the volumes of the two spheres must be in the respective place of the ratio for the radiuses of the two similar spheres. Therefore,
Ratio form: [tex]\underline{(\small\text{Volume of sphere}_1 : \text{Volume of sphere}_2)}[/tex]
[tex]\implies \dfrac{500x^{3} }{3} \pi: 288x^{3} \pi[/tex]
Step-4) Simplify both sides of the ratio:
[tex]\implies \dfrac{500x^{3} }{3}: 288x^{3}[/tex]
[tex]\implies \dfrac{500 }{3}: 288[/tex]
[tex]\implies \dfrac{500 }{3}} \div{\dfrac{288}{1} } \implies \dfrac{500}{3} \times \dfrac{1}{288} \implies \dfrac{500}{864} \implies \boxed{\dfrac{125}{216}}[/tex]
Therefore, the ratio for the volumes of two similar spheres is 125 : 216.
Pls kindly help, it's urgent
Answer to number 6 please
Answer:
Step-by-step explanation:
C
2. Determine the cost to cover the top of the fire pit with a piece of sheet metal that costs $25 per square foot. (6 points)
3. Determine the cost to lay down pebbel in the seating area one bag of pebbels covers 5 ft² and costs $8.99
A computer generates 80 integers from 1 to 8 at random. The results are recorded in this table.
Outcome 1 2 3 4 5 6 7 8
Number of times outcome occurred 14 16 10 12 4 7 6 11
What is the experimental probability of the computer generating a 2 or a 5?
9%
15%
20%
25%
WILL GIVE BRAINLIST TO THE CORRECT ANSWER!
Answer:
25%
Step-by-step explanation:
Using negative numbers, what is 4+(-5) ?
Answer:
-1
Step-by-step explanation:
4+(-5) is basically 4-5 which is -1
slope (12,-7) and (4,5)
[tex](\stackrel{x_1}{12}~,~\stackrel{y_1}{-7})\qquad (\stackrel{x_2}{4}~,~\stackrel{y_2}{5}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{5}-\stackrel{y1}{(-7)}}}{\underset{run} {\underset{x_2}{4}-\underset{x_1}{12}}}\implies \cfrac{5+7}{-8}\implies \cfrac{12}{-8}\implies -\cfrac{3}{2}[/tex]
Suppose that grade point averages of undergraduate students at one university have a bell-shaped distribution with a mean of 2.52 and a standard deviation of 0.43. Using the empirical rule, what percentage of the students have grade point averages that are between 1.23 and 3.81?
Answer:
Using the Empirical Rule, we find that .997 (99.7%) of students have grade point averages that are between 1.23 and 3.81.
Step-by-step explanation:
Calculate the z-scores corresponding to a GPA of 1.23 and 3.81.
[tex]\displaystyle z=\frac{1.23-2.52}{.43} = \frac{-1.29}{.43}= -3[/tex] [tex]\displaystyle z=\frac{3.81-2.52}{.43}= \frac{1.29}{.43} =3[/tex]We want to find the area between the z-scores of -3 and 3.
The Empirical Rule tells us that 99.7% of the data lies within three standard deviations under the normal curve.
Therefore, the area between -3 < z < 3 is about .997, or around 99.7%.
Please show your work! I'll give you brainliest as well lol, thanks!
To know the area of a regular hexagon:
⇒ must know the formula:
[tex]Area = \frac{3\sqrt{3} }{2} s^2[/tex]
s: length of the sideConsider the information given:
Length of side ⇒ 5 cmLet's solve:
[tex]Area=\frac{3\sqrt{3} }{2} (5)^2=64.95cm^2[/tex]
Answer: 65.0 cm²
Hope that helps!
Answer:
64.1 cm²
Step-by-step explanation:
Central Angle = 360 °
∴ ∠AOB = 360 ° / 12
⇒ Tan 30° = AB/ 4 · 3
⇒ AB = 4.3 tan 30°
∴ (ΔAOB) = 1/2 × AB × OB
= 1/2 × 4.3 tan 30° × 4.3
= 5.34 cm
∴ Area of regular hexagon = 12 (a⊃(ΔAOB))
= 12 (5.34 cm²)
= 64.1 cm²
there are 5 green,7blue and 3 red pens. if one ball pen is chosen at random, then what is the probability of getting a red pen??
