The probability that during the next three months it has;
(a) at least five breakdowns is 0.036.(b) at most eight breakdowns is 0.00085.(c) more than five breakdowns is 0.012.Probability refers to potential. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. Mathematics has included probability to forecast the likelihood of certain events.
The degree to which something is likely to happen is basically what probability means. You will understand the potential outcomes for a random experiment using this fundamental theory of probability, which is also applied to the probability distribution.
The plant has on the average two breakdowns per month,
so the Poisson distribution is,
[tex]P(X=k) = \frac{e^{-\lambda} \lambda^k}{k!}[/tex]
where,
X is the random variable representing the number of events
λ is the average rate at which the events occur
k is the number of events that occur
a) at least five breakdowns
[tex]P(X=k) = \frac{e^{-\lambda} \lambda^k}{k!}[/tex]
P(X =5) = [tex]\frac{e^{-2} 2^5}{5!}[/tex]
= 0.036
Thus, probability that at least five breakdowns in three months is 0.036.
b) at most eight breakdowns
[tex]P(X=k) = \frac{e^{-\lambda} \lambda^k}{k!}[/tex]
[tex]P(X=8) = \frac{e^{-2} 2^8}{8!}[/tex]
= 0.00085.
Therefore, probability of at most eight breakdowns is 0.00085.
c) more than five breakdowns.
[tex]P(X=k) = \frac{e^{-\lambda} \lambda^k}{k!}[/tex]
P(X = 6) = [tex]\frac{e^{-2} 2^6}{6!}[/tex]
=0.012
Therefore, probability of more than five breakdowns is 0.012.
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Solve the differential equation. dy + 6ydx=9e -⁶x dx y=
The general solution to the given differential equation:
[tex]y = (9x + C)e^(-6x)[/tex]
To solve the given differential equation, dy + 6ydx = 9e^(-6x)dx, we can first rewrite it as a first-order linear differential equation:
[tex]dy/dx + 6y = 9e^(-6x)[/tex]
Now, we will find the integrating factor, which is e^(∫P(x)dx), where P(x) is the coefficient of y in the equation:
Integrating factor =[tex]e^(∫6dx) = e^(6x)[/tex]
Next, we multiply the entire differential equation by the integrating factor:
[tex]e^(6x)(dy/dx + 6y) = 9e^(-6x)e^(6x)[/tex]
This simplifies to:
[tex]e^(6x)(dy/dx) + 6e^(6x)y = 9[/tex]
Now, the left side of the equation is the derivative of the product of y and the integrating factor:
[tex]d/dx(y * e^(6x)) = 9[/tex]
To solve for y, integrate both sides with respect to x:
[tex]∫[d/dx(y * e^(6x))]dx = ∫9dx[/tex]
This results in:
[tex]y * e^(6x) = 9x + C[/tex]
Finally, we solve for y by dividing by e^(6x):
[tex]y = (9x + C)e^(-6x)[/tex]
And that is the general solution to the given differential equation.
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Find the sum of the first 10 terms of the following series, to the nearest integer.
8,20/3,50/9
The sum of the first 10 terms of the given series 8,20/3,50/9... is 140.
Given series: 8,20/3,50/9...
The given series is not in a standard form, but it appears to be an arithmetic sequence with a common difference of 4/3. To check this, we can find the difference between consecutive terms:
20/3-8=4/3
50/9-20/3=4/3
Thus, the common difference is indeed [tex]\frac{4}{3}[/tex].
We notice that each term of the series can be written as:
a_n=a+(n-1)d
a_n=8+(n-1)(4/3)
where n is the index of the term, and 4/3 is the common difference between the consecutive terms.
To find the sum of the first 10 terms of the series, we use the formula for the sum of an arithmetic series:
S=(n/2)[2a_1+(n-1)d]
where S is the sum of the series, a_1 is the first term of the series, d is the common difference, and n is the number of terms to be added.
Substituting the given values, we get:
S=(10/2)[2*8+(10-1)(4/3)]
Simplifying the expression:
S=5[16+9(4/3)]
S=5[16+12]=5(28)=140
Therefore, the sum of the first 10 terms of the series is 140.
