Answer:160
formula:y=kx
16=(16)(10)
=160
Step-by-step explanation:
Altina Restaurant Flexible Budget for November 2010
A. What was Watson’s actual check average? Was this higher or lower than the original budget and flexible budget check average?
b. Were Watson’s actual food sales higher or lower than the flexible budget? By how much? Was this favorable or unfavorable?
c. Was Watson’s actual food cost higher or lower than the original budget? Why do you think this is so?
d. Was Watson’s actual food cost higher or lower than the flexible budget? By how much? Was this favorable or unfavorable? How can Watson use this information in his report to his general manager?
e. Were Watson’s variable salaries, wages, and benefits higher or lower than the original budget?
f. Were Watson’s variable salaries, wages, and benefits higher or lower than the flexible budget? By looking at both the original budget and the flexible budget, what conclusion can you draw about Watson’s ability to control his labor costs?
g. Was Watson’s actual net income higher or lower than the flexible budget? By how much? Was this favorable or unfavorable?
h. Overall, how do you think Watson is doing at meeting the budget goals set by the general manager? How should he respond to his general manager’s claim that his department is operating at a “sub-par” performance level?
Walton's actual check average is $9.52
The actual food cost is lower than the flexible budget by $5020
What is Net Income?Net income considered a vital financial metric of an organization, delineates the earned sum after deducting expenses and taxes from total revenue.
The measure is indicative of the profitability status of an entity, portraying cash flow left over subsequent to settling all obligations. To uncover net income, business expenditures spanning across areas such as salaries, interest payments and rents alongside taxations are subtracted from entire receipts.
Ascertaining net income facilitates assessing the fiscal robustness and future prospects of a company for interested investors.
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Find the balance in the account after the given period.
$4000 principal earning 7% compounded annually, 8 years
The balance in the account after the given period is [tex]\$6,872.74[/tex]
we know that
The compound interest formula is equal to
[tex]\text{A}=\text{P}(1+\frac{\text{r}}{\text{n}})^{\text{nt}}[/tex]
where
A is the Final Investment Value
P is the Principal amount of money to be invested
r is the rate of interest in decimal
t is Number of Time Periods
n is the number of times interest is compounded per year
in this problem we have
[tex]\text{t}= 8 \ \text{years}[/tex]
[tex]\text{P}=\$4,000[/tex]
[tex]\text{r}=0.07[/tex]
[tex]\text{n}=1[/tex]
substitute in the formula above
[tex]\text{A}=\$4,000(1+\frac{0.07}{1})^{1\times8}=\$6,872.74[/tex]
Consider the quadratic function f(x) = 1/5x2 – 5x + 12. Which statements are true about the function and its graph? Select three options. The value of f(–10) = 82 The graph of the function is a parabola. The graph of the function opens down. The graph contains the point (20, –8). The graph contains the point (0, 0).
The three statements that are true about the function and its graph are:
The graph of the function is a parabola.
The graph opens downwards, since the coefficient of x² is positive.
The graph contains the point (0, 12), which can be obtained by substituting x=0 in the function.
To check the other statements:
What is the value of f(–10) = 82?To find f(-10), we substitute x=-10 in the function:
f(-10) = 1/5*(-10)² - 5*(-10) + 12 = 82. So the statement "The value of f(–10) = 82" is true.
To check if the graph contains the point (20,-8), we substitute x=20 in the function:
f(20) = 1/5*(20)² - 5*(20) + 12 = -68. This means the point (20,-8) does not lie on the graph of the function.
To check if the graph contains the point (0,0), we substitute x=0 in the function:
f(0) = 1/5*(0)² - 5*(0) + 12 = 12. This means the point (0,0) does not lie on the graph of the function.
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How many ways can 5 different cards be dealt from a standard 52-card deck?
Answer:
There are 2598960 different ways to choose 5 cards from a standard 52-card deck.
Answer:
(52−5)5 = 2598960 different ways to choose 5 cards from the available 52 cards.
Step-by-step explanation:
Find the Center and Radius (x-9)^2+(y+4)^2=36
Answer:
The center is (9, -4), and the radius is
√36 = 6.
