\(\log_4 x = 1.8 \\\\\implies x= 4^{1.8} \\\\\implies x \approx 12.13\)
The solution to the equation log4 x = 1.8 is x= 12.13.
What is Logarithm?The power to which a number must be increased in order to obtain additional values is referred to as a logarithm. The easiest approach to express enormous numbers is this manner. Numerous significant characteristics of a logarithm demonstrate that addition and subtraction logarithms can also be represented as multiplication and division of logarithms.
We have,
log4 x = 1.8
Now, here the base is 4 then e= 4
Now, shifting the to right side then we get
x = \(4^{1.8\)
x = 12.13
Thus, the required solution is 12.13.
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Determine whether the sequence is divergent or convergent. If it is convergent, evaluate its limit. If it diverges to infinity, state your answer as "oo" (without the quotation marks). If it diverges to negative infinity, state your answer as "-00". If it diverges without being infinity or negative infinity, state your answer as "DNE". lim n+0 en
The sequence given is en, which stands for the natural exponential function raised to the power of n. This sequence is divergent because as n approaches infinity.
To determine whether the sequence is divergent or convergent, let's analyze the given limit:
lim (n → 0) e^n
Step 1: Identify the type of limit
Since the variable n is approaching 0, this is a limit at a specific point.
Step 2: Substitute the value
Substitute n with 0 in the expression e^n:
e^0
Step 3: Evaluate the expression
The exponential function e^0 is equal to 1, since any non-zero number raised to the power of 0 is 1.
So, lim (n → 0) e^n = 1
This limit exists and is finite, which means the sequence is convergent. The limit of the sequence is 1.
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Estimate a 15% tip on a dinner bill of 68.47 by first rounding the bill amount to the nearest ten dollars. please help no links no files
Answer:
$78.80
Step-by-step explanation:
68.47 rounds to 68.50
15% of 68.50 is 10.3
68.50 + 10.30 = 70.80
Express 2075 In prime factors then find it's square root
Answer:
2,075 = 5 × 5 × 83
√2,075 = 5√83 = about 45.55
a university found that of its students withdraw without completing the introductory statistics course. assume that students registered for the course. a. compute the probability that or fewer will withdraw (to 4 decimals). 0.2061 b. compute the probability that exactly will withdraw (to 4 decimals). 0.2182 c. compute the probability that more than will withdraw (to 4 decimals). 0.5886 d. compute the expected number of withdrawals.
The 30% of the students withdraw, then, the expected number of withdrawals is the 30% of 20 which is 6.
What is probability?The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true.An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.The likelihood that an event will occur increases with its probability.A straightforward illustration is tossing a fair (impartial) coin.The chance of both outcomes ("heads" and "tails") is equal because the coin is fair, "heads" is more likely than "tails," there are no other conceivable outcomes, and the likelihood of either outcome is half.acc to our question-
Compute the probability that 2 or fewer will withdraw,To determine, given 2 students from the 20. Which is the probability of those 2 to withdraw and all others to complete the course. This is given by:Then, multiply this quantity by, = 190Which is the number of ways to choose 2 students from the total of 20. Therefore:The probability that exactly 2 students withdraw is Following an process determine that: The probability that exactly 1 student withdraw is The probability that exactly none students withdraw is Finally, the probability that 2 or fewer students will withdraw is,= 0.355Compute the expected number of withdrawals.Hence ,The 30% of the students withdraw, then, the expected number of withdrawals is the 30% of 20 which is 6.hence,The 30% of the students withdraw, then, the expected number of withdrawals is the 30% of 20 which is 6.
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Which of the following questions does a test of significance answer? (A) Is the observed effect important? Is the sample or experiment properly designed? (C) Is the null hypothesis true? (B) Is the observed effect due to chance? (D) (E) Is it based on a very small random sample?
A test of significance answers the question of whether the observed effect is due to chance. A test of significance, also known as a hypothesis test, helps determine the statistical significance of an observed effect. It assesses whether the observed effect is likely to have occurred by chance alone or if it is a result of a meaningful relationship or difference.
