Answer:
[tex]\ln (y) = 0.210x-2.601[/tex]
Step-by-step explanation:
Given table:
[tex]\begin{array}{|c|c|}\cline{1-2} \sf Length & \sf Diameter \\x & y\\\cline{1-2} \vphantom{\dfrac12} 2 & 0.113\\\cline{1-2} \vphantom{\dfrac12} 3& 0.151\\\cline{1-2} \vphantom{\dfrac12} 4& 0.192\\\cline{1-2} \vphantom{\dfrac12} 5& 0.222\\\cline{1-2} \vphantom{\dfrac12} 6& 0.262\\\cline{1-2} \end{array}[/tex]
To convert y = abˣ to linear form, take natural logs of both sides and rearrange:
[tex]\begin{aligned}y=ab^x \implies \ln y &= \ln ab^x\\\implies \ln y &= \ln a + \ln b^x\\\implies \ln y &= \ln a + x \ln b\\\implies \ln y &=x \ln b+ \ln a\end{aligned}[/tex]
This is in the straight-line form y = mx + c.
Substitute the first and last values of x and y from the table into the natural log formula:
[tex]\ln 0.113 = 2 \ln b+\ln a[/tex][tex]\ln 0.262 = 6 \ln b+\ln a[/tex]Subtract the first equation from the second equation to eliminate ln(a);
[tex]\implies \ln 0.262 - \ln 0.113 = 6 \ln b - 2 \ln b[/tex]
[tex]\implies \ln 0.262 - \ln 0.113 = 4 \ln b[/tex]
Apply the quotient log law:
[tex]\implies \ln \dfrac{0.262}{0.113} = 4\ln b[/tex]
Rearrange and solve for ln(b):
[tex]\implies \ln b = \dfrac{1}{4}\ln \dfrac{0.262}{0.113}[/tex]
[tex]\implies \ln b = 0.210\; \sf (3\;d.p.)[/tex]
Substitute the found value of ln(b) into one of the equations and solve for ln(a):
[tex]\implies \ln 0.262 = 6 \cdot \dfrac{1}{4}\ln \dfrac{0.262}{0.113}+\ln a[/tex]
[tex]\implies \ln a=\ln 0.262 -\dfrac{6}{4}\ln \dfrac{0.262}{0.113}[/tex]
[tex]\implies \ln a = -2.601\; \sf (3\;d.p.)[/tex]
Substitute the found values of ln(a) and ln(b) into the formula to create an equation for ln(y):
[tex]\boxed{\ln (y) = 0.210x-2.601}[/tex]
Hannah signs on a $148,500 mortgage at a 4.5% annual interest rate for 20 years. This results in a monthly payment is
$938.48. If only the minimum payment is made in month one, how much of the first payment goes toward reducing her
balance?
First let's find the amount of interest she paid in month 1, then find the amount toward reducing the balance.
Round to the nearest cent.
Answer:
Interest in one month= 556.88
Her balance is reduced by= 381.6
Step-by-step explanation:
Let f(x) = cxe−x2 if x ≥ 0 and f(x) = 0 if x < 0.
(a) For what value of c is f a probability density function?
(b) For that value of c, find P(1 < X < 3).
(a) If f(x) is to be a proper density function, then its integral over the given support must evaulate to 1:
[tex]\displaystyle\int_{-\infty}^\infty f(x)\,\mathrm dx = \int_0^\infty cxe^{-x^2}\,\mathrm dx=1[/tex]
For the integral, substitute u = x ² and du = 2x dx. Then as x → 0, u → 0; as x → ∞, u → ∞:
[tex]\displaystyle\frac12\int_0^\infty ce^{-u}\,\mathrm du=\frac c2\left(\lim_{u\to\infty}(-e^{-u})-(-1)\right)=1[/tex]
which reduces to
c / 2 (0 + 1) = 1 → c = 2
(b) Find the probability P(1 < X < 3) by integrating the density function over [1, 3] (I'll omit the steps because it's the same process as in (a)):
[tex]\displaystyle\int_1^3 2xe^{-x^2}\,\mathrm dx = \boxed{\frac{e^8-1}{e^9}} \approx 0.3678[/tex]
A basket contains 5 purple pencils and 9 brown pencils. If two pencils are picked at random
one after the other without replacement, then what is the probability that both the pencils
are purple?
5/182
10/91
2/91
9/182
please state reasoning as to why it is what ever answer you provide..
Answer:
sorry id.k this im so sorry
Step-by-step explanation:
Answer:
10/91
Step-by-step explanation:
3
Delete
12
4
EVAN
8
15
Drag one value into each box to
make each expression equivalent
to 4x + 20.
20
(x + 5)
x + 3x + 5+
x + 40
2
7x -x + 25 - 5
Answer:
the answer to the problem is 4,15,8,3
Please help me thank youuuu!
