Marianne’s box for camp measures 24 inches by 24 inches by 14 inches. Will her field hockey stick , which is 1 yard long , fit in the box ? Explain your answer
Answers
Answer:
Yes
Step-by-step explanation:
1 yard is approximately 3 feet. The hypotenuse of the base (24 x 24) of the box is 33.94 inches. Then the hypotenuse of the Base's hypotenuse and the height of 14 inches is 36.72 inches, which is just over 3 feet, so the stick should fit.
Related Questions
Converting Real Life Scale.. -Page 2-
NEED HELP ASAPPP 50 POINTS
(picture is linked belowww)
tysm like fr <33
Answers
The table with the scale measurements is given by the image shown at the end of the answer.
How to obtain the measurements?The measurements are obtained applying the proportion given for each table.
The symbols are given as follows:
': feet.'': inches.For the first table, we have that every inch on the table represents one feet in real life, hence:
2'' on the paper represents 2' in real life.2' on the paper represents 24' in real life. (as one feet = 12 inches, hence 24 inches = 24 feet according to the scale).0.5'' on the paper represents 0.5' in real life.9'' on the paper represents 9' in real life.For the second table, we have that every inch on the paper represents two feet in real life, hence the measurements are given as follows:
2'' on the paper represents 4' in real life.2' on the paper represents 48' in real life.0.5'' on the paper represents 1' in real life.9'' on the paper represents 18' in real life.More can be learned about scale measurements at https://brainly.com/question/29229124
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Two countries are identical except that the representative agent of country A has a larger subjective discount factor (0) than the representative agent of country B. The C-CAPM with power utility and lognormal consumption growth predicts that we will observe that country A's representative agent consumes ______ the current period and that the price of an
identical financial asset is ______ than country A
Answers
the C-CAPM with power utility and lognormal consumption growth predicts that the representative agent in country A will consume more in the current period and that the price of an identical financial asset will be lower compared to country B.
The C-CAPM is a financial model that relates the consumption patterns and asset prices in an economy. In this scenario, the difference in subjective discount factors implies that the representative agent in country A values future consumption relatively less compared to country B. As a result, the representative agent in country A tends to consume more in the current period, prioritizing immediate consumption over saving for the future.
Furthermore, the C-CAPM suggests that the price of an identical financial asset, such as a stock or bond, will be lower in country A. This is because the higher subjective discount factor in country A implies a higher expected return requirement for investors. As a result, investors in country A will demand a higher risk premium, leading to a lower price for the financial asset.
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Combining like terms
-2x+3-4x+5-4^2+11+2x^2-14
plz help me
Answers
Answer: 2x2 - 6x - 11
Step-by-step explanation:
1. Evaluate
2. Collect like terms and calculate
3. Reorder the terms
Answer:
2x2-6x-11 ( the second two is above the x)
In triangle IJK, JK = 18, KI = 11, and IJ = 14. Which statement about the angles of triangle IJK must be true?
Answers
Answer:
∠I > ∠K > ∠J
Explanation:
In triangle IJK:
• JK=18
,• KI=11
,• IJ=14
In any triangle, the larger a line segment, the larger the opposite angle.
\(JK>IJ>KI\)• The angle opposite JK = Angle I
,• The angle opposite IJ =Angle K
,• The angle opposite KI = Angle J
Therefore:
\(\angle I>\angle K>\angle J\)The 5th option is the correct choice.
Write an equation of a circle with the given center and radius. Check your answers.
center (-1.5,-3) , radius 2
Answers
The equation of the circle with radius 2 and center at (-1.5 , -3) is (x + 1.5)^2 + (y + 3)^2 = 4.
The general form of the equation of circle is given by (x - h)^2 + (y - k)^2 = r^2, where (h , k) is the location of the center and r is the radius of the circle.
Given the radius and center of the circle, substitute these values to the general form of the equation of the circle.
