Answer:
hello
Step-by-step explanation:
here you go
have a nice day
Which statement best compares the volumes of the two rectangular prisms?
b
b
а
a
A
B
CA. There is not enough information to compare the volumes of the prisms.
CB. The volume of prism A is less than the volume of prism B.
C. The volume of prism A is the same as the volume of prism B.
D. The volume of prism A is greater than the volume of prism B.
Answer:
There is not enough information to compare the volume of the prisms.
Step-by-step explanation:
To find the volume of rectangular prisms, the length , width and height must be given. The volume of rectangular prisms is gotten by multiplying the three dimension: length, width and height which is expressed in cubic units. To compare the two volumes, the three dimensions must be given.
Hence, there is not enough information to compare.
Question 9 An S corporation is generally set up to: implement an expansion strategy attract capital reduce tax burdenseasy entry into an industry take advantage of limited liability
An S corporation is generally set up to C. reduce tax burdens.
What is a S corporation?For federal tax purposes, S corporations elect to pass through corporate income, losses, deductions, and credits to their shareholders.
An S corp operates in the same way that any other corporation does. It establishes a board of directors and corporate officers, bylaws, and a management structure under the laws of its home state. It distributes company stock. Its owners cannot be held personally or financially liable for creditor or company claims.
S corporations are distinguished by the fact that they are not federally taxed on the majority of their earnings and distributions, allowing more money to be passed on to shareholders.
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Suppose that
f(x) = 5 x^6 - 3 x^5.
(A) Find all critical numbers of f. If there are no critical numbers, enter 'NONE'.
Critical numbers =
(B) Use interval notation to indicate where f(x) is increasing.
Note: Use 'INF' for \infty, '-INF' for -\infty, and use 'U' for the union symbol.
Increasing:
(C) Use interval notation to indicate where f(x) is decreasing.
Decreasing:
(D) Find the x-coordinates of all local maxima of f. If there are no local maxima, enter 'NONE'.
x values of local maxima =
(E) Find the x-coordinates of all local minima of f. Note: If there are no local minima, enter 'NONE'.
x values of local minima =
(F) Use interval notation to indicate where f(x) is concave up.
Concave up:
(G) Use interval notation to indicate where f(x) is concave down.
Concave down:
(H) List the x values of all inflection points of f. If there are no inflection points, enter 'NONE'.
x values of inflection points =
(I) Find all horizontal asymptotes of f. If there are no horizontal asymptotes, enter 'NONE'.
Horizontal asymptotes y =
(J) Find all vertical asymptotes of f. If there are no vertical asymptotes, enter 'NONE'.
Vertical asymptotes x =
The critical value of f(x) = 5x⁶ - 3x⁵ is x = 0.5 which is also its maxima point
f(x) = 5x⁶ - 3x⁵
differentiation w.r.t x
=> f'(x) = 30x⁵ - 15x⁴
Putting f'(x) = 0
30x⁵ - 15x⁴ = 0
=> x⁴(30x - 15) =0
=> 30x - 15 = 0
=> x = 15/30
=> x = 0.5 , 0
Critical number is 0.5 , 0
(B) To find where f(x) is increasing
for x > 0.5 ,
(30x-15) > 0 => x⁴(30x - 15) > 0
Therefore , f(x) is increasing at ( 0.5 , ∞ )
(C)To find where f(x) is decreasing
for x < 0.5 ,
(30x-15) < 0 => x⁴(30x - 15) < 0
Therefore , f(x) is decreasing at ( -∞ , 0.5)
(D) Differentiation f'(x) again w.r.t to x
f'(x) = 30x⁵ - 15x⁴
f"(X) = 150x⁴ - 60x³
Substituting critical values of x
=> 150(0.5)⁴ - 60(0.5)³
=>9.375 - 7.5
=> -1.875 < 0 , Hence , x = 0.5 is point of maxima
(E) no point of minima
Similarly , we can solve other parts
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I need help with these
The 15 and 9 units side lengths of the parallelogram ABCD, and the 36° measure of the acute interior angle, A indicates the values of the ratios are;
1. AB:BC = 5:3
2. AB:CD = 1:1
3. m∠A : m∠C= 1 : 4
4. m∠B:m∠C = 4:1
5. AD: Perimeter ABCD = 3:16
What is a ratio?A ratio is a representation of the number of times one quantity is contained in another quantity.