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Geometry
three squares with areas of 64, 225, and 289 square units are arranged so that when their vertices coincide a triangle is formed. find the area of that triangle.
please explain how you solved this along with the answer.
Answer:
The area of the largest square is 289 square units, because it is the sum of areas of the two smaller squares, 64 square units and 225 square units.
Step-by-step explanation: JUST PASSED IT ON STUDY ISLAND 100% CORRECT ANSWER
Find the surface area of the composite figure.
2 in.
4 in.
9 in.
SA
=
7 in.
2
[?] in.²
4 in.
4 in.
If you'd like,
you can use a
calculator.
Answer:
236 in²
Step-by-step explanation:
You want the surface area of the figure comprised of two cuboids.
AreaThe surface area of the figure will be the sum of the total surface area of the purple cuboid, plus the lateral surface area of the yellow cuboid.
SA = 2(LW +H(L +W)) + Ph
SA = 2(9·4 +2(9 +4)) +(4·4)(7) = 236 . . . . square inches
The surface area of the composite figure is 236 square inches.
__
Additional comment
You can consider the face on the right side to be equal in area to the area of the purple cuboid that is covered by the yellow one. So, figuring the total area of the purple cuboid effectively includes the area of the face on the right side.
Then the remaining part of the area of the yellow cuboid is the area of the four 7×4 rectangles that are its lateral area.
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If the points a,b and c have the coordinates a(5,2) , b(2,-3) and c(-8,3) show that the triangle abc is a right angled triangle
Points a,b and c satisfied the Pythagoras theorem. Thus, the triangle abc is a right angled triangle.
Define about the right angled triangle:Every triangle has inner angles that add up to 180 degrees. A right angle and a right triangle are both formed when one of their internal angles is 90 degrees.
The internal 90° angle of right triangles is denoted by a little square in the vertex. The complimentary angles of the other two sides of a right triangle sum up to 90 degrees.The triangle's legs, which are typically denoted by the letters a and b, are the sides that face the complimentary angles.Given coordinates :
a(5,2) , b(2,-3) and c(-8,3).
Find the distance between the points using the distance formula:
d = √[(x2 - x1)² + (y2 - y1)²]
ab = √[(2 - 5)² + (- 3 - 2)²]
ab = √[(-3)² + (- 5)²]
ab = √[9 + 25]
ab = √34
ab² = 34
bc = √[(2 + 8)² + (- 3 - 3)²]
bc = √[(10)² + (- 6)²]
bc = √[100 + 36]
bc = √136
bc² = 136
ac = √[(-8 - 5)² + (3 - 2)²]
ac = √[(-13)² + (1)²]
ac = √[169 + 1]
ac = √170
ac² = 170
Now,
(ac)² = (bc)² + (ab)²
170 = 136 + 24
170 = 170
This, points a,b and c satisfied the Pythagoras theorem. Thus, the triangle abc is a right angled triangle.
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HELP DUE TOMORROW!!!!!!!!
Answer:
The third choice is the correct answer.
square peg sydney smith wrote in ""on the conduct of the understanding"" that it is im-possible to fit a square peg in a round hole.
On the basic of square peg sydney smith written point the probability that it is im-possible to fit a square peg in a round hole is equals to the zero.
Probability is defined as the number of chances of occurrence of an event. It is the ratio of the number of favorable outcomes to the total outcomes in that sample space. Mathematical formula is written as, probability of an event, P(E) = (Number of favorable outcomes)/(Total possible outcomes). Now, we have specify that according to sydney smith written in on the conduct of the understanding about square peg that it is impossible to fit a square peg in a round hole. Let consider an event A of fit a square peg in a round hole. We have specify that it is impossible to fit a square peg in a round hole. So, the favourable possible outcomes for event A = 0. Therefore, the probability that to fit a square peg in a round hole, P(A) = 0
Hence, required probability value is zero.
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Can someone please help me ASAP? It’s due tomorrow.
Answer:
There are 16 total outcomes for tossing 4 quarters
This is because each coin flip has 2 possibilities, so if you flip the coin 4 times it will equal
2x2x2x2.
