We can expect to roll a prime number 48 times.
Theoretically, when you roll a number cube all the possible numbers have the same probability, 1/6.
We know that the numbers in a number cube are {1, 2, 3, 4, 5, 6}
Of these, the primes are: 2, 3, and 5.
So half of the outcomes of a number cube are primes.
This means that, in every single roll, the probability of getting a prime number is 1/2. (1/6 + 1/6 + 1/6 = 3/6 = 1/2)
Then for 96 rolls, we should expect to see in half of these a prime number as an outcome.
This means that we should expect to roll a prime number 96/2 = 48 times.
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You should expect to roll a prime number 64 times.
To determine, if you roll a number cube 96 times, how many times would you expect to roll a prime number, the following calculation must be performed, knowing that the prime numbers are those that can only be divided by 1 or by themselves:
A cube has 6 sides. Therefore, the numbers in the cube will be 1, 2, 3, 4, 5 and 6. Of these numbers, only 4 and 6 are not prime, since 4 is divisible by 2 and 6 is divisible by 2 and 3.
Therefore, 4/6 numbers are prime, that is, 66.66% of the numbers in the cube.
Therefore, if you roll a number cube 96 times, since 96 x 4/6 equals 64, you should expect to roll a prime number 64 times.
Learn more in https://brainly.com/question/23715861.
What is the inequality?
Answer:
The best option would be the second one.
Step-by-step explanation:
This is the only option that shows that x can only be greater than -8. The circled dot means x cannot be the number the dot is sitting on, in this case, -8.
Tom is a builder and earns $38.50 an hour. Calculate his weekly wage if he works for 38 hours?
Answer:
$1,463
Step-by-step explanation:
38.50x38=1,463
GEOEMTRY- PLEASE HELP , solve for x
Answer:
[tex]17x-23=1/2\times81[/tex]
[tex]17x-23=40.5[/tex]
[tex]17x=40.5+23[/tex]
[tex]17x=63.5[/tex]
[tex]x=63.5/17[/tex]
[tex]x=3.73[/tex]
OAmalOHopeO
Please help!!!......
Answer:
12*12=144
8*10=80
80+144=224
224*2=448
10*4=40
8*10=80
80*2=160
40+160=200
12*10=120
120+200=320
20*10=200
320+200=520
448+520=968
Hope This Helps!!!
Determine the measure of the angle theta to the nearest degree
Answer: B. θ = 36°
Step-by-step explanation:
Concept:
Here, we need to know the idea of the Law of sines.
In trigonometry, the law of sines, sine law, sine formula, or sine rule is an equation relating the lengths of the sides of a triangle (any shape) to the sines of its angles.
The Law of sines: a / sinA = b / sinB = c / sinC
If you are still confused, please refer to the attachment below for a graphical explanation.
Solve:
a = 10 m
c = 11.2 m
C = 41°
Given formula
a / sinA = c / sinC
Substitute the value into the formula
10 / sinA = 11.1 / sin (41)
Cross-multiply to simplify the equation
sinA × 11.1 = 10 · sin (41)
Divide 11.1 on both sides
sinA × 11.1 / 11.1 = 10 · sin (41) / 11.1
sinA = 10 · sin (41) / 11.1
Apply arcsine or the inverse of sine (basically representing the division of sine)
A = sin⁻¹ (10 · sin (41) / 11.1)
A = 36°
Hope this helps!! :)
Please let me know if you have any questions
Jerome solved the equation below by graphing. log Subscript 2 Baseline x + log Subscript 2 Baseline (x minus 2) = 3 Which of the following shows the correct system of equations and solution?
Answer:
B. on edge 2021
Step-by-step explanation:
y 1 = StartFraction log x Over log 2 EndFraction + StartFraction log (x minus 2) Over log 2 EndFraction, y 2 = 4; x = 4
Answer:
It's B :))
Step-by-step explanation:
SHOW YOUR STEPS PLEASE. SOMEONE PLEASE HELP ME I NEED THE ANSWER ASAP!!!