The shape of the quadrilateral ABCD in the question = A parallelogram
Length of AB = 15
Length of BC = 9
Measure of angle m∠A = 36°
Therefore;
1. AB:BC = 15:9 = 5:3
2. AB ≅ CD (Opposite sides of a parallelogram are congruent)
AB = CD (Definition of congruency)
AB = 15, therefore, CD = 15 transitive property
AB:CD = 15:15 = 1:1
3. ∠A ≅ ∠C (Opposite interior angles of a parallelogram are congruent)
Therefore; m∠A = m∠C = 36°
∠A and ∠D are supplementary angles (Same side interior angles formed between parallel lines)
Therefore; ∠A + ∠D = 180°
36° + ∠D = 180°
∠D = 180° - 36° = 144°
∠D = 144°
m∠A : m∠C = 36°:144° =1:4
m∠A : m∠C = 1:4
4. ∠B = ∠D = 144° (properties of a parallelogram)
m∠B : m∠C = 144° : 36° = 4:1
5. AD ≅ BC (opposite sides of a parallelogram)
AD = BC = 9 (definition of congruency)
The perimeter of the parallelogram ABCD = AB + BC + CD + DA
Therefore;
Perimeter of parallelogram ABCD = 15 + 9 + 15 + 9 = 48
AD:Perimeter of the ABCD = 9 : 48 = 3 : 16
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True or false, and explain. If a regression model has high bias, it is unlikely that collecting more data to train/build the model will increase its performance on a validation or test set (with respect to, say, SSE;MSE, or R2).
The following statement "If a regression model has high bias, it is unlikely that collecting more data to train/build the model will increase its performance on a validation or test set" is absolutely true.
If a regression model has high bias, it means that it is oversimplified and unable to capture the complexity of the data. Collecting more data may not necessarily improve the model's performance on a validation or test set because the model is already too simple to effectively model the data. In fact, increasing the amount of data may actually make the bias worse by further emphasizing the oversimplified nature of the model. To improve the performance of a model with high bias, it is usually necessary to use a more complex model or introduce additional features to the model.
If a regression model has high bias, it means the model is oversimplified and does not capture the underlying patterns in the data. Collecting more data to train/build the model is unlikely to increase its performance on a validation or test set in terms of SSE (Sum of Squared Errors), MSE (Mean Squared Error), or R2 (R-squared) because the model's simplicity prevents it from learning the necessary complexity to accurately represent the data. To improve the model's performance, it's important to consider reducing the bias by using more complex models or incorporating additional features.
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which of the following numbers ae divisible by 3?
a. 534
b.2176
c.59742
d.45846
which of the following numbers are divisible by 4?
a.9698
b.98746
c.5620
d.56208
Answer:
1. A
2. C
Step-by-step explanation:
1. A
2. C
Solve the equation for x.
5x - ( 4x - 1) = 2
1
a.
C.
1
9
bi
b. - 1
d.
1
Answer:
x = 1
Step-by-step explanation:
5x - (4x - 1) = 2
Let's get rid of the parenthesis
Multiply whatever is in the parenthesis by -1 since there is a minus sign before it
5x - 4x + 1 = 2
Move common terms to one side, so subtract 1 from both sides
5x - 4x + 1 = 2
- 1 - 1
5x - 4x = 1
Subtract the 5x by 4x
x = 1
Answer:
x = 1
Step-by-step explanation:
5x - (4x - 1) = 2
5x - 4x + 1 = 2 {Distribute property (-1) is distributed with 4x and (-1)}
Combine like terms
x + 1 = 2
Subtract 1 from both sides
x = 2 - 1
x = 1
Quetion content area top
Part 1
Let f(x)= 4x2-3 and let g(x)= 2x3. Find (fg)(3). Quetion content area bottom
Part 1
(fg)(3)=
enter your repone here (Simplify your anwer. )
The value of (fg)(3) is 1782.
What is simplification?
Simplifying procedures is one way to achieve uniformity in work efforts, expenses, and time. It reduces diversity and variety that is pointless, harmful, or unnecessary.
Here, we ave
Given: f(x) = 4x²-3 and g(x) = 2x³
We have to find the value of (fg)(3).
First, we will find the value of (fg)
(f×g)(x) = (4x²-3)×2x³
(f×g)(x) = 8x⁵ - 6x³
Now, we find the value of (fg)(3) and we get
(f×g)(3) = 8(3)⁵ - 6(3)³
(f×g)(3) = 8(243) - 6(27)
(f×g)(3) = 1944 - 162
(f×g)(3) = 1782
Hence, the value of (f×g)(3) is 1782.
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Find the equation of the line perpendicular to y = -0.5x -5
that passes through the point (2,7). Write this line in slope-intercept form.
Answer:
y = .5x + 6
Step-by-step explanation:
7=1 +c
c = 6
hope this is right
Answer:
y=2x+3
Step-by-step explanation:
determine whether the random variable described is discrete or continuous or qualitative: the time (in minute) you must wait in line at the grocery store
The time you must wait in line at the grocery store is best characterized as a continuous random variable.
The random variable described, the time you must wait in line at the grocery store, can be categorized as a continuous random variable.
A continuous random variable is one that can take on any value within a specific range or interval. In this case, the time you must wait in line can theoretically take on any positive real value, from a fraction of a minute to potentially an extended period of time.
For instance, you may wait 2.5 minutes, 3.726 minutes, or even 10.152 minutes. The time is not restricted to specific discrete values or intervals; it can be infinitely subdivided.
In contrast, a discrete random variable would be one that can only take on a countable number of distinct values. For example, the number of people in line at the grocery store would be a discrete random variable since it can only be a whole number (1 person, 2 people, 3 people, etc.).
Additionally, it is important to note that the random variable in question is not qualitative. Qualitative variables are typically categorical or non-numerical in nature, representing qualities or attributes rather than quantities.
Examples of qualitative variables could be the color of a car or the type of grocery items purchased.
In this case, the time you wait in line is a quantitative variable measured in minutes and is thus not qualitative. Therefore, the time you must wait in line at the grocery store is best characterized as a continuous random variable.
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Boyce invested an average of $450 per month since age 34 in various securities for his retirement savings. His investments averaged a 4% annual rate of return until he retired at age 63. Given the same monthly investment and rate of return, how much more would Boyce have in his retirement savings had he started investing at age 20? Assume monthly compounding.
a $113,320. 00
b $321,946. 93
c $78,624. 00
d $224,749. 27
If Boyce had started investing when he was 20 the amount he would have more than he does in his retirement savings would be b. $321,946.93.
How much more would Boyce have?First convert the interest to a monthly rate:
= 4% / 12 months
= 1 / 3 %
Period:
= (63 - 34) x 12 months a year
= 348 months
Amount saved:
= Amount x ( (1 + rate) ^ number of periods - 1) / rate
= 450 x ( (1 + 1/3%)³⁴⁸ - 1 ) / 1/3%
= $294,811.07
If he started saving at 20, the number of periods would be:
= (63 - 20) x 12
= 516 months
Amount saved:
= 450 x ( (1 + 1/3%)⁵¹⁶ - 1 ) / 1/3%
= $616,758
The difference is:
= 616,758 - 294,811.07
= $321,946.93
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Having the mean delivery time (10:28am) and the standard deviation (0:55 mins), you now estimate the times within which 95% of the deliveries are made. the interval is: between 8:12 am and 12:43 pm between 8:38 am and 12:18 pm between 9:45 am and 10:15 am between 10:17 am and 12:32 pm
Based on the given mean delivery time of 10:28am and the standard deviation of 0:55 mins, the estimated times within which 95% of the deliveries are made is (a) between 8:38 am and 12:18 pm.
To calculate this interval, we need to use the z-score formula, where we find the z-score corresponding to the 95th percentile, which is 1.96. Then, we multiply this z-score by the standard deviation and add/subtract it from the mean to get the upper and lower bounds of the interval.
The upper bound is calculated as 10:28 + (1.96 x 0:55) = 12:18 pm, and the lower bound is calculated as 10:28 - (1.96 x 0:55) = 8:38 am.
Therefore, we can conclude that the interval between 8:38 am and 12:18 pm represents the estimated times within which 95% of the deliveries are made based on the given mean delivery time and standard deviation.
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find a parametric representation using spherical-like coordinates for the upper half of the ellipsoid 4(x 1)2 9y2 36z2
A parametric representation using spherical-like coordinates for the upper half of the ellipsoid 4(x₁)² + 9y² + 36z² is given by:
x = 2r cosθ sinφ
y = 3r sinθ sinφ
z = 6r cosφ, where 0 ≤ θ ≤ 2π and 0 ≤ φ ≤ π/2.
We want to find a parametric representation for the upper half of the ellipsoid 4(x₁)² + 9y² + 36z² = 36. To do this, we can use spherical-like coordinates, which are similar to spherical coordinates but with an additional parameter to account for the asymmetry of the ellipsoid.
We start by assuming that the ellipsoid is centered at the origin, so we can write it as:
(x₁/3)² + y²/4 + z²/1 = 1
We can then express x, y, and z in terms of the parameters r, θ, and φ:
x = r cosθ sinφ
y = r sinθ sinφ
z = r cosφ
We can use these equations to find r, θ, and φ in terms of x, y, and z, and substitute into the equation of the ellipsoid to obtain:
[(x₁/3)² + (y/2)² + z²]/1 = 1
Simplifying, we get:
r² = 36/(4 cos²θ sin²φ + 9 sin²θ sin²φ + 36 cos²φ)
We can then use the equations for x, y, and z in terms of r, θ, and φ to obtain the desired parametric representation:
x = 2r cosθ sinφ
y = 3r sinθ sinφ
z = 6r cosφ
We restrict φ to the range 0 ≤ φ ≤ π/2 to obtain only the upper half of the ellipsoid. The range of θ is 0 ≤ θ ≤ 2π, which allows us to cover the entire surface of the ellipsoid.
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find the arc length of the polar curve r = e5θ where 0 ≤ θ ≤ 2π.
The arc length of the polar curve r = e^5θ from 0 to 2π is √26 [(e^10π - 1) / 5].
What is an arc?To find the arc length of a polar curve, we use the formula:
L = ∫[a,b] √(r(θ)² + [dr(θ)/dθ]²) dθ
where r(θ) is the polar equation of the curve, and dr(θ)/dθ is its derivative with respect to θ.
In this case, we have r(θ) = e^5θ, so:
dr(θ)/dθ = 5e^5θ
Plugging these into the arc length formula, we get:
L = ∫[0,2π] √(e^10θ + (5e^5θ)²) dθ
Simplifying the integrand, we have:
L = ∫[0,2π] √(e^10θ + 25e^10θ) dθ
L = ∫[0,2π] √(26e^10θ) dθ
L = √26 ∫[0,2π] e^5θ dθ
Using the formula for the integral of e^x, we get:
L = √26 [e^5θ / 5] |_0^(2π)
L = √26 [(e^10π - 1) / 5]
So the arc length of the polar curve r = e^5θ from 0 to 2π is √26 [(e^10π - 1) / 5].
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80 divided by 192.0!!!!!!!!!!!!!!!
Answer: .416666667
Step-by-step explanation: Take 80 and divide it by 192.0= .416666667
what is the slope intercept for the line below?
Answer:
A
Step-by-step explanation:
Its a positive slope and you go up 2 and to the right 5
The following data points represent the total weight loss
(in kilograms) for each member of omar's final fitness
team. 61,90, 31, 35, 69, 37, 78
The histogram shows that the majority of Omar's Final Fitness Team had weight loss between 30 to 49 kg, with only a few members achieving higher weight loss of 60 to 69 kg.
To create a histogram from the given data, follow these steps:
Step 1: Determine the range of the data (largest value - smallest value): Range = 90 - 31 = 59
Step 2: Choose a number of classes for the histogram. A convenient number of classes is usually between 5 and 15. For this data set, we can choose 6 classes.
Step 3: Determine the width of each class by dividing the range by the number of classes:
Class width = Range / Number of classes
Class width = 59 / 6 = 9.83
Round the class width up to 10 to make it a convenient number.
Therefore, the class width is 10.
Step 4: Determine the lower limit of the first class. Choose a value that is equal to or less than the smallest data point.
Lower limit of first class = 30
Step 5: Create the frequency distribution table by counting how many data points are in each class:
| Class Interval | Frequency |
|:----:|:----:|
| 30 - 39 | 2 |
| 40 - 49 | 2 |
| 50 - 59 | 0 |
| 60 - 69 | 2 |
| 70 - 79 | 1 |
| 80 - 89 | 1 |
Step 6: Draw the histogram. On a horizontal axis, mark the class intervals. On the vertical axis, mark the frequency for each class. Draw vertical bars to represent the frequency in each class. Make the bars touch each other so that it shows a continuous distribution.
Here's the histogram of the given data:
```
Frequency
|
| x
| x
--------|----|----|----|----|---|---
30 40 50 60 70 80 90
| Class intervals |
```
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2. Gamma Tail BoundLetXhave the gamma(r, λ)distribution.a)Show thatP(X≥2E(X))≤(2/e)r.[Remember that ifhis a positive function ofx, then the value ofxthat minimizeshis the sameas the value ofxthat minimizes log(h).]b) [CODE]Fixλ= 1. Display overlaid plots of the following three graphs as functions ofr, forrin the interval (0.5, 15)$ :•P(X≥2E(X))•(2/e)r• Markov’s bound onP(X≥2E(X))The code usesplt.plotwhich is also used in Lab 9.The expressionstats.gamma.cdf(x, r,scale=1)evaluates to the cdf of the gamma(r,1)distribution at the pointx
P(X≥2E(X)) ≤ E(X)/2E(X) = 1/2For minimizing log(h), consider g(x) = log(h(x)) = -x/r + r log(x/r)g'(x) = -1/r + r/x = 0 => x = r=> Minimum value of g(x) = g(r) = -1 - r log(r/e) => Maximum value of h(x) = e^-1 [r/e]^r=> P(X≥2E(X)) ≤ [e^(1/e)/2]^r = (2/e)^r b) import matplotlib.
a) Let h(x) = e^(-x/r) (x/r)^r P(X≥2E(X)) = P(X/2E(X)≥1) ≥ h(X/2E(X)) = e^(-X/2E(X)) (X/2E(X))^r {By Markov's inequality, for any positive r.v. Y and any positive constant c, P(Y≥c)≤E(Y)/c}
So, P(X≥2E(X)) ≤ E(X)/2E(X) = 1/2
For minimizing log(h), consider g(x) = log(h(x)) = -x/r + r log(x/r)g'(x) = -1/r + r/x = 0 => x = r
=> Minimum value of g(x) = g(r) = -1 - r log(r/e)
=> Maximum value of h(x) = e^-1 [r/e]^r=> P(X≥2E(X)) ≤ [e^(1/e)/2]^r = (2/e)^r b) import matplotlib.pyplot as pltimport numpy as npfrom scipy import statsdef markov(r): return (2/e)**rdef gamma(r): return stats.gamma.cdf(2*stats.gamma.mean(r, scale=1), r, scale=1)def main(): lmbda = 1 r = np.linspace(0.5, 15, 1000) plt.plot(r, gamma(r), label='P(X>=2E(X))') plt.plot(r, [(2/e)**i for i in r], label='(2/e)^r') plt.plot(r, [markov(i) for i in r], label="Markov's bound on P(X>=2E(X))") plt.legend(loc="upper left") plt.show()if __name__ == '__main__': main()The overlaid plots are as follows:
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Write the standard form of the equation of theline passing through the point (-5, 3) andperpendicular to the line - 2x – 3y = -6.
The first step we need to follow is to find the slope of the perpendicular line to -2x-3y = -6.
Then, we have:
\(-2x-3y=-6\Rightarrow-3y=-6+2x\Rightarrow y=\frac{-6}{-3}+\frac{2}{-3}x\Rightarrow y=-\frac{2}{3}x+2\)Then, the equivalent equation for the line has a slope of m1 = - 2/3. The perpendicular line must have an inverse and reciprocal to this slope, that is m2 = 3/2. The product of these slopes must be -1, that is: m1 * m2 = -2/3 * 3/2 = -1.
The second step is to find the line equation for the perpendicular. We know that it has a slope of m = 3/2, and that passes through the point (-5, 3). Then, we can use the point-slope form of the line:
\(y-y_1=m(x-x_1)\)\(y-3=\frac{3}{2}(x-(-5))\Rightarrow y-3=\frac{3}{2}(x+5)\Rightarrow y-3=\frac{3}{2}x+\frac{15}{2}\)Then
\(y=\frac{3}{2}x+\frac{15}{2}+3\Rightarrow y=\frac{3}{2}x+\frac{21}{2}\)The Standard Form of the line is of the form:
\(Ax+By=C\)Then, taking the previous equation:
\(2y=3x+21\Rightarrow-3x+2y=21\)Therefore, the Standard Form of the equation is -3x + 2y = 21.
Answer:-3x + 2y = 21.
Step-by-step explanation:
The first step we need to follow is to find the slope of the perpendicular line to -2x-3y = -6.
Then, we have:
Then, the equivalent equation for the line has a slope of m1 = - 2/3. The perpendicular line must have an inverse and reciprocal to this slope, that is m2 = 3/2. The product of these slopes must be -1, that is: m1 * m2 = -2/3 * 3/2 = -1.
The second step is to find the line equation for the perpendicular. We know that it has a slope of m = 3/2, and that passes through the point (-5, 3). Then, we can use the point-slope form of the line:
Then
The Standard Form of the line is of the form:
Then, taking the previous equation:
Therefore, the Standard Form of the equation is -3x + 2y = 21.
help me please !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
11.31
Step-by-step explanation:
Use the pythagorean theorem: c^2=a^2+b^2
18^2=14^2+b^2
324=196+b^2
128=b^2
b=11.31
\([Hello,BrainlyUser]\)
Answer:
\(\sqrt{128}\)
Step-by-step explanation:
Right, let write down the Pythagorean Theorem equation or standard form of it. before we plug in the numbers.
\(a^2+b^2=c^2\)
Right, so that is the equation of Pythagorean Theorem. So let plug in the numbers of b and c.
\(a^2+14^2+18^2\)
So we have our values of b and c. Now, how do we find the missing number?
Well, let simplify thing further by squaring the numbers we have already.
\(a^2+196+324\)
We will now subtract 196 from both side which gives us:
\(a^2=128\)
Now we can square root the answer.
\(\sqrt{a^2} =\sqrt{128}\)
Now, we are left with this:
\(a=\sqrt{128}\)
So the final answer is \(\sqrt{128}\) or the decimal value which is [11.31370849]
Round: 11.31
[CloudBreeze]
anyone know how to do this??
Answer: the answer to the first question is B and the answer to the other question is C
Step-by-step explanation: if im right plz mark as brainliest. Hope this helps :)
Write the following sentence into an expression using x as your variable: Myrna and Tom collect stamps. Tom has four more than half the stamps that Myrna has.
Answer: f(x) = x/2 + 4.
where f(x) is the number of stamps that Tom has, and x is the number of stamps that Myrna has.
Step-by-step explanation:
The statement is:
"Tom has four more than half the stamps that Myrna has"
For how is written, we can model the number of stamps that Tom has as a function f(x).
f(x) represents the number of stamps that Tom has, and x is the number of stamps that Myrna has.
Then:
"four more than a number" is written as:
N + 4 (where N is the number)
"Half the stamps that Myrna has" is written as:
x/2.
Then the whole statement can be modeled as:
f(x) = x/2 + 4.
notice that we have x/2, and f(x) must be a whole number, so Myrna must have an even number of stamps (in that case x/2 will be integer)
Write all lengths in simplest radical form.
Answer:
x = 4√6.
Step-by-step explanation:
sin 60 = x / 8√2
√3/2 = x / 8√2
x = 8√3√2 / 2
= 4√6
= 4√3/√2
Please HELPPP!!!
Givin the figure below,find the values of x and z
Answer:
First, find x.
(12x + 20) + (6x + 70) = 180 (sum of angles on straight line = 180°)
18x + 90 = 180
18x = 90
x = 5
Next, find z.
z = 12x + 20 (vertically opposite angles)
Substitute x = 5 into equation.
z = 12(5) + 20
= 80
PLEASE HELP
Colton earns $7 per hour plus $1.50 for each pizza delivery. The expression 7h+1.50d can be
used to find the total earnings after h hours and d delivers have been made. How much money
will Colten earn after working 15 hours and making 8 deliveries?
Answer:
i believe the answer is 117$
Step-by-step explanation:7*15=105 8*1.50=12... 12+105=117
Segment AC is the angle bisector of
The figure is not to scale.
Which of the following additional statements would allow us to prove that
What does this problem ask for:
--> which statement is sufficient to prove that:
∠ADB ≅ ∠ABD
Let's separate this image into two triangles: ΔADC and ΔABC
--> prove that these triangles are congruent
--> thus proving that: ∠ADB ≅ ∠ABD
Let's consider what evidence we have:
AC is angle bisector of ∠BAD--> thus: ∠ADC = ∠ABC
AC = ACThe minimum information that we have:
--> prove that one pair of sides on both triangles are congruent
--> based on the SSA Triangle Formula
--> Two triangles that have two sides and one angle that are
equal, are therefore congruent
Based on the choices given:
--> if DA = BA or DA is congruent to BA
--> then ΔADC = ΔABC
Thus:
--> ∠ADC = ∠ABC
Answer: DA is congruent to BA
a fishing boat accidentally spills 15 barrels of diesel oil into the ocean. each barrel contains 42 gallons. if the oil film on the ocean is 2.5 x 102 nm thick, how much area in square meters will the oil slick cover? assume 1 gal
The area in square meters will the oil slick cover is 9.5×10⁶ m².
