Answer: Hi!
First, UxV = sin(a)*IUI*IVI
where a is the angle between U and V, in this case 45°.
First, the cross product of UxV points:
Here you can use the right hand method,
Put your hand flat, so the point of your fingers point in the same direction that the first vector, in this case U, so your fingers will point to the north.
Now roll your fingers in the direction of the second vector, so here you will roll your fingers in the northeast direction. Now you will see that your thumb is pointing down, so the cross product of UxV points down.
And the magnitude is 6*5*sin(45) = 21.213
The cross-product u×v points: Option D: Down, and its magnitude |u×v| evaluates to [tex]|u \times v| = 15\sqrt{2}[/tex]
How to find the cross product of two vectors?Suppose that two vectors in consideration are u and v, then their cross product is evaluated as:
[tex]u \times v = |u|.|v|.sin(\theta)\hat{n}[/tex]
where [tex]\hat{n}[/tex] is the normal unit vector whose direction is decided by right hand thumb rule, and theta is the angle between u and v vector.
The two bars around a vector represents the magnitude of that vector.
Cross product returns the result as a vector itself.
For this case, we have:
|u| = 6 points, its direction is in north|v| = 5 points, its direction is in northeastThus, as north and northeast have 45 degrees in between them, therefore, we get:
[tex]u \times v = 6\times 5 \times sin(45^\circ) \hat{n} = 15\sqrt{2} \: \hat{n}[/tex]
Directing index finger of right hand to north direction, and middle to northeast makes the thumb go down, therefore, the direction of normal vector (and therefore direction of the resultant cross product vector too) is downside of this whole north south east west plane.
The magnitude of cross product is [tex]|u \times v| = 15\sqrt{2}[/tex]
Thus, the cross-product u×v points: Option D: Down, and its magnitude |u×v| evaluates to [tex]|u \times v| = 15\sqrt{2}[/tex]
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Show that 2 - sqrt(2) is irrational
Answer:
This proof can be done by contradiction.
Let us assume that 2 - √2 is rational number.
So, by the definition of rational number, we can write it as
[tex]2 -\sqrt{2} = \dfrac{a}{b}[/tex]
where a & b are any integer.
⇒ [tex]\sqrt{2} = 2 - \dfrac{a}{b}[/tex]
Since, a and b are integers [tex]2 - \dfrac{a}{b}[/tex] is also rational.
and therefore √2 is rational number.
This contradicts the fact that √2 is irrational number.
Hence our assumption that 2 - √2 is rational number is false.
Therefore, 2 - √2 is irrational number.
By assuming 2 - √2 is rational and showing this leads to a contradiction as both a and b would have to be even, which violates the initial condition that they have no common factors other than 1, it has been proven that 2 - √2 is irrational.
To show that 2 - √2 is irrational, we shall assume the opposite, that 2 - √2 is rational, and look for a contradiction. By definition, if 2 - √2 is rational, it can be expressed as a fraction of two integers, say √2 = a/b, where a and b are integers with no common factors other than 1, and b is not zero.
We can rearrange the equation to obtain √2 = 2 - a/b. Multiplying both sides by b gives us b√2 = 2b - a. Squaring both sides of this equation gives us 2b² = (2b - a)² = 4b² - 4ab + a².
Rearranging to solve for a² gives us a² = 2b², implying that a² is an even number, and hence a must be even. Let's say a = 2k for some integer k. Substituting this back into the equation gives us (2k)² = 2b², which simplifies to 4k² = 2b², and further to 2k² = b². This implies that b² is also even, which means b is even as well.
However, this is a contradiction because we assumed that a and b have no common factors other than 1; yet, we've just shown that both must be even, so they have at least a factor of 2 in common. This contradiction shows that the assumption that 2 - √2 is rational is false, and therefore 2 - √2 must be irrational.
A box holding pennies, nickels and dimes contains thirteen coins with a total value of 83 cents. How many coins of each type are in the box? (These are US coins; a penny is 1 cent, a nickel is 5 cents, and a dime is 10 cents.)
Answer:
The number of pennies,nickels and dimes are (p,n,d)=(3,4,6).
Further explanation:
Given:
A box holding pennies, nickels and dimes contains thirteen coins in a box.
Total value is 83 cents.
Calculation:
Consider p,n and d be the number of pennies, nickel and dimes.
Now, total is 13 coins so [tex]p+n+d=13[/tex]
As we know that these following are US coin.
Penny=1 cent
Nickel=5 cents
Dime=10 cents
Step 1:
The value is already given as 83 cents that is 80+3 cents.
80 cents can be possible in many combinations as follows:
(N,D)=(0,8),(2,7),(4,6),(6,5),(8,4),(10,3),(12,2),(14,1),(16,0)
It is given that the total number of cents is 13 so we choose (4,6) as (n,d) .
So the value of nickel n=4
Dimes d=6
Step 2:
The value of p is calculated as follows:
Substitute 4 for n, 6 for d in equation [tex]p+n+d=13[/tex] as follows:
[tex]p+4+6=13[/tex]
[tex]p+10=13[/tex]
[tex]p=13-10[/tex]
p=3
Thus, the number of pennies,nickels and dimes are (p,n,d)=(3,4,6).
The problem can be represented by two equations based on the total coins and their total value. The number of pennies, nickels, and dimes cannot be precisely determined without extra constraints or assumptions.
Explanation:This problem is about the trio of pennies, nickels, and dimes, and their corresponding values; 1 cent, 5 cents, and 10 cents, respectively. Let's denote the number of pennies as P, nickels as N, and dimes as D.
