Answer:
-1
Step-by-step explanation:
Slope formula:
[tex]\frac{y2-y1}{x2-x1}[/tex]
x1 = 1
y1 = 8
x2 = -3
y2 = 12
[tex]\frac{12-8}{-3-1}[/tex]
[tex]\frac{4}{-4}[/tex] = -1
If two resistors with resistances R1 and R2 are connected in parallel, as in the figure below, then the total resistance R, measured in ohms (Ω), is given by 1/R = 1/R1 + 1/R2 . If R1 and R2 are increasing at rates of 0.3 Ω/s and 0.2 Ω/s, respectively, how fast is R changing when R1 = 60 Ω and R2 = 80 Ω? (Round your answer to three decimal places.)
The rate of change of R with time in the given equation is 0.004 ohm/s
Given parameters:
[tex]\frac{1}{R} = \frac{1}{R_1} + \frac{1}{R_2} \\\\\frac{dR_1}{dt} = 0.3 \ ohm/s\\\\\frac{dR_2}{dt} = 0.2 \ ohm/s\\\\R_1 = 60 \ ohms\\\\R_2 = 80 \ ohms[/tex]
To find:
The rate of change of R with time in the given equation.First determine the value of R from the given equation;
[tex]\frac{1}{R} = \frac{1}{R_1} + \frac{1}{R_2} \\\\\frac{1}{R} = \frac{1}{60} + \frac{1}{80} \\\\\frac{1}{R} = \frac{4 + 3}{240} \\\\\frac{1}{R} = \frac{7}{240} \\\\R = \frac{240}{7} = 34.286 \ ohms[/tex]
Finally, to determine the rate of change of R, differentiate the given equation.
[tex]\frac{-1}{R^2} \frac{dR}{dt} = \frac{-1}{R_1^2} \frac{dR_1}{dt} - \frac{1}{R_2^2} \frac{dR_2}{dt} \\\\\frac{1}{R^2} \frac{dR}{dt} = \frac{1}{R_1^2} \frac{dR_1}{dt} + \frac{1}{R_2^2} \frac{dR_2}{dt}\\\\\frac{dR}{dt} = R^2(\frac{1}{R_1^2} \frac{dR_1}{dt} + \frac{1}{R_2^2} \frac{dR_2}{dt})[/tex]
[tex]\frac{dR}{dt} = 34.286(\frac{1}{(60)^2} \times 0.3 \ \ \ + \ \ \ \frac{1}{(80)^2} \times 0.2)\\\\\frac{dR}{dt} = 34.286(8.333 \times 10^{-5} \ \ \ + \ \ \ 3.125 \times 10^{-5})\\\\\frac{dR}{dt} = 34.286(11.458 \times 10^{-5})\\\\\frac{dR}{dt} = 0.00393\\\\\frac{dR}{dt} \approx 0.004 \ ohm/s[/tex]
Thus, from the given equation the rate of change of R with time is 0.004 ohm/s
Learn more here: https://brainly.com/question/14796851
Answer:
the verified answer is wrong.
Step-by-step explanation:
OP forgot to square R (34.286)
Please help 20 points. I will give Brainly to who ever get it right.
The range is the an interval on the y-axis where the function is defined.
You can see that your function is y-wise going all the way down to negative infinity but then stops and continues the path along 2 on the upper bound.
The inequality describing the interval is thusly B,
[tex]-\infty\lt y\lt2[/tex]
Hope this helps :)
If 64 > x^3, then the greatest possible integer value
of x is
(a) 1
(c) 3
(b) 2
(d) 4
Answer:
C
Step-by-step explanation:
64>x^3, plugging in x=3, we have 64>27 which is TRUE
Suppose y varies inversely with x, and y = 32 when x = 4. What is the value of y when x = 8?
a. 1/8
b. 64
c. 16
d. 8
NO LINKS OR ANSWERING QUESTIONS YOU DON'T KNOW!!!
Answer:
16
Step-by-step explanation:
Inverse variation is of the form
xy = k where k is a constant
x=4 and y = 32
4*32 = k
128 = k
xy = 128
Let x = 8
8y = 128
Divide each side by 8
8y/8 = 128/8
y =16
What is the arithmetic mean of the following numbers?
3, 5, 6, 7, 9,6,8
Answer:
6.2
Step-by-step explanation:
to fine the mean of numbers
1) add the given no.........3+5+6+7+9+6+8 which is 44
2)divide the result by the amount of the numbers....44/7
the answer will be 6.285.....
how many years will it take for a sum of money to double at 10% compounded annually
Answer:
t=7.27 years
Step-by-step explanation:
Let the money be p and t will be the number of years that will be needed for the money to get double.
