Answer:it’s 1/4
Step-by-step explanation:
NO LINKS!!
The approximate lengths and diameters (in inches) of bright common wire nails are shown in the table. Find a logarithmic equation that relates the diameter y of a bright common wire nail to its length x. (Use the first and last lengths and diameters to form the equation. Round your answers to three decimal places.)
ln(y)=
Length, x Diameter, y
2. 0.113
3. 0.151
4. 0.192
5. 0.222
6. 0.262
Answer:
[tex]\ln (y) = 0.210x-2.601[/tex]
Step-by-step explanation:
Given table:
[tex]\begin{array}{|c|c|}\cline{1-2} \sf Length & \sf Diameter \\x & y\\\cline{1-2} \vphantom{\dfrac12} 2 & 0.113\\\cline{1-2} \vphantom{\dfrac12} 3& 0.151\\\cline{1-2} \vphantom{\dfrac12} 4& 0.192\\\cline{1-2} \vphantom{\dfrac12} 5& 0.222\\\cline{1-2} \vphantom{\dfrac12} 6& 0.262\\\cline{1-2} \end{array}[/tex]
To convert y = abˣ to linear form, take natural logs of both sides and rearrange:
[tex]\begin{aligned}y=ab^x \implies \ln y &= \ln ab^x\\\implies \ln y &= \ln a + \ln b^x\\\implies \ln y &= \ln a + x \ln b\\\implies \ln y &=x \ln b+ \ln a\end{aligned}[/tex]
This is in the straight-line form y = mx + c.
Substitute the first and last values of x and y from the table into the natural log formula:
[tex]\ln 0.113 = 2 \ln b+\ln a[/tex][tex]\ln 0.262 = 6 \ln b+\ln a[/tex]Subtract the first equation from the second equation to eliminate ln(a);
[tex]\implies \ln 0.262 - \ln 0.113 = 6 \ln b - 2 \ln b[/tex]
[tex]\implies \ln 0.262 - \ln 0.113 = 4 \ln b[/tex]
Apply the quotient log law:
[tex]\implies \ln \dfrac{0.262}{0.113} = 4\ln b[/tex]
Rearrange and solve for ln(b):
[tex]\implies \ln b = \dfrac{1}{4}\ln \dfrac{0.262}{0.113}[/tex]
[tex]\implies \ln b = 0.210\; \sf (3\;d.p.)[/tex]
Substitute the found value of ln(b) into one of the equations and solve for ln(a):
[tex]\implies \ln 0.262 = 6 \cdot \dfrac{1}{4}\ln \dfrac{0.262}{0.113}+\ln a[/tex]
[tex]\implies \ln a=\ln 0.262 -\dfrac{6}{4}\ln \dfrac{0.262}{0.113}[/tex]
[tex]\implies \ln a = -2.601\; \sf (3\;d.p.)[/tex]
Substitute the found values of ln(a) and ln(b) into the formula to create an equation for ln(y):
[tex]\boxed{\ln (y) = 0.210x-2.601}[/tex]
the following sorting algorithm is stable and in runs in place. none of the others quicksort counting sort mergesort. true or false
A stable sorting algorithm is one that keeps the relative order of two equal elements. Quicksort is a sorting algorithm that has a high degree of instability, which means that it may alter the relative order of two equal components.
Which sorting algorithm is stable?The Merge Sort, Timsort, Counting Sort, Insertion Sort, and Bubble Sort are just a few examples of popular sorting algorithms that are by their very nature stable. Others, like Quicksort, Heapsort, and Selection Sort, are erratic. Stable sorting algorithms can be modified to be more efficient.
Because we swap elements according on the location of the pivot, QuickSort is an unstable algorithm (without considering their original positions). A sorting algorithm is said to sort in-place if it never stores more than a fixed number of input array members outside of the array. If the order of elements with the same value is not altered by a sorting technique, it is stable. Binary insertion sort is the only stable algorithm available from the options offered.
Therefore the correct answer is false.
