The value of x converges to approximately 2.5615
Given is an equation, we need to solve for x, xˣ = 4ˣ + 16
To solve the equation xˣ = 4ˣ + 16, we'll use algebraic methods. Unfortunately, this equation does not have an explicit algebraic solution that can be found using elementary functions.
However, we can use numerical methods or approximation techniques to find an approximate solution.
One common numerical method for solving equations is the Newton-Raphson method.
Let's apply it to this equation:
Start with an initial guess for x, let's say x = 1.
Iterate using the following formula:
x(n+1) = x(n) - f(x(n)) / f'(x(n))
where f(x) = x^x - 4^x - 16 and f'(x) is the derivative of f(x) with respect to x.
Repeat step 2 until the value of x converges to a solution.
Let's perform a few iterations:
1st iteration:
x(1) = 1 - (1^1 - 4^1 - 16) / (1 * 1^0 - 4 * 4^0)
= 1 - (-11) / (-3)
≈ 3.6667
2nd iteration:
x(2) = 3.6667 - (3.6667^3.6667 - 4^3.6667 - 16) / (3.6667 * 3.6667^2.6667 - 4 * 4^2.6667)
≈ 2.6141
3rd iteration:
x(3) = 2.6141 - (2.6141^2.6141 - 4^2.6141 - 16) / (2.6141 * 2.6141^1.6141 - 4 * 4^1.6141)
≈ 2.5615
By continuing these iterations, you can refine the solution to any desired level of accuracy.
In this case, the value of x converges to approximately 2.5615.
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What is the angle of o in the drawing below? Type in numerical answer only
Answer:
[tex]52 + o = 180[/tex]
[tex]o = 128[/tex]
Angle o measures 128°.
2021: Sales Revenues = $800,000. Cost of good sold = $350,000
2020: Sales Revenues = $795,000. Cost of good sold = $600,000
Answer:
Step-by-step explanation:
Sales Revenue: $800.00
Cost of good sold: $350,000.00
Subtract: $450,000.00
Sales Revenue: $795,000.00
Cost of good sold: $600,000.00
Subtract Sales $195,000.00
Revenue from Cost
of goods sold.
What is the meaning of "it is a subset of any X ∈ C"?
The phrase "it is a subset of any X ∈ C" indicates that the subject in question (denoted by "it") is a subset of every element X that belongs to the set C. In other words, whatever "it" refers to is contained within every element of the set C.
The phrase "it is a subset of any X ∈ C" indicates that the subject in question (denoted by "it") is a subset of every element X that belongs to the set C. In other words, whatever "it" refers to is contained within every element of the set C.
To provide a clearer understanding, let's break it down further:
"Subset": A subset is a collection of elements that are all contained within another set. If set A is a subset of set B, it means that every element of A is also an element of B.
"Any X ∈ C": Here, X represents a generic element of the set C. The phrase "X ∈ C" denotes that X belongs to the set C. It implies that X is one of the elements within the set C.
Combining the two parts, "it is a subset of any X ∈ C" means that "it" (referring to a specific set or collection of elements) is included in every element X of the set C. In other words, every element of C contains "it" as a subset.
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7 ft equal how many inches
Answer:
Step-by-step explanation:
There is 12 inches in a foot: therefore, 12inches x 7ft. = 84 ft.
Answer: 84 inches
Step-by-step explanation:
A conversion factor is a number that is used to multiply or divide one set of units into another. For instance, 12 inches equals one foot when converting between inches and feet.
Since 1 foot = 12 inches
And we are trying to figure out how much inches are in 7 ft.
We can create a conversion (or cross multiply)
[tex]\frac{12}{1} =\frac{x}{7}[/tex]
Where inches are in the numerator and ft are in demoninator.
When cross multiplying (multiplying in a diagonal) you get:
x = 84 inches
So 7 ft equals 84 inches.
---
A quicker method would be to multiply 7 ft by 12 inches/1 ft (foot), and get 84 inches.
--
A steel manufacturer wants to produce a container in the shape of a rectangular solid with volume 84 m3 . The manufacturer wants the length of the container to be one meter longer than the width, and the height to be one meter greater than twice the width. What should the dimensions of the container be?
Answer:
Step-by-step explanation:
Can someone help me with this?
