To find the percent error for the stopwatch's measurement of Stacy's time in her 50-meter freestyle race, we'll use the following formula:
Percent Error = (|(Measured Value - Actual Value)| / Actual Value) * 100
Here, the Measured Value is the stopwatch's time (32.4 seconds), and the Actual Value is the electronic touchpad's time (32.36 seconds).
Step 1: Calculate the absolute difference between the measured and actual values:
|32.4 - 32.36| = 0.04
Step 2: Divide the absolute difference by the actual value:
0.04 / 32.36 = 0.001236
Step 3: Multiply the result by 100 to get the percentage:
0.001236 * 100 = 0.1236%
The percent error for the stopwatch's measurement of Stacy's time in her 50-meter freestyle race is approximately 0.124%.
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The radian measure -1.7 pi is equivalent to -306 degrees.
How does sleep affect memory retention?To find the percent error of the stopwatch's measurement, we need to compare it to the more precise electronic touchpad measurement. The formula for percent error is:
percent error = (|measured value - actual value| / actual value) x 100%
In this case, the measured value is 32.4 seconds, the actual value is 32.36 seconds, and the absolute difference between them is 0.04 seconds. Plugging these values into the formula, we get:
percent error = (|32.4 - 32.36| / 32.36) x 100% = 0.124%
Therefore, the percent error for the stopwatch's measurement is 0.124%. This means that the stopwatch's measurement was very close to the actual value, with an error of only 0.124% of the actual value.
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The temperature at any point (x, y) in a steel plate is T = 900 − 0.7x2 − 1.3y2, where x and y are measured in meters. At the point (3, 9), find the rates of change of the temperature with respect to the distances moved along the plate in the directions of the x- and y-axes.
At point (3, 9), the rate of change of temperature with respect to the x-axis is -4.2 °C/m, and with respect to the y-axis, it is -23.4 °C/m.
To find the rates of change of the temperature with respect to the distances moved along the x- and y-axes at point (3, 9), you need to compute the partial derivatives of the temperature function T(x, y) = 900 - 0.7x^2 - 1.3y^2 with respect to x and y.
For the x-axis:
∂T/∂x = -1.4x
At point (3, 9), ∂T/∂x = -1.4(3) = -4.2 °C/m
For the y-axis:
∂T/∂y = -2.6y
At point (3, 9), ∂T/∂y = -2.6(9) = -23.4 °C/m
So, at point (3, 9), the rate of change of temperature with respect to the x-axis is -4.2 °C/m, and with respect to the y-axis, it is -23.4 °C/m.
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A contractor is building a set of stairs out of concrete. Each stair is exactly the same length, width, and height.
(a) Which solid figures can the stairs be broken into? What are the dimensions of each solid figure?
(b) How much concrete will be needed to form the stairs?
The stairs can be broken up into three rectangular prisms
The concrete that will be needed to form the stairs is 9.72 m ^3
How to solve for the amount of concreteTo get the volume of concrete
Since they are 3
2.7 / 3
= 0.9
1.5 / 3
= 0.5
0.5 + 0.5
= 1
each width is 3.6m
The volume of each = 0.9 x 1.5 x 3.6 = 4.86
Volume 2 = 0.9 x 1.0 x 3.6 = 3.24
Volume 3 = 0.9 x 0.5 x 3.6 = 1.62
amount of concrete = 1.62 + 3.24 + 4.86
= 9.72 m ^3
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The value of P from the formula I= PRT/100 when I = 20, R= 5 and T= 4 is ?
The value of P from the formula I= PRT/100 when I = 20, R= 5 and T= 4 is 100.The formula I = PRT/100 is used to calculate the simple interest on a principle amount, where P is the principle amount, R is the interest rate, and T is the time period.
To find the value of P from the formula I = PRT/100 when I = 20, R = 5, and T = 4,
Write down the formula: I = PRT/100 Plug in the given values: 20 = P(5)(4)/100Simplify the equation: 20 = 20P/100 Solve for P: P = 20(100)/20 = 100Therefore the value of P is 100.
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Elizabeth is considering buying a $30,000 car. Which of these financing options
will likely lead to the LOWEST monthly payment?
