A box has 14 candies in it: 3 are taffy, 7 are butterscotch, and 4 are caramel. Juan wants to select two candies to eat for dessert. The first candy will be selectedat random, and then the second candy will be selected at random from the remaining candies. What is the probability that the two candies selected are taffy?Do not round your intermediate computations. Round your final answer to three decimal places.
Answers
Okay, here we have this:
Considering the provided information we are going to calculate what is the probability that the two candies selected are taffy. So, for this, first we are going to calculate the probability that the first is taffy, and then the probability that the second is taffy. Finally we will multiply these two probabilities to find the total probability.
Remember that the simple probability of an event is equal to favorable events, over possible events.
First is taffy:
At the beginning there are 14 sweets, and 3 are taffy, so there are 3 favorable events and 14 possible, then:
First is taffy=3/14
Second is taffy:
Now, in the bag there are 13 sweets left, and of those 2 are taffy, so now there are 2 favorable events out of 13 possible:
Second is taffy=2/13
The first and second are taffy:
First is taffy*Second is taffy=3/14*2/13
First is taffy*Second is taffy=3/91
First is taffy*Second is taffy=0.033
First is taffy*Second is taffy=3.3%
Finally we obtain that the probability that the two candies selected are taffy is aproximately 0.033 or 3.3%.
Related Questions
1. The law of demand predicts that
a. the more consumers purchase a good, the greater the demand for the good
b. consumers are willing to buy more of a good at a lower price than at a higher price
c. as prices go up, the quantity of a particular good that consumers will buy also rises
Od. consumers are willing to buy more of a good at a higher price than at a lower price
2. The function of price in a market system
a. is a way of adjusting the balance between the forces of supply and demand
b. acts as an incentive to producers to either increase or decrease the quantity supplied
c. is a means of rationing the available supply among those who demand it
d. all of these
3. A key advantage of the corporate form of business organization is
a. that the business lives on even if the owners of the business die
b. limited liability of stockholders
c.
the ability to raise significant amounts of financial capital
d.
all of these
Answers
2. The function of price in a market system is all of these: a way of adjusting the balance between the forces of supply and demand, an incentive to producers to either increase or decrease the quantity supplied, and a means of rationing the available supply among those who demand it. Therefore, the correct answer is d.
3. A key advantage of the corporate form of business organization is all of these: the business lives on even if the owners of the business die, limited liability of stockholders, and the ability to raise significant amounts of financial capital. Therefore, the correct answer is d.
In given figure AB is the diameter of circle. If ∠CAD = 32° and ∠CPB = 28°. Find ∠CDA.
Answers
Answer:
Therefore, the angle ∠CDA is 58°.
Step-by-step explanation:
∠CDA = 58°
In the given figure, let's consider the angle ∠CDA as x.
Since AB is the diameter of the circle, we know that the angle subtended by any diameter at any point on the circumference is always 90°. Therefore, ∠CAB = 90°.
In triangle CAD, the sum of angles is 180°. So, we have:
∠CAD + ∠CDA + ∠CAB = 180°
Substituting the known values:
32° + x + 90° = 180°
Combining like terms:
x + 122° = 180°
Subtracting 122° from both sides:
x = 180° - 122°
x = 58°
If the interval size is decreased from $200 to $100, which of the following must remain the same on the newhistogram?a) The height of the bars will decrease.b) The total number of bars will decrease. c) The width of the bars will increase. d) Each bar will represent more data items than before.
Answers
If the interval size is decreased from $200 to $100, then option a. The height of the bars will decrease.
How is this determined?The height of the bars will decrease if the interval sizes in a histogram are reduced while the scale remains constant. When the intervals are compressed,
For a particular set of data, there will be more histogram bars, but fewer data points will make up each interval. Reducing the interval size will also reduce the height of the histogram's bars because the height of the bars represents the number of items in each interval.
Hence, if the interval size is decreased from $200 to $100, then option a. The height of the bars will decrease.
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How much shorter is the handle than the top of the screwdriver?
