Answer:
69.56 meters
Step-by-step explanation:
Let's call the distance between the two people "y" and the length of the bridge "x". Using trigonometry, we can set up two equations:
tan(72.2°) = y / 25
tan(90° - 72.2°) = y / x
We can simplify the second equation to:
tan(17.8°) = y / x
Now we have two equations with two unknowns. We can solve for one of the variables in terms of the other and substitute into the other equation to solve for the unknowns.
First, let's solve for y in the first equation:
tan(72.2°) = y / 25
y = 25 * tan(72.2°)
y ≈ 69.56 meters
Now we can substitute this value of y into the second equation:
tan(17.8°) = y / x
tan(17.8°) = 69.56 / x
x = 69.56 / tan(17.8°)
x ≈ 202.11 meters
Therefore, the length of the bridge is approximately 202.11 meters and the distance between the two people is approximately 69.56 meters.
Find the value of the indicated trigonometric ratio.
cosβ
The value of the indicated trigonometric ratio.
cosβ is equal to 0.9167
What is trigonometric ratios?The trigonometric ratios is concerned with the relationship of an angle of a right-angled triangle to ratios of two side lengths.
The basic trigonometric ratios includes;
sine, cosine and tangent.
the side CA = 22 is adjacent to the angle β while BA = 24 is the hypotenuse, so:
cosβ = 22/24 {adjacent/hypotenuse}
cosβ = 11/12
cosβ = 0.9167
Therefore, the cosine of the angle β is equal to 0.9167 using the trigonometric ratio.
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Use Conditional Probability Notation to Describe Events Question Let M be the event that a randomly chosen student passes a math test. Let S be the event that a randomly chosen student studies every day. Identify the answer which expresses the following with correct notation: The probability that a randomly chosen student studies every day, given that the student passes a math test Select the correct answer below: O P(MS) OPM AND S) O P(S) AND P(M) O P(SM)
Answer:
Step-by-step explanation:
Which statement best compares and contrasts the two formats?
The infographic shows the movement of water visually, while the text describes it.
The infographic would be less appealing to visual learners than the text.
It is impossible to understand the infographic without the text.
The text is more accurate than the infographic.
The conditional probability that a randomly chosen student studies every day, given that the student passes a math test is O P(M|S). The correct option is A.
P(M|S) is the probability that a randomly chosen student passes a math test given that the student studies every day. But, the question is asking for the probability that a student studies every day given that the student passes a math test.
Considering an P(M|S) situation,
Option D: P(SM) is incorrect because it means the probability that both events S and M occur simultaneously.
Option C: P(S) and P(M) is incorrect because it shows the probabilities of two individual events, not the probability of one event given that the other event has occurred.
Option B: P(M AND S) is incorrect because it means the probability that both events M and S occur simultaneously.
The given problem is based on Conditional Probability Notation to Describe Events. The notation used for conditional probability is P(A|B). Where A and B are two events, the notation represents the probability of event A occurring, given that event B has occurred. Conditional probability can be described as the probability of one event happening given that another event has already happened.
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Maricarmen le pide un préstamo de $24,000 a su amigo, el cuál le dice que cada mes debe pagarle un 20% del préstamo. ¿Qué cantidad del préstamo habrá pagado Maricarmen a los tres meses?
The amount repaid in the three months of the loan amount $24,000 with a condition of 20% repayment is equal to $11,712.
Percent of amount Maricarmen has to pay = 20% of the loan each month.
This implies Maricarmen pay 0.2 times the loan amount each month.
Amount Maricarmen will pay in the first month is equal to,
0.2 x $24,000 = $4,800
Amount left after the first payment,
$24,000 - $4,800 = $19,200
In the second month, Maricarmen will pay,
0.2 x $19,200 = $3,840
Amount left after the second payment,
$19,200 - $3,840 = $15,360
In the third month, Maricarmen will pay,
0.2 x $15,360 = $3,072
Amount left after the third payment,
$15,360 - $3,072 = $12,288
total amount paid in three months,
$4,800 + $3,840 + $3,072 = $11,712
Therefore, after three months Maricarmen will have repaid a total of $11,712 of the loan.
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Help I do not know how to do this and now I’m stuck
Answer:
okay the answer is b[tex]\frac{1}{2}[/tex]
Step-by-step explanation:
One angle of a triangle measures 80°. The other two angles are in a ratio of 3:7. What are the measures of those two angles?