$3000 down payment, 6% interest, 84 months
$3000 down payment, 6% interest, 60 months
$0 down payment, 6% interest, 60 months
$0 down payment, 0% interest, 36 months
The financing option that will likely lead to the lowest monthly payment is:
$3000 down payment, 6% interest, 84 months
The longer loan term (84 months) will spread out the payments over a longer period of time, resulting in a lower monthly payment. The down payment will also help to reduce the monthly payment amount.
The 6% interest rate is relatively low, so it won't have a significant impact on the monthly payment compared to the loan term.
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The diameter of Circle Q terminates on the circumference of the circle at (0,3)and (0,−4). Write the equation of the circle in standard form. Show all of your work.
Need answer ASAP Please!!
Answer:
[tex]x^2+\left(y+\dfrac{1}{2}\right)^2=\dfrac{49}{4}[/tex]
Step-by-step explanation:
The center of the circle is the midpoint of its diameter.
[tex]\boxed{\begin{minipage}{7.4 cm}\underline{Midpoint between two points}\\\\Midpoint $=\left(\dfrac{x_2+x_1}{2},\dfrac{y_2+y_1}{2}\right)$\\\\\\where $(x_1,y_1)$ and $(x_2,y_2)$ are the endpoints.\\\end{minipage}}[/tex]
Given the endpoints of the diameter are (0, 3) and (0, -4), to find the coordinates of the center of the circle, substitute the two endpoints into the midpoint formula:
[tex]\text{Center}=\left(\dfrac{0+0}{2},\dfrac{-4+3}{2}\right)=\left(0,-\dfrac{1}{2}\right)[/tex]
As the x-values of the endpoints of the diameter are the same, the length of the diameter, d, is the absolute value of the difference in y-values of the endpoints:
[tex]d=|3-(-4)|=7[/tex]
Therefore, the diameter of circle Q is 7 units.
The radius, r, of a circle is half its diameter. Therefore:
[tex]r=\dfrac{d}{2}=\dfrac{7}{2}[/tex]
[tex]\boxed{\begin{minipage}{4 cm}\underline{Equation of a circle}\\\\$(x-h)^2+(y-k)^2=r^2$\\\\where:\\ \phantom{ww}$\bullet$ $(h,k)$ is the center. \\ \phantom{ww}$\bullet$ $r$ is the radius.\\\end{minipage}}[/tex]
Now we have determined the center and radius of circle Q, we can substitute these values into the equation of a circle to write the equation of circle Q in standard form:
[tex](x-0)^2+\left(y-\left(-\dfrac{1}{2}\right)\right)^2=\left(\dfrac{7}{2}\right)^2[/tex]
[tex]x^2+\left(y+\dfrac{1}{2}\right)^2=\dfrac{49}{4}[/tex]
Therefore, the equation of circle Q in standard form is:
[tex]\boxed{x^2+\left(y+\dfrac{1}{2}\right)^2=\dfrac{49}{4}}[/tex]
7. A rectangular prism has a volume of 135ft^3. The width of the rectangular prism is (2x+10)ft. The height of the rectangular prism is 5 times it's width. Write a expression that gives the length of the rectangular prism in feet?
A. 4(x+5)/27 B. 27/4(x+5)
C. (2x^2+100)/27. D. 27/(2x^2+100)
The expression that gives the length of the rectangular prism in feet is option D: 27/(2x^2+100).
What is the expression that gives the length of the rectangular prism in feet?The volume of a rectangular prism is given by the formula V = lwh, where l is the length, w is the width, and h is the height.
We are given that the volume of the rectangular prism is 135ft^3, and the width is (2x+10)ft. Also, the height is 5 times the width, so h = 5w.
Substituting these values in the formula for the volume, we get:
135 = l(2x+10)(5w)
Dividing both sides by (2x+10)(5w), we get:
l = 135 / (2x+10)(5w)
l = 135 / [10(x+5)w]
Now we can substitute h = 5w:
l = 135 / [10(x+5)h/5]
l = 135 / [2(x+5)h]
l = 135 / [2(x+5)(5w)]
l = 135 / [10(x+5)^2]
Simplifying the expression, we get:
l = 27 / (2(x+5)^2)
Therefore, the expression that gives the length of the rectangular prism in feet is option D: 27/(2x^2+100).