The cost, c(x), in dollars per hour of running a certain steamboat is modelled by the function c(x)=1.7x^2-13.6+166.4, where x is the speed in kilometres per hour. At what approximate speed should the boat travel to achieve minimum cost? what is the minimum cost?
Answer:
x = 4
139.2
Step-by-step explanation:
Given the Cost function :
C(x) = 1.7x² - 13.6x + 166.4
To achieve minimum cost ;
dc/dx = 0
dc/dx = 2(1.7)x - 13.6
3.4x - 13.6 = 0
3.4x = 13.6
x = 13.6 / 3.4
x = 4
To achieve minimum cost, speed = 4 ;
Minimum cost will be :
C(x) = 1.7x² - 13.6x + 166.4
Put x = 4
C(4) = 1.7(4)² - 13.6(4) + 166.4
C(4) = 27.2 - 54.4 + 166.4 = 139.2
Minimum cost = 139.2
Mrs Dlamini bought a 10kg bag of rice. She cooks 500g of rice per day. How many days will the bag of rice last her family
Answer:
20 days
Step-by-step explanation:
10kg= 10,000g
10,000g/500g= 20 days
Answer:
20 days
Step-by-step explanation:
1 kg=1000 grams
10 kg=10000 grams
10000÷500
=20 days
Will give brainliest to the first person
12.915 to 2 decimal places
Answer:
12.92
Step-by-step explanation:
rounding the 1 hundredth up to 2 because of the 5 thousandth
Answer:
12.915 to 2.d.p :12.92Step-by-step explanation:
See explanation in attached image
[tex]\sqrt{x} +\sqrt{5} =\sqrt{12}[/tex]
2x-3=5
(x+2)(3x-15)=0
Answer:
the first one gat to be x=4
Answer: 17
Step-by-step explanation: :)
1.2 m
1.2 m
Susie is 1.13 metres tall
She has a play tent in the shape of a triangular prism.
The diagram shows the front view of the tent.
The front of the tent has been drawn to scale below.
a) Complete the scale drawing.
1.5m
Not drawn accurately
b) Can Susie stand up in the
middle of the tent?
1.5m
Scale: 1 cm represents 60 cm
Split the triangle into 2 right in the middle so you have 2 identical right triangles. The base on one would be half the base of the triangle shown so, the base would be: 1.5/2 = 0.75 m.
Now using the Pythagorean theorem you can find the height:
Height - sqrt(1.2^2 - 0.75^2)
Height = sqrt(1.44 - 0.5625)
Height = sqrt(0.8775)
Height = 0.93675 meters
The height of the tent is smaller than the height of Suzie so she cannot stand up.
what is the height of the water prism
Answer:
32 because I Don't know please vote my answer please
Answer:
12 (10) cm 937 637 = hafe 2929888389292822
Rewrite the expression with rational exponents as a radical expression.
4 times x to the three sevenths power
Answer:
[tex]\displaystyle 4\sqrt[7]{x^3}[/tex]
General Formulas and Concepts:
Algebra I
Exponential Rule [Root Rewrite]: [tex]\displaystyle \sqrt[n]{x} = x^{\frac{1}{n}}[/tex]Step-by-step explanation:
Step 1: Define
Identify
[tex]\displaystyle 4x^\bigg{\frac{3}{7}}[/tex]
Step 2: Rewrite
Split: [tex]\displaystyle 4(x^\bigg{\frac{1}{7}})^3[/tex]Rewrite [Exponential Rule - Root Rewrite]: [tex]\displaystyle 4\sqrt[7]{x^3}[/tex]Determine the measure of the interior angle at vertex E.