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If the point starts at and rotates counterclockwise, which statement is TRUE? a. x=cosθ andy=sinθ and both functions have a period ofπ . b. x=sinθ andy=cosθ and both functions have a period of 2π . c. x=sinθ andy=cosθ and both functions have a period ofπ . d. x=sinθ andy=cosθ and both functions have a period of 2π .
The correct statement regarding the unit circle is given as follows:
x = cos(θ) and y = sin(θ), and both functions have a period of 2π.
What is the unit circle?For an angle [tex]\theta[/tex] the unit circle is a circle with radius 1 containing the following set of points: [tex](\cos{\theta}, \sin{\theta})[/tex].
These points are contained according to the following identity:
[tex]\cos^2{\theta} + sin^2{\theta} = 1[/tex]
(standard identity of trigonometry).
From the x-coordinate and the y-coordinate of each point on the unit circle, the function definitions are given as follows:
x = cos(θ)y = sin(θ)The period of both functions is of 2π, as the entire unit circle forms an angle of 360º = 2π.
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I found it is 273 Megabytes is being download if the download is 17.7% completed how many megabytes have been downloaded Round your answer to the nearest 10th
The megabytes that have been downloaded will be 48 megabytes.
How to depict the percentage?Based on the information, percentage is a value or ratio that may be stated as a fraction of 100. If we need to calculate a percentage of a number, we should divide it's entirety and then multiply it by 100.
Since 273 megabytes is being download if the download is 17.7%, the megabytes that have been downloaded will be:
= 17.7% × 273
= 48 megabytes.
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What is the equation for the line that passes through the points (3, 4) and (5,8)
The equation of a line is typically given in the form y = mx + b, where m is the slope of the line and b is the y-intercept (the point where the line crosses the y-axis). To find the equation of the line that passes through the points (3, 4) and (5, 8), we need to first calculate the slope of the line.
The slope of a line is given by the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of two points on the line. In this case, we have:
m = (8 - 4) / (5 - 3) = 4/2 = 2
Now that we know the slope of the line, we can use one of the given points to find the y-intercept. Let's use the point (3, 4). If we plug the values of x and y into the equation y = mx + b, we get:
4 = 2 * 3 + b
4 = 6 + b
-2 = b
Therefore, the equation of the line that passes through the points (3, 4) and (5, 8) is:
y = 2x - 2
The height between two floors of a building is 10 feet. How many stairs would be required
if the rise of each stair is 8 inches?
Note: 1 foot = 12 inches
Answer:
15 stairs would be needed
Step-by-step explanation:
10x12= 120
15 x 8 = 120
In a study, the residents of Edinburgh, Scotland, were classified as having either black hair, brown hair, blonde hair, or red hair. The probabilities of a randomly selected resident having black, brown, or blonde hair are 0.17, 0.47, and 0.20 respectively. Assuming each resident has one of these four hair colors,(a) what is the probability that a randomly selected resident has red hair?(b) what is the probability that a randomly selected resident has brown or black hair?(c) what is the probability that a randomly selected resident does not have blonde hair?
a) probability that a randomly selected resident has red hair is 0.16
b) probability that a randomly selected resident has brown or black hair is 0.67
c) probability that a randomly selected resident does not have blonde hair is 0.8.
P(black hair color) = 0.17
P (Brown hair) = 0.47
P (blonde hair) = 0.20
a) Probablity that a randomly chosen resident has red hair is:
P(red hair) = 1 - P(black hair) - P(brown hair) - P(blonde hair)
=> 1 - 0.17 - 0.47 - 0.20
=> 0.16
b) P(brown hair) + P(black hair) is the likelihood that a randomly chosen resident has brown or black hair (black hair)
= 0.47 + 0.20
= 0.67
c) The Probability that a randomly chosen resident does not have blonde hair is equal to 1 - P (blonde hair)
=> 1 - 0.20
=> 0.8
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The probability that a randomly selected resident has red hair and brown or black and black, brown, or blonde hair is 0.16, 0.80 and 0.20
The probabilities of a randomly selected resident having black, brown, or blonde hair are 0.17, 0.47, and 0.20 respectively.