Answer:
30 degrees and 70 degrees
Step-by-step explanation:
A triangle has 180 degrees, and if you take away the known 80, you are left with 100 degrees to be split in a 3:7 ratio.
Angie is x years old. Mandy is 22 years older than Angie. In 2 years’ time, Mandy will be twice Angie’s age. Calculate Angie and Mandy’s current age
Answer:
Angie is 20, Mandy is 42.
Step-by-step explanation:
Angie's current age = x
Mandy's current age = y, also x + 22
Mandy's age in 2 years = 2x+2
2x + 2 = x + 22
x + 2 = 22
x = 20
y = x + 22
y = 20 + 22
y = 42
A circle has a radius of 3/2x^5y^-2 centimeters. To find the area of a circle the formula A = π • r^2 can be used. Which expression represents the are of the circle in square centimeters?
Answer:
Step-by-step explanation:
Correct option is B)
Center is the point of intersection of diagonals.
⇒2x−3y=5
⇒3x−4y=7
Solving simultaneous equation, x=1,y=−1
Center =(1,−1)
For radius r ( let )
⇒r=
π
154
⇒
22
154
×7
=7
Equation -
⇒(x−1)
2
+(y+1)
2
=7
2
⇒x
2
+1−2x+y
2
+1+2y=49
⇒x
2
+y
2
−2x+2y=49−2
⇒x
2
+y
2
−2x+2y=47
Hence, the answer is x
2
+y
2
−2x+2y=47.
Select the shapes that have at least 1 apex.
Right circular cone
Right circular cylinder
Right pyramid
Right triangular prism
A and B
A and C
B and C
C and D
Answer:
A and C : cones and pyramids
Step-by-step explanation:
only cones, pyramids and isosceles triangles have apexes
The shapes that have at least 1 apex are:
Right circular cone
Right pyramid
Therefore, the answer is C and D.
What is the probability of a surveyed college student having a hard time falling asleep on 3 or more days in the last week
Answer:
Without more information about the specific survey and population being surveyed, it is difficult to provide a precise answer to this question. However, I can provide some general information on how probabilities can be calculated in surveys.
Assuming that the survey is a representative sample of college students and that the question about difficulty falling asleep is a binary (yes/no) question, we can calculate the probability of a surveyed college student having a hard time falling asleep on 3 or more days in the last week as follows:
1. Determine the total number of surveyed college students who answered the question about difficulty falling asleep.
2. Determine the number of surveyed college students who reported having a hard time falling asleep on 3 or more days in the last week.
3. Divide the number of surveyed college students who reported having a hard time falling asleep on 3 or more days in the last week by the total number of surveyed college students who answered the question about difficulty falling asleep.
For example, if 1,000 college students were surveyed and 800 of them answered the question about difficulty falling asleep, and 200 of those 800 reported having a hard time falling asleep on 3 or more days in the last week, then the probability of a surveyed college student having a hard time falling asleep on 3 or more days in the last week would be 200/800, or 0.25, or 25%.
adian picks apples at the rate of 11 apples every minute. how many apples would he pick in 36 minutes
Answer:
Adian would pick 396 apples in 36 minutes.
Step-by-step explanation:
Therefore, in 1 minute, Adian picks 11 apples.
In 36 minutes, he will pick:
11 apples/minute x 36 minutes = 396 apples.
Therefore, Adian would pick 396 apples in 36 minutes.
Answer:
396 apples
Step-by-step explanation:
adian picks apples at the rate of 11 apples every minute
So in order to find out how many he picks in 36 minutes we just multiply 36 by 11
36 x 11 = 396 apples in 36 minutes
Hope this helps!
Brainliest and a like is much appreciated.
XY and BD are parallel lines. Work out BXC give a reason for each angle you work out
For XY and BD are parallel lines,
a) Complete sentence: Angle XBC = 55 degrees because XB = XC and angles opposite to equal sides of a triangle are equal.
b) The angle XBC is 55 degrees due to the equal sides XB = XC, and angle BXC is 125 degrees as the sum of angles in a straight line is 180 degrees.
Working out angle BXC:
Angle XBC = 55 degrees (given)
Angles XBC and BXC form a straight line, so:
Angle BXC = 180 - 55 = 125 degrees (sum of angles in a straight line)
Reasoning for each angle:
Angle XBC is given as 55 degrees because XB = XC and angles opposite to equal sides of a triangle are equal.
