A closed circuit is required to carry current. If there is a break anywhere in the path, the circuit will open and no current will flow, and the metal atoms in the wire will quickly become peaceful and electrically neutral.
Current flows in a closed circuit, but electrons are left behind in an open circuit.
Imagine a gallon of water flowing through an open pipe. Water flows for a short time, but stops when all the water comes out of the pipe. If you pump water into a closed system of pipes, it will continue to flow as long as you force it to move.
Closed circuit design:
breaks are often created by design. For example, a simple light switch opens or closes the circuit that connects the light to the power source. When building a circuit, it is recommended that the battery or other power source be disconnected when the circuit is not in use. Technically, this creates an open circuit. The
extinguished flashlight is an open circuit. In the flashlight shown here, the flat black button on the bottom left controls the internal switch. A switch is nothing more than two flexible metal strips in close proximity to each other. Push the black button all the way to the right to open the switch and turn off the flashlight. The switch in the open position disconnects the bulb from the battery, creating an open circuit.So, for the light bulb in a circuit turn on when the switch is closed.
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What is the domain of the square root function graphed?.
The domain of the square root function is x≥0.
What is a function?
A unique kind of relation called a function is one in which each input has precisely one output. In other words, the function produces exactly one value for each input value. The graphic above shows a relation rather than a function because one is mapped to two different values. The relation above would turn into a function, though, if one were instead mapped to a single value. Additionally, output values can be equal to input values.
The x-values are input into the function machine. The function machine then performs its operations and outputs the y-values. The function within can be any function.
The square root function's purpose must now be considered. The positive number that results in the input after being squared is returned as the principal root or output. Since y will be bigger than or equal to 0, we may be certain of that.
To find out a perfect square we need to find out square root is an integer.
Hence, The domain of the square root function is x≥0.
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The marketing group and Rings Are Us is trying to predict if undergraduate or graduate students are more inclined to purchase (y = 1) or not purchase (y=0) a class ring at graduation. Using the following count on the training data set, calculate the conditional probability of both to determine which should be classified to the purchase group. Undergraduate (x = 1) 70 Graduate (x = 0) 100 Purchase (y = 1) No Purchase (y = 0) 30 110 Multiple Choice Undergraduate 0.70 > 0.272; Graduate 0.428 <0.272. The undergraduate is assigned to the purchaser group. Undergraduate 0.30 <0.20; Graduate 0.524 > 0.476. The graduate is assigned to the purchaser group. Undergraduate 0.70 > 0.30; Graduate 0.476<0.524. The undergraduate is assigned to the purchaser group. Undergraduate 0.303 > 0.272; Graduate 0.476< 0.524. The undergraduate is assigned to the purchaser group.
The correct option is that Undergraduate is assigned to the purchaser group.
P ( purchase | Undergraduate ) = [tex]\frac{70}{70 + 30}[/tex] = 70 / 100 = 0.70 ,
⇒ P ( y = 0 | Undergraduate ) = 0.3
P ( purchase | Graduate ) = [tex]\frac{100}{100 + 110}[/tex] = 0.476
⇒ P ( y = 0 | Graduate ) = 0.524
Therefore,
as P ( y = 1 | undergraduate ) = 0.707 > 0.30 and
0.476 > 0.524,
Undergraduate group is assigned to the purchase group.
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Using the ruler postulate, find the distance between -9 and 2
The distance between -9 and 2 using ruler postulate is 11units
What is ruler postulate?Ruler postulate states that the points on a line can be matched one to one with the real numbers. The real number that corresponds to a point is the coordinate of the point. The distance between points A and B, written as AB, is the absolute value of the difference of the coordinates of A and B.
If point A is -9 and point B is 2,
therefore the distance between https://brainly.com/question/28271571 A and B is A-B= -9-2= -11 units
Therefore the absolute value of the distance is 11 units
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consider running golden section search on a function that is unimodal. if the method starts with an initial bracket of , what is the length of the bracket after 1 iteration?
The length of the bracket after 1 iteration is 100%.
Let f(x) = x³-15x² + 50x
a = 0, b=10.