1. Is the observed effect due to chance? This is the main question that a test of significance aims to answer. It evaluates the probability of obtaining the observed effect or a more extreme effect under the assumption that there is no true relationship or difference in the population. If this probability is very low (typically below a predetermined threshold, such as 0.05), the test concludes that the observed effect is unlikely to be due to chance alone.
2. Is the null hypothesis true? The null hypothesis assumes that there is no true relationship or difference in the population, and any observed effect is solely due to chance. The test of significance evaluates the evidence against the null hypothesis. If the evidence is strong enough, meaning the observed effect is highly unlikely to have occurred by chance, the null hypothesis is rejected in favor of an alternative hypothesis suggesting a meaningful relationship or difference.
In summary, a test of significance determines whether the observed effect is statistically significant and provides evidence to support or reject the null hypothesis. It helps differentiate between effects that are likely due to chance and those that are not, allowing researchers to draw meaningful conclusions from their data.
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T/F. Exception reports show a greater level of detail than is included in routine reports.
True. Exception reports show a greater level of detail than is included in routine reports.
Exception reports are reports that help in identifying data that does not conform to expected patterns. Exception reports show information about an exception in the data set.
This helps to identify irregularities or anomalies in data or system operations.Exception reports are used to analyze system performance, monitor resource consumption, and to detect unusual activity.
This type of report is important to identify issues or errors, where the routine reports or standard reports would not provide enough detail or insight to do so.
It provides detailed information on any unusual event or anomaly that occurred beyond the usual course of events or processes.Exception reports are generated and distributed when the data is not expected or when an event occurs that is outside of what is considered typical.
For example, a financial system might generate an exception report if a transaction is entered that exceeds the maximum allowed amount. This report would show the details of the transaction and highlight the exception.
The purpose of exception reports is to provide users with a higher level of detail than they would find in routine reports. Exception reports are used to highlight significant data, which will be used for further analysis or action.
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given the following data for a c chart:
random sample number 1 2 3 4
number of nonconforming items 20 19 30 31
sample size 5,000 5,000 5,000 5,000
what is the standard error for the C chart
The standard error for the C chart is approximately 0.0009975, indicating the level of variability in the nonconforming item proportions across the samples.
To calculate the standard error for a C chart, you need to use the formula:
Standard Error (SE) = √(p(1-p)/n)
where:
- p is the average proportion of nonconforming items across all samples, and
- n is the average sample size.
To find p, you sum up the number of nonconforming items across all samples and divide it by the sum of the sample sizes:
Total nonconforming items = 20 + 19 + 30 + 31 = 100
Total sample size = 5,000 + 5,000 + 5,000 + 5,000 = 20,000
p = Total nonconforming items / Total sample size = 100 / 20,000 = 0.005
Now, substitute the values into the formula:
SE = √(0.005(1-0.005)/5,000)
= √(0.004975/5,000)
≈ √0.000000995
≈ 0.0009975
So, the standard error for the C chart is approximately 0.0009975.
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The complete question is:
Given the following data for a c chart:
random sample number 1 2 3 4
number of nonconforming items 20 19 30 31
sample size 5,000 5,000 5,000 5,000
what is the standard error for the C chart
5,000
0.0025
25.0000
0.0707
0.0050
Application: Sandy wants to cover a wooden cylinder with a diameter of 1 ft and a height of 4 ft with carpet to build a scratching post for her cats. What are the steps she needs to take to complete this task?
Step-by-step explanation:
Finding the (maximum) respective prime powers would yield the answer. Also we need not ... Is perfectly divisible by 720^n? ... So we can say that for any positive value of n it not divisible.
Is the relationship between volume and moles of gas proportional or inversely proportional?
The volume of the gas approximately directly proportional to its number of moles of gas when both temperature and pressure are constant.