(x - h)^2 + (y - k)^2 = r^2
where (h , k) = (-1.5 , -3)
r = 2
(x - -1.5)^2 + (y - -3)^2 = 2^2
(x + 1.5)^2 + (y + 3)^2 = 4
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16. The number of members at a local church since
2006 can be modeled by M(x) = 20x + 150, where 'x'
is the number of years after 2006.
a. How many members were there in 2008
b. Which year were there 230 members
Answers
Answer:
number of members in 2006=190
230members on 2010
Step-by-step explanation:
2008-2006=2
20*2+150= 190 ans (1)
b)
20x+150=230
20x=230-150= 80
x= 80/20=4---ans (2)
Find any intercepts of the graph of the given equation. Do not graph. (If an answer does not exist, enter DNE.)
x = 2y^2 - 6
x-intercept (x, y) =
y-intercept (x, y) = (smaller y-value)
y-intercept (x, y) = (larger y-value)
Determine whether the graph of the equation possesses symmetry with respect to the x-axis, y-axis, or origin. Do not graph. (Select all that apply.)
x-axis
y-axis
origin
none of these`
Answers
The intercepts of the graph of the given equation x = 2y² - 6 are:x-intercept (x, y) = (6, 0)y-intercept (x, y) = (0, ±√3). The graph of the equation possesses symmetry with respect to the y-axis.
To find the intercepts of the graph of the equation x = 2y² - 6, we have to set x = 0 to obtain the y-intercepts and set y = 0 to obtain the x-intercepts. So, the intercepts of the given equation are as follows:x = 2y² - 6x-intercept (x, y) = (6, 0)y-intercept (x, y) = (0, ±√3)Now we have to determine whether the graph of the equation possesses symmetry with respect to the x-axis, y-axis, or origin. For this, we have to substitute -y for y, y for x and -x for x in the given equation. If the new equation is the same as the original equation, then the graph possesses the corresponding symmetry. The new equations are as follows:x = 2(-y)² - 6 ⇒ x = 2y² - 6 (same as original)x = 2x² - 6 ⇒ y² = (x² + 6)/2 (different from original) x = 2(-x)² - 6 ⇒ x = 2x² - 6 (same as original)Thus, the graph possesses symmetry with respect to the y-axis. Therefore, the correct options are y-axis.
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Find the domain of the vector functions, r(t), listed below.
You may use "-INF" for ?? and use "INF" for ? as necessary, and use "U" for a union symbol if a union of intervals is needed.
a) r(t)=?ln(6t),?t+16,1/?10?t?
b) r(t)=??t?9,sin(6t),t^2?
c) r(t)=? e^?9t,t/?t^2?36,t^1/3?
Answers
The domain of r(t) is (-INF, INF). a) The domain of r(t) = [ln(6t), -t + 16, 1/(10t)] is t > 0. a) The domain of the vector function r(t) = [ln(6t), -t + 16, 1/(10t)] can be determined by considering the individual components.
The natural logarithm, ln(6t), is defined only for positive values of 6t, so we need 6t > 0. This implies that t > 0.
The second component, -t + 16, is defined for all real values of t.
The third component, 1/(10t), is defined as long as 10t ≠ 0, which means t ≠ 0.
Putting these conditions together, we find that the domain of r(t) is t > 0.
b) The vector function r(t) = [t - 9, sin(6t), t^2] does not have any explicit restrictions on its domain.
The first component, t - 9, is defined for all real values of t.
The second component, sin(6t), is also defined for all real values of t.
The third component, t^2, is defined for all real values of t.
Therefore, the domain of r(t) is (-INF, INF). a) The domain of r(t) = [ln(6t), -t + 16, 1/(10t)] is t > 0.
b) The domain of r(t) = [t - 9, sin(6t), t^2] is (-INF, INF).
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The domains of the vector functions r(t) are respectively: for the first one t > 0, for the second one t >= 9 and for the third one it is a union of intervals, t < -6 U t > 6.