The value of sinθ is √17/7 and the value of [?] is √17
According to The Pythagorean identity,
Sin²θ + Cos²θ = 1
This is a Trigonometric equation, where 'sin' refers to 'sine' and 'cos' refers to 'cosine' which are functions revealing the shape of a right-angled triangle.
Given, cosθ=4√2/7
Cos²θ = 32/49
From equation 1 we get,
Sin²θ = 1 - Cos²θ
Sin²θ = 1 - (32/49)
Sin²θ = (49-32)/49
Sin²θ = 17/49
Sinθ = √(17/49)
Sinθ = √17 / 7
Given, sinθ = √[?] / [ ]
[?] = 17
Therefore, The value of sinθ is √17/7 and the value of [?] is √17
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What key features does f(x), shown in the graph, share with g(x), shown in the equation? Select three options.
at least one x-intercept
at least one y-intercept
an oblique asymptote
a vertical asymptote
the domain of x
Answer:
(a) at least one x-intercept
(b) at least one y-intercept
(e) the domain of x
Step-by-step explanation:
Given g(x) = (-4x² +36)/(x+3) and f(x) as shown in the graph, you want to know what features the functions have in common.
G(x)The function g(x) can be simplified:
[tex]g(x)=\dfrac{-4x^2+36}{x+3}=\dfrac{-4(x^2 -9)}{x+3}=\dfrac{-4(x+3)(x-3)}{x+3}\\\\g(x)=-4(x-3)\quad x\ne-3[/tex]
This is the equation of a straight line with negative slope and a hole at coordinates (-3, 24). That is, the domain excludes x = -3.
The line has x-intercept (3, 0) and y-intercept (0, 12).
Common featuresBoth functions have an x-intercept at (3, 0), at least one x-intercept, choice A.
Both functions have a y-intercept at (0, 12), at least one y-intercept, choice B.
Only function f(x) has an oblique asymptote.
Only function f(x) has a vertical asymptote.
Both functions exclude x = -3 from their domains, so they have the same domain, choice E.
Choices A, B, E identify the shared features.
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Solve the following system of equations with the substitution method:
y=10/3x-121
y=5/4x-46
Answer:
x = 36
y = -1
Step-by-step explanation:
The substitution method is when the value of one variable from one equation is substituted in the other equation.
y = 10/3x - 121
y = 5/4x - 46
In this case you substitute one of the equations for y.
5/4x - 46 = 10/3x - 121
Lets set the coefficient being multiplied by x to a number with a common demoninator.
15/12x - 46 = 40/12x - 121
Next isolate x and combine like terms.
15/12x - 46 = 40/12x - 121
-15/12x -15/12x
-46 = 25/12x - 121
+121 +121
75 = 25/12x
*12/25 12/25
36 = x
------
Now lets plug x in to solve for y
(you pick either equation to do this)
y = 5/4(36) - 46
y= 45 - 46
y = -1
Find the standard deviation of the sampling distribution of sample means using the given information. Round to one decimal place, if necessary. μ = 64 and o = 12; n = 9
The standard deviation of the data sample is 2.55.
What is the standard deviation of the data sample?The standard deviation of the data sample is calculated by applying the following formula;
S.D = √ (x - μ)²/(n - 1)
where;
μ is the mean of the distributionx is the sample datan is the number of sample dataThe given parameters;
mean, μ = 64
x, = 12
number of samples = 9
The standard deviation of the data sample is calculated as;
S.D = √ (12 - 64)²/(9 - 1)
S.D = 2.55
Thus, the standard deviation of the data sample is calculated by applying the formula for standard deviation.
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A simulation for rolling two number cubes is run with 50 trials. The results are shown below.
(4,6)
(2,4)
(3,1)
(1,6)
(6, 1)
(2, 2)
(2, 2)
(5, 1)
(5,3)
(3,2)
(2,6)
(6,6)
(4,2)
(4,3)
(3,4)
(3, 1)
(1,2)
(3,6)
(6,4)
(4,4)
(5,5)
(3,6)
(1,2)
(2,3)
(4,4)
(3, 3)
(4,4)
(6,6)
(1,5)
(2,3)
(2, 1)
(3,5)
(4,1)
(4,4)
(4,5)
(4, 5)
(4,6)
(2,1)
(6,6)
(5,2)
(1,4)
(1,6)
(6, 6)
(3,6)
(2,1)
What is the experimental probability a total of 9 will be rolled on two number cubes?