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In ms. Oaks class 5/12 of the students wear glasses, 2/9 of the students wear earrings, 2/18 of the students wear hats, and 1/4 of the students wear a watch. No one wears more than one of these items. 4 students wear hats.
A. How many students are in ms. Oaks class?
b. Determine how many students wear each type of item.
please explain how you got the answer, im having trouble figuring out how to find the answer
There are 36 students in Ms. Oaks' class. The number of students who wear each type of item is: Glasses: 15 students, Earrings: 8 students, Hats: 4 students and Watch: 9 students
Let the total number of students in Ms. Oaks' class be x.
a) We know that 2/18 of the students wear hats, which is equivalent to 1/9 of the students. We are also told that 4 students wear hats. So, we can set up an equation:
1/9 * x = 4
Solving for x, we get:
x = 36
Therefore, there are 36 students in Ms. Oaks' class.
b) We can now use the information given to determine how many students wear each type of item.
- Glasses: 5/12 of the students wear glasses, which is equivalent to:
(5/12) * 36 = 15 students
- Earrings: 2/9 of the students wear earrings, which is equivalent to:
(2/9) * 36 = 8 students
- Hats: We are told that 4 students wear hats.
- Watch: 1/4 of the students wear a watch, which is equivalent to:
(1/4) * 36 = 9 students
Therefore, the number of students who wear each type of item is:
Glasses: 15 students
Earrings: 8 students
Hats: 4 students
Watch: 9 students
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The preimage and image of WXYZ are shown. Use coordinate notation to describe the translation.
The image of WXYZ moves two unit to the right and 5 unit down. The coordinate is (x+2, y-5).
The polar system of coordinates is a coordinate system with two dimensions in which the location of each point can be determined by its distance from the origin, a fixed point, and its angle from the polar axis, also known as the polar axis of rotation. A ray beginning at the origin and extending outward at a set angle, typically 0 degrees or horizontal, is how the polar axis is typically depicted. The image of WXYZ moves two unit to the right and 5 unit down. The coordinate is (x+2, y-5).
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if the atlanta hawks free throw percentage is 82%, what is the probability that a player for the hawks will make 2 free shots in a row?
Answer:
Approx 67.24%
Step-by-step explanation: If the Atlanta Hawks' free-throw percentage is 82%, the probability that a player will make one free throw is 0.82.
To find the probability that a player will make two free throws in a row, we can use the multiplication rule of probability which states that the probability of two independent events occurring together is the product of their individual probabilities.
Therefore, the probability of a player making two free throws in a row can be calculated as follows:
P(making two free throws in a row) = P(making first free throw) x P(making second free throw)
P(making two free throws in a row) = 0.82 x 0.82
P(making two free throws in a row) = 0.6724 or 67.24%
Therefore, the probability that a player for the Atlanta Hawks will make two free shots in a row is approximately 67.24%
The likelihood that a child will attend a live musical performance can be modeled by
q = 0.01(0.0005x2 + 0.38x + 35) (15 ≤ x ≤ 100).
Here, q is the fraction of children with annual household income x thousand dollars who will attend a live musical performance during the year. Compute the income elasticity of demand E at an income level of $30,000. (Round your answer to two significant digits.)
E =
Interpret the result.
At a family income level of $_______ , the fraction of children attending a live musical performance is increasing by ________% per 1% increase in household income.
E = 0.01(0.0005(30)^2 + 0.38(30) + 35)(2*0.0005(30) + 0.38) ≈ 0.63
Interpretation: The income elasticity of demand is 0.63, which means that for every 1% increase in household income, the fraction of children attending a live musical performance increases by 0.63%.
At a family income level of $30,000, the fraction of children attending a live musical performance is increasing by 0.63% per 1% increase in household income.