Explanation:The domain of a vector function r(t) is defined as the set of all t-values for which the function is defined.
r(t) = ln(6t), t+16, 1/10t: The domain for this function is all values for which the natural logarithm ln(6t) is defined, which means the inside of the logarithm must be greater than zero. As a result, the domain is t > 0.r(t) = root(t-9), sin(6t), t^2: The domain is all real values of t for both the second and third functions. For the first function, to be defined, the inside of the square root, t-9, must be greater than or equal to zero. As a result, the domain is t >= 9.r(t) = e^(-9t), t/root(t^2-36), t^1/3: Again, the third function has domain for all real values. The exponential function is also defined for all real numbers. However, the second function t/root(t^2-36) is undefined where root(t^2-36) = 0, which makes the domain to be a union of intervals, t < -6 U t > 6.Learn more about Vector Functions here:https://brainly.com/question/31672931
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2. (x3 – 6x2) (x – 7)
Answers
Answer:
I believe this is the answer you are looking for:
x3-6x2-7x
Step-by-step explanation:
Find the difference: -15 - 47
Answers
Answer:
-62
Step-by-step explanation:
One easy way to subtract two negative numbers like this (for me anyway) is to factor out the minus sign and add:
- (15 + 47)
- (62)
Remove the parentheses
-62
Find the circulation of the field f = x i y j around the curve r(t) = [cos(t)] i [sin(t)] j , 0 ≤ t ≤ 2π
Answers
The circulation of the field f = x i y j around the curve r(t) = [cos(t)] i [sin(t)] j is 2π ∫₀ (cos t sin t - sin t cos tj)dt = 0
Integration is described as blending matters or human beings collectively that have been formerly separated. An example of integration is while the schools have been desegregated and there have been now not separate public faculties for African individuals.
The method of finding integrals is referred to as integration. at the side of differentiation, integration is a fundamental, crucial operation of calculus, and serves as a device to solve troubles in mathematics and physics regarding the location of an arbitrary form, the length of a curve, and the extent of a solid, among others.
r (t) = cost i + sin t j = dr( sin ti + cos t)dt
F = -xi -yj = -costi - sin tj
Flux = F .dr = \(\int\limit2n^0_b {-costi - sin tj} \, dx\)j)-( sin ti + cos t)dt
\(\int\limit2n^0_b {-costi - sin tj} \, dx\) -( sin ti + cos t)dt
2π ∫₀ (cos t sin t - sin t cos tj)dt = 0
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Find the scale factor of the model to the real garden. Express your answer as a fraction in simplest form.
Answers
The scale factor of the model to the real garden can be obtained by dividing any two corresponding lengths (or distances) in the model and the actual garden. Here, we will divide the length of the path in the garden and the length of the path in the model.The path in the garden is 16 ft long while the path in the model is 4 ft long.
Scale factor = (length of path in model)/(length of path in garden)
=4/16
=1/4
Therefore, the scale factor of the model to the real garden is 1/4. This means that each distance in the model is 1/4 of the corresponding distance in the actual garden.
We know that a model is a smaller representation of an object or a place.
Models can be used to simulate things that are too large, too small, too expensive, or too dangerous to study directly. The scale factor of a model is the ratio of the length or size of an object in the model to the length or size of the corresponding object in the real world.
A scale factor is usually expressed as a fraction or a ratio. It shows how much the model has been reduced or enlarged from the actual size. For example, if the scale factor of a model is 1/10, this means that every dimension in the model is one-tenth of the size of the corresponding dimension in the real object or place. In other words, the model is ten times smaller than the real object or place.In the given question, we are asked to find the scale factor of a model garden to the real garden. To do this, we need to find the ratio of any two corresponding lengths in the model and the actual garden.
Here, we are given the length of the path in the garden and the length of the path in the model. By dividing these lengths, we get the scale factor of the model to the real garden. We get 1/4 as the scale factor.
The scale factor of the model to the real garden is 1/4. This means that each distance in the model is one-fourth of the corresponding distance in the actual garden. Scale factors are important in model making, architecture, engineering, and many other fields. They help us to create accurate and proportional models of complex objects and structures.
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The table shows the total bill for several parties at a restaurant and the amount the party left as a tip. Find the correlation coefficient to the nearest hundredth and describe the association of the data.
BILL ($)
78
34.50
121.75
54
69.70
100.08
12.90
TIP ($)
5
2
12.10
6
6.90
12
1
Answers
Answer:
Step-by-step explanation:
the tip would be about 100 and the bill is 78.