If full employment is $2000, how large is the recessionary or inflationary gap?
Answer:
inflationary expenditure gap of $500
Step-by-step explanation:
At AE2 there is an inflationary expenditure gap of $500 (assuming full-employment output is $2000). The fiscal authority could increase taxes or decrease expenditures, which will shift the aggregate expenditures schedule down to AE0.
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A manufacturer records data on the battery life of a new product and discovers the data is normally distributed. The mean life of the battery is 120 hours and has a standard deviation of 10 hours. The manufacturer commits to replacing all batteries that last less than 100 hours. If 32,200 batteries were produced, how many would they expect to replace?
The firm expects replacing around 734 batteries out of the 32,200 produced.
How to determine how many batteries many would they expect to replaceusing the normal distribution formula z = (x - )
When z denotes the z-score,
x denotes the battery life of interest, is the mean battery life, and is the standard deviation.
For x = 100, use the z-score: z = (100 - 120) / 10 z = -2
Calculate the area under the normal curve to the left of z = -2.
0.0228 is the approximate value.
The number of batteries expected to be replaced by the manufacturer is equal to the proportion of batteries with a battery life of less than 100 hours multiplied by the total number of batteries produced:
Number of batteries to be replaced = 0.0228 x 32,200
734.16 batteries are expected to be replaced.
As a result, the firm anticipates replacing around 734 batteries out of the 32,200 produced.
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How many meters are in 7 kilometers?
A boat leaves a pier and travels 15 miles due east, then turns and travels 15 miles in the direction N 20° E. Which diagram represents the boat’s current distance, x, from the pier?
(diagrams attached below)
Answer: 20.64 miles.
Step-by-step explanation: The assignment of nomenclature to the location of the boat's initiation as point A, the termination of the first course of the excursion as point B, and the termination of the second course of the journey as point C is proposed. The present study reveals that the spatial positioning of point A and point B is separated by a distance of precisely 15 miles in an eastward direction. Similarly, point B and point C are separated by a distance of 15 miles, but oriented along the vector of N 20° E.
The application of trigonometry provides a means to determine the spatial separation between point B and point C. Based on computations, the distance from point B to point C has been estimated to be approximately 7.83 miles along the northward direction and approximately 14.16 miles along the eastward direction.
Henceforth, the computation of the distance between point A and point C (i.e., the prevailing separation of the boat from the pier) can be determined by the ensuing method:
The mathematical expression denoting the distance between points A and C, designated as AC, is given by the square root of the sum of the squares of the distances between points A and B, designated as AB, and between points B and C, designated as BC. In formulaic notation, this can be expressed as AC = √((AB)² + (BC)²).
The magnitude of the distance denoted by AC, between two points A and C, can be calculated using the Euclidean distance formula, which involves the square root of the sum of the squares of the differences between the corresponding coordinates of the two points. In this particular case, the calculation results in the expression √(15² + 14.16²).
The distance between points A and C, denoted as AC, can be expressed mathematically as the square root of the sum of the squares of the horizontal and vertical distances between them. Thus, AC = √(225 + 200.89), where 225 and 200.89 represent the square of the horizontal and vertical distance, respectively. This equation can be simplified to yield the measurement of the physical distance between points A and C in the applicable units of length.
The distance between points A and C is determined to be the square root of 425.89 in units of length.
The measurement of the distance between point A and point C is approximately equivalent to 20.64 miles.
Answer: Graph A.
Step-by-step explanation:
Please address the question
Answer:
The length of AB is
[tex] \sqrt{ {5}^{2} + {5}^{2} + {5}^{2} } = \sqrt{75} = 3 \sqrt{5} [/tex]
3√5 cm is about 6.7 cm.
helo me right answers only. algbera
The function with y-intercept as 1 is h(x) = 0.5(2)ˣ + 0.5.
How to find the function using the y-intercept?The y-intercept is the point where the graph intersects the y-axis. In other words, the y-intercept of a function is the value of y when x = 0.
Therefore, let's find the function with y-intercept as 1.