To compute the income elasticity of demand E at an income level of $30,000, we need to find the derivative of q with respect to x, and then evaluate it at x=30. The derivative of q with respect to x is:
dq/dx = 0.01(0.001x + 0.38)
Now, let's evaluate this derivative at x=30:
dq/dx = 0.01(0.001(30) + 0.38) = 0.004
To calculate the income elasticity of demand E, we use the formula:
E = (dq/dx)(x/q)
First, let's find q at x=30:
q = 0.01(0.0005(30)^2 + 0.38(30) + 35) = 0.178
Now, we can find E:
E = (0.004)(30/0.178) ≈ 0.67
Interpret the result:
At a family income level of $30,000, the fraction of children attending a live musical performance is increasing by approximately 67% per 1% increase in household income.
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Point A is located at (−2, 2), and point M is located at (1, 0). If point M is the midpoint of segment AB, find the location of point B.
(−0. 5, 1)
(4, −2)
(−5, 4)
(−1, 1)
The location of point B is (4, −2). So the answer is (4, −2).
How to find the location of the point B?To find the location of point B, we can use the midpoint formula, which states that the coordinates of the midpoint of a line segment with endpoints (x1, y1) and (x2, y2) are:
((x1 + x2)/2, (y1 + y2)/2)
In this case, we know that point M is the midpoint of segment AB, and we know the coordinates of point M. We also know the coordinates of point A. So we can use the midpoint formula to solve for the coordinates of point B.
Let's call the coordinates of point B (x, y). We know that point M is the midpoint of segment AB, so we can set up the following equation:
((−2 + x)/2, (2 + y)/2) = (1, 0)
Simplifying this equation, we get:
(−2 + x)/2 = 1 and (2 + y)/2 = 0
Solving for x and y, we get:
x = 4 and y = −2
Therefore, the location of point B is (4, −2). So the answer is (4, −2).
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!!this is for financial mathematics!! please check if I am correct, thank youu :)
The total interest on a 20-year, 5.26% loan with a principal of $50,000 is $52,600.
How to calculate the interestFrom the information,
Principal: $50,000
Interest rate: 5.26%
Loan duration: 20 years
Total Interest = (Principal x Interest Rate x Loan Duration) / 100
Plugging in the values we have, we get:
Total Interest = (50,000 x 5.26 x 20) / 100
Total Interest = $52,600
The interest is $52600.
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3. 14
2. The volume of the cylinder is 141. 3 cubic
centimeters. What is the radius of the cylinder?
Use 3. 14 for T.
Need answer ASAP right now
The radius of the cylinder with volume of 141.3and height of 7 cm is 2.53cm.
The formula for the volume of a cylinder is V = πr²h, where r is the radius and h is the height. Given that V = 141.3 cm³ and using π ≈ 3.14, we can solve for r.
Rearranging the formula, we get r² = V/(πh), and plugging in the given values, we get r² = 141.3/(3.14*7). Since we don't know the height of the cylinder, we cannot solve for r exactly.
However, we can say that the radius of the cylinder is proportional to the square root of the volume, the height is 7 cm, then r = √(141.3/3.14*7) ≈ 2.53cm. If the height is different, the radius will change accordingly.
In summary, using the formula for the volume of a cylinder andheight of 7 cm, the radius of the cylinder with volume 141.3 cm³ and using π ≈ 3.14 is approximately 2.53 cm.
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Complete question:
The volume of the cylinder is 141. 3 cubiccentimeters. What is the radius of the cylinder given that height is 7cm? use π ≈ 3.14
company A charges $50 per month plus $0.05 per minute. Company B has no monthly charge but charges $0.15 per minute. When is the charge for the companies the same?
The charge for the companies is the same at 500 minutes
When is the charge for the companies the same?From the question, we have the following parameters that can be used in our computation:
Company A charges $50 per month plus $0.05 per minute. Company B has no monthly charge but charges $0.15 per minute.This means that
A(x) = 50 + 0.05x
B(x) = 0.15x
When the charge for the companies are the same, we have
0.15x = 50 + 0.05x
So, we have
0.1x = 50
Divide
x = 500
Hence, the number of minutes is 500
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The figure 2 is dilated from figure 1. Find the scale factor.
helpppp pleaseee!!!!