The most likely outcomes for a particular project are estimated as follows;
Unit price:
§ 80
Variable cost:
§ 60
Fixed costi
§ 440,800 Expected
sales:
40,600 units per year However, you recognize that some of these estimates are subject to error. Suppose each variable turns out to be either 5% higher or 5% lower than the initial estimate. The project will last for 10 years and requies an initial investment of $14 milion, which wil be depreciated straight line over the projeci life to a final value of
zero. The firm's tax rate is 21%, and the required rate of retum is 14%. a. What is project's NPV in the best-case scenario, that is, assuming all variables take on the best possible
value?
b. What is project's NPV in the worst-case scenario? Note: For all the requirements, a negative amount should be indicated by a minus sign. Enter your answers in dollars, not in millions. Do not round intermediate calculations. Round your answers to the
nearest dollar amount.
Answers
To calculate the project's NPV in the best-case scenario, we need to consider the best possible values for each variable.
Here are the steps-
Step 1: Calculate the annual cash inflow.
Annual revenue = Unit price * Expected sales
= $80 * 40,600
= $3,248,000
Step 2: Calculate the annual cash outflow.
Annual variable cost = Variable cost * Expected sales
= $60 * 40,600
= $2,436,000
Annual fixed cost = Fixed cost
= $440,800
Annual depreciation = Initial investment / Project life
= $14,000,000 / 10
= $1,400,000
Annual tax = (Annual revenue - Annual variable cost - Annual fixed cost - Annual depreciation) * Tax rate
= ($3,248,000 - $2,436,000 - $440,800 - $1,400,000) * 0.21
= $208,720
Step 3: Calculate the annual net cash flow.
Annual net cash flow = Annual revenue - Annual variable cost - Annual fixed cost - Annual depreciation - Annual tax
= $3,248,000 - $2,436,000 - $440,800 - $1,400,000 - $208,720
= $162,480
Step 4: Calculate the NPV using the best-case scenario cash flows.-
\(NPV = Initial investment + (Annual net cash flow / (1 + Required rate of return)^n)\)
\(= -$14,000,000 + ($162,480 / (1 + 0.14)^1) + ($162,480 / (1 + 0.14)^2) + ... + ($162,480 / (1 + 0.14)^10)\)
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student majoring in mechanical engineering is applying for a job. based on his work experience and grades, he has 70% chance to receive a job offer from a firm he applies. assume that he plans to apply to 8 firms. (a) what is the probability that he receives no job offers? (b) what is the probability that he receives at least one job offer? (b) how many job offers he expects to receive?
Answers
a) The probability that he receives no job offers is given as follows: 0.0001.
b) The probability that he receives at least one job offer is given as follows: 0.9999.
c) The expected number of job offers is given as follows: 5.6.
What is the binomial distribution formula?The mass probability formula for the number of successes x in n trials is defined by the equation presented as follows:
\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)
\(C_{n,x} = \frac{n!}{x!(n-x)!}\)
The parameters, along with their meaning, are presented as follows:
n is the fixed number of independent trials.p is the constant probability of a success on a single independent trial of the experiment.The parameter values for this problem are given as follows:
n = 8, p = 0.7.
Hence the expected value is given as follows:
E(X) = np = 8 x 0.7 = 5.6.
The probability of no offers is:
\(P(X = 0) = (1 - 0.7)^8 = 0.0001\)
Hence the probability of at least one job offer is given as follows:
1 - P(X = 0) = 1 - 0.0001 = 0.9999.
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A table titled Number of Dogs Adopted has entries 3, 3, 4, 4, 4, 5, 5, 6, 6, 6, 7, 7, 7, 7, 8, 8, 8, 8, 8, 9, 9. The total is 132.
A shelter kept track of the number of dogs adopted each day for three weeks. Use the table to find the statistical measures. need mean, median, mode and range.
Answers
Answer:
1) Mean = 6.28
2) Median = 7
3) Mode = 8
4) Range = 6
Step-by-step explanation:
We need to find Mean, Median, Mode and Range of data given in tables.