From the problem, we know two key pieces of information:
There are 13 coins in total. Therefore: P + N + D = 13 The total value of all the coins is 83 cents. So: P(1 cent) + N(5 cents) + D(10 cents) = 83 cents
Mind this information, we'll try to solve it using the system of linear equations method. However, it's impossible to precisely calculate the number of each coin type without additional constraints or assumptions. This math problem is a common example of how real-life situations can pose complex mathematical challenges, requiring more information or advanced techniques of problem solving.
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The owner of a local health food store recently started a new ad campaign to attract more business and wants to test whether average daily sales have increased. Historically average daily sales were approximately $2,700. After the ad campaign, the owner took another random sample of forty-five days and found that average daily sales were $2,984 with a standard deviation of approximately $585. Calculate the upper bound of the 95% range of likely sample means for this one-sided hypothesis test using the CONFIDENCE.NORM function.
Answer:
The upper limit of the confidence interval is 3127 $/day.
Step-by-step explanation:
With the new sample we can estimate the one-sided 95% confidence interval.
For this interval (one sided, 95% of confidence), z=1.64.
The number of observations (n) is 45 days.
The mean is 2984 and the standard deviation is 585.
We can estimate the upper limit of the confidence interval as
[tex]UL=X+z*s/\sqrt{n} \\UL = 2984 + 1.64*585/\sqrt{45}=2984+ 959.4/6.708=2984+143=3127[/tex]
Suppose that 25 days are chosen at random from a calendar. Explain why at least 3 of the 25 days must lie in the same month. Do some research to find the name of the principle you've used, and clearly describe it in your own words.
Answer:
Step-by-step explanation:
If you have to choose 25 days, you have to think how many months there are.
The year has 12 months, so, if you divide 25 days /12 months =2,08333. (more than 2--> 3)
So if you happen to choose 2 of every month you have 24 days chosen, you have to pick one extra day and will add 3 to the month it belongs.
In any way you choose, you an be sure there is at least one month with 3 or more days chosen.
This problem has been solved!
See the answer
Accuracy and Precision
For the following, determine whether the information is accurate, precise, both or neither.
1. During gym class, four students decided to see if they could beat the norm of 45 sit-ups in a minute. The first student did 64 sit-ups, the second did 69, the third did 65, and the fourth did 67.
2. The average score for the 5th grade math test is 89.5. The top 5th graders took the test and scored 89,
93, 91 and 87.
3. Yesterday the temperature was 89 �F, tomorrow it�s supposed to be 88 �F and the next day it�s supposed to be 90 �F, even though the average for September is only 75 �F degrees!
4. Four friends decided to go out and play horseshoes. They took a picture of their results shown to the right:
5. A local grocery store was holding a contest to see who could most closely guess the number of pennies that they had inside a large jar. The first six people guessed the numbers 735, 209, 390, 300, 1005 and
689. The grocery clerk said the jar actually contains 568 pennies.
Accuracy and Precision
For the following, determine whether the information is accurate, precise, both or neither.
1. During gym class, four students decided to see if they could beat the norm of 45 sit-ups in a minute. The first student did 64 sit-ups, the second did 69, the third did 65, and the fourth did 67.
2. The average score for the 5th grade math test is 89.5. The top 5th graders took the test and scored 89,
93, 91 and 87.
3. Yesterday the temperature was 89 �F, tomorrow it�s supposed to be 88 �F and the next day it�s supposed to be 90 �F, even though the average for September is only 75 �F degrees!
4. Four friends decided to go out and play horseshoes. They took a picture of their results shown to the right:
5. A local grocery store was holding a contest to see who could most closely guess the number of pennies that they had inside a large jar. The first six people guessed the numbers 735, 209, 390, 300, 1005 and
689. The grocery clerk said the jar actually contains 568 pennies.
Answer:
1. Precise
2.Both
3.Precise
5.Neither
Step-by-step explanation:
Accuracy is the closeness of a measured value to a standard value.
Precision is the closeness of two or more measurements to each other.
1.The norm is 45 sit-ups in a minute.The students did, 64, 69,65 and 67. Values are not accurate compared to standard value 45.
Values are precise
Answer--Precise
2. Average score is 89.5
Scores are 89,93,91,87
Values are precise i.e a difference of 2 from each score
Values are accurate because the average score is 90 thus compared to the known average score of 89.5 they are accurate.
Answer-Both
3. Yesterday temperature=89
Tomorrow=88
Next day=90
Average =75
Values are precise i.e. difference of ± 1°
Values are not accurate compared to the average temperatures of 75 F
Answer---Precise
5. The jar contained 568 pennies
The 6 people guessed the numbers as
735,209,390,300,1005, 689
The values are not precise
The values are not accurate
Answer---Neither
Accuracy refers to the closeness of a measurement to the true value, while precision is about the repeatability of measurements. The student examples show diverse cases where results can be accurate, precise, both, or neither. Without the actual value or other measurements, assessment of accuracy and precision is often not possible.
Explanation:The terms accuracy and precision have distinct meanings in science. Accuracy refers to how close a measurement is to the correct or accepted value. In contrast, precision indicates how close a set of measurements are to each other, demonstrating the consistency of the measurements.
The gym class students' results are precise because their sit-up counts are close to each other but we don't have a 'true value' with which to assess accuracy.The 5th graders' math test scores are both precise and accurate as they are close to each other and to the average score of 89.5.The temperatures are neither precise nor accurate, as they are not close to each other (relative to the usual fluctuation of daily temperatures) nor close to the average September temperature of 75 °F.Without the results shown to the right, we cannot assess the accuracy or precision of the horseshoe game.The guesses for the number of pennies are neither accurate nor precise; the values are not close to one another and do not closely approximate the actual number of pennies (568).
Evaluate the surface integral ∫∫ F.ds for the given vector field F and the oriented surface S. In other words, find the flux of F across S. For closed surfaces, use the positive (outward) orientation.
F(x,y,z)=xi+yj+5k
S is the coundary of the region enclosed by the cylinder x^2+z^2=1 and the planes y=0 and x+y=2
Use the divergence theorem.