Answer:
Step-by-step explanation:
Part A Convert the mixed fraction into an improper fraction. 5 9 17 5 17 9 = = 94 17 Part B Select the decimal equivalent to the improper fraction in PART A approximated to two decimal places: (b) A 5.525 B 5.535 C 5.55 D 5.625
Part A: To convert the mixed fraction 5 9/17 to an improper fraction, we first multiply the whole number (5) by the denominator of the fraction (17), and then add the numerator (9). This gives us:
5 x 17 + 9 = 94
So 5 9/17 as an improper fraction is 94/17.
Part B: To find the decimal equivalent of 94/17, we divide the numerator (94) by the denominator (17) using a calculator or long division. The answer is approximately 5.53 when rounded to two decimal places.
Therefore, the decimal equivalent of the improper fraction 94/17 approximated to two decimal places is option B: 5.535.
The possible values of 'r' in a-bq + r are 0, 1, 2, 3, 4 and q = 4 then the possible maximum value is
A) 20
B) 25
C) 24
D) None
The possible maximum value of the expression is (d) None
Calculating the possible maximum value of the expressionFrom the question, we have the following parameters that can be used in our computation:
a = bq + r
The above expression is an Euclid's Division statement
The Euclid's Division Algorithm states that "For any two positive integers a, b there exists unique integers q and r such that:"
a = bq + r
where 0 ≤ r < b.
From the question, we have
q = 4
Max r = 4
Using 0 ≤ r < b, we have
Minimum b = 5
So, we have
a = bq + r
This gives
Min a = 5 * 4 + 4
Min a = 24
The above represents the minimum value of a
The maximum value cannot be calculated because as b increases, the value of the expression also increases
Hence, the possible maximum value is (d) None
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please show all work so i can understand! thanks!!
Classify each series as absolutely convergent conditionally convergent, or divergent. DO «Σ a (-1)k+1 k! k=1 b. Σ ka sin 2
For series Σ a(-1)^(k+1)k!, convergence depends on the limit of |a(k+1)/a(k)|. For series Σ ka sin(2), it diverges.
Consider the series Σ a(-1)^(k+1)k!, where a is a sequence of real numbers.
To determine the convergence of this series, we can use the ratio test
lim┬(k→∞)〖|a(k+1)(-1)^(k+2)(k+1)!|/|ak(-1)^(k+1)k!| = lim┬(k→∞)〖(k+1)|a(k+1)|/|a(k)||〗
If this limit is less than 1, then the series converges absolutely. If the limit is greater than 1, the series diverges. If the limit is equal to 1, then the test is inconclusive.
Let's evaluate the limit
lim┬(k→∞)〖(k+1)|a(k+1)|/|a(k)||〗 = lim┬(k→∞)〖(k+1)!/(k!k)|a(k+1)/a(k)||〗 = lim┬(k→∞)〖(k+1)/(k)|a(k+1)/a(k)||〗
Since lim┬(k→∞)〖|a(k+1)/a(k)||〗 exists, we can apply the ratio test again:
if the limit is less than 1, the series converges absolutely.
if the limit is greater than 1, the series diverges.
if the limit is equal to 1, the test is inconclusive.
Therefore, we can classify the series Σ a(-1)^(k+1)k! as either absolutely convergent, conditionally convergent, or divergent depending on the value of the limit.
Consider the series Σ ka sin(2), where a is a sequence of real numbers.
To determine the convergence of this series, we can use the alternating series test, which states that if a series Σ (-1)^(k+1)b(k) is alternating and |b(k+1)| <= |b(k)| for all k, and if lim┬(k→∞)〖b(k) = 0〗, then the series converges.
In this case, we have b(k) = ka sin(2), which is alternating since (-1)^(k+1) changes sign for each term. We also have
|b(k+1)|/|b(k)| = (k+1)|a|/k < k|a|/k = |b(k)|/|b(k-1)|
Therefore, |b(k+1)| <= |b(k)| for all k. Finally, we have
lim┬(k→∞)〖b(k) = lim┬(k→∞)〖ka sin(2)〗 = ∞〗
Since the limit does not exist, the series diverges.
Therefore, we can classify the series Σ ka sin(2) as divergent.
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Kadeesha invested $900 in an account that pays 1. 5% interest compounded annually. Assuming no deposits or withdrawals are made, find how much money Kadeesha
would have in the account 11 years after her initial investment. Round to the nearest
tenth (if necessary)
Kadeesha would have approximately $1187.80 in the account 11 years after her initial investment.
