5. Background Story: Sometimes a transformation can simplify the domain and simplify the inte- grand at the same time. Questions: (3.5 points) Evaluate the integral using a linear change of variables. SITE (x + y)ex?–y dA =* where R is the polygon with vertices (1,0), (0,1), (-1,0), and (0, -1).?
Answers
Using a linear change of variables with u=x+y and v=x-y, the integral ∫∫(x+y)e^(x-y) dA over a polygonal region R is evaluated to be 2(e^-1 - e^-3).
To evaluate the given integral using a linear change of variables, we need to find a transformation that simplifies the integrand and the domain of integration. Let's try the transformation
u = x + y
v = x - y
Then, the Jacobian of the transformation is
J = ∂(u,v)/∂(x,y) =
| 1 1 |
| 1 -1 |
and its determinant is |J| = -2.
Using this transformation, we can rewrite the integral as
∫∫(x+y) e^(x-y) dA = ∫∫ u e^v |J| dudv
where the region R is transformed into a square with vertices (1,1), (-1,1), (-1,-1), and (1,-1) in the uv-plane.
The limits of integration for u and v can be found by considering the lines that bound the region R
For the line x = 1, we have u = x + y = 1 + y, which becomes v = x - y = 1 - 2y. Therefore, the line x = 1 corresponds to v = 1 - 2u.
Similarly, for the line y = 1, we have u = x + y = x + 1, which becomes v = x - y = x - 1. Therefore, the line y = 1 corresponds to v = u - 2.
For the line x = -1, we have u = x + y = -1 + y, which becomes v = x - y = -1 - 2y. Therefore, the line x = -1 corresponds to v = -1 - 2u.
Finally, for the line y = -1, we have u = x + y = x - 1, which becomes v = x - y = x + 1. Therefore, the line y = -1 corresponds to v = u + 2.
Using these limits, we can rewrite the integral as
∫∫(x+y) e^(x-y) dA = ∫^1_-1 ∫^(1-2u)_(u-2) u e^v (-2) dvdud
Integrating with respect to v first, we get
∫^1_-1 ∫^(1-2u)(u-2) u e^v (-2) dvdud = ∫^1-1 [-2u(e^(1-2u)-e^(u-2))] du
Integrating with respect to u, we get
∫^1_-1 [-2u(e^(1-2u)-e^(u-2))] du = [-e^(1-2u)+e^(u-2)]|^1_-1 = 2(e^-1 - e^-3)
Therefore, the value of the integral is 2(e^-1 - e^-3).
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Related Questions
for which data frequency is seasonality not a problem? group of answer choices monthly. weekly. annual. daily. quarterly.
Answers
Seasonality may be less of a problem for annual data frequency as there may be less variation due to the longer time interval.
What is annual data frequency?Annual data frequency refers to data that is collected and reported on an annual basis. This means that the data points in the dataset represent a full year's worth of data, with one data point for each year. Annual data is often used in economic indicators, such as gross domestic product (GDP) or unemployment rates, and can provide insights into long-term trends and changes over time.
What is GDP?GDP stands for Gross Domestic Product, which is a measure of the total value of goods and services produced within a country's borders during a specific time period, typically a year. It is used as an indicator of a country's economic health and growth. GDP is calculated by adding up the total spending on consumption, investment, government spending, and net exports (exports minus imports) during the period.
According to the given informationSeasonality may still be a problem for data frequencies of monthly, weekly, daily, and quarterly as certain patterns or fluctuations may occur within each of these time intervals. Seasonality may be less of a problem for annual data frequency as there may be less variation due to the longer time interval.
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Suppose you revolve the plane region completely about the given line to sweep out a solid of revolution. Describe the solid. Then find its surface area in terms of pi.
Answers
Answer:
The answer is explained below
Step-by-step explanation:
The question is not complete, the complete question is Suppose you revolve the plane region completely about the given line to sweep out a solid of revolution. Describe the solid. Then find its surface area in terms of pi.
i) about the y axis
ii) about the x axis
Also the image is attached below.