Dustin and Lucas decide to investigate Elle’s claims about the pudding. They obtain a sample of 200 chocolate pudding packs and find that only 72 of them contain more than 3. 25oz of pudding. A. (1 point) Construct a 92% CI for the overall proportion of pudding packs containing less than 3. 25oz of pudding. Make a conclusion at α = 0. 08 about whether these pudding packs truly are normally distributed with a mean of 3. 25oz. Use your confidence interval to justify your claim. B. (1 point) Construct a 99% CI for the overall proportion of pudding packs containing more than 3. 25oz of pudding. Make a conclusion at α = 0. 01 about whether these pudding packs truly are normally distributed with a mean of 3. 25oz. Use your confidence interval to justify your claim
(a) The 92% CI for overall proportion of pudding packs containing less than 3.25oz of pudding at α = 0.08 is (0.5806, 0.6994);
(b) The 99% CI for overall proportion of pudding packs containing more than 3.25oz of pudding at α = 0.01 is (0.2726, 0.4474).
Part (a) : To construct a confidence-interval for the overall proportion of pudding packs containing less than 3.25oz of pudding, we use the following formula : CI = p' ± [tex]z_{\frac{\alpha}{2} }[/tex] × √(p'(1-p')/n);
where p' is = sample proportion, [tex]z_{\frac{\alpha}{2} }[/tex] is = critical z-value for the desired confidence level, and n is = sample size.
In this case, p' = (200-72)/200 = 128/200 = 0.64, the sample size is n = 200, and
We know that the critical z-value for a 92% confidence interval(α = 0.08) is approximately 1.75;
Substituting the values,
We get,
CI = 0.64 ± 1.75 × √(0.64(1 - 0.64)/200)
CI = 0.64 ± 0.059421;
CI = (0.5806, 0.6994);
Therefore, the required confidence interval is (0.5806, 0.6994).
Part (b) : In this case, p' = 72/200 = 0.36, the sample-size is n = 200, and
We know that the critical z-value for a 99% confidence interval (α = 0.01) is approximately 2.57;
Substituting the values,
We get,
CI = 0.36 ± 2..57 × √(0.36(1 - 0.36)/200)
CI = 0.36 ± 0.087426;
CI = (0.2726, 0.4474);
Therefore, the required confidence interval is (0.2726, 0.4474).
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Use the rules to find derivatives of the functions at the specified values.
f(x) = 4x^3 at x = 2
f(2) = _____
The value of the function f(x) at x = 2 is 48.
The question asks us to find the value of the function f(x) = 4[tex]x^3[/tex] at x = 2 and its derivative f'(x) at x = 2.
The value of the function f(x) at x = 2, we simply plug in x = 2 into the function and evaluate:
f(2) = 4[tex](2)^3[/tex] = 4(8) = 32
Therefore,
The value of the function f(x) at x = 2 is 32, which we can write as f(2) = 32.
To find the derivative of the function f(x) at x = 2, we first need to find the general formula for the derivative of f(x), which we can do using the power rule for derivatives.
The power rule states that
To find the derivative of f(x) at x = 2, we simply plug in x = 2 into the formula for f'(x) that we just found:
f'(2) = [tex]12(2)^2[/tex] = 48
Therefore,
The derivative of the function f(x) at x = 2 is 48, which we can write as f'(2) = 48To find the derivative of the function
f'(x) = 12[tex]x^2[/tex]
To find the value of f(2), we can simply plug in x = 2 into the original function:
f(2) = 4[tex](2)^3[/tex] = 32
To find the value of f'(2), we can plug in x = 2 into the derivative we just found:
f'(2) = 12[tex](2)^2[/tex] = 48
Therefore,
f(2) = 32 and f'(2) = 48.
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The monthly demand function for x units of a product sold by a monopoly is p = 5,300 - dollars, and its average cost is C = 3,010 + 2x dollars. Production is limited to 100 units. Find the revenue function!
To find the revenue function, we need to multiply the price (p) by the quantity sold (x). The price function given is p = 5,300 - dollars, so we can substitute this into our revenue function as follows:
Revenue = p * x
Revenue = (5,300 - dollars) * x
We also know that production is limited to 100 units, so we need to take that into account when determining the revenue function. If x is greater than 100, then the revenue will be limited to 100 units sold. If x is less than or equal to 100, then the revenue will be based on the actual quantity sold.