Hence,
h(x) = 0.5(2)ˣ + 0.5
Let's make x = 0 to check if the value of y = 1
Therefore,
h(x) = 0.5(2)ˣ + 0.5
h(0) = 0.5(2)⁰ + 0.5
h(0) = 0.5(1) + 0.5
h(x) = 0.5 + 0.5
h(x) = 1
Therefore, the function with y-intercept as 1 is h(x) = 0.5(2)ˣ + 0.5
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can someone please help me
50 Points Please help quickly
Answer:
Step-by-step explanation:
The first one is C!
And the second one is E!
If this helps, go to math-way, and type in each of the equations and it will graph it for you!
Janelle want to know how many square inches of plywood are needed to make the chest and find the number of square inches janelle needs
Therefore, Janelle would need 1872 square inches of plywood to make the chest.
One square inch equals how many inches?A square inch (sometimes known as an in2 or sq. in.) is a unit of area measurement. A square with sides that are one inch long has an area of one square inch: Two lengths are used to measure a square area.
The areas of all the sides must be added up in order to determine the surface area of the chest. For instance, if we use 1/2 inch plywood and the chest is 24 inches by 12 inches by 18 inches, the surface area of the chest would be:
Top and bottom: 2 * (24 inches * 12 inches) = 576 square inches
Front and back: 2 * (18 inches * 12 inches) = 432 square inches
Sides: 2 * (24 inches * 18 inches) = 864 square inches
Total surface area = 576 + 432 + 864 = 1872 square inches
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Substitute the supplied value and simplify both sides of the equation, if necessary. Then decide if the supplied value is or is not a solution.
m + 2(m + 1) = 14 {4}
The left-hand side simplifies to 14, and the right-hand side is also 14. Therefore, the equation is true when m = 4.
What is LHS and RHS?"LHS = RHS" stands for "left-hand side equals right-hand side". It is a notation commonly used in mathematics to show that two expressions are equal to each other.
Define Substitution?In mathematics, to substitute means to replace a variable or expression in an equation or function with a specific value or expression.
To substitute the value 4 for m in the given equation, we replace every occurrence of m:
m + 2(m + 1) = 14
4 + 2(4 + 1) = 14
4 + 2(5) = 14
4 + 10 = 14
14 = 14
14 is the result of simplifying the left and right sides, respectively. Consequently, when m = 4, the equation is accurate.
So, the value 4 is a solution to the given equation.
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Question 1(Multiple Choice Worth 2 points)
(Linear Functions LC)
Which of the following equations represents a linear function?
A x=1
B y=12²
C y-12-1
D4x-2=6
The equation that represents a linear function is D 4x - 2 = 6.
Which equation represents a linear function?A linear function is a function whose graph is a straight line. In general, the equation of a linear function can be written in the form y = mx + b, where m is the slope and b is the y-intercept.
Option A (x = 1) represents a vertical line passing through x = 1. Since the slope of a vertical line is undefined
Option B (y = 12²) represents a horizontal line passing through y = 144. Since the slope of a horizontal line is zero
Option C (y = 12-1) represents a horizontal line passing through y = 11. Since the slope of a horizontal line is zero
Option D (4x - 2 = 6) can be rewritten as 4x = 8 or x = 2. This is the equation of a vertical line passing through x = 2.
Therefore, the only equation that represents a linear function is D 4x - 2 = 6.
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The ratio of cookies to glasses of milk is 4:1. if there are 25 glasses of milk, how many cookies are there?
There are 100 cookies.
To find the number of cookies, we can set up a proportion using the given ratio of cookies to glasses of milk, which is 4:1. Let x be the number of cookies:
4/1 = x/25
Now, cross-multiply and solve for x:
1 * x = 4 * 25
x = 100
PLEASE HELP ASAP!!‼️ (proportional Relationships!) Extra points than 5!!
Please tell me which should I click for the 3 BOXES in each one of them!
Using equations, we can find the required equation for each of the cases as follows:
1. t = cd
2. t = qh
3. t = wm
Define equations?Equations are mathematical expressions that have two algebraic expressions on either side of the equals (=) symbol. It proves that the expressions printed on the left and right sides are equally valid. In each mathematical equation, we have LHS = RHS (left hand side = right hand side). Equations can be solved to find the value of an unknown variable that represents an unknown quantity. If there is no "equal to" symbol, a statement is not an equation. We'll consider that to be a term.
