The required rewritten equation in terms of variable 'r' is r = -u/s²t. By applying simple arithmetic operations, the required equation is obtained.
How to rewrite an equation in terms of another variable?Consider an equation c = ax + by. Solving for variable 'a'.
Step1: Write the required variable terms on one side
Step2: Add/Subtract like terms if any or take common if any
Step3: Divide/Multiply the coefficient of the required variable
Step4: simplify the obtained terms for the required variable
As follows:
c = ax + by
⇒ ax = by - c
⇒ ax/x = (by - c)/x
∴ a = (by - c)/x
Calculation:The given equation is u = -s²rt
dividing by 't' on both sides:
⇒ u/t = -s²rt/t
⇒ u/t = -s²r
dividing by 's²' on both sides:
⇒ u/s²t = -s²r/s²
⇒ u/s²t = -r
∴ r = -u/s²t
Thus, the required equation for variable 'r' is r = -u/s²t.
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What is the value of 8x-25 when x is equal to 12?
Answer:
71
Step-by-step explanation:
Evaluate for x=12
(8)(12)−25
(8)(12)−25
=71
Answer:
71
Step-by-step explanation:
To evaluate [tex]8x - 25[/tex] when [tex]x = 12[/tex], we have to replace x with 12 in the expression:
[tex]8x - 25[/tex]
⇒ [tex]8(12) -25[/tex]
⇒ [tex]96 - 25[/tex]
⇒ [tex]\bf 71[/tex]
Find the height (in meters) of a storage tank in the shape of a right circular cylinder that has a circumference measuring 4 m and a volume measuring 36 m3.
Answer:
[tex]h = \bf 28.3 \space\ m[/tex]
Step-by-step explanation:
• We are given:
○ Volume = 36 m³,
○ Circumference = 4 m
• Let's find the radius of the cylinder first:
[tex]\mathrm{Circumference} = 2 \pi r[/tex]
Solving for [tex]r[/tex] :
⇒ [tex]4 = 2 \pi r[/tex]
⇒ [tex]r = \frac{4}{2\pi}[/tex]
⇒ [tex]r = \bf \frac{2}{\pi}[/tex]
• Now we can calculate the height using the formula for volume of a cylinder:
[tex]\mathrm{Volume} = \boxed{\pi r^2 h}[/tex]
Solving for [tex]h[/tex] :
⇒ [tex]36 = \pi \cdot (\frac{2}{\pi}) ^2 \cdot h[/tex]
⇒ [tex]h = \frac{36 \pi^2}{4 \pi}[/tex]
⇒ [tex]h = 9 \pi[/tex]
⇒ [tex]h = \bf 28.3 \space\ m[/tex]
Answer:
9π m ≈ 28.27m
Step-by-step explanation:
The volume of a right cylinder is given by the formula
πr²h where r is the radius of the base of the cylinder(which is a circle), h is the height of the cylinder
Circumference of base of cylinder is given by the formula 2πr
Given,
2πr = 4m
r = 2/π m
Volume given as 36 m³
So πr²h = 36
π (2/π)² h = 36
π x 4/π² h = 36
(4/π) h = 36
h = 36π/4 = 9π ≈ 28.27m
Find the value of c.
answer choices
A. 26
B. 104
C. 52
D. 93.5
Answer:
option B is the answer of given question
Answer:
D. 93.5
Step-by-step explanation:
Angle Formed by Two Chords= 1/2(SUM of Intercepted Arcs)
The lower arc is twice 52
c = 1/2( 104 +83)
c = 1/2 ( 187)
c =93.5
help me solve this asap
Answer:
a) A = 3, B = 8.
b) C = 2, D = 25
Step-by-step explanation:
See the image below.
Amy and Richard each solved an equation using the quadratic formula.
