Answer:
Step-by-step explanation:
Before we differentiate, let us assign a variable to the function. Let y be equal to the function i.e let y = 3√x -2/x²
In differentiation if [tex]y = ax^{n}[/tex], then [tex]\frac{dy}{dx} = nax^{n-1}[/tex] where n is a constant and dy/dx means we are differentiating the function y with respect to x.
Applying the formula o the question given;
[tex]y= 3\sqrt{x} -2/x^2\\y = 3{x}^\frac{1}{2} - 2x^{-2} \\\\[/tex]
On differentiating the resulting function;
[tex]\frac{dy}{dx} = \frac{1}{2}*3x^{\frac{1}{2}-1 } - (-2)x^{-2-1} \\\\\frac{dy}{dx} = \frac{1}{2}*3x^{-\frac{1}{2}} + 2x^{-3}\\ \\\frac{dy}{dx} = \frac{1}{2}*{\frac{3}{x^{\frac{1}{2} } }} + \frac{2}{x^{3} } \\\\\frac{dy}{dx} = {\frac{3}{2x^{\frac{1}{2} } }} + \frac{2}{x^{3} }\\\\\frac{dy}{dx} = {\frac{3}{2\sqrt{x} }} + \frac{2}{x^{3} }[/tex]
To combine the terms, we will add up by finding their LCM.
[tex]\frac{dy}{dx} = {\frac{3}{2\sqrt{x} }} + \frac{2}{x^{3} }\\\frac{dy}{dx} = \frac{3x^3+4\sqrt{x} }{2x^{3} \sqrt{x}}[/tex]
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 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]
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:
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Christopher collected data from a random sample of 800 voters in his state asking whether or not they would vote to reelect the current governor. Based on the results, he reports that 54% of the voters in his city would vote to reelect the current governor. Why is this statistic misleading?
Answer:
The statistic is misleading because Christopher collects his sample from a population (voters in his state) and make inferences about another population (voters in his city).
Step-by-step explanation:
The statistic is misleading because Christopher collects his sample from a population (voters in his state) and make inferences about another population (voters in his city).
He should make inferences about the population that is well represented by his sample (voters in his state), or take a sample only from voters from his city to make inferences about them.
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
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
can someone help me with this please???
Answer:
Lateral surface area would be (13*4)*2 + (4*4)*2 = (52*2) + (16*2) = 104 + 32 = 136 units^2.
Surface area would be 136 + 104 = 240 units^2.
Step-by-step explanation:
I hope this helps you!
The perimeter of the shape is 28 cm.Find the value of radius.
Answer:
The value of the radius is 4.46cm.
Step-by-step explanation:
Given the perimeter is 28 cm. So, if we want to find the radius then we should consider this perimeter as the circumference of the circle. Thus, we have to equate this value with the circumference (perimeter of the circle).
The perimeter of the circle or circumference = 2π r
Here, π = 22/7
r = radius
Now, 2π r = 28
r = 28 / 2π
r = 4.46 cm
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
Working together, Edith and Rupert can pick 3 quarts of blueberries in an
hour. How many quarts can they pick in 7 hours?
Answer:
21
Step-by-step explanation:
Multiply 3 quarts to 7 hours
Which is 21
Mark me as brainliest
Step-by-step explanation:
Edith picks 3
Rupert picks 3
3 + 3 = 6 quarts of blueberries in 1 hour
6 blueberries = 1 hour
x. =. 7 hours
x = 7 hours ÷ 1 hour × 6 blueberries
x =. 42 quarts of blueberries
3. A 12 % discount on a pair of washer and dryer that Gayle purchased, amounted to $156.00.
Calculate the net price.
Answer:
For this case we know that the price after the 12% of discount is 156 and we want to findd the net price so then we can use the following proportional rule:
[tex] \frac{x}{100} = \frac{156}{100-12}[/tex]
Where x represent the net price. And if we solve for the value of x we got:
[tex] x= 100 *\frac{156}{88}= 177.273[/tex]
So then the net price for this case would be $ 177.273
Step-by-step explanation:
For this case we know that the price after the 12% of discount is 156 and we want to findd the net price so then we can use the following proportional rule:
[tex] \frac{x}{100} = \frac{156}{100-12}[/tex]
Where x represent the net price. And if we solve for the value of x we got:
[tex] x= 100 *\frac{156}{88}= 177.273[/tex]
So then the net price for this case would be $ 177.273
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 ;) ❤❤❤
A simple random sample of 20 items resulted in a sample mean of 10. The population standard deviation is = 3. Round your answers to two decimal places.
a. What is the standard error of the mean, ?
b. At 95% confidence, what is the margin of error?
Answer:
a. 0.67
b. 1.31
Step-by-step explanation:
We have the following information n = 20, mean (m) = 10 and standard deviation (sd) = 3
a.