Answer:
i) about the y axis
If it is revolved about the y axis, the solid produced is a cone with a radius of of 4 units (r = 4) and a height of 3 units (h = 3). The surface area of the cone is:
Surface area = πr (r + √(r² + h²)) = π × 4 (4 + √(4² + 3²)) = 4π (4 + √25) = 4π (4 + 5) = 4π × 9 = 36π unit²
ii) about the x axis
From the image attached, If it is revolved about the x axis, the solid produced is a cone with a radius of of 3 units (r = 3) and a height of 4 units (h = 4). The surface area of the cone is:
Surface area = πr (r + √(r² + h²)) = π × 3 (3 + √(4² + 3²)) = 3π (3 + √25) = 3π (3 + 5) = 3π × 8 = 24π unit²
mathew lucy and finley sold a total of 56 games at a car boot sale the ratio of games that they each sold is 2:5:1 how many more games did lucy sell than finley
Answers
The number of more games that Lucy sells than Finley will be 28 games.
What is the solution to the equation?The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.
Mathew, Lucy, and Finley sold a total of 56 games at a car boot sale. The ratio of games that they each sold is 2:5:1.
Let 'x' be the common factor. Then the equation is given as,
2x + 5x + 1x = 56
8x = 56
x = 7
Then the number of more games that Lucy sells than Finley will be given as,
⇒ 5 × 7 - 1 × 7
⇒ 35 - 7
⇒ 28
The number of more games that Lucy sells than Finley will be 28 games.
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Calculate the 95onfidence interval for the true population mean based on a sample with =225, =8.5, and =45. function
Answers
The true population mean is (222.52, 227.48) with a 95% confidence interval.
What is the critical factor?The critical factor for a 90% confidence interval for the true population mean is given by;
Critical factor = (x-μ)/(s/√n)
where, x = sample mean repair cost
s = standard deviation of a sample
n = sample of stereos
μ = critical value
⇒ P(-1.96< (x-μ)/(s/√n) < 1.96) = 0.95
⇒ P(-1.96×(s/√n) < (x-μ) < 1.96×(s/√n)) = 0.95
⇒ P(x - 1.96×(s/√n) < μ < x + 1.96×(s/√n)) = 0.95
95% confidence interval for
⇒ μ = (x - 1.96×(s/√n) , x + 1.96×(s/√n))
Here, x = 225, s = 8.5, and n = 45
⇒ μ = (225- 1.96×(10.81/√13) , 225+ 1.96×(10.81/√13))
⇒ μ = (222.52, 227.48)
Hence, the true population mean is (222.52, 227.48) with a 95% confidence interval.
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The question seems to be incomplete the correct question would be
Calculate the 95% confidence interval for the true population mean based on a sample with x=225, s=8.5, and n=45.
How do I write this as a equation?Max gets paid $17.50 hourly for his job.
Answers
Answer:
y=17.50x
Step-by-step explanation:
In this case Y is his total income for the number of hours he works. X is the number of hours he works. 17.50 is his hourly income
The equation to represent the given phrase is y= 17.50x.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
Given that, Max gets paid $17.50 hourly for his job.
Let the total income of Max be y and the income Max gets paid hourly be x.
Now, the equation is
y= 17.50x
Therefore, the equation is y= 17.50x.
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True or False. When flipping a penny 14 times the penny likelihood of landing on heads is 7 times.
Answers
Answer:
True
Step-by-step explanation:
Since a penny has head and tails, each has 1/2 chance to land on heads or tales, so 14*1/2=7, so true.
a nutritionist wanted to find out if coffee and tea, as served in restaurants, differed in caffeine content. she went to 30 restaurants. in 15 randomly selected restaurants, she ordered coffee; in the other 15 restaurants, she ordered tea. what statistical test should the nutritionist use to see if coffee and tea differ in mean caffeine content?
Answers
The nutritionist should perform hypothesis testing followed by Independent T-test to see if coffee and tea differ in mean caffeine content .
We need to Know about Hypothesis testing and independent t test to answer this-
Hypothesis testing is a type of statistical test that is used to comapare data and drawing conclusion from them.
An independent t-test is a statistical test that determines whether the means of two unrelated groups are significantly different from each other.
