Answer:
0.3333
Step-by-step explanation:
Given the following :
Sample mean(m) = 4.001 inch
Standard deviation(sd) = 0.002 inch
Key specification : = 4 ± .003 inches
Upper specification LIMIT ( USL) : (4 + 0.003) = 4.003 inches
Lower specification limit (LSL) : (4 - 0.003) = 3.997 inches
Cpk is found using the relation:
min[(USL - mean) / (3 * sd), (mean-LSL) / (3*sd)]
min[(4.003 - 4.001)/(3*0.002), (4.001 - 3.997)/(3*0.002)]
min[(0.002 / 0.006), (0.004 / 0.006)]
min[(0.33333, 0.66667)
Therefore Cpk = 0.3333
Because 0.33333<0.66667
Which of the following is a solution for 5 - 2x ≤ -3?
Answer:
x≥4
Step-by-step explanation:
The required solution for the inequality 5 - 2x ≤ -3 is x ≥ 4 or x ∈ [4, ∞).
What is inequality?Inequality shows relation between two expression which are not equal to each others.
The given inequality is,
5 - 2x ≤ -3.
Solve the inequality,
Add 3 to both the sides,
5 - 2x + 3 ≤ -3 + 3
8 - 2x ≤ 0
-2x ≤ -8
Multiply -1 both the sides,
2x ≥ 8
x ≥ 4
The solution for the inequality is x ≥ 4 or x ∈ [4, ∞).
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i will rate you brainliest
Answer:
D) 3/2(X-4)
Step-by-step explanation:
Invert and multiply to get:
3(x+4)/2(x²-16)
factor the bottom
3(x+4)/2(x+4)(x-4)
The (x+4)’s cancel out, and you’re left with
3/2(X-4)
[tex]\dfrac{{x+4\over2}}{{x^2-16\over3}}[/tex]
[tex]=\dfrac{3(x+4)}{2(x+4)(x-4)}=\frac{3}{2(x-4)} [/tex]
but in original fraction, denominator can't be zero so we have to exclude x=±4
do that answer is D
BOND VALUATION Asiana Fashion's bonds have 10 years remaining to maturity. Interest is paid annually; they have a $1,000 par value; the coupon interest rate is 8% and thebyield to maturity is 9%.What is the bond's current market price?
Answer:
$935.76
Step-by-step explanation:
BOND VALUATION Asiana Fashion's bonds have 10 years remaining to maturity. Interest is paid annually; they have a $1,000 par value; the coupon interest rate is 8% and thebyield to maturity is 9%.What is the bond's current market price?
Step 1
We find the Present value factor of sum
The formula =
(1 + i)^n
Where
i = maturity rate = 9% = 0.09
n = number of years = 10 years
Present Value = ( 1 + 0.09)^-10
= 0.4224
Step 2
We find the present value factor of annuity
The formula is given as:
1 - (1+i)^-n / i
i = maturity rate = 9% = 0.09
n = number of years = 10 years
= 1 - (1 + 0.09)^-10 /0.09
= 1 - 0.4224 /0.09
= 0.5775 /0.09
= 6.417
Step 3
The bond's current market price is calculated as:
= PV factor of Sum × Par Value + PV factor of annuity × coupon payment
Coupon payment is calculated as:
= Coupon interest × par value
= 8% × 1000
= 80
Hence,
= 0.4224 × 1,000 + 6.417 × 80
= 422.4 + 513.36
= 935.76
In this exercise we have to use the knowledge of finance to calculate the corrective value of the market place, in this way we find that:
[tex]\$935.76[/tex]
We find the Present value factor of sum, by the formula of:
[tex](1 + i)^n[/tex]
Where:
i = maturity rate = 9% = 0.09 n = number of years = 10 years
Substituting the values in the formula as;
[tex]Present \ Value = ( 1 + 0.09)^{-10} = 0.4224[/tex]
We find the present value factor of annuity, by the formula as:
[tex]1 - (1+i)^{-n} / i[/tex]
Where:
i = maturity rate = 9% = 0.09 n = number of years = 10 years
Substituting the values in the formula as;