Answers
Answer:
Hey There! Here's Ur Answer
Step-by-step explanation:
one at their standard length of 45-3/4 inches, the other two inches shorter.
Happy to Help!
A die is rolled 2 times. What is the probability of getting a 1 on the first roll and a 2 on the second roll.
Answers
The probability of getting a '1' on the first roll and '2' on the second roll for the given expression is \(\frac{1}{18}\) .
What about probability?
In mathematics and statistics, probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, where 0 indicates an impossible event and 1 indicates a certain event.
The probability of an event A is denoted by P(A) and is defined as the ratio of the number of favorable outcomes to the total number of possible outcomes. In other words, it is the number of ways that event A can occur divided by the total number of possible outcomes.
For example, if you roll a fair six-sided die, the probability of rolling a 4 is 1/6, since there is only one favorable outcome (rolling a 4) out of six possible outcomes (rolling a 1, 2, 3, 4, 5, or 6).
Probability is used in many different fields, such as gambling, statistics, and science, to make predictions about the likelihood of different outcomes. It is also used to model complex systems and to test hypotheses in scientific experiments.
According to the given information:
When a die is rolled 2 times, the output we get
(1, 1) (1, 2) (1, 3) (1, 4) (1, 5) (1, 6)
(2, 1) (2, 2) (2, 3) (2, 4) (2, 5) (2, 6)
(3, 1) (3, 2) (3, 3) (3, 4) (3, 5) (3, 6)
(4, 1) (4, 2) (4, 3) (4, 4) (4, 5) (4, 6)
(5, 1) (5, 2) (5, 3) (5, 4) (5, 5) (5, 6)
(6, 1) (6, 2) (6, 3) (6, 4) (6, 5) (6, 6)
Total no of getting '1' on first roll and '2' on second roll = 2
Total outcomes = 36
⇒ \(\frac{2}{36}\)
⇒ \(\frac{1}{18}\)
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the probability that a student selected in our class will pass mathematics test is 2/3 how many students are likely to feel mathematics in the art class with 69 students
Answers
Out of 69 students in the art class, around 23 are expected to fail the mathematics test, assuming the probability of passing given is 2/3.
To determine how many students are likely to fail mathematics in the art class, we need to use the given probability of passing the mathematics test, which is 2/3.
First, let's find the probability of failing the mathematics test. Since passing and failing are complementary events (i.e., if the probability of passing is p, then the probability of failing is 1 - p), we can calculate the probability of failing as 1 - 2/3, which simplifies to 1/3.
Now, let's consider the art class, which has a total of 69 students. If the probability of failing mathematics is 1/3, then approximately 1/3 of the students in the art class are likely to fail the mathematics test.
To find the number of students likely to fail, we multiply the probability of failing (1/3) by the total number of students in the art class (69).
(1/3) * 69 ≈ 23
Therefore, approximately 23 students are likely to fail mathematics in the art class of 69 students based on the given probability of passing the mathematics test.
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There are 36 boys and 12 girls at the Zephyrs baseball game practice. What is
the ratio of boys to girls?
a 4:1
C. 1.4
b. 3:1
d. 1:3
Answers
Answer:
Step-by-step explanation:
the ration of boys to girls will be:
36/12=3/1
choice b
another way
36 boys.........................12 girls divide by 6
6 boys.............................2 girls divide by 2
3 boys.............................1 girl
\Look at the two equations:
-3x + 6 = 21
-3x + 6 < 21
Which statement best describes the process used to solve the equations?
In both cases, subtract 6 from both sides, but reverse the inequality sign when doing that for the inequality.
In both cases, divide by –3 on both sides, but reverse the inequality sign when doing that for the inequality.
The process is exactly the same for solving the equation and solving the inequality.
The process for solving the equation is entirely different from solving the inequality.
Answers
The statement "In both cases, subtract 6 from both sides, but reverse the inequality sign when doing that for the inequality" best describes the process used to solve the equations.
