Answers
Answer:
a(1) = 10
a(n) = a(n-1)·0.6
Step-by-step explanation:
The first term of the sequence is the one listed first: 10. That means a(1) = 10.
The next term of the geometric sequence will be the first term multiplied by the common ratio. That ratio can be found as the ratio of the second term to the first:
r = 6/10 = 0.6
So, the recursive formula is ...
a(n) = a(n-1)·r
a(n) = a(n-1)·0.6
Answer:
a(1) = 10
a(n) = a(n-1)·0.6
Related Questions
The effect of caffeine on taste is tested by randomly giving one sample of participants regular soda and another sample is given decaffeinated soda.
A) Dependent samples
B) Independent samples
Answers
Answer:
The correct answer is A. Both samples are dependent samples.
Step-by-step explanation:
Both samples are dependent samples, since to verify the effects of one, it is necessary to compare it with the effects and characteristics of the other.
Thus, in the case, it is intended to check the effects of caffeine on taste by using a regular soda sample first, and then comparing it with a decaffeinated soda sample. Therefore, the effects of one sample will be checked and compared with the other sample, so that there is a dependency relationship between the two, since neither could prove the hypothesis on its own.
A researcher records the repair cost for 8 randomly selected refrigerators. A sample mean of $57.89 and standard deviation of $23.69 are subsequently computed. Determine the 95% confidence interval for the mean repair cost for the refrigerators. Assume the population is approximately normal. Step 1 of 2 : Find the critical value that should be used in constructing the confidence interval. Round your answer to three decimal places.
Answers
The question is incomplete! the complete question along with answer and step by step explanation is provided below.
Question:
A researcher records the repair cost for 8 randomly selected refrigerators. A sample mean of $57.89 and standard deviation of $23.69 are subsequently computed. Determine the 95% confidence interval for the mean repair cost for the refrigerators. Assume the population is approximately normal.
Step 1 of 2 : Find the critical value that should be used in constructing the confidence interval. Round your answer to three decimal places.
Step 2 of 2 : Construct the 95% confidence interval. Round your answer to two decimal places.
Given Information:
Sample mean repair cost = $57.89
Sample standard deviation = σ = $23.69
Sample size = 8
Confidence level = 95%
Required Information:
step 1: critical value = ?
step 2: 95% confidence interval = ?
Answer:
step 1: critical value = 2.365
step 2: 95% confidence interval = ($38.08, $77.70)
Step-by-step explanation:
Since the sample size is less than 30 and the standard deviation of the population is also unknown therefore, we can use the t-distribution to find the required confidence interval.
The confidence interval is given by
[tex]CI = \bar{x} \pm MoE\\\\[/tex]
Where [tex]\bar{x}[/tex] is the mean repair cost and MoE is the margin of error that is given by
[tex]$ MoE = t_{\alpha/2}(\frac{s}{\sqrt{n} } ) $ \\\\[/tex]
Where n is the sample size, s is the sample standard deviation, and [tex]t_{\alpha/2}[/tex] is the t-score corresponding to 95% confidence level.
The t-score corresponding to 95% confidence level is
Significance level = 1 - 0.95 = 0.05/2 = 0.025
Degree of freedom (DoF) = n - 1 = 8 - 1 = 7
From the t-table at α = 0.025 and DoF = 7
t-score = 2.365
Therefore, the critical value that should be used in constructing the confidence interval is 2.365
[tex]MoE = 2.365\cdot \frac{23.69}{\sqrt{8} } \\\\MoE = 2.365\cdot 8.3756\\\\MoE = 19.808 \\\\[/tex]
So the required 95% confidence interval is
[tex]CI = \bar{x} \pm MoE\\\\CI = 57.89 \pm 19.808\\\\CI = 57.89 - 19.808 \: and \: 57.89 + 19.808\\\\CI = \$38.08 \: and \:\:\$77.70\\[/tex]
Therefore, we are 95% confident that the mean repair cost for the refrigerators is within the range of ($38.08, $77.70)
Please Help thank you
Answers
Answer:
Missing Number: 70,000,000
Answer:
70,000,000
Step-by-step explanation:
Because 70,000,000 + 500 + 600,000,000 = 670,000,500
Sorry if you get this wrong.