[tex]= 1 - (1 + 0.09)^{-10} /0.09\\= 1 - 0.4224 /0.09\\= 0.5775 /0.09\\= 6.417[/tex]
The bond's current market price is calculated as:
[tex]= PV \ factor\ of\ Sum * Par\ Value + PV\ factor\ of\ annuity * coupon\ payment[/tex]
Coupon payment is calculated as:
[tex]= Coupon\ interest * par\ value\\= 8\% * 1000= 80[/tex]
So continue the calcule;
[tex]= 0.4224 *1,000 + 6.417 * 80\\= 422.4 + 513.36\\= 935.76[/tex]
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Marking as brainyest PLEASE HELP
How does f(x) = 9x change over the interval from x = 3 to x = 4? A) f(x) increases by 100% B) f(x) increases by 800% C) f(x) increases by 900% D) f(x) increases by 1000%
Answer:
C) f(x) increases by 900%
Step-by-step explanation:
The rate of change is
f(4) - f(3)
---------------
4-3
f(4) = 9*4 = 36
f(3) = 9*3 = 27
36 -27
---------------
4-3
9
-----
1
The rate of change is 9
To change to a percent, multiply by 100%
9*100% = 900%
Answer:
Increases by 900%
Step-by-step explanation:
● f(x) = 9x
The rate of change is:
● r = (36-27)/(4-3) = 9
So the function increses nine times wich is equivalent to 900%
The function g is defined as follows for the domain given.
g(x) = 2x+1,
domain = (-5, -1, 2, 3)
Write the range of g using set notation. Then graph g
Answer:
g(x): 2(-5)+1= -10+1=-9
2(-1)+1= -2+1=-1
2(2)+1= 4+1=5
2(3)+1=6+1= 7
Hence, the range of [tex]g[/tex] using the set notation is [tex](-9,-1,5,7)[/tex].
What is the function?
Functions are often defined by a formula that describes a combination of arithmetic operations and previously defined functions; such a formula allows computing the value of the function from the value of any element of the domain.
Here given that,
The function g is defined as follows for the domain given.
[tex]g(x) = 2x+1,[/tex] and domain [tex]= (-5, -1, 2, 3)[/tex]
So,
[tex]x=-5\\2(-5)+1\\= -10+1\\=-9\\\\x=-1\\2(-1)+1\\= -2+1\\=-1\\\\x=2\\2(2)+1\\= 4+1\\=5\\\\x=3\\2(3)+1\\=6+1\\= 7[/tex]
Hence, the range of [tex]g[/tex] using the set notation is [tex](-9,-1,5,7)[/tex].
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What are two solutions of x
Answer:
Answer is attached below :)
The arc length apothem shown below is 15 feet. Part 1) State the equation that relates arc length to central angle. Part 2) Find the angle apothem in radians. Part 3) Convert your answer from Part 2 to degrees and write it to the nearest hundredth of a degree
Answer:
ans right down there
Step-by-step explanation:
Here,Part 1
if the circle has a radius r so,
15 = r theta
here, theta is in radian.
Part 2
[tex]theta = \frac{15}{6} = 2.5[/tex]
part 3
[tex]theta = \frac{2.5 \times 180}{\pi} [/tex]
or theta =
143.2394487827058021919953870352629258310136811664108038729006
Let A and B be events. The symmetric difference A?B is defined to be the set of all elements that are in A or B but not both.
In logic and engineering, this event is also called the XOR (exclusive or) of A and B.
Show that P(AUB) = P(A) + P(B)-2P(AnB), directly using the axioms of probability.
Correction:
P(AΔB) = P(A) + P(B) - 2P(AnB)
is what could be proven using the axioms of probability, and considering the case of symmetric difference given.
Answer:
P(AΔB) = P(A) + P(B) - 2P(AnB)
Has been shown.
Step-by-step explanation:
We are required to show that
P(AUB) = P(A) + P(B) - 2P(AnB)
directly using the axioms of probability.