Let the golden ratio be
GR=√5-1 / 2=0.618
Now, d = GR (b-a)
= 0.618 (10-0) = 6·18
[tex]x_{1}[/tex]= a+d = 0 + 6·18 = 6.18
[tex]x_{2}[/tex] = b-d = 10- 6·18 = 3.82
f([tex]x_{1}[/tex]) = (6·18)³ - 15 (6·18)² + 50(6·18) = -27.887
f([tex]x_{2}[/tex]) = (3.82)³-15(3.82)²+50(3.82)=27.857
so, f([tex]x_{2}[/tex]) > f([tex]x_{1}[/tex]) new interval is [a,x,]
i.e., maximum lies in [0, 6·18]
so, Xmax = [tex]x_{2}[/tex]= 382
Uncertainty in measurement will be,
∈= [tex]\frac{1-GR) (b-a)}{Xopt}[/tex] =[tex]\frac{((1-0.618) X (10-0)}{382}[/tex] × 100%
∈ = 100%
In arithmetic, quantities are within the golden ratio if their ratio is the same as the ratio in their sum to the larger of the 2 portions. Expressed algebraically, for quantities a and b with [tex]a > b > 0[/tex], [tex]\frac{(a+b)}{a}[/tex] = [tex]\frac{a}{b}[/tex]= φ
The golden ratio turned into known as the acute and suggest ratio by way of Euclid, and the divine proportion using Luca Pacioli, and also is going through numerous other names. The golden ratio seems in some patterns in nature, such as the spiral association of leaves and different elements of plants.
A few twentieth-century artists and architects, together with Le Corbusier and Salvador Dalí, have proportioned their works to approximate the golden ratio, believing them to be aesthetically appealing. these uses often appear in the form of a golden rectangle.
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(a) use the extended euclidean algorithm to find the greatest common divisor of the given numbers and express it as the following linear combination of the two numbers. 6,066s 2,286t, where s
the Greatest Common Divisor is 252 and it can be expressed as the linear combination -2 * 6,066 + 3 * 2,286.
What is GCD?The greatest common divisor (GCD) is the biggest positive integer that divides two or more integers without leaving a remainder. It's also referred to as the greatest common factor (GCF) or the highest common factor (HCF). The Euclidean procedure, which continually divides the greater of the two integers by the smaller until a remainder of zero is obtained, is one way to calculate the GCD. The GCD is a crucial idea in mathematics, notably in number theory, and it has several applications in other disciplines, such as computer science and encryption. Finding the greatest common divisor of the coefficients of a linear equation in two variables is another popular geometry task.
How to solve?
The Greatest Common Divisor of 6,066 and 2,286 can be expressed as 252 = 6,066 * (-2) + 2,286 * 3. So, the GCD is 252 and it can be expressed as the linear combination -2 * 6,066 + 3 * 2,286.
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I got 2+12s<50a but it says its wrong
The inequality to represent the number of album and song Jorge can download is 2s + 12a ≤ 50
How to use inequality to represent a situation?It cost 2 dollars to download a song and 12 dollars to download an entire album. Jorge has 50 dollars to spend on downloading music.
The inequality that represents the number of songs(s) and album(a) that Jorge can download can be represented as follow:
Therefore,
a = number of albumss = number of songsHence, the inequality is as follows:
2s + 12a ≤ 50
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If their food and beverage cot $25. 30 and there i an 8% meal tax, how much i the bill? After adding a tip, the total lunch cot wa $32. 24. What percentage tip did they give? Enter your anwer to the nearet percentage
The percentage tip did they give is 18%
If their food and beverage cost $25. 30
There i an 8% meal tax
The tax will be
$25.30(0.08) = $2.024.
Then we add the tax to the price such that
The bill will be
$25.30 + 2.024 = $27.32
Tip = 32.24 - 27.32 = 4.92
percentage tip did they give
= tip given /total amount of the bill x 100
= 4.92/27.32 x 100
= 18%
Therefore, If their food and beverage cot $25. 30 and there i an 8% meal tax and after adding a tip, the total lunch cot wa $32. 24.the percentage tip did they give is 18%
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n this scenario, what is the test statistic? the website developer would like to test the claim that the percent of websites that have serious vulnerabilities is less than 30%. sample size
the test statistic z is 1.7
What is test statistic?