P (black hair) = 0.17
P (brown hair) = 0.47
P (blonde hair) = 0.20
The probability is the measure of the likelihood of an event to happen. It measures the certainty of the event. The formula for probability is given by; P(E) = Number of Favourable Outcomes/Number of total outcomes.
(a). Probability that a randomly selected resident has red hair is
P (red hair) = 1 -P(black hair)-P (brown hair)-P (blonde hair)
= 1 - 0.17 - 0.47 - 0.2
= 0.16
(b). Probability that a randomly selected resident has brown or black hair
= P (brown hair) + P (black hair)
= 0.47 + 0.20
= 0.67
(c). Probability that a randomly selected resident does not have blonde hair
= 1 - P (blonde hair)
= 1 - 0.20
= 0.80
Therefore, the probability is 0.16, 0.80 and 0.20.
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How many groups of \dfrac{7}{4}
4
7
start fraction, 7, divided by, 4, end fraction are in 111?
There are two groups of [tex]\dfrac{7}{4}[/tex], an integer which is equal to 1, and 0.75 which is decimal.
What is a fraction?A fraction is a numeral that represents a rational number.
Let a and b be two numbers, then their fraction can be represented as a/b.
The given fraction is,
[tex]\dfrac{7}{4}[/tex].
To find the groups of fraction,
Simplify the fraction,
[tex]\dfrac{7}{4} = 1 \dfrac{3}{4}\\\\ = 1.75[/tex]
There are two groups in the fraction of [tex]\dfrac{7}{4}[/tex] ,
Integer part which is 1.
And decimal part which is 0.75.
Hence, there are two groups of fraction [tex]\dfrac{7}{4}[/tex].
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Assume that a company uses a standard cost system and applies overhead to production based on direct labor-hours. It provided the following information for its most recent year:
Total budgeted fixed overhead cost for the year $ 300,000
Actual fixed overhead cost for the year $ 276,000
Budgeted direct labor-hours 60,000
Actual direct labor-hours 56,000
Standard direct labor-hours allowed for the actual output 58,000
What is the fixed overhead volume variance?
Multiple Choice
$20,000 U
$20,000 F
$10,000 U
$10,000 F
Group Ends
On solving the provided question, we can say that The $289,000 in fixed overhead that was used in production at that time
What are fixed overhead?In accounting and economics, expenses for a firm are referred to as "fixed costs," often known as "indirect costs" or "overhead costs" since they are independent of the volume of goods or services the organization produces. They often have a periodic nature, such monthly rent or interest payments. These expenses are frequently capital costs as well.
The fixed overhead rate equals the budgeted amount Budgeted hours / Fixed overhead costs
Fixed overhead rate (predetermined) = 300,000/60,000
The fixed overhead rate (predetermined) is $5 per hour.
Applied Standard hours permitted with a predetermined overhead rate equals fixed overhead (fixed)
Fixed overhead applied = 57,800 * $5 per hour
$289,000 for applied fixed overhead
Therefore, $289,000 in fixed overhead was allocated to production during that time.
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Spencer sampled 50 students of a private school who were questioned about their scores in Mathematics. Spencer wants to test the hypothesis that the private school students score better than the general public which has an average of 62 marks with a population standard deviation of 7 marks.
z equals fraction numerator x with bar on top minus mu over denominator begin display style fraction numerator sigma over denominator square root of n end fraction end style end fraction
If the sample mean is 65 marks, what is the z-score? Answers are rounded to the hundredths place.
The answer is 3.03
What is a sample mean?A sample mean is an average of a set of data . The sample mean can be used to calculate the central tendency, standard deviation and the variance of a data set.
Given here μ=62 σ=7 sample mean x = 65 and n=50
now the formula given is z= x-μ / σ÷√n
= 65-62 / 7÷√50
= 3√50/7
= 3.03
Hence the final answer is 3.03
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A family compares the cost of renting a truck from two different companies for its 2-day move to another state.The costs are shown in the table.