To incorporate this constraint into our revenue function, we can use a piecewise function:
Revenue = { (5,300 - dollars) * 100 if x > 100
(5,300 - dollars) * x if x <= 100 }
Simplifying the piecewise function, we get:
Revenue = { 530,000 - (dollars * 100) if x > 100
(5,300 - dollars) * x if x <= 100 }
Therefore, the revenue function for this monopoly is:
Revenue = { 530,000 - 100 * dollars if x > 100
(5,300 - dollars) * x if x <= 100 }
Hi! To find the revenue function, we first need to determine the total revenue, which is the product of the price per unit (p) and the number of units sold (x). Given the demand function p = 5,300 - x dollars and the average cost function C = 3,010 + 2x dollars, we can find the revenue function as follows:
Revenue function, R(x) = p * x
R(x) = (5,300 - x) * x
By simplifying the equation, we get:
R(x) = 5,300x - x^2
So, the revenue function for this monopoly is R(x) = 5,300x - x^2.
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this is reading btw and you get 23 points Fast pls
Think about the article you just read. Write two to three sentences describing what you would visualize in your mental model to understand how the two animals look different from each other.
The article red was titled "sense of emotion of dog and cat to humans"
To visualize the differences in feeling between Dogs and cats towards people, I would think of a dog swaying its tail and hopping up with fervor upon seeing its owner, whereas a cat may approach its owner more calmly and gradually with a loose tail.
I might picture the puppy gasping and looking for physical fondness, whereas the cat may lean toward to be petted or rubbed under the chin.
What is the mental model?Dogs show enthusiasm and affection towards owners, while cats exhibit different behaviors. Dogs show excitement through body language like wagging tails, jumping, seeking affection, and vocalizing.
Pets express joy and eagerness to be around humans, with cats being more reserved towards humans. Although affectionate, cats express emotions subtly such as calm body posture and soft chirping.
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In parallelogram best, diagonals bs and et bisect each other at o.
1. if es = 10cm, how long is bt?
2. if be = 13cm, how long is ts?
3. if eo = 6cm and so = 7cm, what is the length of et? bs?
4. if et + bs = 18cm and so = 5cm, find et and bs.
When the parallelogram, diagonals bs and et bisect at each other at o, we get the following answers:
1. In a parallelogram, the diagonals bisect each other. So, if ES = 10 cm, then EO = OS = 5 cm. Since EO and OS are half of the diagonal ET, then ET = EO + OS = 5 cm + 5 cm = 10 cm. Similarly, diagonal BT will also be equal to 10 cm, as it has the same length as diagonal ET.
2. In a parallelogram, opposite sides are equal. So, if BE = 13 cm, then TS = 13 cm, as they are opposite sides.
3. If EO = 6 cm and SO = 7 cm, then the length of diagonal ET is EO + OS = 6 cm + 7 cm = 13 cm. Since the diagonals of a parallelogram are equal, the length of diagonal BS will also be 13 cm.
4. If ET + BS = 18 cm and SO = 5 cm, we can use the fact that diagonals bisect each other to find ET and BS. Let EO = x cm. Then, ET = 2x cm and BS = 2(5-x) cm. Now, we can set up the equation: 2x + 2(5-x) = 18. Solving for x, we get x = 4 cm. So, ET = 2x = 8 cm and BS = 2(5-x) = 10 cm.
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Brainliest if correct!_A particle is projected vertically upwards from a fixed point O. The speed of projection is u m/s. The particle returns to O 4 seconds later. Find:
a) the value of u
b) the greatest height reached by the particle
c) the total time of which the particle is at a height greater than half its greatest height
Thank you so much!
The value of the velocity, u is 19.6 m/s.
The greatest height reached by the particle is 19.6 m.
The total time during which the particle is at a height greater than half its greatest height is 2.33 s.