If Line segment C B. bisects ∠ACD, what additional information could be used to prove ΔABC ≅ ΔDBC using SAS? Select three options.
m∠ABC = 125° and AB ≅ DB
ΔACD is isosceles with base AD
ΔABD is isosceles with base AD
CD = 52 cm
AB = 29 cm
Answers
Answer:
Option (1)
Step-by-step explanation:
In the figure attached,
BC is the angle bisector of angle ACD.
To prove ΔABC and ΔDBC congruent by SAS property we require two sides and the angle between these sides to be congruent.
Since BC ≅ BC [Reflexive property]
∠ABC ≅ ∠CBD ≅ 125°
And sides AB ≅ BD
Both the triangles will be congruent.
Therefore, additional information required to prove ΔABC ≅ ΔDBC have been given in option (1).
Therefore, Option (1) will be the answer.
The additional information that could be used to prove ΔABC ≅ ΔDBC
using SAS are;
m∠ABC = 125° and [tex]\overline{AB}[/tex] ≅ [tex]\overline{DB}[/tex] ΔACD is isosceles, with base [tex]\overline{AD}[/tex][tex]\overline{CD}[/tex] = 52 cmReasons:
The given information are;
[tex]\overline{CB}[/tex] bisects ∠ACD
The given information from the diagram are;
[tex]\overline{AC}[/tex] = 52 cm
[tex]\overline{BD}[/tex] = 29 cm
∠CBD = 125°
Solution;
First selected option; m∠ABC = 125° and [tex]\overline{AB}[/tex] ≅ [tex]\overline{DB}[/tex]
m∠ABC = 125° and [tex]\overline{AB}[/tex] ≅ [tex]\overline{DB}[/tex][tex]\overline{CB}[/tex] ≅ [tex]\overline{CB}[/tex] (reflexive property)
ΔABC ≅ ΔDBC (SAS rule of congruency)
Second selected option; ΔACD is isosceles, with base [tex]\overline{AD}[/tex]
∠ACB ≅ ∠DCB (definition of angle bisector)
ΔACD is isosceles, with base [tex]\overline{AD}[/tex] (Additional information)[tex]\overline{CD}[/tex] ≅ [tex]\overline{AC}[/tex] (definition of isosceles triangle)
[tex]\overline{CB}[/tex] ≅ [tex]\overline{CB}[/tex] (reflexive property)
ΔABC ≅ ΔDBC (SAS rule of congruency)
Third selected option; [tex]\overline{CD}[/tex] = 52 cm
∠ACB ≅ ∠DCB (definition of angle bisector)
[tex]\overline{CD}[/tex] = 52 cm = [tex]\overline{AC}[/tex] (given) (additional information)[tex]\overline{CD}[/tex] ≅ [tex]\overline{AC}[/tex] (definition of congruency)
[tex]\overline{CB}[/tex] ≅ [tex]\overline{CB}[/tex] (reflexive property)
ΔABC ≅ ΔDBC (SAS rule of congruency)
The Side-Angle-Side, SAS, rule of congruency states that two triangles are
congruent if two sides and an included angle of one triangle are
congruent to the corresponding two sides and included angle on the other
triangle.
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Refer to the data in the table below. The entries are white blood cell counts (1000 cells/ML) and red blood cell counts (million cells / L) from male subjects examined as part of a large health study conducted by the National Center for Health Statis. tics. The data are matched, so that the first subject has a white blood cell count of 8.7 and a red blood cell count of 4.91, and so on. 1 8.7 4.91 White Subject 3 7.3 4.44 2 5.9 5.59 4 6.2 4.80 5.17 21.
Workplace Attire In a survey conducted by Opinion Research Corporation, 1000 adults were asked to identify "what is inappropriate in the workplace." of the 1000 subjects, 70% said that miniskirts were not appropriate in the workplace.
a. What is 70% of 1000?
b. Among the 1000 respondents, 550 said that shorts are unacceptable in the workplace. What percentage of respondents said that shorts are unacceptable in the workplace?