(6,4)
(2,4)
(4,3)
(2,4)
(1, 1)
Answer:
12%
Step-by-step explanation:
chatgpt
To find the experimental probability of rolling a total of 9 on two number cubes, we need to determine the number of times the total of 9 was rolled and divide it by the total number of trials.
From the given results, we can see the following pairs that have a total of 9:
(3, 6)
(4, 5)
(4, 5)
(6, 4)
(2, 1)
(1, 6)
There are 6 trials where the total is 9. Since there were 50 total trials, the experimental probability of rolling a total of 9 is:
Experimental probability = Number of favorable outcomes / Total number of outcomes
Experimental probability = 6 / 50
Experimental probability = 0.12 or 12%
Therefore, the experimental probability of rolling a total of 9 on two number cubes, based on the given 50 trials, is 12%
1. The students rolled two number cubes 50 times and wrote down the results.
2. They counted the number of times the dice added up to 9.
3. They found that the dice added up to 9 six times.
4. To calculate the experimental probability, they divided the number of times the dice added up to 9 (6) by the total number of trials (50).
5. They simplified the fraction and found that the experimental probability of rolling a total of 9 was 6/50 or 0.12.
6. The experimental probability is the likelihood of an event happening based on the results of an experiment.
7. In this case, the students found that there is a 12% chance of rolling a total of 9 on two number cubes based on their 50 trials.
8. The formula used to calculate experimental probability is:
Experimental probability = Number of favorable outcomes / Total number of outcomes
9. The name of the formula is "Experimental Probability."
10. It is important to watch the number of trials and make sure there are enough trials to get accurate results.
11. For example, if the students rolled the dice only 10 times, the experimental probability might not be as reliable.
12. A real-world example of experimental probability could be flipping a coin to see how often it lands on heads. By flipping it many times, we can calculate the experimental probability of getting heads.
bard ai
Here is the answer rewritten in easy-to-understand terms:
There are 4 ways to roll a 9 on two number cubes. In the simulation, there were 2 instances of rolling a 9, so the experimental probability of rolling a 9 is 2/50 = 0.04.
Here is the answer rewritten in a numbered list format:
1. There are 4 ways to roll a 9 on two number cubes.
2. In the simulation, there were 2 instances of rolling a 9.
3. The experimental probability of rolling a 9 is 2/50 = 0.04.
Here is the answer rewritten in a brief format:
The experimental probability of rolling a 9 on two number cubes is 2/50 = 0.04. This means that out of 50 trials, there were 2 instances of rolling a 9.
Here is the answer rewritten in a synopsis format:
In a simulation of 50 trials, there were 2 instances of rolling a 9 on two number cubes. This gives an experimental probability of 2/50 = 0.04.
Here is the answer rewritten in an abstract format:
The experimental probability of rolling a 9 on two number cubes is 2/50 = 0.04. This means that out of 50 trials, there were 2 instances of rolling a 9.
Here is the answer rewritten in a simple and easy 1st grade analogy:
If you flip a coin 50 times, you would expect to get heads about 25 times. This is because there are two sides to a coin, and each side has an equal chance of landing face up. Similarly, if you roll two number cubes 50 times, you would expect to get a total of 9 about 2 times. This is because there are 4 ways to roll a 9, and each way has an equal chance of occurring.
Here is the answer summarized in 1 sentence:
The experimental probability of rolling a 9 on two number cubes is 2/50 = 0.04.
Here is the answer to the math part:
```
Total number of trials: 50
Number of trials where a 9 was rolled: 2
Experimental probability of rolling a 9: 2/50 = 0.04
```
Here is the formula used:
```
Experimental probability = (Number of successes / Total number of trials)
```
Here is the name of the formula:
The formula used is called the experimental probability formula.
Here is what to watch:
When calculating the experimental probability, it is important to make sure that the total number of trials is large enough to be representative of the actual probability. If the total number of trials is too small, the experimental probability may not be accurate.
