The probability that you have seen both the red and green marbles at least once is 0.3104
Given,
1/5 chance of winning a marble of any color in a drawing.
Every draw is independent and has the same probability because the marbles are replaced.
Calculating = 1- the likelihood of not receiving both red and green marbles in any of the four draws yields the same result as P, the probability of receiving both red and green marbles at least once (Q).
The union of the following three examples represents ways to not receive both red and green in all four draws:
(1)
Probability of no red and no green in a draw = 3/5.
Probability of no red and no green in 4 draws,
Q1 = 3/5 * 3/5 * 3/5* 3/5 = 81/54
The probabilities are multiplied as each draw is independent and has the same probabilities.
(2)
The probability of no red and 1 green in 4 draws is given by binomial probability.
= (4 3) (1/5)(3/5)³ = (4 * 3³)/5¹ = 108/5⁴
The probability of no red and 2 green in 4 draws is given by binomial probability.
= (4 2) (1/5)²(3/5)² == (6 * 3²)/54 = 54/5⁴
The probability of no red and 3 green in 4 draws is given by binomial probability.
= (4 3) (1/5)³(3/5) == (4 * 3)/5¹ = 12/5⁴
The probability of no red and 4 green in 4 draws is given by binomial probability.
= (4 4) = 1 * 1/5¹ = 1/5⁴⁴
Q2= sum of all 4 above probabilities.
Q2 (108 +54 + 12+1)/5 = 175/5⁴
(3)
This probability is the same as in Q2. Q3 = 175/5⁴
Therefore the probability of not seeing both red and green at all,
Q = Q1 + Q2 + Q3.
= 81 +175 + 175/5⁴ = 413/5⁴
Finally, the probability of getting both red and green at least once,
P = 1 - Q
= 1-413/5⁴
= (625 431)/625
= 194/625
= 0.3104.
The answer is 0.3104.
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Four small candies cost $.96 how much do six candies cost
Six candies would cost $1.44.
Answer:
$1.44
Step-by-step explanation:
We need to figure out how much one piece of candy costs. So you do .96/4, which is going to equal 0.24.
1 piece of candy = $0.24
So we do 0.24*6= 1.44
I hope this helps!!!
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if a fair coin is tossed 5 times, what is the probability, to the nearest thousandth, of getting exactly 0 heads?
The probability of getting exactly 0 heads is, 0.031.
What is probability?
The area of mathematics known as probability deals with numerical descriptions of how likely it is for an event to happen or for a proposition to be true. A number between 0 and 1 is the probability of an event, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes its certainty.
Given:
A fair coin is tossed 5 times.
So, the the total number of possibilities are,
[tex]2^5= 32[/tex]
We have to find the probability of getting exactly 0 heads.
The only possible set of flips that yields 0 heads is {T, T, T, T, T}.
So,
The probability is, [tex]\frac{1}{32}=0.03125[/tex]
Probability ≈ 0.031
Hence, the probability of getting exactly 0 heads is, 0.031.
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1. You'll find the glue and scissors in ___
*There
*Their
* They're
given 2n letters, two of each of n types, how many arrangements are there with no pair of consecutive letters the same?
The arrangements are there with no pair of consecutive letters the same is ∑ₐⁿ(−1)^k2^k(2n−k)!C(n,k).
Explain arrangements are there with no pair of consecutive letters the same.The past step makes six void spots in which three Is might be sorted out, however just three spots should be picked. Request doesn't make any difference, as every one of the three Is are something similar. Along these lines, there are (63) approaches to picking those spots.
According to question:Given 2n letters, two of every one of n types. What number of courses of action of these letters are there without any sets of sequential letters something similar? Kindly look at my answer and let me know where my mix-up is!