A. The functions are given as follows:
Company X: X(m) = 245.9 + 0.59m.Company Y: Y(m) = 91.9 + 0.79m.B. The company from which the family should rent the truck is: Company Y.
How to define the functions?There are two costs in the problem, given as follows:
Fixed costs: base, drop-off and insurance.Variable: cost per mile.The fixed costs for Company X are given as follows:
Base: 2 x 29.95 = 59.90.Drop-off: 150.Insurance: 2 x 18 = 36.The variable cost is of 0.59 per mile, hence the function, considering a trip of m miles, is given as follows:
X(m) = 59.90 + 150 + 36 + 0.59m.
X(m) = 245.9 + 0.59m.
The fixed costs for Company Y are given as follows:
Base: 2 x 19.95 = 39.90.Drop-off: included.Insurance: 2 x 26 = 52.The variable cost is of 0.79 per mile, hence the function, considering a trip of m miles, is given as follows:
Y(m) = 39.90 + 52 + 0.79m
Y(m) = 91.9 + 0.79m.
The trip is of 750 miles, hence the costs are given as follows:
X(750) = 245.9 + 0.59 x 750 = $688.4.Y(750) = 91.9 + 0.79 x 750 = $684.4.Due to the lower cost, Company Y should be chosen.
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In two or more complete sentences, describe the transformation(s) that take place on the parent function,
f(x) = log(x), to achieve the graph of g(x) = log(-3x - 9) - 1.
Answer:
The function g(x) = log(-3x - 9) - 1 is obtained from the parent function f(x) = log(x) through two transformations: a shift to the right and a shift downward. The shift to the right is achieved by multiplying x by -3 and subtracting 9, which results in a rightward shift in the function's graph. The shift downward is achieved by subtracting 1 from the final result, which results in a downward shift in the function's graph. These transformations result in a graph that is shifted to the right and downward compared to the graph of the parent function.
[tex]log( - 3x - 9) = log( 3( - x - 3)) \\ = log( 3) + log( - (x + 3))[/tex]
A vertical shift by 1 unit downwards
A vertical shift by log(3) units upwards
A horizontal shift by 3 units to the left
A reflection along the line x=-3
Consider the following three polynomial functions.
f(x) =3x3 +5x-2
9 (x) =582-3x +2 m(x) =2x2 - 2x
Write an expression to represent f(x) + [g (x) - m(x)].
Use the carrot (^) for exponents and leave no spaces between terms.
The Solution for the given problem is 6x² +4x
What is Polynomial?
A polynomial is a mathematical statement made up of indeterminates and coefficients that solely includes the operations of addition, subtraction, multiplication, and positive-integer powers of variables.
Solution:
We are given with the values of the following terms f(x), g(x), and m(x)
f(x) = 3x² + 5x - z
g(x) = 5x² - 3x + z
m(x) = 2x² - 2x
To find: f(x) + [g(x) - m(x)]
so, we need to put the respective values in the equation and simplify it
3x² + 5x - z + [5x² - 3x + z - 2x² + 2x]
3x² + 5x - z + [3x² - x + z]
6x² +4x
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A card is drawn from a pack of 52 playing cards. Find the probability that the card will be a king, given that it is a face card. (The face cards are the jacks, queens, and kings. Enter your probability as a fraction.)
Answer:
Step-by-step explanation:
There are 4 kings in a deck of playing cards.
There are 52 cards in a deck.
So the probability is 4 out of 52.
Which is 4/52,
Which can be reduced to 1/13.
4 divided by 4 = 1 and 52 divided by 4 =13.
find the measure of m< VTK
Measure of angle VTK is 90°.
Define angle.Angles come in many different varieties in geometry. Angle is among the most crucial and fundamental units. Two rays or lines are linked at their shared terminus when they create an angle. We use angles in many facets of our daily lives, starting with the construction of buildings, dams, and monuments, not only in mathematics. The study of angles is essential to civil engineering. Two rays (half-lines) combined into an angle have a single terminal. The latter is known as the vertex of the angle, while the rays are known as its sides, occasionally as its legs, and occasionally as its arms.
