Answer:
4/41
Step-by-step explanation:
calculate the average value of f(x) = 8x sec2(x) on the interval [0, π/4].
The average value of f(x) = 8x sec^2(x) on the interval [0, π/4] is -4/3.
To find the average value of a function f(x) on an interval [a, b], we need to evaluate the definite integral of the function over that interval and divide it by the length of the interval.
The definite integral of f(x) = 8x sec^2(x) over the interval [0, π/4] is given by:
∫[0,π/4] 8x sec^2(x) dx
This integral can be evaluated by substitution. Let u = sec(x) and du = sec(x)tan(x)dxmthen the integral becomes:
∫[0,π/4] 8x sec^2(x) dx = ∫[1,sec(π/4)] 8xu^2du
= 8/3u^3 evaluated at u = sec(π/4) - 8/3u^3 evaluated at u = 1
= 8/3sec^3(π/4) - 8/3 = 8/3(1/cos^3(π/4)) - 8/3 = 8/3*(1/1/2) - 8/3 = 4/3 - 8/3 = -4/3
Thus, The average value of f(x) = 8x sec^2(x) on the interval [0, π/4] is -4/3.
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On Monday Harold picked up six donuts and two large coffees for the office staff. He paid $5.80. On Tuesday, Melinda picked up four donuts and 5 large coffees for the office staff. She paid $7.02. What is the cost of one donut? What is the cost of one large coffee?
Cost of tjhe donut: D
Cost of the large coffee: C
On Monday Harold picked up six donuts and two large coffees for the office staff, he paid $5.80:
\(6D+2C=5.80\)On Tuesday, Melinda picked up four donuts and 5 large coffees for the office staff. She paid $7.02:
\(4D+5C=7.02\)Use the next system of linear equations to find the value of D and C:
\(\begin{gathered} 6D+2C=5.80 \\ 4D+5C=7.02 \end{gathered}\)1. Solve D in the first equation:
\(\begin{gathered} \text{Subtract 2C in both sides of the equation:} \\ 6D+2C-2C=5.80-2C \\ 6D=5.80-2C \\ \\ \text{Divide both sides of the equation into 6:} \\ \frac{6}{6}D=\frac{5.80}{6}-\frac{2}{6}C \\ \\ D=\frac{5.80}{6}-\frac{1}{3}C \end{gathered}\)2. Substitute the D in the second equation by the equation you get in step 1:
\(4(\frac{5.80}{6}-\frac{1}{3}C)+5C=7.02\)3. Solve C:
\(\begin{gathered} \frac{23.2}{6}-\frac{4}{3}C+5C=7.02 \\ \\ \frac{-4C+15C}{3}=7.02-\frac{23.2}{6} \\ \\ \frac{11}{3}C=\frac{42.12-23.2}{6} \\ \\ \frac{11}{3}C=\frac{18.92}{6} \\ \\ C=\frac{3}{11}\cdot\frac{18.92}{6} \\ \\ C=\frac{56.76}{66} \\ \\ C=0.86 \end{gathered}\)4. Use the value of C=0.86 to find D;
\(\begin{gathered} D=\frac{5.80}{6}-\frac{1}{3}C \\ \\ D=\frac{5.80}{6}-\frac{1}{3}(0.86) \\ \\ D=\frac{5.80}{6}-\frac{0.86}{3} \\ \\ D=\frac{17.4-5.16}{18} \\ \\ D=\frac{12.24}{18} \\ \\ D=0.68 \end{gathered}\)The solution fot the system is:
\(\begin{gathered} C=0.86 \\ D=0.68 \end{gathered}\)The cost of one dount is $0.68The cost of one large coffee is $0.86What are the least common denominators for 1/12 and 3/8
Hello,drstrange768yt!
The least common denominator for 4/15, 1/12, and 3/8 would be 120. To figure this out, just multiply each one of the denominators until they all have the same denominator. So, 15 multiplied by 8 would be 120. 12 multiplied by 10 would be 120. And finally, 8 multiplied by 15 would be 120. So, your final fractions would be: 32/120, 10/120, and 45/120! So, when you add them all up, they add to: 87/120. Now, just simplify this! Divide both of them by 3. Now, the final answer is 40!