So such plans where the sets of indistinguishable letters are discernable. Then, at that point, ∑ₐⁿ(−1)^k2^k(2n−k)!C(n,k) gives the quantity of such plans by incorporation avoidance (there are (2n−k)! ways for k given matches to be together (by combining the those sets into single components) and the rest randomly requested, 2k ways of requesting inside those given matches, and C(n,k) ways of picking those k pairs).So we can acquire the recipe
∑ₐⁿ(−1)^k2^k(2n−k)!C(n,k)
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Find the distance from line L to point P for each of the following: Line L contains points (-5,3) and (4,-6). Point P(2,4)
Answer and explanation in one:
(4+9)/(-2-1) = 13/-3 = -13/3
y=-13x/3 + b
4=26/3 + b
b = 4-26/3 = (12-26)/3 = -14/3
y=-13x/3 -14/3 is the line through the two given points
find the line perpendicular and through (14,-6)
y=3x/13 + b, plug in the point to find b
-6 = 3(14)/13 + b
b = -6 -42/13 = -78/13 - 42/13 = -120/3
y= 3x/13 - 120/13
find the intersection point of the two lines, set them equal
3x/13 -120/13 = -13x/3 - 14/3
multiply by 39
9x - 360 = -169x - 182
178x = 360-182 = 178
x = 1
y= -27/3=-9
the point is (1,-9)
calculate the distance from (1,-9) to (14,-6)
d^2 = 9+169 = 178
d = sqr178 = about 13.34
Which set of ordered pairs (x, y) could represent a linear function
A = \{(1, - 2), (3, 1), (5, 4), (8, 7)\}
B = \{(- 6, 6), (- 3, 3), (0, 0), (3, - 4)\}
C = \{(- 2, 8), (- 1, 6), (0, 4), (2, 1)\}
D = \{(- 8, 6), (- 4, 3), (0, 0), (4, - 3)\}
{(- 8, 6), (- 4, 3), (0, 0), (4, - 3)}set of ordered pairs (x, y) could represent a linear function
What is Slope of Line?The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.
The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.
The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is
m=y₂-y₁/x₂-x₁
Linear function is a function whose graph is a straight line
Slope of a line tells us how steep the line is . Slope of a line is same at all the points.
For option A:
m=1+2/3-1=3/2
m=3/2
m=7-4/8-5=3/3=1
Slopes are not same
For option B:
m=3-6/-3+6=-3/3=-1
m=0-3/0+3=-1
m=-4/3
Slopes are not same
For option C:
m=6-8/-1+2=-2
m=4-6/1=-2
m=-3/2
Slopes are not same
For option D:
m=3-6/-4+8=-3/4
m=-3/4
m=-3/4
Slopes are same at every point, so this set of ordered pairs could represent a linear function
Hence, {(- 8, 6), (- 4, 3), (0, 0), (4, - 3)}set of ordered pairs (x, y) could represent a linear function
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At a small savings and loan company, you have to deal with your customers being victims of identity theft. This happens unpredictably to one of your customers once every 9 weeks; and no incident seems to have any connection to any other incident. a) What is the probability that you will have to deal with no more than 4 incidents of identity theft in the next year (52 weeks)? b) When you have had 12 more incidents of identity theft, your company will send a detective to investigate. What are the expected value and variance of the time (in weeks) until a detective is sent to investigate? c) Use normal approximation to find the probability that the detective will be sent within 2 years.
Answer: At a small savings and loan company, you have to deal with your customers being victims of identity theft. This happens unpredictably to one of your customers once every 9 weeks; and no incident seems to have any connection to any other incident.