A test statistic may be a datum employed in applied math hypothesis testing. A hypothesis take a look at is often laid out in terms of a test statistic, thought of as a numerical outline of a data-set that reduces the info to at least one worth that may be wont to perform the hypothesis test.
Main body:
Calculate the test statistic using the formula:
z= [tex]p-p'[/tex]/[tex]\frac{p'(p-p')}{n}[/tex]
where:
p = sample proportion,
n = sample size, and
Po = population proportion under the null hypothesis
Sample size = 34 websites = n
Sample proportion = 0.20 = p'
z = (0.3 - 0.2)/ (0.2*0.1)/34
z = 0.1 *34/0.02
z = 1.7
Hence value of test statistic z is 1.7
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During a four week period you work the following hour
Week 1: 36 3/8
Week 2: 41 1/4
Week 3: 40 1/2
Week 4: 38 3/8
What i the average number of hour you worked in one week?
You work an average of 39 1/8 hours per week.
The given can be used to calculate the average.
(36 3/8 + 41 1/4 + 40 1/2 + 38 3/8) / 4 =
36 + 41 + 40 + 38 = 155
3/8 + 1/4 + 1/2 + 3/8 = 3/8 + 2/8 + 4/8 + 3/8 = 12/8 = 1 1/2
155 + 1 1/2 = 156 1/2
(156 1/2) / 4 =
313/2 * 1/4 = 313/8 = 39 1/8
average weekly hours are 39 1/8.
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The area of a rectangle is 91 square inches. If the length of the rectangle is 1 less than twice its width, write an equation that could be used to find the width, w, of the rectangle.
The equation that can be used to find the width, w, of the rectangle with the given area is 2w² - w - 91 = 0
To determine the equation that can be used to find the width we use the following formula; Area of a rectangle = length × width
Since the area of the rectangle is 91 square inches and the length of the rectangle is 1 less than twice its width, this can be represented as;
Length of the given rectangle = 2w - 1
Using the area formula the equation to find the width would be:
(2w - 1)(w) = 91
2w² - w - 91 = 0
Hence 2w² - w - 91 = 0, is the equation that can be used to find the width.
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Write an equation of a line in lope-intercept for that i perpendicular to the line y=1/2x-5 and pae through the point (1, -2)
Step-by-step explanation:
the slope-intercept form is
y = ax + b
"a" being the slope, "b" being the y-intercept (the y-value when x = 0).
to find the slope of the target line we use the slope of the given line : 1/2.
remember, the slope is expressed as ratio (y coordinate change / x coordinate change).
the given line increases the y- value by 1, when the x-value increases by 2.
a perpendicular slope (90°) simply turns y and x upside-down and flips the sign.
so, 1/2 turns into -2/1 = -2.
so, we see our line equation looks like
y = -2x + b
to get b we use the coordinates of the given point :
-2 = -2×1 + b
-2 = -2 + b
0 = b
so thar equation is simply
y = -2x
What other pair of corresponding congruent parts is needed to prove that the two triangles are congruent by ASA congruence postulate?.
Two triangles if the side between any two corners of one triangle cornor corresponds to the side between the corresponding two angles of the second triangle corner are said to be congruent by the ASA rule.
Create a point F' on ray AC such that BF' is equal to DE.
Angle BAF' = angle BAC, which equal to
angle EDF, AB = DE (given), so ∆ DEF
= ∆ ABP
Point F' has two possibilities: F' is equal to point C please.
If F' is not on C, line AC and ray BC intersect only at C, so F' is not on ray BC. Therefore the angle ABF' is not = the angle ABC. But this is a contradiction. Because angle ABF' = angle DEF (because ∆ DEF = ∆ ABF') and angle DEF = angle ABC (given). So, this case does not occur.
Therefore, F' = C must be true.
∆ABC = ∆ABF' = ∆DEF.
The reasonwe only need some parts to
prove congruence of triangles is that from these parts we can (in Euclidean geometry) derive other parts. This is because the basic axioms and definitions allow us to make "guesses" that turn out to be true every time.
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suppose the starting pressure in the container p1 is below atmospheric pressure when the stopper is popped. draw the adiabatic and isochoric processes on a p-v diagram.
The diagram of adiabatic and isochoric process on a pv diagram is given below.
In the given question we have to suppose the starting pressure in the container p1 is below atmospheric pressure when the stopper is popped the draw the adiabatic and isochoric processes on a p-v diagram.