Answers
Answer:
700
55%
Step-by-step explanation:
70% of 1000 is equal to
{70/100)*1000
= 0.70*1000
= 700.
This, 70% of 1000 means 700 out of 1000 said that miniskirts were not appropriate in the workplace.
b. 550 of 1000 respondents said that shorts are unacceptable in the workplace. The percentage is
{550/1000)*100
= 0.55*100
= 55%
Thus 55% of 1000 respondents said that shorts are unacceptable in the workplace.
Frazier's total monthly expenses are $1,425. His fixed expenses amount to $750. How much are his variable expenses?
Answers
Answer:
675 = variable expenses
Step-by-step explanation:
Take the total expenses and subtract the fixed expenses to find the variable expenses
1425-750 = variable expenses
675 = variable expenses
The population of a town grows at a rate proportional to the population present at time t. The initial population of 500 increases by 5% in 10 years. What will be the population in 20 years
Answers
Answer:
551 people
Step-by-step explanation:
We have that for this type of situation the equation that models the population depending on the time is:
P (t) = I * e ^ (k * t)
Where I is the initial population, that is to say that for this case it would be:
P (t) = 500 * e ^ (k * t)
k is the constant of proportionality and t the time, they tell us that in 10 years it increases 5%, therefore the population would be:
500 + 500 * 0.05 = 525, therefore:
525 = 500 * e ^ (k * 10)
we solve:
525/500 = e ^ (k * 10)
ln 1.05 = k * 10
k = 0.00488
Now, to calculate how much the population is in 20 years it would be:
P (t) = 500 * e ^ (0.00488 * 20)
P (t) = 551.26
In other words, the population would be approximately 551 people
The state education commission wants to estimate the fraction of tenth grade students that have reading skills at or below the eighth grade level. Suppose a sample of 1537 tenth graders is drawn. Of the students sampled, 1184 read above the eighth grade level. Using the data, construct the 95% confidence interval for the population proportion of tenth graders reading at or below the eighth grade level.
Answers
Answer:
The 95% confidence interval for the population proportion of tenth graders reading at or below the eighth grade level is (0.2087, 0.2507).
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].
For this problem, we have that:
Suppose a sample of 1537 tenth graders is drawn. Of the students sampled, 1184 read above the eighth grade level. So 1537 - 1184 = 353 read at or below this level. Then
[tex]n = 1537, \pi = \frac{353}{1537} = 0.2297[/tex]
95% confidence level
So [tex]\alpha = 0.05[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].
The lower limit of this interval is:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.2297 - 1.96\sqrt{\frac{0.2297*0.7703}{1537}} = 0.2087[/tex]
The upper limit of this interval is:
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.2297 + 1.96\sqrt{\frac{0.2297*0.7703}{1537}} = 0.2507[/tex]
The 95% confidence interval for the population proportion of tenth graders reading at or below the eighth grade level is (0.2087, 0.2507).
A regular octagon has what type of symmetry?
A.
line symmetry only
B.
point symmetry only
C.
both point and line symmetry
OD.
neither point nor line symmetry
Answers
Answer:
C
Step-by-step explanation:
A regular octagon has 8 lines of symmetry.
The point of intersection of the lines of symmetry of a regular octagon is the point of symmetry.
A regular octagon has both point and line symmetry. Thus, option C is the right choice.
What are the different types of symmetry?The different types of symmetry are:
Line symmetry: A shape is symmetric about a line when the two images formed on the two sides of the line are identical.Point symmetry: A shape is symmetric about a point, when the shape is rotated about the point for 180°, gives the same shape.Rotational symmetry: A shape is rotationally symmetric, when the shape on rotation about a point, with an angle of value less than 360°, gives the same shape back.How to solve the given question?In the question, we are asked about the types of symmetry that a regular octagon has.
A regular octagon has 8 lines of symmetry about which the shape divides itself into equal halves.
These are the 4 lines joining each opposite vertex, and the other 4 are the lines passing through the midpoints of opposite sides.
