A fruit bowl contains a mixture of bananas, lemons and apples. The ratio of bananas to lemons is 4:5. Sophie picks a piece of fruit at random from the fruit bowl. The probability that it is a banana is 1/3. What is the probability that it is an apple? Give your answer as a fraction in its simplest form.
Answers
Step-by-step explanation:
bananas to lemons is 4:5
probability of choosing a banana is 1/3 so 4 is 1/3 of the total parts
4 = 1/3 of 4+ 5 + A
A = 3
so the ratio of B: L: A is 4:5:3
in other words A is 3 out of (4+5+3) = 3 out of 12 = 3/12 = 1/4
Related Questions
Convert 3.9m^2 into cm^2
I will leave good review!
Answers
Answer:
Step-by-step explanation:
To convert square meters to square centimeters, we need to multiply by the conversion factor (100 cm / 1 m)^2.
So,
3.9 m² = 3.9 × (100 cm / 1 m)²
3.9 m² = 3.9 × 10,000 cm²
3.9 m² = 39,000 cm²
Therefore, 3.9 square meters is equal to 39,000 square centimeters.
What is 1-2n+5=6? What is the value
Answers
Answer:
n = 0
Step-by-step explanation:
1 - 2n + 5 = 6
Add the numbers on the left side.
-2n + 6 = 6
Subtract 6 from both sides.
-2n = 0
Divide both sides by -2.
n = 0
Answer:
n=0
Step-by-step explanation:
1-2n+5=6
6 −2n=6
-2n=6-6
-2n=0
n=0
Candace runs a company that installs fences. She calculates the total cost C of installing a fence using the function rule C(x) = 5x + 25, where x is the length of the fence in feet.
Answers
Answer:
g
Step-by-step explanation:
(7m+3)+(7m+6)
I really need help with this
Answers
Answer:
Step-by-step explanation:
The parenthesis can cancel because the lack of anything you can do in them, so that will leave you with 7m + 3 + 7m + 6
Next step is to add like numbers, you should start by adding 7m + 7m, which would be 14m.
Next would be to add 3 + 6, which is nine.
To end this equation, simply put 14m + 9
There is no one-number answer because we do not know what m is. So the equation 14m + 9 is the final answer.
Help help help plz plz hi hi
Answers
Answer:
Angle b=41.
Step-by-step explanation:
(2x+8) + (2x+8)=180...4x+16=180... subtract 16 from 180...4x=164 divide by 4 you get 41.
Answer:
The Real Answer is 82 721 x 912 Because of its high rotation
Step-by-step explanation:
a ow network with supplies is a directed capacitated graph with potentially multiple sources and sinks, which may have incoming and outgoing edges respectively.
Answers
A flow network with supplies is a directed capacitated graph where each edge has a capacity indicating the maximum flow that can pass through it. The flow in the network represents the movement of a certain resource (e.g., water, electricity, goods) from sources to sinks.
In a flow network with supplies, there may be multiple sources, which are nodes that generate the resource and have outgoing edges, and multiple sinks, which are nodes that consume the resource and have incoming edges.
The sources and sinks can have different supply or demand values, indicating the amount of resource they generate or consume.
The edges in the flow network have capacities that restrict the maximum flow that can pass through them. The capacity represents the limit on the amount of resource that can traverse the edge. The flow through an edge cannot exceed its capacity.
The objective in a flow network is to determine the maximum flow that can be sent from sources to sinks while respecting the capacities of the edges. This is typically solved using algorithms such as the Ford-Fulkerson algorithm or the Edmonds-Karp algorithm.
The concept of a flow network with supplies is important in various applications, such as transportation networks, communication networks, and supply chain management, where resources need to be efficiently distributed from multiple sources to multiple sinks, taking into account the capacity constraints of the network.
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Simplify
4x - 3(2 + x) +6y
Answers
Answer:
x + 6y - 6
Step-by-step explanation:
Answer:
x+6y-6
Step-by-step explanation:
how are mimes and tableaus different. and how are they similar
Answers
Simplify. 5/12x1/12=
Answers
Answer:
Step-by-step explanation:
720
Find the point where the lines intersect: y = 3x and y = x + 16
A: (8,24)
B: (4,12)
C: (4,20)
D: (0,0)
Answers
X
Work out the mean for the data set
below:
6.8, 5.7, 0.8, 4.7, 1.3
Give your answer as a decimal.
Answers
Average = Sum / Count
= 19.3 / 5
= 3.86
let u = (1, 0, 1) and v = (0, 2, 2). find a vector w that is orthogonal to both u and v. find a vector x which is orthogonal to u and lies in the same plane defined by u and v.
Answers
A vector w that is orthogonal to both u and v is w = (-1,-1,-1) and a vector x which is orthogonal to u and lies in the same plane defined by u and v is x = (-1,2,1).