What is the value of the velocity, u?a) To find the value of the velocity, u, we can use the formula for the time of flight of a vertically projected particle:
t = 2u/g
Since the particle returns to the same point after 4 seconds, we have:
2t = 4
Substituting the value of t in the first equation, we get:
u = gt/2 = 9.8 x 2
u = 19.6 m/s
b) To find the greatest height reached by the particle, we can use the formula for the maximum height reached by a vertically projected particle:
h = u^2/2g
Substituting the value of u, we get:
h = 19.6^2/(2 x 9.8)
h = 19.6 m
c) To find the total time during which the particle is at a height greater than half its greatest height, we can first find the height at which the particle is at half its greatest height:
h/2 = (u^2/2g)/2 = u^2/4g
Substituting the value of u, we get:
h/2 = 19.6^2/(4 x 9.8) = 24.01 m
So, the particle is at a height greater than half its greatest height when it is above 24.01 m.
Next, we can find the time taken by the particle to reach this height:
h = ut - (1/2)gt^2
24.01 = 19.6t - (1/2)9.8t^2
Solving this quadratic equation, we get:
t = 2.33 s or t = 4.10 s
The particle takes 2.33 s to reach a height of 24.01 m, and it takes another 1.67 s (4 - 2.33) to return to the ground.
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2. Reemplaza los valores correspondientes de "a", "b" y "c", y calcula: a = -2 b = 3 c = 4 a) a + b – c = b) a – b + c = c) a + 2. B – 2c = d) (7. B) : (b + c) = e) a ∙ c + 2. B – 2. C = f) c · (b – a) =
For each expression, the value is calculated by following the order of operations, i.e. first solving any multiplication or division, then addition or subtraction. The resulting values are: a + b - c = -3, a - b + c = -1, a + 2b - 2c = -5, (7b)/(b+c) = 3, ac + 2b - 2c = -10, and c(b-a) = 20.
To calculate a + b - c, we substitute a = -2, b = 3, and c = 4. So,
a + b - c = -2 + 3 - 4 = -3
To calculate a - b + c, we substitute a = -2, b = 3, and c = 4. So,
a - b + c = -2 - 3 + 4 = -1
To calculate a + 2b - 2c, we substitute a = -2, b = 3, and c = 4. So,
a + 2b - 2c = -2 + 2(3) - 2(4) = -5
To calculate (7b) / (b + c), we substitute b = 3 and c = 4. So,
(7b) / (b + c) = (7(3)) / (3 + 4) = 21 / 7 = 3
To calculate ac + 2b - 2c, we substitute a = -2, b = 3, and c = 4. So,
ac + 2b - 2c = (-2)(4) + 2(3) - 2(4) = -10
To calculate c(b - a), we substitute a = -2, b = 3, and c = 4. So,
c(b - a) = 4(3 - (-2)) = 4(5) = 20
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• use the regression function from the previous step as a mathematical model for the demand function
(e.g. d(p)) and find the general expression for the elasticity of demand:
ep)
To find the general expression for the elasticity of demand (e_p), we need to differentiate the demand function with respect to price (p) and multiply it by the ratio of price to quantity (p/q). The elasticity of demand measures the responsiveness of quantity demanded to changes in price.
The general expression for elasticity of demand (e_p) can be calculated as:
e_p = (dQ/dp) * (p/Q)
Where dQ/dp represents the derivative of the demand function with respect to price, and Q represents the quantity demanded.
The elasticity of demand helps us understand how sensitive the quantity demanded is to changes in price. If e_p is greater than 1, demand is considered elastic, meaning that quantity demanded is highly responsive to price changes. If e_p is less than 1, demand is inelastic, indicating that quantity demanded is less responsive to price changes.
In conclusion, the general expression for the elasticity of demand (e_p) is calculated by taking the derivative of the demand function with respect to price and multiplying it by the ratio of price to quantity. This measure helps determine the responsiveness of quantity demanded to changes in price.
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you select a marble without looking and then put it back if you do this 90 times what is the best predictions that you will pick an orange or a pink marble?
If you select a marble without looking and then put it back if you do this 90 times, the probability of selecting an orange or a pink marble on any given trial is 1/2 or 0.5.
