The volume of air inside the cube is 1887.4 cubic inches. Then the correct option is C.
What is Geometry?It deals with the size of geometry, region, and density of the different forms both 2D and 3D.
A ball inside of a cube has a volume of 113 cubic inches. If each side of the cube measures 12.6 inches.
Then the volume of air inside the cube will be given as the difference between the volume of the cube and the sphere.
Air volume = Volume of the cube - Volume of the sphere
Air volume = 12.6³ - 113
Air volume = 2000.376 - 113
Air volume = 1887.376
Air volume ≅ 1,887.4
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Answer:
1887.4 cubic inches
Step-by-step explanation:
Question A volleyball team sold raffle tickets to raise money for the upcoming season. They sold three different types of tickets: premium for $10, deluxe for $4, and regular for $2. The total number of tickets sold was 208, and the total amount of money from raffle tickets was $714. If 78 more regular tickets were sold than deluxe tickets, how many premium tickets were sold?
Answer:
24 premium tickets were sold.
Step-by-step explanation:
Let :
Deluxe ticket = x
Regular tickets = x + 78
Premium tickets = y
x + (x + 78) + y = 208
4x + 2(x+78) + 10y = 714
2x + y = 208 - 78
4x + 2x + 156 + 10y = 714
2x + y = 130 - - - - - (1)
6x + 10y = 558 - - - - (2)
Now we can solve the simultaneous equation using elimination method :
From (1)
y = 130 - 2x
Put y = 130 - 2x in (2)
6x + 10(130 - 2x) = 558
6x + 1300 - 20x = 558
- 14x = 558 - 1300
-14x = - 742
x = 742 / 14
x = 53
Put x = 53 in y = 130 - 2x
y = 130 - 2(53)
y = 130 - 106
y = 24
which of the following is q point slope equation of a line that passes through the point (5,2)and (-1,-6)
Answer:y - y1 = m(x + x1)
m = (y2 - y1)/(x2 - x1) = (-6 - 2)/(-1 - 5) = -8/(-6) = 4/3
y - 2 = 4/3(x - 5) is a possible answer
y + 6 = 4/3(x + 1) is also a possible answer
Step-by-step explanation:
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if the r-value, or correlation coefficient, of a data set is 0.941, what is the coefficient of determination
Answer:0.824
Step-by-step explanation:
The coefficient of determination is approximately 0.885 or 88.5%.
What is the correlation coefficient?A correlation coefficient (r) is a number between -1 and 1 that measures the strength and direction of a linear relationship between two variables.
The coefficient of determination (R-squared) is equal to the square of the correlation coefficient (r).
Therefore, to find the coefficient of determination with an r-value of 0.941, we can simply square it:
R-squared = r² = 0.941² = 0.885481
Thus, the coefficient of determination is approximately 0.885 or 88.5%.
This means that 88.5% of the variation in the dependent variable can be explained by the independent variable(s) in the data set.
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6. A sporting goods store receives an order of 100 baseball caps, of which 22 are green. If 1 of
the 100 caps is selected at random, what is the probability it will not be green?
A. 39/50
B. 11/25
C. 11/50
D. 1/2
Answer:
[tex]\text{A. }39/50[/tex]
Step-by-step explanation:
The probability that a randomly selected cap will not be green is equal to the number of non-green caps divided by the total number of caps.
Since there are 100 caps total and 22 are green, there must be [tex]100-22=78[/tex] non-green caps.
Divide this by the total number of caps (100) to get the probability that a randomly selected cap will not be green:
[tex]\frac{78}{100}[/tex]
Simplify by dividing both the numerator and denominator by 2:
[tex]\frac{78}{100}=\boxed{39/50}[/tex]
The slope of a line is −6. What is the slope of any line parallel to this line?
Answer:
-6
Step-by-step explanation:
Parallel lines have the same slope
If a line has a slope of -6, all lines parallel to this will have a slope of -6
The
equation of the line in the graph is y= Blank x+ blank
Answer:
y = mx + b
Step-by-step explanation:
This is the basic equation for a line where m is the slope and b is the y intercept.
If you have a right triangle with legs a =6 and b= 8, what is the value of the hypotenuse? show work.
Answer:
10
Step-by-step explanation:
1. [tex]6^{2} + 8^{2} = c^{2}[/tex]
2 [tex]100 = c^{2}[/tex]
3. c = 10
ASAP!!!!!! SHOW WORK!!!! Thank you!!!!!!!!!