ATQ, 2p=p*(1+0.1)^t
2=(1.1)^t
log(2)/log(1.1)=t, t=7.27
A 100.0 m long polymer cable of uniform circular cross section and of diameter 0.4cm has a mass of 1885.0 gm. What is the mass density, of the polymer in kg/m3?
The mass density in kg/m3 will be - 15 x [tex]10^{-2}[/tex] Kg/m3.
We have a 100.0 m long polymer cable of uniform circular cross section and of diameter 0.4cm has a mass of 1885.0 gm.
We have to determine its mass density in kg/m3.
What is Mass density ?The amount of mass per unit volume present in the body is called its mass density.
According to question, we have -
Length of polymer cable = 100.0 m
diameter of polymer cable = 0.4 cm = 0.004 m
Therefore, its radius = 0.002 m
The mass density of the wire will be -
[tex]\rho =\frac{m}{\pi r^{2} l}[/tex]
[tex]\rho[/tex] = [tex]\frac{1885}{3.14 \times0.002 \times 0.002 \times 100 }[/tex]
[tex]\rho = \frac{1885}{0.001256}[/tex] = 1500796.1 g/m3
1 Kg = 1000g
1g = 1/1000kg
1500796.1g = 1500.7 Kg = 15 x [tex]10^{-2}[/tex] Kg
Therefore, mass density = 15 x [tex]10^{-2}[/tex] Kg/m3
Hence, the mass density in kg/m3 will be - 15 x [tex]10^{-2}[/tex] Kg/m3.
To solve more questions on mass density, visit the link below -
https://brainly.com/question/4893600
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Nick needs one more class to complete his schedule. There are 5 writing classes, 3 history classes, and 4 mathematics classes that can fit into his schedule. If Nick chooses a class at random, what is the probability that he chooses a history class? Give your answer as a fraction.
Answer:
1/4
Step-by-step explanation:
Probability = 3/(5+3+4)
= 3/12 or 1/4
Solve for h.
H+6/4= 5
If Q(x) = x2 – 2 – 2, find Q(-3).
Answer: A (10)
Step-by-step explanation:
Plug in Q(-3) into formula x^2-x-2
(-3)^2-(-3)-2= 9+3-2
=10
A biologist was interested in determining whether sunflower seedlings treated with and an extract from Vinca minor roots resulted in a lower average height of sunflower seedlings that the standard height of 15.7 cm. The biologist treated a random sample of 33 seedlings with the extract and subsequently measured the height of those seedlings. At the 0.01 significance level, is there evidence that the true average height of the seedlings treated with an extract from Vinca minor roots is less than 15.7 cm?
Height
15.5
15.8
15.7
15.1
15.1
15.5
15.2
15.7
15.8
15.4
16.2
15.5
16.2
15.5
15.4
16.3
14.9
15.3
15.1
16.1
15.3
15.4
15.1
15.3
14.6
15.1
15.0
15.3
15.8
15.5
14.8
15.2
14.8
a. State the null and alternative hypotheses.
b. Report the value of the test statistic. Round answer to 2 decimal places. (Either calculate or use software such as minitab)
c. Using the p-value, do you reject the null hypothesis or fail to reject the null hypothesis? Explain your decision.
d. Based on your decision in part (c), write a conclusion within the context of the problem.
Answer:
Kindly check explanation
Step-by-step explanation:
H0 : μ = 15.7
H1 : μ < 15.7
This is a one sample t test :
Test statistic = (xbar - μ) ÷ (s/√(n))
n = sample size = 33
Using calculator :
The sample mean, xbar = 15.41
The sample standard deviation, s = 0.419
Test statistic = (15.41 - 15.70) ÷ (0.419/√(33))
Test statistic = - 3.976
Using the Pvalue calculator :
Degree of freedom, df = n - 1 ; 33 - 1 = 32
Pvalue(-3.976, 32) = 0.000187
Decison region :
Reject H0 if Pvalue < α
Since Pvalue < α ; we reject H0
There is significant evidence to conclude that the true average height of the seedlings treated with an extract from Vinca minor roots is less than 15.7 cm.
Given f (x) = 4x - 3,g(2) = x3 + 2x
Find (f - g) (4)
A professor knows that her statistics students' final exam scores have a mean of 79 and a standard deviation of 11.3. In his class, an "A" is any exam score of 90 or higher. This quarter she has 22 students in her class. What is the probability that 6 students or more will score an "A" on the final exam?
prob =
0.1449 = 14.49% probability that 6 students or more will score an "A" on the final exam.
---------------
For each student, there are only two possible outcomes. Either they score an A, or they do not. The probability of a student scoring an A is independent of any other student, which means that the binomial probability distribution is used to solve this question.