If you select a marble without looking and then put it back, the probability of selecting any particular marble on any given trial is the same for all marbles. Assuming there are only two possible outcomes - selecting an orange marble or a pink marble - the probability of selecting an orange or a pink marble on any given trial is 1/2 or 0.5.
Since the probability of selecting an orange or a pink marble on each trial is the same, the best prediction for the number of times you will select an orange or a pink marble out of 90 trials is an equal number of times for each color. Therefore, the best prediction for the number of times you will select an orange or a pink marble is 45 times each.
This is only a prediction based on probability, and the actual number of times you select an orange or a pink marble may differ from the prediction due to chance. However, over a large number of trials, the actual outcomes should approach the predicted probabilities.
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SIMPLIFYYY THIS EXPRESSION
Answer:
x - 5y
Step-by-step explanation:
6x - 8y - 5x + 3y =
= 6x - 5x - 8y + 3y
= x - 5y
Answer:
1x + 11y
Step-by-step explanation:
1 1/5, 1 2/5,1 2/5, 1 2/5, 1 3/5, 1 3/5 , 1 3/5, 1 4/5, 1 4/5, 2 What fraction of the packages weighed more than 1 2 /5 pounds?
2/5 of the packages weighed more than 1 2/5 pounds.
To find the fraction of packages that weighed more than 1 2/5 pounds, we need to count the number of packages that weighed more than 1 2/5 pounds and divide it by the total number of packages.
There are a total of 10 packages. Out of these, we can see that 4 packages weighed more than 1 2/5 pounds: 1 1/5, 1 3/5, 1 3/5, and 1 4/5.
Therefore, the fraction of packages that weighed more than 1 2/5 pounds is:
4/10
This can be simplified to:
2/5
Hence, only 2/5 of the package weighed more.
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HELPPPPPPP PLEASEEEE
Answer:
The first box and whisker plot
Step-by-step explanation:
A box and whisker plot gives you the five number summary for a set of data. The five number summary is
The minimum/lowest value (looks like the top of capital T turned sideways and is the leftmost part of the box-and-whisker plot The first quartile or Q1, representing 25% of the data (the first point represented in the "box" of the plot and serves as an endpoint of the box)The median or Q2, representing 50%/the middle of the data (the line that splits the box into two parts/the line in the middle of the box)The third quartile or Q3, representing 75% of the data (the last point represented in the "box" of the plot and serves as another endpoint of the box)The maximum/highest value (also looks like the top of capital T turned sideways and is the rightmost part of the box-and-whisker plotMaximum and minimum:
We know from the data that the minimum value is 100 and the maximum value is 200. However, because both boxes available as answer choices have the correct minimum and maximum, we'll need to find more data.
Median:
We can start finding the median first by arranging the data from the least to greatest. Then, we find the middle of the data. Because there are 9 points and 9 is odd, we know that there will be 4 points to the left of the median and 4 points to the right of the median:
100, 100, 120, 120, 150, 165, 180, 180, 200
150 has 4 numbers both on its left and right sides so its the median.
Because both of the plots available as answer choices have the correct median, we we'll need to find more data.
First Quartile/Q1:
In order to find Q1, we must find the middle number of the four numbers to the left of the median.
Because we have an even number of points, we will get two middle numbers, 100 and 120. To find the middle of all four points, we average these two numbers:
(100 + 120) / 2 = 220 / 2 = 110
Only the first box has the accurate Q1 value, so it's our answer.
We don't have to find Q3, since both boxes have the correct Q3, but only the first box has the correct minimum, correct Q1, correct median, correct Q3, correct maximum.
1. The cost of renting a car for a day is $0.50 per mile plus a $15 flat fee.
(a) Write an equation to represent this relationship. Let x be the number of miles driven and y be the total cost for the day.
(b) What does the graph of this equation form on a coordinate plane? Explain.
(c) What is the slope and the y-intercept of the graph of the relationship? Explain
Answer:
a) y=0.50x+15
b) The graph of this equation form on a coordinate plane is a line.
c) Slope =0.50 and y-intercept = 15
Step-by-step explanation:
Let x = Number of miles driven by car
Given: The cost of renting a car for a day is $0.50 per mile plus a $15 flat fee.
a) Total cost = 0.50x+15
If y =total cost of renting the car, then y=0.50x+15 (i)
b) Above equation is similar to y= mx+c (ii) [m = slope , xc=y-intercept] which a linear equation .
So the graph of this equation form on a coordinate plane is a line.
c) Comparing (i) and (ii)
m=0.50 , c=15
Hope this helps :)
Dante has a tent shaped like a triangular prism. The tent has an equilateral base that measures 5 feet on each side. The tent is 8 feet long and 4. 3 feet tall.
101. 5ft
120 ft.
141. 5 ft.
184 ft
What is the surface area of the tent
The surface area of Dante's tent is approximately 180 square feet.
To find the surface area of Dante's tent, we need to find the area of each of its faces and then add them up. Since the tent is in the shape of a triangular prism, it has three rectangular faces and two triangular faces.
First, let's find the area of each rectangular face. We know that the tent is 8 feet long and 4.3 feet tall. To find the width of each face, we need to use the Pythagorean theorem since the base of the tent is equilateral. So, we can use a triangle with sides of 5 feet (the base of the tent) and 4.3 feet (the height of the triangular face) to find the width of each rectangular face.
a^2 + b^2 = c^2
5^2 + 4.3^2 = c^2
25 + 18.49 = c^2
43.49 = c^2
c = √43.49
c ≈ 6.6 feet
Now that we know the width of each rectangular face, we can find the area of each face:
Area of rectangular face = length x width
Area of rectangular face = 8 x 6.6
Area of rectangular face ≈ 52.8 square feet
Next, let's find the area of each triangular face. Since the base of the tent is equilateral, each triangular face has a base of 5 feet and a height of 4.3 feet. The area of each triangular face is:
Area of triangular face = (base x height) / 2
Area of triangular face = (5 x 4.3) / 2
Area of triangular face ≈ 10.8 square feet
Now we can add up the areas of all five faces to find the total surface area of the tent:
Surface area of tent = 3 x area of rectangular face + 2 x area of triangular face
Surface area of tent = 3 x 52.8 + 2 x 10.8
Surface area of tent = 158.4 + 21.6
Surface area of tent ≈ 180 square feet
Therefore, the surface area of Dante's tent is approximately 180 square feet.
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Robert, by 3/4 pound of Grace, and divided into six equal portions. What is the way of each portion
Each portion of Grace weighs 1/8 pound.
What is weight?It gauges how much gravity is pulling on a body.
If Robert has 3/4 pound of Grace and he wants to divide it into six equal portions, we can find the weight of each portion by dividing 3/4 by 6:
(3/4) / 6 = (3/4) * (1/6) = 1/8
So each portion of Grace weighs 1/8 pound.
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A student is painting a brick for his teacher to use as a doorstop in the classroom. He is only painting the front of the brick. The vertices of the face are (−6, 2), (−6, −7), (6, 2), and (6, −7). What is the area, in square inches, of the painted face of the brick? 144 in2 108 in2 72 in2 42 in2
The area of the painted face of the brick is given as follows:
108 in².
How to obtain the area of a rectangle?The area of a rectangle of length l and width w is given by the multiplication of dimensions, as follows:
A = lw.
The dimensions for this problem are given as follows:
Width: 6 - (-6) = 12.Length: 2 - (-7) = 9.Hence the area of the painted face of the brick is given as follows:
A = 12 x 9 = 108 in².
(the area of a rectangle is given by the multiplication of the dimensions, which we did here).
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1pt A clothing company needs to determine how much fabric to use for a sleeve on a shirt. It uses the following model arm as a way to test the fit. The sleeve needs to cover
the 20 centimeters from the shoulder to the elbow.
Upper Arm
What solid best represents the model for the sleeve? What is the minimum surface area of fabric needed for the sleeve?
The minimum surface area of fabric needed for the sleeve is approximately 628.32 cm².
How much fabric for sleeve?Based on the given model arm, a right circular cylinder would best represent the model for the sleeve.
To calculate the minimum surface area of fabric needed for the sleeve, we need to find the lateral surface area of the right circular cylinder.
The lateral surface area of a right circular cylinder is given by the formula:
Lateral surface area = 2πrh
where r is the radius of the cylinder, h is the height of the cylinder.
In this case, the height of the cylinder needs to be 20 cm (to cover the distance from the shoulder to the elbow), and the radius can vary depending on the desired fit. Let's assume a radius of 5 cm for the purposes of this calculation.
Plugging in the values, we get:
Lateral surface area = 2π(5 cm)(20 cm)
= 628.32 cm²
Therefore, the minimum surface area of fabric needed for the sleeve is approximately 628.32 cm².
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Maria invests $6,154 in a savings account with a fixed annual interest rate of 8% compounded weekly. What will the account balance be after 10 years? There are 52 weeks in a year. (Round our answer to the nearest cent)
Answer:
A = P(1 + r/n)^(n*t) is the formula
Where:
A = the account balance after t years
P = the principal amount (initial investment)
r = the annual interest rate (as a decimal)
n = the number of times the interest is compounded per year
t = the time in years
P = $6,154
r = 0.08 (8% expressed as a decimal)
n = 52 (compounded weekly)
t = 10
A = 6154(1 + 0.08/52)^(52*10)
A ≈ $14,239.44
Therefore, the account balance after 10 years will be approximately $14,239.44.
Which expression is equivalent to 1/4(8 - 6x + 12)?
The expression that is equivalent to 1/4(8 - 6x + 12) is 2 - 3x/2 + 6
What are algebraic expressions?
Algebraic expressions are simply defined as those mathematical expressions that are composed of terms, variables, their coefficients, their factors and constants.
These mathematical expressions are also comprised of arithmetic operations.
These operations are listed thus;
BracketParenthesesAdditionSubtractionMultiplicationDivisionFrom the information given, we have that;
1/4(8 - 6x + 12)
expand the bracket, we have;
8 - 6x + 12/4
Divide in group, we have;
8/4 - 6x/4 + 12/4
Divide the values
2 - 3x/2 + 6
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Gareth pays $60 for 9m of climbing rope. How much will Sophie pay for 15m at the same store?
Sophie will pay money equivalent to $100 for 15m at the same store.
What is Money?The term "money" in mathematics refers to a form of payment, such as bills, coins, and demand deposits, that is used to purchase goods and services. Money is used to pay for the worth or price of an item or service.
A country's monetary system is referred to as its currency.
In the case of Gareth,
Money paid for 9 m of climbing [tex]=\$60[/tex]
Money paid per m of climbing [tex]=\$60\div9[/tex]
Thus, money paid by Sophie for 15 m of climbing [tex]= 15 \times (60\div9)[/tex]
[tex]\boxed{\bold{= \$100}}[/tex]
Hence Sophie will pay money equivalent to $100 for 15m at the same store.
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Answer:
$100
Step-by-step explanation:
We know that for 9m of rope, Gareth had to pay $60.
The question is asking us to find out how much Sophie will pay for 15m of rope. To do this, we have to find out how much is paid per meter of rope.
[tex]60/9\\=6\frac{2}{3}[/tex]
For the sake of not using fractions, let's keep it as an improper fraction: 60/9
So, we can write an equation for the price of 15m of rope:
(60/9)·15
=100
So, Sophie will pay $100 for 15m of rope.
Hope this helps! :)
Every morning Jim runs for 15 minutes. If Jim runs 4 miles per hour, how far does Jim travel? Use the equation d=rt, where d is distance, r is rate, and t is time.
Segments OT and OV are?
True, The more variables that are deployed to segment a market, the more useful is the resulting segmentation likely to be.
We have,
The factors which are be used to member a request are the segmentation variables. Common variables include demographic, geographic, psychographics and behavioral considerations.
Quantifiable population characteristics, similar as age, gender, income, education, family situation.
The primary ideal of segmentation is to identify guests with analogous attributes, and to find which parts of guests that are seductive from a profit perspective.
Understanding the request segmentation allows marketers to produce a more effective and effective marketing blend.
Hence, True, The more variables that are deployed to segment a market, the more useful is the resulting segmentation likely to be.
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complete question:
The more variables that are deployed to segment a market, the more useful is the resulting segmentation likely ot be.[See p.104]Group of answer choicesTrueFalse