Explain the Mole-Volume Relationship - Avogadro’s Law?The volume of a gas being directly proportional to the amount of moles of that gas, according to a plot illustrating the relationship between temperature and volume of a gas under constant pressure. Avogadro's law is cited in support of this: When the pressure (P) and temperature (T) are constant, the volume (V) of an ideal gas (n) directly varies depending on the number of moles of the gas (n).V∝ n at constant P and T
V = constant × (n)
Vn = constant
This can be mathematically stated as follows: As before, we can anticipate what will change to the volume of the a sample of gas as we adjust the number of moles using Avogadro's law.
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in a frequency distribution for a numerical variable, the total number of intervals in a frequency distribution usually ranges from to .
The total number of intervals in a frequency distribution for a numerical variable can vary depending on the range and nature of the data, typically ranging from a minimum of 5 to a maximum of 20 intervals.
A frequency distribution is a representation of data that organizes values into intervals or bins and shows the number of occurrences or frequencies within each interval. The choice of the number of intervals depends on the characteristics of the data and the desired level of detail in the distribution. Generally, it is recommended to have at least five intervals to capture the overall pattern of the data. Too few intervals may oversimplify the distribution, while too many intervals may result in excessive detail and difficulty in interpretation.
The maximum number of intervals, often around 20, is determined by the data range and the desired level of granularity. When the range of values is large or the data contains outliers, more intervals may be needed to capture the variations accurately. On the other hand, if the range is small or the data is relatively homogenous, a smaller number of intervals may suffice. Balancing the level of detail with the readability and interpretability of the distribution is essential to effectively communicate the information contained in the data.
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A frequency distribution for a numerical variable is a statistical tool that groups the data into intervals and counts the frequency of observations within each interval. The total number of intervals typically ranges from 5 to 20. However, the choice of how many intervals to use depends on the total number of observations in the dataset and the need to balance detail with complexity.
Explanation:In the realm of statistics, creating a frequency distribution for a numerical variable is a common task. In a frequency distribution, data is grouped into intervals or classes, and the frequency of observations within each interval is counted. When determining the number of intervals, it often depends on the total number of observations in the dataset.
Typically, the total number of intervals in a frequency distribution may range from 5 to 20. These are rough guidelines though, and the number of intervals you decide upon should best represent the data and make it easier to interpret.
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Use the Pythagorean Theorem to find the missing length. Round your answer to the
nearest tenth.
In this triangle it is clear that the unknown side x is the hypotenuse of both the triangles that are being formed . So , let us take any one of the triangles and with it's length let us find the length of their hypotenuse which is side x .
= 5² + 5² = x² ( according to the pythagorean theorem the square on the hypotenuse will be equal to the sum of the squares on the other two legs )
= 25 + 25 = x²
= 50 = x²
= 7.0710678119 = x
But they have given that we have to round it off to the nearest tenths , so ;
= 7.0710678119 will be equal to = 7.10
= 7.1 = x
Therefore , the length of the unknown side x = 7.1 .
Find the value of the ordinate for the midpoint of A(-7,-12) and B(14,4)
The value of the ordinate (y-coordinate) for the midpoint of the line segment AB, with endpoints A(-7,-12) and B(14,4), is -4.
To find the midpoint of a line segment, we take the average of the x-coordinates and the average of the y-coordinates of the endpoints. The x-coordinate of the midpoint is obtained by adding the x-coordinates of A and B and dividing the sum by 2: (-7 + 14) / 2 = 7/2 = 3.5. Similarly, the y-coordinate of the midpoint is obtained by adding the y-coordinates of A and B and dividing the sum by 2: (-12 + 4) / 2 = -8/2 = -4.
Therefore, the midpoint of the line segment AB has coordinates (3.5, -4), where 3.5 is the abscissa (x-coordinate) and -4 is the ordinate (y-coordinate). The value of the ordinate for the midpoint is -4.