The vectors are
u = (1, 0, 1)
v = (0, 2, 2)
If the scalar product of two vectors is equal to zero, then the vectors are orthogonal.
If we let let w = (a, b, c)
Then (u, w) ≥ 0
1×a + 0×b + 1×c = 0
a + c = 0
Subtract c on both side, we get
a = -c
and (v, w) = 0
0×a + 2×b + 2×c = 0
2b + 2c = 0
2(b + c) = 0
b + c = 0
b = -c
Then w = (-c, -c, -c)
If c=1
Then the orthogonal vector
w = (-1,-1,-1)
Let x = (x, y, z)
x is now orthogonal to u.
That is (u, x) = 0
1×x + 0×y + 1×z = 0
x + z = 0
x = -z
u × v = \(\begin{vmatrix}\hat{i} & \hat{j} & \hat{k}\\ 1 & 0 & 1\\ 0 & 2& 2\end{vmatrix}\)
u × v = \(\hat{i}\begin{vmatrix} 0 & 1\\ 2& 2\end{vmatrix}-\hat{j}\begin{vmatrix} 1 & 1\\ 0& 2\end{vmatrix}+\hat{k}\begin{vmatrix} 1 & 0\\ 0& 2\end{vmatrix}\)
u × v = \(\hat{i}\)(-2) - \(\hat{j}\)(2) + \(\hat{k}\)(2)
u × v = -2i-2j+2k
The given condition x lies on the plane u and v
(-2, -2, -2), x ≥ 0
-2x - 2y + 2z = 0
[x = -z]
2z - 2y + 2z = 0
-2y = -4z
y = 2z
That is x = (-z, 2z, z)
Now put z = 1
x = (-1,2,1)
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pls answer!!
In the figure below, ABC is similar to FED. Find the length of BC.
Answers
choose the correct vertical asymptote(s).
Glven the function, f(x) =
x+1
X-4
O x= -4, x= 4
O x= 4
O x= -2, x = 2
O x= 2
Answers
Think of a vending machine on campus. The vending machine has a coin collector that should be emptied regularly. In the past, the vending machine company emptied the coin collector every 14 days, and recorded the weight of the coin collector when it is emptied. In the past 100 visits, the average weight of the coin collector was 22 pounds and the standard deviation was 8.
If the coin collector is full, the vending machine is unusable. But emptying the collector is also an expense. The company finds that it is optimal to empty a coin collector when it weighs 20 pounds. The company wants to test the following hypotheses:
Null hypothesis: the mean weight of the coin collector emptied every 14 days is 20 pounds.
Alternative hypothesis: the mean weight of the coin collector emptied every 14 days is not 20 pounds.
Find the t-statistic of the test, and determine if the null hypothesis is rejected at the significance level of 5%. (Round the t-statistic to the second decimal place.)
a. t-statistic is 2, so the null hypothesis is not rejected.
b. t-statistic is 1.25, so the null hypothesis is not rejected.
c. t-statistic is 2, so the null hypothesis is rejected.
d. t-statistic is 2.5, so the null hypothesis is not rejected
e. t-statistic is 1.25, so the null hypothesis is rejected.
f. t-statistic is 2.5, so the null hypothesis is rejected.
Answers
The null hypothesis is rejected at the significance level of 5%. (Round the t-statistic to the second decimal place.)- t-statistic is 2.5, so the null hypothesis is rejected.
Hypothesis
In statistics, hypothesis testing is used to identify the variance in the group of data that results from genuine variation. Based on the presumptions, the sample data are taken from the population parameter. The hypothesis can be divided into many categories. A hypothesis is described in statistics as a formal statement that explains the relationship between two or more variables belonging to the specified population.
It aids the researcher in converting the stated issue into an understandable justification for the study's findings. It provides examples of various experimental designs and guides the investigation of the research procedure.
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M is the midpoint of AB¯. The coordinates of A are (2, 3) and the coordinates of M are (4.5, 6). What is the coordinate of B?
Answers
Answer:
B = (7, 9)
Step-by-step explanation:
Midpoint between two points
\(\textsf{M}=\left(\dfrac{x_2+x_1}{2},\dfrac{y_2+y_1}{2}\right)\)
Where (x₁, y₁) and (x₂, y₂) are the endpoints.
Given:
A = (2, 3)M = (4.5, 6)Substitute the coordinates into the formula:
\(\implies (x_M, y_M)=\left(\dfrac{x_B+x_A}{2},\dfrac{y_B+y_A}{2}\right)\)
\(\implies (4.5, 6)=\left(\dfrac{x_B+2}{2},\dfrac{y_B+3}{2}\right)\)
\(\implies (9,12)=\left(x_B+2,y_B+3\right)\)
\(\implies (9-2,12-3)=\left(x_B,y_B\right)\)
\(\implies (7,9)=\left(x_B,y_B\right)\)
Therefore, the coordinates of B are (7, 9).