We can find the difference caffeine content following these steps -
1)H0=Null hypothesis=tea and coffee has same caffeine level
HA=tea and coffee has different caffeine level
2)The independent samples t-test is utilized to determine whether two different sample means come from the same population or whether they come from two distinct populations with different mean values. Two populations can be considered independent when the data in one group is not connected to the data in the other group.
The t value obtained should be then performed under hypothesis testing.
3)And the calculated T value should be comaperd with the desired significance level (generally =0.05) and if the t value comes in between the critical values the nutritionist can assume that both tea and coffee has same caffeine level in this null hypothesis will be accepted.
Whereas if the calculated t value doesn't falls in between the critical value then the nutritionist can assume that tea and coffee has different caffeine level.
Hence null hypothesis will be rejected.
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Jack claims that the average score for the final exam is less than 60%. You gather a sample of 51 test papers and calculate the sample mean to be 57% and the population standard deviation to be 12%. The significant level is 0. 10. A researcher said that the average weight of high schools' students in Riyadh city is 230 pounds or less. Another researcher claims that the average wight of high schools' students is grater than 230 pounds. Test the claim • a=0. 1. Ž=232 • S=10 n=52
Answers
To test the claim about the average weight of high school students in Riyadh city, we can use a one-sample t-test. Here are the steps to perform the test:
Define the null hypothesis (H0) and the alternative hypothesis (Ha):
Null hypothesis (H0): The average weight of high school students in Riyadh city is 230 pounds or less.
Alternative hypothesis (Ha): The average weight of high school students in Riyadh city is greater than 230 pounds.
Set the significance level (α): The significance level is given as α = 0.1, which means we are willing to accept a 10% chance of making a Type I error.
Calculate the test statistic:
Sample mean (): 232
Population standard deviation (σ): 10
Sample size (n): 52
The test statistic is calculated using the formula:
t = (- μ) / (σ / √n)
where μ is the hypothesized population mean.
Plugging in the values, we get:
t = (232 - 230) / (10 / √52)
Determine the critical value: Since the alternative hypothesis is one-tailed (greater than), we need to find the critical value from the t-distribution table at the given significance level and degrees of freedom (n - 1 = 52 - 1 = 51).
Compare the test statistic with the critical value:
If the test statistic is greater than the critical value, we reject the null hypothesis.
If the test statistic is less than or equal to the critical value, we fail to reject the null hypothesis.
Calculate the p-value: If desired, you can calculate the p-value associated with the test statistic and compare it with the significance level. If the p-value is less than the significance level, we reject the null hypothesis.
Please provide the critical value associated with the given significance level (α) and the degrees of freedom (df = n - 1).
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PLS HELP!!
What is the distance between C(2, 1) and D(5, 5)?
Answers
Answer:
3,4
Step-by-step explanation:
5,5
- 2,1
======
3,4
Answer:
3,4
Step-by-step explanation:
you take 5,5 and subtract 2,1
An artists creates a scale model of a sculpture with a scale of 2 inches = 5 feet. if the scale moderl of the sculpture measures 8 inches tall, how many feet tall is the actual sculpture?
Answers
Answer:
The actual sculpture is 20 feet.
-
Step-by-step explanation:
\( \frac{2 \: inches}{5 \: feet} = \frac{8 \: inches}{x} \\ \\ \frac{40}{2} = \frac{2x}{2} \\ \\ x = 20\)
Complete the inequality so that it represents the whole-number values that side a could be to create a triangle.
Answers
13 is the inequality so that it represents the whole-number values.
What is Triangle Inequality Theorem?
Triangle inequality, in Euclidean figure, theorem that the sum of any two sides of a triangle is lesser than or equal to the third side; in symbols, a b ≥ c. In substance, the theorem states that the shortest distance between two points is a straight line.
the Triangle Inequality Theorem, which states that
the sum of the lengths of two sides of a triangle must always be greater than the length of the third side
a = c + b
= 7 + 6
= 13
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Write the sentence as an equation.
the quotient of j and 11 is equal to 367
Type a slash (/) if you want to use a division sign.
Submit
Answers
Answer: j/11 = 367
Step-by-step explanation:
Keywords: QUOTIENT. Quotient indicates a division answer. The quotient, in this case, is 367.