Step-by-step explanation:
New game You pay 10 and roll a 6 die. If you get a you win 50 If not, you get to roll again. If you get a 6 this time, you get your 10 back.
a) Create a probability model for this game.
b) Find the expected value and standard deviation of your prospective winnings.
c) You play this game five times. Find the expected value and standard deviation of your average winnings.
d) 100 people play this game. What's the probability the person running the game makes a profit?
a) Probability model
P(40) = 1/6
P(0) = 5/36
P(-10) = 25/36
b) E(X) = -5/18
standard deviation = 18.331
c) standard deviation = 91.65
d) Probability = 0.560
From the question, we have
a) X = -10, 0 or 40 for your winnings (or losses). The corresponding probabilities are:
P(40) = 1/6
P(0) = (5/6)(1/6) = 5/36
P(-10) = 1 - 1/6 - 5/36 = 25/36
b) E(X) = (-10)(25/36) + 0(5/36) + 40(1/6) = -5/18
E(X^2) = (100)(25/36) + 1600(1/6) = 3025 / 9
Var(X) = E(X^2) - [E(X)]^2 = 3025 / 9 - (-5/18)^2 = 108875 / 324
standard deviation = sqrt [Var X] = 119043 / 6494 =18.331
c) E(X) = (-10)(25/36) + 0(5/36) + 40(1/6) = -5/18
5 * E(X) = - 25/18
standard deviation = 5 * 18.331 = 91.65
d) Probability :
P(X < 0) = P{ z < [0 - (-5/18)] / [(119043 / 6494) / sqrt 100] } = P(z < 0.1515) = 0.560
Probability:
Possibility is referred to as probability. This branch of mathematics deals with the occurrence of a random event. The value's range is 0 to 1. Probability has been applied into mathematics to predict the likelihood of different events. Probability generally refers to the degree to which something is likely to occur. This fundamental theory of probability, which also applies to the probability distribution, can help you comprehend the possible outcomes for a random experiment. Gonna determine how likely something is to occur, use probability. Many things are hard to predict with 100% certainty. We can only anticipate the possibility of an event occurring using it, or how likely it is.
Complete question:
From the Data at Hand to the World at Large 4. New game You pay $10 and roll a die. If you get a 6, you win $50. If not, you get to roll again. If you get a 6 this time, you get your $10 back. a) Create a probability model for this game. b) Find the expected value and standard deviation of your prospective winnings. c) You play this game five times. Find the expected value and standard deviation of your average winnings. d) 100 people play this game. What's the probability the person running the game makes a profit?
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Use the given zero to find the remaining zeros of each function.
Thank you!! :)
Answer:
remaining zeros: {-1/2, √3}
Step-by-step explanation:
Given the polynomial function f(x) = 2x³ +x² -6x -3 has one zero at x = -√3, you want the remaining zeros.
Conjugate zerosA polynomial with rational real coefficients and zeros that are roots or complex numbers will have all such roots in conjugate pairs.
The root that is the conjugate of -√3 is +√3.
Product of rootsThe product of the roots of an odd-degree polynomial will be the opposite of the ratio of the constant to the leading coefficient. Here, that means the product of roots is ...
-(-3/2) = 3/2
We already know that two of the three roots are ±√3, so their product is -3. The remaining root will be ...
(3/2)/(-3) = -1/2
The remaining zeros of f(x) are √3 and -1/2.
__
Additional comment
When the degree of the polynomial is even, the constant term will be the product of the roots. This odd/negative, even/positive behavior comes from the fact that each zero (q) corresponds to a factor (x -q).
The product of these binomial factor constants is the constant in the standard-form polynomial. It will have a negative sign if there are an odd number of factors.
(5+9i)+(4-5i) simplify
Answer:
9 + 4i
Step-by-step explanation:
5 + 4 + 9i - 5i
=> 9 + 4i
Write an equation of the line that passes through (-6, 0) and (0, -24) .
Answer: y= -4x -24
Step-by-step explanation:
The equation is y=mx + b
We know the b is -24 because it already tells us the coordinate of the y-intercept is (0, -24), so we only need to find x by looking at the rise over run.
The rise is -24, and the run is 6, so -24/6 = -4
So the equation is y= -4x -24
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On a coordinate plane, 2 trapezoids are shown. Trapezoid 1 has points A (negative 4, 3), B (1, 3), C (0, 0), and D (negative 3, 0). Trapezoid 2 has points A prime (negative 1, 1), B prime (4, 1), C prime (3, negative 2), and D prime (0, negative 2).