Find two numbers which add to give 0 and multiply to give -16
Answer:
4 and -4
Step-by-step explanation:
i don’t need to show work but it would help :)
Answer:
d. (73.9 in^2)
Step-by-step explanation:
I suppose that 9.7 in is the diameter.
R=D/2=9.7/2=4.8in
A=π*(R^2)=3.14*(4.8)^2=73.9 in^2
Which algebraic expression best represents the following verbal
description: Four more than the price, p?
Answer: I think it is 4+$p
Step-by-step explanation:
67 1/2% of what number of people is 135 people
Answer:
go to omnicalculator.com they have all sorts of calculators including one called a percent changer calculator
Step-by-step explanation:
A scale drawing of a rectangle is made by using a scale factor of StartFraction 5 over 8 EndFraction. The original and the scale drawing are shown below. A rectangle has a length of 18 inches and width of 12 inches. [Not drawn to scale] Which method can be used to find the dimensions of the original rectangle? 18 minus StartFraction 5 over 8 EndFraction = 17 and StartFraction 3 over 8 EndFraction inches and 12 minus StartFraction 5 over 8 EndFraction = 11 and StartFraction 3 over 8 EndFraction inches StartFraction 5 over 8 EndFraction divided by 18 = StartFraction 5 over 144 EndFraction inches and StartFraction 5 over 8 EndFraction divided by 12 = StartFraction 5 over 96 EndFraction inches 18 times StartFraction 5 over 8 EndFraction = 11 and one-fourth inches and 12 times StartFraction 5 over 8 EndFraction = 7 and one-half inches 18 divided by StartFraction 5 over 8 EndFraction = 28 and four-fifths inches and 12 divided by StartFraction 5 over 8 EndFraction = 19 and one-fifth inches
Answer:
its dddddddddddddddddddddddd
Step-by-step explanation:
The method that can be used to determine the dimensions of the orginal rectangle is multiply the length and the width of the scale drawing of rectangle by 8/5.
What is a scale drawing?
A scale drawing is smalleer image of a bigger diagram.The scale drawing is usually reduced at a constant dimension
The orginal dimensions can be determined by multiplyinf the dimensions of the scale drawing by 8/5
To learn more about scale drawings, please check: https://brainly.com/question/26388230
Find the ratio of the areas.
9514 1404 393
Answer:
3 -2√2
Step-by-step explanation:
For a regular octagon of side length s, the "flat-to-flat" dimension across the center is s(1+√2). The flat-to-flat dimension of the shaded center octagon is simply s. The ratio of areas is the square of the ratio of linear dimensions, so we have ...
small area / large area = (1/(1+√2))^2 = 1/(3+2√2)
small area/large area = 3 -2√2
_____
The attachment shows octagons after the fashion described here. The side length of the larger one is 2 units. The numbers inside are the areas. They have the ratio shown above.
What is the measure of angle X? Enter your answer as a decimal in the box. (Units are degrees - please only enter numbers in the box.) Round only your final answer to the nearest hundredth.
Answer:
81.20
Step-by-step explanation:
I took the test and got it right
Can you plz help me by solving the equation and showing how you got the answer
Answer:80
Step-by-step explanation: It is 80
A certain type of legal proceeding has three possible outcomes: in favor of party A, in favor of party B, or not in favor of either party. The outcomes are expected to be 40 percent, 20 percent, and 40 percent, respectively. A random sample of 40 cases is selected from a certain judge to investigate whether the judgeâs outcomes are consistent with the expected outcomes. A chi-square goodness-of-fit test is conducted, and the value of the chi-square test statistic is Ï2=9.19 with a corresponding pâvalue of 0.01. Assuming the conditions for inference were met, which of the following is the correct interpretation of the pâvalue?
a. There is a 1 percent chance that the company's claim is correct.
b. If the null hypothesis is true, there is a 1 percent chance that the company's claim is correct.
c. If the null hypothesis is true, there is a 1 percent chance of obtaining a chi-square value of 9.19.
d. If the null hypothesis is true, there is a 1 percent chance of obtaining a chi-square value of at least 9.19.
e. There is a 1 percent chance of obtaining a chi-square value of at least 9.19.
The basically it tells us the chances of the claim being true
If we assume the null hypothesis is correct.
What is the method of chi-square test?The Chi-Square Test of Independence determines whether there is an association between categorical variables.
We have given that,
The outcomes are expected to be 40 percent, 20 percent, and 40 percent, respectively.
If the null hypothesis is true, there is a 1 percent chance that the company’s claim is correct.
The p-value tells us the likeliness of our data occurring under the null hypothesis.
Therefore ,basically it tells us the chances of the claim being true
If we assume the null hypothesis is correct.