It also makes sense that j is the dividend and 11 is the divisor.
---
For the SOLVED version: j = 4037.
Multiply 11 on both sides, canceling the 11 on one side and getting 4037 when you multiply 11 by 367.
Answer:
J/11 = 367; this is the equation as When J is divided by 11 it answers to 367
Step-by-step explanation:
total answer;
J = 367(11)
J= 4037
. a cell phone company offers two plans for minutes. plan a: $20 per month and $1 for every one hundred texts. plan b: $50 per month with free unlimited texts. how many texts would you need to send per month for plan b to save you money?
Answers
Answer:
Over 3000 texts/mo
Step-by-step explanation:
A $30 + $1/100 texts
B $50
For option B to save money, you would have to send an additional $30 worth of texts
$30 * 100 texts = 3000
If you send more than 3000 texts per month, plan B will save you money compared to plan A.
To find out how many texts you would need to send per month for plan b to save you money, you need to compare the cost of both plans for the same number of texts.
Let's assume you send x number of texts per month.
For plan A, you would pay $20 per month plus $0.01 per text, so your total cost would be $20 + $0.01x.
For plan B, you would pay a flat fee of $50 per month, regardless of how many texts you send.
So to find out when plan B becomes cheaper than plan A, you need to solve the inequality:
$50 < $20 + $0.01x
Subtracting $20 from both sides gives:
$30 < $0.01x
Dividing both sides by $0.01 gives:
x > 3000
The calculation compares the total cost of both plans for a certain number of texts. Plan A has a fixed monthly fee of $20, and an additional cost of $0.01 per text. Plan B, on the other hand, has a flat monthly fee of $50 with unlimited texts. By setting these two costs equal to each other, you can solve for the number of texts that makes Plan B cheaper than Plan A. In this case, sending more than 3000 texts per month makes Plan B the cheaper option.
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Suppose a least-squares regression line is given by y=4. 302x−3. 293. What is the mean value of the response variable if x=20?
Answers
The mean value of the response variable is 82.747.
Regression line
The equation of the line with the best fit for the provided data points is determined via linear regression. A linear relationship between the input variable x and the output variable y is modelled by linear regression.
Here, regression line;
y= 4.302x - 3.293 --------(1)
Value of x is given; x = 20
Substitute the value of x in equation (1), we get
y = 4.302 X 20 - 3.293
y = 86.04 - 3.293
y = 82.747
Thus, the mean value of the response variable is 82.747.
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Pls help I need it ASAP it’s easy tho
Answers
Answer:
Step-by-step explanation:
360/2=180
5x+4x=180
9x=180
x=20
5×20:4×20
100:80
Anna opened a savings account and deposited $300.00 as principal. The account earns 1%
interest, compounded annually. What is the balance after 2 years?
Answers
Answer:
$6
Step-by-step explanation:
First, converting R percent to r a decimal
r = R/100 = 1%/100 = 0.01 per year,
then, solving our equation
I = 300 × 0.01 × 2 = 6
I = $ 6.00
The simple interest accumulated
on a principal of $ 300.00
at a rate of 1% per year
for 2 years is $ 6.00.
Wendell is looking over some data regarding the strength, measured in Pascals (Pa), of some building materials and how the strength relates to the length. The data are represented by the exponential function f(x)
Answers
The Logarithmic function is \(g(y)=\log_2y\).
\(x=3\) is the length corresponding to the strength 8 Pa
The relation between the length and the strength of the building materials is given by an exponential function, \(f(x) = 2^x\) ,
where x is the length.
We have to convert this function into a logarithmic function where the strength is given as 8 Pa.
Let \(y = f(x)\)
i.e., \(y=2^x\) where y represents the strength.
We know that logarithmic function is the inverse of the exponential function up to the bases.
Taking Logarithm on both sides, we get,
\(log y = x log 2\)
⇒ \(x=log_2y\)
i.e., the length is given by the function \(g(y)=\log_2y\) when y, the strength is known. This is the required logarithmic function.