Its A trapezium
For Calculations Refer to the attachment
Answer:
SquareStep-by-step explanation:
Plot the points.
See the attached.
It is easy to calculate the length of sides and diagonals using the coordinates and the distance formula.
The sides are all equal to [tex]\sqrt{5}[/tex] units and the diagonals are both equal to [tex]\sqrt{10}[/tex] units.
This is a property of a square.
A set of triplets weighted 4lb 3oz , 3 lb 9oz and 4 lb 5 oz . What is the total weight of all three babies ?
Answer:
12 lb 1 oz
Step-by-step explanation:
Add the amounts together
4lb 3oz ,
3 lb 9oz
4 lb 5 oz
-------------------
11 lb 17 oz
But 16 oz is 1 lb so subtract 16 oz and add 1 lb
11 lb 17 oz
+1lb - 16 oz
--------------------
12 lb 1 oz
Which ratio represents the tangent of an angle?
a. adjacent/hypotenuse
b. opposite/hypotenuse
c. adjacent/opposite
d. opposite/adjacent
Answer:
option d.opposite / adjacent
Step-by-step explanation:
opposite /adjacent ratio represents the tangent of an angle .
hope it is helpful to you ☺️
Answer:
D.
Step-by-step explanation:
From the trigonometry shortcuts we can use the acronyms:
SOH CAH TOA
for an arbitrary angle Ф, plug in the length of the sides:
sin(Ф) = opposite/hypotenuse
cos(Ф) = adjacent/hypotenuse
tan(Ф) = opposite/adjacent
Solve for:
∫_(-1)^1 x^3+1/2 dx
Answer:
[tex]\int _{\left(-1\right)}^1\frac{x^3+1}{2}dx[/tex]
[tex]=\frac{1}{2}\cdot \int _{\left(-1\right)}^1x^3+1dx \Leftarrow(take \: constant\: out)[/tex]
[tex]=\frac{1}{2}\left(\int _{\left(-1\right)}^1x^3dx+\int _{\left(-1\right)}^11dx\right) \Longleftarrow (Sum\:Rule)[/tex]
[tex]\int _{\left(-1\right)}^1x^3dx=0[/tex]
[tex]\int _{\left(-1\right)}^11dx=2[/tex]
[tex]=\frac{1}{2}\left(0+2\right)[/tex]
[tex]=1[/tex]
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OAmalOHopeO❃❃❃❃❃❃❃❃❃❃❃
Find the length of AC
A. 12.84
B. 43.92
C. 12.28
D. 40.16
Answer: 40.16
Step-by-step explanation:
The length of the side AC will be 12.28 units. The correct option is C.
What is trigonometric indentity?
Trigonometric Identities are equality statements that hold true for all values of the variables in the equation and that use trigonometry functions. There are numerous distinctive trigonometric identities that relate to a triangle's side length and angle.
Given that the hypotenuse of the triangle is 42 and the angle B is 17 degrees.
The side AC will be calculated as below:-
sin(47) = P / 42
AC = 42 x sin42
AC = 12.27
Therefore, the length of the side AC will be 12.28 units. The correct option is C.
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A patient is a member of a health plan that have a 20% discount from the provider and a 15% copay if the day's charges are to 10 what are the amounts that the ancient bow in the patient each pay
Answer: A
Step-by-step explanation:
a game is played with a circular spinner that contains 7 different colors. the design of the spinner is the order in which the colors are arranged. how many ways can this spinner be designed
Answer:
This spinner can be designed in 5040 ways.
Step-by-step explanation:
Number of possible arrangements:
The number of possible arrangements of n elements is given by:
[tex]A_{n} = n![/tex]
In this question:
7 colors, so:
[tex]A_{7} = 7! = 5040[/tex]
This spinner can be designed in 5040 ways.
Devaughn is 10 years older than Sydney. The sum of their ages is 104. What is Sydney's age?
I
Answer:
Sydney's age = 42
Step-by-step explanation:
104 divided by 2 = 52
52 - 10 = 42
I am sorry if this is wrong. But this is what I learned at my school.