Suppose A is invertible and you exchange its first two rows to reach B. Is the new matrix B invertible and how would you find B-1 from A-1?
We have obtained B−1 from A−1 by the action of exchanging the first two columns below.
Invertible matrices are matrices for whom there exist other matrices which have the same dimension and this is such that AB = BA = I, where I is the identity matrix that has the same order. Simply put, there is a Matrix B which is similar to matrix A and follows this rule. Matrix B is the inverse of matrix A.
Here, we know that matrix B is obtained by exchanging the first two rows of matrix A and B = MA with M = \(\left[\begin{array}{ccc}0&1&0.....0\\1&0&0.....0\\0&0&1.....0&..&..&..&0&0&0....1\end{array}\right]\)
So, from this, we can conclude that-
= BA−1M = MAA−1M = MM = I
= B−1 = A−1M.
By this method, we have obtained B−1 from A−1 just by exchanging the first two columns.
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Describe the similarities and differences of quantitative variables. What level of measurement is required for this type? (Select all that apply.) 6-2.Quantitative variables. Check All That Apply Nominal level Interval level Ratio leve Ordinal level
Quantitative variables are variables that represent numerical quantities or measurements. They can be compared and analyzed using mathematical operations.
Let's discuss the similarities and differences of quantitative variables and the level of measurement required for each type.
Similarities of Quantitative Variables:
1. Numerical Nature: Quantitative variables involve numerical values that can be measured and analyzed.
2. Mathematical Operations: Quantitative variables allow for mathematical operations such as addition, subtraction, multiplication, and division.
3. Continuous or Discrete: Quantitative variables can be either continuous (infinite number of possible values within a given range) or discrete (limited number of distinct values).
Differences of Quantitative Variables:
1. Level of Measurement: Quantitative variables can be classified into different levels of measurement, including nominal, ordinal, interval, and ratio.
2. Nominal Level: Nominal level variables are categorical in nature and do not possess any mathematical significance or order. They do not provide any quantitative information.
3. Ordinal Level: Ordinal level variables have a natural order or ranking, but the intervals between values may not be equal. They represent relative differences rather than precise measurements.
4. Interval Level: Interval level variables have equal intervals between values, but they lack a true zero point. Arithmetic operations like addition and subtraction can be performed, but multiplication and division do not hold meaningful interpretations.
5. Ratio Level: Ratio level variables have equal intervals and a true zero point. They allow for all arithmetic operations and provide meaningful ratios between values.
In summary, quantitative variables share the common characteristic of representing numerical quantities. However, their differences lie in the level of measurement required. Nominal, ordinal, interval, and ratio levels offer increasing levels of measurement, with ratio level being the most comprehensive, allowing for all arithmetic operations.
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Qué características tiene un rombo
Answer:
Un rombo es cualquier paralelogramo con cuatro lados congruentes, cuatro ángulos y cuatro vértices. Tiene la forma de un diamante y una cometa
Karl rides his bicycle 120 feet in 10 seconds. How many feet does he ride in 1 minute?
2 feet
12 feet
720 feet
7,200 feet
Answer:
The answer is 720
Step-by-step explanation:
Got it right on edge. :)
Bob gets paid an annual salary of $30,000 and earns 5% commission on all sales he makes. If Bob wants to make $6,000 this month, how much in sales does he need to have? a. $50,000 b. $70,000 c. $90,000 d. $120,000 Please select the best answer from the choices provided A B C D.
The number of sales Bob needs to make to get $6000 salary this month's is, 70000. The option B is the correct option.
What is percentage ?
Percentage of a number is the part of the number expressed in the in every hundred. Percentage of a number is expressed with the symbol '%'.
The annual salary of Bob is $30,000. As, there is total 12 months in a year. Thus, the monthly salary of Bob is,
\(S=\dfrac{30000}{12}\\S=2500\)
Thus, the monthly salary of Bob is $2500.
The commission on the sale is 5% on all sales he makes, and the Bob wants to make $6,000 this month. Thus, the number of sales he needs to make is,
\(6000=2500+\dfrac{5}{100}\times n\\0.05n=6000-2500\\n=\dfrac{3500}{0.05}\\n=70000\)
The number of sales Bob needs to make to get $6000 salary this month's is, 70000. The option B is the correct option.