As per the question,
The total number of caps per day = c
Total number of caps made = t
Total number of days = d.
Now, the required equation will be:
t = c × d
⇒ t = cd
Coming to the next question,
Quizzes graded per hour = q.
Total number of quizzes = t.
Total number of hours = h.
So, the required equation will be:
t = q × h
⇒ t = qh.
Coming to the final question,
Words typed per minute = w.
Total number of words = t.
Total number of minutes = m
So, the required equation will be:
t = w × m
⇒ t = wm.
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Consider the quadratic function f(x) = x2 – 5x + 12. Which statements are true about the function and its graph? Select three options. The value of f(–10) = 82 The graph of the function is a parabola. The graph of the function opens down. The graph contains the point (20, –8). The graph contains the point (0, 0).
Answer:
Okay, based on your previous question and the analysis, the 3 statements that are true about the function f(x) = x2 – 5x + 12 and its graph are:
The graph of the function is a parabola.
The graph contains the point (0, 0).
So the options you should select are:
2) The graph of the function is a parabola.
The graph contains the point (0, 0).
Let me know if selecting options 2 and 5 makes sense! I can provide any additional details or clarification if needed.
Please let me know if you have any other questions! I'm happy to help explain any other concepts related to this quadratic function and its graph.
Consider the quadratic function f(x) = x2 – 5x + 12. Which statements are true about the function and its graph? Select three options. The value of f(–10) = 82 .The graph of the function is a parabola. The graph of the function opens down. The graph contains the point (20, –8). The graph contains the point (0, 0).
Okay, just to reiterate, based on the previous analysis, the 3 statements that are TRUE about the quadratic function f(x) = x2 – 5x + 12 and its graph are:
The graph of the function is a parabola. (true)
The graph contains the point (0, 0). (true)
The graph of the function opens down. (false, unknown without seeing graph)
The value of f(–10) = 82 (false)
The graph contains the point (20, –8). (false)
So you should select options:
2) The graph of the function is a parabola.
The graph contains the point (0, 0).
Please let me know if selecting these 3 options makes sense and matches the analysis. I can re-explain anything if needed.
Your selected options should be:
2) The graph of the function is a parabola.
The graph contains the point (0, 0).
The graph of the function opens down.
Let me know if these look correct or if you have any other questions! I'm happy to help explain further or go over any part of the analysis.
Please select options 2, 5 and 3 as the statements that are true about the quadratic function and its graph.
Step-by-step explanation:
A store is having a sale on jelly beans and trail mix. For 5 pounds of jelly beans and 3 pounds of trail mix, the total cost is $20. For 7 pounds of jelly beans and
9 pounds of trail mix, the total cost is $46. Find the cost for each pound of jelly beans and each pound of trail mix.
Cost for each pound of jelly beans:
Cost for each pound of trail mix:
Answer:
1 pound of jelly beans cost $1.75 , 1 pound of trail mix cost $3.75
Step-by-step explanation:
let j represent 1 pound of jelly beans and t represent 1 pound of trail mix , then
5j + 3t = 20 → (1)
7j + 9t = 46 → (2)
multiplying (1) by - 3 and adding to (2) will eliminate t
- 15j - 9t = - 60 → (3)
add (2) and (3) term by term to eliminate t
(7j - 15j) + (9t - 9t) = 46 - 60
- 8j + 0 = - 14
- 8j = - 14 ( divide both sides by - 8 )
j = [tex]\frac{-14}{-8}[/tex] = 1.75
substitute j = 1.75 into either of the 2 equations and solve for t
substituting into (1)
5(1.75) + 3t = 20
8.75 + 3t = 20 ( subtract 8.75 from both sides )
3t = 11.25 ( divide both sides by 3 )
t = 3.75
then
cost of 1 pound of jelly beans = $1.75
cost of 1 pound of trail mix = $3.75
Answer:
Cost for each pound of jelly beans: $1.75
Cost for each pound of trail mix: $3.75
Step-by-step explanation:
Define the variables:
Let J be the cost of one pound of jelly beans.Let T be the cost of one pound of trail mix.Using the given information and defined variables, create a system of equations:
[tex]\begin{cases}5J+3T=20\\7J+9T=46\end{cases}[/tex]
To solve the system of equations, multiply the first equation by 3 to create a third equation:
[tex]5J \cdot 3+3T \cdot 3=20\cdot 3[/tex]
[tex]15J+9T=60[/tex]
Subtract the second equation from the third equation to eliminate the term in T:
[tex]\begin{array}{crcrcl}&15J & + & 9T & = & 60\\\vphantom{\dfrac12}- & (7J & + & 9T & = & 46)\\\cline{2-6}\vphantom{\dfrac12} &8J&&&=&14\end{array}[/tex]
Solve the equation for J by dividing both sides by 8:
[tex]\dfrac{8J}{8}=\dfrac{14}{8}[/tex]
[tex]J=1.75[/tex]
Therefore, the cost of each pound of jelly beans is $1.75.
