As we discovered in chapter, there is a 1/12 chance of getting a 3.
What is a probability example?By reducing the number of successful effects by the total amount of possible outcomes, probability—the chance that a will occur—is determined. A coin toss serves as the most fundamental example. There are just two results when users flip a coin: either it shows up heads or tails.
There are 12 potential results in total because the die has 12 sides.
(1) Since there is only one side of the die with a 3 on it and all sides are equally probable, the chance of rolling the die and having the 3 face on top is 1/12.
(2) The likelihood that the die will fall on top with a 3 or a 7 is calculated as the product of the odds of rolling a 3 and a 7 minus the likelihood of simultaneously rolling a 3 and a 7. (which is zero, since the die has only one side).
As we discovered in chapter, there is a 1/12 chance of getting a 3. (1). Given that the dice only has a 7 on one side, the likelihood of getting a 7 is also 1/12. The likelihood of tossing the dice and having the 3 or 7 face up is therefore:
1/12 + 1/12 - 0 = 1/6
(3) Since the die doesn't have a face marked "15," there is no chance that tossing the die will result in a 15 face landing on top.
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Suppose that a farmer has 75 rods (4 rods = 1 acre) on which to plant two crops: wheat and corn. To produce these crops, it costs the farmer (for seed, water, fertilizer, etc. ) $120 per rod for the wheat, and $210 per rod for the corn. The farmer has $15,000 available for expenses, but after the harvest the farmer must store the crops while awaiting favorable or good market conditions. The farmer has storage space for 4,000 bushels. Each rod yields an average of 110 bushels of wheat or 30 bushels of corn. If the net profit per bushel of wheat (after all the expenses) is $1.30 and for corn is $2.00, how should the merry farmer plant the 75 rods to maximize profit?
Use the optimization method described in the lecture.
Difference of density per acre of wheat and corn = 105
What is division?Division is the process of splitting a number or an amount into equal parts. Division is one of the four basic operations of arithmetic, the ways that numbers are combined to make new numbers. The other operations are addition, subtraction, and multiplication.
here, we have,
Given:
Yield in 110 acre farm = 17,600 Bushes of corn
Yield in 250 acre farm = 13,750 Bushes of wheat
Find:
Difference of density per acre of wheat and corn
Computation:
Yield per acres Bushes of corn = 17,600 / 110
Yield per acres Bushes of corn = 160
Yield per acres Bushes of wheat = 13,750 / 250
Yield per acres Bushes of wheat = 55
Difference of density per acre of wheat and corn = Yield per acres Bushes of corn - Yield per acres Bushes of wheat
Difference of density per acre of wheat and corn = 160 - 55
Difference of density per acre of wheat and corn = 105
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40 Answer:
Solve the equation by a method of your choice:
x2 - 36 = 0
If there are two solutions, separate the solutions by a comma.
41 Answer:
Solve the equation by a method of your choice:
x2 + 12x + 36 = 0
If there are two solutions, separate the solutions by a comma.
The solution of the equations are
x^2 - 36 = 0
x = 6, -6
The equation x2 + 12x + 36 = 0
x = -6, -6
How to solve the equationsThe equation x^2 - 36 = 0 is solved as follows
x^2 - 36 = 0
x = ±√36
x = 6 or -6
The quadratic equation x^2 + 12x + 36 = 0 is solved as follows
x^2 + 6x + 6x + 36 = 0
x(x + 6) + 6(x + 6) = 0
(x + 6)(x + 6) = 0
hence
x = -6 and -6
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help!!!!!!!!!!!!!!!!!
Answer:
y = 4x + 3
Step-by-step explanation:
See picture below :)
solve for d
60 = 4d-8
8=?
Answer:
17
Step-by-step explanation:
60=4d-8
We move all terms to the left:
60-(4d-8)=0
We get rid of parentheses
-4d+8+60=0
We add all the numbers together, and all the variables
-4d+68=0
We move all terms containing d to the left, all other terms to the right
-4d=-68
d=-68/-4
d=17
To find the volume of a prism, Frank multiplies the area of the base by the height. Frank finds the area of the base of a rectangular prism is 24 square inches.