1) Mean
The formula used to calculate mean is: \(Mean=\frac{Sum\:of\:all\:data\:points}{Number\:of\:data\:points}\)
The data given is: 3, 3, 4, 4, 4, 5, 5, 6, 6, 6, 7, 7, 7, 7, 8, 8, 8, 8, 8, 9, 9
Sum of all data points = 132
Number of data points = 21
Finding mean:
\(Mean=\frac{Sum\:of\:all\:data\:points}{Number\:of\:data\:points}\\Mean=\frac{132}{21}\\Mean=6.28\)
So, Mean = 6.28
2) Median
The formula used to calculate median is: \(Median=\frac{n+1}{2}\:th\: term\) because we have n = odd
Number of data points n = 21
Putting values and finding the position of median term
\(Median=\frac{n+1}{2}\:th\: term\\Median=\frac{21+1}{2}\:th\: term\\Median=\frac{22}{2}\:th\: term\\Median=11\:th\:term\)
So, in the given data : 3, 3, 4, 4, 4, 5, 5, 6, 6, 6, 7, 7, 7, 7, 8, 8, 8, 8, 8, 9, 9
The 11 th term is 7
So, Median = 7
3) Mode
The mode is the most repetitive value of data set.
In the given data set: 3, 3, 4, 4, 4, 5, 5, 6, 6, 6, 7, 7, 7, 7, 8, 8, 8, 8, 8, 9, 9
The most repetitive value is 8
So, Mode = 8
4) Range
The range can be calculated using formula: \(Range=Maximum\:Value-Minimum\:Value\)
In the given data set: 3, 3, 4, 4, 4, 5, 5, 6, 6, 6, 7, 7, 7, 7, 8, 8, 8, 8, 8, 9, 9
Maximum value = 9
Minimum value = 3
So, the range is:
\(Range=Maximum\:Value-Minimum\:Value\\Range=9-3\\Range =6\)
So, Range = 6
Answer:
Step-by-step explanation:
got it right on Edge
Look at the equation below f(x)= x³ + x² - 10x + 8 Find the real roots using the method a. bisection. b. Newton-Raphson c. Secant With stop criteria is relative error = 0.0001%. You are free to make a preliminary estimate. Show the results of each iteration to the end.
Answers
a. Bisection Method: To use the bisection method to find the real roots of the equation f(x) = x³ + x² - 10x + 8, we need to find an interval [a, b] such that f(a) and f(b) have opposite signs.
Let's make a preliminary estimate and choose the interval [1, 2] based on observing the sign changes in the equation.
Iteration 1: a = 1, b = 2
c = (a + b) / 2
= (1 + 2) / 2 is 1.5
f(c) = (1.5)³ + (1.5)² - 10(1.5) + 8 ≈ -1.375
ince f(c) has a negative value, the root lies in the interval [1.5, 2].
Iteration 2:
a = 1.5, b = 2
c = (a + b) / 2
= (1.5 + 2) / 2 is 1.75
f(c) = (1.75)³ + (1.75)² - 10(1.75) + 8 ≈ 0.9844
Since f(c) has a positive value, the root lies in the interval [1.5, 1.75].
Iteration 3: a = 1.5, b = 1.75
c = (a + b) / 2
= (1.5 + 1.75) / 2 is 1.625
f(c) = (1.625)³ + (1.625)² - 10(1.625) + 8 is -0.2141
Since f(c) has a negative value, the root lies in the interval [1.625, 1.75].
Iteration 4: a = 1.625, b = 1.75
c = (a + b) / 2
= (1.625 + 1.75) / 2 is 1.6875
f(c) = (1.6875)³ + (1.6875)² - 10(1.6875) + 8 which gives 0.3887.
Since f(c) has a positive value, the root lies in the interval [1.625, 1.6875].
Iteration 5: a = 1.625, b = 1.6875
c = (a + b) / 2
= (1.625 + 1.6875) / 2 is 1.65625
f(c) = (1.65625)³ + (1.65625)² - 10(1.65625) + 8 is 0.0873 .
Since f(c) has a positive value, the root lies in the interval [1.625, 1.65625].
Iteration 6: a = 1.625, b = 1.65625
c = (a + b) / 2
= (1.625 + 1.65625) / 2 which gives 1.640625
f(c) = (1.640625)³ + (1.640625)² - 10(1.640625) + 8 which gives -0.0638.