The Adiabatic Process
A thermodynamic process known as adiabatic means that no heat is transferred into or out of the system. For an ideal gas, an adiabatic process is a reversible process with constant entropy. The adiabatic process is mathematically represented by the expression ∆Q=0.
The Isochoric Process
A thermodynamic process known as an isochoric process, also known as a constant-volume process, isovolumetric process, or isometric process, occurs when the volume of the closed system undergoing the process remains constant.
The diagram of adiabatic and isochoric process on a pv diagram is given below:
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mr. imani wants to purchase paper and notebooks for his classroom. at dollar discount he can buy packs of paper, p, for $1.25 each and notebooks, n, for $2.50 each. this is modeled by 1.25p + 2.50n. evaluate for p = 10 and n=30 to find how much it will cost mr. imani to purchase 10 packs of paper and 30 notebooks.
1.$450.00
2.$62.50
3.$43.75
4.$87.50
The total cost for buying 10 packs of paper and 30 notebooks is $87.50.
What is equation?The definition of an equation is a mathematical statement that shows that two mathematical expressions are equal.
Given that, Mr. Imani wants to purchase paper and notebooks for his classroom. at dollar discount he can buy packs of paper, p, for $1.25 each and notebooks, n, for $2.50 each. this is modelled by 1.25p + 2.50n. evaluate for p = 10 and n=30
Putting p = 10 and n = 30, we get,
1.25*10+2.50*30 = 87.50
Hence, The total cost for buying 10 packs of paper and 30 notebooks is $87.50.
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Over the summer, paulo opens a dog-washing business and begins with $32. The table shows how much he earns and spends each week. Weekly revenue and expenses revenue expense sales $124 supplies $8 he works for 8 weeks washing dogs. When he starts back at school, he budgets $60 to spend each week. How many weeks pass before he needs to wash more dogs?.
16 weeks would pass before any further dogs need to be bathed.
Define the term profit?Profit is the term used to describe the financial gain experienced when the revenue from a commercial activity exceeds the costs, costs, and taxes associated with maintaining that activity.The parameters being:
Initial investment = $32Eight weeks were worked.From the formula;
Profit = Sales - Expenses.
Weekly profit is $124 - $8 = $116.
Total revenue generated:
Number of weeks Profit per week.:
= $116 × 8
= $928
Total ownership is total revenue plus initial investment.
Owned in total:
$928 + $32 = $960.
The number of weeks until the entire amount owned is spent can be computed as follows:
Total amount owned weekly spending
= ($960 / $60) = 16
Thus, 16 weeks would pass before any further dogs need to be bathed.
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b. in the below figure, the system has been balanced using lean techniques to meet the takt time as much as possible and the facility works 1 shift of 8 hours with two 15 min breaks, what is the daily demand?
The system has been balanced using lean techniques to meet the takt time as much as possible and the facility works 1 shift of 8 hours with two 15 min breaks, so the daily demand is 2700 units / day.
In the given question, the system has been balanced using lean techniques to meet the takt time as much as possible and the facility works 1 shift of 8 hours with two 15 min breaks.
We have to find the daily demand.
The figure is given below:
Total operating time of the facility = 8 hours - 2 breaks of 15mins each
Total operating time of the facility = 480 mins - (2*15 mins)
Total operating time of the facility = 480 mins - 30 mins
Total operating time of the facility = 450 minutes.
Time taken for 1 output = Cycle time of system = Bottleneck of the supply-demand matched process = 10 seconds.
Total output = Total operating time / Time taken for 1 output
Total output = 450 minutes / 10 seconds
Total output = 2700 units / shift.
Since the market's demand and operational time are in balance, all production is created using the pull principle.
That means; Supply = demand.
Therefore the market demand for the product = 2700 units / day.
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What are the coordinates of the point on the directed line segment from (−9,−6) to (−2,1) that partitions the segment into a ratio of 3 to 4?