So when the strength, y = 8 Pa,
the length, \(x = log_2 8\) ⇒ \(x=log_2 2^3\)
⇒ \(x=3\) is the length corresponding to the strength 8 Pa.
The question provided is incomplete. Here you can find the complete question:
Wendell is looking over some data regarding the strength, measured in Pascals (Pa), of some building materials and how the strength relates to the length. The data are represented by the exponential function f(x) = \(2^x\), where x is the length. Explain how he can convert this equation to a logarithmic function when strength is 8 Pascals.
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When cooper was 15 years old, he scored an 85 on an iq test. he took the test again when he was 35 years old and scored an 85 again. this indicates that the iq test is highly: __________
Answers
Answer:
When cooper was 15 years old, he scored an 85 on an iq test. he took the test again when he was 35 years old and scored an 85 again. this indicates that the iq test is highly: __________
Reliable
Because his scores were so close together the test would be considered as Reliable.
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A man is twice as old as sum of ages of his two sons. After ten years the sum of his age and ages of his sons is equal to 105 then present age of man is:
50
60
70
80
Answers
The present age of the man is 70
What are the linear equations that represent the question?a = 2b equation 1
105 = a + b equation 2
Where:
a = man's age b = sum of his son's ageWhat is the man's present age?Substitute for a in equation 2
105 = 2b + b
105 = 3b
3b = 105
b = 35
Substitute for b in equation 1 : a = 2 x 35 = 70
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if the odds in favor of a horse winning a race is 4:7 , what is the probability of the horse winning the race?
Answers
The probability of the horse winning the race is 4/11 or approximately 0.36 or 36%.
The odds in favor of a horse winning a race is expressed as a ratio of the number of favorable outcomes to the number of unfavorable outcomes. In this case, the odds in favor of the horse winning the race is 4:7.
This means that for every 4 favorable outcomes, there are 7 unfavorable outcomes.
To determine the probability of the horse winning the race, we can use the formula:
Probability = favorable outcomes / total outcomes
In this case, the total number of outcomes is the sum of the favorable and unfavorable outcomes, which is 4 + 7 = 11.
Therefore, the probability of the horse winning the race is:
Probability = 4 / 11
This means that the horse has a probability of approximately 0.36 or 36% of winning the race.
In summary, the odds in favor of a horse winning a race of 4:7 means that there are 4 favorable outcomes for every 7 unfavorable outcomes.
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An object is moving with a uniform acceleration a= 2t - b ms^2 determine the functions for:
A) velocity v (ms^-1) - given v (0) = 10ms^-1 ?
B) displacement s (m) - given s (0) = 5m ?
C) calculate the values of v and s for:
i) t = 2s
ii) t = 5s
b= 3/5
Answers
Answer:
Acceleration
\(a=\left(2t-\dfrac{3}{5}\right)\:\sf ms^{-2}\)
Part (A)
Velocity
\(\begin{aligned}\displaystyle v= \int a\:dt & =\int \left(2t-\dfrac{3}{5}\right)\:dt\\\\ & = t^2 -\dfrac{3}{5}t+C \end{aligned}\)
\(\begin{aligned} \textsf{As }\:v(0)=10 \implies (0)^2-\dfrac{3}{5}(0)+C & =10\\C & = 10 \end{aligned}\)
\(\implies v(t)=\left(t^2-\dfrac{3}{5}t+10\right)\: \sf ms^{-1}\)
Part (B)
Displacement
\(\begin{aligned}\displaystyle s= \int v\:dt & =\int \left(t^2-\dfrac{3}{5}t+10\right)\:dt\\\\ & = \dfrac{1}{3}t^3-\dfrac{3}{10}t^2+10t+C \end{aligned}\)
\(\begin{aligned} \textsf{As }\: s(0)=5 \implies \dfrac{1}{3}(0)^3-\dfrac{3}{10}(0)^2+10(0)+C & =5\\C & = 5\end{aligned}\)
\(\implies s(t)=\left(\dfrac{1}{3}t^3-\dfrac{3}{10}t^2+10t+5\right)\: \sf m\)
Part (C)
(i) t = 2 s
\(v(2)=(2)^2-\dfrac{3}{5}(2)+10=\dfrac{64}{5}=12.8\: \sf ms^{-1}\)
\(s(2)=\dfrac{1}{3}(2)^3-\dfrac{3}{10}(2)^2+10(2)+5=\dfrac{397}{15}=26.47\: \sf m\:(2\:dp)\)
(ii) t = 5 s
\(v(5)=(5)^2-\dfrac{3}{5}(5)+10=32\: \sf ms^{-1}\)
\(s(5)=\dfrac{1}{3}(5)^3-\dfrac{3}{10}(5)^2+10(5)+5=\dfrac{535}{6}=89.17\: \sf m\:(1\:dp)\)
An investment has grown from $50,000 to $100,000 (which means it doubles) in 5 years compounding quarterly.
