Answer: 16 litres
Step-by-step explanation:
A: 1l x km
B: 1l x+5 km
Running 400 km A used 400/x litres
Running 400 km B used 400/(x+5) litres
400/x- 400/(x+5)= 4
400*(x+5)- x*400-4*x*(x+5)=0
400*x+2000-400*x-4*x²-20*x=0
2000-4*x²-20*x=0 difide by 4 both sides of equation
500-x²-5*x=0
Lets solve the equation using discriminant:
D=5²-(-1)*4*500=2025
sqrt(D)=45
x1= (5+45)/(-2)= -25 x2=(5-45)/(-2)=20
x1=-25 x2=20
x1<0 so is not the solution of the problem ( number of litres can't be negative)
So A uses litr per x=20 km and B uses 1 litr per 20+5=25 km
Running 400 km B uses 400/25=16 litres
HURRRRYYYY PLEASEEE ABC will undergo two transformations to give ABC which pair of transformations will give a different image of ABC if the order fo the tranformations is reversed A. a rotation 90 counterclockwise about the origin followed by a reflection across the y-axis b. a translation 5 units down followed by a translation 4 units to the right C. a reflection across the x-axis followed bt a reflection across the y-axis d. a rotation 180 clockwise about the origin followed by a reflection across the y axis
Answer:
C. A reflection across the x-axis followed by a reflection across the y-axis
Step-by-step explanation:
A. is incorrect because you would get the same graph again.
B. is incorrect because you would get the same image but moved to a different location.
D. is incorrect because it would just give you a reflection over the x-axis.
Answer:
The answer is rotate 90° clockwise I’m pretty sure.
Step-by-step explanation:
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:
PLEASEEEE HELPPPP!!!!
Amanda has been employed at a company for 37 years. The company is 24 years older than Amanda. The sum of Amanda age and the company’s age is 121 years. How old was Amanda when she started her job?
Answer:
11 1/2 years old
Step-by-step explanation:
Let Amanda's age be a.
Let the company's age be c.
The company is 24 years older than Amanda. This means that:
c = 24 + a ______(1)
The sum of Amanda's age and the company's age is 121 years. This means that:
c + a = 121 ________(2)
Put (1) in (2):
24 + a + a = 121
2a = 121 - 24
2a = 97
a = 97 / 2 = 48 1/2 years
She has been there for 37 years, therefore, her age when she started working there is:
48 1/2 - 37 = 11 1/2 years old
NOTE: This age doesn't seem right but I worked based on the parameters given.
What is the angle of rotation of the figure? A.0° B.90° C.120° D.180°
Answer:
B. 90
Step-by-step explanation:
angle of rotation = 360/4= 90
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.
The length of a rectangle is seven times its width. The area of the rectangle is 175 square centimeters. Find the dimensions of the rectangle.
Answer:
The length is 35cmThe width is 5cmStep-by-step explanation:
Area of a rectangle = l × w
where
l is the length
w is the width
The length is seven times the width is written as
l = 7w
Area of the rectangle = 175 cm²
7w × w = 175
7w² = 175
Divide both sides by 7
w² = 25
Find the square root of both sides
w = √25
w = 5cm
But l = 7w
l = 7(5)
l = 35cm
The length is 35cm
The width is 5cm
Hope this helps you.
Evaluate the integral using integration by parts with the indicated choices of u and dv. (Use C for the constant of integration.) xe2x dx; u = x, dv = e2x dx
Answer:
[tex]\displaystyle \int {xe^{2x}} \, dx = \frac{e^{2x}}{2} \bigg( x - \frac{1}{2} \bigg) + C[/tex]
General Formulas and Concepts:
Calculus
Differentiation
DerivativesDerivative NotationDerivative Property [Multiplied Constant]: [tex]\displaystyle \frac{d}{dx} [cf(x)] = c \cdot f'(x)[/tex]
Basic Power Rule:
f(x) = cxⁿf’(x) = c·nxⁿ⁻¹Integration
Integrals[Indefinite Integrals] Integration Constant CIntegration Property [Multiplied Constant]: [tex]\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx[/tex]
U-Substitution
Integration by Parts: [tex]\displaystyle \int {u} \, dv = uv - \int {v} \, du[/tex]
[IBP] LIPET: Logs, inverses, Polynomials, Exponentials, TrigStep-by-step explanation:
Step 1: Define
Identify
[tex]\displaystyle \int {xe^{2x}} \, dx[/tex]
Step 2: Integrate Pt. 1
Identify variables for integration by parts using LIPET.
