The inverse function theorem says
[tex]\dfrac{\mathrm df^{-1}}{\mathrm dx}(16)=\dfrac1{\frac{\mathrm df}{\mathrm dx}(f^{-1}(16))}[/tex]
We have
[tex]f(x)=x^2+4x-5[/tex]
defined on [tex]x>-2[/tex], for which we get
[tex]f^{-1}(x)=-2+\sqrt{x+9}[/tex]
and
[tex]f^{-1}(16)=-2+\sqrt{16+9}=3[/tex]
The derivative of [tex]f(x)[/tex] is
[tex]f'(x)=2x+4[/tex]
So we end up with
[tex]\dfrac{\mathrm df^{-1}}{\mathrm dx}(16)=\dfrac1{\frac{\mathrm df}{\mathrm dx}(3)}=\dfrac1{10}[/tex]
If Q(x)=x2−6x−2, find Q(−4).
Answer:
Q(-4) = 38Step-by-step explanation:
Q(x)=x² − 6x − 2
To find Q(−4) substitute the value of x which is - 4 into Q(x)
That's
Q(-4) = (-4)² - 6(-4) - 2
Q(-4) = 16 + 24 - 2
We have the final answer as
Q(-4) = 38Hope this helps you
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.
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.
Solve for x. 2x+3≤x−5 x≤−8 x≤2 x≤8 x≤−2
Answer:
x≤−8
Step-by-step explanation:
2x+3≤x−5
Subtract x from each side
2x-x+3≤x-x−5
x+3≤−5
Subtract 3 from each side
x+3-3≤−5-3
x≤−8
Answer:
[tex]\huge \boxed{x \leq -8}[/tex]
Step-by-step explanation:
[tex]2x+3 \leq x-5[/tex]
[tex]\sf Subtract \ x \ from \ both \ parts.[/tex]
[tex]2x+3 -x\leq x-5-x[/tex]
[tex]\sf Simplify \ the \ inequality.[/tex]
[tex]x+3 \leq -5[/tex]
[tex]\sf Subtract \ 3 \ from \ both \ parts.[/tex]
[tex]x+3-3 \leq -5-3[/tex]
[tex]\sf Simplify \ the \ inequality.[/tex]
[tex]x \leq -8[/tex]
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.
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:
Which expression is equivalent to 8 square root 6 ?
Answer:
(2.13982638787^3) x 2
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.
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
-10 + 7x + 24 - 2x
Your answer
I WILL RATE YOUR BRAINLIEST Marius opened a savings account. The sequence {200, 208, 216.30, 225, …} describes the amount of interest he earns each year his account is active. If this pattern continues, how much total interest will Marius have earned by the 30th year the account is active?
Answer:
11,215Step-by-step explanation:
Given the sequence of interest earned by Marius on his savings account as
200, 208, 216.30, 225, …, the sequence of interest forms a geometric sequence since they have a common ratio.
[tex]r =\frac{T_2}{T_1}= \frac{T_3}{T_2}= \frac{T_4}{T_3}\\ r =\frac{208}{200}= \frac{216.30}{208}= \frac{225}{216.30} \approx 1.04[/tex]
To get how much total interest will Marius have earned by the 30th year the account is active, we will find the sum of the first 30 terms of the geometric sequence as shown.
[tex]S_n =\frac{ a(r^n-1)}{r-1} \ for \ r> 1\\ \\\\ n = 30, a = 200, r = 1.04\\S_{30} = \dfrac{ 200(1.04^{30}-1)}{1.04-1}\\\\S_{30} = \dfrac{ 200(3.243-1)}{0.04}\\\\S_{30} = \dfrac{ 200(2.243)}{0.04}\\\\S_{30} = \dfrac{ 448.6}{0.04}]\\\\S_{30} = 11,215[/tex]
Hence total interest that Marius will earn by the 30th year the account is active is 11,215.
the correct answer is
S30= 200(1-1.04^n)/1-1.04
i took the test
Answer the questions attached about the given sequence: -33, -27, -21, -15, ...
Answer:
see below
Step-by-step explanation:
-33, -27, -21, -15,....
-33 +6 = -27
-27+6 = -21
-21+6 = -15
This is an arithmetic sequence
The common difference is +6
explicit formula
an=a1+(n-1)d where n is the term number and d is the common difference
an = -33 + ( n-1) 6
an = -33 +6n -6
an = -39+6n
recursive formula
an+1 = an +6
10th term
n =10
a10 = -39+6*10
= -39+60
=21
sum formula
see image
The sum will diverge since we are adding infinite numbers
Charlie needs a $275,000 mortgage and he'd like to pay it off in 30 years. He is considering two banks. Bank A: 3.5% with monthly payments of $1234.87 Bank B: 4% with monthly payments of $1312.89 Charlie doesn't think a 0.5% difference is that much. What is the difference between these two bank loans with total interest paid over the life of the loan?
Answer:
Difference in interest= $41,250
Step-by-step explanation:
To calculate the interest paid on each bank loan we use the following formula
Interest = Principal * Rate * Time
For Bank A
Interest = 275,000 * 0.035 * 30
Interest = $288,750
For Bank B
Interest = 275,000 * 0.04 * 30
Interest = $330,000
Therefore
Difference in interest= 330,000 - 288,750
Difference in interest= $41,250
Therefore if the mortgage is taken from Bank B he will pay an extra $41,250 on the loan.
The 0.5% difference in rates has a large impact over the 30 year term loan
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 bold answer is incorrect. what is the right answer?
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
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
Using the FOIL method, find the product of x - 2 and x - 3 .
Answer:
[tex] \boxed{ {x}^{2} - 5x + 6}[/tex]Step-by-step explanation:
[tex] \mathsf{(x - 2)(x - 3)}[/tex]
Multiply each term in the first parentheses by each term in the second parentheses ( FOIL )
[tex] \mathsf{x×x - 3x - 2x - 2 × ( - 3 )}[/tex]
Calculate the product
[tex] \mathsf{ {x}^{2} - 3x - 2x - 2 \times (- 3)}[/tex]
Multiply the numbers
[tex] \mathsf{ {x}^{2} - 3x - 2x + 6 }[/tex]
Collect like terms
[tex] \mathsf{ {x}^{2} - 5x + 6}[/tex]
Hope I helped!
Best regards!
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.
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%
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]
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
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
find the value of x - Secant and Tangent Angles in Circles
Answer:
C. 70°
Step-by-step explanation:
The inscribed angle marked 15° intercepts an arc that is double that measure, so the intercepted arc on the right is 2×15° = 30°.
The external angle marked 20° is half the difference of the intercepted arcs, so is ...
20° = (1/2)(x - 30°)
40° = x - 30° . . . . . . multiply by 2
70° = x . . . . . . . . . . . add 30°
The value of x is 70°.
How many 4 digit palidromes are there?
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]
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]
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.
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:
what is the end point of a ray
Answer:
point A is the rays endpoint
Step-by-step explanation:
Answer:
The "endpoint" of a ray is the origin point of the ray, or the point at which the ray starts.
Step-by-step explanation:
A ray starts at a given point, the endpoint, and then goes in a certain direction forever ad infinitum. The origin point of a ray is called "the endpoint".
Cheers.
