Answer:
$25
Step-by-step explanation:
.5 * 50 = 25
25<27.5<30
The cheapest supplier is the first one.
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 ).
The joint density function for a pair of random variables X and Y is given. f(x, y) = Cx(1 + y) if 0 ≤ x ≤ 4, 0 ≤ y ≤ 4 0 otherwise f(x,y) = 0
A) Find the value of the constant C. I already have 1/24.
B) Find P(X < = 1, Y < = 1)
C) Find P(X + Y < = 1).
Answer:
A) C = 1/96
B) P(x<=1, y<=1) = 1/128 or 0.0078125 to 7 places
C) P(x+y<=1) = 5/2305, or 0.0021701 to 7 places
Step-by-step explanation:
f(x,y) = C x (1+y)
A)
To find C, we need to integrate the volume under region bound by
0 <= x <= 4, and
0 <= y <= 4
This volume equals 1.0.
Find integral,
int( int(f(x,y),x=0,4), y = 0,4) = 96C
therefore C = 1/96
or
F(x,y) = x (1+y) / 96 ............................(1)
B)
P(x<=1, y<=1)
Repeat the integral, substitute the appropriate limits,
P = int( int(F(x,y),x=0,1), y = 0,1)
= 1/128 or 0.0078125
P(x<=1, y<=1) = 1/128 or 0.0078125 to 7 places
C)
P(x+y<=1)
From the function, we know that this is going to be less than one half of the probability in (B), closer to 1/4 of the previous.
It will be again a double integral, as follows:
P = int( int(F(x,y),x=0,1-y), y = 0,1)
= 5/2304
= 0.0021701 (to 7 decimals)
P(x+y<=1) = 5/2305, or 0.0021701 to 7 places
Scores on a college entrance examination are normally distributed with a mean of 500 and a standard deviation of 100. What percent of people who write this exam obtain scores between 350 and 650?
Answer:
The percentage is [tex]P(350 < X 650 ) = 86.6\%[/tex]
Step-by-step explanation:
From the question we are told that
The population mean is [tex]\mu = 500[/tex]
The standard deviation is [tex]\sigma = 100[/tex]
The percent of people who write this exam obtain scores between 350 and 650
[tex]P(350 < X 650 ) = P(\frac{ 350 - 500}{ 100} <\frac{ X - \mu }{ \sigma } < \frac{650 - 500}{ 100} )[/tex]
Generally
[tex]\frac{X - \mu }{\sigma } = Z (The \ standardized \ value \ of \ X )[/tex]
[tex]P(350 < X 650 ) = P(\frac{ 350 - 500}{ 100} <Z < \frac{650 - 500}{ 100} )[/tex]
[tex]P(350 < X 650 ) = P(-1.5<Z < 1.5 )[/tex]
[tex]P(350 < X 650 ) = P(Z < 1.5) - P(Z < -1.5)[/tex]
From the z-table [tex]P(Z < -1.5 ) = 0.066807[/tex]
and [tex]P(Z < 1.5 ) = 0.93319[/tex]
=> [tex]P(350 < X 650 ) = 0.93319 - 0.066807[/tex]
=> [tex]P(350 < X 650 ) = 0.866[/tex]
Therefore the percentage is [tex]P(350 < X 650 ) = 86.6\%[/tex]
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
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].
To know more about the function
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Even though the population standard deviation is unknown, an investigator uses z rather than the more appropriate t to test a hypothesis at the .01 level of significance. In this situation the true level of significance of this test is
Answer:
The true true level of significance of this test is more than 0.01.
Step-by-step explanation:
No standard deviation and we are told that the investigator still used z rather than the more appropriate t - distribution.
This method of using the z-distribution when standard deviation is unknown will definitely result in a smaller critical value and this in turn simply means that the p-value will be smaller than what it should really be.
Thus, it means the critical value is getting closer to the mean value than the way it should be.
Therefore, means that for a given significance of 0.01 and using the z-distribution under this no standard deviation situation, the true true level of significance of this test is more than 0.01.
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.
How many 4 digit palidromes are there?
Chloe wants to wrap a present in a box for Sarah. The top and bottom of the box is 8 in. by 3 in., the sides are both 3 in by 2 in. and the front and back are 8 in by 2 in. How much wrapping
paper will Chloe need to wrap the present?
Answer:
92 inches squared
Step-by-step explanation:
T/P = 8 * 3
L/R = 3 * 2
F/B = 8 * 2
Solving for surface area!
2(24) + 2(6) + 2(16) = 92
A planet rotates on an axis through its poles and 1 revolution takes 1 day 1 day is 24 hours. The distance from the axis to a location the planet 30 degrees north latitude is about 3387.5 miles. Therefore, a location on the planet at 30 degrees north latitude is spinning on a circle of radius 3387.5 miles.