Given
∠VTK = 90°
∠VMK = 90°
∠VTK is given
∠VTK = 90°
Measure of angle VTK is 90°.
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round 87388 to the nearest thousand
Answer:
To round a number to the nearest thousand, we first need to identify the thousands digit in the number. In this case, the thousands digit is 8, because 87388 is between 80000 and 90000.
To determine whether to round up or down, we need to look at the hundreds digit, which is 7 in this case. If the hundreds digit is 5 or greater, we round up. If the hundreds digit is less than 5, we round down. In this case, the hundreds digit is 7, which is greater than or equal to 5, so we need to round up.
To round up, we add 1000 to 87388, which gives us 88388. So, 87388 rounded to the nearest thousand is 88000.
tan^2x/sec^2x + cot^2x/csc^2x
The value of the trigonometric expression will be 1. Then the correct option is C.
What is trigonometry?Mathematical capabilities inspect the collaboration between the aspects and points of a three-sided structure.
The meaning of straightforwardness is simplifying something to accomplish or get a handle on while likewise making it somewhat less troublesome.
The expression is given below.
⇒ tan²x / sec²x + cot²x / cosec²x
Simplify the expression, then the value of the expression is given as,
⇒ tan²x / sec²x + cot²x / cosec²x
⇒ (sin²x × cos²x) / cos²x + (cos²x × sin²x) / sin²x
⇒ sin²x + cos²x
⇒ 1
The worth of the mathematical articulation will be 1. Then, at that point, the right choice is C.
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which of the following graphs shows the solution set to the system of inequalities below? {y>12x 4y>5
Answer:
Step-by-step explanation:
The graph of the function f(x) = −1 + 0.5x is shown on the coordinate plane. For what value of x does f(x) = 2?
A.
x = -6
B.
x = 5
C.
x = 5
D.
x = 6
x = 6 is the value of x does f(x) = 2.
What is a function?
A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output. Each function has a range, codomain, and domain.
Here, we have
Given function: f(x) = −1 + 0.5x
We have to find the value of x does f(x) = 2.
For this, we put the different values of x and see what value satisfies the given function.
For x = -6
f(x) = −1 + 0.5(-6)
f(x) = -4
For x = 5
f(x) = −1 + 0.5(5)
f(x) = 1.5
For x = 6
f(x) = −1 + 0.5(6)
f(x) = 2
Hence, x = 6 is the value of x does f(x) = 2.
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An experiment is carried out to determine the relationship between the average speed (rpm) and power (hp) of a mixer.
Construct a scatter plot for the data obtained in the experiment. Complete your work in the space provided or upload a
file that can display math symbols if your work requires it. Be sure to label the axes and include an appropriate scale for
the numerical labels.
Answer:
Step-by-step explanation:
So your first point has x=325.0 and y=1.10, your second point has x=348.9 and y=1.40, and so on.
The graph should look something like this:
The conclusion that you would draw from your plot is that the power seems to vary linearly with the speed. The data points are almost in a straight line. They are not perfectly aligned, of course. There is always some variability in real data, but you can see a trend.
One hundred offices need to be painted. The workers choose between yellow, blue, or red paint. They decide that 45% of the offices will be painted yellow; 28% will be painted blue, and the remaining offices will be painted red. What amount of offices will be painted red?
Answer:
27 offices will be painted red-------------------------------------------------
Out of 100 offices:
45% of the offices will be painted yellow ⇒ 45 offices28% of the offices will be painted blue ⇒ 28 officesRemaining offices will be painted red:
100 - (45 + 28) = 100 - 73 =27Answer:
27 offices will be painted red.
Step-by-step explanation:
Yellow offices:
= 45% of 100 offices
= 0.45 × 100
= 45 yellow offices
Blue offices:
= 28% of 100 offices
= 0.28 × 100
= 28 blue offices
Red offices:
= Total number of offices - yellow offices - blue offices
= 100 - 45 - 28
= 55 - 28
= 27 red offices
Therefore, 27 offices will be painted red.