What was the interest rate? Round to the nearest tenth of a percent.
Answers
Answer:
We can use the formula for compound interest to find the interest rate:
A = P*(1 + r/n)^(n*t)
where A is the final amount, P is the initial principal, r is the annual interest rate, n is the number of compounding periods per year, and t is the time in years.
In this case, P = $50,000, A = $100,000, n = 4 (since compounding is quarterly), and t = 5. We want to solve for r.
First, we can find the factor by which the initial amount is multiplied after each compounding period:
(1 + r/n)
Since the investment doubles in value, this factor is 2. Therefore,
2 = (1 + r/4)^(4*5)
Simplifying this equation, we get:
2 = (1 + r/4)^20
Taking the 20th root of both sides, we get:
1 + r/4 = 2^(1/20)
Subtracting 1 from both sides and multiplying by 4, we get:
r = 4*(2^(1/20) - 1)
Using a calculator, we get:
r ≈ 6.1%
Therefore, the interest rate is approximately 6.1% per year, compounded quarterly.
Step-by-step explanation:
Investigators measure the temperature of a body found inside a home. The body has cooled to 76.5F°. How long has it been since they died?
Answers
Answer: The cooling of a body can be modeled using Newton's Law of Cooling, which states that the rate of cooling of an object is proportional to the temperature difference between the object and its surroundings. The equation for Newton's Law of Cooling is:
T(t) = T_0 + (T_s - T_0) * e^(-kt)
where T(t) is the temperature of the body at time t, T_0 is the initial temperature of the body, T_s is the temperature of the surroundings, k is the cooling constant, and e is the base of the natural logarithm.
Assuming that the temperature of the surroundings is constant at 68°F, we can use the given information to solve for t:
76.5°F = 68°F + (T_0 - 68°F) * e^(-kt)
Simplifying this equation, we get:
8.5°F = (T_0 - 68°F) * e^(-kt)
Taking the natural logarithm of both sides, we get:
ln(8.5°F / (T_0 - 68°F)) = -kt
Solving for t, we get:
t = -ln(8.5°F / (T_0 - 68°F)) / k
The cooling constant k depends on various factors such as the body's mass, the body's surface area, and the body's initial temperature. For a human body, k is typically estimated to be around 0.00087 per minute.
Assuming that the initial temperature of the body was 98.6°F (the average temperature of a living human body), we can plug in the values and solve for t:
t = -ln(8.5°F / (98.6°F - 68°F)) / 0.00087
t ≈ 16.5 hours
Therefore, it has been approximately 16.5 hours since the person died.
Step-by-step explanation:
Jim is making a mixture in science class. Jim uses $5times 10{-3}$ liters of water. He uses $9times 10{-1}$ liters of salt.
Answers
When comparing exponential form of water and salt the result is obtained as option B: Jim uses about 1/200 as much water as salt.
What is an exponent?
The way of representing huge numbers in terms of powers is known as an exponent. Exponent, then, is the number of times a number has been multiplied by itself.
Amount of water used by Jim expressed in exponent form = 5 × 10^-3 liters
Amount of salt used by Jim expressed in exponent form = 9 × 10^-1 liters
To compare the measurements use the arithmetic operation of division.
Amount of water used / Amount of salt used
Substitute the value into the expression -
= (5 × 10^-3) / (9 × 10^-1)
= (5/9) × [10^(-3) - (-1)]
= (5 × 10^-2)/9
Simplify the expression further -
= 5/9 × 10²
= 5/900
= 1/180 ≈ 1/200
Therefore, the comparison gives result 1/200.