[tex]\vec F(x,y,z)=x\,\vec\imath+y\,\vec\jmath+5\,\vec k\implies\mathrm{div}\vec F(x,y,z)=2[/tex]
By the divergence theorem,
[tex]\displaystyle\iint_S\vec F\cdot\mathrm d\vec S=\iiint_R\mathrm{div}\vec F\,\mathrm dV[/tex]
where [tex]R[/tex] is the region with boundary [tex]S[/tex].
Compute the latter integral in cylindrical coordinates, taking
[tex]\begin{cases}x=r\cos\theta\\y=y\\z=r\sin\theta\end{cases}\implies\mathrm dV=r\,\mathrm dr\,\mathrm d\theta\,\mathrm dy[/tex]
[tex]\displaystyle\iint_R2\,\mathrm dV=2\int_0^{2\pi}\int_0^1\int_0^{2-r\cos\theta}r\,\mathrm dy\,\mathrm dr\,\mathrm d\theta=\boxed{4\pi}[/tex]
Adam and brianna each made a number pattern. Adam's pattern starts with number 3 and follows rule add 6. What are first four terms of Adam's pattern?
Answer:3 9 15 21
Step-by-step explanation:
3+6=9
9+6=15
15+6=21
or think of it as 3+3+3+3+3+3+3=21
Final answer:
Adam's number pattern starts with 3, and by adding 6 to each previous term, the first four terms are 3, 9, 15, and 21.
Explanation:
The student is asking about creating a number pattern based on a given rule. In this instance, the pattern begins with the number 3, and the rule is to add 6 to the previous term to get the next term. To determine the first four terms of Adam's pattern, we start with the number 3 and repeatedly add 6.
First term: 3 (starting number)
Second term: 3 + 6 = 9
Third term: 9 + 6 = 15
Fourth term: 15 + 6 = 21
Therefore, the first four terms of Adam's number sequence are 3, 9, 15, and 21.
Digoxin (Lanoxin) is available for parenteral pediatric use in a concentration of 0.1 mg/mL. How many milliliters would provide a dose of 40 μg?
To give a dose of 40 μg of Digoxin using a solution with a concentration of 0.1 mg/mL, you should administer 0.4 mL of the solution. This is achieved by first converting the dose to the same units as the concentration, then applying the formula: Volume (mL) = Dose (mg) / Concentration (mg/mL).
Explanation:To determine how many milliliters would provide a dose of 40 μg of Digoxin, we first need to convert the dose from μg to mg because the concentration provided is in mg/mL. 1 mg is equivalent to 1000 μg. Hence, 40 μg would be the same as 0.04 mg.
Since the concentration of the Digoxin solution is 0.1 mg/mL, this means that every 1 mL of the solution contains 0.1 mg of Digoxin. Therefore, the volume in milliliters that would provide a dose of 0.04 mg (or 40 μg) can be calculated by the following equation: Volume (mL) = Dose (mg) / Concentration (mg/mL).
In this case, the calculation is: Volume = 0.04 mg / 0.1 mg/mL = 0.4 mL. Therefore, 0.4 mL of the solution will provide a dose of 40 μg of Digoxin.
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To provide a dose of 40 μg using a concentration of 0.1 mg/mL, 2.5 mL of the digoxin solution is needed.
Explanation:To find the volume of digoxin (Lanoxin) needed to provide a dose of 40 μg, we can use the formula:
C₁V₁ = C₂V₂
Given:
C₁ = 0.1 mg/mL (0.1 mg per 1 mL)
C₂ = 40 μg (0.04 mg)
V₂ = ? mL (unknown volume)
Rearranging the formula, we get:
V₂ = (C₁V₁) / C₂
Substituting in the given values:
V₂ = (0.1 mg/mL) / (0.04 mg) = 2.5 mL
Therefore, 2.5 milliliters of the digoxin solution would provide a dose of 40 μg.
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In 1970 the male incarceration rate in the U.S. was approximately 190 inmates per 100,000 population. In 2008 the rate was 960 inmates per 100,000 population. What is the percent increase in the male incarceration rate during this period?
Answer:
40.53%
Step-by-step explanation:
[tex]Percentage Increase = \frac{New Value - Old Value}{Old Value}\times100[/tex]
Here, New Value = 960÷100,000
Old Value = 190÷ 100,000
∴ [tex]Percentage Increase = \dfrac{\frac{960}{100,000} - \frac{190}{100 ,000} }{\frac{190}{100,000}}\times100[/tex]
⇒ Percentage Increase = 40.53%
Thus, percent increase in the male incarceration rate during given period is 40.53%.
4(8x + 7) = 17x - 8
help!!!
Answer:
x = 2.4 or 12/5 or 2 and 2/5
Step-by-step explanation:
4(8x + 7) = 17x - 8
4 * 8x = 32x
4 * 7 = 28
32x + 28 = 17x - 8
-28 - 28
32x = 17x - 36
-17x -17x
15x = -36
---- ----
15 15
x = 2.4 or 12/5 or 2 and 2/5
Hey!
---------------------------------------------------
Solution:
4(8x + 7) = 17x - 8
32x - 28 = 17x - 8
32x - 28 + 28 = 17x - 8 + 28
32x = 17x + (-36)
32x - 17x = 17x - (36) - 17x
15x = -36
15x/15 = -36/15
x = -36/15 or -12/5
---------------------------------------------------
Answer:
x = -12/5
---------------------------------------------------
Hope This Helped! Good Luck!
The probability that a customer's order is not shipped on time is 0.06. A particular customer places three orders, and the orders are placed far enough apart in time that they can be considered to be independent events. Round your answers to four decimal places.
(a) What is the probability that all are shipped on time?