Holly wants to invest $6,800.00 in a savings account.
Determine the simple interest rate required for Holly's investment to grow to $16,500.00 in 14 years.
Round your answer to the nearest tenth of a percent and don't forget to include a percent sign, %, in
your answer.
The interest rate required to grow the investment to $16,500.00 is______
Answer:
Below
Step-by-step explanation:
16500 - 6800 = 9700 interest required to meet this situation in 14 years
6800 * i * 14 = 9700 where i = decimal interest
i = 9700/(6800*14) = .1018 = 10 .2 %
A restaurant wants to make sure that they are serving customers quickly enough. Every day for 10 days, they sample 16 random customers, and measure how long it is until the waiter shows up. Using this sample data, the company calculates the 3-sigma control limits as LCL = 3.5 minutes and UCL = 6.5 minutes.
What would be the LCL and UCL if the company uses 2-sigma control limits instead?
O LCL = 4.5 minutes and UCL = 5.5 minutes
O LCL = 4.5 minutes and UCL = 7.5 minutes
O LCL = 3 minutes and UCL = 7 minutes
O LCL = 4 minutes and UCL = 6 minutes
LCL would be 4 minutes and UCL would be 6 minutes if the company uses 2-sigma control limits instead.
Describe mean.The average of a group of variables is referred to as the mean in mathematics and statistics. There are several methods for calculating the mean, including simple arithmetic means (adding the numbers together and dividing the result by the number of observations), geometric means, and harmonic means. The arithmetic mean, also known as the arithmetic average or simply the mean or average, is the sum of a set of numbers divided by the total number of numbers in the set. The collection frequently consists of a series of findings from a survey, experiment, or observational study.
Given
LCL = 3.5 minutes
UCL = 6.5 minutes
Mean = LCL + UCL/2
Mean = 3.5 + 6.5/2
Mean = 5
Standard deviation = UCL - LCL/6
Standard deviation = 6.5 - 3.5/6
Standard deviation = 0.5
LCL = 5 - 2(0.5)
LCL = 4
UCL = 5 + 2(0.5)
UCL = 6
LCL = 4 minutes and UCL = 6 minutes
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Manuel watered all the flowers at a business park. While watering, he noticed the daisies had been planted in groups of 11 and the lilies had been planted in groups of 12. If Manuel watered the same number of each flower, what is the minimum number of each that he must have watered?
Answer:
The minimum number of daisies and lilies that Manuel must have watered is 11.Step-by-step explanation:
To find the minimum number of daisies and lilies that Manuel must have watered, we need to find the least common multiple (LCM) of 11 and 12. The LCM of two numbers is the smallest positive integer that is a multiple of both numbers.
To find the LCM of 11 and 12, we can list the multiples of each number and find the smallest number that appears in both lists. The multiples of 11 are 11, 22, 33, 44, 55, 66, 77, 88, 99, 110, 121, etc. The multiples of 12 are 12, 24, 36, 48, 60, 72, 84, 96, 108, 120, 132, etc.
We can see that the smallest number that appears in both lists is 11, which is the LCM of 11 and 12. Therefore, the minimum number of daisies and lilies that Manuel must have watered is 11. If he watered the same number of each flower, he must have watered at least 11 daisies and 11 lilies.
Evaluate 8a+3b-10+c^28a+3b−10+c
2
8, a, plus, 3, b, minus, 10, plus, c, squared when a=2a=2a, equals, 2, b=5b=5b, equals, 5, and c=4c=4c, equals, 4.
4
The solution is A = 37
The value of the equation A = 8a + 3b - 10 + c² is A = 37
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is given by
A = 8a + 3b - 10 + c²
When the value of a = 2 , the value of b = 5 and the value of c = 4 ,
The equation A is given as
Substitute the value of a , b and c in the equation , we get
A = 8a + 3b - 10 + c²
A = 8 ( 2 ) + 3 ( 5 ) - 10 + 4²
A = 16 + 15 - 10 + 16
On simplifying the equation , we get
A = 31 + 6
The value of A = 37
Therefore , the value of A is 37
Hence , The value of the equation A = 8a + 3b - 10 + c² is A = 37
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A circular rug is cut from a square piece of carpet. Each side of the square piece of Carpet is 40 inches long. After cutting out the circular rug, approximately how much carpet will be left over?