To find the cost of one pound of trail mix, substitute the found value of J into one of the original equations and solve for T.
Using the second equation:
[tex]7(1.75)+9T=46[/tex]
[tex]12.25+9T=46[/tex]
[tex]12.25+9T-12.25=46-12.25[/tex]
[tex]9T=33.75[/tex]
[tex]\dfrac{9T}{9}=\dfrac{33.75}{9}[/tex]
[tex]T=3.75[/tex]
Therefore, the cost of each pound of jelly beans is $3.75.
ayuda porfavor
necesito resolver esto es simplificarlo no resolverlo ayuda pls
The Simplification of the algebraic expression gives:
a. -2/3x² - (4/15)xy + (11/4)y²
b. -(12/7)x³ + (20/9)y
How to simplify algebraic expressions?Simplification of an algebraic expression is the process of writing an expression in the most efficient and compact form without affecting the value of the original expression
a. (1/3)x² - (2/5)xy + 2y² + (2/15)xy - 3x² + (3/4)y²
To simplify this, add or subtract like terms. That is:
(1/3)x² - (2/5)xy + 2y² + (2/15)xy - 3x² + (3/4)y²
= (1/3)x² - 3x² - (2/5)xy + (2/15)xy + 2y² + (3/4)y²
= -2/3x² - (4/15)xy + (11/4)y²
b. (2/7)x³ - (1/3)y + 2y - 2x³ + (5/9)y
To simplify this, add or subtract like terms. That is:
(2/7)x³ - (1/3)y + 2y - 2x³ + (5/9)y = (2/7)x³- 2x³ - (1/3)y + 2y + (5/9)y
= -(12/7)x³ + (20/9)y
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If you deposit $2000 in an account paying 2% annual interest compounded monthly, how much money will you have in the account after 40 years?
Answer: To calculate the amount of money you will have in the account after 40 years, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
where A is the amount of money in the account after t years, P is the principal (the initial amount of money deposited), r is the annual interest rate (as a decimal), n is the number of times the interest is compounded per year, and t is the number of years.
In this case, P = $2000, r = 0.02 (since the interest rate is 2%), n = 12 (since the interest is compounded monthly), and t = 40. Plugging these values into the formula, we get:
A = 2000(1 + 0.02/12)^(12*40)
A = $5,837.85
So you will have $5,837.85 in the account after 40 years.
The probability that a certain science teacher trips over the cords in her classroom during any independent period of the day is 0.35. What is the probability that she trips for the first time during the 4th period of the day?
0.0150
0.0279
0.0961
0.1116
0.2275
The probability that the science teacher trips over the cords for the first time during the 4th period of the day is 0.0279.
What is discrete and continuous probability?A discrete probability distribution has countable alternative values for the random variable and a stated probability for each one. Since the potential values are 0, 1, or 2, and the probability of each conceivable value can be determined, the probability distribution of the number of heads acquired after two coin flips is an example of a discrete probability distribution.
In contrast, a continuous probability distribution has a continuous range of possible values for the random variable and a probability of zero for any given value.
Given that, the probability of tripping is given as: 0.35.