Here is an example:
If you roll two number cubes 10 times, you might not get a total of 9 at all. This does not mean that the experimental probability of rolling a 9 is 0. In fact, the experimental probability of rolling a 9 is still 2/50 = 0.04. However, because the total number of trials is so small, the experimental probability may not be accurate.
Geometry
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Please answer fast
Applying the Angle Addition Postulate, the measure of angle BDC is calculated as: 57 degrees.
How to Apply the Angle Addition Postulate?The Angle Addition Postulate establishes that when two angles are adjacent, the measure of the resulting angle formed by their combination is equal to the sum of their individual measures.
Therefore, according to the Angle Addition Postulate, we would have:
(-6x + 11) + (-7x + 15) = 104
Solve for x:
-6x + 11 - 7x + 15 = 104
-13x + 26 = 104
-13x = 104 - 26
-13x = 78
x = -6
Measure of angle BDC = -7x + 15
Plug in the value of x:
Measure of angle BDC = -7(-6) + 15 = 57°
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if y is directly porportional to x^2 and the difference in the values of y when x=1 and x=3 is 32, find the value of y when x=-2
Answer:
Step-by-step explanation:
y=kx²
y₁=k(1)²=k
y₃=k(3)²=9k
y₁-y₃=k-9k=32
-8k=32
k=-4
y=-4x²
y₋₂=-4(-2)²=-16
workers can finish the job in days. For the first days, only workers worked on the job. Then for the next days more workers joined them. To finish the job, more workers joined them. After how many days was the whole job done?
Based on the information given, it takes 16 days for the whole job to be competed.
What is Workers Efficiency?Worker's efficiency is a term that is used to describe the effectiveness in which a worker performs their job, therefore increasing productivity.
General, the efficient worker is productive, and tend to organize their time and effort in order to complete daily tasks.
In this case, we know that 10 workers can finish the remaining 15 days
Then 1 worker will do the same job in 15x10= 150 days
Therefore, we have one worker one-day job = 1/150
=>6 workers 5 days job = 6x5/150= 1/5 ..(1)
=>8 workers 3 days job = 8x3/150= 4/25 ..(2)
Hence, 4 more workers joined after 8 days
=> Making a total number of workers now available 12.
=> Work remaining = 1 - 1/5- 4/25= 16/25
=. Remaining work completed by 12 workers in 150/12 x 16/25= 8 days …(3)
Thus, the total work was completed in
5 + 3 +8 = 16 days
Hence, in this case, it is concluded that the correct answer is 16 days.
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The full question
10 workers can finish the job in 15 days. For the first 5 days, only 6workers worked on the job. Then for the 3 next days 2 more workers joined them. To finish the job, 4 more workers joined them. After how many days was the whole job done?
Which equation can be used to calculate the surface area of the triangular prism net show below?
The surface area of the triangular base prism is 360 cm².
How to find the surface area of a prism?The prism above is a triangular base prism. The surface area of the triangular base prism can be calculated as follows:
Therefore,
surface area of a triangular prism = (a + b + c)l + bh
where
a, b and c are the side of the trianglel = height of the prismb = base of the triangleh = height of the triangleTherefore,
surface area of a triangular prism = (5 + 12 + 13)10 + 5(12)
surface area of a triangular prism = (30)10 + 60
surface area of a triangular prism = 300 + 60
surface area of a triangular prism = 360 cm²
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If 3 cos 0=2 then prove that: 6sin²0-5cos 0 = 0.
Answer:
Step-by-step explanation: 6(1 - cos²0) - 5/3.3cos0
= 6 - 2.3cos²0 - 5/3.3cos0 = 6 - 2.4 - 10/3 = -16/3
Match the histogram with the description that best fits the distribution of the data
shown in the histogram.
1. Uniform
2. Approximately Bell-Shaped
3. Skewed Left
4. Skewed Right
The correct matches are 1) Approximately Bell-Shaped, 2) Skewed Right, 3) Uniform and 4) Skewed Left.
Uniform: In a uniform distribution, the data is evenly spread across the entire range, resulting in a rectangular-shaped histogram. All values have roughly the same frequency or probability. It suggests that there is an equal chance of observing any value within the given range.
Approximately Bell-Shaped: This description refers to a distribution that closely resembles a bell curve or a normal distribution. The data is symmetrically distributed around a central peak, with most values clustered near the mean. The histogram will have a characteristic bell shape, with the highest frequency at the center and gradually decreasing frequencies on both sides.