Amy's Equation and Method
Latex: 4x^2+7x-20=0
4
x
2
+
7
x
−
20
=
0
Step 1: Latex: x=\frac{-7\pm \sqrt{7^2-4(1)(20)}}{2(4)}
x
=
−
7
±
√
7
2
−
4
(
1
)
(
20
)
2
(
4
)
Step 2: Latex: x=\frac{-7\pm \sqrt{49-80}}{8}
x
=
−
7
±
√
49
−
80
8
Step 3: Latex: x=\frac{-7\pm \sqrt{-31}}{8}
x
=
−
7
±
√
−
31
8
Step 4: Latex: x=\frac{-7\pm i\sqrt{31}}{8}
x
=
−
7
±
i
√
31
8
Richard's Equation and Method
Latex: x^2-6x+8=0
x
2
−
6
x
+
8
=
0
Step 1: Latex: x=\frac{6\pm \sqrt{(-6)^2-4(1)(8)}}{2(1)}
x
=
6
±
√
(
−
6
)
2
−
4
(
1
)
(
8
)
2
(
1
)
Step 2: Latex: x=\frac{6\pm \sqrt{36-32}}{2}
x
=
6
±
√
36
−
32
2
Step 3: Latex: x=\frac{6\pm \sqrt{4}}{2}
x
=
6
±
√
4
2
Step 4: Latex: x=\frac{6+\sqrt{4}}{2}
x
=
6
+
√
4
2
and Latex: x=\frac{6-\sqrt{4}}{2}
x
=
6
−
√
4
2
Step 5: Latex: x=\frac{6+2}{2}
x
=
6
+
2
2
and Latex: x=\frac{6-2i}{2}
x
=
6
−
2
i
2
Step 6: Latex: x=4
x
=
4
and Latex: x=3-i
x
=
3
−
i
Both students made a mistake.
Describe the mistake each student made.
Explain what each student needs to do to fix their mistake.
Create your own quadratic equation, and explain how to use the quadratic formula to solve it. Be specific, using Latex: a\textsf{, }b\textsf{,} and Latex: c
c
of your equation and giving the solutions to the equation you chose.
Number your responses from 1 to 3 so your instructor can tell which question you're responding to. You may not receive full credit if your teacher cannot determine that you've answered each question.
Search entries or author
The mistake each student made and what each student needs to do to fix their mistake is;
Amy didn't include the negative sign for the 20, so she should include itRichard added a negative sign underneath the radicalQuadratic equationx² - 6x + 8 = 0
x = - b ± √b² - 4ac / 2a
where,
a = 1b = -6c = 8x = - b ± √b² - 4ac / 2a
= -(-6) ± √(-6)² - 4(1)(8) / 2(1)
= 6 ± √36 - 32 / 2
= 6 ± √4 / 2
= 6 ± 2 / 2
x = 6/2 + 2/2 or 6/2 - 2/2
= 3 + 1 or 3 - 1
x = 4 or 2
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EVALUATE THE FOLLOWING:
A) 85!/82!
B) nC0
C) nPn
Answer:
Step-by-step explanation:
85!/82! = 85*84*83 = 592620
n choose 0 is always equals 1
n P n also always equals 1
Karsten is preparing his will. He wants to leave the same amount of money to his two daughters. His elder daughter is careful with money, but the younger daughter spends it carelessly, so he decides to give them the money in different ways. How much must his estate pay his younger daughter each month over 20 years, so that the accumulated present value will be equal to the $50000 cash his elder daughter will receive upon his death? Assume that the younger daughters inheritance earns 6%/a compounded monthly
The amount that Karsten's estate should pay his younger daughter each month over 20 years so that the accumulated present value will be equal to $50,000 is $358.22.
How to calculate periodic payments?The monthly payments out of the present value of $50,000 can be computed using an online finance calculator.
The periodic payment represents the equal amount that can be paid to the daughter monthly so that it equals the PV of $50,000 of the estate share.
Data and Calculations:N (# of periods) = 240
I/Y (Interest per year) = 6%
PV (Present Value) = $50,000
FV (Future Value) = $0
Results:
Monthly Payment = $358.22
Sum of all periodic payments = $85,971.73 ($358.22 x 2400
Total Interest = $35,971.73
Thus, Karsten's younger daughter can be paid $358.22 to equal the accumulated present value of $50,000.