Which rule describes the translation?
T–3, –2(x, y)
T–3, 2(x, y)
T3, –2(x, y)
T3, 2(x, y)
The rule of translation will be; Horizontal shift by 3 units right and vertical shift by 2 units down (x, y) → (x + 3, y -2)
What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s range(involving values of y) or in it’s domain(involving values of x).
For the shift left, shift right, shift down, shift up, vertical stretching, horizontal stretching, vertical compression, horizontal compression, reflection over the x-axis, reflection over the y-axis, and rotations by a determined amount(in degrees). All these translations have predetermined rules that we apply to the figures.
Given that Trapezoid 1 with vertices
A(-4, 3), B(1, 3), C(0, 0), D(-3, 0)
Trapezoid 2 with vertices are;
A'(-1, 1), B'(4, 1), C'(3, -2), D'(0, -2)
It can be observed by comparison that the x-values have increased by 3 units and the y-values have decreased by 2 units
So the rule of translation will be; Horizontal shift by 3 units right and vertical shift by 2 units down (x, y) → (x + 3, y -2)
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Find the indicated side of the
right triangle.
30°
X
60°
3
Answer:
6
Explanation:
x = 3 /cos(60) = 6
What was the beginning balance in the incomplete register shown? Date 10/21/03 Description of Transaction Payment Deposit Balance Beginning Balance Mike's Cafe 10/26/03 Sporting Goods Store Paycheck Amusement Park $38.25
The required balance at the beginning of the incomplete register is $38.25.
Given that,
To determine the beginning balance in the incomplete register.
The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
here,
In the table, in the register, the balance starts with an entry of $38.25 paycheck. So, the 1 st entry of the register shows the balance in the beginning.
Thus, the required balance at the beginning of the incomplete register is $38.25.
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Akira is running around a circular track. Akira runs counterclockwise. From where he starts, it takes him 22 seconds to reach the easternmost point of the track. It takes him 95 seconds to run one complete lap. Bob starts running at the same time as Akira. Bob starts from the northernmost point and runs clockwise. Bob and Akira pass each other for the first time after 26 seconds. How long does Bob take to run one lap of the track? (round off your answer to four decimal digits)
The time taken for Bob take to run one lap of the track is 69 seconds
Akira is running around a circular track. Akira runs counterclockwise.
It takes him 95 seconds to run one complete lap
Bob starts running at the same time as Akira
Bob and Akira pass each other for the first time after 26 seconds
It takes him 95 seconds to run one complete lap
In 26 seconds he covers 26/95 laps
In this time Bob must have covered 69/95 laps
An inverse relationship
c/95 = 69/95
c = (69/95) x 95
c = 69
Therefore, time taken for Bob take to run one lap of the track is 69 seconds.
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Evaluate the surface integral. s (x + y + z) ds, s is the parallelogram with parametric equations x = u + v, y = u − v, z = 1 + 2u + v, 0 ≤ u ≤ 3, 0 ≤ v ≤ 2.
the surface integral. s (x + y + z) ds, s is the parallelogram with parametric equations x = u + v, y = u − v, z = 1 + 2u + v is 10[tex]\sqrt{14}[/tex]
The surface element is
dS = || ∂r/∂u x ∂r/dv || du dv
where
r (u, v) = x (u, v) i + y (u, v) j + z (u, v) k
r (u, v) = (u + v) i + (u - v) j + (1 + 2u + v) k
is the vector parameterization for the surface S.