Skewed Left: A left-skewed distribution, also known as negatively skewed or left-tailed, is characterized by a long tail extending towards the lower values. The majority of the data is concentrated on the right side of the distribution, and the tail extends to the left. The histogram will show a longer tail on the left side and a shorter right side.
Skewed Right: A right-skewed distribution, also known as positively skewed or right-tailed, has a long tail extending towards the higher values. The majority of the data is concentrated on the left side of the distribution, and the tail extends to the right. The histogram will exhibit a longer tail on the right side and a shorter left side.
Hence the correct matches are 1) Approximately Bell-Shaped, 2) Skewed Right, 3) Uniform and 4) Skewed Left.
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Which function is represented by the graph below?
Natural and common logarithms
The function represented by the graph is f(x) = ln(0.5x).
How do we know?The graph displays a diminishing curve that begins above the x-axis and moves closer to it as x grows.
Logarithmic functions most typically take this structure of graph.
Only f(x) = ln(0.5x), where ln stands for the natural logarithm, is one of the many functions that can express a logarithm.
The inverse of the exponential function with base e is the natural logarithm, which has a base of e (about 2.718).
The rate at which the function decrements is determined by the 0.5 coefficient in ln(0.5x).
The argument of the logarithm (0.5x) as it grows as x increases, causes the function to approach the x-axis more slowly.
This is consistent with how the graph in the provided graphic behaves.
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If you’re walking on icream
Answer: clean your shoes
Step-by-step explanation:
since you're walking on ice cream , your shoes will be sticky so one should clean them shoes with water.
A spinner is divided into five colored sections that are not of equal size: red, blue, green, yellow, and purple. The spinner is spun several times, and the results are recorded below:
The probability of landing on purple to the nearest hundredth: 0.15
How to solveThe total number of spins is 84, and the probability of landing on purple is 13/84 = 0.15476.
Rounding to the nearest hundredth, this is 0.15.
Elaborating:
Number of times the spinner landed on purple: 13
Total number of spins: 84
Probability of landing on purple: (13/84) = 0.15476
Probability of landing on purple to the nearest hundredth: 0.15
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The Complete Question
A spinner is divided into five colored sections that are not of equal size: red, blue, green, yellow, and purple. The spinner is spun several times, and the results are recorded below:
Spinner Results
Color Frequency
Red 18
Blue 15
Green 20
Yellow 18
Purple 13
Based on these results, express the probability that the next spin will land on purple as a decimal to the nearest hundredth.
write each info entire radical √48
The value of the radical √48 is 4√3.
Radical is a symbol (√) that denotes square roots and nth roots. The number inside the symbol is called Radicand and the expression containing the radical or a square root is called a Radical expression.
Here, we are given the radical √48
To find the value of the radical, we will factorize 48
i.e., 48 = 2×2×2×2×3
= 16×3
Now, the square root of 48, that is, √48
= [tex]\sqrt{16\cdot3}[/tex] =[tex]\sqrt{16} \cdot \sqrt{3}[/tex]
We know 16 is a perfect square of 4, that is, the square root of 16= 4
⇒√16=4
Using this, we have √48= 4√3
The correct answer is 4√3.
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Simplify each expression. Write your answer in exponential notation.
13. [(-0.5) (-0.5)²12²
14. (3.3³)3
تبر4 + 2( 20) .15
16. (a¹. a)³
(a^)³
Help I really need the extra credit
For simplification the exponent rules must be known to us .
The exponent rules are mentioned below:
a^0 = 1a^1 = aa^m × a^n = a^m+na^m / a^n = a^m−na^−m = 1/a^m(a^m)^n = a^mn(ab)m = a^mb^m(a/b)m = a^m/b^m1)
Now,
Simplifying,
[(-0.5)² *(-0.5)²]²
Apply property 3,
[(-0.5)^4]^2
(-0.5)^8
2)
(3.3³)3
Simplify by property 3
= 3 ^12
3)
(y² × y)²÷4y²
Simplify by rule 3 and 4,
= y^6 ÷ 4 y²
= y^4/4
4)
(a^3 × a^6)^3/(a^4)^5
Simplify by rule 3 and 4,
=a^7
Hence with the use of exponent rules the expressions can be simplified.