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If k and b are constant such that lim x approach infinity (kx+b-(x^3+1)/(x^2+1)=0. Find the values of k and b
Combining the terms into one fraction, we have
[tex]kx + b - \dfrac{x^3+1}{x^2+1} = \dfrac{(k-1)x^3 + bx^2 + kx + b - 1}{x^2+1}[/tex]
If this converges to 0 as [tex]x\to\infty[/tex], then the degree of the numerator must be smaller than the degree of the denominator.
To ensure this, take [tex]k=1[/tex] and [tex]b=0[/tex]. This eliminates the cubic and quadratic terms in the numerator, and we do have
[tex]\displaystyle \lim_{x\to\infty} \frac{x - 1}{x^2 + 1} = \lim_{x\to\infty} \frac{\frac1x - \frac1{x^2}}{1 + \frac1{x^2}} = 0[/tex]
Alternatively, we can compute the quotient and remainder of the rational expression.
[tex]\dfrac{x^3+1}{x^2+1} = x - \dfrac{x-1}{x^2+1}[/tex]
Then in the limit, we have
[tex]\displaystyle \lim_{x\to\infty} \left(kx + b - x + \frac{x-1}{x^2+1}\right) = (k-1) \lim_{x\to\infty} x + b = 0[/tex]
Both terms on the left vanish if [tex]k=1[/tex] and [tex]b=0[/tex].
what the milk and and butter
Answer:
1/4 cups of milk and 1 1/3 Tbsp of butter.
Step-by-step explanation:
Milk : 3/4 multiplied by 1/3 = 3/12 = 1/4
Butter : 4 multiplied by 1/3 = 4/3 = 1 1/3
a fisherman travels 9mi downstream with the current in the same time he travels 3 mi upstream against the current. if the speed of the current is 5mph what is the speed at which the fisherman travels in still water
Answer:
10 mph
Step-by-step explanation:
speed of boat in still water = x
speed of current = 5
speed of boat with current (downstream) = x + 5
speed of boat against current (upstream) = x - 5
distance downstream = 9
distance upstream = 3
time = t
speed = distance/time
distance = speed × time
downstream:
9 = (x + 5)t
upstream:
3 = (x - 5)t
9 = xt + 5t
3 = xt - 5t
9 = xt + 5t
-3 = -xt + 5t
-----------------
6 = 10t
t = 0.6
9 = (x + 5)0.6
15 = x + 5
x = 10
How can 25 e42 n=1 be rewritten?
Answer:
The 'n = 1' below sigma represents the lower bound. meaning the number from which you start adding.
'25' above sigma is the upper bound.
In general it means adding 42 from 1 to 25 times.
so 42(25).
Answer:
C. 42(25)
Step-by-step explanation:
Took the unit test review and this was the correct option choice.
Goodluck on your unit test, I am sure that you will do good :)
A) AB and BC
B) AC and BD
tell if each pair of segments is congruent
a. Line AB and line BC are not congruent because their distance of separation are not equal
b. Line AC and line BD are not congruent because their distance of separation are not equal
How to proof the statementFrom the number line drawn, we have the following deductions;
Line AB = -5 to -2 = 3
Line BC = -2 to 0 = 2
Line AC = -5 to 0 = 5
Line AD = -5 to 5 = 10
Line BD = -2 to 5 = 7
We can see that;
a. Line AB and line BC are not congruent because their distance of separation are not equal
b. Line AC and line BD are not congruent because their distance of separation are not equal
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In 2016, the CDC estimated the mean weight of U.S. women over the age of 20 years old was 168.5 pounds with a standard deviation of 68 pounds.
1. What is the expected mean for a sample of 150 women?
2. What is the standard deviation of the mean for a sample of 150 women?
3. What is the probability of 150 women having a sample mean below 160 pounds?
4. What is the probability of 150 women having a sample mean above 175 pounds?
5. What is the probability of 200 women having a sample mean below 160 pounds? Note the change in sample size.
6. What is the probability of 200 women having a sample mean above 175 pounds?
Step-by-step explanation:
1.
the expected sample mean is always the general mean : 168.5 pounds.
2.
the SD of a sample is the general SD / sqrt(sample size).
in our case
the sample SD = 68/sqrt(150) = 5.55217675...
