Answer:
The dimension that maximizes area is 144ft by 144ft
Step-by-step explanation:
Given
[tex]P = 576[/tex] -- perimeter
Required
The dimension that gives maximum area
Perimeter is calculated as:
[tex]P= 2 * (L + W)[/tex]
So, we have:
[tex]2 * (L + W) = 576[/tex]
Divide through by 2
[tex]L + W = 288[/tex]
Make L the subject
[tex]L = 288 -W[/tex]
Area is calculated as:
[tex]A = L * W[/tex]
Substitute [tex]L = 288 -W[/tex]
[tex]A = (288 - W) * W[/tex]
Open bracket
[tex]A = 288W - W^2[/tex]
Differentiate A with respect to W
[tex]A' = 288 - 2W[/tex]
Set to 0 to calculate W
[tex]288 - 2W = 0[/tex]
Collect like terms
[tex]2W = 288[/tex]
Divide by 2
[tex]W = 144[/tex]
Recall that:
[tex]L = 288 -W[/tex]
[tex]L = 288 - 144[/tex]
[tex]L = 144[/tex]
The calculation of the mean of a population and the expected value of the probability mass function of a Random Variable (RV) are quite similar. Consider a probability mass function that contains 4 unique Random Variables: 100, 200, 300, 400. If the expected value of the RV can be calculated by simply taking the average of the RVs, what can be said about the corresponding probabilities of each of the 4 RVs
Answer: Hello the options related to your question is missing attached below are the missing options.
A.) The probabilities of the RVs may be equal
B.) The sum of the probabilities of the RVs exceed 1
C.) This is an impossible occurrence
D.) The probabilities of the RVs must be equal
E.) None of the above
answer:
The probabilities of the RVs may be equal ( A )
Step-by-step explanation:
Given that the value of the population mean and the value of probability mass function of a set of random variables are similar
For the Random Variables : 100,200,300,400
The Probability mass function of RV = ( 100 + 200 + 300 + 400 ) / 4
Hence The probabilities of the RVs may be equal
Megan and Suzanne each have a plant. They track the growth of their plants for four weeks.
Whose plant grew at a faster rate, and what was the rate?
Suzanne’s at 2 inches per week
Suzanne’s at 1.5 inches per week
Megan’s at 3 inches per week
Megan’s at 2.5 inches per week
Megan’s plant grew at a faster rate, Growing at a rate of 3 inches per week.
What is the slope?The y-rate axis of change with respect to the x-axis is known as the slope.
y = mx + b, where slope = m and y-intercept = b, is the slope-intercept form equation of a line.
We are aware that a slope's graph or rate of change will be steeper the higher its absolute value.
Given, Megan and Suzanne each have a plant. They track the growth of their plants for four weeks.
From the given options, Megan's plant which is growing at a rate of 3 inches per week has a faster growth rate.
learn more about slopes here :
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A small airplane flies 1160 miles with an average speed of 290 miles per hour. 2 hours after the plane leaves, a Boeing 747 leaves from the same point. Both planes arrive at the same time; what was the average speed of the 747 ?
Answer:
[tex]580\text{ miles per hour}[/tex]
Step-by-step explanation:
To solve this problem, we can use the formula [tex]d=rt[/tex], where [tex]d[/tex] is distance, [tex]r[/tex] is rate, and [tex]t[/tex] is time.
Let's start by calculating how long the small airplane takes to complete the journey. The distance is 1160 miles and the rate is 290 miles per hour. Therefore, we have:
[tex]1160=290t,\\t=\frac{1160}{290}=4\text{ hours}[/tex]
Since the Boeing 747 left 2 hours after the small airplane left, the small airplane has just [tex]4-2=2[/tex] hours left of travelling time.
Therefore, to arrive at the same time as the small airplane, the Boeing 747 must cover the same distance of 1160 miles in only 2 hours. Hence, the Boeing 747's speed must have been:
[tex]1160=2r,\\r=\frac{1160}{2}=\boxed{580\text{ miles per hour}}[/tex]
Question 6 of 10
The domain of a function f(x) is x = 0, and the range is ys -1. What are the
domain and range of its inverse function, '(x)?
Answer: y = 0 and x = -1
Find the measure of the missing angles.
Answer:
Step-by-step explanation:
Please help me with this on the image
Answer:
Step-by-step explanation:
a). Given expression in the question is,
[tex]\frac{13822\times 623}{14}[/tex]
Exact value of the expression will be,
[tex]\frac{13822\times 623}{14}=615079[/tex]
b). By using approximations to 1 significant figure,
13822 ≈ 10000
623 ≈ 600
14 ≈ 10
615079 ≈ 60000
Now use the expression,
[tex]\frac{13822\times 623}{14}=\frac{10000\times 600}{10}[/tex]
= 60000
Calculate the break even sales dollars if the fixed expenses are $7,000 and the contribution ratio is 40%.