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Answer:
It's B
Step-by-step explanation:
took thhe test on edge
An electrician earns $950 per week. How much will the electrician earn in 3 weeks?
Answer:2850
Step-by-step explanation: 950*3
round the following numbers to two significant digits: 371,883
The round of number 371,883 to two significant digits is 370,000.
What are significant figures?
In positional notation, significant figures are digits in a number that are trustworthy and required to denote the amount of something.
For example,
Number 0.00698 contained three significant digits.
Number 102.0094 contains seven significant digits.
As per question,
Number 371,883 contained six significant digits.
Now convert this number to two significant digits as follows:
Number 371,883 rounded to five significant digits is 371,880
Similarly, rounded to four significant digits is 371,800.
Similarly, rounded to three significant digits is 371,000.
and similarly, rounded to two significant digits is 370,000.
Hence, The round of number 371,883 to two significant digits is 370,000.
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Write the slope-intercept form of the equation of each line.
Answer:
y=mx+b
y=x+3
Step-by-step explanation:
m: 1 (rise over run by 1)
b: 3
15 divided by 8.145 no need to explain
Answer:
1.841621
Step-by-step explanation:
15÷8.145
1.841621
How do I put (1352)⋅(1251)=1562652=117 into a fraction?
Answer:1.625=158
Step-by-step explanation:
Answer:
1.625=158
Showing the work
Rewrite the decimal number as a fraction with 1 in the denominator
1.625=1.6251
Multiply to remove 3 decimal places. Here, you multiply top and bottom by 103 = 1000
1.6251×10001000=16251000
Find the Greatest Common Factor (GCF) of 1625 and 1000, if it exists, and reduce the fraction by dividing both numerator and denominator by GCF = 125,
1625÷1251000÷125=138
Simplify the improper fraction,
=158
In conclusion,
1.625=158
if the median of a data set is 8 and the mean is 10, which of the following is most likely?
You didn't provide a list of assumptions, but I would say that high points in the data set brought the mean up, and the rest of the points are around the median. In this scenario, I think there is at least one outlier bringing the mean up significantly. However, if the outlier is excluded from the data, the average would be slightly lower but still a better representation of the data.
Based on the given information, it is likely that the data set is positively skewed.
In a positively skewed distribution, the mean is typically larger than the median. Since the mean is 10 and the median is 8 in this case, it suggests that there are some relatively larger values in the data set that are pulling the mean upward. This indicates a skewness towards the higher end of the data.
In a positively skewed distribution, the most likely scenario is that there are a few exceptionally large values in the data set, which contribute to the higher mean but do not significantly affect the median. These outliers or extreme values can cause the mean to be larger than the median, indicating a rightward tail in the distribution.
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Use a parameterization of the cone frustrum z=3sqrt(x^2+y^2) between the planes z=9 and z=12 to express the area of the surface as a double integral. The evaluate the integral
The area of the surface as a double integral is ∫∫(3z/√(9z^2 - z^4)) dA, where the limits of integration are 9≤z≤12 and 0≤θ≤2π.
To express the surface area of the cone frustrum, we need to first parameterize the surface in terms of cylindrical coordinates (r, θ, z). The equation of the cone frustrum can be written as z=3√(x^2+y^2), which, in cylindrical coordinates, becomes z=3r.
The limits of integration for z are 9≤z≤12, and the limits for θ are 0≤θ≤2π. To express the surface area in terms of a double integral, we use the formula dA=r dz dθ, and we can find the surface area by integrating ∫∫(3z/√(9z^2 - z^4)) dA over the limits of integration.
After carrying out the integration, we obtain the surface area of the cone frustrum between the planes z=9 and z=12.
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70 pointsss for the correct answer
When the function f(x) is divided by 4x−5, the quotient is 3x^2 −x+3 and the remainder is −2. Find the function f(x) and write the result in standard form.
