In complete two or more sentences, determine the appropriate model for the given data and explain how you made your decision. (1,0), (2,1.5), (5,2.5), (8,3)
Answers
see if this helps
Answer:
The model for the given point is [tex]y=1.4004\ln (x) + 0.2158[/tex]
Step-by-step explanation:
Given : Data (1,0), (2,1.5), (5,2.5), (8,3).
To find : Determine the appropriate model for the given data?
Solution :
Data (1,0), (2,1.5), (5,2.5), (8,3).
We plot the data points on the graph and get the best fit line using trend line of the function.
Using regression calculator,
The function has a logarithmic behavior so the best line which represent the data is given by
[tex]y=1.4004\ln (x) + 0.2158[/tex]
and the value of R² i.e. correlation coefficient is given by
[tex]R^2=0.9691[/tex] which is approximately equal to 1 gives you the best fit line.
Therefore, The model for the given point is [tex]y=1.4004\ln (x) + 0.2158[/tex]
Refer the attached figure below.
Related Questions
how do you solve 5y+26=4y-56?
Answers
5y+26=4y-56
Subtract 26 from both sides
5y=4y-82
Subtract 4y from both sides
y= -82
Check:
Substitute the answer in equation
5y+26=4y-56
5(-82)+26=4(-82)-56
-410+26= -328-56
-384 = -384
Hope this helps! :)
Alexa knock down 70 bowling pins in 10 frames. in each frame, alexa nocked down the same number of pins. how many pins did Alexa knock down in each frame?
Answers
PLZ HELP :,( Select all that apply. Which quadrilaterals always have four congruent sides? trapezoid rhombus parallelogram square
Answers
Answer:
square is the answer
What is the area of this figure?
Enter your answer in the box.
Answers
S=S1+S2, where S1 is area of the parallelogram, S2 is area of the triangle.
S=9*5+0.5*8*9=45+32=77 m².
Answer: 77 m.²
is 1.5 miles greater than 2500 yards
Answers
1.5 miles > 2500 yards
1 mile = 5280 feet
1 yard = 3 feet
1.5 miles = 7920 feet
2500 yards = 7500 feet
7920 feet > 7500 feet
Hope I helped!
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According to our customary units of miles, 1 mile is equal to 5,280 feet - and 3 feet is a yard. That means, we have to divide 5,280 by 3 to figure out how many yards are in a mile:
5280/3 = 1760
That means that one mile is 1760 yards. But we're not finished yet. It says 1/5 miles, not one mile. Therefore, we take one half of the total distance in yards of a mile and add it to that 1760, because it's 1.5, or 1-and-a-half. Which, in technical terms means "1-plus-a-half".
We have:
1760 + 1760/2 = 1760 + 880 = 2640
Therefore, 1/5 miles, since it's 2640 yards, is greater than the 2500 yards specified in the question.
Hope this helps!
Find the exact area of a circle having the given circumference. 8 pi
Answers
= 5.09
Answer: [tex]16\pi\ \text{ units}^2[/tex]
Step-by-step explanation:
We know that the circumference of a circle is given by :-
[tex]\text{Circumference}=2\pi r[/tex], where r is the radius of the circle.
Given : The circumference of a circle = [tex]8\pi[/tex]
Then , the circumference of a circle will be :-
[tex]8\pi=2\pi r\\\\\Rightarrow\ r=4\text{ units}[/tex]
Now, the area of circle is given by :-
[tex]A=\pi r^2\\\\\Rightarrow\ A=\pi(4)^2\\\\\Rightarrow\ A =16\pi\ \text{ units}^2[/tex]
Using the transformation T: (x, y) (x + 2, y + 1), find the distance named.
Find the distance AA'
Answers
distance(AA') = √(2^2 + 1^2)
= √5
= 2.24
answer
Distance AA' = √5 or = 2.24
Answer with Step-by-step explanation:
As we can see from the graph:
A=(0,0) and A'=(2,1)
Distance between (x1,y1) and (x2,y2) is given by:
[tex]\sqrt{{(x1-x2)}^2+{(y1-y2)}^2}[/tex]
Here (x1,y1)=(0,0) and (x2,y2)=(2,1)
Hence, distance between A and A' is:
[tex]\sqrt{{(0-2)}^2+{(0-1)}^2}[/tex]
= [tex]\sqrt{4+1}[/tex]
= [tex]\sqrt{5}[/tex]
Hence, distance AA'=√5
Find the constant of proportionality k as a fraction in simplest form. Then enter an equation for the relationship between x and y.
x 12 24 36 48
y 2 4 6 8
The constant of proportionality, k =
The equation is y =
Answers
The equation for y is, y=1/6x
The calculated value of the constant of proportionality that relates the variable y, to x, is 1/6
How to determine the constant of proportionalityFrom the question, we have the following parameters that can be used in our computation:
x 12 24 36 48
y 2 4 6 8
The constant of proportionality (k) is calculated as
k = y/x
So, we have
k = 2/12
Evaluate
k = 1/6
Hence, the constant of proportionality is 1/6
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Which statement about BQ←→ is correct?
BQ←→ is a tangent line because m∠ABQ=90°.
BQ←→ is a tangent line because △ABQ is not a right triangle.
BQ←→ is not a tangent line because ∠BAQ is an acute angle.
BQ←→ is not a tangent line because ∠BQA is an acute angle.
Answers
We have a circle A and a line segment BQ is passing through the circle A such that it forms a triangle ABQ.
From the diagram, we have some information about the angles of triangle ΔABQ as follows :-
angle QAB = 36 degrees and angle BAQ = 54 degrees.
We know about the Triangle Sum theorem which states "The sum of all interior angles of any triangle is 180 degrees".
We can use this theorem to find the third angle of the triangle ΔABQ.