In the equation -3x + 6 = 21, to isolate the variable x, we subtract 6 from both sides of the equation, which yields -3x = 15. Then, we divide both sides by -3 to solve for x, resulting in x = -5. This process is applicable to equations where we aim to find the exact value of the variable.
Similarly, in the inequality -3x + 6 < 21, we want to find the range of values for x that satisfy the inequality. By subtracting 6 from both sides, we obtain -3x < 15.
However, since we performed the same operation on both sides of the inequality, the direction of the inequality sign remains the same.
Thus, the correct inequality is -3x < 15. To isolate x, we divide both sides by -3. However, since we reversed the inequality sign, we must also reverse it again, resulting in x > -5.
This process allows us to determine the range of values for x that satisfy the inequality.
Therefore, the statement accurately describes the process for solving both the equation and the inequality, highlighting the significance of reversing the inequality sign when manipulating inequalities.
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Grace wants to collect data on the weight of her puppy as it grows. She decides to construct a table with age in weeks and weight in kilograms as variables. Will the ordered pairs from Grace’s data represent a function, a relation or a neither?
Answers
How her dogs age relates to its weight.
A triangle has a base length of 3ac2 and a height 2 centimeters more than the base length. Find the area of the triangle if a = 2 and c = 3.
Answers
The area of the triangle, when a = 2 and c = 3, is 1512 square centimeters.
We must apply the formula for the area of a triangle, which is provided by: to determine the triangle's area.
(1/2) * Base * Height = Area
We can enter the values of a = 2 and c = 3 into the formula given that the base length is 3ac2 and the height is 2 centimetres greater than the base length.
Base length =\(3ac^2 = 3 * 2 * (3^2) = 3 * 2 * 9 = 54\) centimeters
Height is calculated as Base Length + 2 (54 + 2 = 56 centimetres).
Using these values as a substitute in the formula, we obtain:
Area =\((1/2) * 54 * 56 = 1512\) square centimeters
centimetres square
It's crucial to understand that the calculation assumes the triangle is a right triangle with the specified base and height and that the given values of a and c are accurately used in the formula.
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Can I please get some help I’ve been stuck on this question for a while!
Answers
Using the radius of the Ferris wheel and the angle between the two positions, the time spent on the ride when they're 28 meters above the ground is 12 minutes
How many minutes of the ride are spent higher than 28 meters above the ground?The radius of the Ferris wheel is 30 / 2 = 15 meters.
The highest point on the Ferris wheel is 15 + 4 = 19 meters above the ground.
The time spent higher than 28 meters is the time spent between the 12 o'clock and 8 o'clock positions.
The angle between these two positions is 180 degrees.
The time spent at each position is 10 minutes / 360 degrees * 180 degrees = 6 minutes.
Therefore, the total time spent higher than 28 meters is 6 minutes * 2 = 12 minutes.
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Graph the linear equation. 3x - 4t = 12
Answers
A graph of the linear equation 3x - 4t = 12 has been plotted as shown in the image attached below.
What is a graph?In Mathematics, a graph can be defined as a type of chart that is typically used to graphically represent data points or ordered pairs on both the horizontal and vertical lines of a cartesian coordinate, which are the x-axis (x-coordinate) and y-axis (y-coordinate) respectively.
Next, we would use an online graphing calculator to plot the relationship between the value of x and the value of t as shown in the image attached below.
In conclusion, a graph which represents the linear equation (3x - 4t = 12) does not represent or show a proportional relationship between the value of x and t because they didn't pass through the origin (0, 0).
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(08.03|08.04 HC)
For the regions A and B shown in the graph:
Part A: Discuss the limits of integration. (3 points)
Part B: Set up an integral expression that represents the total area. (4 points)
Part C: Calculate the total area. (3 points)
Answers
The total area from the graph is 2.737.
What is area?Area is the amount of space occupied by a two-dimensional figure. In other words, it is the quantity that measures the number of unit squares that cover the surface of a closed figure. The standard unit of area is square units which is generally represented as square inches, square feet, etc.