The normal vector to the surface is
∂r/∂u x ∂r/dv
… = (i + j + 2 k) x (i - j + k)
… = 3 i + j - 2 k
and has norm
|| ∂r/∂u x ∂r/dv || = √(3² + 1² + (-2)²) = √(14)
Now compute the integral:
∫∫ (x + y + z) dS = √(14) ∫₀¹ ∫₀² ((u + v) + (u - v) + (1 + 2u + v)) du dv
… = √(14) ∫₀¹ ∫₀² (3u + v + 1) du dv
… = √(14) ∫₀¹ (3/2 u² + uv + u) |₀² dv
… = √(14) ∫₀¹ (8 + 2v) dv
… = √(14) (8v + 2v²) |₀¹
… = 10 √(14)
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Zoe goes to a restaurant and the subtotal on the bill was xx dollars. A tax of 5% is applied to the bill. Zoe decides to leave a tip of 15% on the entire bill (including the tax). Write an expression in terms of xx that represents the total amount that Zoe paid.
The expression in terms of x that represents the total amount that Zoe paid is 1.2075x.
What is an expression that represents the total amount that Zoe paid?Expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both.
From the information, Zoe goes to a restaurant and the subtotal on the bill was x dollars. A tax of 5% is applied to the bill and Zoe decides to leave a tip of 15% on the entire bill.
The expression will be:
= x + (5% × x) + (15% × 1.05x)
= x + 0.05x + 0.1575x
= 1.2075x
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Pls help me, Brainliest + 100 points if correct and well explained:
What are the vertex and range of y = |x − 5| + 4?
a: (5, 4); −∞ < y < ∞
b: (5, 4); 4 ≤ y < ∞
c: (−5, 4); −∞ < y < ∞
d: (−5, 4); 4 ≤ y < ∞
The vertex and range of the function y = |x - 5| + 5 is (5, 4) and [4, ∞) respectively
Vertex and RangeThe vertex of the function is located at (h,k) of its vertex form, and will be located at the peak or trough of the parabola on a graph. This is the highest or lowest point of the function, depending on its direction.
The range of a function is the complete set of all possible resulting values of the dependent variable (y, usually), after we have substituted the domain.
In the given function;
y = |x - 5| + 4
Using a graph, the lowest point of the function is at x = 5 and y = 4 is the vertex of this function.
vertex = (5, 4)
Range = [4, ∞)
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Terry has a goal of making $300 in commission for the week. If her commission is based on 18% of sales how much does she need to sell to make her goal? I need an answer ASAP pls
The amount of sales Terry must make is $1667
How to determine the amount in sales?From the question, we have the following parameters that can be used in our computation:
Commission = 18% of sales
Commission = $300
These parameters mean that
Commission = 18% of sales
Substitute the known values in the above equation, so, we have the following representation
18% of sales = 300
Divide both sides by 18%
Sales = 1667
Hence, the amount is $1667
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3) A class of 168 students went on a field
trip. They took 6 vehicles, some vans and
some buses. Find the number of vans and
the number of buses they took if each van
holds 6 students and each bus hold 50
students.
Answer:
They took 3 vans and 3 buses.
Step-by-step explanation:
Given:
The number of students in the class = 168The number of vans and buses = 6The number of students each van can hold = 6The number of students each bus can hold = 5To find:
The number of vans and the number of buses they took.
Explanation:
Let the number of vans = v
Let the number of buses = b
The total number of vans and buses is 6:
[tex]v+b=6[/tex]
⇒[tex]v=6-b....[/tex]Equation(1)
Each van holds 6 students and each bus hold 50 students.
The number of students on the trip is 168.
[tex]6v+50b=168[/tex]....Equation(2)
Substitute equation (1) into equation (2):
[tex]6v+50b=168[/tex]
[tex]6(6-b)+50b=168[/tex]
Then solve the equation for b:
[tex]36-6b+50b=168[/tex]
[tex]44b=168-36[/tex]
[tex]44b=132[/tex]
[tex]\frac{44b}{44}=\frac{132}{44}[/tex]
[tex]b=3[/tex]
Then, solve for v:
[tex]v=6-b=6-3=3[/tex]
Answer:
They took 3 vans and 3 buses.