(b) What is the probability that exactly one is not shipped ontime?
(c) What is the probability that two or more orders are not shipped on time?
Answer:
a) There is a 83.06% probability that all orders are shipped on time.
b) There is a 15.90% probability that exactly one order is not shipped ontime.
c) The probability of at least two orders being late is 1.02% + 0.02% = 1.04%.
Step-by-step explanation:
Probability:
What you want to happen is the desired outcome.
Everything that can happen iis the total outcomes.
The probability is the division of the number of possible outcomes by the number of total outcomes.
In our problem, there is:
-A 6% probability that a customer's order is not shipped on time.
-A 94% probability that a customer's order is shipped on time.
We have these following orders:
O1 - O2 - O3.
(a) What is the probability that all are shipped on time?
The probabilities that each order is shipped on time are O1 = 0.94, O2 = 0.94 and O3 = 0.94. So:
[tex]P = (0.94)^{3}[/tex] = 0.8306
There is a 83.06% probability that all orders are shipped on time.
(b) What is the probability that exactly one is not shipped ontime?
The order's can be permutated. What this means? It means that we can have O1 late and O2,03 on time, O2 late and O1,O3 on time and O3 late and O1, O2 on time. We have a permutation of 3 elements(the orders) with 2 and 1 repetitions(2 on time and one late).
The probability that an order is late is:
[tex]P = (0.94)^{2}(0.06)[/tex] = 0.053 for each permutation
Considering the permutations:
[tex]P = 0.053*p^{3}_{2,1} = 0.053\frac{3!}{2!*1!} = 0.053*3 = 0.1590[/tex]
There is a 15.90% probability that exactly one order is not shipped ontime.
(c) What is the probability that two or more orders are not shipped on time?
P = P1 + P2, where P1 is the probability that two orders are late and P3 is the probability that all three orders are late.
P1
Considering the permutations, the probability that two orders are late is:
[tex]P_{1} = p^{3}_{2,1}*(0.94)*(0.06)^{2} = 3*(0.94)*(0.06)^{2} = 0.0102[/tex]
There is a 1.02% probability that two orders are late
P2
[tex]P_{2} = (0.06)^3 = 0.0002[/tex]
There is a 0.02% probability that all three orders are late.
The probability of at least two orders being late is 1.02% + 0.02% = 1.04%.
An oral liquid concentrate of sertraline hydrochloride (Zoloft) contains 20 mg/mL of the drug. How many grams of sertraline hydrochloride are in each 60-mL container of the concentrate?
Answer:
1.2 grams.
Step-by-step explanation:
We have been given that an oral concentrate of sertraline hydro-chloride (Zoloft) contains 20 mg/mL of the drug.
First of all, we will find number of mg in 60 mL container of the concentrate as:
[tex]\frac{\text{20 mg}}{\text{ml}}\times \text{60 ml}[/tex]
[tex]\text{20 mg}\times 60[/tex]
[tex]\text{1200 mg}[/tex]
We know 1 gram equals 1000 mg.
[tex]\text{1200 mg}\times \frac{\text{1 gram}}{\text{1000 mg}}[/tex]
[tex]1.2\times\text{1 gram}[/tex]
[tex]1.2\text{ grams}[/tex]
Therefore, 1.2 grams of sertraline hydrochloride are in each 60-mL container of the concentrate.
An automobile shop manager timed 27 employees and recorded the time, in minutes, it took them to change a water pump. Assuming normality, use Excel to find the 99% confidence interval for the true mean. Round your answers to three decimal places and use increasing order.
18.4 16.1 19.5 16.5 12.5 17.2 13.8 17.9 19.1 9.8 23.8 18.7 19.1 15.0 19.2 17.0 11.5 15.7 22.5 23.7 19.9 17.6 15.0 17.8 20.7 14.2 15.4
The 99% confidence interval for the true mean time to change a water pump is approximately (14.650, 20.850) minutes, based on the recorded times.
To find the 99% confidence interval for the true mean time it takes to change a water pump, follow these steps in Excel:
Compute the sample mean [tex](\(\bar{x}\))[/tex] using the AVERAGE function and the sample standard deviation (s) using the STDEV.S function for the recorded times.
Calculate the degrees of freedom (n - 1) using the COUNT function to count the number of samples and subtracting 1.
Use the T.INV.2T function to find the critical value for the 99% confidence level with the obtained degrees of freedom.
Compute the margin of error using the formula:
[tex]\(t_{\alpha/2} \times \frac{s}{\sqrt{n}}\)[/tex], where [tex]\(t_{\alpha/2}\)[/tex] is the critical value, s is the sample standard deviation, and n is the sample size.
Determine the confidence interval by subtracting and adding the margin of error to the sample mean.
Round the lower and upper bounds of the confidence interval to three decimal places.
Following these steps, the 99% confidence interval for the true mean time to change a water pump is approximately (14.650, 20.850) minutes based on the given recorded times.
What is the total resistance of a parallel circuit that has three loads? Load one has a resistance of 6 ohms. Load two has a resistance of 3 ohms. Load three has a resistance of 12 ohms. (YOU MUST SHOW YOUR WORK)!!! 3R 2
Answer:
The total resistance of these three resistors connected in parallel is [tex]1.7143\Omega[/tex]
Step-by-step explanation:
The attached image has the circuit for finding the total resistance. The circuit is composed by a voltage source and three resistors connected in parallel: [tex]R_1=6\Omega [/tex], [tex]R_2=3\Omega [/tex] and [tex]R_3=12\Omega [/tex].
First step: to find the source current
The current that the source provides is the sum of the current that each resistor consumes. Keep in mind that the voltage is the same for the three resistors ([tex]R_1[/tex], [tex]R_2[/tex] and [tex]R_3[/tex]).