Compute the linear speed on the surface of the planet at 30 degrees north latitude.
Answer:
The velocity is [tex]v = 886.96 \ m/s[/tex]
Step-by-step explanation:
From the question we are told that
The period of each revolution is [tex]T = 1\ day = 24 \ hours[/tex]
The angle is [tex]\theta = 30^o[/tex]
The radius is [tex]r = 3387.5 \ miles[/tex]
Generally the linear speed is mathematically represented as
[tex]v = w * r[/tex]
Where [tex]w[/tex] is the angular speed which is mathematically represented as
[tex]w = \frac{2 \pi }{T}[/tex]
substituting values
[tex]w = \frac{2 *3.142 }{24}[/tex]
[tex]w = 0.2618 \ rad/s[/tex]
Thus
[tex]v = 0.261833 * 3387.5[/tex]
[tex]v = 886.96 \ m/s[/tex]
Given: AQRS where m2Q = 20° and m2S = 90°
R
1,000 meters
Q
S
What is the length of segment RS?
342 m
364 m
500 m
940 m
Answer:
342 m
Step-by-step explanation:
SIn(20) * 1000 = RS
342 = RS
Choose the best answer to the following question. Explain your reasoning with one or more complete sentences. At 11:00 you place a single bacterium in a bottle, and at 11:01 it divides into 2 bacteria, which at 11:02 divide into 4 bacteria, and so on. How many bacteria will be in the bottle at 11:30?
Answer:
we could work this out by geometric sequence
Step-by-step explanation:
G1=2, G2=4, we have a formula,Gn=G1r^n-1
G2=G1 (r)^1, 4=2r, r=2
G30=G1 (2)^29=1,073,741,824 bacterium
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
-10 + 7x + 24 - 2x
Your answer
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
please solve quick
Answer:
x = 5
AC = 6
DC = 8
Step-by-step explanation:
∆ABC ~ ∆CDE
Therefore, [tex] \frac{AB}{ED} = \frac{AC}{DC} [/tex]
AB = 3
ED = 4
AC = x + 1
DC = x + 3
Plug in the values and solve for x:
[tex] \frac{3}{4} = \frac{x + 1}{x + 3} [/tex]
Cross multiply
[tex] 3(x + 3) = 4(x + 1) [/tex]
[tex] 3x + 9 = 4x + 4 [/tex]
[tex] 3x - 4x = -9 + 4 [/tex]
[tex] -x = -5 [/tex]
[tex] x = 5 [/tex]
Plug in the value of x and find AC and DC
AC = x + 1 = 5 + 1 = 6
DC = x + 3 = 5 + 3 = 8
Scott start his banking account with 150 and is spending $7 per day on lunch . How would one describe the graph of this model?
Answer:
So this is giving us the slope the slope is y=-7x+150
Step-by-step explanation:
It is giving us the Y intercept which is $150 because thats how much he starts out with
It is giving us the slope -7 dollars because he is spending that everyday
What is 2-(-8)????? And how do you solve it????
Subtracting a negative is the same as adding a positive. So 2-(-8) is really 2+8 = 10.
With something like 2-8, we start at 2 and move to the left 8 units to arrive at -6 on the number line. When we do 2-(-8), we start at 2 and move 8 units in the opposite direction since -8 is the opposite of 8.
In terms of money, you can think of a negative number as an IOU or it represents the amount of debt. Writing -8 means you are 8 dollars in debt. If we subtract away debt, then we have less of it and effectively its the same as adding dollars to your pocket. Subtracting away 8 dollars of debt is the same as adding 8 dollars to your pocket, which is one interpretation of how 2-(-8) is the same as 2+8.
the bold answer is incorrect. what is the right answer?
Nala can spend no more than $150 per month on gasoline. She has already purchased $60 in gas this month. Which inequality can be used to find the maximum number of fill-ups she can purchase during the rest of the month, assuming each fill-up costs $30? 30n + 60 > 150 30n + 60 150
Answer:
150<60+30n
Step-by-step explanation:
150 is the maximum amount that she can spend on gas. (which is the total)
she already spend $60
each fill up (n) costs 30
Answer:
the answer is B)
Step-by-step explanation:
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%
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:
Question 15 please and i will mark the brainliest!!! And thank you to whoever answers
Explanation:
We have 4 options for the first choice and 3 options for the next. So there are 4*3 = 12 different combos possible. The tree diagram below shows 12 different paths to pick from. For instance, the right-most path has us pick the number 4 and the color yellow.