Set u: [tex]\displaystyle u = x[/tex][u] Basic Power Rule: [tex]\displaystyle du = dx[/tex]Set dv: [tex]\displaystyle dv = e^{2x} \ dx[/tex][dv] Exponential Integration [U-Substitution]: [tex]\displaystyle v = \frac{e^{2x}}{2}[/tex]Step 3: Integrate Pt. 2
[Integral] Integration by Parts: [tex]\displaystyle \int {xe^{2x}} \, dx = \frac{xe^{2x}}{2} - \int {\frac{e^{2x}}{2}} \, dx[/tex][Integral] Rewrite [Integration Property - Multiplied Constant]: [tex]\displaystyle \int {xe^{2x}} \, dx = \frac{xe^{2x}}{2} - \frac{1}{2} \int {e^{2x}} \, dx[/tex]Step 4: Integrate Pt. 3
Identify variables for u-substitution.
Set u: [tex]\displaystyle u = 2x[/tex][u] Basic Power Rule [Derivative Property - Multiplied Constant]: [tex]\displaystyle du = 2 \ dx[/tex]Step 5: Integrate Pt. 4
[Integral] Rewrite [Integration Property - Multiplied Constant]: [tex]\displaystyle \int {xe^{2x}} \, dx = \frac{xe^{2x}}{2} - \frac{1}{4} \int {2e^{2x}} \, dx[/tex][Integral] U-Substitution: [tex]\displaystyle \int {xe^{2x}} \, dx = \frac{xe^{2x}}{2} - \frac{1}{4} \int {e^{u}} \, dx[/tex][Integral] Exponential Integration: [tex]\displaystyle \int {xe^{2x}} \, dx = \frac{xe^{2x}}{2} - \frac{e^u}{4} + C[/tex][u] Back-Substitute: [tex]\displaystyle \int {xe^{2x}} \, dx = \frac{xe^{2x}}{2} - \frac{e^{2x}}{4} + C[/tex]Factor: [tex]\displaystyle \int {xe^{2x}} \, dx = \frac{e^{2x}}{2} \bigg( x - \frac{1}{2} \bigg) + C[/tex]Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Integration
Write a two column proof Given: AB || DC; BC || AE Prove: BC/EA = BD/EB
Answer:
Step-by-step explanation:
Given:
AB║DC and BC║AE
To prove:
[tex]\frac{\text{BC}}{\text{EA}}=\frac{\text{BD}}{\text{EB}}[/tex]
Statements Reasons
1). ∠ABE ≅ ∠CDB 1). Alternate interior angles
2). ∠AEB ≅ ∠CBD 2). Alternate interior angles
3). ΔCBD ~ ΔAEB 3). AA property of similarity
4). [tex]\frac{\text{BC}}{\text{EA}}=\frac{\text{BD}}{\text{EB}}[/tex] 4). Property of similarity [Corresponding sides of two similar triangles are proportional]
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
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
Find the first 5 terms of the sequence an defined below.
a_n = { -2n+3 if n is divisible by 3}
{-n -2 if n is not divisible by 3}
Answer:
Step-by-step explanation:
A_n = a + (n-1)d
a_n = -2n + 3
when n=1
a_1 = a = -2(1) + 3 = -2 + 3 = 1
when n = 2
a-_2 = -2(2) + 3 = -4 +3 = -1
a_2 = a + d
therefore,
a + d = -1
d = -1 - a
d = - 1 - 1
d = -2
Therefore the sequence is ,
1 , -1, -3, -5, -7.......
The first 5 terms of the sequence are -3, -4, -3, -6, and -7.
What is an expression?An expression contains one or more terms with addition, subtraction, multiplication, and division.
We always combine the like terms in an expression when we simplify.
We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.
Example:
1 + 3x + 4y = 7 is an expression.com
3 + 4 is an expression.
2 x 4 + 6 x 7 – 9 is an expression.
33 + 77 – 88 is an expression.
We have,
To find the first 5 terms of the sequence, we can simply evaluate the formula for n = 1, 2, 3, 4, and 5.
For n = 1, we have:
a_1 = -(1) - 2 = -3 (not divisible by 3)
For n = 2, we have:
a_2 = -(2) - 2 = -4 (not divisible by 3)
For n = 3, we have:
a_3 = -2(3) + 3 = -3 (divisible by 3)
For n = 4, we have:
a_4 = -(4) - 2 = -6 (not divisible by 3)
For n = 5, we have:
a_5 = -(5) - 2 = -7 (not divisible by 3)
Therefore,
The first 5 terms of the sequence are -3, -4, -3, -6, and -7.