Note the following:
AUB = (AΔB) U (AnB)
Because (AΔB) U (AnB) is disjoint, we have:
P(AUB) = P(AΔB) + P(AnB)..................(1)
But again,
P(AUB) = P(A) + P(B) - P(AnB)...............(2)
Comparing (1) with (2), we have
P(AΔB) + P(AnB) = P(A) + P(B) - P(AnB)
P(AΔB) = P(A) + P(B) - 2P(AnB)
Where AΔB is the symmetric difference of A and B.
find the slope of the line y = 4
Answer:
Brainleist!
Step-by-step explanation:
0
there is no y=mX+b
there is no x no XXXX
that means the slope must be 0 (bc theres a y)
Sorry if my explanation is bad... let me know in comments if u need more help
Use the given data to find the minimum sample size required to estimate the population proportion. Margin of error: 0.028; confidence level: 99%; p and q unknown
Answer:
The minimum sample size is [tex]n = 2123[/tex]
Step-by-step explanation:
From the question we are told that
The margin of error is [tex]E = 0.028[/tex]
Given that the confidence level is 99% then the level of significance is evaluated as
[tex]\alpha = 100 - 99[/tex]
[tex]\alpha = 1 \%[/tex]
[tex]\alpha =0.01[/tex]
Next we obtain the critical value of [tex]\frac{ \alpha }{2}[/tex] from the normal distribution table
The value is [tex]Z_{\frac{ \alpha }{2} } = 2.58[/tex]
Now let assume that the sample proportion is [tex]\r p = 0.5[/tex]
hence [tex]\r q = 1 - \r p[/tex]
=> [tex]\r q = 0.50[/tex]
Generally the sample size is mathematically represented as
[tex]n =[ \frac{Z_{\frac{ \alpha }{2} }}{ E} ]^2 * \r p * \r q[/tex]
[tex]n =[ \frac{2.58}{ 0.028} ]^2 * 0.5 * 0.5[/tex]
[tex]n = 2123[/tex]
Choose the situation that represents a function.
A) The number of raisins in an oatmeal raisin cookie is a function of the diameter of the cookie.
B) The inches of rainfall is a function of the day’s average temperature.
C) The time it takes to cook a turkey is a function of the turkey’s weight.
D) The number of sit-ups a student can do in a minute is a function of the student’s age.
Answer:c
Step-by-step explanation:
Answer: The answer is C.
Hope this helps you!
What is the domain of h?
Answer:
{-2, -1, 1, 5, 6}
Step-by-step explanation:
The domain includes the five x-values (inputs): {-2, -1, 1, 5, 6}
Answer:
The x-values -2, -1,1,5 and 6
Step-by-step explanation:
In the last 10 years, the population of Indonesia has grown at a rate of 1.12% per year to 258,316,051. If this rate continues, what will be the population in 10 more years? Round your answer to the nearest whole number.
Answer:
Final population after 10 years
= 288911718
Step-by-step explanation:
Present population p = 258,316,051
Rate of growth R%= 1.12%
Number of years t= 10 years
Number of times calculated n = 10
Final population A
= P(1+r/n)^(nt)
A= 258,316,051(1+0.0112/10)^(10*10)
A= 258,316,051(1+0.00112)^(100)
A= 258,316,051(1.00112)^100
A= 258,316,051(1.118442762)
A= 288911717.6
Approximately A= 288911718
Final population after 10 years
= 288911718
A sample of a radioactive substance decayed 11% over the course of 3 weeks. How many grams were in the sample originally if 30.26 grams of the substance were remaining after the 3 weeks?
Answer:
34 grams
Step-by-step explanation:
If the remaining sample has 30.26 grams of radioactive substance, and 11% of it decayed, that means that 30.26 grams is 89% of the original. Let the original be x.
30.26=0.89x
Multiply both by one hundred
3026=89x
Divide both by 89
34=x
x=original, so the original was 34 grams.