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The scores of students on a standardized test are normally distributed with a mean of 300 and a standard deviation of 40. (c) The top 25% scores are above what value? Explicitly compute the value.
To find the value above which the top 25% of scores lie, we need to find the z-score corresponding to the 75th percentile and use it to compute the corresponding raw score.
The z-score corresponding to the 75th percentile can be found using a standard normal distribution table or calculator. The 75th percentile corresponds to a cumulative probability of 0.75, so we need to find the z-score such that the area under the standard normal curve to the left of that score is 0.75.
Using a standard normal distribution table, we can look up the z-score corresponding to a cumulative probability of 0.75, which is approximately 0.67.
Alternatively, we can use the inverse cumulative distribution function (also known as the percent point function) of the standard normal distribution to find the z-score. In Python, we can use the scipy.stats.norm.ppf function to do this:
from scipy.stats import norm
z_score = norm.ppf(0.75)
Either way, we find that the z-score corresponding to the 75th percentile is approximately 0.67.
To find the raw score corresponding to this z-score, we can use the formula:
z = (x - mu) / sigma
where x is the raw score, mu is the mean, and sigma is the standard deviation. Solving for x, we get:
``x = z * sigma + mu
Plugging in the values for `z`, `sigma`, and `mu`, we get:
x = 0.67 * 40 + 300
Simplifying the expression, we get:
x = 326.8
Therefore, the top 25% scores are above the value of 326.8.
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(q1) Find the length of the curve described by the function
The value of the Integral at the lower limit from the value of the integral at the upper limit to get the length of the curve.
The length of the curve described by the function f(x) = 1 + 3x^2 + 2x^3 is to be found. The formula used to find the length of a curve is:
L = ∫(sqrt(1 + [f'(x)]^2))dx where f'(x) is the derivative of f(x)We have to first find f'(x):f(x) = 1 + 3x^2 + 2x^3f'(x) = 6x + 6x^2
The integral becomes:L = ∫(sqrt(1 + [6x + 6x^2]^2))dx = ∫(sqrt(1 + 36x^2 + 72x^3 + 36x^4))dx The integral appears to be difficult to evaluate by hand.
Therefore, we use software like Mathematica or Wolfram Alpha to solve the problem. Integrating the expression using Wolfram Alpha gives:
L = 1/54(9sqrt(10)arcsinh(3xsqrt(2/5)) + 2sqrt(5)(2x^2 + 3x)sqrt(9x^2 + 4))The limits of integration are not given. Therefore, the definite integral be solved.
We can, however, find a general solution. We use the above formula and substitute the limits of integration.
Then, we subtract the value of the integral at the lower limit from the value of the integral at the upper limit to get the length of the curve.
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Of the 32 students in Joe's class, 8 students ride their bikes to school, 5 walk to school, 4 get a ride to school in a car, and 15 take the bus to school. What is the experimental probability of choosing a student who walks to school?
The experimental probability of choosing a student who walks to school is given by 0.15625 or 15.625%.
Given data ,
The experimental probability of choosing a student who walks to school can be calculated by dividing the number of students who walk to school by the total number of students in Joe's class.
Number of students who walk to school = 5
Total number of students in the class = 32
Experimental probability = Number of students who walk to school / Total number of students
= 5 / 32
P = 0.15625
Hence , the experimental probability of choosing a student who walks is 0.15625 or 15.625%.
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a racer is traveling 150 miles per hour how many feet dose it travel in 5 seconds
150 miles is the same as 150*5280 = 792000 feet, and one hour is equivalent to 60*60 = 3600 seconds. Now we divide 792000 feet by 3600 seconds to get the equivalent rate: 792000 ft/3600 sec = 220 ft/second. Now, we multiply the rate by 5 and get 1100 feet per 5 seconds. So, our answer is 1100 feet.
Calculate the dimensions of an irregular hexagon whose perimeter in 98 cm. Answer will vary.