First of all, lets calculate the points of intersection (P, Q, R)
x²+3=(x+2) +5
x²-2=√(x+2)
x⁴+4-4x²=x+2
x⁴-4x²-x+2=0
(x-2)(x³+2x²-1)=0
(x-2)(x+1)(x²+x-1)=0
x=2, -1, -1±√(1+4)/2
Clearly, the x-coordinate of Q is -1, P is -1-√5/2, R is -1+√5/2, S is 2
So the limit of integration will be
P( (-1-√5)/2, (-1-√5/2)² +3)=P((-1-√5)/2, (3+√5/2))
Q(-1, (-1)²+3)=Q(-1, 4)
Area A:
\(\int\limits^\frac{3+\sqrt{5} }{2} _4 {-\sqrt{-y-3}-((y-5)^2 -2)} \, dx\)
= \([\frac{-(y-3)^\frac{3}{2} }{\frac{3}{2} }-\frac{(y-5)^3}{3}+3y]^{\frac{3+\sqrt{5} }{2} }_4\)
= 2.07
Area B:
\(\int\limits^\frac{-1+\sqrt{5} }{2} _4 {-\sqrt{x+2}+5-(x^2+3)} \, dx\)
= \([\frac{-(x+2)^\frac{3}{2} }{\frac{3}{2} }+5x-\frac{x^3}{3}-3x]^{\frac{-1+\sqrt{5} }{2} }_{-1}\)
= 0.667
Total area = 2.07+0.667
= 2.737
Therefore, the total area from the graph is 2.737.
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a farmer wants to fence in three sides of a rectangular field shown below with 960 feet of fencing. The other side of the rectangle will be a river. If the enclosed area is to be a maximum, find the dimensions of the field.
Answers
9514 1404 393
Answer:
240 ft by 480 ft
Step-by-step explanation:
Area is maximized when the long side is half the total length of the fence. That makes the short side (out from the river) be half the length of the long side.
The fenced field dimensions are 240 feet by 480 feet.
__
You can let x represent the length of the long side. Then the length of the short side is half the remaining fence: (960 -x)/2.
The total area is the product of these dimensions:
A = x(960 -x)/2
We note that this is the equation of a parabola with zeros at x=0 and x=960. The maximum will be found on the line of symmetry, halfway between the zeros. That is at x = (0 +960)/2 = 480.
The area is maximized for a long-side dimension of 480 feet. The short sides are 240 feet.
HELP ASAP PLEASE I need it this doesn’t make sense
Answers
Answer:
good luck i just answered for the 5 points
Step-by-step explanation:
he universal set is U = {q, w, e, r, t, y}
Subsets are:
A = {q, w, e}
B = {w, e, r, t}
Use roster form to indicate the set: A' U B'
Answers
The roster form of the set of A' ∪ B' is A' ∪ B' = {q, r, t, y}
SetsFrom the question, we are to use the roster form to indicate the set A'∪B'
First, we will determine the complements of the sets, that is A' and B'
From the given information,
A = {q, w, e}
B = {w, e, r, t}
Then,
A' = {r, t, y}
B' = {q, y}
Thus,
A' ∪ B' = {q, r, t, y}
Hence, the roster form of the set of A' ∪ B' is A' ∪ B' = {q, r, t, y}
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Tyler is 6 feet tall and Blake measures his shadow to be 10 ½ feet long. Maddie measures the shadow of the tree to be 21 feet long. How tall is the tree to the nearest tenth of a foot.
20 Points
Answers
The tree is approximately 12 feet tall to the nearest tenth of a foot.
We have,
To find the height of the tree, we can set up a proportion using the measurements of the shadow.