Answer:
Break even sales = $17,500 (Approx.)
Step-by-step explanation:
Given:
Fixed expenses = $7,000
Contribution ratio = 40%
Find:
Break even sales dollars
Computation:
Break even sales = Fixed expenses / Contribution ratio
Break even sales = 7,000 / 40%
Break even sales = 7,000 / 0.40
Break even sales = 17,500
Break even sales = $17,500 (Approx.)
Instructions are in the picture
Answer:
123123 3213123 12312 dasdsd aw dasd sda asdasd
Step-by-step explanation:
The doubling time for an investment is 7.5 yeas. Find an exponential model for the growth of your money. Then find how long will take your investment to grow by factor of 5(Assume that you make an investment P)
Answer:
The correct answer is "17.414 years".
Step-by-step explanation:
Given:
Doubling time,
= 7.5 years
As we know,
[tex]P(t) = P_oe^{rt}[/tex]
now,
⇒ [tex]2P_o=P_o e^{r\times 7.5}[/tex]
[tex]2 = e^{r\times 7.5}[/tex]
[tex]r = \frac{ln2}{7.5}[/tex]
[tex]=0.092[/tex]
[tex]=9.2[/tex]%
then,
⇒ [tex]P(t) = P_o e^{0.092 t}[/tex]
here,
[tex]P(t) = 5P_o[/tex]
hence,
⇒ [tex]5P_o = P_o e^{0.092 t}[/tex]
[tex]e^{0.092t}=5[/tex]
[tex]t = \frac{ln5}{0.092}[/tex]
[tex]=17.414 \ years[/tex]
Answer:
The correct answer is "17.414 years".
Step-by-step explanation:
What is a segment parallel to ba in a cube
Answer:
Two planes that do not intersect are said to be parallel. Parallel planes are found in shapes like cubes, which actually has three sets of parallel planes. The two planes on opposite sides of a cube are parallel to one another. ... So those will be 2 that are in the same plane that will never intersect.
Triangles ABC and DEF are similar. Find the
perimeter of triangle DEF.
a. 34.7 cm
b. 25.3 cm
c. 15 cm
d. 38 cm
Please show work to help me understand.
If Both triangles are similar the ratio of sides will be same
[tex]\\ \sf\longmapsto \dfrac{AB}{AC}=\dfrac{DE}{DF}[/tex]
[tex]\\ \sf\longmapsto \dfrac{8}{10}=\dfrac{12}{DF}[/tex]
[tex]\\ \sf\longmapsto 8DF=120[/tex]
[tex]\\ \sf\longmapsto DF=\dfrac{120}{8}[/tex]
[tex]\\ \sf\longmapsto DF=15cm[/tex]
Now
[tex]\\ \sf\longmapsto Perimeter=DF+DE+EF[/tex]
[tex]\\ \sf\longmapsto Perimeter=15+11+12[/tex]
[tex]\\ \sf\longmapsto Perimeter=38cm[/tex]
What is the value of x?
X + y = 10;
Z + z = 6;
Z + y = 5;
A) 9
B) 8
C) 7
D) 6
E) 1
Answer:
B
Step-by-step explanation:
z+z=6, z=3. z+y=5, y=2, x+y=10, x=8
I have a final for summer schoollll due midnight and it’s 10:23!!!!!!!!!!!!
salifye pizza charges a base pizza of $12.77 for large plus 7.44 additional topping.
a) Find a function that models the price of a pizza with toppings.
Find the inverse of the function. What does−1 represent?
If a pizza costs $20.20, how many toppings does it have?
Answer:
Sharjah Call Girls +971529238486 | Call Girls In Sharjah
Step-by-step explanation:
Sharjah Call Girls and our group are very a good deal satisfied to participate withinside the boom of the leisure field. Lots of customers are touring Sharjah now no longer handiest for playing the splendor of the town however additionally to the sensual entertainments our profiles.
What ordered pairs are the solutions of the system of equations shown in the graph below?
The solutions are where the two lines cross over each other.
(0,3) and (4,-5)
What is the length of the missing leg??
Answer:
12.04 cm
Step-by-step explanation:
Pythagoras in general :
c² = a² + b²
c is the Hypotenuse (the side opposite of the 90 degree angle).
a and b are the side legs.
so, in our example here
17² = 12² + b²
289 = 144 + b²
145 = b²
b = sqrt(145) = 12.04 cm
Use the graph to complete the statement. O is the origin. r(180°,O) ο Ry−axis : (2,5)
A. ( 2, 5)
B. (2, -5)
C. (-2, -5)
D. (-2, 5)
9514 1404 393
Answer:
B. (2, -5)
Step-by-step explanation:
Reflection across the y-axis is the transformation ...