The dimensions of the irregular hexagon are 17 cm, 15 cm, 14 cm, 13 cm, 22 cm and 17 cm
Calculating the dimensions of the irregular hexagonFrom the question, we have the following parameters that can be used in our computation:
Shape = irregular hexagon
Also, we have
Perimeter = 98 cm
The perimeter of a shape is the sum of its side length
An irregular hexagon has six unequal sides
using the above as a guide, we have the following:
17 + 15 + 14 + 13 + 17 + 22 = 98
This means that the side lengths are 17 cm, 15 cm, 14 cm, 13 cm, 22 cm and 17 cm
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Magic Realm, Inc., has developed a new fantasy board game. The company sold 15,000 games last year at a selling price of $20 per game. Fixed costs associated with the game total $182,000 per year, and variable costs are $6 per game. Production of the game is entrusted to a printing contractor. Variable costs consist mostly of payments to this contractor.
Required:
1) Prepare a contribution format income statement for the game last year and compute the degree of operating leverage.
2) Management is confident that the company can sell 18,000 games next year (an increase of 3,000 games, or 20%, over last year).
Compute:
a) The expected percentage increase in net operating income for next year.
b) The expected total dollar net operating income for next year.
The expected total dollar net operating Income for next year = $70,000
1) The contribution format income statement for the game last year, and the degree of operating leverage is computed below:
Contribution format income statement for the game last year Sales (15,000 × $20) = $300,000
Variable expenses (15,000 × $6) = $90,000
Contribution margin = $210,000
Fixed expenses = $182,000Net operating income = $28,000
Degree of operating leverage = Contribution margin / Net operating income= $210,000 / $28,000= 7.5 2)
The expected percentage increase in net operating income for next year:
The expected sales in next year = 18,000
games selling price per game = $20
Therefore, Total sales revenue = 18,000 × $20 = $360,000
Variable expenses = 18,000 × $6 = $108,000
Fixed expenses = $182,000
Expected net operating income = Total sales revenue – Variable expenses – Fixed expenses
= $360,000 – $108,000 – $182,000= $70,000
The expected percentage increase in net operating income = (Expected net operating income - Last year's net operating income) / Last year's net operating income*100= ($70,000 - $28,000) / $28,000*100= 150%
The expected total dollar net operating income for next year = $70,000
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A Ferris wheel with a diameter of 60 completes 2 revolutions in one minute. The center of the wheel is 30 feet above the ground. If a person taking a ride starts at the lowest point, which trigonometric function can be used to model the riders height, h(t), above the ground after t seconds?
Answer:
define the height above the ground, h, as a function of time, t, using the sine function:
h(t) = A * sin(B * t + C) + D
A represents the amplitude of the function, which is half of the vertical distance covered by the rider (in this case, 30 feet).
B represents the frequency of the function, which is related to the number of complete cycles or revolutions in a given time period. In this case, the Ferris wheel completes 2 revolutions per minute, so B = 2π (since 2π radians represents one complete revolution).
C represents the phase shift of the function, which accounts for the initial position of the rider. Since the rider starts at the lowest point, there is no phase shift, so C = 0.
D represents the vertical displacement of the function, which is the average height above the ground. In this case, the center of the wheel is 30 feet above the ground, so D = 30.
Putting it all together, the trigonometric function that can be used to model the rider's height, h(t), above the ground after t seconds is:
h(t) = 30 * sin(2π * t) + 30
Therefore, the sine function can be used to model the rider's height
6. Weight of 200 sweets is equal to 5 kg. What is the weight of 150 sweets?
Hello!
sweets 200 150
kg 5 x
x = 5 × 150 ÷ 200 = 3.75
the answer is 3.75kgAnswer:
3.75kg
Step-by-step explanation:
200 sweet = 5kg
So 150 sweet will be X kg
200 sweet= 5kg
150 sweet =X
CROSS MULTIPLY
Therefore
200 × X =150×5
200X =750
divide both sides by 200
X=750\200
X= 3.75kg
one serving of vegetables has 96 grams of protein witch is 30% of the recommended daily amount find the recommended daily amount of protein
Answer:
320 g
Step-by-step explanation:
To find the recommended daily amount of protein, we can set up a proportion using the given information:
30% of the recommended daily amount = 96 grams
Let "x" represent the recommended daily amount of protein. We can set up the proportion as:
30/100 = 96/x
To solve for x, we can cross-multiply and solve the equation:
30x = 100 * 96
30x = 9600
Dividing both sides by 30:
x = 9600 / 30
x ≈ 320