[tex]I_{R_1}=\frac{V_S}{R_1}[/tex]
[tex]I_{R_2}=\frac{V_S}{R_2}[/tex]
[tex]I_{R_3}=\frac{V_S}{R_3}[/tex]
The total current is:
[tex]I_S=I_{R_1}+I_{R_2}+I_{R_3}=\frac{V_S}{R_1}+\frac{V_S}{R_2}+\frac{V_S}{R_3}=\frac{R_2\cdot R_3 \cdot V_S+R_1\cdot R_3 \cdot V_S+R_1\cdot R_2 \cdot V_S}{R_1\cdot R_2\cdot R_3}[/tex]
[tex]I_S=V_S\cdot \frac{R_2\cdot R_3+R_1\cdot R_3+R_1\cdot R_2}{R_1\cdot R_2\cdot R_3}[/tex]
The total resistance ([tex]R_T[/tex]) is the source voltage divided by the source current:
[tex]R_T=\frac{V_S}{I_S}[/tex]
Now, replace [tex]I_S[/tex] by the previous expression and the total resistance would be:
[tex]R_T=\frac{V_S}{V_S\cdot \frac{R_2\cdot R_3+R_1\cdot R_3+R_1\cdot R_2}{R_1\cdot R_2\cdot R_3}}[/tex]
Simplify the expression and you must get:
[tex]R_T=\frac{R_1\cdot R_2\cdot R_3}{R_2\cdot R_3+R_1\cdot R_3+R_1\cdot R_2}[/tex]
The last step is to replace the values of the resistors:
[tex]R_T=\frac{(6\Omega )\cdot (3\Omega)\cdot (12\Omega)}{(3\Omega)\cdot (12\Omega)+(6\Omega)\cdot (12\Omega)+(6\Omega)\cdot (3\Omega)}=\frac{12}{7}\Omega=1.7143\Omega [/tex]
Thus, the total resistance of these three resistors connected in parallel is [tex]1.7143\Omega[/tex]
The total resistance of a parallel circuit with resistors of 6 ohms, 3 ohms, and 12 ohms is calculated using the parallel resistance formula, resulting in approximately 1.71 ohms.
The subject of your question falls under Physics, where we need to calculate the total resistance of a parallel circuit with three different resistors.
To find the total resistance in a parallel circuit, we use the formula:
1/Rtotal = 1/R1 + 1/R2 + 1/R3
For the given values, R1 = 6 ohms, R2 = 3 ohms, and R3 = 12 ohms. Plugging in these values:
1/Rtotal = 1/6 + 1/3 + 1/12
1/Rtotal = 2/12 + 4/12 + 1/12
1/Rtotal = 7/12
Rtotal = 12/7 ohms
Rtotal ≈ 1.71 ohms
Thus, the total resistance of the parallel circuit is approximately 1.71 ohms.
A car is driven for 2 hours at 50 mph and gets 25 miles per gallon: how many miles are driven and how much gas is used?
Answer: 100 miles, 4 gallons used
Step-by-step explanation:
Dist = rate * time = 50 mi/hr * 2 hr = 100 mi
Miles = gallons * miles/gallon. 100 = gallons*25mpg. Gallons = 100/25 = 4
Mr. Chang wants to retire in 10 years. He deposits $650.00 every three months into his retirement investment account. If the account's interest rate is 7.8% compounded quarterly, how much will he have at the end of 5 years, when 20 quarterly deposits of $650.00 have been made?
Give answer in US dollars and cents rounded to the nearest cent (do NOT enter "$" sign)
Answer:
Mr. Chang will have 15714.90 dollars.
Step-by-step explanation:
p = 650
r = [tex]7.8/4/100=0.0195[/tex]
Number of periods or n = [tex]5\times4=20[/tex]
Future value formula is : [tex]p[\frac{(1+r)^{n}-1}{r} ][/tex]
Putting the values in formula we get;
[tex]650[\frac{(1+0.0195)^{20}-1}{0.0195} ][/tex]
= $15714.90
Hence, Mr. Chang will have 15714.90 dollars.
a 55 ft long drainage pipe must be cut into two pieces before installation. one piece is two-thirds as long as the other. find the length of each piece
Answer:
33 feet
22 feet
Step-by-step explanation:
Let the longer piece be x
Therefore the shorter piece is (2/3)x
x + (2/3)x = 55 Combine the left 2 terms.
(3/3)x + (2/3)x = 55 Add
(5/3)x = 55 Multiply both sides by (3/5)
(3/5) * (5/3)x = (3/5)*55
x = 33
The larger piece is 33 feet
The smaller piece is (2/3) * 33 = 22 feet
Assume n and m are integers. Prove if m divides n, then m divides -n
Answer: So, if m divides n then n/m = x, and x is integer.
then -n/m = (-1*n)/m = -1*n/m = -1*x = -x.
So if x is integer, -x also is integer, then -n/m is integer and then m divides -n.
Where you used that in the integers set each number a has a opposite (also in the set ) such that a + b= 0, and b = -a = -1*a.
A heavy rainstorm dumps 1.0 cm of rain on a city 4 km wide and 8 km long in a 2-h period. Part A How many metric tons (1 metricton = 103 kg) of water fell on the city? (1 cm3 of water has a mass of 1 gram = 10-3 kg.) Express your answer using o
To find the mass of water that fell on the city, multiply the volume of the rainstorm by the density of water.
Explanation:To calculate the amount of water that fell on the city, we first calculate the volume of water by multiplying the width, length, and height of the rainstorm. Using the given values of 1.0 cm of rain, 4 km wide, and 8 km long, we find that the volume is 1.5 × 1018 m³. Since water has a density of 1 ton per cubic meter, we can calculate the mass by multiplying the volume by the density, which gives us 1.5 × 1018 metric tons.
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What is the probability that Saturday is the day after Wednesday?