The higher the bowling score the better. The lower the golf score the better. Assume both are normally distributed. a. Suppose we have a sample of the Santa Ana Strikers' bowling scores. Q1 = 125 and Q3 = 156. Would it be usual or unusual to have a score of 200?b. Suppose the mean bowling score is 155 with a standard deviation of 16 points. What is the probability that in a sample of 40 bowling scores, the mean will be smaller than 150?c. Suppose the mean golf score is 77 with a standard deviation of 3 strokes We will give a trophy for the best 5% of scores. What score must you get to receive a trophy? d. Suppose the mean golf score is 77 with a standard deviation of 3 strokes. Would a golf score of 70 be ordinary, a mild outlier, or an extreme outlier?
Answer:
Explained below.
Step-by-step explanation:
(a)
The first and third quartiles of bowling scores are as follows:
Q₁ = 125 and Q₃ = 156
Then the inter quartile range will be:
IQR = Q₁ - Q₃
= 156 - 125
= 31
Any value lying outside the range (Q₁ - 1.5×IQR, Q₃ + 1.5×IQR) are considered as unusual.
The range is:
(Q₁ - 1.5×IQR, Q₃ + 1.5×IQR) = (125 - 1.5×31, 156 + 1.5×31)
= (78.5, 202.5)
The bowling score of 200 lies in this range.
Thus, the bowling score of 200 is usual.
(b)
Compute the probability that the mean bowling score will be smaller than 150 as follows:
[tex]P(\bar X<150)=P(\frac{\bar X-\mu}{\sigma/\sqrt{n}}<\frac{150-155}{16/\sqrt{40}})[/tex]
[tex]=P(Z<-1.98)\\=1-P(Z<1.98)\\=1-0.97615\\=0.02385\\\approx 0.024[/tex]
Thus, the probability that in a sample of 40 bowling scores, the mean will be smaller than 150 is 0.024.
(c)
It is provided that, the lower the golf score the better.
So, the best 5% of scores would be the bottom 5%.
That is, P (X > x) = 0.05.
⇒ P (Z > z) = 0.05
⇒ P (Z < z) = 0.95
⇒ z = 1.645
Compute the value of x as follows:
[tex]z=\frac{x-\mu}{\sigma}\\\\1.645=\frac{x-77}{3}\\\\x=77+(3\times 1.645)\\\\x=81.935\\\\x\approx 82[/tex]
Thus, the score is 82.
(d)
A z-scores outside the range (-2, +2) are considered as mild outlier and the z-scores outside the range (-3, +3) are considered as extreme outlier.
Compute the z-score for the golf score of 70 as follows:
[tex]z=\frac{x-\mu}{\sigma}[/tex]
[tex]=\farc{70-77}{3}\\\\=\frac{-7}{3}\\\\=-2.33[/tex]
As the z-score for the golf score of 70 is less than -2, it is considered as a mild outlier.
Identify the recursive formula for the sequence given by the explicit formula f(n) = 20 – 4(n − 1).
Answer:
[tex]\huge\boxed{f(n)=\left\{\begin{array}{ccc}f(1)=20\\f(n)=f(n-1)-4\end{array}\right}[/tex]
Step-by-step explanation:
[tex]f(n)=20-4(n-1)=20+(n-1)(-4)\\\\\text{It's an explicit formula of an arithmetic sequence:}\\\\f(n)=a_1+(n-1)(d)\\\\a_1-\text{first term}\\d-\text{common difference}\\\\\text{Conclusion:}\\\text{Next term}=\text{previous one}\ -4\\\\\text{The recursive formula:}\\\\\huge\boxed{f(n)=\left\{\begin{array}{ccc}f(1)=20\\f(n)=f(n-1)-4\end{array}\right}[/tex]
Answer:
Step-by-step explanation:
someone answered already
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.
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]
Write down the name of the shape for question D. Please help!
Step-by-step explanation:
thats shape is a delta
:)
Answer:
arrow head
Step-by-step explanation:
Enter an expression that is equivalent to (6x2−1)+(x2+3)−2(x2−5)−15x2, combining all like terms. Use the on-screen keyboard to type the correct polynomial in the box below.
Answer:
Its 10x^2+12
Step-by-step explanation:
Answer:
-10X^2+12
Step-by-step explanation:
While you can use the correlation coefficient as its own test statistic, what is the other appropriate test statistic often used to examine the significance of a correlation
Answer:
T-test
Step-by-step explanation:
Significance of correlation between two variables x and y measures the strength and direction of their relationship. This is used to make future forecasts of the behaviour of a variable under study.
Correlation coefficient can be used to measure significance of correlation, but we can also use the t-test.
T-test is a statistics that is inferential. It measures the significance of difference between the means of two groups.
T-test is the statistic of choice when carrying out hypothesis testing.
T distribution values and degrees of freedom are used to determine statistical significance.
For example the means of two samples can be compared to determine of the come from the same population
