A rectangular prism is thought of as being created by stacking congruent polygons.
What is rectangular prism?A solid (3-dimensional) object which has six faces that are rectangles. It has the same cross-section along a length, which makes it a prism.
When the two geometric figures are called congruent?Two geometric figures are said to be congruent, or to be in the relation of congruence, if it is possible to superpose one of them on the other so that they coincide throughout.
What is stacking of congruent figures?Stacking congruent figures means arranging the congruent figures on the top of the other until it become a large pile.
According to the given question.
We have to stack the congruent polygons.
As we know that stacking up means to keep increasing in quantity until we get a large pile.
Since, when we piled up of stack the congruent polygons we will get a prism.
For example when we stack congruent squares we will get cube or we can say a rectangular prism.
If we stack congruent octagons we will get an octagon prism.
Hence, a rectangular prism is thought of as being created by stacking congruent polygons.
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6. Find the variance and standard deviation for the given data using the formula. Round your answer to one more decimal place than the original data g
Answer and Step-by-step explanation:
Variance is the measurement of the spread bewteen the numbers of the data set and can be calculated by the formula:
σ² = ∑(x - ⁻x)² / n
1) With the data, find its mean (⁻x) by adding all the values and dividing the sum by total number of elements the data has;
2) Subtract each value of the data to the mean;
3) Square the result of the subtractions;
4) Add the squares;
5) Divide the sum by the total number of elements of the set;
6) The result is the Variance (σ²);
Standard Deviation is the measure of how far the values of the data set are from the mean and it is the square root of Variance:
σ = [tex]\sqrt{(variance)^{2}}[/tex]
So, to calculate standard deviation, you just take the square root of the variance.
5.b) If z^(1/2)=x^(1/2)+y^(1/2) , show that (x+y-z)^2=4xy
Answer:
Step-by-step explanation:
(x+y-z)²= 4xy (x+y-z)²- 4xy = 0(x+y-z)²-(2√x√y)² = 0(x+y-z-2√x√y)(x+y-z+2√x√y) =0[(√x-√y)²-z]*[(√x+√y)²-z]=0(√x-√y)²-z = 0 or (√x+√y)²-z = 0We have : z^(1/2)= x^(1/2)+y^(1/2) ⇒ √z = √x + √y ⇒ z = (√x + √y)²
so (√x+√y)²-z = 0so (x+y-z)²= 4xy
The half-life of radium-226 is 1590 years. If a sample contains 400 mg how many mg will remain after 4000 years?
Answer:
69.9 mg
Step-by-step explanation:
A = A₀ (½)^(t / T)
where A is the final amount,
A₀ is the initial amount,
t is time,
and T is the half life.
A = 400 (½)^(4000 / 1590)
A = 69.9 mg
Determine whether each function is even, odd, or neither.g(x) = |x-3| g(x) = x + x
Answer:
Step-by-step explanation:
g(x) = |x-3| is neither even nor odd; the graph is not symmetric about the y-axis (as characterizes even functions), and is not symmetric about the origin either.
g(x) = x + x is actually g(x) = 2x, which is an odd function. The graph is symmetric about the origin.
ABCD IS a rectangle and line OA is perpendicular to line OB, line BC is equal to 2cm, line CD is equal to 6cm and tan x degree is equal to 3 / 4.find the values of a.sinx b.cos x and c.line OZ.
Answer:
a) sinx = 3/5
b) cosx = 4/5
c) line OZ = 3cm
Step-by-step explanation:
Two different questions are stated here:
The first is rectangle ABCD where two of its sides are given and we are to find line OZ
The second is on trigonometry. We have been given the tangent ratio and we are to find the sine and cosine ratio.
1) Rectangle ABCD dimensions:
AB = 2cm
CD = 6cm
So we know when we are drawing the rectangle, the smallest side = 2cm and biggest side = 6cm
AO is perpendicular to OB
Line OZ cuts line AB into two
Find attached the diagram
To determine Line OZ, we would apply tangent rule since we know adjacent but opposite is missing.
All 4 angles in a rectangle = 90°
∠OAZ = 45
tan 45 = opposite/adjacent
tan 45 = OZ/3
OZ = 3 × tan45
OZ = 3×1
OZ = 3cm
2) tanx = 3/4
Tangent ratio = opposite/adjacent
opposite = 3, adjacent = 4
see attachment for diagram
Sinx = opposite/hypotenuse
Using Pythagoras theorem
hypotenuse² = opposite² + adjacent²
hypotenuse² = 3²+4² = 9+16 = 25
hypotenuse = √25
hypotenuse = 5
Sinx = opposite/hypotenuse
Sinx = 3/5
Cosx = adjacent/hypotenuse
Cosx = 4/5
a) 3/5
b) 4/5
c) 3cm
Using the matrix solver on your calculator, find the solution to the system of
equations shown below.