How many inch cubes are needed to fill the bottom layer of the prism?
Answer:
24 inch cubes are needed to fill the bottom layer of the prism.
In a function, any input yields exactly __________ output.
Answer: one
Step-by-step explanation:
A local bakery celebrated its one-year anniversary on Saturday. On that day, every 4 customer
received a free cookie. Every 6th customer received a free muffin.
3. (20 points) Casey was the 3rd customer to receive both a free cookie and a free muffin. What
number was Casey?
Casey's number is given as follows:
36.
How to obtain Casey's number?Considering periodic events, they will repeat on the same day for the least common factor of the periods of each event.
The periods are given as follows:
Free cookie: Every 4th customer.Free muffin: Every 6th customer.The least common factor of 4 and 6 is obtained as follows:
4 - 6|2
2 - 3|2
1 - 3|3
1
Hence:
lcm(2,3) = 2² x 3 = 12.
This means that one in 12 customers receive both the free cookie and the free muffin. Casey is the third customer to receive both of them, hence the number is given as follows:
3 x 12 = 36.
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I need the answer to the question.
Step-by-step explanation:
clearly, the price is marked down to $9.60.
so, the 1st and 4th answer options are wrong.
is it marked down by 12% or by 20% ?
the basic price was $12. = 100%
how much are 10% of that ? well, 12/10 = $1.20.
but we marked down by $2.40.
when you compare $1.20 and $2.40, what do to see ?
that the second number is exactly twice the first number.
10%×2 = 20%
therefore, the 3rd answer is correct.
In a population of 6000 cave-dwelling fish, eyesight is under selection. Fish that are homozygous for allele A1 have good eyesight, fish that are homozygous for A2 are blind and fish that are heterozygous have poor eyesight. In the dark caves that these fish live in, the cost of good eyesight is higher than the benefits and having good eyesight is thus deleterious. Blind fish have a selective advantage of 0.25, fish with poor eyesight have a selection coefficient of 0.05. Which statement is true?
I. Fish with good eyesight have a fitness W = 0
II. The trait blindness is likely to increase in this population
I
II
Both are false
Both are true
Answer: I am in high school so this may not be the best answer, but I would say that eventually eye sight would simply become useless to the fish because they live in a cave and don’t really need to see, there for I would say that the second answer is correct.
Solve the equation :step by step
f/24 = 27
f =
Answer:
f = 648
Step-by-step explanation:
[tex]\frac{f}{24} =27[/tex]
Multiply both sides by 24
[tex]f=648[/tex]
Which is a correct classification for this triangle?
Answer: Obtuse Triangle
Step-by-step explanation:
63 + 22 = 85
180 - 85 = 95
Since the unknown angle is over 90 degrees, it is an obtuse triangle.
the function is increasing on the interval (s):
The function graphed above is:
Increasing on interval: (-3 0.5),
Decreasing on interval(s): (-∞ -3) and (0.5 ∞)
What is decreasing and increasing interval?
Real number intervals with growing and decreasing real-valued functions are referred to as increasing and decreasing intervals.
We apply the first-order derivative test to examine the sign of the derivative in each interval and identify the growing and decreasing intervals.
For the graph attached, the decreasing interval is
from negative infinity to -3 and
0.5 to positive infinity
While the increasing interval is from -3 to 0.5
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What is the future value of $700 deposited for one year earning 4 percent interest rate annually
Answer:$728
Step-by-step explanation: 4 percent increase= 104% which is x1.04
=700*1.04
A market research company was interested in comparing three communities A, B and C to determine whether there are any differences in their use of water filters in homes. Each of 100 homeowners sampled from each community was asked whether or not they have installed water-filtering system in their homes. Their responses (Yes or No) are summarized in the following contingency table.