Now, the probability of tripping on the 4th period is given by:
[tex]P(X=k) = (1-p)^{(k-1)} * p[/tex]
Now, for k = 4 and p = 0.35 we have:
[tex]P(X=4) = (1-0.35)^{(4-1)} * 0.35[/tex]
P(X=4) = 0.0279
Hence, the probability that the science teacher trips over the cords for the first time during the 4th period of the day is 0.0279.
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125 pounds decreased by 4%
Answer:
Step-by-step explanation:
125 pounds decreased by 4% it would be 120 because 4% of 125 is 5, so you subtract 5 from 125 and then you get 120.
Damon recorded the snowfall in his town for each day of January. This line plot shows the distribution.
Snowfall in January
0
1
2
3
4
5
6
7
Inches
Complete the sentences.
The distribution of snowfall amounts is best described as
. So, the
is a more appropriate measure of variation than the
.
The distribution of snowfall amounts is best described as bimodal, with modes at 2 inches and 7 inches. So, the range is a more appropriate measure of variation than the standard deviation.
What is a bimodal distribution?A bimodal distribution can be identified in a histogram when two distinct groups can be seen there. A bimodal distribution actually has two modes or two different data clusters.
In a bimodal distribution, no particular data value has the highest frequency of occurrence, rather two data values have the highest frequency.
The line plot of the distribution by Damon has two modes and is, therefore, bimodal.
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abc x abc x abc in condensed form
The condensed form of the expression abc x abc x abc is (abc)^3
Expressing the expression in a condensed formWhen we have the same base raised to different exponents that are being multiplied together, we can simplify or condense the expression by adding the exponents.
In this case, we have the same base "abc" being raised to the exponent of 1 three times, so we can write it as:
abc x abc x abc
To condense this expression, we add the exponents 1+1+1=3, and write it as:
(abc)^3
So, the condensed form of the expression "abc x abc x abc" is "(abc)^3".
This is an example of the exponent rule for multiplying powers with the same base.
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The base of a triangle is 6 inches more than 4 times the height. If the area of the triangle is 90 square
inches, find the base and height.
The height of the triangle is 6 inches and the base of the triangle is 30 inches.
How can we find the height of the triangle ?Let's denote the height of the triangle as h inches. According to the given information, the base of the triangle is 6 inches more than 4 times the height, which can be expressed as 4h + 6 inches.
The formula for the area of a triangle is given by the formula A = (1/2) * base * height. Substituting the given values, we have:
90 = (1/2) * (4h + 6) * h
To solve for h, we can first multiply both sides of the equation by 2 to eliminate the fraction:
180 = (4h + 6) * h
Next, we can distribute the h on the right-hand side:
[tex]180 = 4h^2 + 6h[/tex]
Rearranging the equation to form a quadratic equation in standard form:
[tex]4h^2 + 6h - 180 = 0[/tex]
Now, we can solve this quadratic equation for h using factoring, completing the square, or the quadratic formula. Let's use the quadratic formula:
The quadratic formula states that for an equation of the form ax^2 + bx + c = 0, the solutions for x are given by:
[tex]x = (-b ± \sqrt{(b^2 - 4ac)) / (2a)}[/tex]
In our equation, a = 4, b = 6, and c = -180. Plugging in these values, we get:
[tex]h = (-6 ± \sqrt{(6^2 - 4 * 4 * -180)} ) / (2 * 4)[/tex]
Simplifying further:
[tex]h = (-6 ± \sqrt{(36 + 2880)} ) / 8h = (-6 ± \sqrt{(2916)} ) / 8[/tex]
h = (-6 ± 54) / 8
Now we can find the two possible values for h:
h1 = (-6 + 54) / 8 = 48 / 8 = 6
h2 = (-6 - 54) / 8 = -60 / 8 = -7.5
Since height cannot be negative in this context, we discard the solution h2 = -7.5.
So, the height of the triangle is 6 inches.
Now, we can use this value of h to find the base of the triangle:
Base = 4h + 6 = 4 * 6 + 6 = 24 + 6 = 30 inches.
So, the height of the triangle is 6 inches and the base of the triangle is 30 inches.
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Whitney bought a fountain online. It cost $60 plus 10% shipping and handling. What was the total cost?