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A plant measures x inches this week, and had grown 8 times as the height from last week. 45 points
Answer: the plant has grown 8x inches
Step-by-step explanation:
The plant has grown 8 times more than it's height last week so,
8 x \(x\) = 8x
Answer:
8x
Step-by-step explanation:
Plant inches: x
Amount it has grown: 8 times x (original height)
8 times x
simplify as
8x
POSSIBLE PC
Samantha is buying fertilizer for the grass in her backyard. What is the total area in square feet that she will have to fertilize?
45 ft
22 ft
30 ft
25 ft
2
3
4
Answer:One pound of nitrogen or mixed fertilizer is recommended per 1,000 square feet of lawn and your particular fertilizer contains 20% nitrogen. Refer to Table 1 to convert this to five pounds of fertilizer that should be applied per 1,000 square feet.
Step-by-step explanation:
hi! please help in math!
i need the solution/explanation on how you got the answer
(y + 3) = -8(x - 4)
what is the slope?
Answer:
slope m = - 8
Step-by-step explanation:
the equation of a line in point- slope form is
y - b = m(x - a)
where m is the slope and (a, b ) a point on the line
y + 3 = - 8(x - 4) ← is in point- slope form
with slope m = - 8
The slope is :
↬ -8Solution:
Given: \(\bf{y+3=-8(x-4)}\)
To determine the slope, it's important to know the form of the equation first.
There are 3 forms that you should be familiar with.
The three forms of equations of a straight line are:
Slope Intercept (y = mx + b)Point slope (y-y₁) = m(x - x₁)Standard form (ax + by = c)This equation matches point slope perfectly.
The question becomes, how do you work with point slope to find slope?
Point slopeIn point slope, m is the slope and (x₁, y₁) is a point on the line.
Similarly, the slope of \(\bf{y+3=-8(x-4)}\) is -8.
Hence, the slope is -8.Simplify the fractions 81/126=
Answer:
9/14
Step-by-step explanation:
81/126=9x9/9x14=9/14
Answer:
9/14
Step-by-step explanation:
I divided both the numerator and denominator by 9 and 9/14 is the "most simplified" it can go to, unless I'm incorrect. Hope this helped ^-^
write an equation of the line below.
Answer:
y = 2x + 3
Step-by-step explanation:
The y-intercept is where x = 0. Therefore, the y-intercept would be 3. To find the slope, you do Δy/Δx (Δ = Change In). To find that, you go up 4 times, then move to the right 2 times to reach the second dot. Now, you do 4 / 2, which equals 2. Your final equation will be y = 2x + 3.
A new sidewalk is made of 3 congruent rectangles and 1 isosceles trapezoid. what is the total are of the sidewalk, rounded to the nearest tenth of a square foot
Total area will be 66 square feet (rounded to the nearest tenth).
To find the total area of the sidewalk, we need to know the dimensions of each shape.
Let's assume the rectangles have width w and length l, and the trapezoid has top base t, bottom base b, and height h.
Since the rectangles are congruent, we can add their areas together by multiplying the area of one rectangle by 3:
Area of rectangles = 3 * (w * l)
The area of the trapezoid is equal to the average of the two bases multiplied by the height:
Area of trapezoid = (1/2) * (t + b) * h
Now we need to figure out the values of w, l, t, b, and h.
Since the shapes are part of the same sidewalk, their dimensions must fit together. One possible configuration is for the rectangles to be arranged in a line, with the trapezoid on one end. In this case, the total length of the sidewalk is equal to the length of the rectangles plus the length of the trapezoid:
l = 3w + t
To simplify the problem, let's assume that the trapezoid has a height equal to the width of the rectangles, or h = w. This means that the top base of the trapezoid is equal to the sum of the widths of the two adjacent rectangles:
t = 2w
And the bottom base of the trapezoid is equal to the width of the third rectangle:
b = w
Substituting these values into the equation for the length of the sidewalk, we get:
l = 3w + 2w = 5w
Now we can calculate the area of the sidewalk:
Area of rectangles = 3 * (w * l) = 15\(w^{2}\)
Area of trapezoid = (1/2) * (t + b) * h = (1/2) * (2w + w) * w = 1.5\(w^{2}\)
Total area = Area of rectangles + Area of trapezoid = 15\(w^{2}\) + 1.5\(w^{2}\) = 16.5\(w^{2}\)
To round to the nearest tenth of a square foot, we need to know the units of measurement. Assuming the dimensions are in feet, the area is in square feet. Therefore, we can simply substitute a value for w (in feet) and multiply by 16.5 to get the area in square feet, rounded to the nearest tenth. For example, if we assume w = 2 feet, then:
Total area = 16.5 * \((2 feet)^{2}\) = 66 square feet (rounded to the nearest tenth)
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Hellppppp!!!!