15 barrels of diesel spilt into the ocean, where each barrel contains 42 gallons. Thereby the total volume of the oil spilt by 15 barrels is calculated as follows:
The total volume of the oil spilt by 15 barrels = 15× 42 gallons.
=630 gallons
1 gallon = 3.78541 liters
Volume in L = 630 gallons × 3.78541 liters/ 1 gallon
= 2384.8083 L
1 L = 10⁻³ m³
2384.8083 L = 2384.8083 × 10⁻³ m³
= 2.3848083 m³
The area covered by the oil spill has to be determined, where the thickness of the oil spill is given to be 2.5×10² nm.
1 nm = 10⁻⁹ m
Thereby, 2.5×10² nm = 2.5×10²×10⁻⁹ m
= 2.5×10⁻⁷ m
Area (m²) = volume (m³)/thickness (m)
= 2.3848083 m³/ 2.5×10⁻⁷ m
= 0.95392×10⁷ m²
= 9.5×10⁶ m²
To know more about conversion factor, here
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What is the value of the expression below when y=4 and z=4
5y+7z
Step-by-step explanation:
5y+7z when Y=4 Z=4
=5*(4) + 7*(4)
=20 + 28
=48
Find the solution to the system of equations: x + 3y = 7 and 2x + 4y = 8 1. Isolate x in the first equation: 2. Substitute the value for x into the second equation: 3. Solve for y: 4. Substitute y into either original equation: 5. Write the solution as an ordered pair: x = 7 – 3y 2(7 – 3y) + 4y = 8 14 – 6y + 4y = 8 14 – 2y = 8 –2y = –6 y = 3 x + 3(3) = 7
Answer:
(-2,3)
Step-by-step explanation:
The function c(x) = 400x – 0.2x2 represents the total costs for a company to produce a product, where c is the total cost in dollars and x is the number of units sold. which statement is true? one thousand units have the minimum cost of $200,000. one thousand units have the maximum cost of $200,000. two thousand units have the minimum cost of $800,000. two thousand units have the maximum cost of $800,000.
At x = 1000 we get the c(1000) = 2000,000. Second statement 'one thousand units have the maximum cost of $200,000' is true.
It is given that the function \(\rm c(x)=400x-0.2x^2\) represents the total costs for a company to produce a product, where c is the total cost in dollars and x is the number of units sold.
It is required to find which statement is true, mentioned in the question.
What are the maxima and minima of a function?Maxima and minima of a function are the extrema within the range, in other words, the maximum value of a function at a certain point is called maxima and the minimum value of a function at a certain point is called minima.
We have a function:
\(\rm c(x)=400x-0.2x^2\)
To find the maxima and minima of any function we differentiate the function with respect to \(\rm x\) and equate to zero.
\(\rm \frac{d \ c(x)}{dx} =\frac{d}{dx} (400x-0.2x^2)\)
\(\rm \frac{d \ c(x)}{dx} =\frac{d}{dx} (400x)-\frac{d}{dx} (0.2x^2)\\\rm \frac{d \ c(x)}{dx} =400-(0.2\times2x)\\\rm \frac{d \ c(x)}{dx} =400-0.4x\)
For maxima and minima \(\rm \frac{d \ c(x)}{dx} =0\)
\(\rm 400-0.4x=0\\\rm x=\frac{400}{0.4} \\\rm x=1000\)
If we find the seconnd differentiate, we get
c''(x) = -0.4 < 0
It means at x = 1000 we will get the maximum value of a function.
\(\\\\\rm c(1000) = 400(1000) - 0.2(1000)^2\\\rm c(1000)= 200,000\)
Thus, at x = 1000 we get the c(1000) = 2000,000. Second statement is true.
Know more about the maxima and minima here:
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Answer:
B
Step-by-step explanation:
To determine the maxima and minima of the polynomial, differentiate the given based on x and equate to 0. C(x) = 400x - 0.2x² dC(x) / dt = 400 - 0.4 x = 0 The value of x is 1000. This is the value of the maxima. As the value of C(x) continously becomes lesser as the value of x is set higher, the minima is not identified. Substitute x to the original equation, C(x) = (400)(1000) - 0.2(1000²) = $ 200,000Thus, the answer is letter B.