1
2
1/7
0
0 = 0% probability that Saturday is the day after Wednesday.
---------------------------------------------
A probability is the number of desired outcomes divided by the number of total outcomes.
In this question, we have to consider that:
There are events that are certain to happen, that is, Thursday being the day after Wednesday, which have 1 = 100% probability.There are events that are certain not to happen, that is, Saturday being the day after Wednesday, which have 0 = 0% probability.Thus, 0 = 0% probability that Saturday is the day after Wednesday.
A similar question is given at https://brainly.com/question/16763692
the correct answer is 1/7.
To determine the probability that Saturday is the day after Wednesday, let's consider the days of the week in order:
1. List the days of the week**: Sunday, Monday, Tuesday, Wednesday, Thursday, Friday, Saturday.
2. Identify the position of Wednesday**: Wednesday is the 4th day of the week.
3. Determine the position of Saturday, the day after Wednesday: Saturday is the 6th day of the week.
4. Calculate the probability:
- There are 7 days in total.
- Wednesday is followed by Thursday, Friday, and then Saturday, making Saturday the 6th day after Wednesday.
5. Probability calculation:
- There is only one Saturday in the week.
- Therefore, the probability that Saturday is the day after Wednesday is [tex]\( \frac{1}{7} \).[/tex]
PLEASE HELP ASAP PLEASE
Choose the equation below that represents the line passing through the point (2, -4) with a slope of one half.
y = one half x + 5
y = one half x − 3
y = one half x − 5
y = one half x + 3
Answer:
The equation that represents the line passing through the point (2, -4) with a slope of one half is
[tex]f(x) = \frac{1}{2}x - 5[/tex]
Step-by-step explanation:
The equation of a line can be described by a first order equation in the following format:
[tex]f(x) = ax + b[/tex]
In which a is the slope of the line.
Solution:
The line slope is [tex]\frac{1}{2}[/tex], so [tex]a = \frac{1}{2}[/tex].
The equation of the line now is:
[tex]f(x) = \frac{1}{2}x + b[/tex]
The problem states that the line passes through the point(2,-4). This means that when x = 2, f(x) = -4
So:
[tex]f(x) = \frac{1}{2}x + b[/tex]
[tex]-4 = \frac{1}{2}*(2) + b[/tex]
[tex]-4 = 1 + b[/tex]
[tex]b = -5[/tex]
So, the equation that represents the line passing through the point (2, -4) with a slope of one half is
[tex]f(x) = \frac{1}{2}x - 5[/tex]
Triangles are formed by the intersection of the lines y=x, y 2x, y=-2x, and y=-4. Solve for angles ABC and ABD A D B
Answer and Step-by-step explanation:
To find the angles between the lines, we can use the formula:
tanα = |ms - mr| / | 1 + ms.mr|
where ms and mr are the linear coefficients of the lines you want to find. It always finds the smaller angle formed.
Let's find all the angles from the triangles formed.
y=x ms = 1
y=2x mr = 2
tanα = |1 - 2| / | 1 + 1.2|
tanα = |-1| / | 1 + 2|
tanα = |-1/3|
tanα = 1/3
α = tan⁻¹1/3
α = 18.4°
y=x ms = 1
y=-4 mr = 0
tanα = |1 - 0| / | 1 + 1.0|
tanα = |1| / | 1 + 0|
tanα = |1/1|
tanα = 1
α = tan⁻¹1
α = 45°
y=2x ms = 2
y=-4 mr = 0
tanα = |2 - 0| / | 1 + 2.0|
tanα = |2| / | 1 + 0|
tanα = |2/1|
tanα = 2
α = tan⁻¹2
α = 63.4°
As these 2 lines are in both triangles, the suplement of this angle is also asked, so, 180° - 63.4° = 116.6°
For y=2x and y=-4, it's the same: α = 63.4°
y=2x ms = 2
y=-2x mr = -2
tanα = |2 - (-2)| / | 1 + 2.(-2)|
tanα = |4| / | 1 - 4|
tanα = |4/3|
tanα = 4/3
α = tan⁻¹ 4/3
α = 53.1°
Final answer:
To find angles ABC and ABD in the intersecting lines problem, analyze the slopes of the lines and their intersections.
Explanation:
Triangles can be formed by the intersection of lines with given equations. In this case, the lines are y=x, y= 2x, y=-2x, and y=-4. To find angles ABC and ABD, one must analyze the slopes of these lines and their intersections.
Angle ABC= arctan(∣ m2 −m 1 ∣)
Angle ABC = arctan(∣2−1∣)
Angle ABC = 45 degree
Angle ABD:
This angle is formed by the lines
Angle ABD= arctan (∣m 2 −m 1 ∣)
Angle ABD = arctan(∣−2−1∣)
Angle ABD ≈ 71.57 degree
Are the irrational numbers closed under addition?
Answer:
Irrational numbers are not closed under addition.
Step-by-step explanation:
Irrational numbers are the numbers that cannot be expressed in the form of a fraction [tex]\frac{x}{y}[/tex]. In other words we can say that irrational number,s decimal expantion does not cease to end.
The closure property of addition in irrational numbers say that sum of two irrational number is always a rational number, But this is not true. It is not necessary that the sum is always irrational some time it may be rational.
This can be understood with the help of an example:
let (2+√2) and (-√2) be two irrational number. Their sum is (2+√2)+(-√2) = 2, which is clearly a rational number.
Hence, irrational numbers are not closed under addition.
1. Find the 16-bit computer representation of -2972.
Answer:
-B9C
Step-by-step explanation:
Hi!