Use Filters
Community | Yes | No
A 62 38
B 58 42
C 73 27
a) Clearly state the null and alternative hypotheses in this problem.
b) Calculate the expected count for the bottom right cell (i.e., Community ‘C’ and ’No’), and explain what the number means.
c) The Chi-square statistic has been calculated to be 13.22. What can we conclude from this finding?
a) The null hypothesis is that there is no difference in the proportion of homeowners using water filters among the three communities. The alternative hypothesis is that at least one community has a different proportion of homeowners using water filters than the other communities.
b) To calculate the expected count for the bottom right cell, we can use the formula:
Expected count = (row total x column total) / grand total
The row total for Community C and the column total for No are both 100, and the grand total is 300. Therefore:
Expected count = (100 x 100) / 300 = 33.33
The expected count of 33.33 for the bottom right cell means that if there were no difference in the proportions of homeowners using water filters among the three communities, we would expect 33.33 of the 100 homeowners in Community C to answer 'No' to the question about water filters.
c) To determine what we can conclude from the Chi-square statistic of 13.22, we need to compare it to the critical value for a Chi-square distribution with (3-1) x (2-1) = 2 degrees of freedom at the desired level of significance. Let's assume a level of significance of 0.05. From a Chi-square distribution table, the critical value with 2 degrees of freedom at 0.05 level of significance is 5.99.
Since 13.22 is greater than 5.99, we can reject the null hypothesis and conclude that there is a significant difference in the proportion of homeowners using water filters among the three communities. However, we cannot determine from this test alone which communities have different proportions of homeowners using water filters. We would need to conduct further tests, such as post-hoc tests, to investigate the specific differences among the communities.
Your itinerary contains a grid map of Washington D.C., with each unit on the grid representing 0.25
miles. If Arlington Cemetery is located at (−1,1)
and the Pentagon is located at (5,−6)
, what is the direct distance (not walking distance, which would have to account for bridges and roadways) between the two landmarks in miles? Round your answer to two decimal places, if necessary.
It is found that the distance between the two memorials is of 1,42 miles.
The distance between two points (x1 , y1) and (x2 , y2) is of:
Distance formula = [tex]\sqrt{(x2-x1)^{2} +(y2-y1)^{2} }[/tex]
One memorial is at point (3,-1).
The other is at point (7, -5).
Thus, in the coordinate grid, the distance is of:
D = 5.66
In the coordinate, the distance is of 5.66 units. Each unit is worth 0.25 miles, thus:
D = 5.66 units
The distance between the two parks is of 1.42 miles.
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The area of a triangular sail is given by the expression
1
2
bh, where b is the length of the base and h is the height. What is the area of a triangular sail in a model sailboat when b = 12 inches and h = 7 inches?
The area of a triangular sail in a sail model is
in2.
The area of the triangular sail in the sail model is 42 square inches.
According to given information:The area of a triangular sail is given by the formula:
Area = (1/2)bh
where b is the length of the base and h is the height.
Substituting b = 12 inches and h = 7 inches, we get:
Area = (1/2)(12 inches)(7 inches) = 42 square inches
Therefore, the area of the triangular sail in the sail model is 42 square inches.
What is area of triangle ?The area of a triangle is given by the formula:
Area = (1/2) * base * height
where "base" is the length of the base of the triangle and "height" is the height of the triangle perpendicular to the base.
To find the area of a triangle, you simply need to plug in the values of the base and height into the formula and perform the calculation. The resulting value will be the area of the triangle.
Note that the base and height of the triangle must be measured in the same units (e.g., inches, centimeters) in order for the formula to work correctly.
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Answer:
24
Step-by-step explanation:
N/A
(2x + 3) (3x − 2) + (3 - 4x) (2x + 3) - 4x²+9 is equivalent to which of the following expressions?
Answer:
Step-by-step explanation:
(2x + 3)(3x - 2) + (3 - 4x)(2x + 3) - 4x² + 9 FOIL the first and second set of parentheses.
6x² - 4x + 9x - 6 + 6x + 9 - 8x² - 12x - 4x² + 9 Combine like terms
-6x² - x + 12 Factor.
(-3x + 4)(2x + 3)
Please help me with this one ?
=9/2
According to me when you simplify these numbers on the calculator it gave me 9/2.