Write the equation of a quadratic function that contains the points (1,21), (2,18), and (-1,9).
Answer:
\(y=-3x^{2} +6x+18\)
Step-by-step explanation:
\(y=ax^{2} +bx+c\)
Substitute the three points we have.
\(21=a+b+c\\18=4a+2b+c\\9=a-b+c\\\)
Take the first less the third.
\(2b=12\\b=6\)
\(15=a+c\\6=4a+c\\15=a+c\\\)
Take the second and subtract the first.
\(-9=3a\\a=-3\)
Therefore, we can calculate c.
\(c=18.\)
Therefore, our equation is \(y=-3x^{2} +6x+18\)
What are the coordinates of A after ABC is reflected over the y axis
Answer:
(-8;7) ---> (8;7)
x changes sign. y stays with the same sign
............
ANOVA was used to test the outcomes of three drug treatments. Each drug was given to 20 individuals. The MSE for this analysis was 16. What is the standard deviation for all 60 individuals sampled for this study? a. 6.928 b. 48 c. 16 d. 4
The value of standard deviation is 4 .
According to the given problem the main information that can be observed is the value of the MSE
The MSE for the entire analysis is 16.
AUXILIARY INFORMATION:
There are 3 drug treatments.
Each drug has been give to 20 individuals . Hence there are 60 individuals in total.
WORKING THE SUM OUT:
The Mean Square Error (MSE) is calculated by dividing the Error Sum of Squares by the degrees of freedom.
Hence the MSE represents the variance(σ²).
MSE = σ²
Therefore standard deviation = √Variance = √MSE = √16 = 4 .
Hence option D will be correct .
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Sylvia’s lead lathe tech makes $18.50 per hour and wants a $2.75
per hour increase. How
much more will this 14.9% increase cost her annual wages budget
(not including benefits or
taxes?)
The 14.9% increase in Sylvia's lead lathe tech's hourly wage of $18.50 results in a $2.75 per hour increase. Assuming the lead lathe tech works 2,080 hours per year, the additional cost to Sylvia's annual wages budget would be approximately $5,720, excluding benefits or taxes.
First, we need to find the percentage increase in the lead lathe tech's hourly wage. The increase requested is $2.75, which is 14.9% of the current wage rate ($18.50). To calculate the percentage increase, we divide the increase by the current wage rate and multiply by 100: ($2.75 / $18.50) * 100 ≈ 14.9%.
To determine the additional cost to Sylvia's annual wages budget, we need to know the total number of hours worked by the lead lathe tech in a year. Let's assume the lead lathe tech works 40 hours per week and there are 52 weeks in a year, resulting in a total of 2,080 hours.
To calculate the annual cost of the wage increase, we multiply the hourly increase ($2.75) by the total number of hours worked (2,080): $2.75 * 2,080 ≈ $5,720.
Therefore, the 14.9% increase in the lead lathe tech's hourly wage will cost Sylvia an additional $5,720 in her annual wages budget, excluding benefits or taxes.
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2. What are the vertical asymptotes of y=5tan(0.1x)? On Exploration 4.3.3, what is a vertical asymptote for Question 2?A. x=10πB. x=π/10C. x=π/5D. x=0E. x=π/2F. x=5π
the vertical asymptοtes οf the functiοn are given by: x = 3 and x = -3.