3a-27=0
How to solve
Answer:
a = 9
Step-by-step explanation:
3a - 27 = 0
3a = 27
a = 27/3
a = 9
3*9 - 27 = 0
27 - 27 = 0
Answer:
a = 9
Step-by-step explanation:
3a-27=0
Add 27 to each side
3a = 27
Divide by 3
3a/3 = 27/3
a = 9
A patio 20 feet wide has a slanted roof, as shown in the figure. Find the length of the roof if there is an 8-inch overhang. Show all work and round the answer to the nearest foot. Be sure to label your answer appropriately. Then write a sentence explaining your answer in the context of the problem.
Answer:
[tex]Slanted\ Roof = 20.77\ ft[/tex]
Step-by-step explanation:
The question has missing attachment (See attachment 1 for complete figure)
Given
Width, W = 20ft
Let the taller height be represented with H and the shorter height with h
H = 10ft
h = 8ft
Overhang = 8 inch
Required
Determine the length of the slanted roof
FIrst, we have to determine the distance between the tip of the roof and the shorter height;
Represent this with
This is calculated by
[tex]D = H - h[/tex]
Substitute 10 for H and 8 for h
[tex]D = 10 - 8[/tex]
[tex]D = 2ft[/tex]
Next, is to calculate the length of the slant height before the overhang;
See Attachment 2
Distance L can be calculated using Pythagoras theorem
[tex]L^2 = 2^2 + 20^2[/tex]
[tex]L^2 = 4 + 400[/tex]
[tex]L^2 = 404[/tex]
Take Square root of both sides
[tex]\sqrt{L^2} = \sqrt{404}[/tex]
[tex]L = \sqrt{404}[/tex]
[tex]L = 20.0997512422[/tex]
[tex]L = 20.10\ ft[/tex] -------Approximated
The full length of the slanted roof is the sum of L (calculated above) and the overhang
[tex]Slanted\ Roof = L + 8\ inch[/tex]
Substitute 20.10 ft for L
[tex]Slanted\ Roof = 20.10\ ft + 8\ inch[/tex]
Convert inch to feet to get the slanted roof in feet
[tex]Slanted\ Roof = 20.1\ ft + 8/12\ ft[/tex]
[tex]Slanted\ Roof = 20.10\ ft + 0.67\ ft[/tex]
[tex]Slanted\ Roof = 20.77\ ft[/tex]
Hence, the total length of the slanted roof in feet is approximately 20.77 feet
Find the probability.
Two dice are rolled. Find the probability that the score on the dice is either 5 or
10.
Answer:
7/36
Step-by-step explanation:
1 die has 6 faces
When two dice are rolled, the total number of outcomes
= 6 × 6 = 36
The Probability of having(5) =
(1 & 4), (2 & 3) , ( 3 & 2), (4 & 1)
= 4
The probability of having (10) =
(5 & 5), (4 & 6) , ( 6 & 4)
= 3
The probability that the score on the dice is either 5 or 10.
P(5) + P(10)
= 4/36 + 3/36
= 7/36
Answer: 7/36
Step-by-step explanation:
36 outcomes
4 chances of getting 5 (1+4, 2+3, 4+1, 3+2)
3 chances of getting 10 (4+6, 5+5, 6+4)
4+3=7
so 7/36 chance
name all the pairs of angles which are vertical angles , alternate interior angles , alternate exterior angles , co interior angles , co exterior angles , and corresponding angles from the given figure . (co interior - interior angles on the same side of transversal)
Answer:
Step-by-step explanation:
Since m and k are the parallel lines and a transverse 'l' is intersecting these lines at two different points.
- Opposite angles at the point of intersection of parallel lines and the transverse will be the vertical angles.
∠1 ≅ ∠3, ∠2 ≅ ∠4, ∠5 ≅ ∠8 and ∠6 ≅ ∠7 [Vertical angles]
- Pair of angles between parallel lines 'k' and 'm' but on the opposite side of the transversal are the alternate interior angles.
∠4 ≅ ∠6 and ∠3 ≅ ∠5 [Alternate interior angles]
- Angles having the same relative positions at the point of intersection are the corresponding angles.