Angle BXC is found by subtracting the given angle XBC from the sum of angles in a straight line (180 degrees).
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The question is -
XY and BD are parallel lines.
X is a point on AB and C is a point on BD.
XB = XC.
a) complete this sentence.
Angle XBC = 55 Degrees Because . . .
b) Work out angle BXC.
give a reason for each angle you work out.
Algebraic proofs geometry
The method used to prove the values of the variables consists of solving the equations as presented in the following section.
What is an equation?An equation is a statement of equivalence between two expressions which is indicated by joining them with an '=' sign.
8. Statement [tex]{}[/tex] Reasons
(5·y - 1)/2 = 7 [tex]{}[/tex] Given
5·y - 1 = 2 × 7 [tex]{}[/tex] Multiplicative property of equality
5·y = 2 × 7 + 1 = 10 [tex]{}[/tex] Additive property of equality
5 = 10/5 = 2 [tex]{}[/tex] Division property of equality
9. Statement [tex]{}[/tex] Reasons
10·k - 4 = 2·k - 20 [tex]{}[/tex] Given
10·k = 2·k - 20 + 4 = 2·k - 16 [tex]{}[/tex] Additive property of equality
10·k - 2·k = 8·k = -16 [tex]{}[/tex] Subtraction property of equality
k = -16/2 = -8 [tex]{}[/tex] Division property of equality
10. Statement [tex]{}[/tex] Reasons
-8·(w + 1) = -5·(w + 10) [tex]{}[/tex] Given
-8·w - 8 = -5·w - 50 [tex]{}[/tex] Distributive property of equality
-5·w + 8·w = 3·w = 50 - 8 = 42 [tex]{}[/tex] Subtraction property of equality
4 = 42/3 = 14 [tex]{}[/tex] Division property of equality
11. Statement [tex]{}[/tex] Reasons
14 - 2·(x + 8) = 5·x - (3·x - 34) [tex]{}[/tex] Given
14 - 2·x - 16 = 5·x - 3·x + 34 [tex]{}[/tex] Distributive property of equality
2·x + 2·x = 4·x = -2 - 34 = -36 [tex]{}[/tex] Subtraction property of equality
x = -36/4 = -9 [tex]{}[/tex] Division property of equality
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Find the first five non-zero terms of Maclaurin series (Taylor series centered at x=0) for the function below as well as radius of convergence.
f(x)=xe^x
Answer:
To find the Maclaurin series for $f(x) = xe^x$, we can use the formula for the Maclaurin series of $e^x$ and differentiate the product term by term:
$$e^x = \sum_{n=0}^\infty \frac{x^n}{n!}$$
$$xe^x = x \sum_{n=0}^\infty \frac{x^n}{n!} = \sum_{n=0}^\infty \frac{x^{n+1}}{n!}$$
So the first few terms of the Maclaurin series for $f(x)$ are:
$$f(x) = xe^x = x + x^2 + \frac{x^3}{2} + \frac{x^4}{3} + \frac{x^5}{24} + \cdots$$
To find the radius of convergence, we can use the ratio test:
$$\lim_{n\to\infty} \left| \frac{a_{n+1}}{a_n} \right| = \lim_{n\to\infty} \left| \frac{x^{n+2}/(n+1)!}{x^{n+1}/n!} \right| = \lim_{n\to\infty} \frac{|x|}{n+1} = 0$$
Since the limit is less than 1 for all values of $x$, the Maclaurin series converges for all values of $x$, and the radius of convergence is infinite.
What two criteria must a graph meet to show a proportional relationship?
A graph shοws a prοpοrtiοnal relatiοnship if it meets the fοllοwing twο criteria Linearity and Cοnstant ratiο.
What is the ratiο and prοpοrtiοn?A ratiο is an οrdered pair οf numbers a and b, written a / b where b dοes nοt equal 0. A prοpοrtiοn is an equatiοn in which twο ratiοs are set equal tο each οther. Fοr example, if there is 1 bοy and 3 girls yοu cοuld write the ratiο as 1 : 3 (fοr every οne bοy there are 3 girls).
A graph shοws a prοpοrtiοnal relatiοnship if it meets the fοllοwing twο criteria:
Linearity: The graph must shοw a straight line passing thrοugh the οrigin (0,0). This means that as οne variable increases, the οther variable increases in prοpοrtiοn.