3.
if we are looking for only the probability that any single woman is below 160 pounds, we would use the normal z calculation :
z = (x - mean)/SD = (160 - 168.5)/68 = -8.5/68
but we have here the question about the probability of the mean value of a whole sample of 150 women.
so, we need to adapt the z-calculation by the principle of 2) for the SD of a sample :
z = (x - mean)/(SD × sqrt(sample size)) =
= (160 - 168.5)/(68 × sqrt(150)) = -8.5/(68×sqrt(150)) =
= -0.010206207 ≈ -0.01
that gives us in the z-table the p-value 0.49601
this 0.49601 is the probability that a sample of 150 women has a mean value of below 160 pounds.
4.
similar to 3.
the z value we are looking for
z = (175 - 168.5)/(68 × sqrt(150)) = 6.5/(68 × sqrt(150)) =
= 0.007804747... ≈ 0.01
that gives us the p-value 0.50399.
that would be the probability of a sample mean of 175 or below.
to get above 175 we need to get the other side of the bell-curve :
1 - 0.50399 = 0.49601
so, this case has about the same probability as 3.
5.
as 3), just with the sqrt(200) instead of the sqrt(150).
z = -8.5/(68 × sqrt(200)) = -0.008838835... ≈ 0.01
so, the probability is still about the same as in 3) :
0.49601
6.
as 4) just with sqrt(200).
z = 6.5/(68 × sqrt(200)) = 0.006759109... ≈ 0.01
so, the probability is still about the same as for 4) :
0.49601
The answers are :
1) The expected mean for a sample of 150 women is 168.5 pounds.
2) The standard deviation (SD) of the mean for a sample of 150 women is 5.55.
3) The probability of 150 women having a sample mean below 160 pounds will be 0.49601.
4) The probability of 150 women having a sample mean above 175 pounds will be 0.49601.
5) The probability of 200 women having a sample mean below 160 pounds will be 0.49601.
6) The probability of 200 women having a sample mean above 175 pounds will be 0.49601.
What is probability ?
Probability is a measure of the likelihood of event to occur. The probability of all the events in a sample space adds up to 1.
1)
We know that the expected mean of a sample is always equal to general mean.
As per the question, mean weight is 168.5 pounds.
This implies :
The expected mean for a sample of 150 women is :
= 168.5 pounds
2)
The standard deviation (SD) of the mean for a sample of 150 women is :
= 68 / (√150)
= 5.55
3)
The probability of 150 women having a sample mean below 160 pounds will be represented by z and will be :
z = ( x - mean) / ( SD × (√sample size))
= (160 - 168.5) / (68 × √150)
= 0.01
If we use the z table then the probability will be :
= 0.49601
4)
Similarly as part 3 :
z = (175 - 168.5) / (68 × √150)
z = 0.01 (approximately)
The probability of 150 women having a sample mean below 175 pounds will be :
= 0.50399
And the probability of 150 women having a sample mean above 175 pounds will be :
= 1 - 0.50399
= 0.49601
5)
Here , we have to find probability of 200 women , so 150 in formula of z in 3rd part will be replaced by 200.
i.e.,
z = (160 - 168.5) / (68 × √200)
z = 0.01 ( approximately)
and probability will be :
= 0.49601
6)
Here , we have to find probability of 200 women , so 150 in formula of z in 4th part will be replaced by 200.
z = (175 - 168.5) / (68 × √200)
z = 0.01
And probability equal to :
= 0.49601
Therefore , the answers are :
1) The expected mean for a sample of 150 women is 168.5 pounds.
2) The standard deviation (SD) of the mean for a sample of 150 women is 5.55.
3) The probability of 150 women having a sample mean below 160 pounds will be 0.49601.
4) The probability of 150 women having a sample mean above 175 pounds will be 0.49601.
5) The probability of 200 women having a sample mean below 160 pounds will be 0.49601.
6) The probability of 200 women having a sample mean above 175 pounds will be 0.49601.