∠2 ≅ ∠6, ∠3 ≅ ∠8, ∠4 ≅ ∠7 and ∠1 ≅ ∠5 [Corresponding angles]
- Co interior angles are the angles between the parallel lines located on the same side of the transversal.
∠4 and ∠5, ∠3 and ∠6 [Co interior angles]
- Co exterior angles are the angles on the same side of the transverse but outside the parallel lines.
∠2 and ∠8, ∠1 and ∠7 [Co exterior angles]
Determine the number of degrees of freedom for the two-sample t test or CI in each of the following situations. (Round your answers down to the nearest whole number.)
(a) m = 12, n = 15, s1 = 4.0, s2 = 6.0
(b) m = 12, n = 21, s1 = 4.0, s2 = 6.0
(c) m = 12, n = 21, s1 = 3.0, s2 = 6.0
(d) m = 10, n = 24, s1 = 4.0, s2 = 6.0
Answer:
a
[tex]df = 24.32[/tex]
b
[tex]df = 30.10[/tex]
c
[tex]df = 30.7[/tex]
d
[tex]df = 25.5[/tex]
Step-by-step explanation:
Generally degree of freedom is mathematically represented as
[tex]df = \frac{ [\frac{ s^2_i }{m} + \frac{ s^2_j }{n} ]^2 }{ \frac{ [ \frac{s^2_i}{m} ]^2 }{m-1 } +\frac{ [ \frac{s^2_j}{n} ]^2 }{n-1 } }[/tex]
Considering a
a) m = 12, n = 15, s1 = 4.0, s2 = 6.0
[tex]df = \frac{ [\frac{ 4^2 }{12} + \frac{ 6^2 }{15} ]^2 }{ \frac{ [ \frac{4^2}{12} ]^2 }{12-1 } +\frac{ [ \frac{6^2}{15} ]^2 }{15-1 } }[/tex]
[tex]df = 24.32[/tex]
Considering b
(b) m = 12, n = 21, s1 = 4.0, s2 = 6.0
[tex]df = \frac{ [\frac{ 4^2 }{12} + \frac{ 6^2 }{21} ]^2 }{ \frac{ [ \frac{4^4}{12} ]^2 }{12-1 } +\frac{ [ \frac{6^2}{21} ]^2 }{21-1 } }[/tex]
[tex]df = 30.10[/tex]
Considering c
(c) m = 12, n = 21, s1 = 3.0, s2 = 6.0
[tex]df = \frac{ [\frac{ 3^2 }{12} + \frac{ 6^2 }{21} ]^2 }{ \frac{ [ \frac{3^4}{12} ]^2 }{12-1 } +\frac{ [ \frac{6^2}{21} ]^2 }{21-1 } }[/tex]
[tex]df = 30.7[/tex]
Considering c
(d) m = 10, n = 24, s1 = 4.0, s2 = 6.0
[tex]df = \frac{ [\frac{ 4^2 }{10} + \frac{ 6^2 }{24} ]^2 }{ \frac{ [ \frac{4^2}{10} ]^2 }{10-1 } +\frac{ [ \frac{6^2}{24} ]^2 }{24-1 } }[/tex]
[tex]df = 25.5[/tex]
In terms of the trigonometric ratios for ΔABD, what is the length of line segment BD?
In terms of the trigonometric ratios for ΔABD, what is the length of line segment BD?
Answer:
[tex] BD = c*sin(A) [/tex]
[tex] BD = c*cos(B) [/tex]
[tex] BD = b*tan(A) [/tex]
Step-by-step explanation:
∆ABD is a right triangle.
Recall: trigonometric ratios of any right triangle can easily be understood or remembered with the acronym, SOHCAHTOA.
SOH => sin(θ) = opposite/hypotenuse
CAH => Cos(θ) = adjacent/hypotenuse
TOA = tan(θ) = opposite/adjacent
Thus, the length of segment BD, in terms of trigonometric ratios for ∆ABD can be done as follows:
Let BD = x
AB = c
AD = b
=>The sine ratio for the length of line segment BD = x, using SOH.