3x - y = 4
6x - 2y = 7
A. x = 6, y = 2
B. No solution
C. x= 3, y= 1
D. More than 1 solution
SUBMIT
Answer:
B. No solution.
Step-by-step example
I will try to solve your system of equations.
3x−y=4;6x−2y=7
Step: Solve3x−y=4for y:
3x−y+−3x=4+−3x(Add -3x to both sides)
−y=−3x+4
−y
−1
=
−3x+4
−1
(Divide both sides by -1)
y=3x−4
Step: Substitute3x−4foryin6x−2y=7:
6x−2y=7
6x−2(3x−4)=7
8=7(Simplify both sides of the equation)
8+−8=7+−8(Add -8 to both sides)
0=−1
Therefore, there is no solution, and the lines are parallel.
1)
Check all the expressions that are equal to this one:
5. (4+1)
A. (5 • 4) + 1
B. 5.4 + 5 - 1
C. (4+1) • 5
D. 5. (1 + 4)
60 points +brainleist to best answer!
Answer:
A and B are independent because P(A) * P(B) = P(A and B).
Step-by-step explanation:
If A and B are independent, then P(A) * P(B) = P(A and B)
since
P(A)*P(B) = (2/3*1/4) = 2/12 = 1 / 6 = P(A and B)
A and B are independent.
Answer:
YES THANKS FOR 30
Step-by-step explanation:
Exponential function f is represented by the table. x -1 0 1 2 3 4 f(x) 7.5 7 6 4 0 -8 Function g is an exponential function passing through the points (0,27) and (3,0). Which statement correctly compares the behavior of the two functions on the interval (0, 3)? A. Both functions are positive and decreasing on the interval. B. Both functions are positive on the interval, but one function is increasing while the other is decreasing. C. Both functions are positive and increasing on the interval. D. One function is positive on the interval, and the other is negative.
Answer:
A. Both functions are positive and decreasing on the interval.
Step-by-step explanation:
The table shows that f(x) decreases when x increases in the interval (0,3).
All the values of f(x) are positive in the interval (0,3).
For the exponential function that passes through the points (0, 27) and (3, 0), we also see that f(x) is decreasing when x increases: when x goes from 0 to 3, f(x) goes from 27 to 0.
Also all the values of f(x) are positive in the interval.
Then, both functions are positive and dereasing in the interval.
Answer:
A. Both functions are positive and decreasing on the interval.
Step-by-step explanation:
I did the test and I got it correct. Hope this helps. :DD
Select the correct equations in the image.
Identify the ellipses, represented by equations, whose eccentricities are less than 0.5.
Answer:
equations 1, 2, 6 . . . (top two, bottom right)
Step-by-step explanation:
For the standard-form equation of an ellipse:
Ax^2 +Bx +Cy^2 +Dy +E = 0
we can define ...
p = min(A, C)
q = max(A, C)
Then the eccentricity can be shown to be ...
e = √(1 -p/q)
p/q = 1 -e^2
For eccentricity < 0.5, we want ...
p/q > 3/4
__
Checking the values of p/q for the given equations left-to-right, top-to-bottom, we have p/q = ...
49/64 ≈ 0.765 . . . e < 0.581/100 ≈ 0.810 . . . e < 0.56/54 ≈ 0.111 . . . e > 0.536/49 ≈ 0.734 . . . e > 0.54/25 ≈ 0.160 . . . e > 0.564/81 ≈ 0.790 . . . e < 0.5Equations 1, 2, 6 are of ellipses with eccentricity < 0.5.
Answer:
The two at the top and the one in the bottom right are the correct answers
Step-by-step explanation:
by how much is 25% of #25 greater than 15% of #15
Answer:
4
Step-by-step explanation:
25% of 25
0.25 × 25 = 6.25
15% of 15
0.15 × 15 = 2.25
Find the difference.
6.25 - 2.25
= 4
Suppose CAequalsISubscript n (the ntimesn identity matrix). Show that the equation ABold xequalsBold 0 has only the trivial solution. Explain why A cannot have more columns than rows
Answer:
See Explanation
Step-by-step explanation:
(a)For matrices A and C, given that: [tex]CA=I_n[/tex].