a country uses as currency coins with values of 1 peso, 2 pesos, 5 pesos, and 10 pesos and bills with values of 5 pesos, 10 pesos, 20 pesos, 50 pesos, and 100 pesos. find a recurrence relation for the number of ways to pay a bill of n pesos if the order in which the coins and bills are paid matters
when we pay n pesos, then recurrence relation for all the number are in a ways to pay a bill is in this order:[tex]a_{n} =a_{n-1}+a_{n-2}+2a_{n-5}+2a_{n-10}+ a_{n-20}+a_{n-50}+a_{n-100}[/tex]
A recurrence relation is an equation which represents a chain primarily based totally on a few rule. It enables in locating the following time period (subsequent time period) established upon the previous time period (preceding time period). If we recognise the preceding time period in a given series, then we will without difficulty decide the following time period.
Recurrence family members are used to lessen complex issues to an iterative procedure primarily based totally on less difficult variations of the trouble. An instance trouble wherein this technique may be used is the Tower of Hanoi puzzle. Recurrent is some thing that happens frequently or repeatedly. However, in case you are speakme approximately a recurrence relation, then you definitely have a mathematical shape which you are handling and it's miles really specific than a recursive formula. Recursion is the repeated use of a process or action.
pay 1 pesos coin , then n-1 pesos
pay 2 pesos coin , then n-2 pesos if n ≥ 2
pay 5 pesos coin , then n-5 pesos if n ≥ 5
pay 10 pesos coin , then n-10 pesos if n ≥ 10
pay 5 pesos bill , then n-5 pesos if n ≥ 5
pay 10 pesos bill , then n-10 pesos if n ≥ 10
pay 20 pesos bill , then n-20 pesos if n ≥ 20
pay 50 pesos bill , then n-50 pesos if n ≥ 50
pay 100 pesos bill , then n-100 pesos if n ≥ 100
a0=1
so i have recurrence relation as follows:
[tex]a_{n} =a_{n-1}+a_{n-2}+2a_{n-5}+2a_{n-10}+ a_{n-20}+a_{n-50}+a_{n-100}[/tex]
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If you walk around a circular path twice which has a diameter of 100 m, how far did you walk in total?
The total distance Is
m.
Use π = 3.14 and round your answer to the nearest hundredth.
Answer:
628 m
Step-by-step explanation:
We need to find the circumference, C, of the circle.
C = πd
C = 3.14 × 100 m
C = 314 m
Walking around the circular path twice is twice the length of the circumference.
distance = 2C = 2 × 314 m = 628 m
can someone please help me?
The value of x in the given function, f(x) = 3/2x - 4 when f(x) = 5, is x = 6
Determining the value of x in a functionFrom the question, we are to determine the value of x in the given function for the given value of f(x).
The given function is
f(x) = 3/2x - 4
and
f(x) = 5
Now, to determine the value of x, put f(x) = 5 in the given function
f(x) = 3/2x - 4
5 = 3/2x - 4
Add 4 to both sides of the equation
5 + 4 = 3/2x - 4 + 4
9 = 3/2x
Multiply both sides by 2
2 × 9 = 2 × 3/2x
18 = 3x
Divide both sides by 3
18/3 = 3x/3
6 = x
Therefore,
x = 6
Hence, the value of x is 6
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Given the equation |x+10|=15
, x= 5 is one solution. What is the other solution?
Answer:
x = - 25
Step-by-step explanation:
the absolute value function always gives a positive value , however , the expression inside the bars can be positive or negative, that is
| - a | = | a | =a
given
| x + 10 | = 15 , then
x + 10 = 15 ( subtract 10 from both sides )
x = 5
OR
-(x + 10) = 15
- x - 10 = 15 ( add 10 to both sides )
- x = 25 ( multiply both sides by - 1 )
x = - 25
solutions are x = 5 , x = - 25
Answer: -25
Step-by-step explanation:
Of the 47 plays attributed to a playwright, 11 are comedies, 16 are tragedies, 20 are histories. If one play is selected at random, find the odds against selecting a
The odds against selecting a history are 31/16.