θ = A
Opposite = DB = x
hypotenuse = AB = c
[tex] sin(A) = \frac{x}{c} [/tex]
Make x the subject of formula.
[tex] c*sin(A) = x [/tex]
[tex] BD = x = c*sin(A) [/tex]
=>The Cosine ratio for the length of line segment BD = x, using CAH
θ = B
Adjacent = DB = x
hypotenuse = AB = c
[tex] cos(B) = \frac{x}{c} [/tex]
Make x the subject of formula.
[tex] c*cos(B) = x [/tex]
[tex] BD = x = c*cos(B) [/tex]
=>The Tangent ratio for the length of line segment BD = x, using TOA
θ = A
Adjacent = DB = x
hypotenuse = AD = b
[tex] tan(A) = \frac{x}{b} [/tex]
Make x the subject of formula.
[tex] b*tan(A) = x [/tex]
[tex] BD = x = b*tan(A) [/tex]
PLEASE HELP!!! The question is.. [tex]163-y=-5[/tex] ANSWER GETS BRAINLIEST
Answer:
y = 168Step-by-step explanation:[tex]163 -y =-5\\Collect\:Like\:terms\\163+5 = y\\Simplify\\168 =y\\\\y = 168[/tex]
Hello There!
Answer: [tex]163-168=-5[/tex]Explanation:[tex]163-y=-5[/tex]
To solve your equation, you can just change the -5 to 5 and move it to where y is. After that, change the minus sign to addition.
[tex]163+5=y[/tex]
Now all you have to do is sum it up.
[tex]163+5=168[/tex]
So y = to 168
So your answer is
[tex]163-168=-5[/tex]
Hope this Helps!
Find the measure of c.
Answer:
149 degrees
Step-by-step explanation:
This shape is a cyclic, so opposite angles add up to 180 degrees.
180-31 = 149
explain why the APR does not compare loans for different lengths of time
Answer:
APR does not tell you how long your rate is locked for. A 15-year loan may have a lower interest rate, but could have a higher APR, since the loan fees are amortized over a shorter period of time. It is not wise to compare a 30-year loan with a 15-year loan using their respective APRs.
Step-by-step explanation:
A researcher wishes to estimate the percentage of adults who support abolishing the penny. What size sample should be obtained if he wishes the estimate to be within 3 percentage points with 99% confidence if (a) he uses a previous estimate of 22%?
Answer:
Sample size n [tex]\simeq[/tex] 1269.15
Step-by-step explanation:
From the information given ,
At 99% of confidence interval,
the level of significance ∝ = 1 - 0.99
the level of significance ∝ = 0.01
the critical value for 99% of confidence interval is:
[tex]\mathtt{\dfrac{\alpha }{2} = \dfrac{0.01}{2}}[/tex]
= 0.005
[tex]\mathtt {z_{\alpha/2} = z_{0.005/2} }[/tex]
The value for z from the standard normal tables
= 2.58
The Margin of error E= 3% = 0.03
The formula to determine the sample size n used can be expressed as follows:
[tex]\mathtt { n = (\dfrac{z_{\alpha/2}}{E})^2 \ \hat p (1 - \hat p) }[/tex]
where;
[tex]\mathtt{\hat p }[/tex] = 22% = 0.22
Then:
[tex]\mathtt { n = (\dfrac{2.58}{0.03})^2 \ \times 0.22 \times (1 - 0.22) }[/tex]
[tex]\mathtt { n = (86)^2 \ \times 0.22 \times (0.78) }[/tex]
[tex]\mathtt { n = 7396 \ \times 0.22 \times (0.78) }[/tex]
n = 1269.1536
Sample size n [tex]\simeq[/tex] 1269.15
Find the work W done by a force of 7pounds acting in the direction 30 degreesto the horizontal in moving an object 7feet from (0 comma 0 )to (7 comma 0 ).