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witch expression is equivalent
The equivalent expression of -14 - 6 is -14 - (+6)
What are equivalent expression?Equivalent expressions are expressions that have the same value when evaluated
How to determine the equivalent expression?The expression is given as:
-14 - 6
Put the terms of the expression in brackets
-14 - (6)
Rewrite 6 as +6
-14 - (+6)
Hence, the equivalent expression of -14 - 6 is -14 - (+6)
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Which is the best approximation of the solutions to the system of equations graphed below?
According to the direct inspection, we conclude that the best approximation of the two solutions to the system of quadratic equations are (x₁, y₁) = (- 1, 0) and (x₂, y₂) = (1, 2.5). (Correct choice: C)
What is the solution of a nonlinear system formed by two quadratic equations?
Herein we have two parabolae, that is, polynomials of the form a · x² + b · x + c, that pass through each other twice according to the image attached to this question. We need to estimate the location of the points by visual inspection on the Cartesian plane.
According to the direct inspection, we conclude that the best approximation of the two solutions, that is, the point where the two parabolae intercepts each other, to the system of two quadratic equations are (x₁, y₁) = (- 1, 0) and (x₂, y₂) = (1, 2.5). (Correct choice: C)
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Katrina has the option of an 8-year nonsubsidized student loan of $29,000 at an annual interest rate of 2.5% or an 8-year subsidized loan of $29,000 at an annual interest rate of 4.5%. Determine for which loan Katrina will pay less interest over the term of the loan if she starts making payments 2 years after obtaining the loan. (Assume Katrina makes monthly payments for each loan. Round your answers to the nearest cent, as appropriate.) The total interest paid on the nonsubsidized loan is $
Katrina would pay less amount of interest on the nonsubsidized student loan
The total interest paid on the nonsubsidized loan is $3,860.80
What is monthly compounding?
Monthly compounding means that the interest is computed and added to existing outstanding loan balance at the end of each month.
In this case, the loan would be repaid monthly but the first monthly payment would occur after 2 years of taking out the loans.
In other words, for the first 2 years, the interest would increase the balances with no corresponding reductions by a way of loan repayment, note that interest to be added monthly, as a result, we can compute outstanding balance 2 years for both loans using the future value formula of a single cash flow shown below:
FV=PV*(1+r/n)^(n*t)
FV=balance after 2 years=unknown
PV=loan amount
r=annual interest rate
n=number of times interest is compounded annually=12
t=number of years before repayments commence=2
Non-subsidized loan:
FV=$29,000*(1+2.5%/12)^(12*2)
FV=$30,485.28
Subsidized loan:
FV=$29,000*(1+4.5%/12)^(12*2)
FV=$31,725.71
Having determined the loan balances after 2 years, we can now compute the monthly payments that would be made in the remaining 6 years using the present value formula of an ordinary annuity because monthly payments would occur at the end of each month:
PV=PMT*(1-(1+r)^-N/r
PV=balance of loan after 2 years
PMT=monthly payment=unknown
r=monthly interest rate=annual interest rate/12
N=number of monthly payments in 6 years=12*6=72
Non-subsidized loan:
$30,485.28=PMT*(1-(1+2.5%/12)^-72/(2.5%/12)
PMT=$456.40
total monthly payments=$456.40*72
total monthly payments=$32,860.80
Interest= total monthly payments-loan
interest=$32,860.80-$29,000
interest=$3,860.80
Subsidized loan:
$31,725.71 =PMT*(1-(1+4.5%/12)^-72/(4.5%/12)
PMT=$503.61
total monthly payments=$503.61 *72
total monthly payments=$36,259.92
Interest= total monthly payments-loan
interest=$36,259.92 -$29,000
interest=$7,259.92
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If there are 12 donuts per box, which of the following equations will give you the number of boxes, x, that Joe needs to buy?
The equation that would give the number of boxes, x, that Joe needs to buy is 12x = 60. The correct option is c.) 12x = 60
Writing an equationFrom the question, we are to determine the equation that will give the number of boxes, x, that Joe needs to buy
From the given information,
Joe needs 60 donuts to feed his construction crew
Also,
There are 12 donuts per box
This means he needs to buy 60/12 boxes of donut
Since the number of boxes Joe needs to buy is x
∴ 60/12 = x
60 = 12x
12x = 60
Hence, the equation that would give the number of boxes, x, that Joe needs to buy is 12x = 60. The correct option is c.) 12x = 60
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Find the volume of a cylinder that has a height of 6.5 feet and a radius of 1.3 feet.