Define probability.Probability is the concept that describes the likelihood of an event occurring. In many situations, it is necessary to foresee how something will turn out in the actual world. We may be aware of the result of an event or not. When this occurs, we state that there is a possibility that the event will occur.
Probability is the ratio of the most likely outcomes to all other possible outcomes of an event. The number of successful outcomes for an experiment with 'n' outcomes may be expressed using the symbol x. The following formula can be used to determine the likelihood of an event.
Probability(Event) = favorable outcome/Total outcome = x/n
Number of playwrights = 47
Number of tragedies = 16
Therefore, the odds against selecting tragedies are
(47 - 16) / 16
= 31/16
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The complete question is:
Of the 47 plays attributed to a playwright, 11 are comedies, 16 are tragedies, 20 are histories. If one play is selected at random, find the odds against selecting a tragedy.
19. a television set is on sale for 15% off the original price. if the sale is $340, what was the original price of the televisions set?
Using the percentage method, we know that the original price of the TV set was $400.
What is the percentage?Percentages are just fractions with a denominator of 100.
To show that a number is a percentage, we place the percent sign (%) next to it.
For instance, if you properly answered 75 out of 100 questions on a test, you would have received a 75% grade (75/100).
So, we know that the percentage is always out of 100.
Then we automatically know that:
100% - 15% = 85%
We know:
85% = $340
15% = ?
Now, calculate the reduced price as follows:
85/340 = 15/x
85x = 15(340)
85x = 5,100
x = 5100/85
x = $60
Original price of the TV set:
Sold cost + Reduced cost
$340 + $60
$400
Therefore, using the percentage method, we know that the original price of the TV set was $400.
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PLS HELP ASAP!!!! 50 PTS
Answer: x=4
Step-by-step explanation:
6x + 10 = 5x + 14
x + 10 = 14
x = 4
A double recipe of cookies calls for 5 cups of flour.
Which of the following proportions could be used to find the amount of flour for a triple recipe?
3/2 = 5/f
5/2= f/3
2/3 = f/5
2/5 = f/3
Answer:
You could divide 5 in half and then add that to the five to find the amount of flour to use in a triple recipe. Hope this helps.
Step-by-step explanation:
Clingman Dome, in the Great Smoky Mountains, is the highest point in Tennessee.
Clingman Dome is 6,643 feet above sea level. Use the information to answer questions 4-5.
a) Considering the scale factor, the height that she should build the model is of: 22.1 inches.
b) Essence has enough information to build the accurate scale model, as she needs only the scale and either the actual or the drawn model.
What are scales?An scale is defined as the relation between the actual length of a segment and the length of drawn segment, as follows:
Scale = Actual length/drawn length
The scale for this problem is given as follows:
Scale factor = 300 ft/1 in.
Which means that each inch on the drawing represents an actual height of 300 ft.
The height of the Clingman Dome is given as follows:
6,643 feet.
Considering the scale factor of 300 ft/1 in, the height of the drawing is obtained as follows:
6643/300 = 22.1 inches.
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discrete 5 dice of different colors are rolled, and the number coming up on each die is recorded. how many different outcomes are possible?
The number of total different outcomes are, 7,776.
What is rolling dice?
Every face of a cube known as a dice has a unique number.
By throwing a dice into the air, players can advance in any game by getting a certain number. Typically, this dice or dice has numbers from 1 to 6 written on each face or side of the cube-like shape.
Given:
Discrete 5 dice of different colors are rolled, and the number coming up on each dice is recorded.
Since all the dice are of different colors.
So any combination of the numbers on the dice is unique.
Dice has numbers 1 to 6.
So, for each dice there are 6 possibilities.
Since number coming on a dice is independent to the number coming on the another dice.
So, total different outcomes are = 6 x 6 x 6 x 6 x 6 = 6^5 = 7776.
Hence, the number of total different outcomes are, 7,776.
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