A regular octagon is point symmetric as 180° rotation about the point of intersection of the lines of symmetry gives the same shape back.
Thus, we can say that a regular octagon has both point and line symmetry. Thus, option C is the right choice.
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did cherise use algebra tiles to correctly represent the product of (x-2)(x-3)
Answers
No, she did not multiply the negative integer tiles by the other negative integer tiles correctly aka B
Answer:
B
Step-by-step explanation:
edge2020
A complex electronic system is built with a certain number of backup components in its subsystems. One subsystem has eight identical components, each with a probability of 0.45 of failing in less than 1,000 hours. The sub system will operate if any four of the eight components are operating. Assume that the components operate independently. (Round your answers to four decimal places.)
Required:
Find the probability that the subsystem operates longer than 1000 hours.
Answers
Answer:
0.7396 = 73.96% probability that the subsystem operates longer than 1000 hours.
Step-by-step explanation:
For each component, there are only two possible outcomes. Either they fail in less than 1000 hours, or they do not. The components operate independently. So we use the binomial probability distribution to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
Eight components:
This means that [tex]n = 8[/tex]
Probability of 0.45 of failing in less than 1,000 hours.
So 1 - 0.45 = 0.55 probability of working for longer than 1000 hours, which means that [tex]p = 0.55[/tex]
Find the probability that the subsystem operates longer than 1000 hours.
We need at least four of the components operating. So
[tex]P(X \geq 4) = P(X = 4) + P(X = 5) + P(X = 6) + P(X = 7) + P(X = 8)[/tex]
In which
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 4) = C_{8,4}.(0.55)^{4}.(0.45)^{4} = 0.2627[/tex]
[tex]P(X = 5) = C_{8,5}.(0.55)^{5}.(0.45)^{3} = 0.2568[/tex]
[tex]P(X = 6) = C_{8,6}.(0.55)^{6}.(0.45)^{2} = 0.1569[/tex]
[tex]P(X = 7) = C_{8,7}.(0.55)^{7}.(0.45)^{1} = 0.0548[/tex]
[tex]P(X = 8) = C_{8,8}.(0.55)^{8}.(0.45)^{0} = 0.0084[/tex]
[tex]P(X \geq 4) = P(X = 4) + P(X = 5) + P(X = 6) + P(X = 7) + P(X = 8) = 0.2627 + 0.2568 + 0.1569 + 0.0548 + 0.0084 = 0.7396[/tex]
0.7396 = 73.96% probability that the subsystem operates longer than 1000 hours.
A jar contains 5 red marbles and 8 white marbles . Event A = drawing a white marble on the first draw Event B = drav drawing a red marble on the second draw If two marbles are drawn from the jar , one after the other without replacement , what is P(AandB) expressed in simplest form?
a: 3/13
b: 10/39
c: 5/12
d: 8/13
Answers
Answer:
(B) [tex]\dfrac{10}{39}[/tex]
Step-by-step explanation:
Number of red marbles = 5
Number of white marbles = 8
Total =8+5=13
Event A = drawing a white marble on the first draw
Event B = drawing a red marble on the second draw
P(A)=8/13
P(B)=5/12
Therefore:
P(A and B)
[tex]=\dfrac{8}{13} \times \dfrac{5}{12}\\\\=\dfrac{10}{39}[/tex]
Answer:
Your answer is B
Step-by-step explanation:
According to the Center for Disease Control and Prevention (CDC), up to 20% of Americans contract the influenza virus each year, and approximately 3% of all births in the United States result in birth defects each year. Consider two babies being born independently of one another. 1. The probability that both babies have birth defects is;______ a. 0.0009. b. 0.0400.c. 0.0606. d. 0.2000. 2. The probability that neither baby catches the flu in a given year is:_____ a. 0.024. b. 0.040. c. 0.230 d. 0.640. 3. Event A occurs with probability 0.1. Event B occurs with probability 0.6. If A and B are independent, then:______ a. P(A and B) = 0.06. b. P(A or B) = 0.70. c. P(A and B) = 0.70. d. P(A or B) = 0.06. 4. Event A occurs with probability 0.2. Event B occurs with probability 0.9. Event A and B:______ are disjoint cannot be independent. cannot be disjoint. are reciprocating. The center for Disease Control and Prevention reports that the rate of Chlamydia infections among American women ages 20 to 24 is 2791.5 per 100,000. Take a random sample of three American women in this age group. 5. The probability that all of them have a Chlamydia infection is:_____ a. nearly 0. b. 0.028. c. 0.084. d. 0.837 6. The probability that none of them have a Chlamydia infection is:_______ a. 0.084. b. 0.919. c. 0.972. d. nearly 1.
Answers
Answer:
(1) a. 0.0009
(2) d. 0.640
(3)
a. P(A and B) = 0.06. b. P(A or B) = 0.70.(4)Not disjoint
(5) a. nearly 0.
(6)b. 0.919
Step-by-Step Explanation:
(1)Probability of a baby being born with a birth defect =3%=0.03
The probability that both babies have birth defects=0.03 X 0.03= 0.0009.
(2)The probability of contracting the influenza virus each year = 20%=0.2
Therefore, the probability of not contracting the influenza virus =1-0.2=0.8
The probability that neither baby catches the flu in a given year:
=0.8 X 0.8
=0.64
(3)
P(A)=0.1
P(B)=0.6
P(A or B)=P(A)+P(B)=0.1 + 0.6 =0.7
P(A and B)=P(A)XP(B)=0.1 X 0.6 =0.06
(4)
P(A)=0.2
P(B)=0.9
Event A and B cannot be disjoint.
(5)
The probability of an American woman aged 20 to 24 having Chlamydia infection [tex]=\dfrac{2791.5}{100000}[/tex]
The probability that three randomly selected women in this age group have the infection
[tex]=\dfrac{2791.5}{100000} \times \dfrac{2791.5}{100000} \times \dfrac{2791.5}{100000} \\\\=0.00002175\\\approx 0[/tex]
(6)The probability of an American woman aged 20 to 24 not having Chlamydia infection [tex]=1-\dfrac{2791.5}{100000}[/tex]
The probability that three randomly selected women in this age group do not have the infection
[tex]=\left(1-\dfrac{2791.5}{100000}\right)^3\\\\=0.9186\\\approx 0.919[/tex]
What is the algebraic expression for "the sum of three times a number and seven"? A. 3 x + 7 B. 3 x + 11 x C. 3 + 7 x
Answers
Answer:
3x+7
Step-by-step explanation:
Three times a number, let x be the number and 7 so plus 7
The algebraic expression for the given phrase is 3x+7. Therefore, the correct answer is option A.
The given phrase is "the sum of three times a number and seven".
Variables and constants are combined to generate algebraic expressions using a variety of techniques. Terms comprise expressions. A term is the sum of several elements. Both numerical and algebraic (literal) factors are acceptable.
Let the unknown number be x.
Three times of a number = 3x
The number 7 is added to the obtained sum.
That is, 3x+7
So, the expression is 3x+7
The algebraic expression for the given phrase is 3x+7. Therefore, the correct answer is option A.
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Find the area of a circle with diameter, d = 5.9m. Give your answer rounded to 1 DP.
Answers
Answer: 27.34 sq. m.
Step-by-step explanation:
Area of a circle = πr^2
= π x 2.95^2
= π x 8.7025
= 27.33971
How many units of insulin are in 0.75 ML a regular U – 100 insulin
Answers
Answer:
0.75 ML of insulin contains 75 units of insulin
Step-by-step explanation:
U - 100 insulin hold 100 units of insulin per ml
This means that:
1 ML = 100 units
∴ 0.75 ML = 100 × 0.75 = 75 units
Therefore 0.75 ML of insulin contains 75 units of insulin
IM Systems assembles microcomputers from generic components. It purchases flat screen monitors from a manufacturer in Taiwan; thus, there is a long lead time of 25 days. Daily demand is normally distributed with a mean of 3.5 monitors and a standard deviation of 1.2 monitors. The company maintains a 90% customer service level. How much safety stock of monitors should IM Systems hold
Answers
Given Information:
Mean daily demand = 3.5 monitors
standard deviation daily demand = 1.2 monitors
Lead time = 25 days
customer service level = 90%
Required Information:
Safety Stock = ?
Answer:
Safety Stock = 8 monitors
Step-by-step explanation:
The safety stock of monitors that IM Systems should hold is given by
[tex]Safety \:\: Stock = z \times \sigma \times \sqrt{n}[/tex]
Where σ is the standard deviation of daily demand, n is the lead time and z is the z-score corresponding to 90% service level.
From the z-table, the z-score corresponding to 90% is found to be
z = 1.282
So the required safety stock is
[tex]Safety \:\: Stock = z \times \sigma \times \sqrt{n} \\\\Safety \:\: Stock = 1.282 \times 1.2 \times \sqrt{25} \\\\Safety \:\: Stock = 1.282 \times 1.2 \times 5 \\\\Safety \:\: Stock = 7.692\\\\[/tex]
Rounding off to nearest whole number yields
Safety Stock = 8 monitors
Therefore, IM Systems should hold 8 monitors.
Find the area of the triangle.
[?] square units
Answers
Answer:
A =54 units^2
Step-by-step explanation:
The area of a triangle is given by
A = 1/2 bh
A = 1/2 (12) (9)
A =54 units^2
Explanation: Formula for area of a triangle is 1/2(bh)
So just plug the numbers in, 1/2(12 times 9). You then get 1/2 of 108, and half of 108 is 54. Therefore, the area of this triangle is 54 square units.
Dilate line f by a scale factor of 2 with the center of dilation at the origin to create line f. Where are points A' and B' located after dilation, and how are lines fand f related?
(A) The locations of A' and B' are A' (0,4) and B' (4,0); lines f and f are parallel.
(B) The locations of A' and B' are A' (0, 2) and B' (2, 0); lines f and f are the same line.
(c) The locations of A' and B' are A' (0, 2) and B' (4, ); lines f and f intersect at point A.
(D) The locations of A' and B' are A' (0,4) and B' (2, 0); lines f and f intersect at point B.
Answers
Answer:
Option A
Step-by-step explanation:
We are given that
Scale factor=2
Center of dilation=(0,0)
Point A(0,2) and point B (2,0).
Slope of line f=[tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
Substitute the values
Slope of line f=[tex]\frac{0-2}{2-0}=-1[/tex]
Distance between A and Origin (0,0) is given by
[tex]OA=\sqrt{(0-0)^2+(0-2)^2}=2 units[/tex]
Using distance formula
[tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
OB=[tex]\sqrt{(0-2)^2+(0-0)^2}=2 units[/tex]
Length of OA'=2OA=2(2)=4 units
Length of OB'=2(OB)=2(2)=4 units
x-intercept of line f' at x=4
y-intercept of line f' at y=4
Therefore, the points A' and B' are given by
(0,4) and (4,0)
Slope of line f'=[tex]\frac{0-4}{4-0}=-1[/tex]
Slope of line f and f' are equal.Therefore, lines f and f' are parallel.
Option A is true.
What is the relative change from 6546 to 4392
Answers
Answer:
The relative change from 6546 and 4392 is 49.04
Step-by-step explanation:
If the radius of a circle is 31.2 cm, what is the approximate area if you use 3.14 for pi and the area is rounded to the nearest tenth?
Answers
Answer:
3056.6 cm^2
Step-by-step explanation:
A = (pi)r^2 = 3.14 * 31.2 cm * 31.2 cm = 3056.6 cm^2
Answer: 3056.60 sq. cm.
Step-by-step explanation:
Area of a circle = π x r^2
= 3.14 x 31.2^2
= 3056.60
A line passes through the points (–1, 10) and (3, 2). Which shows the graph of this line?
Answers
Answer:
Hope this helps!!
Answer:
the correct answer is ...... A
Step-by-step explanation:
Hope this helps
Find an equation for the plane that is tangent to the surface z equals ln (x plus y )at the point Upper P (1 comma 0 comma 0 ).
Answers
Let [tex]f(x,y,z)=z-\ln(x+y)[/tex]. The gradient of [tex]f[/tex] at the point (1, 0, 0) is the normal vector to the surface, which is also orthogonal to the tangent plane at this point.
So the tangent plane has equation
[tex]\nabla f(1,0,0)\cdot(x-1,y,z)=0[/tex]
Compute the gradient:
[tex]\nabla f(x,y,z)=\left(\dfrac{\partial f}{\partial x},\dfrac{\partial f}{\partial y},\dfrac{\partial f}{\partial z}\right)=\left(-\dfrac1{x+y},-\dfrac1{x+y},1\right)[/tex]
Evaluate the gradient at the given point:
[tex]\nabla f(1,0,0)=(-1,-1,1)[/tex]
Then the equation of the tangent plane is
[tex](-1,-1,1)\cdot(x-1,y,z)=0\implies-(x-1)-y+z=0\implies\boxed{z=x+y-1}[/tex]
What is the x-intercepts of y= -2(x-3)[2]+2?
Answers
Answer: (x,y)=(14/4,0)
Step-by-step explanation:
y=-2(x-3)(2)+2
Clear the brackets
y=-2(2x-6)+2
y=-4x+12+2
y=-4x+14
To get the x-intercept y=0
0=-4x+14
4x=14
x=14/4
(x,y)=(14/4,0)
A data set is shown in the table. The line of best fit modeling the data is y = 2.69x – 7.95.
Answers
Answer:
It’s 0.12
Step-by-step explanation:
Took test
Is (1,2), (2,3) (3,4), (4,5) a function?
Answers
Answer:
yes
Step-by-step explanation:
The domain is the set of x-values: {1, 2, 3, 4}. None of these are repeated, so this relation is a function.
HELPPP PLEASE THANKS
Answers
Answer:
ur dumb kid
Step-by-step explanation
learn it your self
find the value of x
if xfit
2(x+3)=2
Answers
Answer:
-2
Step-by-step explanation:
2(x+3)=2
Divide both sides by 2:
x+3=1
Subtract 3 from both sides:
x=-2
Hope this helps!
Answer:
x = -2
Step-by-step explanation:
2(x + 3) = 2
Apply distributive property, we have:
2*x + 2*3 = 2
or
2x + 6 = 2
Transfer 6 to the right, we have:
2x = 2 - 6
or
2x = -4
Divide both sides by 2, we have:
(2/2)x = -4/2
or
x = -2
Hope this helps!
A polynomial is factorable, but it is not a perfect square trinomial or a
difference of two squares. Can you factor the polynomial without finding the GCF?
Answers
Answer:
So in this problem, we're told that a polynomial is fact herbal and it's not a perfect square. Try no meal or a difference of two squares. Can you factor the pie? Nomi bite or polynomial without finding the G C F. So no Jacey after is allowed. So if it's not a perfect squared, try no meal. So not a perfect square. We know it's not this, and we also know it's not a difference of two squirt if it's not any of these or if it's not either of these, but we can't find the G. C F. There are three different ways we could find the factored form. You could do it by grouping where you separating the polynomial into two parts and factor them individually before combining. You could also use the sum or a difference of cubes. This is for a cubic or a um, polynomial of third degree, and you could also use fractional or negative exponents. So even if you can't find the G c f or use these methods, there are still three ways you can factor the
Step-by-step explanation:
Glad i could help!
What is the midpoint of the line segment with endpoints (1,-6) and (-3,4)?
O A. (-1,-1)
O B. (-2,-2)
O C. (-1,-2)
OD. (-2,-1)
please help
Answers
Answer:
(-1,-1)
Step-by-step explanation:
To find the x coordinate of the midpoint, add the x coordinates of the endpoint and divide by 2
(1+-3)/2 = -2/2 = -1
To find the y coordinate of the midpoint, add the y coordinates of the endpoint and divide by 2
(-6+4)/2 = -2/2 = -1
(-1,-1)