"97.72% of the female students have scores above," seems to be a misinterpretation as the correct statement is that approximately 99.72% of the female students have scores between the lower and upper limits
To calculate the scores that are three standard deviations above and below the mean, we use the formula:
Lower limit = Mean - (Standard Deviation * 3)
Upper limit = Mean + (Standard Deviation * 3)
Given:
Mean = 269
Standard Deviation = 33
Using the formula, we can calculate the limits:
Lower limit = 269 - (33 * 3) = 269 - 99 = 170
Upper limit = 269 + (33 * 3) = 269 + 99 = 368
Therefore, the lower limit is 170 and the upper limit is 368.
To calculate the probability that a female student will have a score between these limits, we need to find the area under the normal distribution curve between the lower and upper limits. This can be calculated using a standard normal distribution table or calculator.
Since the distribution is assumed to be normal, approximately 99.72% of the scores will fall within three standard deviations from the mean. Therefore, the probability that a female student will have a score between these limits is approximately 99.72%.
For a score of 302, which is above the mean of 269, we can calculate the percentage of female students with scores below 302:
Percentage = (1 - Probability) * 100
= (1 - 0.9972) * 100
= 0.0028 * 100
= 0.28%
Therefore, approximately 0.28% of the female students have scores below 302.
It's important to note that the value mentioned, "97.72% of the female students have scores above," seems to be a misinterpretation as the correct statement is that approximately 99.72% of the female students have scores between the lower and upper limits
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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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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?
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 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
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
You have contracted business to weld nine fuel storage tanks to fit into the bed of 9 pickup trucks. The inside dimensions are h = 40"; w = 40"; l = 48". What is the total volume in cubic feet? Round answer to the nearest whole number.
691,200
76,800
400
4800
Answer:
It's C: 400
Step-by-step explanation:
The inside dimensions of the tank are:
h = 40 inches
w = 40 inches
l = 48 inches
Convert to Feet:
h = 40 inches / 12 = 3.33 feet
w = 40 inches / 12 = 3.33 feet
l = 48 inches / 12 = 4 feet
Volume of one tank = 3.33 feet * 3.33 feet * 4 feet
= 44 cubic feet (approximately)
Since there are nine tanks, we multiply the volume of one tank by nine to get the total volume:
Total volume = 44 cubic feet * 9
= 396 cubic feet
Rounding the answer to the nearest whole number, the total volume is approximately 396 cubic feet.
Therefore, the correct answer among the given options is 400.
Hope that helped!
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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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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A rectangular room has length L and width W, where L and W are measured in feet.
a. Express the area in square feet algebraically.
b. If carpeting costs x dollars per square yard, express the cost of carpeting this room algebraically.
The area of rectangular room with length L and width W is LW/9 square yard.
Given that, a rectangular room has length L and width W, where L and W are measured in feet.
Here, L feet = L/3 yard and W feet = W/3 yard
a) Area = Length×Width
= L/3 × W/3
= LW/9 square yard.
b) Carpeting costs x dollars per square yard.
Total cost = x×LW/9
= LWx/9 dollars
Therefore, the area of rectangular room with length L and width W is LW/9 square yard.
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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
can you help me silve this please
Answer: Area of Cylinder = 753.982
Step-by-step explanation:
Given:
h = 7 cm
r = 8cm
Formula for cylinder:
A = (Perimeter of base) x height + 2 (Area of Base)
Breakdown:
Perimeter of base = 2[tex]\pi r[/tex]
Perimeter of base = 2 [tex]\pi[/tex] (8)
Perimeter of base = 50.2655
Area of Base = [tex]\pi r^{2}[/tex]
Area of Base = [tex]\pi 8^{2}[/tex]
Area of Base = 201.0619
Area of Cylinder = (Perimeter of base) x height + 2 (Area of Base)
Area of Cylinder = (50.2655)(7) +2(201.0619)
Area of Cylinder = 753.982
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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(q4) Which of the following integrals can be used to find the length of the curve described by the function
The arc length of a Curve is given by the formula:`L = int_a^b sqrt(1 + [f'(x)]^2) dx , the correct option is given by `L = int_0^1 sqrt(1 + 4x^2) dx`.
The arc length of a curve is given by the formula:`L = int_a^b sqrt(1 + [f'(x)]^2) dx
where L is the length of the curve between x = a and x = b. In this formula, `f(x)` is the equation of the curve being considered and `f'(x)` is the derivative of `f(x)` with respect to x.
Using this formula, the following integrals can be used to find the length of the curve described by the function:`L = int_0^1 sqrt(1 + 4x^2) dx`This is because the function being described by this integral is the equation of a curve, and the integral finds the length of this curve between `x = 0` and `x = 1`.