To learn more about the chi-square method visit:
https://brainly.com/question/4543358
Find the greatest common factor of 9n3 and 8n4.
Answer:
9 and 3 GCF is 3
8 and 4 GCF is 4
the GCF of 8,3,4,9 = 1
Step-by-step explanation:
Help I need answers now
Answer:
The Answer in Exact Form:
-3/22
In Decimal Form:
-0.136
Step-by-step explanation:
-[tex]\frac{3}{2}[/tex]÷5[tex]\frac{1}{2}[/tex]=-3/22
What is the measure of A?
А [?] degrees
B 87
C 35
Answer:
B 87
Step-by-step explanation:
Answer: 58
explanation: Acellus
answer.......pls NOW
Answer:
3. 224 cm3
4. 35 cm3
5. 60 cm3
Step-by-step explanation:
To find the volume you need to multiple the base times the height times the length.
You spin a spinner that is equally divided into 7 parts, and then you spin it again. 1 part is red, 2 parts are white, 3 parts are yellow and 1 part is black.
What is the probability of the spinner stopping on a white section on the first spin and then a red section on the second spin?
Answer:
[tex] \frac{2}{7} \: and \: \frac{1}{7} [/tex]
Express using algebra A stick l feet long is broken into 2 parts one of which is twice as long as the other. How long is the shorter piece
Answer:
20 is the longer piece, and 9 is the shorter piece
Step-by-step explanation:
9*2=18
18+2=20
20+9
What’s the slope ?
Please help I’ll mark u as Brainliest
9514 1404 393
Answer:
5/2 = 2.5
Step-by-step explanation:
The slope is given by ...
m = (y2 -y1)/(x2 -x1)
Using the first two lines in the table, this is ...
m = (10 -5)/(2 -0) = 5/2
The slope of the line is 5/2.
__
As a decimal, that is 2.5.
The volume of this rectangular prism is 240 cubic centimeters. What is the surface area?
2a^2 + 7 + 5b^3
when a = 2 and b= 3
Answer:
150
Step-by-step explanation:
2(2^2)+7+5(3^3)
2(4)+7+5(27)
8 + 7 + 135= 150
Help me I need to finish this today
Answer:
24 glasses
Step-by-step explanation:
Factor and solve 121r^2-64t^2
Answer:
(11r + 8t)(11r - 8t)
Step-by-step explanation:
difference of two squares
Write the form of the partial fraction decomposition of the rational expression.
11x - 10/ (x-6)(x+7)
Answer:
x+7x2+3x+2=6x+1+−5x+2
Step-by-step explanation:
Simplify the expression: x+7x2+3x+2=x+7(x+1)(x+2)
The form of the partial fraction decomposition is
x+7(x+1)(x+2)=Ax+1+Bx+2
Write the right-hand side as a single fraction:
x+7(x+1)(x+2)=(x+1)B+(x+2)A(x+1)(x+2)
The denominators are equal, so we require the equality of the numerators:
x+7=(x+1)B+(x+2)A
Expand the right-hand side:
x+7=xA+xB+2A+B
Collect up the like terms:
x+7=x(A+B)+2A+B
The coefficients near the like terms should be equal, so the following system is obtained:
{A+B=12A+B=7
Solving it (for steps, see system of equations calculator), we get that A=6, B=−5
Therefore,
x+7(x+1)(x+2)=6x+1+−5x+2
Answer: x+7x2+3x+2=6x+1+−5x+2
The given spinner has equal sectors. If you spin the spinner, what is the sample space?
A. {3}
B. {1, 2, 3, 4
C. {1, 2, 3, 4, 5)
Jayda is watching a movie that lasts 1 hour and 37 minutes. She has watched 52 minutes so far. How many minutes are left in the movie? *
Answer:
45 minutes
Step-by-step explanation:
97-52 = 45
What is the ratio of the wavelengths of these two notes?
a. 5 to 4
b. 3 to 2
c. 6 to 5
d. 2 to 1
Answer:
d
Step-by-step explanation:
edge 2021
The ratio of the wavelength of the red note and blue note is 2 : 1.
What is wavelength?Wavelength is the distance between two consecutive crest and troughs.
Mathematically, we can write wavelength as -
λ = c/ν
where -
λ : wavelength
ν : frequency
Given are the two notes as shown in the image.
For the red note, the distance between the consecutive crests is twice to that of the distance between the consecutive crests in case of blue note. We can write the ratio of the wavelengths as -
λ(R)/λ(B) = 2/1
Therefore, the ratio of the wavelength of the red note and blue note is 2 : 1.
To solve more questions on wavelengths, visit the link-
https://brainly.com/question/29213222
#SPJ2
help me please i will give you brainliest
Answer:
its b!
please brainliest