Since f(c) has a negative value, the root lies in the interval [1.640625, 1.65625].
teration 7: a = 1.640625, b = 1.65625
c = (a + b) / 2
= (1.640625 + 1.65625) / 2 results to 1.6484375
f(c) = (1.6484375)³ + (1.6484375)² - 10(1.6484375) + 8 is 0.0116
Since f(c) has a positive value, the root lies in the interval [1.640625, 1.6484375].
Continuing this process, we can narrow down the interval further until we reach the desired level of accuracy.
b. Newton-Raphson Method: The Newton-Raphson method requires an initial estimate for the root. Let's choose x₀ = 1.5 as our initial estimate.
Iteration 1:
x₁ = x₀ - (f(x₀) / f'(x₀))
f(x₀) = (1.5)³ + (1.5)² - 10(1.5) + 8 which gives -1.375.
f'(x₀) = 3(1.5)² + 2(1.5) - 10 which gives -1.25.
x₁ ≈ 1.5 - (-1.375) / (-1.25) which gives 2.6.
Continuing this process, we can iteratively refine our estimate until we reach the desired level of accuracy.
c. Secant Method: The secant method also requires two initial estimates for the root. Let's choose x₀ = 1.5 and x₁ = 2 as our initial estimates.
Iteration 1: x₂ = x₁ - (f(x₁) * (x₁ - x₀)) / (f(x₁) - f(x₀))
f(x₁) = (2)³ + (2)² - 10(2) + 8 gives 4
f(x₀) = (1.5)³ + (1.5)² - 10(1.5) + 8 gives -1.375
x₂ ≈ 2 - (4 * (2 - 1.5)) / (4 - (-1.375)) gives 1.7826
Continuing this process, we can iteratively refine our estimates until we reach the desired level of accuracy.
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in the trepezium,a=7cm,b=10.4cm and h=6.7cm.work out the area of the trepezium.
Answers
Answer:
58.29
Step-by-step explanation:
1/2 × (7+10.4) × 6.7
= 58.29
What complex number does the ordered pair (5,-3) represent on the complex plane? Explain.
Answers
Answer:
Step-by-step explanation:This is a standard question which is to be answered according to the definition.If any complex number is written in the form of an ordered pair (a, b), it is written as'z = a + ib.Here, a=3 and b=4Hence, z=3+4i
(Total 3 marks)
5. Dave and Tanvir each think of a number, where Dave's number is larger,
The difference between their numbers is $. Dave's number plus twice Tanvir's number is 26
By forming simultaneous equations, determine each bloke's number.
Answers
Dave and Tanvir each think of a number, where Dave's number is larger,
The difference between their numbers is 5. Dave's number plus twice Tanvir's number is 26. By forming simultaneous equations, determine each bloke's number. The numbers are 12 and 7.
The number of Dave is 12 and the number of Tanvir is 7.
Given that
Dave and Tanvir each think of a number, where Dave's number is larger.
The difference between their numbers is 5.
Dave's number plus twice Tanvir's number is 26.
To find
By forming simultaneous equations, determine each bloke's number.
So, according to the question
Let's assume that numbers are x and y.
So, we can say that
x - y = 5 ------------(1) and
x + 2y = 26 ------------(2)
We have to solve that equations by using forming simultaneous equations.
For forming simultaneous equations, we have multiply equation(1) by 2, then add eq(2) with result.
So, we will get
2x - 2y = 10
(+) x + 2y = 26
---------------------------
3x +0 = 36
3x = 36
x = 36/3
x = 12
Putting the value of x in equation (1),
We will get,
x - y = 5 ------------(1)
12 - y = 5
- y = 5 - 12
- y = -7
y = 7
The numbers are 12 and 7.
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I’ll give you Brainliest
Answers
Answer:
line k im pretty sure and 34
suppose gre verbal scores are normally distributed with a mean of 459 and a standard deviation of 120. a university plans to offer tutoring jobs to students whose scores are in the top 14%. what is the minimum score required for the job offer? round your answer to the nearest whole number, if necessary.
Answers
The minimum gre score is 588.6
Define Standard normal variable
The formula z = (x-mean) / standard deviation can be used to transform any point (x) from a normal distribution to the standard normal distribution (z).The value of z for each given x value indicates how far away from the mean for all x values x is.