Answer:
34.51ft³
Step-by-step explanation:
The formula to find the volume of a cylinder is :
V = π r² h
Here,
r ⇒ radius ⇒ 1.3ft
h ⇒ height ⇒ 6.5ft
Let us find now.
V = π r² h
V = π × ( 1.3 )² × 6.5
V = π × 1.69 × 6.5
V = 34.51ft³
A COUPLE PLAN TO HAVE THREE CHILDREN.
A) LIST ALL THE POSSIBILITIES FOR THE SAMPLE SPACE.
B) WHAT IS THE PROBABILITY THAT THEY HAVE AT MOST TWO BOYS?
C) WHAT IS THE PROBABILITY THAT THEY HAVE AT LEAST TWO GIRLS?
D) WHAT IS THE PROBABILITY THAT THEY ARE ALL OF THE SAME SEX?
Using the sample space and probability concepts, we have that:
A) All the possibilities for the sample space are: {{G,G,G}, {G,G,B}, {G,B,G}, {G,B,B}, {B,G,G}, {B,G,B}, {B,B,G}, {B,B,B}}.
B) The probability is: 7/8.
C) The probability is: 1/2.
D) The probability is: 1/4.
What is a probability?A probability is given by the number of desired outcomes divided by the number of total outcomes.
The sample space is the set that contains all possible outcomes, hence in this problem, considering G for girl and B for boy, it is given by:
{{G,G,G}, {G,G,B}, {G,B,G}, {G,B,B}, {B,G,G}, {B,G,B}, {B,B,G}, {B,B,B}}.
For item B, 7 outcomes have at most two boys, hence the probability is 7/8.
For item C, 4 outcomes have at least two girls, hence the probability is 4/8 = 1/2.
For item D, 2 outcomes have all the babies with the same sex, hence the probability is 2/8 = 1/4.
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A poll was conducted by a home mortgage company regarding home ownership in the United States. The company polled 1,488 Americans and found that 69% of those polled own a home. What is the approximate margin of error, assuming a 99% confidence level?
If the sample size is 1488 and confidence interval of 99% then the margin of error is 0.03088.
Given sample size of 1488, percentage of those polled own a home be 69% and confidence level be 99%.
We are required to find the approximate margin of error.
Margin of error is the difference between calculated values and real values.
n=1488
p=0.69
Margin of error=z*[tex]\sqrt{p(1-p)/n}[/tex]
Z score when confidence level is 99%=2.576.
Margin of error=2.576*[tex]\sqrt{0.69(1-0.69)/1488}[/tex]
=2.576*[tex]\sqrt{(0.69*0.31)/1488}[/tex]
=2.576*[tex]\sqrt{0.2139/1488}[/tex]
=2.576*[tex]\sqrt{0.0001437}[/tex]
=2.576*0.01198
=0.03088
Hence if the sample size is 1488 and confidence interval of 99% then the margin of error is 0.03088.
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Answer:
0.031
Step-by-step explanation:
Plato/Edmentum
PLEASE HELP 100 POINTS!!!!!!
A piecewise function g(x) is defined by g of x is equal to the piecewise function of x cubed minus 9 times x for x is less than 3 and negative log base 4 of the quantity x minus 2 end quantity plus 2 for x is greater than or equal to 3
Part A: Graph the piecewise function g(x) and determine the domain. (5 points)
Part B: Determine the x-intercepts of g(x). Show all necessary calculations. (5 points)
Part C: Describe the interval(s) in which the graph of g(x) is positive. (5 points)
Answer:
A) See attached for graph.
B) (-3, 0) (0, 0) (18, 0)
C) (-3, 0) ∪ [3, 18)
Step-by-step explanation:
Piecewise functions have multiple pieces of curves/lines where each piece corresponds to its definition over an interval.