Find the inverse relationship of the function y=2x+5
Answer:
y=x-5/2
Step-by-step explanation:
Swap y and x
x=2y+5
since a function has to be in the form y=mx+c
take 5 to the other side in order to remain with 2y then divide both sides by 2
x-5/2=y
y=x-5/2
Answer:
Duke is a very good team and
a - c = d - r, for a
Answer:
a = d+c - r
Step-by-step explanation:
a - c = d - r
Add c to each side
a - c+c = d - r+c
a = d+c - r
The duration of shoppers' time in Browse Wrld's new retail outlets is normally distributed with a mean of 27.8 minutes and a standard deviation of 11.4 minutes. How long must a visit be to put a shopper in the longest 10 percent
Answer:
A visit must be of at least 42.39 minutes to put a shopper in the longest 10 percent.
Step-by-step explanation:
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Mean of 27.8 minutes and a standard deviation of 11.4 minutes.
This means that [tex]\mu = 27.8, \sigma = 11.4[/tex]
How long must a visit be to put a shopper in the longest 10 percent?
The 100 - 10 = 90th percentile, which is X when Z has a p-value of 0.9, so X when Z = 1.28.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]1.28 = \frac{X - 27.8}{11.4}[/tex]
[tex]X - 27.8 = 1.28*11.4[/tex]
[tex]X = 42.39[/tex]
A visit must be of at least 42.39 minutes to put a shopper in the longest 10 percent.
Using Suitable property Evaluate :
(10)3 – (2)³ – (8)3
Answer:
480
Step-by-step explanation:
(10)3- (2)3- (8)3
1000- 8- 512
= 480
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A cone has a volume of 4000cm3
. Determine the height of the cone if the diameter of the cone
is 30 cm.
Answer:
17cm
Step-by-step explanation:
Given that the Volume of a cone is 4,000 cm³. And we need to determine the height of the cone , if the diameter is 30cm .
Diagram :-
[tex]\setlength{\unitlength}{1.2mm}\begin{picture}(5,5)\thicklines\put(0,0){\qbezier(1,0)(12,3)(24,0)\qbezier(1,0)(-2,-1)(1,-2)\qbezier(24,0)(27,-1)(24,-2)\qbezier(1,-2)(12,-5)(24,-2)}\put(-0.5,-1){\line(1,2){13}}\put(25.5,-1){\line(-1,2){13}}\multiput(12.5,-1)(2,0){7}{\line(1,0){1}}\multiput(12.5,-1)(0,4){7}{\line(0,1){2}}\put(17.5,1.6){\sf{15cm }}\put(9.5,10){\sf{17\ cm }}\end{picture} [/tex]
Step 1: Using the formula of cone :-
The volume of cone is ,
[tex]\rm\implies Volume_{(cone)}=\dfrac{1}{3}\pi r^2h [/tex]
Step 2: Substitute the respective value :-
[tex]\rm\implies 4000cm^3 =\dfrac{1}{3}(3.14) ( h ) \bigg(\dfrac{30cm}{2}\bigg)^2 [/tex]
As Radius is half of diameter , therefore here r = 30cm/2 = 15cm .
Step 3: Simplify the RHS :-
[tex]\rm\implies 4000 cm^3 = \dfrac{1}{3}(3.14) ( h ) (15cm)^2\\ [/tex]
[tex]\rm\implies 4000 cm^3 = \dfrac{1}{3}(3.14) ( h ) 225cm^2\\ [/tex]
Step 4: Move all the constant nos. to one side
[tex]\rm\implies h =\dfrac{ 4000 \times 3}{ (3.14 )(225 )} cm \\[/tex]
[tex]\implies \boxed{\blue{\rm Height_{(cone)}= 16.98 \approx 17 cm }}[/tex]
Hence the height of the cone is 17cm .
mited
Find any relative extrema of the function. List each extremum along with the x-value at which it occurs. Identify intervals over which the function is
increasing and over which it is decreasing. Then sketch a graph of the function.
f(x) = -x^3+ 9x?
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Answer:
relative minimum -6√3 at x = -√3relative maximum 6√3 at x = √3decreasing on x < -√3 and x > √3increasing on -√3 < x < √3see below for a graphStep-by-step explanation:
I find it convenient to draw the graph first when looking for relative extrema.
The function can be differentiated to get ...
f'(x) = -3x^2 +9
This is zero when ...
-3x^2 +9 = 0
x^2 = 3
x = ±√3 . . . . . x-values of relative extrema
Then the extreme values are ...
f(±√3) = x(9 -x^2) = (±√3)(9 -3) = ±6√3
The lower extreme (minimum) corresponds to the lower value of x (-√3), so the extrema are ...