Additionally, to find the proportion of students who scored an A, the normal distribution is used.
----------------
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 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 a success.
----------------
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set with mean and standard deviation , the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
----------------
Proportion of students that scored an A:
Scores have a mean of 79 and a standard deviation of 11.3, which means that [tex]\mu = 79, \sigma = 11.3[/tex]
Scores of 90 or higher are graded an A, which means that the proportion is 1 subtracted by the p-value of Z when X = 90, so:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{90 - 79}{11.3}[/tex]
[tex]Z = 0.97[/tex]
[tex]Z = 0.97[/tex] has a p-value of 0.8340.
1 - 0.8340 = 0.166
The proportion of students that scored an A is 0.166.
----------------
Probability that 6 students or more will score an "A" on the final exam:
Binomial distribution.
22 students, which means that [tex]n = 22[/tex]
The proportion of students that scored an A is 0.166, which means that [tex]p = 0.166[/tex]
The probability is:
[tex]P(X \geq 6) = 1 - P(X < 6)[/tex]
In which
[tex]P(X < 6) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5)[/tex]
Then
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{22,0}.(0.166)^{0}.(0.834)^{22} = 0.0184[/tex]
[tex]P(X = 1) = C_{22,1}.(0.166)^{1}.(0.834)^{21} = 0.0807[/tex]
[tex]P(X = 2) = C_{22,2}.(0.166)^{2}.(0.834)^{20} = 0.1687[/tex]
[tex]P(X = 3) = C_{22,3}.(0.166)^{3}.(0.834)^{19} = 0.2239[/tex]
[tex]P(X = 4) = C_{22,4}.(0.166)^{4}.(0.834)^{18} = 0.2117[/tex]
[tex]P(X = 5) = C_{22,5}.(0.166)^{5}.(0.834)^{17} = 0.1517[/tex]
Then
[tex]P(X < 6) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) = 0.0184 + 0.0807 + 0.1687 + 0.2239 + 0.2117 + 0.1517 = 0.8551[/tex]
[tex]P(X \geq 6) = 1 - P(X < 6) = 1 - 0.8551 = 0.1449[/tex]
Thus
0.1449 = 14.49% probability that 6 students or more will score an "A" on the final exam.
For a problem that used the normal distribution, you can check https://brainly.com/question/15181104, and for a problem that used the binomial distribution, you can check https://brainly.com/question/15557838
What is the solution to the system of equations?
y = 2/3x+3
x=-2
Answer:
solution (-2, 5/3 ).
Step-by-step explanation:
Given : y = + 3 and x = –2.
To find : What is the solution to the system of equations.
Solution : We have given that y = + 3 ------equation (1)
and x = –2. ------equation (2)
On plugging the x = -2 in equation (1)
y = + 3
y = + 3 .
On simplification we get ,
y = .
Therefore, solution (-2, 5/3 ).
15 = g + 8 pllllllllllssssss help
Find the product of 2x 3 xy and 5
Answer:
30x²y
Step-by-step explanation:
2x × 3xy × 5
= 2 × 3 × 5 × x × xy
= 30x²y
how do you change 79/8 to a decimal
Answer:
Divide 79 by 8
Step-by-step explanation:
79/8
= 9.875
Use AABC to find the value of sin B.
Answer:
35/37
Step-by-step explanation:
sin(B)=(AC)/(AB) = 35/37
Each side of a regular polygon is 3.2 cm in length. The perimeter of the polygon is 19.2 cm. How many sides does the polygon have? What is the name of the polygon?
Answer:
The polygon consists of 6 sides and the given polygon is a regular hexagon.
Step-by-step explanation:
The definition of perimeter is the total measure of the side lengths of a polygon. If the polygon said is regular, it means the polygon has equal sides and equal angles.
So the perimeter of a regular polygon is given by the formula:
P = (length of one side) x (number of sides)
In this case, the perimeter of the polygon is 19.2 cm and one side is equal to 3.2 cm.
DIVIDE (use the formula but in division to maintain a proportonal relationship):
19.2 ÷ 3.2 = 6
You could alsk check if its correct using the formula:
19.2 = 3.2 x 6 (TRUE)
A 6 sided regular polygon is known as a HEXAGON.
Hope this helps!
What is the height of a room which is 8m long, 6m wide and contains 144 meters cube of air?
Please answer this and show the work/explain for me
2/7m - 1/7 = 3/14
The graph of the equation y = 3x + 1 is shown below.
If the graph is reflected across the y-axis, what will be the equation of the new graph?
Answer:
I think its B. Y = -3x + 1
Step-by-step explanation:
Sorry if this is wrong.