Given piecewise function:
[tex]g(x)=\begin{cases}x^3-9x \quad \quad \quad \quad \quad \textsf{if }x < 3\\-\log_4(x-2)+2 \quad \textsf{if }x\geq 3\end{cases}[/tex]
Therefore, the function has two definitions:
[tex]g(x)=x^3-9x \quad \textsf{when x is less than 3}[/tex][tex]g(x)=-\log_4(x-2)+2 \quad \textsf{when x is more than or equal to 3}[/tex]Part AWhen graphing piecewise functions:
Use an open circle where the value of x is not included in the interval.Use a closed circle where the value of x is included in the interval.Use an arrow to show that the function continues indefinitely.First piece of function
Substitute the endpoint of the interval into the corresponding function:
[tex]\implies g(3)=(3)^3-9(3)=0 \implies (3,0)[/tex]
Place an open circle at point (3, 0).
Graph the cubic curve, adding an arrow at the other endpoint to show it continues indefinitely as x → -∞.
Second piece of function
Substitute the endpoint of the interval into the corresponding function:
[tex]\implies g(3)=-\log_4(3-2)+2=2 \implies (3,2)[/tex]
Place an closed circle at point (3, 2).
Graph the curve, adding an arrow at the other endpoint to show it continues indefinitely as x → ∞.
See attached for graph.
Part BThe x-intercepts are where the curve crosses the x-axis, so when y = 0.
Set the first piece of the function to zero and solve for x:
[tex]\begin{aligned}g(x) & = 0\\\implies x^3-9x & = 0\\x(x^2-9) & = 0\\\\\implies x^2-9 & = 0 \quad \quad \quad \implies x=0\\x^2 & = 9\\\ x & = \pm 3\end{aligned}[/tex]
Therefore, as x < 3, the x-intercepts are (-3, 0) and (0, 0) for the first piece.
Set the second piece to zero and solve for x:
[tex]\begin{aligned}\implies g(x) & =0\\-\log_4(x-2)+2 & =0\\\log_4(x-2) & =2\end{aligned}[/tex]
[tex]\textsf{Apply log law}: \quad \log_ab=c \iff a^c=b[/tex]
[tex]\begin{aligned}\implies 4^2&=x-2\\x & = 16+2\\x & = 18 \end{aligned}[/tex]
Therefore, the x-intercept for the second piece is (18, 0).
So the x-intercepts for the piecewise function are (-3, 0), (0, 0) and (18, 0).
Part CFrom the graph from part A, and the calculated x-intercepts from part B, the function g(x) is positive between the intervals -3 < x < 0 and 3 ≤ x < 18.
Interval notation: (-3, 0) ∪ [3, 18)
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what is the measure of angle B from the right triangle below ?
Answer:
d
Step-by-step explanation:
using the cosine ratio in the right triangle
cos B = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{BC}{AB}[/tex] = [tex]\frac{2}{10}[/tex] , then
B = [tex]cos^{-1}[/tex] ( [tex]\frac{2}{10}[/tex] ) ≈ 78.46° ( to 2 dec. places )
louizah baked 8 dozen muffins and sold them all at the school for R5,50. if louizah bought the ingredients for R12,50. Determine louizahs profit
Answer:
3550
Step-by-step explanation:
C.P=Rs 1250
S.P=8(12)(50)
Rs4800
P=S.P-C. P
=Rs4800-Rs1250
= Rs3550
To win at LOTTO in one state, one must correctly select 7 numbers from a collection of 61 numbers (1 through 61). The order in which the selection is made does not matter. How many different selections are possible?
Using the combination formula, it is found that 436,270,780 different selections are possible.