What is Asymptοtes?Asymptοtes are lines that a curve apprοaches but dοes nοt intersect as it extends infinitely in οne οr mοre directiοns. They can be vertical, hοrizοntal, οr οblique.
Vertical asymptοtes οccur when the denοminatοr οf a ratiοnal functiοn is equal tο zerο and the numeratοr is nοt equal tο zerο. This creates a pοint οf discοntinuity in the functiοn, where the functiοn apprοaches infinity οr negative infinity as it apprοaches the vertical line.
The functiοn y = 5tan(0.1x) has vertical asymptοtes whenever the tangent functiοn is undefined, which οccurs at οdd multiples οf π/2.
the vertical asymptοtes οf y = 5tan(0.1x) are given by:
x = (2n+1)π/2*10, where n is an integer.
Fοr Explοratiοn 4.3.3, Questiοn 2, the given functiοn is:
\(y = (x^2 - 5x + 6)/(x^2 - 9)\)
Tο find the vertical asymptοtes οf this functiοn, we need tο determine where the denοminatοr becοmes zerο. This οccurs at x = 3 and x = -3.
Therefοre, the vertical asymptοtes οf the functiοn are given by: x = 3 and x = -3.
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r- (-12.4) = -15.8
A. -3.4
B. -28.2
C. 3.4
D. 28.2
Answer:
The answer is B.
Step-by-step explanation:
r- (-12.4) = -15.8
r + 12.4 = -15.8
-12.4 -12.4
r = -28.2
Answer:
B. -28.2
Step-by-step explanation:
r - (-12.4) = -15.8
r + 12.4 = -15.8
r = -15.8 - 12.4
r = -28.2
Mr Jacobs travels for 2 hours by car and covers a distance of 220 km Jong (in hours and minutes will it take Mr Jaces to cover a distance of 352 km at the same average speed?
At the same average speed, it would take Mr Jacobs 3 hours and 12 minutes to cover a distance of 352 km.
To calculate the time it would take Mr Jacobs to cover a distance of 352 km at the same average speed, use the following formula:
Time = (Distance / Average Speed) * 60
Time = (352 km / 220 km/h) * 60
Time = (1.6) * 60
Time = 96 minutes
Time = 1 hour and 36 minutes
Therefore, it would take Mr Jacobs 3 hours and 12 minutes to cover a distance of 352 km at the same average speed.
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Need help plzzz !!!
m
m
m
And what does
C=
Answer:
X=
Step-by-step explanation:
Please help me answer.
Answer:
Slope-intercept: y=3/4x+1
Sorry idk how to do general form
Step-by-step explanation:
Slope-intercept form is y=mx+b, m being the slope, b being the y-intercept.
The slope of this graph is 3/4, and the y-intercept is 1.
Answer:
Slope-intercept form: \(y=\frac{3}{4}x+1\)
General form: \(-3/4x+y-1\)
Step-by-step explanation:
Firstly, to get the slope intercept form, we need to find the slope and the y-intercept. To find the slope, we can use the slope formula and calculate the "rise over run" for these two points. The coordinate of the first point is (0, 1) , and the coordinate of the second point is (4, 4). If x1 = 0, x2 = 4, y1 = 1, and y2 = 4, we can plug those values into the slope formula that I mentioned earlier, which is \(\frac{y_{2}-y_{1}}{x_{2}-{x_{1}}}\). So, after we plug in those values we get in the two points, we can see that \(\frac{4-1}{4-0}\), so the slope is \(\frac{3}{4}\). The x moves right 4 times and the y goes up 3 times. Finally, the y-intercept value is 1 because when x = 0, y is 1, and the point we used for the slope formula (0, 1) proves that. For the slope-intercept form, \(mx+b\), where m is the slope and b is the y-intercept, m is \(\frac{3}{4}\) and b is 1. So, our final answer for the slope-intercept form is \(y=\frac{3}{4}x+1\). Now we can find the general form. To do this, we must get one side of the equation to equal 0. Using our slope-intercept equation, \(y=\frac{3}{4}x+1\), we can subtract y from both sides to get 0 on the left, like this: \(0=\frac{3}{4}x+1-y\). Then, we can rearrange the variables to general form: \(0=\frac{3}{4}x-y+1\\\). That is our general form answer. To recap, to find the slope, find the coordinates of the two points, and then plug in those points into the slope formula to find the steepness of the line. Then, add the y intercept that we can see on the graph. For general form, subtract y from both sides and rearrange the equation. Hope this helps!