Given,
normally distributed with a mean μ = 459
standard deviation σ = 120
University plans to offer tutoring jobs to students whose scores are in the top = 14% or 0.14
Standard normal variable is given by,
Z = (x - μ) / σ
P(X ≥ x₁) = 0.14
⇒P( [ (x - μ)/ σ ] ≥ [ (x₁ - μ)/ σ ] ) = 0.14
⇒P( z ≥ [ (x₁ - 459)/ 120 ] ) = 0.14
⇒P( z ≥ z₁ ) = 0.14
⇒P(0 < z < z₁ ) = 0.5 - 0.14 = 0.36
From standard normal tables
z₁ = 1.08
Where, z₁ = (x₁ - 459)/ 120
1.08 = (x₁ - 459)/ 120
After solving , we get
x₁ = 588.6
Therefore, the minimum gre score is 588.6 or 589
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two carts, a and b, are connected by a rope 39 ft long that passes over a pulley p. the point q is on the floor 12 ft directly beneath p and between the carts. cart a is being pulled away from q at a speed of 2 ft/s. how fast (in ft/s) is cart b moving toward q at the instant when cart a is 5 ft from q? (round your answer to two decimal places.)
Answers
The velocity of the cart b is found as 20/23 ft/s over the pulley.
What is defined as the rate of change?The momentum of a variable is represented by the rate of change, which is used to mathematically define the percentage change in value over such a defined period of time.For the given data in the question.
q's velocity is 2 feet per second.
Rope length is 39 feet.
Assume x is the distance between A and Q. (refer the image).
Assume y is the distance between Q and B. (refer the image).
As a result of the image,
x² + 12² = L²
Now, with respect to time t, differentiate the above equation.
2x(dx/dt) + 0 = 2L.(dL/dt)
For x = 5 ft and L = 13 ft
dL/dt = (5×2)/13 = 10/13
In the case of B,
y² + 12² = (39 - L)² ; from diagram.
Differentiating now,
2y(dy/dt) + 0 = -2(39 - L).(dL/dt)
At x = 5 ft and y = 23 ft.
dy/dy = -20/23
(A negative sign indicates the opposite direction)
Thus, the velocity of cart b is found as 20/23 ft/s.
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Please help and hurry please thank you!
Choose the equation that
represents this situation. Use c to represent the
variable.
Tori received a $50 gift card for her birthday. After buying some clothes, she
had $32 left on the card. How much did she spend on the clothes?
A.c=32+50
B.32c=50
C.32-c=50
D.50-c=32
Answers
Answer:
oh i have done these before but this one is a little confusing bc i got 2 answers B or C
If a dealer's profit, in units of $3000, on a new automobile can be looked upon as a random variable X having the density function below, find the average profit per automobile.
f(x) = { (1/4(3-x), 0 < x < 2), (0, elsewhere)
Answers
The average profit per automobile is $5000/6 or approximately $833.33.
To find the average profit per automobile, we need to calculate the expected value or mean of the profit random variable X.
The formula for the expected value of a continuous random variable is:
E(X) = ∫[x × f(x)] dx
Given the density function f(x) for the profit random variable X, we can calculate the expected value as follows:
E(X) = ∫[x × f(x)] dx
= ∫[x × (1/4(3-x))] dx
= ∫[(x/4)×(3-x)] dx
To evaluate this integral, we need to split it into two parts and integrate separately:
E(X) = ∫[(x/4)×(3-x)] dx
= ∫[(3x/4) - (\(x^2\)/4)] dx
= (3/4) ∫[x] dx - (1/4) ∫[\(x^2\)] dx
Integrating each term, we get:
E(X) = (3/4) * (\(x^2\)/2) - (1/4) * (\(x^3\)/3) + C
Now we need to evaluate this expression over the range where the density function is non-zero, which is 0 < x < 2.
Plugging in the limits, we have:
E(X) = (3/4) × [(\(2^2\)/2) - (\(0^2\)/2)] - (1/4) × [(\(2^3\)/3) - (\(0^3\)/3)]
= (3/4) × (2) - (1/4) × (8/3)
= 6/4 - 8/12
= 3/2 - 2/3
= (9/6) - (4/6)
= 5/6
Therefore, the average profit per automobile is $5000/6 or approximately $833.33.