To evaluate the integral, we can use trigonometric substitution. Let `x = (1/2) tan(theta)`. Then `dx/dtheta = (1/2) sec^2(theta)`, so `1 + 4x^2 = 1 + 2 tan^2(theta) = sec^2(theta)`.Substituting these expressions into the integral, we have:
`L = int_0^1 sqrt(1 + 4x^2) dx = int_0^(pi/4) sec(theta) (1/2) sec^2(theta) theta = (1/2) int_0^(pi/4) sec^3(theta) dtheta`
This integral can be evaluated using integration by parts, and the final answer will be in terms of trigonometric functions.
Therefore, the correct option is given by `L = int_0^1 sqrt(1 + 4x^2) dx`.
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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
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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enter the number that belongs in the green box
Answer:
Set your calculator to degree mode.
[tex] \frac{ \sin(29) }{6.78} = \frac{ \sin(x) }{4} [/tex]
[tex]6.78 \sin(x) = 4 \sin(29) [/tex]
[tex] \sin(x) = \frac{4 \sin(29) }{6.78} [/tex]
[tex]x = {sin}^{ - 1} ( \frac{4 \sin(29) }{6.78} ) = 16.62[/tex]
The number that belongs in the green box is 16.62.
Question 13 (2 points)
If Mary bought 16 of the Brand X batteries, how many of them lasted more than 14 hours? (Please
show how you calculated this to get your answer) (2 points)
The number of brand X batteries that would last more than 14 hours is 12.
Interpreting the BoxplotBatteries with 14 hours battery life falls in the first quartile which is 25% of the distribution. Hence, 75% lasted more than 14 hours.
From the information we have established, If Mary bought 16 brand X batteries , then;
75% of the number of batteries would give us the answer :
75% of 16
0.75 × 16 = 12.
Therefore, 12 batteries would last more than 14 hours .
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Determine the value of x in the figure below:
NO LINKS!
Answer:
x = 4
Step-by-step explanation:
Vertically opposite angles are equal.
5x + 3 = 2x + 15
Make x the subject:
Take 2x away from both sides.3x + 3 = 15
Take 3 away from both sides.3x = 12
Divide both sides by 3.x = 4
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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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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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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Find the least number which should be Subtracted from 56037 so that the difference is exactly divisible by 139.
Answer:
Answer will be 55898.
Step-by-step explanation:
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.
Four people started a business by investing the following amounts: A: N30 000, B: N40 000, C: N60 000, D: N70 000. They agreed that A, as manager, should get one third of the profits, the rest being divided between all four in proportion to their investments. a Draw a pie chart showing the ratio of their investments. b Draw a pie chart to show how the profit was divided.
Answer: Ratio of their investments is 3:4:6:7. Ratio of profits is 13:4:6:7.
Step-by-step explanation:
a. we know that their investments are 30,000 , 40,000 , 60,000 , 70,000 respectively.
so the ratio o their investments is, A:B:C:D = 3:4:6:7
A: (360-120) x (30000/ 30000+40000+60000+70000) = 36
B: (360-120) x (40000/ 30000+40000+60000+70000) = 48
C: (360-120) x (60000/ 30000+40000+60000+70000) = 72
D: (360-120) x (70000/ 30000+40000+60000+70000) = 84
b. For dividing the profit, it is given that 1/3rd of the profit is reserved for the manager. So,
1/3 of360 = 120
A: 120 + (360-120) x (30000/ 30000+40000+60000+70000) = 156
B: (360-120) x (40000/ 30000+40000+60000+70000) = 48
C: (360-120) x (60000/ 30000+40000+60000+70000) = 72
D: (360-120) x (70000/ 30000+40000+60000+70000) = 84
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Help!!
a^n+3 -3a^n+2 -4a^n+1 -a^n by -a^n x²
[tex] \bold{a {}^{n + 3} - 3a {}^{n + 2} - 4a {}^{n + 1} - a {}^{n} \: \: by \: \: - a {}^{n} \: \: x {}^{2} }[/tex]
Step by step explanation :Case of multiplication of a Polynomial by a monomial. The rule says that, to multiply the monomial by each of the terms of the polynomial, taking into account the law of signs, separating the partial products with their own signs. That is, we apply the Distributive Law of multiplication.
Then, we will solve by Distributive law.
[tex]\bold{(a {}^{n + 3} - 3a {}^{n + 2} - 4a {}^{n + 1} - a {}^{n})( \: \: - a {}^{n} \: \: x {}^{2} ) }[/tex]
[tex] \sf{a {}^{n + 3}( - a {}^{n}x {}^{2}) - 3a {}^{n + 2}( - a {}^{n}x {}^{2}) - 4a {}^{n + 1} ( - a {}^{n} x {}^{2} ) - a {}^{n} ( - a {}^{n} x {}^{2}) }[/tex]
[tex] \sf{ - 1 \cdot 1a {}^{n + 3 + n}x {}^{2} + 3 \cdot1 a{}^{n + 2 + n}x {}^{2} + 4 \cdot1a {}^{n + 1 + n}x {}^{2} + 1 \cdot1a {}^{n + 2}x {}^{2} }[/tex]
[tex]\bold{ Answer}=\sf{- a {}^{2n + 3} x {}^{2} + 3a {}^{2n + 2}x {}^{2} + 4a {}^{2n + 2}x {}^{2} + a {}^{2n} x {}^{2}} [/tex]
You are contracted to fabricate a gate with specifications shown below. You are using 1/4" x 3/4" flat bar. How many feet of flat bar is needed to complete the gate? Regardless of the remainder amount - round up to the nearest whole number
44
46
42
48
The number of feet of flat bar needed to complete the gate is 34 feet (rounded up to the nearest whole number).