We can use the formula for compound interest to solve this problem. The formula is given by:
A = P(1 + r/n)^(nt)
where A is the amount after t years, P is the principal amount, 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 = $900, r = 0.015, n = 1 (since interest is compounded annually), and t = 11. Plugging these values into the formula, we get:
A = $900(1 + 0.015/1)^(1*11) = $1187.7989
Rounding this to the nearest tenth, we get $1187.80. Therefore, Kadeesha would have approximately $1187.80 in the account 11 years after her initial investment.
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3. Represent and Connect A jar has 20 marbles: 6 black, 4 brown, 8 white, and 2 blue. Julie draw
a marble from the jar.
a. What is the sample space?
b. What is the probability Julie will draw a white marble?
c. Which is more likely to happen, drawing a black marble or drawing either a brown
or blue marble?
d. Using this jar of marbles, what event has a probability of 0?
The event that has a probability of 0 is selecting a yellow marble
Other probabilities are listed below
Identifying the sample space and the probabilitiesThe items in the jar are given as
6 black, 4 brown, 8 white, and 2 blue.
These items are the sample space of this event
Hence, the sample space is 6 black, 4 brown, 8 white, and 2 blue.
For the probability Julie will draw a white marble, we have
P(White) = White/Total
So, we have
P(White) = 8/20
Simplify
P(White) = 2/5
For the event that is more likely to happen, we have
P(black marble) = 6/20
P(brown or blue marble) = (4 + 2)/20
P(brown or blue marble) = 6/20
The probabilities are equal
So, both events have equal likelihood
The event that has a probability of 0 could be the probability of selecting a yellow marble
This is because the jar has no yellow marble
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A project is budgeted for 1,200 hours and will last 6 weeks. a technician will be 25% billable to the project for the first three weeks and then 100% for the final three weeks. if a technician normally works 40 hours per week, how many total hours will the technician bill to the job?
The technician will bill a total of 150 hours to the job. To find the total hours, we need to determine how many hours the technician will work during the first three weeks and the last three weeks, and then add them together.
1. First three weeks:
The technician will be 25% billable during these weeks. They work 40 hours per week, so we need to calculate 25% of 40 hours for each week:
25% of 40 hours = 0.25 * 40 = 10 hours per week
Since there are three weeks, we'll multiply these hours by 3:
10 hours/week * 3 weeks = 30 hours
2. Last three weeks:
The technician will be 100% billable during these weeks. They work 40 hours per week, so they'll bill 40 hours for each of these weeks:
40 hours/week * 3 weeks = 120 hours
3. Finally,
we need to add the hours from the first and last three weeks together to find the total hours the technician will bill to the job:
30 hours (first three weeks) + 120 hours (last three weeks) = 150 hours
The technician will bill a total of 150 hours to the job.
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Please show me explanations on these
Answer:
1)55,44
2)6,4
3)49,8
4)11,7
5)12,444
6)23,04
7)12,46
8)15,06
9)31,68
10)30,4
Step-by-step explanation:
Recheck them and make sure there are no mistakes
Leland wants to paint a portrait for his parents using a photograph of them that is 5 inches wide by 8 inches high. He wants the portrait to be proportional to the photograph and 42 inches high. Which proportion can Leland use to find , the width he needs to use to make the portrait proportional?
The ratio to make the portrait proportional is width/42 = 5/8
Which proportion can Leland use to find , the width he needs to useFrom the question, we have the following parameters that can be used in our computation:
Photograph that is 5 inches wide by 8 inches high.
This means that
Ratio = width/height
Substitute the known values in the above equation, so, we have the following representation
Ratio = 5/8
Given that he wants the portrait to be proportional to the photograph and 42 inches high.
Then, we have
width/42 = 5/8
Hence, the ratio to make the portrait proportional is width/42 = 5/8
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There is 1. 75 liter of water in a rectangular container. The base of the container is square on the side 12 cm and its height is 16. 5 cm. How much more water is needed to fill the container to its brim? Give your answer in liter
0.626 liters of water is needed to fill the container to its brim.
The volume of the rectangular container can be found by multiplying the area of the base (length x width) by the height:
Volume of rectangular container = length x width x height
Since the base is a square with a side of 12 cm, the area of the base is:
Area of base = 12 cm x 12 cm = 144 cm^2
Converting the height to cm, we have:
Height = 16.5 cm
So the volume of the container is:
Volume = 144 cm^2 x 16.5 cm = 2376 cm^3
To convert the volume from cubic centimeters to liters, we divide by 1000:
Volume = 2376 cm^3 ÷ 1000 = 2.376 liters
Since there is already 1.75 liters of water in the container, the amount of water needed to fill the container to its brim is:
Amount of water needed = 2.376 liters - 1.75 liters = 0.626 liters
Therefore, 0.626 liters of water is needed to fill the container to its brim.
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(5)/(6)a+4(1)/(4)a
pls help i need it to finish
The required answer to the algebraic fraction [ {(5)/(6)}a + 4 {(1)/(4)}a ] is [ {(11)/(6)}a ] .
We can simplify this algebraic fraction problem by simple rule of fraction addition and with application LCM rule as,
{(5)/(6)}a + 4 {(1)/(4)}a
= {(5)/(6)}a + (1)a
= [{ (5)+ (6) }/(6)]a
= {(11)/(6)}a
The LCM (or, Least Common Multiple) rule is used for the two algebraic fraction here as the value that is divisible by the two given numbers in the denominator of the algebraic fractions. Then by rule, the numerators are multiplied by the factor of LCM of the denominator and then the numerators are added.
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The floor of a storage unit is 6.4 feet long and 6.2 feet wide. What is the distance between two opposite corners of the floor? If necessary, round to the nearest tenth.
Answer: 8.9
Step-by-step explanation:
This is pythagoras.
[tex]a^{2} + b^{2} = c^{2}\\6.4^{2} + 6.2^{2} = c^{2}\\40.96 + 38.44 = 79.4\\\sqrt{79.4} = 8.91066776398[/tex]
8.91066776398 = 8.9 (nearest tenth)
Consider the function f(x) = x^3 – 5x on the closed interval [ - 1,3). Find the exact value of the slope of the secant line connecting ( - 1, f( - 1)) and (3, f(3)). m = ?
To find the slope of the secant line connecting two points on a curve, we can use the formula: slope of secant line = (change in y) / (change in x).
In this problem, we are given the function f(x) = x^3 - 5x on the closed interval [-1, 3), and we need to find the slope of the secant line connecting (-1, f(-1)) and (3, f(3)). To do this, we first need to find the y-coordinates of these points by plugging the given x-values into the function f(x). Then, we can use the formula for the slope of a secant line to find the slope of the line connecting these two points.
The slope of a secant line is an important concept in calculus and is used to approximate the instantaneous rate of change of a function at a particular point.
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Apple Inc. Stock closes at $109. 99 per share. The next day the stock goes up $1. 49. What is the new price per share? (Just type the amount of money. Do not type the words "per share". )
The new price per share is $111.48.
Stock price is the current market value of a share of a publicly traded company's stock. It represents the price at which buyers and sellers agree to trade shares in the open market. Stock prices are determined by a variety of factors, including the company's financial performance, industry trends, and overall market conditions. The stock price is often used as an indicator of investor sentiment about the company and its future prospects.
To find the new price per share, follow these steps:
1. Note the initial stock price: $109.99
2. Note the increase in stock price: $1.49
3. Add the increase to the initial stock price: $109.99 + $1.49 = $111.48
The new price per share is $111.48.
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if a slope is when xincome in thousands of dollars, then what is the slope when income in dollars? (hint: a one-dollar change has only 1/1000 of the impact of a one-thousand-dollar change.)
If the slope is defined as the change in the dependent variable (y) divided by the change in the independent variable (x), then the slope would depend on how the dependent variable and independent variable are measured.
Assuming that the dependent variable y is some form of economic outcome (e.g., consumption, savings, investment) and the independent variable x is income, then the slope of the relationship would depend on the units in which income is measured.
If income is measured in thousands of dollars, then a one-unit change in income would correspond to a $1,000 change. Therefore, the slope would reflect the change in the economic outcome associated with a $1,000 change in income.
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