Since we know that Tyler is 6 feet tall and his shadow is 10 ½ feet long, we can set up the following expression:
Tyler's height / Tyler's shadow length = Tree's height / Tree's shadow length
6 feet / 10.5 feet = Tree's height / 21 feet
To find the tree's height, we can cross-multiply and solve for it:
6 feet x 21 feet = 10.5 feet x Tree's height
126 feet = 10.5 feet x Tree's height
Dividing both sides of the expression by 10.5 feet:
126 feet / 10.5 feet = Tree's height
12 feet = Tree's height
Therefore,
The tree is approximately 12 feet tall to the nearest tenth of a foot.
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Sheila went shopping. She spent 4 of her money on a hat and į of
her remaining money on a shirt. After those two purchases she had
$20.
How many dollars did Sheila have at the start of her shopping trip?
Answers
Answer:$32
Step-by-step explanation: so you add 4 and 8 to get 12 and then add to 20 to get the start of her money. good luck on your grades
2/5 of employees in a company drive to work, 1/3 travel by bus and the rest walk. 1. Find the fraction of who walk.
Answers
Answer:
4/15
Step-by-step explanation:
2/5 drive
1/3 bus
and rest walk
fraction of those who walk is 1-(2/5+1/3)
2/5+1/3=(6+5)/15=11/15
15/15-11/15=4/15
Please Help Me ASAP.
Answers
Answer:
C
Step-by-step explanation:
cuz itz IRRATIONAL
not understanding it
Answers
Answer:
C. x = ±\(\sqrt{10}\)i
Step-by-step explanation:
To solve for the solution, solve for x.
x^2 + 10 = 0
x^2 = -10
x = \(\sqrt{-10}\)
x = \(\sqrt{10}\)\(\sqrt{-1}\)
x = ±\(\sqrt{10}\)i
A
B
C
D
37. What is the length of side P in the figure below?
6.7 cm
11 cm
15 cm
45 cm
20 cm
25 cm
P
Answers
The length of the side P is 15 cm. And the right option is C.
What is Pythagoras theorem?Pythagoras theorem states that “In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides.
To calculate the length of side P we use Pythagoras theorem's formula
Pythagoras formula:
a² = b²+c²......................... Equation 1Where:
a = Diagonal of the rectangleb = Length of the rectanglec = Width of the rectangleFrom the diagram,
Given:
a = 25 cmb = 20 cmc = p cmSubstitute these values into equation 1
25² = 20²+p²p² = 25²-20²p² = 225p = √225p = 15 cmHence, the right option is C 15 cm.
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Help plzzz will give brainliest
Answers
Answer:
1/3 and false at least i think wait for other answer to make sure it is correct
Step-by-step explanation:
It takes two scoops of detergent for every
three scoops of fabric softener. If there
are 28 scoops of detergent remaining, how
many scoops of fabric softener will be
needed?
Answers
Answer: 42
Step-by-step explanation: 3 x 14
Each of the 9 parking lots at an automobile plant holds the same number of new cars. The lots are full. If there are 431 cars in the lots, about how many cars are in each lot? Show how you estimated.
Answers
Answer:
50, I just took a number that was the closet to this and divided it by 9
(450/9=50)
45% of the population of a city are men
and 15% are children. If the number of
women is 64,400, find the number of
children.
Answers
Answer:
\(\boxed{\textsf{ The number of children is \textbf{24150}.}}\)
Step-by-step explanation:
Given that the 45% of the population of a city are men and 15% are children . The number of women is 64,400 . And we need to find the number of children . Here ,
\(\sf\implies Percentage_{(men)}= 45/% .\\\\\sf\implies Percentage_{(children)}= 15\% . \)
So the percentage of women will be equal to [ 100 - ( 45 -15) ]% = [ 100 - 60 ]% = 40% .