[tex]\textit{internal division of a line segment using ratios} \\\\\\ A(-9,-6)\qquad B(-2,1)\qquad \qquad \stackrel{\textit{ratio from A to B}}{3:4} \\\\\\ \cfrac{A\underline{C}}{\underline{C} B} = \cfrac{3}{4}\implies \cfrac{A}{B} = \cfrac{3}{4}\implies 4A=3B\implies 4(-9,-6)=3(-2,1)[/tex]
[tex](\stackrel{x}{-36}~~,~~ \stackrel{y}{-24})=(\stackrel{x}{-6}~~,~~ \stackrel{y}{3}) \implies C=\underset{\textit{sum of the ratios}}{\left( \cfrac{\stackrel{\textit{sum of x's}}{-36 -6}}{3+4}~~,~~\cfrac{\stackrel{\textit{sum of y's}}{-24 +3}}{3+4} \right)} \\\\\\ C=\left( \cfrac{ -42 }{ 7 }~~,~~\cfrac{ -21}{ 7 } \right)\implies \boxed{C=(-6~~,~~-3)}[/tex]
find the area of the triangle below. carry your intermediate computations to at least four decimal places. round your answer to the nearest hundredth.
The area of the given triangle is 20 square kilometers.
Here, we are given a triangle as shown in the figure below.
There are many ways of calculating the area of a triangle but since here, we are given only one angle and 2 sides of the triangle we will use the following formula to calculate the area-
area of triangle = 1/2 × sinФ × side 1 × side 2
where, Ф = angle formed by side 1 and side 2
Here, Ф = 35
Sin 35 = 0.5736
Thus, the area of the triangle will be-
1/2 × 0.5736 × 7 × 10
= 35 × 0.5736
= 20.076
20.076 rounded off to nearest hundredth is 20
Thus, the area of the given triangle is 20 square kilometers.
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Your question was incomplete. Check for the missing figure below
A sample of 64 observations is selected from a normal population. The sample mean is 215, and the population standard deviation is 15. Conduct the following test of hypothesis using the 0.025 significance level. H0: μ ≥ 220 H1: μ < 220 Is this a one- or two-tailed test? One-tailed test Two-tailed test What is the decision rule? (Negative amount should be indicated by a minus sign. Round your answer to 2 decimal places.) What is the value of the test statistic? (Negative amount should be indicated by a minus sign. Round your answer to 2 decimal places.) What is your decision regarding H0? Reject Do not reject What is the p-value? (Round your answer to 4 decimal places.)
Therefore, the p-value is 0.0031, and our decision is to reject the null hypothesis on coducting a one tail test.
What is Hypothesis?A hypothesis is a theory put up to explain a phenomena. A link between two or more variables is described, and the proposition is testable. A hypothesis is an informed estimate or forecast made before undertaking any tests or research to determine its validity. A strong hypothesis should be definable, testable, and supported by prior data. It should also be stated in a way that allows it to be disproven, so that it can be tested using empirical evidence. Generally speaking, a hypothesis serves as the basis for additional research and testing in a scientific endeavour.
How to solve?
The decision rule for a one-tailed test with a significance level of 0.025 is to reject the null hypothesis if the test statistic is less than -1.96.
To calculate the test statistic, we use the formula:
z = (x - μ) / (s / √n)
x = 215, μ = 220, s = 15, and n = 64. Plugging these values into the formula gives:
z = (215 - 220) / (15 / √64) = -5 / (15 / 8) = -5 / 1.875 = -2.67
The test statistic is -2.67, which is less than the critical value of -1.96, so we reject the null hypothesis.
To calculate the p-value, we can use the z-table to look up the area under the normal curve that is to the left of -2.67. This area is approximately 0.0031, which is the p-value.
Therefore, the p-value is 0.0031, and our decision is to reject the null hypothesis.
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8^x/2=2^3/8×4^3/4 find x
The solution to the equation 8^x/2=2^3/8×4^3/4 is x = 15/14
What is Simplify?To simplify an expression: to remove brackets, unnecessary terms and numbers
[tex]8^{x/2} = 2^{3/8} * 4^{3/4}[/tex]
[tex]2^{3x/2} = 2^{3/8} * 2^{2 (3/4)}[/tex]
using law of Indices
[tex]2^{3x/2} = 2^{3/8 + 6/4}[/tex]
[tex]\frac{3x}{2} = \frac{3}{8} + \frac{3}{2}[/tex]
[tex]\frac{3x}{2} = \frac{3+12}{8}[/tex]
[tex]\frac{3x}{2} = \frac{15}{8}[/tex]
cross multiply
24x =30
Divide both sides by 24
[tex]\frac{24x}{24} = \frac{30}{28}[/tex]
x = 15/14
Therefore, the solution to the equation is x = 15/14
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A Three integers have a mean of 10, a median of 12 and a range of 10. Find the three integers.