Firstly,
1) Start dividing -2972 : 16 = -185 (quotient) *(16) -12 Remainder
2) Do it again! Divide -185 for 16 = -185 / 16 = -11 (quotient) *(16) - 9 Remainder
3) Divide = -11/16 there's no integer result (since it's 0.68) we put it 0*16 -11 (Remainder) = 11
(Since the result gave us a 0 as integer. We had to lower it one unit the Remainder to satisfy the division algorithm which says = a:b=q*b +r,
11 =0*16+11
4) Gathering all Remainders from bottom to top: 12912
Comparing with the Table (below), from the last remainder to the first, and checking it with the table:
Decimal = Hex (multiplying by minus 1 since it's negative):
-11912 =-B9C
The mean weight of an adult is 62 kilograms with a variance of 144.If 195 adults are randomly selected, what is the probability that the sample mean would differ from the population mean by greater than 2.2 kilograms? Round your answer to four decimal places.
Answer:
The probability that the sample mean would differ from the population mean by greater than 2.2 kilograms is 0.0104 .
Step-by-step explanation:
The mean weight of an adult is 62 kilograms with a variance of 144
i.e. [tex]\mu = 62 \\\sigma^2 = 144[/tex]
We are supposed to find probability that the sample mean would differ from the population mean by greater than 2.2 kilograms
i.e. [tex]P(\bar{x}<62-2.2) or P(\bar{x}>62+2.2)=1-P(59.8<\bar{x}<64.2)[/tex]
Using formula : [tex]\frac{x-\mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
[tex]P(\bar{x}<62-2.2) or P(\bar{x}>62+2.2)=1-P(59.8<\bar{x}<64.2)[/tex]
[tex]P(\bar{x}<62-2.2) or P(\bar{x}>62+2.2)=1-P(\frac{59.8-62}{\frac{12}{\sqrt{195}}}<\frac{64.2-62}{\frac{12}{\sqrt{195}}})[/tex]
[tex]P(\bar{x}<62-2.2) or P(\bar{x}>62+2.2)=1-P(-2.56<z<2.56)[/tex]
[tex]P(\bar{x}<62-2.2) or P(\bar{x}>62+2.2)=1-{P(z<2.56)-P(z<-2.56)}[/tex]
Refer the z table
[tex]P(\bar{x}<62-2.2) or P(\bar{x}>62+2.2)=1-{0.9948-0.0052}[/tex]
[tex]P(\bar{x}<62-2.2) or P(\bar{x}>62+2.2)=0.0104[/tex]
Hence The probability that the sample mean would differ from the population mean by greater than 2.2 kilograms is 0.0104 .
0.0104 or 1.04% is the probability that the sample mean weight of 195 adults will differ from the population mean .
We have to use the central limit theorem.
Given the mean weight (62 kg) and variance (144 kg²) of the population, we first calculate the standard deviation:
Step 1: Calculate the population standard deviation.
Population standard deviation (σ) = √variance = √144 = 12 kg.Step 2: Calculate the standard error of the mean.
Standard error (SE) = σ / √n = 12 / √195 = 12 / 13.9642 ≈ 0.8594 kg.Step 3: Find the z-scores corresponding to ±2.2 kg difference from the mean.
Z = (X - µ) / SEFor X = 62 + 2.2 = 64.2 kg: Z = (64.2 - 62) / 0.8594 ≈ 2.56.For X = 62 - 2.2 = 59.8 kg: Z = (59.8 - 62) / 0.8594 ≈ -2.56.Step 4: Use the standard normal distribution to find the probabilities.
P(Z > 2.56) = 1 - P(Z ≤ 2.56) ≈ 1 - 0.9948 = 0.0052.Similarly, P(Z < -2.56) = 0.0052.Step 5: Calculate the total probability.
P(|X - µ| > 2.2) = P(Z > 2.56) + P(Z < -2.56) ≈ 0.0052 + 0.0052 = 0.0104.Therefore, the probability that the sample mean differs from the population mean by more than 2.2 kg is approximately 0.0104 or 1.04%.
jacob the dog eats dry food that contains 324kcal/cup. Jacob eats 3.5 cups a day. The food contains 3.6 g of fat in 100 kcals of energy. what is his daily fat intake?
the food contains 25.6 IU of Vitamin D3 in 100 kcals of energy. what is his daily Vitamin D inake?
Answer:
His daily fat intake is 40.824g.
His daily Vitamin D intake is 290.304 IU.
Step-by-step explanation:
The first step to solve this problem is finding the daily kcal intake of the dogs.
Each cup has 324 kcal, and he eats 3.5cups a day. So:
1 cup - 324 kcals
3.5 cups - x kcals
[tex]x = 324*3.5[/tex]
[tex]x = 1134[/tex] kcals.
His daily intake is of 1134 kcals.
The food contains 3.6 g of fat in 100 kcals of energy. what is his daily fat intake?
There are 3.6g of fat in 100 kcals of energy. How many g of fat are there in 1134 kcals?
3.6g - 100 kcals
xg - 1134 kcal
[tex]100x = 1134*3.6[/tex]
[tex]x = \frac{1134*3.6}{100}[/tex]
[tex]x = 11.34*3.6[/tex]
[tex]x = 40.824[/tex]g
His daily fat intake is 40.824g.
The food contains 25.6 IU of Vitamin D3 in 100 kcals of energy. what is his daily Vitamin D inake?
Similar logic as above.
25.6IU - 100 kcals
x IU - 1134 kcal
[tex]100x = 1134*25.6[/tex]
[tex]x = \frac{1134*25.6}{100}[/tex]
[tex]x = 11.34*25.6[/tex]
[tex]x = 290.304[/tex]IU
His daily Vitamin D intake is 290.304 IU.
A bag contains three red marbles, three green ones, one lavender one, one How many sets of five marbles include at least two red ones?
Answer: There are 18 sets of five marbles including at least two red ones.