We want to show that Ax=0 has only the trivial solution
If Ax=0
Multiply both sides by C
[tex]C(Ax)=C \times 0\\\implies (CA)x=0$ (Recall: CA=I_n)\\\implies I_nx=0 $ (Since I_n$ is the n\times n$ identity matrix)\\\implies x=0[/tex]
This means that the system has only the trivial solution.
(b)If the system has more columns than rows, a free variable would occur when a column does not have a pivot. This would lead to a non-trivial solution.
The graph represents function 1 and the equation represents function 2: A graph with numbers 0 to 4 on the x-axis and y-axis at increments of 1. A horizontal straight line is drawn joining the ordered pairs 0, 3 and 4, 3. Function 2 y = 5x + 1 How much more is the rate of change of function 2 than the rate of change of function 1? PLEASE ANSWER SOON I NEED IT BAD WHO EVER ANSWERS FIRST GETS VOTE FOR BRAINLYIEST
Answer:
Rate of change of function 1: ZERO
Rate of change of function 2: TWO
The rate of change of function 2 is 2 more than the rate of change of function 1.
Step-by-step explanation:
Hope this helps and please mark as brainiest!
Answer:
The answer is 2.
Step-by-step explanation:
An object moves along a horizontal coordinate line in such a way that its position at time t is specified by s equals t cubed minus 3 t squared minus 24 t plus 8. Here s is measured in centimeters and t in seconds. When is the object slowing down; that is, when is its speed decreasing?
Answer:
a)
The object slowing down S = -72 centimetres after t = 4 seconds
b)
The speed is decreasing at t = -2 seconds
The objective function S = 36 centimetres
Step-by-step explanation:
Step(i):-
Given S = t³ - 3 t² - 24 t + 8 ...(i)
Differentiating equation (i) with respective to 'x'
[tex]\frac{dS}{dt} = 3 t^{2} - 3 (2 t) - 24[/tex]
Equating Zero
3 t ² - 6 t - 24 = 0
⇒ t² - 2 t - 8 = 0
⇒ t² - 4 t + 2 t - 8 = 0
⇒ t (t-4) + 2 (t -4) =0
⇒ ( t + 2) ( t -4) =0
⇒ t = -2 and t = 4
Again differentiating with respective to 'x'
[tex]\frac{d^{2} S}{dt^{2} } = 6 t - 6[/tex]
Step(ii):-
Case(i):-
Put t= -2
[tex]\frac{d^{2} S}{dt^{2} } = 6 t - 6 = 6 ( -2) -6 = -12 -6 = -18 <0[/tex]
The maximum object
S = t³ - 3 t² - 24 t + 8
S = ( -2)³ - 3 (-2)² -24(-2) +8
S = -8-3(4) +48 +8
S = - 8 - 12 + 56
S = - 20 +56
S = 36
Case(ii):-
put t = 4
[tex]\frac{d^{2} S}{dt^{2} } = 6 t - 6 = 6 ( 4) -6 = 24 -6 = 18 >0[/tex]
The object slowing down at t =4 seconds
The minimum objective function
S = t³ - 3 t² - 24 t + 8
S = ( 4)³ - 3 (4)² -24(4) +8
S = 64 -48 - 96 +8
S = - 72
The object slowing down S = -72 centimetres after t = 4 seconds
Final answer:-
The object slowing down S = -72 centimetres after t = 4 seconds
The speed is decreasing at t = -2 seconds
The objective function S = 36 centimetres
Need Help With This
Answer:
4n-13
Step-by-step explanation:
Terms= -13 (constant)
Coefficient= 3, -5, 6
Like term= 3n, -5n, 6n
3n-13-5n+6n
3n+6n-5n-13
9n-5n-13
4n-13
Hope this helps ;) ❤❤❤
The difference in the x coordinates of two points is 3, and the difference in the y coordinates of the two points is 6.
What is the slope of the line that passes through the points?
O 2
O 3
O 6
O 9
Answer:
2
Step-by-step explanation:
Slope =( difference in the y coordinates)/ (difference in the x coordinates)
= 6/3
= 2
the resendez family pays a monthy base charge for their electricity plus a charge for each kilowatt-hour used. In april, their electric bill was $144.50 for 750 kwh and in May, it was $122.0 for 600kWh. What is the charge per killowatt-hour?