Cοnstant ratiο: The slοpe οf the line (i.e., the change in the y-variable divided by the change in the x-variable) must be cοnstant thrοughοut the entire graph.
This cοnstant ratiο represents the prοpοrtiοnality cοnstant between the twο variables.
Hence, A graph shοws a prοpοrtiοnal relatiοnship if it meets the fοllοwing twο criteria Linearity and Cοnstant ratiο.
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A pharmaceutical company receives large shipments of aspirin tablets. The acceptance sampling plan is to randomly select and test 17 tablets, then accepts the whole batch if there is only one or none that doesn't meet the required specifications. If a particular shipment of thousands of aspirin tablets actually has a 3% rate of defects, what is the probability that this whole shipment will be accepted?The probability that this whole shipment will be accepted is ____.
The probability that this whole shipment will be accepted is 0.000133. The probability that this whole shipment will be accepted can be found using the binomial probability formula, where n is the number of trials, x is the number of successes, p is the probability of success, and q is the probability of failure.[tex]P(x) = (n! / (x! * (n - x)!)) * (p^x) * (q^(n - x))[/tex]
In this case, n = 17, p = 0.97 (the probability of a tablet meeting the required specifications), and q = 0.03 (the probability of a tablet not meeting the required specifications).
We want to find the probability of either 0 or 1 defects, so we will calculate the probabilities for both and add them together.
[tex]P(0) = (17! / (0! * (17 - 0)!)) * (0.97^0) * (0.03^(17 - 0)) = 0.00000497P(1) = (17! / (1! * (17 - 1)!)) * (0.97^1) * (0.03^(17 - 1)) = 0.000128P(0 or 1) = P(0) + P(1) = 0.00000497 + 0.000128 = 0.000133[/tex]
Therefore, the probability that this whole shipment will be accepted is 0.000133.
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Find the area of the parallelogram below:
What is the area?
Answer:
The area of the parallelogram is 630.4 square units, to the nearest tenth.
Step-by-step explanation:
The formula to find the area of a parallelogram is:
[tex]A=bh[/tex]
where b is the base and h is the height.
For the given parallelogram ABCD, BC and AD are the bases and h is the height. Therefore, we need to calculate the height, h, before we can calculate the area of the parallelogram.
The height of the parallelogram is also the side opposite angle 62° in the right triangle of the given diagram. As we also know the hypotenuse of this triangle, we can use the sine trigonometric ratio to find "h".
[tex]\boxed{\begin{minipage}{9 cm}\underline{Sine trigonometric ratio} \\\\$\sf \sin(\theta)=\dfrac{O}{H}$\\\\where:\\ \phantom{ww}$\bullet$ $\theta$ is the angle. \\ \phantom{ww}$\bullet$ $\sf O$ is the side opposite the angle. \\\phantom{ww}$\bullet$ $\sf H$ is the hypotenuse (the side opposite the right angle). \\\end{minipage}}[/tex]
Given:
θ = 62°O = hH = 21Therefore, the expression for h is:
[tex]\implies \sin 62^{\circ}=\dfrac{h}{21}[/tex]
[tex]\implies h=21\sin 62^{\circ}[/tex]
Given the base of the parallelogram is 34 units, substitute b = 34 and the expression for h into the formula for the area:
[tex]\begin{aligned}\implies \textsf{Area}&=34 \cdot 21\sin 62^{\circ}\\&=630.424581...\\&=630.4\; \sf square\;units\;(nearest\;tenth) \end{aligned}[/tex]
Therefore, the area of the parallelogram is 630.4 square units, to the nearest tenth.
I NEED THIS FAST PLEASEEE!!
The population of Cirque City was 43,129 in 1999 and was 56,780 in 2010. If the population was growing exponentially, what was the growth rate?
Answer:
Step-by-step explanation:
If we call 1999 year 0, then 2010 would be year 11. This makes the coordinates for our problem (0, 43129) and (11, 56780). That means that the initial value, a, is 43129 and we can use that to solve for b.
[tex]56780=43129(b)^{11[/tex]
Divide both sides by 43129 to get
[tex]1.31651557=b^{11[/tex] and take the 11th root on your calculator to get that
b = 1.025314051
Not sure how you need to round that.
A freight train left the main station heading east at average speed of 100kph. An hour later an express train left the same station heading west at an average of 170kph. At what time will they be 600kms apart from each other?