(x, y) ⇒ (-x, y)
Rotation 180° about the origin is the transformation ...
(x, y) ⇒ (-x, -y)
Applying the rotation after the reflection, we get ...
(x, y) ⇒ (x, -y)
(2, 5) ⇒ (2, -5)
_____
Additional comment
For these transformations, the order of application does not matter. Either way, the net result is a reflection across the x-axis.
Answer:
(2,-5)
Step-by-step explanation:
Find the missing side of the triangle
Answer:
x = 15
Step-by-step explanation:
Pytago: a^2 + b^2 = c^2
x = [tex]\sqrt{25^{2} -20^{2} }[/tex] = 15
A bag contains 35 marbles, 11 of which are red. A marble is randomly selected from the bag, and it is blue. This blue marble is NOT placed back in the bag. A second marble is randomly drawn from the bag. Find the probability that this second marble is NOT red.
Answer:
11 red + 24 blue = 35 marbles
If 1 blue is withdrawn
11 red + 23 blue = 34 marbles
P = 23 / 34 = .38 probability of drawing blue marble
HELP ASAP!!
If the circle below is cut from the square of plywood below, how many square inches of plywood would be left over?
Use π = 3.14, and round your answer to the nearest hundredth.
Answer:
13.73 in^2 because the circle's area is 50.27 in^2
in the figure above, the square ABCD is inscribed in a circle. if the radius of the circle is r, the hatbis the length of arc APD in terms of r?
a) (pi)r/4
b) (pi)r/2
c) (pi)r
d) (pi)r^2/4
The length of arc APD is: [tex]\frac{\pi r}{2}[/tex]
A square when inscribed in a circle will fit the circle such that, the 4 edges of the square touches the sides of the circle. The radius of the circle can be drawn from any of the 4 edges.
Given that ABCD is a square:
This means that:
[tex]AB = BC = CD = DA[/tex] --- equal side lengths
To calculate the length of arc APD, we make use of the following arc length formula
[tex]APD = \frac{\theta}{360} * 2\pi r[/tex]
Where
[tex]\theta = \angle ADO[/tex] and O is circle center
Since ABCD is a square, then:
[tex]\theta = \angle ADO = 90^o[/tex]
So, we have:
[tex]APD = \frac{90}{360} * 2\pi r[/tex]
[tex]APD = \frac{1}{4} * 2\pi r[/tex]
[tex]APD = \frac{\pi r}{2}[/tex]
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Please help me determine the general equation for the graph above as well as solve for a. Thank you.
Observe that the x coords of the roots of a polynomial are,
[tex]x_{1,2,3,4}=\{-3,0,1,4\}[/tex]
Which can be put into form,
[tex]y=a(x-x_1)(x-x_2)(x-x_3)(x-x_4)[/tex]
with data
[tex]y=a(x-(-3))(x-0)(x-1)(x-4)=ax(x+3)(x-1)(x-4)[/tex]
Now if I take any root point and insert it into the equation I won't be able to solve for y because they will always multiply to zero (ie. when I pick [tex]x=-3[/tex] the right hand side will multiply to zero,
[tex]y=-3a(-3+3)(-3-1)(-3-4)=0[/tex]
and a will be "lost" in the process.
If we observed a non-root point that we could substitute with x and y and result in a non-loss process then you could find a. But since there is no such point (I don't think you can read it of the graph) there is no other viable way to find a.
Hope this helps :)
Find the cash value of the lottery jackpot (to the nearest dollar). Yearly jackpot payments begin immediately (26 for Mega Millions and 30 for Powerball). Assume the lottery can invest at the given interest rate. Powerball: $360 million; 5.4% interest
a. $188,347,953
b. $282,573,702
c. $185,870,742
d. $298,386,685
Answer:
The right response is Option c ($185,870,742).
Step-by-step explanation:
Given:
n = 30
r = 5.4%
or,
= 0.054
Periodic payment will be:
[tex]R = \frac{360000000}{30}[/tex]
[tex]=12000000[/tex] ($)
Now,
The present value will be:
= [tex]R+R(\frac{1-(1+r)^{-n+1}}{r} )[/tex]
By substituting the values, we get
= [tex]12000000+12000000(\frac{1-(1+0.054)^{-30 + 1}}{0.054} )[/tex]
= [tex]12000000+12000000\times 14.4892[/tex]
= [tex]185,870,742[/tex] ($)
What is the image of -8 ,8 after a dilation by a scale factor of one fourth centered at the origin?