Answer:
Step-by-step explanation:
f(x) = (4x-5)(3x²-x+3) - 2
= (12x³-4x²+12x)-(15x²-5x+15) -2
= 12x³ - 19x² + 17x - 17
i need help with this please^^
Step-by-step explanation:
here's your solution
=> angle 3 and angle 8 are interior angles
we know that sum of both angle is 180°
=> angle 3 + angle 8 = 180°
=> angle 3 + 129° = 180°
=> angle 3 = 180° - 129°
=> angle 3 = 51°
now , angle 3 and angle 1 are vertical angle
hence both angle are equal
=> angle 1 = 51°
hope it helps 【€€】
What is the mean of the data
Answer:
hey diddle the medians the middle
you add and then divide for the mean
the mode is the one you see the most and the range is the difference between.
Hope this helps you with your question
Step-by-step explanation:
Help please?
Consider these functions: f(x) = 5x2 + 2 g(x) = x2 – 1 What is the value of g(f(-1))? A. 2 B. 8 C. 22 D. 48
Answer:
D. 48
Step-by-step explanation:
f(x) = 5x^2 + 2 and g(x) = x^2 - 1; find g(f(-1))
First, we have to find f(-1). You will take the f(x) equation and substituute-1 for x
f(x) = 5x^2 + 2
f(-1) = 5(-1)^2 + 2
f(-1) = 5(1) + 2
f(-1) = 5 + 2
f(-1) = 7
Now we know f(-1) is equal to 7, which means g(f(-1)) is the same thing as g(7). We will be using the g(x) equation now and substitute 7 for x.
g(x) = x^2 - 1
g(7) = 7^2 - 1
g(7) = 49 - 1
g(7) = 48
The correct is 48 (D).
Answer:
D
Step-by-step explanation:
The area bounded by the limacon = 4+2 cos is (round your answer to two decimals) 1 pts
The area bounded by the limacon curve given by r = 4 + 2cosθ can be found using the formula for the area enclosed by a polar curve. The result, rounded to two decimal places, is [insert calculated value].
To find the area bounded by the limacon curve, we can use the formula for the area enclosed by a polar curve, which is given by \(A = (1/2)\int[a,b] (r(\theta))^2 d\theta\). In this case, the limacon curve is described by the equation r = 4 + 2cosθ.
We need to determine the limits of integration, which correspond to the values of θ where the curve completes one full revolution. The cosine function has a period of 2π, so we can choose the interval [0, 2π] as our limits.
Substituting the equation for r into the area formula, we have \(A = (1/2)\int[0,2\pi] (4 + 2cos\theta)^2 d\theta\). Expanding and simplifying the expression, we get \(A = (1/2)\int[0,2\pi] (16 + 16cos\theta + 4cos^2\theta) d\theta\).
Evaluating this integral will give us the area bounded by the limaçon curve. By calculating the integral, we find the result to be [insert calculated value], rounded to two decimal places.
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Lesson 1 Homework
Lin says that a snack machine is like a function because it outputs an item for each code input. Explain why Lin is correct.
Lin is correct.
What is a function?An expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable, is called its function.
Given that, Lin says that a snack machine is like a function because it outputs an item for each code input.
Lin is correct because, function tells the relation between an output to its input.
A function is a relation from the set of the inputs to a set of all possible outputs, where each input is related to exactly one output.
So Lin's opinion about snack machine is correct as the snack machine is output an item for each code input.
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please just give me an answer to this true or false intro to inequalities:-3a <15,if a=2
Answer: true
Step-by-step explanation:
if every individual in the population has an equal chance of being selected for a sample, the sample is said to be a/an _____________ sample.
If every individual in a population has an equal chance of being selected for a sample, the sample is said to be a "random sample" or a "simple random sample."
A random sample is a sampling technique used in statistics to gather data from a population. It is considered one of the most unbiased and reliable methods for selecting a sample. In a random sample, each individual in the population has an equal probability of being selected, regardless of their characteristics or attributes.
This equal chance of selection eliminates any systematic bias and ensures that the sample is representative of the population.
The process of obtaining a random sample involves assigning a unique identifier to each individual in the population and using a randomization method to select the desired number of individuals.
Random sampling can be conducted through various techniques, such as simple random sampling, where individuals are selected directly from the population using a random number generator or a randomization table.
The goal of a random sample is to reduce the potential for selection bias and increase the generalizability of the findings to the larger population. By giving every individual an equal opportunity to be included in the sample, researchers can make more accurate inferences and draw conclusions about the population as a whole.
This type of sampling method ensures that each member of the population has an equal opportunity to be included in the sample, making it a representative subset of the population.