Apart from each other 3.33 hours
To determine at what time the freight and express trains will be 600 km apart from each other, we must first determine the distance covered by each train. We can then use these distances to determine the total distance between the two trains at any given time.In this problem, we are given the following information:A freight train leaves the main station heading east at an average speed of 100 km/h.An hour later, an express train leaves the same station heading west at an average speed of 170 km/h.We are asked to determine the time at which they will be 600 km apart from each other.We can use the following formula to determine the distance covered by each train:D = RTwhere:D is the distance coveredR is the average speedT is the time takenTo find the distance covered by the freight train, we can use the following formula:D1 = RT1where:D1 is the distance covered by the freight trainR is the average speed of the freight trainT1 is the time taken by the freight trainTo find the distance covered by the express train, we can use the following formula:D2 = RT2where:D2 is the distance covered by the express trainR is the average speed of the express trainT2 is the time taken by the express trainNow, let's determine the distances covered by each train:D1 = 100(T1+1)D2 = 170T2We know that the total distance between the two trains is 600 km, so we can use the following equation to solve for the time at which they will be 600 km apart:D1 + D2 = 600100(T1+1) + 170T2 = 600100T1 + 170T2 + 100 = 600100T1 + 170T2 = 500(100/170)T1 + T2 = 5.9 hoursThe time taken by the freight train is T1 + 1, so we can substitute T1 + 1 for T1 in the equation above to solve for T1:T1 + T2 = 5.9100(T1+1)/170 + T2 = 5.9T1 + 1 + 1.7T2 = 5.9T1 + 1.7T2 = 4.9T1 = (4.9 - 1.7T2)/1.9Now, we can substitute this value of T1 into the equation we used earlier to solve for T2:100T1 + 170T2 = 500100((4.9 - 1.7T2)/1.9) + 170T2 = 500T2 ≈ 2.33Therefore, the time at which the two trains will be 600 km apart from each other is approximately 2.33 hours after the express train leaves the main station. To find the exact time, we need to add this value to the time at which the express train left the main station:Time = 1 + 2.33 = 3.33 hoursTherefore, the two trains will be 600 km apart from each other 3.33 hours after the express train leaves the main station.
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The measurement of an angle is 3/4 the measurement of its complement. What is the measure of the angle?
Answer:
270
Step-by-step explanation:
360×3/4=270 as per given information in the qustion a complete circle is 360 so then 3/4 × 360
Tu is a Tangent to the circle at v. Find the value of x
Answer:2.333...
Step-by-step explanation:
A tangent meets a radius (also works with diameters) at 90°.
This means (98 - 3x) = 90
98 = 90 + 3x
8 = 3x
x = 8 / 3 = 2.3333333......
Step-by-step explanation:
Arc wxv is 360 - 176 = 184 degrees
this makes angle 98-3x = 1/2 (184) = 92°
( 98 -3x )°= 92°
- 3x = -6
x = 3
Find possible roots
The answer of the given question based on finding roots are roots of the equation are -3, 3/2, and 1.
What is Synthetic division?Synthetic division is shortcut method used to divide polynomial by linear factor of form (x-a), where "a" is a constant. It is simplified method of polynomial long division, and it is especially useful when dividing by linear factor, as it avoids the need to write out all powers of x.
We list the factors of the leading coefficient 2 and the constant term 9:
Factors of 2: ±1, ±2
Factors of 9: ±1, ±3, ±9
Possible rational roots are: ±1, ±2, ±3, ±9
Using synthetic division with x = -1, we get:
-1 | 2 1 -12 9
-2 1 11
2 -1 -1 20
The remainder is not zero, so x = -1 is not a root of the equation.
Using synthetic division with x = -2, we get:
-2 | 2 1 -12 9
-4 6 -88
2 -3 -6 -79
The remainder is not zero, so x = -2 is not a root of the equation.
Using synthetic division with x = -3, we get:
-3 | 2 1 -12 9
-6 15 -9
2 -5 3 0
The remainder is zero, so x = -3 is a root of the equation. This means that (x + 3) is a factor of the equation.