7 10/3 x 3 1/10= Can you explain step by step to me
Thanks
Answer:
710/3×31/10
[tex]reduce \: fraction \: to \: the \: lowest \\ term \: by \: canceling \: the \: greatest \\ common \: factor \: \\ = \frac{71 \times 31}{3} \\ calculate \: the \: first \: two \: terms \\ = \frac{2201}{3} \: is \: the \: answer[/tex]
For Americans using library services, the American Library Association claims that at most 67% of patrons borrow books. The library director in Owensboro, Kentucky feels this is not true, so she asked a local college statistic class to conduct a survey. The class randomly selected 100 patrons and found that 82 borrowed books. Did the class demonstrate that the percentage was higher in Owensboro, KY? Use α = 0.01 level of significance. What is the possible proportion of patrons that do borrow books from the Owensboro Library?
Answer:
The p-value of the test is 0.0007 < 0.01, which means that the class demonstrates that the percentage was higher in Owensboro, KY.
The possible proportion of patrons that do borrow books from the Owensboro Library is 0.82.
Step-by-step explanation:
For Americans using library services, the American Library Association claims that at most 67% of patrons borrow books. Test if the proportion is higher in Owensboro, KY.
At the null hypothesis, we test if the proportion is of at most 0.67, that is:
[tex]H_0: p \leq 0.67[/tex]
At the alternative hypothesis, we test if the proportion is of more than 0.67, that is:
[tex]H_1: p > 0.67[/tex]
The test statistic is:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.
0.67 is tested at the null hypothesis:
This means that [tex]\mu = 0.67, \sigma = \sqrt{0.67*0.33}[/tex]
The class randomly selected 100 patrons and found that 82 borrowed books.
This means that [tex]n = 100, X = \frac{82}{100} = 0.82[/tex]
Value of the test statistic:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
[tex]z = \frac{0.82 - 0.67}{\frac{\sqrt{0.67*0.33}}{\sqrt{100}}}[/tex]
[tex]z = 3.19[/tex]
P-value of the test and decision:
The p-value of the test is the probability of a finding a sample proportion of 0.82 or above, which is 1 subtracted by the p-value of z = 3.19.
Looking at the z-table, z = 3.19 has a p-value of 0.9993.
1 - 0.9993 = 0.0007
The p-value of the test is 0.0007 < 0.01, which means that the class demonstrates that the percentage was higher in Owensboro, KY.
What is the possible proportion of patrons that do borrow books from the Owensboro Library?
The sample proportion of 0.82.
What is
88x3-7+198-34x15+76-126=
-105
Multiply first, then subtract, then add.
Answer: the answer would be -105.
What is the order of rotational symmetry for the figure?
A. 4 or more
B. 2
C. 1
D. 3
9514 1404 393
Answer:
C. 1
Step-by-step explanation:
The only rotation that maps the figure to itself is rotation by 360°. The rotational order is 1.
Four friends go to the movies. How many different ways can they sit in a row?
Answer:
120 ways
..................
Answer:
24
Step-by-step explanation:
4 friends
1st seat: 4 different people could sit here
Now there are 3 friends left
2nd seat: 3 different people could sit here
Now there are 2 friends left
3rd seat: 2 different people could sit here
Now there are 1 friends left
4th seat: 1 different people could sit here
4*3*2*1
24 ways
Find f(3) given f(x) = -3x3 + 2x2 + 24
Answer:
-39
Step-by-step explanation:
Plzzz I’m giving a away 25 points
Answer:
sin ß = opposite / hypotenuse
sin45° = x / 4√2
Cross multiply
x = sin 45° × 4√2
x = √2/2 × 4√2
x = 4 × √2 ×√2 / 2
x = 4 × 2 / 2
x = 8 / 2
x = 4
The number of people attending graduate school at a university may be
modeled by the quadratic regression equation y = 8x2 - 40x+6, where x
represents the year. Based on the regression equation, which year is the best
prediction for when 1206 people will attend graduate school?
A. Year 15
B. Year 18
C. Year 24
D. Year 20
Answer:
15 years
Step-by-step explanation:
Given the quadratic regression model:
y = 8x² - 40x+6 ; where
y = Number of people attending graduate school ;
x = number of years
The value of x when y = 1206
The equation becomes :
1206 = 8x² - 40x+6
1206 - 6 = 8x² - 40x
1200 = 8x² - 40x
Divide through by 8
150 = x² - 5x
x² - 5x - 150 = 0
x² - 15x + 10x - 150 = 0
x(x - 15) + 10(x - 15)
x - 15 = 0 or x + 10 = 0
x = 15 or x = - 10
Number of years can't be negative,
Hence, x = 15 years