To calculate the number of feet of flat bar needed to complete a gate with the given specifications of 1/4" x 3/4" flat bar, we can follow these steps:
Step 1: Convert the measurements to Feet To convert the measurements from inches to feet, we can divide them by 12. So, 1/4" = 0.02083 ft and 3/4" = 0.0625 ft.
Step 2: Calculate the length of each flat bar piece Needed For each flat bar piece, we need to add up the length of all the sides that will be made from the flat bar.
From the specifications given, we can see that there will be six pieces of flat bar needed:
four vertical pieces and two horizontal pieces. The length of each vertical piece will be the height of the gate plus an additional 2 inches at the top for the curve, and the length of each horizontal piece will be the width of the gate plus an additional 2 inches on either side for the curves.
So, the length of each piece can be calculated as follows:
Vertical pieces: (48 + 2 + 2) x 2 x 0.02083 ft = 2.083 ft Each Horizontal pieces: (120 + 2 + 2) x 2 x 0.0625 ft = 15.625 ft Each
Step 3: Add up the total length of flat bar Needed Finally, we can add up the total length of flat bar needed by multiplying the length of each piece by the number of pieces, which is 6 in this case:
Total length of flat bar needed = 2.083 ft x 4 + 15.625 ft x 2= 33.33 ft (rounded up to the nearest whole number)
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The volume of the rectangular pyramid below is 468 units. Find the value of x.
Answer:
12
Step-by-step explanation:
Note that the area B of the rectangular base with length x and width 9 units is:
[tex]B=9x[/tex]
Then, the volume [tex]V=468[/tex] cubic units of the pyramid is related to its base area [tex]B=9x[/tex] and height [tex]h=13[/tex] as follows:
[tex]V=\frac{1}{3}Bh\\468=\frac{1}{3}\times 9x\times 13\\x=\frac{468\times3}{9\times 13}=12[/tex]
So, the value of x is 12.
Hello !
Answer:
[tex]\Large \boxed{\sf x=12}[/tex]
Step-by-step explanation:
The volume of a pyramid is given by [tex]\sf V_{pyramid}=\frac{1}{3}\times B\times h[/tex] where B is the area of the base and h is the height.
This is a rectangular pyramid. We have [tex]\sf B=l\times w[/tex] where l is the length and w is the witdth.
So [tex]\sf V_{pyramid}=\frac{1}{3}\times l \times w\times h[/tex]
Given :
l = xw = 9h = 13Let's substitute l, w and h with their values in the previous formula :
[tex]\sf V_{pyramid}=\frac{1}{3}\times x\times 9 \times 13\\\sf V_{pyramid}=3\times13\times x\\\sf V_{pyramid}=39x[/tex]
Moreover, we know that [tex]\sf V_{pyramid}=468\ units^3[/tex].
Therefore [tex]\sf 39x=468[/tex]
Let's solve for x :
Divide both sides by 39 :
[tex]\sf \frac{39x}{39} =\frac{468}{39} \\\boxed{\sf x=12}[/tex]
Have a nice day ;)
PLS HELP WITHIN 5 MINS
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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Can someone graph f(x)={3x-5 if x≤-1 -2x+3 if -1
Thanks!
The graph of the piecewise function for this problem is given by the image presented at the end of the answer.
What is a piece-wise function?A piece-wise function is a function that has different definitions, depending on the input of the function.
The definitions to the function in this problem are given as follows:
Increasing line from negative infinity to point (-1, -8), with a closed interval at (-1,-8).Decreasing line from (-1, 5), with an open interval, to positive infinity.Hence the graph of the piecewise function for this problem is given by the image presented at the end of the answer.
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Let f(x) be defined by the graph below.
Let g(x) = log(x+2) and h(x) = 2x/x+4
Select TWO x-values below that lie in the domain of all three functions
A) x = -4
B) x = -2
C) x = 0
D) x = -1
TWO x-values below that lie in the domain of all three functions are
C) x = 0
D) x = -1
How to find the domain valuesDomain values refer to the set of possible input values for a function or mathematical expression. In other words, the domain is the set of all possible x-values for which the function or expression is defined.
The equations is investigated as follows
h(x) = 2x / (x + 4) : would not have a domain of -4
log(x + 2 : would not have a domain of -2
The graph can have a domain of 0 and -1 hence this remains the correct option
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