Answer:
1/5
Step-by-step explanation:
there are 15 pens totally, there are 3 red pens.
probability-> 3/15=1/5
How many matchs played in a 5 team round robin
[tex]\huge[\sum_{k=0}^{4}(k)][/tex] [tex] = 0+1+2+3+4=\boxed{10} [/tex]
=[tex]\huge(\binom {5}{2}) [/tex] [tex] =(5!)/(3! \times 2!) = (5\times 4)/(2)= \boxed{10}[/tex]
Since there are 5 teams..
The number of matches played in a 5 team round Robin is 10.
How does round robin tournament work for 5 teams?A round-robin tournament is a sports competition where each player or team competes against every other player or team; each contestant faces off against the other contestant in turn. A round-robin tournament differs from an elimination tournament in that participants are eliminated after a set number of losses.
From 5 teams we choose 2 to form combinations (need combinations of 2 different teams to play a match).
Here, 5C2 = 5!/2!(5-2)!
= 5×4×3×2!/2!×3!
= 10
Hence, the number of matches played in a 5 team round Robin is 10.
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P(S) = 3/5
P(T) = 1/3
If S and T are mutually exclusive events, find P(S or T).
Answer:
14/15
Step-by-step explanation:
P(S or T) = P(S) + P(T) = 3/5 + 1/3
= 9/15 + 5/15 = 14/15
Which point is between points C and E?
A
B
D
S
Answer:
it's the 'D' ..............,..
A number a is a root of P(x) if and only if the remainder, when dividing the
polynomial by x + a, equals zero.
O A. True
O B. False
Answers is false
Answer: False
Reason: It should be x-a instead of x+a
answer please i need one fast
A 2-column table with 6 rows. The first column is labeled x with entries negative 1, 0, 1, 2, 3, 4. The second column is labeled f of x with entries negative 9, negative 8, negative 7, 0, 19, 56.
What is the x-intercept of the continuous function shown in the table?
(0, –8)
(0, 2)
(–8, 0)
(2, 0)
Answer: i think option c
Step-by-step explanation:
PLEASE HELP
For the right triangle below, find the measure of the angle.
Figure is not to scale.
use tan since you are given the opposite and adjacent sides
tan θ = [tex]\frac{opp}{adj}\\\\[/tex]
tan θ = [tex]\frac{2}{12}[/tex]
use the inverse of tan to find the angle
θ = [tex]tan^{-1}(\frac{2}{12})[/tex]
θ = 9.462322208...
θ = 9.46°
Let f(x)=x^2+4x+3 for what values of x will satisfy the equation f(x)=8
a combination lock is opened by setting each of five barrels to the correct digit. if digits are randomly chosen from the digits 0 through 9, how many unique combinations can be generated? repetition of numbers is allowed
Answer:
A. 0.3204
B. 0.59049
Step-by-step explanation:
Data:
The total number of combinations:
= [tex](10)^5=100000[/tex]
A.
The number of ways = [tex]10*9*8*7=30240[/tex]
[tex]\frac{30240}{100000}[/tex]
The probability for an event P taking place = [tex]=0.3024[/tex]
B.
Number of ways to arrange the subjects = [tex](9)^4=59049[/tex]
[tex]\frac{59049}{100000}[/tex]
The probability = [tex]=0.59049[/tex]
NO LINKS!! PART 3. Please help me with these graphs
Answer:
[tex]\textsf{13)} \quad y=(x+5)^2+4[/tex]
[tex]\textsf{14)} \quad y=-\dfrac{1}{2}(x-2)^2-3[/tex]
Step-by-step explanation:
Vertex form of a parabola:
[tex]y=a(x-h)^2+k[/tex] where (h, k) is the vertex
Question 13From inspection of the graph, the vertex is (-5, 4)
[tex]\implies y=a(x+5)^2+4[/tex]
To find [tex]a[/tex], substitute the coordinates of a point on the curve into the equation.