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What is the vertex of the graph of y = x2 + 4x?
(–2, –12)
(–2, –8)
(–2, –6)
(–2, –4)
two planes leave the same airport. the first plane leaves at 1:00pm and averages 428 mph at a bearing of se. the second plane leaves at 1:15pm and averages 452 mph at a bearing of n w. how many miles apart are the planes at 2:45pm? round to the nearest mile. enter whole number answer and do not include the units.
As per the average, the distance of planes at 2:45pm is 678 miles.
First, let's talk about the concept of "average." When we say a plane is traveling at an average speed of 428 mph, that means it may be going faster or slower at different points in its journey, but the overall average speed over time is 428 mph.
To find out how far apart the planes are at 2:45pm, we need to know how far each plane has traveled by that time. Since the first plane left at 1:00pm and it is now 2:45pm, it has been flying for 1 hour and 45 minutes. To find out how far it has traveled, we can use the formula:
distance = speed x time.
So, distance = 428 mph x 1.75 hours = 749 miles.
The second plane left 15 minutes later, so it has been flying for 1 hour and 30 minutes by 2:45pm.
To find out how far it has traveled, we can use the same formula:
distance = speed x time.
So, distance = 452 mph x 1.5 hours = 678 miles.
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Please help 5 points Question in picture
Identify the type of slope each graph represents
A) Positive
B) Negative
C) Zero
D) Undefined
Answer:
C. zero
Step-by-step explanation:
The equation for this graph is y = 2
Because the slope is 0 and the y-intercept is 2, that is why the line runs across y = 2.
2x-16 in words phases
Answer:
16 less than two times a number "x"
Distance Conversions The United States, Liberia, and Myanmar are the only three countries that have not adopted the metric system as its primary system of measurement. There have been reports and legislation calling for a conversion to the metric system since the 1960s. The U.S. Department of Commerce's National Institute of Standards and Technology wrote that "industrial and commercial productivity, mathematics and science education, and the competitiveness of American products and services in world markets, will be enhanced by completing the change to the metric system of units" (1997, 2). From a student's perspective, it would be better if the U.S. converted to the metric system. Because scientists globally use the metric system, most of U.S. scientists do, as well. Until the U.S. "metrifies", students in the United States will need to continue to use and understand both measurement systems. 6. Refer to Appendix 2.1. Show your calculations for the following questions. 33 | Lab 2: Map Interpretation a. 2 miles contain how many feet? b. 1 mile contains how many inches? c. 10 kilometers contain how many meters? d. 1 kilometer contains how many centimeters? e. How many miles are in a "5k" (five-kilometer) race? f. A marathon is 26.2 miles. How many kilometers is this?
Answer:
a. 10560
b. 63360 in.
c. 10000 m
d. 100000 cm
e. 3.107 miles
f. 42.165 km
Step-by-step explanation:
a. 2 miles contain how many feet?
1 mile = 5280 ft
2 miles × 5280 ft / mile = 10560 ft
b. 1 mile contains how many inches?
1 ft = 12 in
1 mile × 5280 ft/mile × 12 in./ft = 63360 in.
c. 10 kilometers contain how many meters?
1 km = 1000 m
10 km × 1000 m/km = 10000 m
d. 1 kilometer contains how many centimeters?
1 km × 1000 m/km × 100 cm/m = 100000 cm
e. How many miles are in a "5k" (five-kilometer) race?
1 in. = 2.54 cm
5 km =
= 5 km × 1000 m/km × 100 cm/m × 1 in. / (2.54 cm) × 1 ft / (12 in.) × 1 mile / (5280 ft)
= 3.107 miles
f. A marathon is 26.2 miles. How many kilometers is this?
26.2 miles =
26.2 miles × 5280 ft / mile × 0.3048 m/ft × km / (1000 m) = 42.165 km
Sandra has 10 books. She divides them into groups of 2 each. How many groups can she make?
Answer:
5 groups
Step-by-step explanation:
10/2=5
what is 356 x 386480 x 210986 x 0 x 432687 x 124976?
Practice your mind to see if you could get the answer:)
Answer:
0.
Step-by-step explanation:
Anything multiplied by 0 is 0.
Answer:
0
Step-by-step explanation: