Answers
Answer:
Bonsoir,
f'(-5)=-4/3
f'(-1) =3/4
Step-by-step explanation:
f'(-5) = ?
2 points : (-6,9) and (-3,5)
f'(-5)=(9-5)/(-6-(-3))=-4/3
f'(-1) = ?
2 points : (-3,5) and (1,8)
f'(-1)=(5-8)/(-3-1)=3/4
The lines are perpendicular
The derivative at the points -5 and -1 are:
f’(-5) = -4/3
f’(-1) = 3/4
What is derivative at a point on line?The slope of the tangent line to the graph of a function at a point is called the derivative of the function at that point.
We consider the line on which where the x coordinate -5 lies.
It is the line with points (-3, 5) and (-6, 9).
Slope of the line = [tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex] = [tex]\frac{9-5}{-6+3} = \frac{-4}{3}[/tex]
f'(-5) = -4/3
We consider the line on which where the x coordinate -1 lies.
It is the line with points (-3, 5) and (1, 8).
Slope of the line = [tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex] = [tex]\frac{8-5}{1+3} = \frac{3}{4}[/tex]
f'(-1) = 3/4
Learn more about derivative at a point here
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Related Questions
Ian and Keith make extra money in the summer picking strawberries. Yesterday, they picked 384 pounds of strawberries altogether. Ian is more experienced and picked 3 times as many pounds as Keith. How many pounds of strawberries did Keith pick yesterday?
Answers
40 percent of the teachers at a meeting are male.
Of the male teachers at the meeting, 20 percent
teach mathematics. Which of the following
could be the possible number of teachers at the
meeting?
(A) 60
(B) 64
(C) 72
(D) 75
(E) 80
Answers
Answer:
D. 75
Step-by-step explanation:
To find the possible number of teachers at the meeting, find which answer choice creates a whole number answer when calculating the 40% of teachers that are male and the 20% of them that teach math.
This number is answer choice D, 75.
40% of 75 is 30.
Of those 30 teachers, 20% of 30 is 6.
So, since each quantity is a whole number, this could be the possible number of teachers at the meeting.
The correct answer is D. 75
Clue is a board game in which you must deduce three details surrounding a murder. In the original game of Clue, the guilty person can be chosen from 66 people, and there are 66 different possible weapons and 99 possible rooms. At one point in the game, you have narrowed the possibilities down to 44 people, 55 weapons, and 77 rooms. What is the probability of making a random guess of the guilty person, murder weapon, and location from your narrowed-down choices, and the guess being correct
Answers
Answer:
The probability of making a correct random guess is 0.00053%.
Step-by-step explanation:
Since Clue is a board game in which you must deduce three details surrounding a murder, and in the original game of Clue, the guilty person can be chosen from 66 people, and there are 66 different possible weapons and 99 possible rooms, and at one point in the game, you have narrowed the possibilities down to 44 people, 55 weapons, and 77 rooms, to determine what is the probability of making a random guess of the guilty person, murder weapon, and location from your narrowed-down choices , and the guess being correct, the following calculation must be performed:
(1 / (44x55x77)) x 100 = X
(1 / 186,340) x 100 = X
0.0005366 = X
Therefore, the probability of making a correct random guess is 0.00053%.
What is the inverse of the function g (x) = 5 (x - 2)
Answers
Answer:
g − 1 ( x ) = x/ 5 + 2
Step-by-step explanation:
See the pic for solutions :)
solve above question
Answers
2 Substitute
y
=
2
−
3
x
y=2−3x into
x
+
y
=
7
x+y=7.
−
2
x
+
2
=
7
−2x+2=7
3 Solve for
x
x in
−
2
x
+
2
=
7
−2x+2=7.
x
=
−
5
2
x=−
2
5
4 Substitute
x
=
−
5
2
x=−
2
5
into
y
=
2
−
3
x
y=2−3x.
y
=
19
2
y=
2
19
5 Therefore,
x
=
−
5
2
y
=
19
2
x=−
2
5
y=
2
19
g According to a report from a particular university, % of female undergraduates take on debt. Find the probability that of the female undergraduates have taken on debt if female undergraduates were selected at random. What probability should be found
Answers
Answer:
P(0 female undergraduate takes on debt) ;
0.00635
Step-by-step explanation:
Probability of taking on debt, p = 0.43
q = 1 - p = 1 - 0.43 = 0.57
Number of samples, number of trials, n = 9
To obtain the probability that none of the female undergraduate take on debt :
P(0 female undergraduate takes on debt)
P(x = 0) ; using the binomial probability relation :
P(x = x) = nCx * p^x * q^(n-x)
P(x = 0) = 9C0 * 0.43^0 * 0.57^(9-0)
P(x = 0) = 9C0 * 0.43^0 * 0.57^9
P(x = 0) = 1 * 1 * 0.006351461955384057
P(x = 0) = 0.006351461955384057
P(x = 0) = 0.00635
Write the expression as a trinomial (3a+4)(8-a).
Answers
Answer:
-3a² + 20a + 32
Step-by-step explanation:
(3a+4)(8-a)
24a - 3a² + 32 - 4a
-3a² + 24a - 4a + 32
-3a² + 20a + 32
 evaluate P(6,2) or 6p2
Answers
Answer:
30
Step-by-step explanation:
Permutation equation: [tex]\frac{n!}{(n-r)!}[/tex]
n = Total number of objects, r = Number of objects selected
[tex]_6P_2=\frac{6!}{(6-2)!}=30[/tex]
A plane flying horizontally at an altitude of 3 mi and a speed of 460 mi/h passes directly over a radar station. Find the rate at which the distance from the plane to the station is increasing when it is 4 mi away from the station (Round your answer to the nearest whole number.) 368 X mi/h Enhanced Feedback Please try again. Keep in mind that distance - (altitude)2 + (horizontal distance)? (or y = x + n ). Differentiate with respect to con both sides of the equation, using the Chain Rule, to solve for the given speed of the plane is x.
Answers
Answer:
[tex]\frac{dy}{dt}=304mi/h[/tex]
Step-by-step explanation:
From the question we are told that:
Height of Plane [tex]h=3mi[/tex]
Speed [tex]\frac{dx}{dt}=460mi/h[/tex]
Distance from station [tex]d=4mi[/tex]
Generally the equation for The Pythagoras Theorem is is mathematically given by
[tex]x^2+3^2=y^2[/tex]
For y=d
[tex]x^2+3^2=d^2[/tex]
[tex]x^2+3^2=4^2[/tex]
[tex]x=\sqrt{7}[/tex]
Therefore
[tex]x^2+3^2=y^2[/tex]
Differentiating with respect to time t we have
[tex]2x\frac{dx}{dt}=2y\frac{dy}{dt}[/tex]
[tex]\frac{dy}{dt}=\frac{x}{y}\frac{dx}{dt}[/tex]
[tex]\frac{dy}{dt}=\frac{\sqrt{7}}{4} *460[/tex]
[tex]\frac{dy}{dt}=304.2614008mi/h[/tex]
[tex]\frac{dy}{dt}=304mi/h[/tex]
enter the number that belongs in the green box (please enter both numbers for the empty boxes)
Answers
Given:
The equation is:
[tex]5x-2=4+2x[/tex]
To find:
The number that belongs in the green box and another box.
Solution:
We have,
[tex]5x-2=4+2x[/tex]
Subtracting 2x from both sides, we get
[tex]5x-2-2x=4+2x-2x[/tex]
[tex]3x-2=4[/tex]
Adding 2 on both sides, we get
[tex]3x-2+2=4+2[/tex]
[tex]3x=6[/tex]
We need to divide both sides by 3 to isolate the variable x.
On dividing both side by 3, we get
[tex]\dfrac{3x}{3}=\dfrac{6}{3}[/tex]
Therefore, the missing values are 3 and 3, and the required equation is [tex]\dfrac{3x}{3}=\dfrac{6}{3}[/tex].
Teacher gives 2 questions to a class of 50 student. 30 students correctly answer ther first question, 25 students correctly answer the second question, 7 wongly answer both question, there are _ students correctly answer both question
Answers
Answer:
43
Step-by-step explanation:
only 7 out of the 50 got both wrong
Answer:
Step-by-step explanation:
Write the options so they are homogeneous in content. • Use answers given in previous open-ended exams to provide realistic distractors. 2. Use a Question ...
Find the length of BC again
Answers
Since this is a right triangle, we can use one of the three main trigonometric functions: sine, cosine, or tangent.
Remember: SOH-CAH-TOA
Looking from the angle, we know the opposite side and want to know the adjacent side. Therefore, we should use the tangent function.
tan(61) = 47 / BC
BC = 47 / tan(61)
BC = 26.05 units
Hope this helps!
Answer:
BC = 26.05
Step-by-step explanation:
SOH CAH TOA
tan 61 = 47/BC
BC = 47/tan 61
PLS HELP !! Is the following a fair sampling of the contents of the jar? Why?
Pour a 2” layer of lentils into a jar. Then pour a 2” layer of kidney beans into the jar. Then pour a 2” layer of pinto beans into the jar. Stir the contents of the jar well. Then pull out a handful of beans.
Answers
please help me with geometry
Answers
Answer:
x = 7
Explaination:
ABC = 40°
and BD bisects the angle so ABD = 20°
so 3x-1=20
solving for x gets us
x = 7
Infues Gentamicin 100 mg in 100ml in 15 minutes. What will you set the infusion pump at ml/hr
Answers
9514 1404 393
Answer:
400 mL/h
Step-by-step explanation:
The required rate is ...
(100 mL)/(1/4 h) = 100×(4/1) mL/h = 400 mL/h
25 scores from all of the students who took the test. She sees that the mean score is 134 with a standard deviation of 6.0547. The superintendant wants to know if the standard deviation has changed this year. Previously, the population standard deviation was 13. Is there evidence that the standard deviation of test scores has decreas
Answers
Answer:
WE fail to reject the Null and conclude that ; Standard deviation of test hasn't decreased.
Step-by-step explanation:
The hypothesis :
H0 : σ = 13
H1 : σ < 13
Using the Chisquare Square statistic :
χ² = (n-1)*s²/σ²
Sample size, n = 25
s² = 6.0547²
σ² = 13²
χ² = (25 - 1)*6.0547² / 13²
χ² = 879.82541016 / 169
χ² = 5.206
The degree of freedom, df = 25 - 1 = 24
The Pvalue(5.206, 24) = 0.99981
Reject H0, if Pvalue < α ;
Since Pvalue > α ; WE fail to reject the Null and conclude that ; Standard deviation of test hasn't decreased.
There are 6 people named A,B,C,D,E,F. The people named A,B, and C are all over the age of 40. The people named D,E,F are all under the age of 40. How many different orders are there for the people to sit on a bench, if both ends of the bench must be occupied by someone over the age of 40?
Answers
Please solve this l am in many problem please please please please help me
Answers
Answer:
h) a+20 = 80 (vert. opp angles)
a = 60
i) 3a+48 = 180
3a = 132
a = 44
a) 3x + 2x = 180
5x = 180
x = 36
∡y = 72
∡z = 108
∡r = 144
∡x = 180-144 = 36
b) p:b = 3:1
4u = 180
u = 45
∡p = 135
∡b = 45
∡q = ∡p = 135 (vert. opp)
∡a = ∡b = 45 (vert. opp)
Answer:
hello,
as i have taken the time to draw the picture
Step-by-step explanation:
Find the range of the function f(x) = 2 cos πx:
A) R
B) [-π,π]
C)[-2,2]
D) [-1,1]
PLEASE I NEED HELP IM REALLY BAD AT FINDING RANGES , I WILL MARK BRAINLIEST!!!
Answers
Answer:
A) R
Step-by-step explanation:
f(x) = 2 cos π x, but cos π = -1 therefore
f(x) = -2x, this is a line that has the slope m= -2, and goes trough the origin
the range is given by all the values of y so is R
Imagine that you are given two linear equations in slope-intercept form. You
notice that both the slopes and the y-intercepts are the same. How many
solutions would you expect for this system of equations?
O A. 1
ОВ. о
C. infinitely many
O D. cannot be determined
SURAT
Answers
Answer:
C. infinitely many
Step-by-step explanation:
If two equations in slope-intercept form have the same slope and y-intercept they must be the same line. Additionally, the solutions of a system of equations are wherever the two lines intersect. Since the lines are the same they must intersect at every point. Therefore, there are infinitely many solutions.
4. A solution of 60% fertilizer is to be mixed with a solution of 21% fertilizer to form 234 liters of a 43% solution. How many liters of the 60% solution must be used?
SHOW YOUR WORK
Answers
Given:
A solution of 60% fertilizer is to be mixed with a solution of 21% fertilizer to form 234 liters of a 43% solution.
To find:
The quantity of the 60% solution in the mixture.
Solution:
Let x be the quantity of the 60% solution and y be the quantity of the 21% solution.
Quantity of mixture is 234. So,
[tex]x+y=234[/tex]
[tex]x=234-y[/tex] ...(i)
The mixture has 43% fertilizer. So,
[tex]\dfrac{60}{100}x+\dfrac{21}{100}y=\dfrac{43}{100}\times 234[/tex]
Multiply both sides by 100.
[tex]60x+21y=10062[/tex] ...(ii)
Using (i) and (ii), we get
[tex]60(234-y)+21y=10062[/tex]
[tex]14040-60y+21y=10062[/tex]
[tex]-39y=10062-14040[/tex]
[tex]-39y=-3978[/tex]
Divide both sides by -39.
[tex]\dfrac{-39y}{-39}=\dfrac{-3978}{-39}[/tex]
[tex]y=102[/tex]
Putting this value in (i), we get
[tex]x=234-102[/tex]
[tex]x=132[/tex]
Therefore, 132 liters of the 60% solution must be used.
Air-USA has a policy of booking as many as 22 people on an airplane that can only seat 20 people. (Past studies have revealed that only 82% of the booked passengers actually show up for the flight.) a) Find the probability that if Air-USA books 22 people, not enough seats will be available. Round your answer to 4 decimal places. P ( X > 20 )
Answers
Answer:
The answer is "0.07404893".
Step-by-step explanation:
Applying the binomial distribution:
[tex]n = 22\\\\p= 82\%=0.82\\\\q = 1-0.82 = 0.18\\\\[/tex]
Calculating the probability for not enough seats:
[tex]=P(X>20)\\\\= P(21) + P(22)\\\\[/tex]
[tex]= \binom{22}{21} (0.82)^{21}(0.18)^1+ \binom{22}{22} (0.82)^{22}(0.18)[/tex]
[tex]=0 .06134598+ 0.01270295\\\\=0.07404893[/tex]
According to Statcast, the average left field home run travels 378 feet and reaches a maximum height of 81 feet. Assuming the ball is hit from 3 feet in the air, write an equation for its height as it travels from home plate.
Answers
Answer:
H = V0y t - 1/2 g t^2 equation for vertical height of object with initial speed (V0y = V0 sin theta)
If H is to be considered an absolute value from t = 0
h = H + 3 = V0y t - 1/2 g t^2 + 3 where h is height from ground
16 is what percent of 4
Answers
Answer:
400%
Step-by-step explanation:
Is means equals and of means multiply
16 = P *4
Divide each side by 4
16/4 = P4/4
4 = P
Change to a percent by multiply by 100 and adding the percent sign
400% = P
A survey showed that, in one city, 20.7% of the population used
product X, 50% use product Y and among users Y, 36.5% use X. Randomized interview
However, a resident in that city, calculate the probability that that person
a) Use both X and Y;
b) Neither X nor Y
Answers
Answer:
Step-by-step explanation:
a) 0.5*0.365=18.25%
b) (100%-20,7%-50%)=29.3
Suppose a six-sided die is tossed 1200 times and a 6 comes up 419 times. (a) Find the empirical probability for a 6 to occur. (Enter your probability as a fraction.) (b) On the basis of a comparison of the empirical probability and the theoretical probability, do you think the die is fair or biased
Answers
Answer:
Here both probabilities are not equal.
Therefore the die is not fair and biased.
Step-by-step explanation:
Now n= 1200 times and x = 419 times.
a) Empirical Probability:
[tex]=\frac{x}{n} \\\\= \frac{419}{1200}\\ \\=0.349[/tex]
Probability = 0.349
b) Theoretical Probability:
[tex]=\frac{1}{6}[/tex]
Here both probabilities are not equal.
Therefore the die is not fair and biased.
Please answer! These r my last questions
Answers
Answer:
8. -2a+14
9. w=3/2
Step-by-step explanation:
8.
The distributive property states that we can multiply each component in the parenthesis separately by the number on the outside, and then add that up to get our final answer.
For -2(a-7), this means that we can multiply -2 by a and then -2 by -7 (as 2 is the number on the outside, and a and -7 are the components in the parenthesis), add them up, and get our answer. This can be expressed as
-2 * a + (-2) * (-7) = final answer
= -2 * a + 14
We know that -2 * -7 = 14 because 2 * 7 = 14, and the two negatives in multiplication cancel each other out
9.
Using the subtraction property of equality, we can isolate the variable (w) and its coefficient (-2/3) by subtracting 5, resulting in
(-2/3)w = 4-5 = -1
Next, we can use the multiplication property of equality to isolate the w. To isolate the w, we can multiply its coefficient by its reciprocal. The reciprocal is the fraction flipped over. For (-2/3), its reciprocal is (-3/2), flipping the 2 and 3. We can multiply both sides by (-3/2) to get
w = (-3/2)
To check this, we can plug (-3/2) for w in our original equation, so
(-2/3) * (-3/2) + 5 = 4
-1 + 5 = 4
4 = 4
This works!
In 1990, the average math SAT score for students at one school was 498. Five years later, a teacher wants to perform a hypothesis test to determine whether the average SAT score of students at the school has changed from the 1990 mean of 498.
The hypotheses are shown below. Identify the Type II error.
H0:μ=498
Ha:μ≠498
A. Fail to reject the claim that the average math SAT score is 498 when in fact it is not 498.
B. Reject the claim that the average math SAT score is 498 when in fact it is not 498.
C. Reject the claim that the average math SAT score is 498 when in fact it is 498.
D. Fail to reject the claim that the average math SAT score is 498 when in fact it is 498.
Answers
Answer:
A. Fail to reject the claim that the average math SAT score is 498 when in fact it is not 498.
Step-by-step explanation:
Type II Error:
A type II error happens when there is a non-rejection of a false null hypothesis.
In this question:
The null hypothesis is H0:μ=498.
Since there is a type II error, there was a failure to reject the claim that the average math SAT score is 498 when in fact it is not 498, and thus, the correct answer is given by option A.
Please help me to find this answer
Answers
Step-by-step explanation:
question 1
angle DBA=90°, meaning to find m<D you have to add 90+38 then subtract by 180, because ABD is a triangle
90+18+m<D=180
108+m<D=180
m<D=180-108
=72°
question 2
m<D again in this case angle ABD is also 90
m<D=180-(90+48)
=180-138
=42°
I hope this helps
How many minutes will the bus take to complete the trip If a bus completes half a trip at 40 km per hour and the other half at 50 20. if the whole trip was 60 k.m. ?
Answers
Answer:
The bus will take 81 minutes to complete the trip.
Step-by-step explanation:
To determine how many minutes will the bus take to complete the trip if a bus completes half a trip at 40 km per hour and the other half at 50 km per hour, and the whole trip was 60 km, the following calculation must be performed:
60/2 = 30
30/40 = 3/4 of an hour = 45 minutes
30/50 = 3/5 of an hour = 36 minutes
45 + 36 = 81
Therefore, the bus will take 81 minutes to complete the trip.