Answer:
(-2, 2)
Step-by-step explanation:
If you have a point (x, y) and you do a dilation by a scale factor K centered at the origin, the new point will just be (k*x, k*y)
So, if the original point is (-8, 8)
And we do a dilation by a scale factor k = 1/4
Then the image of the point will be:
(-8*(1/4), 8*(1/4))
(-8/4, 8/4)
(-2, 2)
P,W,R & S form the vertices of a quadrilateral. PQR = 74 degrees
RSP = 121 degrees
Find the value of SPQ
Answer:
∠ SPQ = 75°
Step-by-step explanation:
The sum of the 4 angles in a quadrilateral = 360°
Subtract the sum of the 3 angles from 360 for ∠ SPQ
∠ SPQ = 360° - (90 + 74 + 121)° = 360° - 285° = 75°
The number of perpendicular bisectors a segment can have is:
1 point
a) 0
b) 1
c) 3
d) 10
Answer:
0
Step-by-step explanation:
0co
If we decrease a dimension on a figure, how is the figure’s area affected?
The area decreases.
The area increases.
The area becomes 0.
The area remains the same.
The pair of figures to the right are similar. The area of one figure is given. Find the area of the other figure to the nearest whole number. Area of larger triangle = 165 ft^2 Thank you!!
9514 1404 393
Answer:
73 ft²
Step-by-step explanation:
The ratio of areas is the square of the ratio of linear dimensions.
smaller area = larger area × ((10 ft)/(15 ft))² = 165 ft² × (4/9)
smaller area = 73 1/3 ft² ≈ 73 ft²
Answer:
Area of the smaller triangle = 73 square feet
Step-by-step explanation:
Area of the larger triangle = 165 square feet
Area of a triangle = [tex]\frac{1}{2}(\text{Base})(\text{Height})[/tex]
[tex]\frac{1}{2}(\text{Base})(\text{Height})=165[/tex]
[tex]\frac{1}{2}(15)(\text{Height})=165[/tex]
Height = 22 ft
Since, both the triangles are similar.
By the property of similar triangles,
Corresponding sides of the similar triangles are proportional.
Let the height of smaller triangle = h ft
Therefore, [tex]\frac{h}{22}=\frac{10}{15}[/tex]
h = [tex]\frac{22\times 10}{15}[/tex]
h = 14.67 ft
Area of the smaller triangle = [tex]\frac{1}{2}(10)(14.67)[/tex]
= 73.33
≈ 73 square feet
A local rental car agency has 200 cars. The rental rate for the winter months is 60%. Find the probability that in a given winter month fewer than 140 cars will be rented. Use the normal distribution to approximate the binomial distribution.
Answer:
[tex]P(Z\leq2.89)=0.9981[/tex]
Step-by-step explanation:
Sample size [tex]n=200[/tex]
Rental Rate [tex]R=60\%[/tex]
Probability =(P<140)
Generally the equation for mean of distribution is mathematically given by
[tex]\mu=nR\\\\\mu=200*0.60\\\\\mu=120[/tex]
Generally the equation for Standard deviation of distribution is mathematically given by
[tex]\sigma=\sqrt{npq}[/tex]
[tex]\sigma=\sqrt{200*0.60*0.40}[/tex]
[tex]\sigma=6.9[/tex]
Therefore
Z-score for x=140 is
[tex]Z=\frac{x-\mu}{\sigma}[/tex]
[tex]Z=\frac{140-120}{6.9}[/tex]
[tex]Z=2.89[/tex]
From table
[tex]P(Z\leq2.89)=0.9981[/tex]
A distribution of values is normal with a mean of 60 and a standard deviation of 16. From this distribution, you are drawing samples of size 25. Find the interval containing the middle-most 76% of sample means.
Answer:
The interval containing the middle-most 76% of sample means is between 56.24 and 63.76.
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
A distribution of values is normal with a mean of 60 and a standard deviation of 16.
This means that [tex]\mu = 60, \sigma = 16[/tex]
Samples of size 25:
This means that [tex]n = 25, s = \frac{16}{\sqrt{25}} = 3.2[/tex]
Find the interval containing the middle-most 76% of sample means.
Between the 50 - (76/2) = 12th percentile and the 50 + (76/2) = 88th percentile.
12th percentile:
X when Z has a p-value of 0.12, so X when Z = -1.175.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]-1.175 = \frac{X - 60}{3.2}[/tex]
[tex]X - 60 = -1.175*3.2[/tex]
[tex]X = 56.24[/tex]
88th percentile:
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]1.175 = \frac{X - 60}{3.2}[/tex]
[tex]X - 60 = 1.175*3.2[/tex]
[tex]X = 63.76[/tex]
The interval containing the middle-most 76% of sample means is between 56.24 and 63.76.