So let us take the total number of people be x . So ,
\(\purple{\bigstar}\underline{\underline{\boldsymbol{ According\ to \ Question :- }}}\)
\(\sf\implies 40\% \ of \ x \ = \ 64,400 \\\\\sf\implies \dfrac{40x}{100}= 64,400 \\\\\sf\implies x =\dfrac{64,400\times 100}{40}\\\\\sf\implies \boxed{\pink{\sf x = 161,000 }}\)
\(\rule{200}2\)
The percentage of children = 15% :-
\(\sf\implies Number_{(children)}= 15\% \ of 161,000\\\\\sf\implies Number_{(children)}= \dfrac{15}{100}\times 161,000 \\\\\sf\implies \boxed{\pink{\frak {Number_{(children)}= 24150 }}}\)
10) A survey of business students who had taken the Graduate Management Admission Test (GMAT) indicated that students who have spent at least five hours studying GMAT review guides have a probability of 0.85 of scoring above 400. Students who do not spend at least five hours reviewing have a probability of 0.65 of scoring above 400. It has been determined that 70% of the business students spent at least five hours reviewing for the test. a. Find the probability of scoring above 400. b. Find the probability that given a student scored above 400, he/she spent at least five hours reviewing for the test.
Answers
Answer:
0.79 ; 0.753
Step-by-step explanation:
Given that:
Students who have spent at least five hours studying GMAT review guides have a probability of 0.85 of scoring above 400 :
≥ 5 hours review = 0.85
Students who do not spend at least five hours reviewing have a probability of 0.65 of scoring above 400
< 5 hours = 0.65
70% (0.7) of business students spend atleast 5 hours review time
A.) probability of scoring above 400
(Proportion who spend atleast 5 hours review time * 0.85) + (Proportion who do not spend atleast 5 hours * 0.65)
Proportion who do not spend atleast 5 hours = (1 - proportion who spend atleast 5 hours) = 1 - 0.7 = 0.3
Hence,
P(scoring above 400) = (0.7 * 0.85) + (0.3 * 0.65) = 0.595 + 0.195
= 0.79
B.) probability that given a student scored above 400, he/she spent at least five hours reviewing for the test.
P(spent ≥5 hours review | score above 400) :
P(spent ≥5 hours review) / P(score > 400)
(0.7 * 0.85) / 0.79
0.595 / 0.79
= 0.753
Select the three statements that represent a unit rate.
6 plates per stack
4 cupcakes per box
20 minutes for ten songs
18 plants in three rows
5 orders per day
Answers
Answer:
I think it's 6 plates per stack, 4 cupcakes per box, and 5 orders per day. Not sure about 20 minutes for 10 songs.
Which is the value of this expression when m-3 and n=-5
Answers
Answer:
1/8
Step-by-step explanation:
(6m^-1n^0)^-3 =
= (6 × 1/3 × (-5)^0)^-3
= (6/3)^-3
= 2^-3
= 1/2^3
= 1/8
Determine whether f(x) = 0 has any repeated real solutions
Answers
Answer:
Yes
Step-by-step explanation:
These are the rules regarding polynomial graphs and their real zeros (solutions)
If the graph crosses the x-axis and appears almost linear at the intercept, it is a single zero.If the graph touches the x-axis and bounces off of the axis, it is a zero with even multiplicity. That means it will have 2, 4 repeated solutionsIf the graph crosses the x-axis at a zero, it is a zero with odd multiplicity i.e. multiplicity of 3, 5 etcThe sum of the multiplicities cannot be greater than the degree of the polynomialIn the above graph we see that the graph touches the x-axis at x = 3. This means (x - 3)ᵃ is a factor of the polynomial where p is an even number (2, 4, 6 etc)
That means x = 3 is a repeated real solution. It appears that the multiplicity is 2 so one factor of the polynomial is (x - 3)²
More inf o(ignore if you want)
The other real roots are x = -1 and x = 5 because the graph crosses the x axis at these two values of x. So the multiplicity of both factors ( x + 1) and (x - 5) is odd. Since at the crossover point, the graph is almost linear, we can safely assume that the multiplicity of the graph is odd at these points and equal to 1
Therefore the polynomial can be factored as
(x + 1)(x - 5)(x - 3)²
The degree of the polynomial is the sum of the multiplicities and is equal to 1 + 1 + 2 = 4 so it is a quartic polynomial of the form ax⁴ + bx³ + cx² + dx + e