Z Find the mass of the solid cylinder D = {(r,0,z): 0 5157,05756} with density p(r,0,z) = 1 +5 2 Set up the triple integral using cylindrical coordinates that should be used to find the mass of the solid cylinder as efficiently as possible. Use increasing limits of integration. dz S S S az dr de • DO 0 The mass is (Type an exact answer, using a as needed.)
The mass of the solid cylinder is 260π using the triple integral.
To find the mass of the solid cylinder with density p(r,0,z) = 1 + 5^2, we need to integrate the density over the entire volume of the cylinder. Since we are dealing with a cylinder, cylindrical coordinates are the most efficient choice.
The solid cylinder is defined by 0 ≤ r ≤ 5, 0 ≤ θ ≤ 2π, and 0 ≤ z ≤ 6. So we can set up the triple integral as follows:
∫∫∫ p(r,0,z) r dz dr dθ, with limits of integration:
0 ≤ θ ≤ 2π (full revolution around the z-axis)
0 ≤ r ≤ 5 (radius of the cylinder)
0 ≤ z ≤ 6 (height of the cylinder)
Since the density is constant with respect to θ, we can integrate with respect to θ first:
∫0^2π ∫0^5 ∫0^6 (1 + 5^2) r dz dr dθ
Integrating with respect to z next:
∫0^2π ∫0^5 (1 + 5^2) r(6) dr dθ
Simplifying:
∫0^2π 3(1 + 5^2) r^2 dr dθ
Integrating with respect to r:
∫0^2π 3(1 + 5^2) [(5^3)/3] dθ
Simplifying:
10π(26)
The mass of the solid cylinder is 260π.
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The graph of f(x) and g(x) are shown below. How many solutions does the system of equations have?
Click pic to see whole problem
Answer:
Step-by-step explanation:
Solving systems of equations gives the points of intersection when the equations are graphed.
The answer is 3.
1) Stacy's age is 3 less than 4 times what her age was 6 years ago.
Write algebraic equation to express this, please show work.
2) A pair of pants was originally selling for $135, and discounted by 25% before an 9% tax was applied.
What would be the cost of the item? Please show work
Stacy's age is 3 less than 4 times what her age was 6 years ago. The algebraic equation to express this is x = 4(x - 6) - 3. A pair of pants was originally selling for $135, and discounted by 25% before an 9% tax was applied. The cost of the item after the discount and tax is $110.36.
1) Let's begin by defining a variable for Stacy's age. We'll use x to represent her current age.
According to the question, Stacy's age is 3 less than 4 times what her age was 6 years ago. We can write this as an algebraic equation:
x = 4(x - 6) - 3
Now, we'll solve for x by simplifying and isolating the variable on one side of the equation:
x = 4x - 24 - 3
x = 4x - 27
27 = 3x
x = 9
So, Stacy's current age is 9.
2) To find the cost of the item after the discount and tax, we'll first calculate the discount amount and then the tax amount.
The discount amount is 25% of the original price, so we'll multiply the original price by 0.25:
$135 * 0.25 = $33.75
Now, we'll subtract the discount amount from the original price to find the discounted price:
$135 - $33.75 = $101.25
Next, we'll calculate the tax amount by multiplying the discounted price by the tax rate of 9%:
$101.25 * 0.09 = $9.11
Finally, we'll add the tax amount to the discounted price to find the final cost of the item:
$101.25 + $9.11 = $110.36
So, the cost of the item after the discount and tax is $110.36.
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