Step-by-step explanation:
Since we have given that
Number of red marbles = 3
Number of green marbles = 3
Number of lavender marbles = 1
total number of marbles = 3+3+1+1 = 8
We need to find the sets of five marbles including at least two red ones.
so, it becomes,
[tex]^3C_2\times ^4C_3+^3C_3\times ^4C_2\\\\=18[/tex]
hence, there are 18 sets of five marbles including at least two red ones.
To determine the total number of sets of five marbles that include at least two red ones, you need to figure out the total number of ways you can choose 5 marbles out of the 8 in the bag, and then calculate combinations for cases with at least 2 red ones and add them up.
Explanation:To determine the total number of sets of five marbles that include at least two red ones, you need to use combinatorics, which is a branch of Mathematics dealing with combinations of objects belonging to a finite set in accordance with certain constraints, such as those posed by questions concerning the possibility of constructing.
Firstly, you need to figure out the total number of ways you can choose 5 marbles out of the 8 in the bag. This is calculated using the combination formula: C(n, k) = n! / [k!(n-k)!]. Where n is the total number of items, and k is the number of items to choose. For this case, n is 8 (total marbles) and k is 5 (marbles we want to choose), so total possible combinations will be C(8, 5).
We want sets that include at least two red marbles, so the sets can have 2, 3 or all red marbles. So, calculate combinations for each case and add them up, like this:
2 Red and 3 Non-Red: C(3, 2) × C(5, 3)3 Red and 2 Non-Red: C(3, 3) × C(5, 2)All red: C(3, 3) × C(5, 0)Learn more about Combinations & Probability here:https://brainly.com/question/3901018
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The graph below shows four straight lines, A, B, C, and D:
Graph of line A going through ordered pairs negative 2, negative 3 and 2, 5. Graph of line B going through ordered pairs negative 2, negative 4 and 2, 4. Graph of line C going through ordered pairs negative 2, negative 5 and 3, 5. Graph of line D going through ordered pairs 0, negative 4 and 4, 4
Which line is represented by the function f(x) = 2x + 1?
Answer:
Line A is represented by the function f(x) = 2x + 1.
Step-by-step explanation:
This can be solved by trial and error. What it means? It means that we are going to replace the ordered pairs in the function, and the equality must be satisfied.
Line A
(-2,-3)
When x = -2, f(x) = -3. Does it happen in the function?
[tex]f(x) = 2x + 1[/tex]
[tex]-3 = 2(-2) + 1[/tex]
[tex]-3 = -3[/tex]
The first equality is OK. Let's see the second
(2,5)
When x = 2, y = 5.
[tex]f(x) = 2x + 1[/tex]
[tex]5 = 2(2) + 1[/tex]
[tex]5 = 5[/tex]
Also OK.
So line A is represented by the function f(x) = 2x + 1.
Now let's see why the other lines are not represented by this function.
Line B
(-2,-4)
[tex]f(x) = 2x + 1[/tex]
[tex]-4 = 2(-2) + 1[/tex]
[tex]-4 = -3[/tex]
False
Line C
(-2,-5)
[tex]f(x) = 2x + 1[/tex]
[tex]-5 = 2(-2) + 1[/tex]
[tex]-5 = -3[/tex]
False
Line D
(0,-4)
[tex]f(x) = 2x + 1[/tex]
[tex]-4 = 2(0) + 1[/tex]
[tex]-4 = 1[/tex]
False
Answer:
line a
Step-by-step explanation:
how to solve this problem step by step (3×4)÷(7+9-10)
Answer:
2
Step-by-step explanation:
1. solve for the multiplication (3x4)= 12
2. solve for (7+9-10) take 7+9 which =16 and then subtract by 10. (16-10=6)
3. take the 12 and divide by 6
To solve the expression (3×4)÷(7+9-10), perform the operations inside the brackets first, then multiply and divide according to BODMAS/BIDMAS rules. The correct answer after simplifying is 2.
Explanation:To solve the problem (3×4)÷(7+9-10), you should follow the steps of BEDMAS/BIDMAS (Brackets, Exponents/Indices, Division and Multiplication, Addition and Subtraction), also known as the order of operations.
Firstly, address the operations within the parentheses. Calculate the sum and difference within the second set of brackets (7+9-10), which simplifies to 6.Next, perform the multiplication within the first set of brackets (3×4), which equals 12.Now you have simplified the original expression to 12÷6.Finally, divide 12 by 6 to get the answer, which is 2.Always remember to check the answer to see if it is reasonable by reviewing your calculation steps.
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Determine whether the quantitative variable is discrete or continuous. Number of students in a class Is the variable discrete or continuous? A. The variable is continuous because it is not countable. B. The variable is discrete because it is not countable. C. The variable is continuous because it is countable. D. The variable is discrete because it is countable.
Answer:
D) The variable is discrete because it is countable.
Step-by-step explanation:
Both discrete and continuous falls under the numeric category.
Discrete variables are the variable that are countable and cannot be expressed in decimal form.
Example: Tosses of a coin, Number of rooms in an house.
Continuous variables on the other hand cannot be counted, they are countable and can be expressed in the form of decimals. Its value can be expressed in the form of interval.
Example: Time, Length.
Now, number of students in a class is a discrete variable since students are countable and they cannot be expressed in decimal form.
So the correct option is D) The variable is discrete because it is countable.
Final answer:
The number of students in a class is a quantitative discrete variable because student numbers are countable and would always be a whole number.
Explanation:
The number of students in a class is a quantitative discrete variable. This is because the number of students can be counted, and would always be a whole number. There is no situation in which you could have a fraction of a student. Discrete random variables like this are countable, as opposed to continuous random variables which result from measurements and can take on any value in a range, including decimals and fractions. For instance, if we were discussing the heights of students, which can vary in continuous increments, we would be talking about a continuous variable.
Therefore, the correct option for the provided question is: D. The variable is discrete because it is countable.