What is the combination formula?[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by:
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
In this problem, 7 numbers are taken from a set of 61, hence the number of different selections is given by:
C(61,7) = 61!/(7! x 54!) = 436,270,780
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f(x)=ax+b/2 then f^-1 (x-1) =2x-5/2 find a and b
From the given inverse function, we have
[tex]f^{-1}(x-1) = 2x - \dfrac52 \\\\ \implies f^{-1}(x) = f^{-1}((x+1)-1) = 2(x+1) - \dfrac52 = 2x-\dfrac12[/tex]
By definition of inverse function,
[tex]f\left(f^{-1}(x)\right) = x[/tex]
so that
[tex]f\left(2x-\dfrac12\right) = x[/tex]
[tex]a\left(2x-\dfrac12\right) + \dfrac b2 = x[/tex]
[tex]2ax - \dfrac a2 + \dfrac b2 = x[/tex]
[tex]\implies\begin{cases}2a=1 \\\\ -\dfrac a2+\dfrac b2 = 0\end{cases}[/tex]
[tex]\implies \boxed{a=\dfrac12}[/tex]
[tex]\implies \dfrac b2 = \dfrac a2 \implies \boxed{b=\dfrac12}[/tex]
the five-number summary calculated in part C to create a box plot representing the data. Draw a box plot representing the following data. Be sure to mark the outlier. 10 13 15 12 12 4 12 17 12 13 15 18 10 11 20 19 Lines Shapes Fill: Line: Width: 2 pt
The five-number summary is:
Minimum: 4
Quartile Q1: 11.25
Median: 12.5
Quartile Q3: 16.5
Maximum: 20
The box plot is attached below.
What is the Five-number Summary?The five-number summary of a data that is displayed on a box plot include: minimum and maximum values, lower and upper quartiles, and the median.
Given the data, 10, 13, 15, 12, 12, 4, 12, 17, 12, 13, 15, 18, 10, 11, 20, 19, the five-number summary is:
Minimum: 4
Quartile Q1: 11.25
Median: 12.5
Quartile Q3: 16.5
Maximum: 20
There are no outliers. Thus, the box plot that represents the five-number summary is shown in the image attached below.
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Answer: it is correct i got it from edmentum
Step-by-step explanation:
Dante is a software salesman. Let represent his total pay (in dollars). Let represent the number of copies of History is Fun he sells. Suppose that and are related by the equation 2400+120x=y
Considering the given linear function, we have that:
The change for each copy that he sells is of $120.If he sells no copies, he makes $2400.What is a linear function?A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.His payment for x copies bought is:
y = 120x + 2400.
Hence:
The change for each copy that he sells is of $120, as the slope is of $120.If he sells no copies, he makes $2400, which is the y-intercept.More can be learned about linear functions at https://brainly.com/question/24808124
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Please help I need to turn this in by Monday!
Answer: Rational, Irrational, Rational, Natural, Natural, Integer
Step-by-step explanation:
-4.2 is a rational number as it can be converted into a fraction
3√5 is an irrational number as it can't be converted into a fraction
5/3 is a rational number as it is a fraction
9 is a natural number as it is a positive whole number
√16 is a natural number as despite the square root, √16 is 4 which is a natural number
-8/2 is an integer as -8/2 is -4 which is a negative whole number
Please help
Use the parabola tool to graph the quadratic function f(x)=−2(x+4)^2−3
Graph the parabola by first plotting its vertex and then plotting a second point on the parabola.
Due to length restrictions, we kindly invite to read the explanation of this question and the image of parabola on Cartesian plane attached below to see the results.
How to graph a quadratic function
To graph a parabola, we shall follow the following procedure:
Mark the vertex of the parabola on the Cartesian plane.Mark at least two pairs of values on the Cartesian plane, one on the right of the vertex and other on the left of the vertex.Match the points to create the resulting curves.By following all the steps, we generate the curve with the help of a graphing tool.
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What is the solution to the system of equations?
y = 2/3 x + 3
X= -2
The solution to the given system of equations is x = -2, y = 5/3. That is (-2, 5/3)
Solving system of equationsFrom the question, we are to determine the solution to the given system of equations
The given system of equation is
y = 2/3 x + 3 ----------- (1)
x= -2 ----------- (2)
The value of x has been given in the second equation of the system of equations.
Now, we will determine the value of y
From the second equation, we have that
x = -2
Substitute the value of x into the first equation,
y = 2/3 x + 3
y = 2/3 (-2) + 3
y = -4/3 + 3
y = 5/3
Hence, the solution to the given system of equations is x = -2, y = 5/3. That is (-2, 5/3)
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