Learn more about expressions here:
https://brainly.com/question/3118662
#SPJ2
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 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 $0.20 per kilowatt-hour. i hope this helps
Step-by-step explanation:
Arun bought a ball with a 20$ note and received 7$ change. Then, he bought a bat with three 10$ notes and received 8$ change. Altogether he had 25$ left. How much money did Arun have before he bought a ball and a bat?
Answer:
50$
Step-by-step explanation:
First money he had = 20$
Second = 10$ * 3 = 30$
Total money he had = 20$+30$ =
= 50$
Mark as Brainliest
=====50$
Step-by-step explanation:
First money he had = 20$
Second = 10$ * 3 = 30$
Total money he had = 20$+30$ =
= 50$
I need help plz someone help me solved this problem I need help ASAP! I will mark you as brainiest!
Answer: k = 12
Step-by-step explanation:
x² + kx + 36 = 0
In order for x to have exactly one solution, it must be a perfect square.
(x + √36)² = 0
(x + 6)² = 0
(x + 6)(x + 6) = 0
x² + 6x + 6x + 36 = 0
x² + 12x + 36 = 0
k = 12
. 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]
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:
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
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
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].
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
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.
How many solutions does this linear system have? y=-1/2x+4 x+2y=-8
Answer:
no solution
Step-by-step explanation:
y=-1/2x+4
2y=-x-8, t=-1/2x-4
These are parallel so no solution
Answer:
The correct answer is no solution.
Step-by-step explanation:
y = -1/2x + 4
x + 2y = -8 → -1/2x + 4
The lines are parallel therefore, leaving us with no solution.
Hope this helped! :)
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.
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
Find a formula for the general term an of the sequence, assuming that the pattern of the first few terms continues. text({) 1/4, - 2/9, 3/16, - 4/25, ...text(})
Answer:
The general term for the given sequence is:
[tex]a_n=(-1)^{n+1}\dfrac{n}{(n+1)^2}[/tex]
Step-by-step explanation:
The given series is:
[tex]\dfrac{1}4, - \dfrac{2}9, \dfrac{3}{16}, - \dfrac{4}{25}, ......[/tex]
First of all, let us have a look at the positive and negative sign of the sequence.
2nd, 4th, 6th ..... terms have a negative sign.
For this we can use the following
[tex](-1)^{n+1}[/tex]
i.e. Whenever 'n' is odd, power of (-1) will become even resulting in a positive term for odd terms i.e. (1st, 3rd, 5th ........ terms)
Whenever 'n' is even, power of (-1) will become odd resulting in a negative term for even terms i.e. (2nd, 4th, 6th ..... terms)
Now, let us have a look at the numerator part:
1, 2, 3, 4.....
It is simply [tex]n[/tex].
Now, finally let us have a look at the denominator:
4, 9, 16, 25 ......
There are squares of the (n+1).
i.e. 1st term has a square of 2.
2nd term has a square of 3.
and so on
So, it can be represented as:
[tex](n+1)^2[/tex]
[tex]\therefore[/tex] nth term of the sequence is:
[tex]a_n=(-1)^{n+1}\dfrac{n}{(n+1)^2}[/tex]
Answer:
7
Step-by-step explanation:
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.
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
Johnny and Elizabeth were playing a video game and trying to get all of the treasure. Johnny got \dfrac{1}{3} 3 1 start fraction, 1, divided by, 3, end fraction of the treasure. Elizabeth got \dfrac{5}{9} 9 5 start fraction, 5, divided by, 9, end fraction of the treasure. Together, Johnny and Elizabeth got what fraction of the treasure?
Answer:
8/9
Step-by-step explanation:
The proportion of the treasure which Johnny got [tex]= \dfrac{1}{3}[/tex]
The proportion of the treasure which Elizabeth got [tex]=\dfrac{5}{9}[/tex]
Together, the proportion of the treasure which they got
[tex]= \dfrac{1}{3}+\dfrac{5}{9}[/tex]
Take the LCM of the denominators
LCM of 3 and 9 is 9.
Therefore:
[tex]\dfrac{1}{3}+\dfrac{5}{9} \\\\=\dfrac{3+5}{9}\\\\=\dfrac{8}{9}[/tex]
Together, Johnny and Elizabeth got 8/9 of the treasure.