Problem: (3/2) + (3/2) + (3/2) = unknown value, times (1/2)
Solution:
First, we can simplify the left side by adding the fractions:
(3/2) + (3/2) + (3/2) = 9/2
Next, we can divide both sides by (1/2) to solve for the unknown value:
(9/2) ÷ (1/2) = 9
Therefore, the answer is 9.
A right triangle has a base, b
, that is 6
inches. The area of the triangle, with h
representing the height, is given by the expression
The height of the triangle is h = 2A/6.
What is height?Height is the measure of vertical distance, either how "tall" something or someone is, or how "high" the point is. For example, a person's height is typically measured using a stadiometer and is recorded in centimeters or feet and inches. The height of a mountain is usually measured in meters or feet. In aviation, height is measured from the surface of the earth, either above ground level (AGL) or above mean sea level (AMSL).
To find the height of a right triangle given the base, we can use the area formula A = 1/2bh. Rearranging this equation gives us the height: h = 2A/b. In this case, the base is 6 inches and the area is given as A. Therefore, the height of the triangle is h = 2A/6.
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What is the radius of the
circle?
C = 3.5 m
Pls help
Answer:
r≈0.56m
Step-by-step explanation:
C=2πr
r=C
2π=3.5
2·π≈0.55704m
If <1 in the figure above measures 25 degrees, what is the measure of <4
65°
25°
50°
155°
A wall is to be constructed by using tiles, each of the tile's dimensions are 10cm by 20cm by 0.67cm. What is the volume of each tile?
Responses
96.2 cm³
44.7 cm³
200 cm³
134 cm³
The volume of each tile is 134 cm³.
Describe Volume of Cuboid?The volume of a cuboid is the amount of space it occupies in three-dimensional space. A cuboid is a three-dimensional geometric shape with six rectangular faces, where each face has perpendicular edges to two other adjacent faces. The formula for calculating the volume of a cuboid is V = l x w x h, where V is the volume, l is the length of the cuboid, w is the width of the cuboid, and h is the height of the cuboid.
To calculate the volume of a cuboid, first measure its length, width, and height. Then, multiply the length by the width and the height, and then multiply the result by the height again. This gives the volume of the cuboid in cubic units, such as cubic inches, cubic centimeters, or cubic meters.
For example, if a cuboid has a length of 5 cm, a width of 3 cm, and a height of 2 cm, the volume can be calculated as follows:
V = l x w x h
V = 5 cm x 3 cm x 2 cm
V = 30 cubic centimeters
Therefore, the volume of the cuboid is 30 cubic centimeters.
The volume of each tile can be calculated by multiplying its length, width, and height:
Volume = 10 cm × 20 cm × 0.67 cm = 134 cm³
Therefore, the volume of each tile is 134 cm³.
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A large grocery store chain pays all workers time and a half on Saturdays and double time on Sundays. If an employee's regular pay is $10.50 per hour, use the expression 10.50(1.5)(x) + 10.50(2)(y) to find their gross income if they worked 5 hours on Saturday and 3.5 hours on Sunday. (4 points)
$160.13
$152.25
$312.38
$143.31
Determine the unknown side of the similar triangle
btw ik this isn't college math it was automatically set to it
The required measure of the unknown side in similar triangles is 4.
What are Similar triangles?Similar triangles are two triangles that have the same shape but are not necessarily the same size. More specifically, two triangles are similar if their corresponding angles are congruent (i.e., have the same measure), and the corresponding sides are proportional (i.e., have the same ratio).
Here,
Two similar triangles are given in the figure,
Let the unknown side be x
For a similar triangle, the ratio of the corresponding sides are equal So,
a / 8 = 6 / 12
a = 8/2
a = 4
Thus, the required measure of the unknown side in similar triangles is 4.
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Can 10 18 10 make a triangle
Answer:
No
Step-by-step explanation:
Btw, you know this using Pythagorean therom
10^2 equals 100 and you have two 10's so now you have 200
18^2 equals 324
And because even in a straight line 200 is not long enough for the 324 so it would not fit.