SE (m) = sd / n ^ (1/2)
replacing we have:
SE (m) = 3/20 ^ (1/2) = 0.67
Therefore the standard error of the mean is 0.67
b.
the critical value is obtained as shown below:
the level of sifnificance is alfa = 1 - 0.95 = 0.05
the critical value with level of significance alfa / 2 = 0.05 / 2 = 0.025
and to this value corresponds z = 1.96 (z table)
The margin of error with 95 confidence is calculated as follows:
E = z * SE
E = 1.96 * 0.67
E = 1.31
Therefore the margin of error is 1.31
(a) The standard error will be "0.67".
(b) The margin of error will be "1.31".
According to the question,
Standard deviation,
sd = 3Sample size,
n = 20(a)
As we know,
→ The Standard error,
= [tex]\frac{sd}{\sqrt{n} }[/tex]
= [tex]\frac{3}{\sqrt{20} }[/tex]
= [tex]0.67[/tex]
(b)
As we know,
→ The margin of error,
= [tex]Z_{a/2}\times \frac{sd}{\sqrt{n} }[/tex]
By substituting the values, we get
= [tex]Z_{a/2}\times \frac{3}{\sqrt{20} }[/tex]
= [tex]1.96\times 0.67[/tex]
= [tex]1.31[/tex]
Thus the above response is right.
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Past studies have indicated that the percentage of smokers is estimated to be about 35%. Given the new smoking cessation programs that have been implemented, you now believe that the percentage of smokers has reduced. a) If you going to test this claim at the 0.05 significance level, what would be your null and alternative hypotheses
Answer:
H0: p = 3.5
H1: p < 3.5
Step-by-step explanation:
We are told that past studies have indicated that the percentage of smokers is estimated to be about 35%, but with the new smoking cessation programs that have been implemented, it is believed that the percentage of smokers has been reduced, we must propose our null and alternative hypotheses, which would be the following:
Null hypothesis: H0: p = 3.5
Alternative hypothesis: H1: p < 3.5
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! :)
Find the slope-intercept form of the line through (6, – 3) and perpendicular to the line y = 3x – 5.
Answer:
y=-1/3x-1
Step-by-step explanation:
We have the information y=3x-5, the lines are perpendicular, and the new line passes through (6,-3). The slopes of perpendicular lines are negative reciprocals so you need to find the negative reciprocal of 3, so flip it to 1/3 and multiply by -1, we get the slope of the new line as -1/3. So far we have the equation y=-1/3x+b. We are given a point on the line, (6,-3), so we can plug these into the equation as x and y to solve for the y-intercept, b. You set it up as -3=-1/3(6)+b. First you multiply to get -3=-2+b, then you add 2 to both sides to isolate the variable and you get b=-1. Then you can use b to complete your equation with y=-1/3x-1.
. 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 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:
purse contains four $1 bills, five $10 bills and two $5 bills. The odds of pulling out a $1 bill on the first draw are
-1/11
-4/11
-11/4
-5/11
Hey there! :)
Answer:
4 /11.
Step-by-step explanation:
Given:
4 $1 bills
5 $10 bills
2 $5 bills
Add up the number of bills to find the total:
4 + 5 + 2 = 11 total bills.
The probability of pulling a 1 dollar bill would be expressed as:
# of $1 bills / total
Therefore:
4 / 11 would represent this situation.
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.
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
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.
1
Select the correct answer.
Which inequality's graph will have a solid boundary line?
OA.
2x + 3y> 7
OB.
X+ y<5
O c.
3x + 2y< 1
OD. x- y< 5
Answer:
None of the above
Step-by-step explanation:
An inequality will only have a solid boundary line when it has ≤ or ≥. Since all of our answer choices have < or >, we will only have a dotted boundary line.
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.
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.
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:
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
Each of the conditions below create different numbers of triangles. Match the conditions based on the number of triangles the conditions create. Assume inches are the only units used. PLEASE HELP!!
Answer:
1 -- C2 -- A3 -- B4 -- EStep-by-step explanation:
A: 2 given sides and the given angle between them will produce 1 triangle.
B: The sum of angle is 190°. 0 triangles are possible.
C: An infinite number of triangles can have the given base and height.
D: The remaining side must be from the set {3, 4, 5}. 3 triangles are possible.
E: Leg lengths can be from the set {(2, 2), (2, 4), (2, 6), (2, 8), (4, 4)}. 5 triangles are possible.
__
1: An infinite number of triangles can have those angle measures.
2: The remaining side must have length 2. 1 triangle is possible.
3: The perimeter constrains the remaining side length to a value too short to form a triangle. 0 triangles are possible.
4: The remaining side length must be from the set {1, 2, 3, 4, 5}. 5 triangles are possible.
__
So, the matchups are ...
1 -- C (an infinite number)
2 -- A (1 triangle)
3 -- B (0 triangles)
4 -- E (5 triangles)
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.