Answer:
about $0.20 per kilowatt-hour. i hope this helps
Step-by-step explanation:
ope Equation
fy
What is the equation of the line in point-slope form?
4
= {(x + 4)
Oy+4=;
O y-4 = 2(x + 4)
N
Oy - 0 = 2(x-4)
Oy - 4 = 2(x -0)
4
-2.
2.
Answer:
A
Step-by-step explanation:
For point-slope form, you need a point and the slope.
y - y₁ = m(x - x₁)
Looking at the graph, the points you have are (4, 0) and (-4, -4). You can use these points to find the slope. Divide the difference of the y's by the difference of the x's/
-4 - 0 = -4
-4 - 4 = -8
-4/-8 = 1/2
The slope is 1/2. This cancels out choices C and D.
With the point (-4, -4), A is the answer.
the equation of the line in slope-intercept form is:
y = (1/2)x - 2
What is the Linear equation?A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. Sometimes, the aforementioned is referred to as a "linear equation of two variables," with y and x serving as the variables.
From the graph, two points on the line are (-4, -4) and (4,0),
The formula for the slope of a line is:
m = (y₂ - y₁) / (x₁ - x₁)
where (x₁, y₁) and (x₂, y₂) are two points on the line.
Using the given points (-4, -4) and (4, 0), we can calculate the slope:
m = (0 - (-4)) / (4 - (-4))
m = 4 / 8
m = 1/2
Now that we know the slope, we can use the slope-intercept form of a line, which is:
y = mx + b
where m is the slope and b is the y-intercept.
To find the y-intercept, we can use one of the given points on the line. Let's use the point (-4, -4):
y = mx + b
-4 = (1/2)(-4) + b
-4 = -2 + b
b = -2
Therefore, the slope-intercept form of the line is y = (1/2)x - 2.
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Determine the domain and range for the relations. (11, 1), (9,2), (7,3), (5,4)
Hey there! I'm happy to help!
The domain is all of the x-values of a relation and the range is all of the y-values. When you write them out, you order the numbers from least to greatest and put it in brackets.
The domain of our relation is the x-values of these points, which are 11, 9, 7, and 5. The domain is {5,7,9,11}.
The range is the y-values, which are 1, 2, 3, and 4. So, the range is {1,2,3,4}.
Now you can find the domain and range given a few ordered pairs!
Have a wonderful day!
. The client was hoping for a likability score of at least 5.2. Use your sample mean and standard deviation identified in the answer to question 1 to complete the following table for the margins of error and confidence intervals at different confidence levels. Note: No further calculations are needed for the sample mean. (6 points: 2 points for each completed row) Confidence Level | Margin of error | Center interval | upper interval | Lower interval 68 95 99.7
Answer:
The 68% confidence interval is (6.3, 6.7).
The 95% confidence interval is (6.1, 6.9).
The 99.7% confidence interval is (5.9, 7.1).
Step-by-step explanation:
The Central Limit Theorem states that if we have a population with mean μ and standard deviation σ and take appropriately huge random-samples (n ≥ 30) from the population with replacement, then the distribution of the sample-means will be approximately normally distributed.
Then, the mean of the sample means is given by,
[tex]\mu_{\bar x}=\bar x[/tex]
And the standard deviation of the sample means (also known as the standard error)is given by,
[tex]\sigma_{\bar x}=\frac{\sigma}{\sqrt{n}} \ \text{or}\ \frac{s}{\sqrt{n}}[/tex]
The information provided is:
[tex]n=400\\\\\bar x=6.5\\\\s=4[/tex]
As n = 400 > 30, the sampling distribution of the sample-means will be approximately normally distributed.
(a)
Compute the 68% confidence interval for population mean as follows:
[tex]CI=\bar x\pm z_{\alpha/2}\cdot \frac{s}{\sqrt{n}}[/tex]
[tex]=6.5\pm 0.9945\cdot \frac{4}{\sqrt{400}}\\\\=6.5\pm 0.1989\\\\=(6.3011, 6.6989)\\\\\approx (6.3, 6.7)[/tex]
The 68% confidence interval is (6.3, 6.7).