Using polynomial long division, we get:
2x³ + x² - 12x + 9 = (x + 3)(2x² - 5x + 3)
quadratic factor can factored further we get:
2x² - 5x + 3 = (2x - 3)(x - 1)
Therefore, roots of given equation is:
x = -3 (root obtained earlier)
x = 3/2 (from 2x - 3 = 0)
x = 1(from x -1=0)
For the given equation 2x³ + x² - 12x + 9 = 0, the factors of the leading coefficient 2 are ±1, ±2, and the factors of the constant term 9 are ±1, ±3, ±9. Therefore, possible rational roots of equation are:
±1/1, ±3/1, ±1/2, ±3/2, ±9/2, ±1/9, ±3/9, ±9/9
Using synthetic division or other methods, we can check that the real rational roots of the equation are -3, 3/2, and 1.which we found in part (a).
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The largest marine animal is the blue whale, with an average mass of about 1.7×105 1.7 × 10 5 kg. The largest land animal ever is thought to be a dinosaur that had a mass of about 8×104 8 × 10 4 kg. What is the approximate difference in mass between these two animals
The approximate difference in mass between these two animals is 154,000 kg.
Describe Algebra?Algebra is a branch of mathematics that deals with mathematical symbols and the rules for manipulating these symbols. It is a broad area of study that includes a wide range of topics, such as equations, inequalities, functions, polynomials, matrices, and more.
Algebraic expressions are composed of variables, constants, and mathematical operations, such as addition, subtraction, multiplication, division, exponentiation, and logarithms. Equations, on the other hand, are mathematical statements that assert the equality of two algebraic expressions. Inequalities are mathematical statements that assert the relationship between two algebraic expressions using the symbols "<", ">", "<=", or ">=".
Functions in algebra are mappings from one set of numbers to another set of numbers that obey certain rules. These rules may involve properties such as continuity, differentiability, and invertibility.
The difference in mass between these two animals is:
1.7 x 10⁵ kg - 8 x 10⁴ kg = 1.54 x 10⁵ kg
Therefore, the approximate difference in mass between these two animals is 154,000 kg.
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Consider a box with dimensions 3 cm × 5 cm × 11 cm. If all of its dimensions are increased by x cm, what values of x will give a box with a volume between 300 cm3 and 900 cm3?
Explain your solution and solve using the topic of inequalities.
The correct answers are x³ + 19 x² + 103 x - 135 = 0 and x³ + 19 x² + 103 x - 735 = 0.
Given:
A box with dimensions 3 cm × 5 cm × 11 cm
Current volume of given box = 3×5×11 = 165 cm^3
New volume of box = (3+x) × (5+x) × (11+x)
= (15 + 8 x + x²) × (11+x)
= 165 + 103 x + 19 x^2 + x³
For volume to be 300 cm³
=> x³+ 19 x² + 103 x + 165 = 300
=> x³ + 19 x² + 103 x - 135 = 0
For volume to be 900 cm³ -
=> x³ + 19 x² + 103 x + 165 = 900
=> x³ + 19 x²+ 103 x - 735 = 0
Therefore, x^3 + 19 x^2 + 103 x - 135 = 0 and x³ + 19 x² + 103 x - 735 = 0 are the solution.
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NO EXPLANATION JUST ANSWER!
Answer: 1456 square yds
Step-by-step explanation: Please mark brainliest and give thanks!
Answer:728
Step-by-step explanation:
V=abc=19*14*c=266c=3724
c=14
S=(19c+14c+14*19)=33c+266=33*14+266=728
Lisa walked from south Pier to the North Pier along the beachfront. Deanna walked from the South Pier to the North Pier along Harbor Drive and Park Street. Which statement best describes the distances the two women walked?
Answer:
2
Step-by-step explanation:
If variance of the data a, b, c, ta, e is 2032 , then variance of 3a+2,3b+2, 3c+2,3d+2,3c+2, is :
The variance of 3a+2,3b+2, 3c+2,3d+2,3c+2, is 3657.6.
What is Variance?
Variance is a statistical measurement of the variation in numbers within a data set. Variance, in more precise terms, indicates how far apart any number in the set is from both the mean (average) and, consequently, from every other number in the set.
First, we can calculate the mean of the original dataset:
Mean = (a + b + c + ta + e) / 5
Then, we can calculate the variance using the formula:
Variance = ((a - Mean)² + (b - Mean)² + (c - Mean)² + (ta - Mean)² + (e - Mean)²) / 5
Given that the variance of the original dataset is 2032, we can substitute this value in the formula and solve for the mean:
2032 = ((a - Mean)² + (b - Mean)² + (c - Mean)² + (ta - Mean)² + (e - Mean)²) / 5
Simplifying this equation, we get:
(a - Mean)² + (b - Mean)² + (c - Mean)² + (ta - Mean)² + (e - Mean)² = 10160
Now, we can apply the transformation to the dataset by adding 2 and multiplying by 3:
New dataset: 3a + 2, 3b + 2, 3c + 2, 3d + 2, 3e + 2
To find the variance of the new dataset, we follow the same steps as before:
Mean = (3a + 2 + 3b + 2 + 3c + 2 + 3d + 2 + 3e + 2) / 5 = 3Mean + 2
Variance = ((3a + 2 - Mean)² + (3b + 2 - Mean)² + (3c + 2 - Mean)² + (3d + 2 - Mean)² + (3e + 2 - Mean)²) / 5
Simplifying this equation, we get:
Variance = ((3a - 3Mean)² + (3b - 3Mean)² + (3c - 3Mean)² + (3d - 3Mean)² + (3e - 3Mean)²) / 5
Variance = 9((a - Mean)² + (b - Mean)² + (c - Mean)² + (d - Mean)² + (e - Mean)²) / 5
Variance = 9(2032) / 5
Variance = 3657.6
Therefore, the variance of the new dataset is 3657.6.
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EXERCISE
Based on what you've read, decide which of the four basic operations you need to use. Then, solve the problems.
On a trip to Florida, Santina drove 203 miles and Carole drove 189 miles. How many more miles did Santina drive than Carole?
A restaurant uses 80 pounds of potatoes per week. The restaurant owner buys the potatoes in 10-pound bags from a local farmer. How many bags will the owner need to buy this week?
Six-packs of cola were on sale at a grocery store. John bought the limit, which was 8 six-packs. How many individual cans of cola is this?
Lori is reading The Grapes of Wrath for her American literature class. She read 85 pages last weekend, 135 pages during the week, and 98 pages this weekend. What is the total number of pages she has read so far?
A football team scored 34 points in their first game, 21 points in their second game, 9 points in their third game, and 28 points in their fourth game. What is the team’s average score for the season so far?
Reuben chews four pieces of chewing gum a day. The gum is sold in packages containing seven pieces. How many packages of gum will he need to buy this week?
Apply the rules of order of operations to solve the following problems.
52 – 6 × 7 = ?
108 ÷ 9 × 5 = ?
(54 + 42) ÷ 12 =?
183 – [(12 + 7) × 4] = ?
Chan wants to buy a used car that costs $8,500. He took out a loan for the cost of the car, and his payments are $209 per month for four years. At the end of four years, how much more than the car’s original price will he have paid? (Remember, there are twelve months in one year.)
Linda commutes a total of 54 miles to and from work every day. She needs a new car, and good gas mileage is important to her. She’s considering two models. The first model averages 30 miles per gallon, and the second averages 27 miles per gallon. How many gallons of gas will she save in a five-day work week if she buys the first car instead of the second car?
A waitress earned the following tips during one hour: $4.50, $3.00, $5.00, and $3.75. She gave each of the two busboys working with her $2.50. In addition to tips, the restaurant pays her $4.25 per hour. How much did she earn during that one hour of work?
Juan went out to lunch with five friends. They decided to divide the bill evenly among them. Juan estimated that his lunch cost $5.25. The entire bill came to $37.20. Would Juan’s lunch have cost more or less if he paid for it separately? How much more or less?
Santina drive 14 miles more than Carole. The owner needs to buy 8 bags this week. John bought 48 individual can of cola.
What do you means by mile?Mile is measurement unit of land or any surface. We use it to calculate the distance.
Now we have to calculate these questions,
a. Santina drive 203 miles and Carole drive 189 Miles.
Santina drive 14 miles more than Carole.
b. A restaurant uses 80 pounds of potatoes per week and the owner buys the potatoes in 10 pound bags.
So, Number of bags, 80/10 = 8 bags.
The owner needs to buy 8 bags this week.
c. Six-packs of cola were on sale at a grocery store (i.e. 6 cola in pack) and he buy 8 six-packs of cola.
Total number of cola can = 8 X 6 = 48 cola can
John bought 48 individual can of cola.
d. Lori read 85 pages last weekend, 135 pages during the week, and 98 pages this weekend.
So, total number of pages read by Lori = 85 + 135 + 98
= 318
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Handy Automobiles produces two scooters: Basic and Discord. These scooters are produced by assembling multiple units of two key components C1 and C2. The component usage for the two scooters is given below:
Basic Discord
C1 6 10
C2 10 4
These components are produced within the plant. Marginal production costs for C1 and C2 are $8 and $12 respectively. The selling price of Discord is $500 and that of Basic is $400. The demand for these products are uncertain. Handy has to plan for the following 3 demand scenarios:
Basic Discord Prob
Scenario 1 600 200 30%
Scenario 2 400 400 40%
Scenario 3 300 500 30%
Due to the long lead times associated with production, Handy has to produce the components before they know which of the demand scenarios they need to plan for. However the components can be assembled to produce the two products after demand information is available. Unused components have no value and are discarded.
1. Develop a production plan for Handy
2. Suppose Handy can retool its production system and develop an additional component C3 which can serve as a substitute for both C1 and C2. However, the marginal cost of production of this component is $14. Should they go ahead with the retooling? If so, what is their new production plan?
Handy should produce 5400 units of C1 and 5600 units of C2 and the production plan should remain the same, with 5400 units of C1 and 5600 units of C2 being produced.
1. To develop a production plan for Handy, we need to calculate the expected demand for each component under each scenario. This is done by multiplying the demand for each scooter by the number of components used in its production, and then multiplying by the probability of each scenario occurring.
Expected demand for C1 = (600 x 6 x 0.3) + (400 x 6 x 0.4) + (300 x 6 x 0.3) + (200 x 10 x 0.3) + (400 x 10 x 0.4) + (500 x 10 x 0.3) = 5400
Expected demand for C2 = (600 x 10 x 0.3) + (400 x 10 x 0.4) + (300 x 10 x 0.3) + (200 x 4 x 0.3) + (400 x 4 x 0.4) + (500 x 4 x 0.3) = 5600
Therefore, Handy should produce 5400 units of C1 and 5600 units of C2.
2. To determine whether Handy should retool its production system to develop C3, we need to compare the expected cost of production with and without the new component.
Without C3:
Expected cost = (5400 x $8) + (5600 x $12) = $43,200 + $67,200 = $110,400
With C3:
Expected cost = (5400 x $14) + (5600 x $14) = $75,600 + $78,400 = $154,000
Since the expected cost of production with C3 is higher than without C3, Handy should not retool its production system to develop the new component. The production plan should remain the same, with 5400 units of C1 and 5600 units of C2 being produced.
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6 A farmer has 2 400 sheep. He loses 32 and a half % due to the drought. After that he loses 15% due to sickness. How many sheep does he have now?
Answer: The farmer has 1377 sheeps.
Step-by-step explanation:
Farmer loses sheeps due to drought = 32½% of 2400
32½% of 2400
= 65 × 2400 × 1
2100
After cutting it will be,
65×12
=780
Number of sheeps that are left with him = 2400 - 780
=1620
After that,
The farmer loses due to sickness = 15% of 1620
15% of 1620
= 15 × 1620
100
After cutting it will be,
3 × 81
= 243
Total amount of sheeps that the farmer loses = 780 + 243
= 1023
Now the number of sheeps he has is 2400-1023
= 1377
Calculate the money you will have in the following accounts after 5 years assuming you earn simple interest,
51. you deposit $700 in an account with an annual interest rate of 4%
54. you deposit $1800 in an account with an annual interest rate of 3.8%
We will have $840 and $2142 respectively. The solution has been obtained by using simple interest.
What is simple interest?
Simple Interest (S.I.) is a way for figuring out how much interest will accrue on a specific principal sum of money at a certain rate of interest.
We know that amount after simple interest is given by
A = P (1 + rt)
We are given that $700 are deposited in an account with an annual interest rate of 4%.
Here,
P = $700
r = 4%
t = 5 years
On substitution, we get
⇒A = 700 (1 + (0.04 * 5))
⇒A = 700 (1 + 0.2)
⇒A = 700 (1.2)
⇒A = $840
Similarly, in the second case,
P = $1800
r = 3.8%
t = 5 years
On substitution, we get
⇒A = 1800 (1 + (0.038 * 5))
⇒A = 1800 (1 + 0.19)
⇒A = 1800 (1.19)
⇒A = $2142
Hence, we will have $840 and $2142 respectively.
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