Using point (-4, 5):
[tex]\implies a(-4+5)^2+4=5[/tex]
[tex]\implies a(1)^2+4=5[/tex]
[tex]\implies a+4=5[/tex]
[tex]\implies a=1[/tex]
Therefore, the equation of the parabola in vertex form is:
[tex]y=(x+5)^2+4[/tex]
Question 14From inspection of the graph, the vertex is (2, -3)
[tex]\implies y=a(x-2)^2-3[/tex]
To find [tex]a[/tex], substitute the coordinates of a point on the curve into the equation.
Using point (0, -5):
[tex]\implies a(0-2)^2-3=-5[/tex]
[tex]\implies a(-2)^2-3=-5[/tex]
[tex]\implies 4a-3=-5[/tex]
[tex]\implies 4a=-2[/tex]
[tex]\implies a=-\dfrac{1}{2}[/tex]
Therefore, the equation of the parabola in vertex form is:
[tex]\implies y=-\dfrac{1}{2}(x-2)^2-3[/tex]
#1
Vertex at (-5,4)Equation
y=a(x+5)²+4As there is no y inetercept present and the function is same as general quadratic equation y=x^2 just change in coordinates a=1
Final equation
y=(x+5)²+4#2
Vertex (2,-3)y=a(x-2)²-3
Use (4,-5)
-4=a(4-2)²-3-1=a(2)²4a=-1a=-1/4Equation
y=-1/4(x-2)²-3How to solve this. A Japanese train can travel 321km in 3hours.At that rate, how could it travel in 5hours?
Answer:
535km
Step-by-step explanation:
train speed = 321/3 km per hour = 107kmh
in 5 hours, travel distance = speed x time = 107 x 5 = 535km
You are asked to find the space occupied by the shape below. Will you calculate its area or volume? A cube shape. area volume
Answer:
volume
Step-by-step explanation:
the amount of space enclosed by an object or shape, how much 3-dimensional space
A company is started by four friends. The company was Erica’s idea, so she wants to fill 70% of the orders. Jen, Heather, and Tonya each agree to fill 10% of the orders. After a successful first year, Erica wants to determine if the distribution of the number of orders filled is adhering to the agreed-upon percentages. She decides to test:
To do so, she selects a random sample of 100 orders from the large number of orders that were filled and determines who filled the order. She finds that Erica filled 56 orders, Jen filled 18, Heather filled 14, and Tonya filled 12. The chi-square test statistic for goodness of fit is χ2 = 11.20 and the P-value is between 0.01 and 0.02.
Because the P-value is less than 0.05, Erica rejects the null hypothesis. Because the null hypothesis is rejected, she would like to know which term contributed the significance of the test. Complete a follow-up analysis. Which term contributed the most to the significance of this test? Were there more or fewer orders being filled by this person than expected?
Erica, more than expected
Erica, fewer than expected
Jen, more than expected
Jen, fewer than expected
The appropriate hypotheses for this test are
Erica filled 70
Jen filled 10
Heather filled 10
Tonya filled 10
A company is started by four friends.
The company was Erica’s idea,
So she wants to fill 70% of the orders. Jen, Heather, and Tonya each agree to fill 10% of the orders.
What is the meaning of the hypothesis?A hypothesis is a statement that proposes a result that will be tested to get a verified result.
A hypothesis is not hundred percent true, that is why it is always put to test.
The hypothesis is singular while the hypothesis is plural.
Making a hypothesis in this case is an attempt to predict an answer or result that will be verified by doing the experiment.
We can conclude by saying that a hypothesis is not hundred percent true.
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Kalon and his friend Marna own a chimney sweep service company. Working together, they can clean a 20-foot chimney in 1Five-sevenths hours. If it takes Kalon 4 hours to clean a 20-foot chimney by himself, how long does it take Marna to clean the same size chimney by herself?