The margin of error is:
[tex]MOE=\frac{UL-LL}{2}=\frac{6.7-6.3}{2}=0.20[/tex]
(b)
Compute the 95% confidence interval for population mean as follows:
[tex]CI=\bar x\pm z_{\alpha/2}\cdot \frac{s}{\sqrt{n}}[/tex]
[tex]=6.5\pm 1.96\cdot \frac{4}{\sqrt{400}}\\\\=6.5\pm 0.392\\\\=(6.108, 6.892)\\\\\approx (6.1, 6.9)[/tex]
The 95% confidence interval is (6.1, 6.9).
The margin of error is:
[tex]MOE=\frac{UL-LL}{2}=\frac{6.9-6.1}{2}=0.40[/tex]
(c)
Compute the 99.7% confidence interval for population mean as follows:
[tex]CI=\bar x\pm z_{\alpha/2}\cdot \frac{s}{\sqrt{n}}[/tex]
[tex]=6.5\pm 0.594\cdot \frac{4}{\sqrt{400}}\\\\=6.5\pm 0.392\\\\=(5.906, 7.094)\\\\\approx (5.9, 7.1)[/tex]
The 99.7% confidence interval is (5.9, 7.1).
The margin of error is:
[tex]MOE=\frac{UL-LL}{2}=\frac{7.1-5.9}{2}=0.55[/tex]
Find the percent of increase. Original Price: $200 Retail Price: $250
Answer:
The percent of increase is 25%
Step-by-step explanation:
Percentage increase = increase in price/original price × 100 = ($250 - $200)/$200 × 100 = $50/$200 × 100 = 25%
Denise is planning to put a deck in her back yard. The deck will be a 10-by-7-foot rectangle with a semicircle of diameter 4 feet, as shown below. Find the area of the deck (in square feet).(round your answer to two decimal places)
Answer:
[tex]approx. = 85.28 {ft}^{2} [/tex]
Step-by-step explanation:
You can think of this as adding the area of the rectangular portion of the deck (length x width) and the semicircular portion (πr^2)/2.
(l×w)+(πr^2)/2
(10×7)+((π2^2)/2
79+2π
[tex]approx. = 85.28 {ft}^{2} [/tex]
A ranch in "Smart Town" claimed that the cows they raise are smarter than the rest of the population of US cows. To prove that they announced that the average weight of their "Smart Cow" brain is 485 grams instead of the regular 458 grams. Assume that the standard deviation of Smart Cow brain weights is the same as the entire population's standard deviation=64 g.
a) What is the Probability that the Brain of a randomly selected Smart Cow will weigh at least 500 grams
b) What is the probability that the average brain weight of a sample of 36 Smart Cows will be at least 480 grams
Answer:
(a) The probability that the Brain of a randomly selected Smart Cow will weigh at least 500 grams is 0.4091.
(b) The probability that the average brain weight of a sample of 36 Smart Cows will be at least 480 grams is 0.6808.
Step-by-step explanation:
We are given that the average weight of their "Smart Cow" brain is 485 grams instead of the regular 458 grams.
Assume that the standard deviation of Smart Cow brain weights is the same as the entire population's standard deviation = 64 g.
Let X = weight of the brain of a randomly selected Smart Cow
So, X ~ Normal([tex]\mu=485, \sigma^{2} = 64^{2}[/tex])
The z-score probability distribution for the normal distribution is given by;
Z = [tex]\frac{X-\mu}{\sigma}[/tex] ~ N(0,1)
where, [tex]\mu[/tex] = population mean weight = 485 grams
[tex]\sigma[/tex] = standard deviation = 64 grams
(a) The probability that the Brain of a randomly selected Smart Cow will weigh at least 500 grams is given by = P(X [tex]\geq[/tex] 500 grams)
P(X [tex]\geq[/tex] 500 g) = P( [tex]\frac{X-\mu}{\sigma}[/tex] [tex]\geq[/tex] [tex]\frac{500-485}{64}[/tex] ) = P(Z [tex]\geq[/tex] 0.23) = 1 - P(Z < 0.23)
= 1 - 0.59095 = 0.4091
The above probability is calculated by looking at the value of x = 0.23 in the z table which has an area of 0.59095.
(b) Let [tex]\bar X[/tex] = sample mean weight of the brain of a randomly selected Smart Cow
The z-score probability distribution for the sample meanis given by;
Z = [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] ~ N(0,1)
where, [tex]\mu[/tex] = population mean weight = 485 grams
[tex]\sigma[/tex] = standard deviation = 64 grams
n = sample of cows = 36
Now, the probability that the average brain weight of a sample of 36 Smart Cows will be at least 480 grams is given by = P([tex]\bar X[/tex] [tex]\geq[/tex] 480 grams)
P([tex]\bar X[/tex] [tex]\geq[/tex] 480 g) = P( [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] [tex]\geq[/tex] [tex]\frac{480-485}{\frac{64}{\sqrt{36} } }[/tex] ) = P(Z [tex]\geq[/tex] -0.47) = P(Z < 0.47)
= 0.6808
The above probability is calculated by looking at the value of x = 0.47 in the z table which has an area of 0.6808.