Simplify. (a²b) ³.(b²c²)
Answers
Answer:
(a²b)³(b²c²)=a⁶b⁵c²
An employee produces 17 parts during an 8-hour shift in which he makes $109 per shift. What is the labor content (abor dollar per unit) of the product
Answers
Labor content (labor dollar per unit) is the total cost of labor required to produce one unit of a product. It can be calculated by dividing the total labor cost by the number of units produced.
In this scenario, we are given that an employee produces 17 parts during an 8-hour shift and earns $109 per shift.
To calculate the labor content, we first determine the labor cost per hour. This is done by dividing the total amount earned in the 8-hour shift by 8.
Labor cost per hour = $109 ÷ 8 = $13 per hour
Next, we calculate the number of parts produced per hour by dividing the total number of parts produced (17) by the duration of the shift (8 hours).
Parts produced per hour = 17 ÷ 8 = 2.125 parts per hour
Finally, we calculate the labor cost per part by dividing the labor cost per hour by the number of parts produced per hour.
Labor cost per part = $13 ÷ 2.125 = $6.12 per part
Therefore, the labor content (labor dollar per unit) of the product is $6.12 per part.
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Assume that the number of days it takes a homebuilder to complete a house is normally distributed with a mean time of 176.7 days and a standard deviation of 24.8 days:
Answers
The probability that a homebuilder takes 200 days or less to complete a house is approximately 0.8238, or 82.38%.
Explanation :
To answer this question, we can use the concept of the z-score. The z-score tells us how many standard deviations a data point is from the mean.
Let's calculate the z-score for a completion time of 200 days:
z = (x - μ) / σ
where x is the completion time, μ is the mean, and σ is the standard deviation.
Plugging in the values, we get:
z = (200 - 176.7) / 24.8 = 0.93
To find the probability associated with this z-score, we can use a z-table or a calculator. In this case, the probability is 0.8238.
This means that there is an 82.38% chance that the completion time of a house will be 200 days or less, given that the completion time follows a normal distribution with a mean of 176.7 days and a standard deviation of 24.8 days.
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What is next year's expected cash flow if there is a 50/50 probability that it will be either $10 million or $60 million?
Answers
The next year's expected cash flow if there is a 50/50 probability that it will be either $10 million or $60 million is $35 million.
What is probability?Probability refers to possibilities. This branch of mathematics deals with the occurrence of a random event. The value's range is 0 to 1. The probability formula states that the ratio of positive outcomes to all other outcomes determines how likely an event is to occur.
Sum of outcomes= 410+$60=$70 million
Number of outcomes=2
As the probability is 50/50, the next year’s expected cash flow will be
10+60/(2)
=70/2
=35 million dollars.
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To make violet paint, Iris mixes 0. 25
liter of red paint, 0. 25 liter of blue paint,
and 4. 5 centiliters of white paint. How
many centiliters of paint are in the
mixture?
Answers
There are 54.5 centiliters of paint in the mixture.
To find the total amount of paint in the mixture, we need to convert the volumes of red and blue paint from liters to centiliters, since white paint is already given in centiliters.
0.25 liter of red paint is equal to 25 centiliters (since 1 liter = 100 centiliters)
0.25 liter of blue paint is equal to 25 centiliters
So the total amount of paint in the mixture is:
25 centiliters (red paint) + 25 centiliters (blue paint) + 4.5 centiliters (white paint)
= 54.5 centiliters
Therefore, there are 54.5 centiliters of paint in the mixture Iris made to make violet paint.
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Pens cost 43p and booklets cost £1.85 How much change will I get from £10 if I buy 3 pens and 4 booklets
Answers
Answer:
Step-by-step explanation:
lets see how much will cost 3 pens
3*.43=1.29
booklets
1.85*4=7.4
total
7.40+1.29=8.69
10-8.69=1.31
If it wouldn’t bother someone would someone also mind giving me the steps to get the answer?
Answers
Answer:
SA = 10,800 ft²
Step-by-step explanation:
To find the surface area of a rectangular prism, you can use the equation:
SA = 2 ( wl + hl + hw )
SA = surface area of rectangular prism
l = length
w = width
h = height
In the image, we are given the following information:
l = 40
w = 60
h = 30
Now, let's plug in the information given to us to solve for surface area:
SA = 2 ( wl + hl + hw)
SA = 2 ( 60(40) + 30(40) + 30(60) )
SA = 2 ( 2400 + 1200 + 1800 )
SA = 2 ( 5400 )
SA = 10,800 ft²
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y-intercept y=1/4x-2
Answers
Answer:
(0,-2)
Step-by-step explanation:
y intercept is when x=0
y=1/4(0)-2
y=-2
(0,-2)
I’m just really confused rn
Answers
Answer:
\(\frac{3}{5} *5\) or \(5*\frac{3}{5}\)
Step-by-step explanation:
Each circle has 3/5 shaded, and there are 5 circles.