Answer:
4 , 12 , 14
Step-by-step explanation:
1) We are told that the median (middle number) is 12 and that the mean is 10
This means that the numbers added together, divided by 3 which equals to ten. From this we can understand that the numbers should add up to 30 as 30 divided by 3 is 10
2) We already know one of the middle numbers which is 12 so the next step would be to subtract 12 from 30 which would be 18.
3) We are also told that the range is 10 meaning that the difference between the smallest and biggest number is 10. If the difference between the smallest and biggest is 10 and the number that they can add to is 18, all we have to do to get our numbers subtract 10 from 18 which is 8 and divide it by 2 which is 4. We have to divide it because we need to find two more numbers
4) From the information we have so far we know that one of our numbers is 4 and the other is 12. To get the final number, add 12 and 4 together which is 16, and subtract that from 30 which is 14. Meaning our numbers are 4 , 12 and 14
5) To check if this is right we can see that the range is 10 (14 - 4 = 10) the mean is 10 (4 + 12 + 14 = 30) and the median is 12!!
Hope this helps, have a great day!
PLSSS SOMEONE HELP ME I JUST NEED HELP PLEASEE!! IM OFFERING 40 PTS FOR THIS!! IM BEGGING YOU!!
Match each description with its corresponding value for the system below:
y = 4 x + 1 and y = -2 x + 7
-2
-1
-7
-5
The y -intercept of the exponential function.
The y -value of the solution in Quadrant I.
The number of points of intersection.
The y -intercept of the linear function.
Why is partitioning a directed line segment into a ratio of 1/2 is not the same as finding half the length of the directed line segment?.
The difference between partitioning into a ratio of 1/2 and finding half of a line segment is that partitioning in that ratio means one part is longer than the other, whereas finding half the length means both parts are the same length.
What is the partition of the line?
Partition means to separate or to divide. A line segment can be partitioned into smaller segments which are compared as ratios.
When we say we want to partition a line into a ratio of say x/y, it means that the line has been divided in that ratio and as such, the total number of parts is x + y.
Similarly, when we partition a line in the ratio 1/2, it implies that the total number of parts of the line segment is 1 + 2 = 3.
This means one part of the divided segment is bigger than the other one.
In contrast, half of the line segment means that the line segment is divided into two equal parts.
Thus, the fundamental difference between partitioning into a ratio of 1/2 and finding half of the line segment is that partitioning in that ratio means one part is longer than the other while half the length means that both parts are the same length.
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Because 1:2 is not a fraction while 1/2 is, you cannot assume that 1:2 is one-half of a line or anything that is being delt with in fact. The length of the line might be 18 units, and if it says that there needs to be some sort of action with a ratio of 1:2, you are not splitting that length in half, you are taking one unit from the left side, and two from the right, which does not equal the length of half of 18 units.
Which linear equations have an infinite number of solutions?.
Linear equations have an infinite number of solutions are-
a) (x – 3\7) = 2\3 (3\2x – 9\14 )
c) 12.3x – 8 = 3(–6 + 4.1x)
What is Linear equations?
A linear equation is an equation within which the very best power of the variable is usually one.
Main body:
A linear equation can be said to have an infinite number of solutions when the number of the right hand side is the same at the number on the left hand side of the equation.
For example:
2 = 2 or x = x or 0 = 0
Solving the question above:
Which linear equations have an infinite number of solutions? Check all that apply.
a) (x – 3\7) = 2\3 (3\2x – 9\14 )
x - 3/7 = 6x/6 - 18/42
x - 3/7 = x - 3/7
Collect like terms
x - x = -3/7 + 3/7
0 = 0
The linear equation in option a has an infinite number of solutions
b) 8(x + 2) = 5x – 14
8x + 16 = 5x - 14
Collect like terms
8x - 5x = -14 - 16
3x = -30
x = -30/3
x = -10.