A. 135
B. 45
C. 225
D. 75
Answer:
135
Step-by-step explanation:
The sum of the interior angles of a pentagon is 540
3x+3x+2x+2x+2x = 540
12x = 540
Divide by 12
12x/12 = 540/12
x = 45
E = 3x = 3*45 = 135
Answer:
135
Step-by-step explanation:
Hamid had gained weight he is now 88k which is 10% more then he uses to be what was his original weight
Answer:
80k
Step-by-step explanation:
let the previous weight be x
88=x + 10%of x
88=x+(10/100)of x
8800=110x
8800/110=x
x=80k
Answer: Original weight = 80 kg
Step-by-step explanation:
Given:
Current weight = 88 Kg
Gain weight rate = 10%
Solve:
Original weight = Current weight / Gain rate
Original weight = (88) / (1 + 10%)
Original weight = 80 Kg
Hope this helps!! :)
Please let me know if you have any questions
Please hurry I will mark you brainliest
Answer:
q = 1/4
Step-by-step explanation:
-5/4 - (-1/4) = -1
-1/(q-1/2) = 4
-1 = 4(q-1/2)
-1 = 4q - 2
1 = 4q
q = 1/4
15) A new BMW decreases in value exponentially after it is purchased. If a new BMW is valued at $55,000 and
depreciate at a rate of 22% a year, what is the value after 4 years? After 8 years)
The values of BMW after 2, 4 and 8 years according to the EXPONENTIAL FUNCTION are $33,462, $20,358.28 and $7,535.63 respectively.
Using the parameters given, we define an decreasing exponential function :
[tex]A = A_{0} (1 - r)^{t}[/tex]
Where,
[tex]A_{0}[/tex] = initial amount ; r = Rate ; t = time ; A = final amount
Value after 2 years :
t = 2
A = 55000(1 - 0.22)²
A = 55000(0.78)²
A = $33,462
Value after 4 years :
t = 4
A = 55000(1 - 0.22)^4
A = 55000(0.78)^4
A = $20,358.28
Value after 8 years :
t = 4
A = 55000(1 - 0.22)^8
A = 55000(0.78)^8
A = $7,535.63
Therefore, the value of BMW after 2, 4 and 8 years are $33,462, $20,358.28 and $7,535.63 respectively.
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I am struggling with this question anyone help
9514 1404 393
Answer:
b, c
Step-by-step explanation:
The factor (x+7) is common to both numerator and denominator. The function can be simplified by cancelling that factor.
y = (x -3)/(x -9) . . . . . . x ≠ -7
The restriction x ≠ -7 is put on the simplified function because the original function is undefined there. The denominator factor x+7 makes the denominator 0 at that point.
The point at x=-7 is called "hole" in the graph. A properly drawn graph will show the function is undefined there (has a hole).
__
The denominator of the simplified function is zero when x=9. This means there is a vertical asymptote at x=9.
__
The ratio of the highest-degree terms of the numerator and denominator will tell you the end behavior of the function — its value when x is large. Here, that ratio is y = x/x = 1. This represents a horizontal asymptote at y=1. The function approaches this line as x gets large, but never reaches it.
The appropriate descriptors are ...
Asymptote: x=9, y=1Hole: x=-7a sequence starts 2,-1,-4,-7 what is the 25th term
Answer:
-70
Step-by-step explanation:
They have a common difference of -3
cosec^2θ-1/cosec^2θ=cos^2θ
cosec(2t)=1/sin(2t) ==> 1/(2×cos(t)×sin(t))
cos(2t)= 1-2sin²t
or 2cos²t-1
or cos²t - sin²t
after we knew this informations we have to write it in the question
1/2×sint×cost-1/1/2×sint×cost=cos2t
-2×sint×cost+1/2sint×cost/1/2sint×cost=cos2t
the 2sint×cost will gone
-2×sint×cost+1=cos2t
lets take cos2t =1-2sin²t
-2×sint×cost+1=1-2sin²t
-2sint×cost=-2sin²t
cost=sint
that means the t is equal to 45 because sin45 and cos45 equal to √2/2
hopefully i didn't waste your time by reading and not understanding my English is not that good sorry
Answer:
see explanation
Step-by-step explanation:
Using the identities
cosec x = [tex]\frac{1}{sinx}[/tex] , 1 - sin²θ = 1
Consider the left side
[tex]\frac{cosec^20-1}{cosec^20}[/tex]
= [tex]\frac{\frac{1}{sin^20}-\frac{sin^20}{sin^20} }{\frac{1}{sin^20} }[/tex]
= ( [tex]\frac{1}{sin^20}-\frac{sin^20}{sin^20}[/tex] ) × [tex]\frac{sin^20}{1}[/tex] ← distribute parenthesis by sin²θ
= 1 - sin²θ
= cos²θ
= right side, thus proven
R. White and Co. Has total profit of 6/7 million dollars. The spinning department gave a profit 1/4 of million dollars. Find the fraction of profit from other departments.