(x, y) = (-√3, -6√3) and (√3, 6√3)
__
Since the leading coefficient is negative and the degree is odd, the function is decreasing for values of x below the minimum and above the maximum. It is increasing for values of x between the minimum and the maximum.
decreasing: x < -√3, and √3 < x
increasing: -√3 < x < √3
13/16= (-5/4) + g
G= what
NEDD HELP NOW plz
Identify the errors made in finding the inverse of
y = x2 + 12x
x= y2 + 12x
y2 = x -12
y2 = -11x
y= V-11x, for x 20
Describe the three errors
Answer:
x = y² + 12x
y² = x - 12
y² = -11x.
Step-by-step explanation:
We need to find the inverse of the given function , which is ,
[tex]\rm\implies y = x^2 + 12x [/tex]
Step 1 : Interchange x and y :-
[tex]\rm\implies x = y^2 + 12y [/tex]
But according to the steps given in the Question , in very first step in 12x , x is not replaced by y . After which , the steps go wrong in the question .
The 3 errors :-
x = y² + 12x y² = x - 12 y² = -11x.What function is represented by the graph? Of(x)=-2|x|+1 Of(x)=-1/2|x|+1 Of(x)=-2|x+1| Of(x)=-1/2|x+1|
Answer:
f(x)= -2[x+1]
this is the answer of the question
The test statistic of z=2.08 is obtained when testing the claim that p≠0.611. a. Identify the hypothesis test as being two-tailed, left-tailed, or right-tailed. b. Find the P-value. c. Using a significance level of α=0.01, should we reject H0 or should we fail to reject H0?
Answer:
Following are the solution to the given points:
Step-by-step explanation:
When the two-tailed were testing then:
Null and alternative hypothesis:
[tex]H_0 : p = 0.611\\\\H_a : p \neq 0.611[/tex]
Testing the statistics:
[tex]\to z = 2.08\\\\P-value = 0.0375\\\\\alpha = 0.01\\\\0.0375> 0.01\\\\P-value < \alpha\\\\[/tex]
therefore, it fails to reject the null hypothesis.
11/12 - 5/8 in simplest form
Answer:
7/24
Step-by-step explanation:
11/12 - 5/8
Get a common denominator of 24
11/12 * 2/2 = 22/24
5/8 *3/3 = 15/24
22/24 -15/24 = 7/24
❤❤❤❤PLEASE HELP ASAP AND BE CORRECT PLEASE❤❤❤❤
Answer: move each corner (where you see the right triangles) 2 units to the left and three units up. Then, draw the quadrilateral.
Step-by-step explanation:
R0,180 is the same rotation as ____.
R0,-180
R-90,180
R90,180
R0,90
Write a linear equation in point slope form with the given slope of 1/4 and passing through the point (8,-3)
Answer:
The equation is
y=1/4x-3
Answer:
y = 1/4x - 5
Step-by-step explanation:
If gradient or slope (m) equal to 1/4
then y - y¹ = m( x - x¹) ..........(1)
where the line happen to be passing through the point given above
therefore let x¹ be 8.........(2)
and y¹ be -3...............(3)
substitute (3) and (2) into (1)
we have y -(-3) = 1/4 (x - 8)
so 4(y+3)= (x-8)
4y = x - 8 - 12
therefore y = 1/4x - 5
2. Caveman Sampson chases a saber tooth tiger at an average speed of 3 miles per hour. The tiger runs at an average speed of 5 miles per hour, but rests for 2 hours after running for 2 hours. How long, in hours, will it take Sampson to catch the tiger if the tiger starts 2 miles in front of him and they start running at the same time?
A. 7 hours B. 6 hours C. 5 hours D. 4 hours
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Answer:
D. 4 hours
Step-by-step explanation:
The tiger will run (5 mi/h)(2 h) = 10 mi in 2 hours. That will put it 2+10 = 12 miles from Sampson's starting location.
Samson can run 12 miles in time ...
time = distance/speed = (12 mi)/(3 mi/h) = 4 h
Sampson will get to the tiger's location after 4 hours, just as the tiger is ending its rest period.
__
The graph shows the position of Sampson (red) and the tiger (blue) x hours after the chase starts. The distance (y miles) is measured from Sampson's starting point, assuming the tiger is running away.