The linear equation in Option b has a true solution.
c) 12.3x – 18 = 3(–6 + 4.1x)
12.3x - 18 = -18 + 12.3x
Collect like terms
12.3x - 12.3x = -18 + 18
0 = 0
The linear equation in Option c has infinite number of solutions
d) 1\2(6x + 10) = 7(3\7x – 2)
6x/2 + 5 = 21/7x - 14
3x + 5 = 3x - 14
Collect like terms
3x - 3x = -14 - 5
0 = -19
The linear equation Option d has no solution
e) 4.2x – 3.5 = 2.1 (5x + 8)
4.2x - 3.5 = 10.5x + 16.8
Collect like terms
4.2x - 10.5x = 16.8 + 3.5
-6.3x = 20.3
x = -20.3/6.3
x = -3.22
Hence, the linear equation in Option e has a true solution
Therefore, the linear equations have an infinite number of solutions are:
a) (x – 3\7) = 2\3 (3\2x – 9\14 )
c) 12.3x – 18 = 3(–6 + 4.1x)
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Suppose A is a 2×2 real matrix with an eigenvalue λ=1+5i and corresponding eigenvector v⃗ =[−1+ii]. Determine a fundamental set (i.e., linearly independent set) of solutions for y⃗ ′=Ay⃗ , where the fundamental set consists entirely of real solutions. Enter your solutions below. Use t as the independent variable in your answers. y⃗ 1(t)= y⃗ 2(t)=
λ = 1 + 5i and ∨ = [ -1 + i , i ]
The first solution is[tex]y(t)=e^{\lambda t}\eta^1=e^{(1+5i)t}\begin{bmatrix} -1+i\\ i \end{bmatrix}\\y(t)=e^{t}(e^{5t}\begin{bmatrix} -1+i\\ i \end{bmatrix})[/tex]
Expanding the e^((5t)i) by Eulers Formula[tex]y(t) e(cos(5t) isin(5t) \begin{bmatrix} -1+i\\ i \end{bmatrix}\\\\y(t)=e^t\begin{bmatrix} (cos(5t)i+i^2sin(5t))-(cos(5t)+isin(5t))\\ cos(5t)i+i^2sin(5t)) \end{bmatrix}\\y(t)=e^t\begin{bmatrix} (-sin(5t)-cos(5t)+(cos(5t)-sin(5t))i\\ -sin(5t)+(cos(5t))i \end{bmatrix}[/tex]
Write the above solution x+yi[tex]y(t)=\left ( e^t \begin{bmatrix} -(sin(5t)+cos(5t))\\ -sin(5t) \end{bmatrix} \right )+\left ( e^t\begin{bmatrix} (cos(5t)-sin(5t))\\ cos(5t) \end{bmatrix} \right ) i[/tex]
The solution of the DE are[tex]y_{1}(t)= -e^t \begin{bmatrix} sin(5t)+cos(5t)\\ sin(5t) \end{bmatrix}\ and \ y_{2}(t)= e^t\begin{bmatrix} cos(5t)-sin(5t)\\ cos(5t) \end{bmatrix}[/tex]
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the othes solution in this picture: ↓↓↓↓↓↓↓↓↓↓↓↓↓↓↓↓↓↓↓↓↓↓↓↓
How do you list all rational roots using rational root theorem?.
The rational root theorem says that if you take all the factors of the constant term in a polynomial and divide by all the factors of the leading coefficient
The rational root theorem is also known as the rational zero theorem (or) the rational zero test (or) rational test theorem and is used to determine the rational roots of a polynomial function.
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When beth was 9 years old, paul was 3 times younger than her. Now beth is 30 years old, how old is paul?.
Step-by-step explanation:
9÷3=3 so when beth is 30 you need to do 30-6 which is 24
When beth was 9, paul was 3 times younger = 9/3 = 3 years old.
Beth has gained 21 years since, so the age of paul is 3 + 21 = 24 years old.
Is it a zero if it touches the x-axis?.
At the zero point the curve can either cross the x-axis or just touch it. The root of the function is the number c with f(c) = 0.
If the graph intersects the x-axis and looks nearly linear at the intersection, it is a single root. Even multiplicity zero if the graph touches the x-axis and bounces off the axis.
Different graphs with different x-intercepts. The graph may intersect the x-axis at the intersection. Otherwise, the graph touches the x-axis and bounces.