Answer:
Fraction of profit from other departments = 17/28
Step-by-step explanation:
Total profit of R. White and Co = 6/7 million dollars
Profit from the spinning department = 1/4 of million dollars
Fraction of profit from other departments = Total profit of R. White and Co - Profit from the spinning department
= 6/7 million dollars - 1/4 of million dollars
= 6/7 - 1/4
Lowest common multiple (LCM) of 7 and 4 is 28
= (24-7) / 28
= 17/28
Fraction of profit from other departments = 17/28
Simply the expression (x^3/2)^6
Answer:
x**9
Step-by-step explanation:
(x**3/2)**6 = x**18/2 = x**9
What are the first 5 terms?
Answer:
please can you specify which topic exactly is it on Arithmetric or Geometric Progression or on another topic
please kindly specify and send the question back
Thank you
Step-by-step explanation:
Answer:
5, 12, 19, 26, 33
Step-by-step explanation:
Using the recursive rule and a₁ = 5 , then
a₂ = a₁ + 7 = 5 + 7 = 12
a₃ = a₂ + 7 = 12 + 7 = 19
a₄ = a₃ + 7 = 19 + 7 = 26
a₅ = a₄ + 7 = 26 + 7 = 33
The first 5 terms are 5, 12, 19, 26, 33
Find he probability of no more than 35 defective CD's in a batch of 80 CD's if the probablility of any one CD being defective is 0.1.
Answer:
0.999999
Step-by-step explanation:
Given that :
Probability of CD being defective, p = 0.1
q = 1 - p = 1 - 0.1 = 0.9
Total number of CD's = number of trials = 80
Probability, that no more than 35 CD's are defective ;
The question satisfied the requirements for a binomial probability problem ;
Recall :
P(x = x) = nCx * p^x * q^(n-x)
Hence,
P(x ≤ 35) = 80C35 * 0.1^35 * 0.9^(45)
Using calculator to save computation time :
P(x ≤ 35) = 0.999999
Find the volume and surface area of the composite figure. Give four answer in terms of pi
Answer:
B
Step-by-step explanation:
Volume = Volume of cylinder + Volume of semi sphere
= pi*r^2*h+(2/3)*pi*r^3
=pi*(4*12+16/3)=pi*53.3
20 points lovelys <3
Answer:
A) 2 cm
Step-by-step explanation:
By definition, regular polygons have equal sides and angles. Therefore, each side of the regular hexagon must be equal. Since one side is marked as 2 cm, the length of PQ must also be 2 cm.
2). 2, x, 14 are in Arithmetic progression, then the value of x is :
A. 28
B. 16
C. 7
D. 8
For g(x) = x - 2 find the value of x for which g(x) = -4.
Answer:
x=-2
Step-by-step explanation:
g(x) = x-2
Let g(x) = -4
-4 =x-2
Add 2 to each side
-4+2 = x-2+2
-2 = x
Answer:
x = -2
Step-by-step explanation:
g(x) = -4
g(x) = x - 2
-4 = x - 2
+2 +2
-2 = -x