Rate
(Chimneys per Hour)
Time
(Hours)
Fraction Completed
Kalon
One-fourth
1 and five-sevenths
Three-sevenths
Marna
x
1 and five-sevenths
StartFraction 12 x Over 7 EndFraction
3 hours
4 hours
5 hours
6 and six-sevenths hours
Answer:
3 hrs
Step-by-step explanation:
What is the value of n in the equation ?Solve the equation.
–9x + 1 = –x + 17
Answer:
-2
Step-by-step explanation:
→ -9x + 1 = -x + 17
→ -9x + x = 17 - 1
→ -8x = 16
→ x = -16/8
→ [ x = -2 ]
2. Rewrite the expression below using the Associative Property of Multiplication: (ab)c
A. (ba)c
B. c(ab)
C. abc
D. a(bc)
E. All of the above
Use substitution to solve the system.
3x + 5y = 23
x = 3y - 11
Answer:
(1,4)
Step-by-step explanation:
Since x is already "alone", you can plug 3y-11 into the x-value for the first equation to get 3(3y-11)+5y=23. Now distribute 3 to the numbers in the parentheses. In the end, the solution to this is (1,4).
Answer:
x=1, y=4
Step-by-step explanation:
Substitute x = 3y - 11
3(3y - 11) + 5y = 23 |
Simplify
|14y – 33= 23 |
Isolate y for 14y-33=23
y=4
For x =3y - 11
Substitute y = 4
X=3• 4- 11
Simplify
X=1,
What are the zeros of the quadratic function f(x) = 6x- + 12x-7?
Answer:
Number 1
Step-by-step explanation:
Vertex is (−1,−13)
[tex]~~~~~6x^2 +12x -7 =0\\\\\implies x^2 +2x - \dfrac 76=0\\\\\implies x^2+2x = \dfrac76\\\\\implies x^2 +2x +1 = \dfrac 76 +1\\\\\implies (x+1)^2 = \dfrac{13}6\\\\\implies x+1 = \pm \sqrt{ \dfrac{13}6}\\\\\implies x = -1 \pm\sqrt{\dfrac{13} 6}\\\\\text{Hence,}~ x = -1 +\sqrt{\dfrac{13} 6}~~ \text{and}~~ x = -1-\sqrt{\dfrac{13} 6}[/tex]
PLS ANSWER ITS FOR 20 POINTS!!!
The information in the table is displayed in the two graphs below.
If an employee wants to request a raise, which graph should that employee use to support his or her case?
A graph is a way to represent a lot of data in such a visual format. The correct option is C, he/she should use graph B.
What is a graph?A graph is a way to represent a lot of data in such a visual format that it is easy for the user to understand the complete information in one go. Usually, the line of the graph is a function that follows the graph.
If an employee wants to request a raise, the graph he/she should use to support his or her case is graph B. Because that graph is showing all thought the company is earning good profit the salary of the employees is still reducing.
Hence, the correct option is C, he/she should use graph B.
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A bottle was tossed 30 times and recorded whether it landed on its base or on its side. What is the experimental probability that the bottle landed on the base?
a) 3/10
b) 11/30
c) 9/2
d) 3/7
The experimental probability that the bottle landed on its base by the data recorded is; 3/10.
What is the experimental probability that the bottle landed on the base?It follows from the frequency recorded for the bottle landing on it's base and side that; base = 9 and side = 21.
The total possible outcome is 30.
On this note, the required probability is; 9/30 = 3/10.
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If x = 3 (y + w) minus 1 what is the value of w in terms of x and y?
Answer:
Step-by-step explanation:
Discussion
The object of this is make w by itself on one side of the equation.
Equation
x = 3 (y + w) - 1 Add 1 to both sides of the equation.
x + 1 = 3(y + w) - 1 + 1 Combine
x + 1 = 3(y + w) Remove the Brackets
x + 1 = 3y + 3w Notice y and w are affected by the 3. Subtract 3y
x + 1 - 3y = 3y-3y + 3w Combine
x + 1 = 3w Divide both sides by 3
(x +1)/3 = 3w/3
(x + 1)/3 = w
Answer: (x + 1)/3 = w