For example, suppose you plot a function.
f (x) = (x + 1) (x - 2)²
See the figure above to see how the function behaves differently for different x intercepts.
x intercept at x = -1 is the solution of the equation
x + 1 = 0 , graph goes straight through the x intercept at x= −1 . We call it a single zero because zero corresponds to a single factor in the function.
x intercept at x = 2 is the iterative solution of the equation ( x - 2 )= 0
The graph touches the axis at the intercept and changes direction. The coefficients are quadratic (order 2), so, (x-2)²= (x - 2 )(x - 2)
coefficients are repeated and appears twice. The number of times a given factor appears in the factored form of a polynomial equation is called its multiplicity. Zero associated with this factor, the factor is (x-2), occurs twice, and has a multiplicity of 2 .
thus, the behaviour of graph shows that any point of f(x) which touch or intersect x-axis is call zero of f(x).
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what is the probabiluity that in a random sample of 500 adults more than 30 percent do not own a credit card
Using p-hat formula and probability,
we get
a) Sampling distribution of p-hat = 0.02029286
b)The probability that in a random sample of 500 adults more than 30% do not own a credit card is
=0.3121
c) The probability that in a random sample of 500 adults between 25% and 30% do not own a credit card is 0.6635
We have given that
29% of adults do not own a credit card according to creditcard.com.
a) Sample size (n) = 500 of adults have own credit card
sample proportion, for the adults do not own a credit= 29% = 0.29
Normal distribution exits here with p
= 1-0.29=0.71 and
Standard error (p-hat) =sqrt(p(1-p)/n)
=sqrt(0.71× 0.29/500)
p-hat = 0.02029286
b) Now, more than 30% do not have own credit card.
P(p-hat>0.3) = P((phat- p)/sqrt(p×(1-p)/n) >(0.3-0.29)/sqrt(0.29× (1-0.29)/500))
=P(Z>0.49) =0.3121 (from standard normal table)
c) Sample size (n) = 500 and p-hat lies between 25% to 30% .
P(0.25<phat<0.3)
= P((0.25-0.29)/sqrt(0.29*(1-0.29)/500) <Z< (0.3-0.29)/sqrt(0.29*(1-0.29)/500))
=P(-1.97<Z<0.49)
=0.6635 (from standard normal table)
Hence, we calculated all the required probabilities.
a) p-hat = 0.02029286
b) P(p-hat>0.3) =0.3121
c) P(0.25<phat<0.3) =0.6635
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Complete question:
According to creditcard.com, 29% of adults do not own a credit card.
a. Suppose a random sample of 500 adults is asked, "Do you own a credit card?" Describe the sampling distribution of p-hat, the proportion of adults who own a credit card.
b. What is the probability that in a random sample of 500 adults more than 30% do not own a credit card?
c. What is the probability that in a random sample of 500 adults between 25% and 30% do not own a credit card?
Jacob wants to buy a $500,000 15-year term life policy, and the annual premium rate (per $1000 of face value) for his age group is $6. 78. If jacob lives until the end of the term of his policy, how much will jacob have paid in premiums overall? a. $101,700 b. $3,390 c. $50,850 d. $73,746 please select the best answer from the choices provided a b c d.
The required annual premium rate for the given term life policy is $50,850.
Explain term life policy and annual premium rate.Term life insurance covers you for a particular measure of time - basically, the strategy's term. The length of the term can change to suit your specific conditions. You can likewise look over two changed sorts of term disaster protection: diminishing term protection and level term protection.
annual premium rate:Annual Premium Rate implies, if pertinent, the exceptional rate so determined on the Statements Page of this Strategy to be utilized in processing a premium to be transmitted yearly.
According to quetion:Jacob needs to purchase a $500,000 15-year term life strategy, and the yearly superior rate (per $1000 of presumptive worth) for his age bunch is $6. 78.
Number of 1000 of every 500000 will be 500000/1000 = 500
the yearly superior rate (per $1000 of assumed worth) for his age bunch is $6. 78.
Absolute premium is 500 x 6.78 = 3390
The premium each year is 3390
For quite some time, the all out premium is
15 x 3390 = 50850
Thus, over all premium jacob have paid $50850.
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