So our multiplication equation is:
\(\frac{3}{5} *5\) or \(5*\frac{3}{5}\) (they mean the same thing)
\(\frac{3}{5} *5=3\)
Hope this helps!
Point N is on line segment MO. Given MN = 16 and NO = 2, determine the
length MO.
Answer: MO =
Submit Answer
attempt 2 out of 2
Answers
Answer:
Step-by-step explanation:
MO = MN + NO
= 16 + 2
= 18
Solve 4x + 3 = 9 for x using the change of base formula log base b of y equals log y over log b.
Answers
The value of x for a given expression 4x + 3 = 9 is equal to -1.415.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that the expression is 4x + 3 = 9. The value of x will be calculated as,
log(4)⁹= x + 3
log9 / log4 = x + 3
0.95424425 / 0.6020599 = x + 3
1.584962725 -3 = x + 3 - 3
x = -1.415037275
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How many positive integers n are there such that is a multiple of 5, and the least common multiple of 5. and n equals 5 times the greatest common divisor of 10! and n? (A) 12 (B) 24 (C) 36 (D) 48 (E) 72
Answers
The number of positive integers n are there such that is a multiple of 5, and the least common multiple of 5. and n equals 5 times the greatest common divisor of 10! and n are (B) 24.
To solve this problem, we need to consider the prime factorization of 10!.
Prime factorization of 10!:
10! = 2^8 * 3^4 * 5^2 * 7^1
Now, let's examine the conditions given:
The least common multiple of 5 and n must be a multiple of 5.
The least common multiple of 5 and n must equal 5 times the greatest common divisor of 10! and n.
Since the least common multiple must be a multiple of 5, n must have at least one factor of 5.
Let's consider the possible combinations of factors of 2, 3, and 7 in n:
If n has no factors of 2, 3, or 7, then it must have one or two factors of 5.
If n has one factor of 2, it can have zero, one, or two factors of 5.
If n has two factors of 2, it can have zero, one, or two factors of 5.
If n has three or more factors of 2, it cannot satisfy the conditions.
Based on these considerations, let's count the number of possible values for n:
Case 1: n has no factors of 2, 3, or 7:
There are 2 possibilities for each factor of 5 (either 0 or 1): 2 * 2 = 4 possibilities.
Case 2: n has one factor of 2:
There are 3 possibilities for each factor of 5 (either 0, 1, or 2): 3 * 3 = 9 possibilities.
Case 3: n has two factors of 2:
There are 3 possibilities for each factor of 5 (either 0, 1, or 2): 3 * 3 = 9 possibilities.
Therefore, the total number of positive integers n that satisfy the given conditions is 4 + 9 + 9 = 22.
The correct answer choice is (B) 24, which is the closest option provided.
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Find the intervals in which the function f given by f(x)=2x 2
−3x is (a) strictly increasing (b) strictly decreasing.
Answers
Answer:
the function f(x) = 2x^2 - 3x is strictly decreasing on the interval (-∞, 3/4).
Step-by-step explanation:
To find the intervals in which the function f(x) = 2x^2 - 3x is strictly increasing or strictly decreasing, we need to find the first derivative of the function and then determine the sign of the derivative over different intervals.
(a) To find the intervals in which the function f(x) = 2x^2 - 3x is strictly increasing, we need to find where the first derivative is positive. The first derivative of f(x) is:
f'(x) = 4x - 3
To determine the sign of f'(x), we set it equal to zero and solve for x:
4x - 3 = 0
4x = 3
x = 3/4
This critical point divides the real number line into two intervals: (-∞, 3/4) and (3/4, ∞).
To determine the sign of f'(x) over each interval, we can pick a test point in each interval and plug it into the derivative. For example, if we choose x = 0, we have:
f'(0) = 4(0) - 3 = -3
Since f'(0) is negative, we know that f(x) is decreasing on the interval (-∞, 3/4).
If we choose x = 1, we have:
f'(1) = 4(1) - 3 = 1
Since f'(1) is positive, we know that f(x) is increasing on the interval (3/4, ∞).
Therefore, the function f(x) = 2x^2 - 3x is strictly increasing on the interval (3/4, ∞).
(b) To find the intervals in which the function f(x) = 2x^2 - 3x is strictly decreasing, we need to find where the first derivative is negative. Using the same process as above, we find that f'(x) = 4x - 3 and the critical point is x = 3/4.
Picking test points in the intervals (-∞, 3/4) and (3/4, ∞), we find that f(x) is strictly decreasing on the interval (-∞, 3/4).
Therefore, the function f(x) = 2x^2 - 3x is strictly decreasing on the interval (-∞, 3/4).
what is 28.5 inches in height?