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A quadratic function g(x) passes through the points (-8, 33), (2, 1), and (8, 1).
Which statement correctly describes g(x)?
1. The line x = -5 is an axis of symmetry, and the vertex is a minimum because the y-values increase as the graph moves away from that function.
2. The line x = -5 is an axis of symmetry, and the vertex is a maximum because the y-values increase as the graph moves away from that function.
3. The line x = 5 is an axis of symmetry, and the vertex is a minimum because the y-values increase as the graph moves away from that function.
4. The line x = 5 is an axis of symmetry, and the vertex is a maximum because the y-values increase as the graph moves away from that function.
Answers
Answer:
Correct option: 3
Step-by-step explanation:
The points (2,1) and (8,1) have the same y-coordinate, so to find the vertex of the quadratic function (where the axis of symmetry will be located), we just need to find the average of their x-coordinate:
x_vertex = (2 + 8) / 2 = 5
The points (2, 1) and (-8, 33) show that when the graph moves away from the axis of symmetry (from x = 2 to x = -8), the y value increases (from 1 to 33), so the vertex is a minimum.
Correct option: 3
Answer:
3
Step-by-step explanation:
I had this question and got it right on a test
decreased by ___% = decreased by 10% and decreased by 10% again
Answers
Answer:
is this a trick question? Because if you lose 10 bucks but earn ten bucks its like nothing happened so Its going to be 0% because nothing changed
Given that the confetti is going to be dropped from 25 feet up and land on a person who is about 6 feet tall, use the correct formula (solved for t) from the chart above to find out how long the actor should hold her position before moving on
Answers
Answer:
1.09 seconds
Step-by-step explanation:
I need the image that I am going to attach to solve the exercise.
We have the following information:
Confetti height from the ground is 25 feet
Person's height is 6 feet
So, the distance that the confetti would fall would be the subtraction of these heights, that is:
25-6 = 19 feet
d = 19 feet
We use the 5th equation of the attached image:
t = d ^ (1/2) / 4
replacing:
t = 19 ^ (1/2) / 4
t = 1.09 seconds
6. Find the HCF and LCM of: (b) (a) 4(a²-4), 6(a²-a-2) and 12(a² + 3a-10) 2x²-3xy-2y², 6x² + xy - y² and 3x² - 7xy + 2y² (c) a(c + a)-b(b + c), b(a + b)-c(c + a) and c(b + c)-a(a + b) (d) p² +q²+2pq-1, q²-p² + 2q + 1 and p² - q² + 2p + 1 (e) 6x²-5x-4, 8x² + 2x - 15 and 12x²-43x +35
Answers
The HCF is (a-2) and the LCM is 288(a+2)(a+1)(a+5) of 4(a²-4), 6(a²-a-2) and 12(a² + 3a-10)
To find the highest common factor (HCF) and least common multiple (LCM) of the given expressions, let's factorize each expression first:
4(a²-4) = 4(a+2)(a-2)
6(a²-a-2) = 6(a-2)(a+1)
12(a²+3a-10) = 12(a+5)(a-2)
The common factors among these expressions are (a-2). So the HCF is (a-2).
To find the LCM, we multiply all the distinct factors from the factorizations:
LCM = 4 × 6 × 12 × (a+2)(a+1)(a+5) = 288(a+2)(a+1)(a+5)
Therefore, the HCF is (a-2) and the LCM is 288(a+2)(a+1)(a+5).
Let's factorize each expression:
a(c + a) - b(b + c) = a² + ac - b² - bc
b(a + b) - c(c + a) = ab + b² - c² - ac
c(b + c) - a(a + b) = cb + c² - a² - ab
The common factors among these expressions are (a+b+c). So the HCF is (a+b+c).
To find the LCM, we multiply all the distinct factors from the factorizations:
LCM = (a+b+c)(a² + ac - b² - bc)(ab + b² - c² - ac)
Therefore, the HCF is (a+b+c) and the LCM is (a+b+c)(a² + ac - b² - bc)(ab + b² - c² - ac).
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What is the result of adding these two equations?
4x-4y=-2
-9x-4y=-3
Answers
gather like terms :
4x-9x-4y-4y = -5
-5x-8y = -5