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Analyze the diagram below and complete the instructions that follow.
K
B
A
гс
F
E
Given that ZCFE ZCFA, mZCFB = 68°, and mZEFD= 62°, find the measure of ZAFD.
Answers
The measure of ZAFD is 50 degrees.
Based on the given information:
ZCFE is congruent to ZCFA.
mZCFB = 68°.
mZEFD = 62°.
To find the measure of ZAFD, we can use the fact that angles in the same segment of a circle are equal.
Since ZCFE and ZCFA are congruent, angle ZCFE is equal to angle ZCFA.
Therefore, mZCFA = mZCFE.
Now, let's find the measure of angle ZCFE:
mZCFE = mZCFB + mZEFD (Angle Addition Postulate)
mZCFE = 68° + 62°
mZCFE = 130°
Since ZCFA is congruent to ZCFE, we can conclude that mZCFA is also equal to 130°.
Now, to find the measure of ZAFD, we need to consider the angles in the quadrilateral ZAFD.
The sum of the angles in a quadrilateral is always 360°.
mZAFD + mZAFB + mZBFD + mZBFA = 360°
We know that mZAFB and mZBFD are equal to 90° because they are right angles (angle AFB and angle BFD are right angles in the diagram).
Therefore, we can rewrite the equation as:
mZAFD + 90° + 90° + mZBFA = 360°
Simplifying:
mZAFD + 180° + mZBFA = 360°
Rearranging the equation:
mZAFD + mZBFA = 360° - 180°
mZAFD + mZBFA = 180°
We know that mZBFA is equal to mZCFA, which is 130°.
Substituting the known values into the equation:
mZAFD + 130° = 180°
Subtracting 130° from both sides:
mZAFD = 180° - 130°
mZAFD = 50°
Therefore, the measure of ZAFD is 50 degrees.
for such more question on measure
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Which number is equivalent to 3^(4)÷3^(2) This problem comes straight from a standardized test given in New York in 2014.
Answers
3⁴ = 3² (9)
3²
By subtracting the exponents due to the similar bases.
The number equivalent is 9.
Can somebody plz answer both these questions correctly thanks!! (Word problem)
WILL MARK BRAINLIEST WHOEVER ANSWERS FIRST :DDD
Answers
Answer:
a. 40%
b. 7.5%
Step-by-step explanation:
a. 60/ 150 x 100
b. 4.5/ 60 x 100
Given that z is a standard normal random variable, what is the value of z if the area to the right of z is 0.5?
a. 0.1915
b. 0.0000
c. 1.0000
d. 0.3413
Answers
Answer:
B
Step-by-step explanation:
To find the value of z such that the area to the right of z is 0.5, we can use the standard normal distribution table (also known as the z-table). The z-table provides the cumulative probability to the left of a given z-value.
Since the area to the right of z is 0.5, the area to the left of z is also 0.5. We need to find the z-value that corresponds to a cumulative probability of 0.5 (or 50%).
Referring to the z-table, we find that a cumulative probability of 0.5 corresponds to a z-value of 0. This means that the area to the left of 0 is 0.5, and therefore, the area to the right of 0 is also 0.5.
Thus, the value of z when the area to the right of z is 0.5 is 0.
Therefore, the correct option is b. 0.0000.
Mrs. Carver wants to add wall–to–wall tile to the science lab. If she plots the layout of the science lab on a graph with the vertices A(–7, 8), B(3, 8), C(3, –2), and D(–7, –2), what is the area of the science lab?
Answers
Answer:
o dpB
Step-by-step explanation:
Solve each system by substitution. Show all work.
4x + y = 0
-x - 2y =7
Answers
4x + y = 0
-x - 2y =7
with - x - 2y = 7
we have x = -2y - 7
we replace x by this value in the first one
4 * (-2y - 7) + y = 0
- 8y - 28 + y = 0
- 7y = 28
y = 28/(-7)
y = - 4
since 4x + y = 0
we have 4x + (-4) = 0
4x = 4
x = 1
(1 ; -4)