Answer:
The work done by the force is 42.4 Joules
Step-by-step explanation:
The force F = 7 pounds
angle to the horizontal that the force acts ∅ = 30°
The object is moved a distance d = 7 feet
The coordinate (0 comma 0 )to (7 comma 0 ), indicates that the movement started from the origin, and is along the x-axis.
The work done by this force = F cos ∅ x d
==> 7 cos 30° x 7
==> 7 x 0.866 x 7 = 42.4 Joules
Mark is buying supplies for his students. He is buying a notebook (n) and a pack of pencils for each of his 25 students. Each pack of pencils costs $1.25. If Mark's total cost is $156.25, which of the following equations can be used to find how much each notebook cost? Select TWO that apply.
Answer:
$5
Step-by-step explanation:
Note. There are no options to select.Let the notebook cost x, then Mark spent:
25x + 25*1.25 = 156.2525x + 31.25 = 156.2525x = 156.25 - 31.2525x = 125x= 125/25x= 5Notebook costs $5
PLEASE HELP ASAP Madelyn drove a race car in a race. She averaged 55 mph and began the race 0.5 hours ahead of the other drivers. The variable d represents Madelyn's distance driven, in miles. The variable t represents the number of hours since the other drivers began to race. Which equation can be used to determine the distance Madelyn drove t hours into the race? d=55t−0.5 d=55(t+0.5) d=55(t−0.5) d = 55t + 0.5
Answer:
d=55(t+0.5)
Step-by-step explanation:
d=55(t+0.5)
Answer:
27.5
Step-by-step explanation:
State the correct polar coordinate for the graph shown:
Answer:
Solution : ( - 8, - 5π/3 )
Step-by-step explanation:
There are four cases to consider here, the first two with respect to r > 0, the second two with respect to r < 0. For r < 0 we have the coordinates ( - 8, 60° ) and ( - 8, - 300° ) . - 300° in radians is - 5π/3, and hence our solution is option d. But let me expand on how to receive the coordinates. Again r is the directed distance from the pole, and theta is the directed angle from the positive x - axis.
So when r is either negative or positive, we can tell that this point is 8 units from the pole. Therefore - r = - 8 in both our second cases ( we are skipping the first two cases for simplicity ). For r < 0 the point will lay on the ray pointing in the opposite direction of the terminal side of theta.
Our first coordinate is ( - 8, 60° ). Theta will be 2 / 3rd of 90 degrees, or 60 degrees, for - r. Respectively the remaining degrees will be negative, 360 - 60 = 300, - 300. Our second point for - r will thus be ( - 8, - 300° ) . - 300° = - 5π/3 radians, and our coordinate will be ( - 8, - 5π/3 ).
3(x–6)=18 help plese
Answer:
x = 12
Step-by-step explanation:
3(x–6)=18
x-6 = 18:3
x-6 = 6
x = 6+6
x = 12
Answer:
x=12
Step-by-step explanation:
Marine ecologists estimate the reproduction curve for swordfish in a fishing ground to be f(p) = −0.01p2 + 9p, where p and f(p) are in hundreds. Find the population that gives the maximum sustainable yield, and the size of the yield.
Answer:
The population that gives the maximum sustainable yield is 45000 swordfishes.
The maximum sustainable yield is 202500 swordfishes.
Step-by-step explanation:
Let be [tex]f(p) = -0.01\cdot p^{2}+9\cdot p[/tex], the maximum sustainable yield can be found by using first and second derivatives of the given function: (First and Second Derivative Tests)
First Derivative Test
[tex]f'(p) = -0.02\cdot p +9[/tex]
Let equalize the resulting expression to zero and solve afterwards:
[tex]-0.02\cdot p + 9 = 0[/tex]
[tex]p = 450[/tex]
Second Derivative Test
[tex]f''(p) = -0.02[/tex]
This means that result on previous part leads to an absolute maximum.
The population that gives the maximum sustainable yield is 45000 swordfishes.
The maximum sustainable yield is:
[tex]f(450) = -0.01\cdot (450)^{2}+9\cdot (450)[/tex]
[tex]f(450) =2025[/tex]
The maximum sustainable yield is 202500 swordfishes.