Hope this helps, Brainliest would also help me btw
1/2 x^2 +. 1 =0
solve each equation by graphing related function
Answer:
Step-by-step explanation:
The diameter of a circle is 22 feet. What is the circle's area?
Use 3.14 for .
Answer: 3.14 ft
Step-by-step explanation:
★Given,→ Diameter = 2 feet → Circumference = 2/2 = 1 feet
★Now,→Area of a circle = πr²→ = 3.14 × 1 × 1→ = 3.14 feet
Hence , the circumference is 3.14 ft.
Which point on the number line best represents –1?
Answer:
R
Step-by-step explanation:
-1 is exactly between 0 and -2, meaning that the answer is R.
R is the right answer
1) The eighth grade class has 20% fewer students this year than they
had as seventh graders. Write an expression to show the decline in
class numbers, and then simplify the expression. Use (s) to represent
the number of seventh grade students.
Answer:
Step-by-step explanation:
To represent the number of eighth-grade students, we can use the expression:
0.8s
This is because the problem states that there are 20% fewer students in the eighth grade than in the seventh grade, which means that the number of eighth-grade students is equal to 80% of the number of seventh-grade students.
To simplify this expression, we can use the distributive property:
0.8s = 1s - 0.2s
This shows that the number of eighth-grade students is equal to the number of seventh-grade students minus 20% of the number of seventh-grade students. We can further simplify this to:
0.8s = 0.8s
This means that the number of eighth-grade students is equal to 80% of the number of seventh-grade students, which is consistent with the original problem statement.
In Exercises 9 to 14, find the limit of each function at the given point, or explain why it does not exist. 10. f(z) = Arg z at Zo--1 11. f(z) = (1-Im z)-1 at z,-8 and then at zo-8 +1 12.f(z) = (z _ 2) log(z-21 at zo = 2 13, f(z) =-, z#0 at zo = 0 14. f(z) = 2+21,
Previous question
The limit of each function at the given point i n the question 10 to 14, is explained below.
Limit Of A function:A function may get close to two distinct limits. There are two scenarios: one in which the variable approaches its limit by values larger than the limit, and the other by values smaller than the limit. Although the right- and left-hand limits are present in this scenario, the limit is not defined.
When a variable approaches its limit from the right, the function's right-hand limit is the value that approaches.a
10). The limit of f(z) = Arg z as z approaches Zo = 1 does not exist. This is because the argument function is not continuous at the point z = 1, where there is a branch cut.
11). The limit of f(z) = [tex](1 - lm z)^{-1}[/tex] as z approaches z0 = -8 does not exist. This is because the function approaches infinity as z approaches -8 from the left, and negative infinity as z approaches -8 from the right.
However, if we consider the limit of f(z) as z approaches z0 = -8 + i from both the left and the right, the limit exists and is equal to 0. This is because in the complex plane, the value of Im z cannot exceed 1, so as z approaches -8 + i, the denominator (1 - Im z) approaches 0, and the function approaches infinity. However, the numerator approaches a finite value of 1, which cancels out the denominator, and the overall limit is equal to 0.
12). The limit of f(z) = (z - 2) log(z - 2) as z approaches z0 = 2 is 0. This is because the term (z - 2) approaches 0 as z approaches 2, and log(z - 2) approaches 0 as well because log(z - 2) is continuous at z = 2. Therefore, the limit is equal to 0.
13). The limit of f(z) = -1/z as z approaches z0 = 0 does not exist. This is because as z approaches 0, the magnitude of 1/z approaches infinity, but the direction of approach depends on which quadrant the limit is approached from. Since the limit does not approach a unique value from all directions, the limit does not exist.
14). The limit of f(z) = 2 + [tex]2^{1/z}[/tex] as z approaches infinity does not exist. This is because as z approaches infinity, the term [tex]2^{1/z}[/tex] approaches 1, and the limit approaches 2 + 1 = 3. However, if we approach infinity along the real axis, the limit of [tex]2^{1/z}[/tex] approaches 1, but if we approach infinity along the imaginary axis, the limit of [tex]2^{1/z}[/tex] approaches infinity. Therefore, the limit of f(z) does not exist.
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