Given: g(x) = square root x-4 and h(x) = 2x - 8 What are the restrictions on the domain of g of h. x greater than or equal to
Answer:
Step-by-step explanation:
x-4 greater or equal 0
x greater or equal 4
Answer:
The actual answer is x is greater than or equal to 6 (i used the answer that was on here and got it wrong so here is the correct answer!!)
just did the test on edg 2021
Write the value of the money in dollars Brainliest Awnser gets 7 points for greatness
Answer:
The picture isn't very clear but I think this is the answer.
1. 15 cents
2. $1.31
3. 30 cents
Step-by-step explanation:
1. 10+5
2. 50+50+10+10+10+1
3. 25+5
State the domain and range of the following functions f(x) =1/x+3 g(x) =sqrt x+6
Answer:
For the function [tex]f(x)=\frac{1}{x} +3[/tex]. The domain is [tex]\left(-\infty \:,\:0\right)\cup \left(0,\:\infty \:\right)[/tex] and the range is [tex]\left(-\infty, 3\right) \cup \left(3, \infty\right)[/tex].
For the function [tex]g(x) =\sqrt{x+6}[/tex]. The domain is [tex]\left[-6, \infty\right)[/tex] and the range is [tex]\left[0, \infty\right)[/tex].
Step-by-step explanation:
The domain of a function is the set of input or argument values for which the function is real and defined.
The range of a function is the complete set of all possible resulting values of the dependent variable, after we have substituted the domain.
[tex]f(x)=\frac{1}{x} +3[/tex] is a rational function. A rational function is a function that is expressed as the quotient of two polynomials.
Rational functions are defined for all real numbers except those which result in a denominator that is equal to zero (i.e., division by zero).
The domain of the function is [tex]\left(-\infty \:,\:0\right)\cup \left(0,\:\infty \:\right)[/tex].
The range of the function is [tex]\left(-\infty, 3\right) \cup \left(3, \infty\right)[/tex].
[tex]g(x) =\sqrt{x+6}[/tex] is a square root function.
Square root functions are defined for all real numbers except those which result in a negative expression below the square root.
The expression below the square root in [tex]g(x) =\sqrt{x+6}[/tex] is [tex]x+6[/tex]. We want that to be greater than or equal to zero.
[tex]x+6\geq 0\\x\ge \:-6[/tex]
The domain of the function is [tex]\left[-6, \infty\right)[/tex].
The range of the function is [tex]\left[0, \infty\right)[/tex].
Evaluate the expression ........
Answer:
13
Step-by-step explanation:
p^2 -6p +6
Let p=-1
(-1)^2 -6(-1) +6
1 +6+6
13
How do you find the sum of 74.365 and 9.82?
A company that produces ribbon has found that the marginal cost of producing x yards of fancy ribbon is given by Upper C prime (x )equalsnegative 0.00001 x squared minus 0.02 x plus 58 for x less than or equals 1600, where Upper C prime (x )is in cents. Approximate the total cost of manufacturing 1600 yards of ribbon, using 5 subintervals over [0 comma 1600 ]and the left endpoint of each subinterval.
Answer:
$624.90
Step-by-step explanation:
The total cost is the integral of the marginal cost. Here, you're asked to approximate that integral using 5 equal-width rectangles. The area of each rectangle is the product of its height and width. The height is given by the function value at the left end of the interval.
The table shows the function values at the left end of each of the 5 intervals. The intervals have width 1600/5 = 320. The total estimated cost is the sum of products of 320 and each of the table values. (Of course, 320 can be factored out of the sum to make the math easier.)
The estimated cost is ...
320(58 + 50.576 + 41.104 + 29.584 +16.016) = 62,489.6 . . . cents
≈ $624.90 . . . . cost of manufacturing 1600 yards of fancy ribbon
please help will mark brainliest!
Answer:
1. Vertex (-3,2)
A) (x+3)² + 5
B) (x-3)² + 2
C) (x-1)² -5
I hope these are all correct
Step-by-step explanation: