It would take Annmarie and Gladys 96 minutes to plow the field together.
How long to plow field together?
Annmarie can plow a field in 240 minutes. Gladys can plow the same field 80 minutes faster than Annmarie.
So Gladys can plow the field in 240 - 80 = 160 minutes.
Let x be the time it takes for both of them to plow the field together.
The combined rate of Annmarie and Gladys is the sum of their individual rates.
Annmarie's rate is 1 field per 240 minutes, which is 1/240 field per minute.
Gladys's rate is 1 field per 160 minutes, which is 1/160 field per minute.
Their combined rate is:
1/240 + 1/160 = 1/x
Simplifying this equation:
1/x = (4/960) + (6/960) = 10/960
1/x = 1/96
Multiplying both sides by 96, we get:
x = 96 minutes
Therefore, it would take Annmarie and Gladys 96 minutes to plow the field together.
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Identify a product/service that is currently in the decline stage. Use the Product Lifecycle Concept to explain why you believe the product/service is at that stage .
Describe the strategic options for companies that are competing in a declining market. Provide specific examples too illustrate what these strategic options entail and how they differ .
One product/service that is currently in the decline stage is DVD rentals. The decline can be attributed to the rapid rise of digital streaming platforms and the decreasing popularity of physical media. Companies competing in a declining market have strategic options such as harvesting and divesting. Harvesting involves maximizing profits from the declining product/service by reducing costs and maintaining a loyal customer base, while divesting involves exiting the market and reallocating resources to more profitable ventures.
DVD rentals are in the decline stage of the product lifecycle due to several factors. The advent of digital streaming platforms like Netflix, Hulu, and Amazon Prime Video has revolutionized the way people consume media. The convenience and vast content libraries offered by these platforms have led to a significant decline in DVD rentals. Moreover, the proliferation of high-speed internet connections and the increasing availability of streaming devices have made it easier for consumers to access digital content.
In a declining market, companies have strategic options to consider. One option is harvesting, which involves maximizing profits from the declining product/service. Companies can achieve this by reducing costs associated with production, distribution, and marketing, as the demand for the product/service diminishes. They may also focus on retaining their loyal customer base by providing incentives, discounts, or exclusive offers. For example, DVD rental companies may lower rental fees, offer bundle deals, or introduce loyalty programs to retain their remaining customers.
Another strategic option is divesting, which involves exiting the declining market altogether. Companies may choose to reallocate their resources to more profitable ventures or invest in emerging technologies or industries. In the case of DVD rentals, companies could divest by shutting down physical rental stores and selling off their DVD inventory. They could then shift their focus to digital streaming services or invest in other areas with growth potential, such as content production or streaming device manufacturing.
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the answer is 3(7j 2 4j). translate the algebraic expression you created in question 1 to a verbal expression.
The algebraic expression "3(7j + 2 - 4j)" can be translated to the verbal expression "Three times the sum of seven times a number, two, and the negation of four times the same number."
The algebraic expression "3(7j + 2 - 4j)" can be translated into a verbal expression as follows: "Take a number, multiply it by seven, add two to the result, subtract four times the same number, and finally multiply the entire expression by three."
To break it down further, let's consider the variable j as the unknown number. Multiplying 7 by j gives us seven times the unknown number, 7j. Adding 2 to this term gives us 7j + 2. Then, subtracting 4j from this sum represents subtracting four times the same unknown number. So, we have 7j + 2 - 4j.
Finally, multiplying the entire expression by 3 gives us 3(7j + 2 - 4j). This means that the entire calculation described above is repeated three times.
In summary, the verbal expression for 3(7j + 2 - 4j) can be stated as "Three times the sum of seven times a number, two, and the negation of four times the same number."
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BC = 28 and BD = 32
CD=
FD=
EF=
EC=
The missing measures are:
CD = 28 cmFD = 16 cm EF = 23 cmEC = 46 cmBCDE is a rhombus where ,
BC = 28 and BD = 32
BC is one of the sides of the rhombus, thus, all the sides (CD, DE, EB) will be 28 cm.
So, CD = 28cm
Now, BD = 32 which is the diagonal of the rhombus.
The diagonals bisect each other at a 90-degree angle.
Hence, FD = 1/2 x BD = 1/2x32 = 16 cm.
So, FD = 16 cm
To find EF, we can consider ΔEFD , which is right-angled at F, FD = 16cm and ED = 28cm .
Thus, from Pythagoras theorem,
ED² = EF² + FD²
28² = EF² + 16²
EF = 22.97
EF = 23 cm
So, EF = 23 cm
EC would be two times EF( since diagonals bisect each other)
Therefore, EC = 2x23 = 46 cm
So, EC = 46 cm
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Complete question:
If each quadrilateral is a rhombus, find the missing measures
BC = 28 and BD = 32
Jessica bought a kitten from a pet store and recorded its weight at various times over a 6 month period.
She found the linear model that best fit the data was w = 0.45n + 0.12, where n is the number of months since Jessica bought the kitten and w is the kitten's weight in kilograms.
Drag and drop the correct numbers below to complete the sentence.
According to the model, the kitten gained approximately 0.45 kilograms every month and the kitten weighed approximately 0.12 kilograms when Jessica bought it from the store.
Linear functions: Completing a sentenceFrom the question, we are to drag and drop the correct numbers to complete the given sentence.
The given sentence is
According to the model, the kitten gained approximately ____ kilograms every month and the kitten weighed approximately ____ kilograms when Jessica bought it from the store.
From the given information,
The equation that fits the model is
w = 0.45n + 0.12
By comparing with the slope-intercept form a line,
y = mx + c
Where m is the slope
and c is the y-intercept
m = 0.45
and c = 0.12
This means the kitten gained approximately 0.45 kilogram every month and the initial weight of the kitten is 0.12 kilogram
Hence,
The kitten gained approximately 0.45 kilograms every month and the kitten weighed approximately 0.12 kilograms when Jessica bought it from the store.
Here is the complete question:
Jessica bought a kitten from a pet store and recorded its weight at various times over a 6 month period.
She found the linear model that best fit the data was w = 0.45n + 0.12, where n is the number of months since Jessica bought the kitten and w is the kitten's weight in kilograms.
Drag and drop the correct numbers below to complete the sentence.
According to the model, the kitten gained approximately ____ kilograms every month and the kitten weighed approximately ____ kilograms when Jessica bought it from the store.
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15 8/9 less than the product of 5 and a number b
15 8/9 less than the product of 5 and a number b:
\(\begin{gathered} (5\times b)-15\cdot\frac{8}{9} \\ or \\ 5b-\frac{143}{9} \end{gathered}\)(a) If tan A=x/y
prove that: y.cos2A +x.sin2A= y.
Please help me..
Answer: see proof below
Step-by-step explanation:
Use the following Double Angle Identities: cos 2A = 1 - 2sin²A
sin 2A = 2sinA · cosA
\(\text{Given:}\quad \tan A = \dfrac{x}{y}\)
Proof LHS = RHS
y cos 2A + x sin 2A = y
x sin 2A = y - y cos 2A
x sin 2A = y(1 - cos 2A)
\(\dfrac{x}{y}=\dfrac{1-\cos2A}{sin\ 2A}\)
\(\dfrac{x}{y}=\dfrac{1-(1-2sin^2A)}{2\sin A\cdot \cos A}\)
\(\dfrac{x}{y}=\dfrac{2sin^2A}{2\sin A\cdot \cos A}\)
\(\dfrac{x}{y}=\dfrac{\sin A}{\cos A}\)
\(\dfrac{x}{y}=\tan A}\)
This is a TRUE statement since it was given that \(\tan A = \dfrac{x}{y}\)
Compare the strengths and weaknesses of the horizontal and vertical methods for adding and subtracting polynomials. Include common errors to watch out for when using each of these methods.
Answer:
Overall vertical is visually better, if done correctly
it forces you to "line up" all the common exponents.
The disadvantage is that it usually requires re-writing the problem, and it takes up space.
most problems are presented horizontally, that becomes the issue to locate the common exponents.
in both cases the biggest issue is people forget
that when subtracting "subtracting a negative is like adding a positive"
-5x - (-8x) = 3x [that is a positive 3x]
or:
-7x
- - 10x
-------------
3x
everyone misses those eventually so you have to watch out for that in both methods
Step-by-step explanation:
What is the angle between the vector 3–√i j3i j and the positive x-axis?
The angle between the vector (3 - √2)i + 3j and the positive x-axis can be determined using trigonometry.
To find the angle between the vector and the positive x-axis, we can use the arctan function. The angle can be calculated by taking the arctan of the y-component divided by the x-component of the vector.
In this case, the vector is given as (3 - √2)i + 3j. The x-component is 3 - √2, and the y-component is 3. Using the arctan function, we can calculate the angle as arctan(3 / (3 - √2)).
By substituting the values into a calculator or using trigonometric identities, we can find the angle. It is important to note that the arctan function returns an angle in radians. If we want the result in degrees, we can convert it by multiplying the result by 180/π.
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Uhm i'm not too good at this so i would like an explanation and answer ples
Answer:ok
Step-by-step explanation:
Three customers have accounts owing money. The table shows the account balances.
Which customer owes the least amount of money?
Customer Balance
M. Palmer –$56.72
B. Leftwich –$74.19
R. Jordan –$54.31
Answer:
the answer is 160
Step-by-step explanation:
What is the coefficient of x in 2x + 5 = 8
Answer:
2
General Formulas and Concepts:
Algebra I
Leading Coefficients vs ConstantsStep-by-step explanation:
The leading coefficient will always be the number multiplied to the highest degree variable.
Our highest degree term is 2x. Our leading coefficient would then be 2.
Write aprogram to read the values of the variables X and n and Calculate and print the value of y defined y′=x+cosx+5tan−1x if n<0 y=(x−sinx)^2−sin2x if n=0 y=(x+e2x+sin(x−1.5))^2 if n>0
The given problem requires the solution of the defined function based on the values of the given input parameters in the if else condition.
So, we need to write a program that reads the values of the variables X and n and calculates and prints the value of y, which is defined as follows:
\(y′=x+cosx+5tan−1x if n<0\)
\(y=(x−sinx)^2−sin2x\)if
\(n=0 y=(x+e2x+sin(x−1.5))^2\) if n>0Let's create a Python program to solve the given problem. In Python, we use the if...elif...else statement to execute different blocks of code based on different conditions. Here's the solution:Python Program
:x = int(input("Enter the value of x: "))
n = int(input("Enter the value of n: "))
if n < 0:y = x + cos(x) + 5 * tan(x)
elif n == 0:
y = (x - sin(x)) ** 2 - sin(2 * x)
else:y = \((x + e ** (2 * x) + sin(x - 1.5))\)
** 2print("The value of y is", y)
In the above Python program, we first read the values of the input parameters x and n using the input() function. Then we use the if...elif...else statement to execute different blocks of code based on the value of n. If n is less than 0, we calculate the value of y using the formula\(y′=x+cosx+5tan−1x\). If n is equal to 0, we calculate the value of y using the formula y\(=(x−sinx)^2−sin2x.\)
And, if n is greater than 0, we calculate the value of y using the formula\(y=(x+e2x+sin(x−1.5))^2\). Finally, we print the value of y using the print() function.I hope this helps.
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A regular polygon has exterior angles of 60°
What is the sum of the polygon’s interior angles?
Answer:
720°
Step-by-step explanation:
The sum of the exterior angles of a polygon = 360°
Divide by 60 to find number of sides (n)
n = 360° ÷ 60° = 6
The sum of the interior angles of a polygon is
sum = 180° (n - 2) ← n is the number of sides
Here n = 6 , then
sum = 180° × 4 = 720°
The sum of the exterior angles of a regular polygon is 360º
Each exterior angle of a regular polygon is 60º/n
360º/n=60º
360/60=n
6=n
A polygon with 6 sides is a hexagon.
Use the formula (n-2)×180
(6-2)*180=4*180=720º
another solution...
you have 6 interior angles (hexagon)
if an exterior angle is 60º, the corresponding interior angle is 180-60=120º
you have 6 of these 120º angles
6*120=720º
A triangle has one angle that measures 5º more than twice the smallest angle, and the largest angle
measures 11° less than 3 times the measure of the smallest angle. Find the measures of the three angles.
Answer:
A = 82, B = 67 and C = 31
Step-by-step explanation:
Let the angles in the given triangle be;
A, B and C;
A is the largest angle and C is the smallest angle;
B = 5 + 2C ------ i
A = 3C - 11 ------ ii
A+ B + C = 180° ----- iii
Now, if we add equation i and ii;
A + B = 5+2C + 3C - 11
A+B = 5C - 6 ----- iv
Now insert equation iv into iii;
5C -6 + C = 180
6C = 180 + 6
6C = 186
C = 31
A = 3C - 11 = 3(31) - 11 = 93 - 11 = 82
B = 5 + 2C = 5 + 2(31) = 67
A = 82, B = 67 and C = 31
Determine whether the geometric series is convergent or divergent. 10 - 6 + 18/5 - 54/25 + . . .a. convergentb. divergent
After applying the ratio test to the given geometric series, the answer is option a: the series is convergent.
Is the given geometric series convergent or divergent?The given series is: 10 - 6 + 18/5 - 54/25 + ...
To determine whether this series is convergent or divergent, we can use the ratio test.
The ratio test states that a series of the form ∑aₙ is convergent if the limit of the absolute value of the ratio of successive terms is less than 1, and divergent if the limit is greater than 1. If the limit is equal to 1, then the ratio test is inconclusive.
So, let's apply the ratio test to our series:
|ax₊₁ / ax| = |(18/5) * (-25/54)| = 15/20.24 ≈ 0.74
As the limit of the absolute value of the ratio of successive terms is less than 1, we can conclude that the series is convergent.
Therefore, the answer is (a) convergent.
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the serving size for the granola that ted likes to eat for breakfast is 3/4 cup. how many servings are there in a box that holds 13 cups? (what operation should be used here? solve the problem.)
With one third of a serving remaining, there are 17 servings are there in a box that holds 13 cups.
Given that:
Each cup holds a bit more than 1 serving, so we know there are at least 13 servings in a box.
We need to know how many servings of 3/4 cup can be obtained from 13 cups.
now we need to divide 13 by 3/4
=13 ÷ 3/4
= 13 × 4/3
= 52/3
= 17\(\frac{1}{3}\)
With one third of a serving remaining, there are 17 servings total.
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if the number of times you take the test were independent of the chance you fail what could that mean?
if the number of times you take the test were independent variable of the chance you fail what could that mean the difficulty of the test is consistent and unchanging.
The difficulty of the test is consistent and unchanging, making it so that the chance of failing is solely determined by the individual's performance on the test. Factors such as knowledge of the subject and the ability to focus can play a role in a person's success, but the actual chance of failing is not affected by how many times the test is taken. This means that those who fail the test will have to work harder and prepare better in order to pass it on the next attempt. Taking the test multiple times does not guarantee a higher chance of success, as the difficulty remains the same each time due to independent variable.
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two numbers are in the ratio 2:3. if 3 is added to the numbers,the ratio changes to 11:4. find the numbers
Answer:
The numbers would be
Step-by-step explanation:
Going Accordingly to the question, the nos. are 2x and 3x.
then, \((\frac{2x+3}{3x+3} )=\frac{3}{4}\)
therefore, \(4(2x+3)=3(3x+3)\)
\(8x+12=9x+912-9=9x-8x3=x\)
. ×= & ×=
Food Bill= $48.06 and a 24% tip Tip = $ Total = $
\(\begin{array}{|c|ll} \cline{1-1} \textit{a\% of b}\\ \cline{1-1} \\ \left( \cfrac{a}{100} \right)\cdot b \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{24\% of 48.06}}{\left( \cfrac{24}{100} \right)48.06}\implies 11.5344~\hfill \underset{total}{\stackrel{48.06~~ + ~~11.53}{\approx 59.59}}\)
Answer:
59.59$
Step-by-step explanation:
24% of $48.06=11.5344
Total=11.5+48.06=$59.59
4 = 4 ( x + 10 ) solve for x
Answer:
x = -9
Step-by-step explanation:
mark helpfull give 5str and award brainliest
Answer:
x = -9
Step-by-step explanation:
4 = 4(x + 10)
=> 4/4 = x + 10
=> 1 = x + 10
=> x + 10 = 1
=> x = 1 - 10
=> x = -9
Perform the calculation and report your results to the correct number of significant figures. (10.52)(0.6721)
(19.09−15.347)
The results of the calculations are approximately 7.07 and 3.74, respectively, to the correct number of significant figures.
Performing the calculation:
(10.52)(0.6721) = 7.0671992
Rounding to the correct number of significant figures, we have:
(10.52)(0.6721) ≈ 7.07
Next, let's calculate (19.09 - 15.347):
(19.09 - 15.347) = 3.743
Rounding to the correct number of significant figures, we have:
(19.09 - 15.347) ≈ 3.74
Therefore, the results of the calculations are approximately 7.07 and 3.74, respectively, to the correct number of significant figures.
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describe transformation of \(y= \frac{x^{4} }{6x+6}\)
The transformation of \(\(y= \frac{x^{4} }{6x+6}\)\) graph is compressed by a factor of 2.
The function is a rational function in which the numerator is a degree 4 polynomial, and the denominator is a degree 1 polynomial.
Rational functions are in the form of \(\(f(x) = \frac{p(x)}{q(x)}\)\), where p(x) and q(x) are polynomial functions and the degree of p(x) is less than the degree of q(x).
To transform a graph of a function, one can translate, stretch, or reflect it.
Here are some of the transformations of the function \(\(y= \frac{x^{4} }{6x+6}\)\)
Vertical Shift: To get the new graph, we add or subtract a constant from the function.
When f(x) is replaced with f(x) + k, we get a graph that is k units above the graph of f(x). In this case, if we subtract 2 from the equation, we get the following equation:
\(y = (x^4) / (6x+6) - 2\)
This means that the graph of the function is shifted 2 units downwards.
Horizontal Shift: To get the new graph, we add or subtract a constant to the variable.
When f(x+c) is replaced with f(x), the graph is shifted c units to the left.
When f(x-c) is replaced with f(x), the graph is shifted c units to the right.
In this case, we can shift the graph by substituting x-2 for x in the function.
The new function is: \(y = ((x-2)^4) / (6(x-2)+6)\)
This means that the graph is shifted 2 units to the right.
Vertical Stretch/Compression: When a constant is multiplied to the function, the graph is vertically stretched or compressed.
In this case, if the function is multiplied by 2, we get the following function:
\(y = 2(x^4) / (6x+6)\)
This means that the graph is compressed by a factor of 2.
It can also be stretched by dividing the function by a constant.
Horizontal Stretch/Compression:
When a constant is multiplied to the variable of the function, the graph is horizontally stretched or compressed. In this case, if the variable is divided by 2, we get the following function:
\(y = (x^4) / (3x+3)\)
This means that the graph is compressed by a factor of 2.
It can also be stretched by multiplying the variable by a constant.
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At the deli, 2 turkey subs and 5 veggie subs cost $29. 4 turkey subs and 3 veggie subs cost
$30.
a) Create a linear system to model the equation. Include let statements
b) Solve the linear system to find the cost of a turkey sub and the cost of a veggie sub.
Answer:
4/9 of sales are veggie 5/9 are turkey
4/(4+5)=4/9
5/(4+5)= 5/9
4/9 x 27 = 12
5/9 x 27 = 15
12 veggie subs sold and
15 turkey subs sold
12+15=27 total sold
Step-by-step explanation:
The shop charges $6.72 for an extra large 12 ounce frozen yogurt. Which size gets you more frozen yougurt per dollar?
Answer:
To determine which size gets you more frozen yogurt per dollar, you need to calculate the cost per unit of frozen yogurt for each size. To do this, you can divide the price of the frozen yogurt by the size of the serving in ounces.
In this case, the cost per unit for the extra large 12 ounce frozen yogurt is $6.72 / 12 ounces = $0.56 per ounce.
If you are considering another size of frozen yogurt, you can use the same calculation to determine its cost per unit. For example, if the medium 8 ounce frozen yogurt costs $4.50, its cost per unit would be $4.50 / 8 ounces = $0.56 per ounce.
So, in this case, the extra large and medium sizes of frozen yogurt have the same cost per unit, so they are equal in terms of the amount of frozen yogurt you get per dollar.
Step-by-step explanation:
let f (X)=3x - 2 ; g(x)= 5x+1 compute the indicated values
a. (fof) (0)
b. (gog) (-7)
c. (fogof) (2)
Answer:
PHYLUM PLATYHELMINTHES is a great place to work for
What is the length of the hypotenuse in 2 decimal places
what is 3 x 3/7 as a fraction
hmmmmmmmmmm the. answer. is 9/7
The product 3 x 3/7 as a fraction can be written as 9/7.
Given are two numbers 3 and 3/7.
We have to find the product of these numbers.
These numbers has to written as the product as a fraction.
When a fraction is multiplied by a whole number, the whole number is multiplied with the numerator of the fraction by keeping the denominator same.
Here whole number is 3 and the fraction is 3/7
3 x 3/7 = (3 x 3) / 7
= 9/7
Hence the product is 9/7.
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A team of workers took 167.3 hours to complete a task. A smaller team of workers will complete the same task, but it will take them 1.25 times as long as it took the first team. Based on this information, which statement is true?
209.125
Step-by-step explanation:
Multiply the two: 167.3 *1.25
prove that:cosA/sinA -sinA/cosA=2cos^2A-1/sinA cosA
Answer:
To prove that cosA/sinA -sinA/cosA=2cos^2A-1/sinA cosA, we can start by multiplying both sides of the equation by sinA cosA:
cosA/sinA -sinA/cosAsinA cosA = (2cos^2A-1)/sinA cosAsinA cosA
Now we can simplify the left side of the equation by using the identity sin^2A + cos^2A = 1:
cosAcosA -sinAsinA = (2cos^2A-1)cosAsinA
Now we can simplify the right side of the equation by using the identity cos^2A = 1 - sin^2A:
cosAcosA -sinAsinA = (2(1 - sin^2A)-1)cosAsinA
Finally, we can simplify the right side of the equation by using the identity sinAcosA = (sinAcosA)/(sinA*cosA):
cosAcosA -sinAsinA = (2(1 - sin^2A)-1)(sinAcosA)/(sinA*cosA)
Since both sides of the equation are equal, we can conclude that the statement is true.
how to find side lengths of a triangle using angles
To find the side lengths of a triangle using angles, you can employ trigonometric ratios like sine, cosine, and tangent
To find the side lengths of a triangle using angles, you can follow these steps:
Identify the given information: Determine which angles are known and which angles are unknown. Let's assume you have the measures of angles A, B, and C.
Apply the angle sum property: In a triangle, the sum of the interior angles is always 180 degrees. So, if you have the measures of two angles, you can find the measure of the third angle by subtracting the sum of the known angles from 180 degrees.
Determine the relationship between angles and side lengths: In a triangle, the lengths of the sides are related to the angles through the trigonometric ratios. The most common ratios are sine (sin), cosine (cos), and tangent (tan).
Use the trigonometric ratios: Depending on the given information, you can use the appropriate trigonometric ratio to find the side lengths. For example:
If you know an angle and the length of the side opposite to that angle, you can use the sine ratio: sin(A) = opposite/hypotenuse.
If you know an angle and the length of the adjacent side, you can use the cosine ratio: cos(A) = adjacent/hypotenuse.
If you know an angle and the lengths of the two sides that form that angle, you can use the tangent ratio: tan(A) = opposite/adjacent.
Solve for the unknown side lengths: Once you have the trigonometric equation involving an angle and side lengths, you can solve for the unknown side length using algebraic manipulations or a calculator.
Repeat these steps for the other angles to find the lengths of the remaining sides. Remember to consider the units of measurement (degrees or radians) and apply the appropriate trigonometric functions based on the given information.
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a sign in the elevator of a college library indicates a limit of 16 persons. in addition, there is a weight limit of 2,500 pounds. assume that the average weight of students, faculty, and staff at this college is 155 pounds, that the standard deviation is 29 pounds, and that the distribution of weights of individuals on campus is approximately normal. a random sample of 16 persons from the campus will be selected.
The probability that a randomly selected group of 16 individuals from the campus will be selected is 0.8023 or 80.23%
Based on the sign in the elevator of the college library, the limit of 16 persons and weight limit of 2,500 pounds need to be adhered to. To ensure compliance with both limits, we need to consider both the number of people and their weight.
Assuming that the distribution of weights of individuals on campus is approximately normal with an average weight of 155 pounds and a standard deviation of 29 pounds, we can use this information to estimate the total weight of a group of 16 randomly selected individuals.
The total weight of a group of 16 individuals can be estimated as follows:
Total weight = 16 x average weight = 16 x 155 = 2480 pounds
To determine if this total weight is within the weight limit of 2,500 pounds, we need to consider the variability in the weights of the individuals. We can do this by calculating the standard deviation of the total weight using the following formula:
Standard deviation of total weight = square root of (n x variance)
where n is the sample size (16) and variance is the square of the standard deviation (29 squared).
Standard deviation of total weight = square root of (16 x 29^2) = 232.74
Using this standard deviation, we can calculate the probability that the total weight of the group of 16 individuals is less than or equal to the weight limit of 2,500 pounds:
Z-score = (2,500 - 2,480) / 232.74 = 0.86
Using a standard normal distribution table or calculator, we can find that the probability of a Z-score less than or equal to 0.86 is approximately 0.8023.
Therefore, the probability that a randomly selected group of 16 individuals from the campus will comply with both the number and weight limits in the elevator of the college library is approximately 0.8023 or 80.23%.
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