Answer:
Below
Step-by-step explanation:
Area of square - area of circle = remnant area of circle = pi r^2
(40 x 40) - pi (20^2) = 343 . 4 in^2 left over
( this assumes the circle touches the edges of the square)
Find the equation of the line tangent to the function at the given point. Your answer should be in slope-intercept form. SHOW ALL WORK, LABEL APPROPRIATELY. F(x)= x - 4x² + 7 at x = 1 Find the instantaneous rate of change of the function at the given value. f(x) = 2x² + x +1; -2
On solving the provided question, we can say that - the instantaneous rate of change of the function at the given value, by solving the equation y = 11 - 5x, f'(1) = 3-8 = -5
What is an equation ?A mathematical equation is a formula that uses the equals symbol (=) to link two expressions and represent their equivalence. A mathematical statement that demonstrates the equality of two mathematical expressions is an equation in algebra, in its most basic form. Consider the equation 3x + 5 = 14, where 3x + 5 and 14 are two expressions that are separated by the symbol "equal."
y = f(x) =
[tex]x^3 - 4x^2 + 7 \\at x =1[/tex]
f(x) = 3-4+7
= 6
F'(x) = [tex]3x^2 - 8x[/tex]
f'(1) = 3-8 = -5
equation = y - 6 = -5(x-1)
y = 11 - 5x
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The greatest common factor of 250 and 300 is?
Answer:
GCF: 50
Step-by-step explanation:
Let's test
50 ( 5 + 6)
= 250 + 300
So, my answer is correct!
find the solution of the differential equation dr sec21 dt tant 1 which passes through the point (x,5).
The solution of the differential equation is given by r = 5tan(t + c) where c is the constant of integration, determined by the initial condition (x, 5).
The given differential equation is dr sec21dt tant 1. This is a first order linear differential equation which can be solved using an integrating factor. The integrating factor is given by e^(integral(sec^2(t)dt)). The solution of the equation is given by
[tex]r = (integral(sec^2(t))) + c[/tex]
where c is the constant of integration
Let y = sec(2x)
dy/dt = 2tan(2x)sec(2x)
Now, substituting the given point, we get
5 = sec(2x)
⇒ 2x = arccosec(5)
⇒ x = arccosec(5)/2
Now, substituting this in the equation of the differentiable curve, we get
[tex]\int\limits^a_b {x} \, dx dy/dt = 2tan(arccosec(5))sec(arccosec(5))[/tex]
Hence, the solution of the differential equation passing through the given point is y = sec(2x) = sec(arccosec(5))
or r = sec(arccosec(5))
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5. A recent college graduate hopes to have $200,000 saved in their retirement account 25 years from now by contributing $150 per month in a 401(k) plan. The goal is to earn 10% annually on the monthly contribution. Will they have the $200,000 at the end of the 25 years?
Answer: No
Step-by-step explanation:
To determine whether the college graduate will have $200,000 saved in their retirement account after 25 years, we can use the formula for compound interest:
A = P * (1 + r/n)^(nt)
where A is the total amount of money in the account after the specified time, P is the initial amount of money deposited in the account, r is the annual interest rate, n is the number of times the interest is compounded per year, and t is the number of years the money is invested.
In this case, the initial amount deposited each month is $150, the annual interest rate is 10%, the number of times the interest is compounded per year is 12 (once per month), and the number of years the money is invested is 25. Plugging these values into the formula above gives us:
A = $150 * (1 + 10%/12)^(12*25) = $150 * (1.0083)^300 = $150 * 3.4955 = $524.33
Since the goal is to have $200,000 saved in the account after 25 years, the college graduate will not have enough money in their account if they contribute $150 per month at 10% interest. In order to reach their goal, they would need to save more money each month or earn a higher interest rate on their contributions.