Answer:
66 because 10 percent of 60 is 6 so add 60 and 6
An inductor of l = 250 is subjected to a voltage v(t) = 8 e-4t V:
A. Knowing that, integrate both sides to determine the current i(t). You may assume that the initial current is zero.
B. Given that the absorbed power is, determine the total stored energy.
Total stored energy = (1/625) ∞
What understand by voltage?Voltage, also known as electric potential difference, is the measure of the electric potential energy per unit of charge in an electric circuit. It is the force that drives the electric charge in a circuit, similar to how pressure drives water through a pipe. Voltage is measured in volts (V) and is usually represented by the symbol "V". Voltage can be either positive or negative, depending on the direction of current flow and the orientation of the voltage source.
A. The voltage across an inductor is proportional to the time derivative of the current through it, according to Faraday's law of electromagnetic induction. This can be expressed mathematically as:
v(t) = L di/dt
where v(t) is the voltage across the inductor, L is the inductance in henries, and di/dt is the time derivative of the current through the inductor.
In this case, we have [tex]v(t) = 8e^{(-4t)[/tex] V and L = 250 H. Integrating both sides of the above equation with respect to time gives:
∫v(t) dt = L ∫di/dt dt
∫[tex]8e^{(-4t)} dt = 250[/tex] ∫di/dt dt
[tex]-2e^{(-4t)[/tex]= 250i(t) + C
where C is the constant of integration. We can assume that the initial current is zero, so at t = 0, i(0) = 0. This means that C = -2. Substituting this into the equation above, we get:
[tex]-2e^{(-4t)[/tex]= 250i(t) - 2
Solving for i(t), we get:
i(t) = (2/250) [tex]- (2/250)e^{(4t)[/tex]
B. The power absorbed by an inductor is given by:
P = i² R
where P is the power, i is the current, and R is the resistance of the circuit. In an ideal inductor, the resistance is zero, so the power absorbed is also zero.
However, the energy stored in an inductor can be calculated using the following formula:
E = 1/2 L i²
where E is the energy stored, L is the inductance, and i is the current.
In this case, we have L = 250 H and i(t) = (2/250) [tex]- (2/250)e^{(4t)[/tex]Substituting these values into the above equation, we get:
E = 1/2 (250) [(2/250) [tex]- (2/250)e^{(4t)]^2[/tex]
Simplifying this expression, we get:
E = (1/625) [tex]- (2/625)e^{(4t)[/tex]+ (2/625)e^(8t)
To determine the total stored energy, we need to integrate this expression over the interval 0 to infinity, since the voltage and current are given for all values of t. This gives:
Total stored energy = ∫E dt from 0 to infinity
Total stored energy = (1/625) ∫1 dt from 0 to infinity[tex]- (2/625) ∫e^{(4t)[/tex]dt from 0 to infinity + (2/625) ∫e^(8t) dt from 0 to infinity
Total stored energy = (1/625) ∞ [tex]- (2/625) [1/4 e^{(4t)][/tex]from 0 to infinity + (2/625) [1/8 e^(8t)] from 0 to infinity
Since the integrals involving exponential functions go to infinity as t goes to infinity, these terms become zero. Therefore, we are left with:
Total stored energy = (1/625) ∞
which is an infinite value. This is because the energy stored in an inductor is not finite, but rather is dependent on the magnetic field generated by the inductor, which can extend infinitely far.
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Determine if the function below is continuous.
A. not continuous
B. both continuous and not continuous
C. cannot be determined
D. continuous
A. not continuous
Step-by-step explanation:Continuous functions have no jumps or vertical asymptotes.
Continuity
For a function to be continuous, each point on the function must be defined. This means that there cannot be points on the graph where there is no value or coordinate point. Additionally, all points must be connected by the graph. Sudden jumps in the graph that are not connected by anything are not continuous.
Determining Continuity
The graph above is not continuous. We know this for 2 reasons. Firstly, the graph is not defined at x = -3. Since there is an open circle at x = -3, the value is not defined. Thus, the function cannot be considered continuous. Additionally, there are multiple jumps. At x = -3, the function suddenly jumps to x = -2 without the points being connected. The same thing happens again at x = 1. This also shows that the graph is not continuous.