∠ABQ + ∠BQA + ∠QAB = 180 degrees
∠ABQ + 54° + 36° = 180°
∠ABQ + 90° = 180°
∠ABQ = 180° - 90°
∠ABQ = 90 degrees
If any line makes a right angle with the radius of any circle, then this line must be a tangent to that circle.
So, BQ would be a tangent line because angle ∠ABQ = 90 degrees. Hence, option A is correct.
WILL GIVE BRAINLIEST TO PERSON THAT IS CORRECT!!!!
Hana rented a car for a week for $200 plus $0.25 per mile. After driving for one week, she owed the rental company $362.50.
Which equation represents the amount she paid to the rental company, and how far did Hana drive during the week?
$200 + $0.25m = $362.50; m = 650 miles
$200 + $0.50m = $250; m = 140 miles
$200 - $0.25m = $725; m = 2,250 miles
$200 - $0.25m = $362.50; m = 1,450 miles
Answers
Hope this helps!!
Which of the following statements about diversification is correct
Answers
Diversification means wide variety of different investment options available in the portfolio so that it becomes lesser risky towards minimizing losses in down market.
It provides better protection towards common issues like inflation, market instability, war effects, hike in exchange rates, interest rates reduction etc. So, we can conclude that :-
Diversification is the method to make investments less vulnerable to a catastrophic loss.
Hence, option A is best answer from given choices.
What is the side length of a square whose area is 1/64 square mile
Answers
Given is the square whose area is 1/64 squared miles, and it says to find the side of the square.
We know the formula for area of square is given by :-
Area of square = (side)²
[tex] (side)^{2} = \frac{1}{64} \\\\
side = \sqrt{\frac{1}{64}} \\\\
side = \frac{1}{8} = 0.125\; miles [/tex]
Hence, side of the square would be 1/8 miles or 0.125 miles.
Find an equation of the plane. the plane through the point (2, 0, 5) and perpendicular to the line x = 7t, y = 6 − t, z = 4 + 5t
Answers
P: (2,0,5)
L: (0,6,4)+t(7,-1,5)
and required plane, Π , passes through P and perpendicular to L.
The direction vector of L is V=<7,-1,5>.
For Π to be perpendicular to V, Π has V as the normal vector.
The equation of a plane with normal vector <7,-1,5> passing through a given point P(xp,yp,zp) is
7(x-xp)-1(y-yp)+5(z-zp)=0
Thus the equation of plane Π passing through P(2,0,5) is
7(x-2)-y+5(z-5)=0
or alternatively,
7x-y+5z = 14+25
7x-y+5z = 39
A rectangular prism has a length of 312 inches, a width of 5 inches, and a height of 112 inches. What is the volume of the prism? Enter your answer in the box as a simplified mixed number or a decimal.
Answers
A rectangular prism has a length of 3 1/2 inches, a width of 5 inches, and a height of 1 1/2 inches. What is the volume of the prism? Enter your answer in the box as a simplified mixed number or a decimal.
we know that
length=3 1/2 in--------> (3*2+1)/2=7/2 in
width= 5 in
height=1 1/2 in--------> (1*2+1)/2=3/2 in
[volume of the prism]=[length]*[width]*[height]
[volume of the prism]=[7/2]*[5]*[3/2]=105/4 in³-------> 26.25=26 1/4 in³
the answer is 26 1/4 in³
Answer:
26 1/4
Step-by-step explanation:
took the test 100% 4.08 Quiz: Finding the Volume of Rectangular Prisms and Problem Solving
Convert 210° from degrees to radians. Use the value of π found on a calculator, and round answers to four decimal places, as needed.
Answers
To solve the exercise above and convert 210° from degrees to radians, you have to mutilply it by π and divide it by 180°, as below:
210° to radians:
=(210°xπ)/180°
Therefore, the result is:
=(7/6)π radians
=3.6651 radians
Answer: 3.6651
Step-by-step explanation:
The formula to convert [tex]\theta[/tex] degrees to radians is given by :-
[tex]\dfrac{\pi}{180^{\circ}}\times\theta[/tex]
Given : Angle : [tex]\theta=210^{\circ}[/tex]
Then , the measure of angle in radians is given by :-
[tex]\dfrac{\pi}{180^{\circ}}\times210^{\circ}[/tex]
Using the value of [tex]\pi=3.14159[/tex], we get
[tex]\dfrac{3.14159}{6}\times7\approx3.6651[/tex]
A girl stands 160 cm tall she stands 360 cm away from a lamp post at night her shadow from the light is 90 cm long how high is the lam post
Answers
h1/b1=h2/b2
h1 is the height asked.
b1=360 cm+ 90 cm
b1=450 cm
h2=160 cm
b2=90 cm
2. When you substitute these values into h1/b1=h2/b2, you obtain:
h1/450 cm=160 cm/90 cm
3. Now, you must clear the height "h1". Then, you have:
h1=(160 cm)(450 cm)/90 cm
h1=72000 cm²/90 cm
h1=800 cm
How high is the lamp post?
The answer is: 800 cm
Final answer:
To find the height of the lamppost given the girl's height, distance from the lamp post, and shadow length, set up a proportion to calculate the lamp post's height.
Explanation:
A girl stands 160 cm tall and stands 360 cm away from a lamp post at night. Her shadow from the light is 90 cm long. How high is the lamppost?
Set up a proportion: Lamp post height / Girl's height = Lamp post shadow length / Girl's shadow length.
Substitute the values: Lamp post height / 160 cm = 360 cm / 90 cm.
Solve for the lamp post height: Lamp post height = (360 cm * 160 cm) / 90 cm = 640 cm.
Sarah and Angela have a collection of pennies and nickels in their piggy banks. Which girl has more coins in her bank? Explain how you know using numbers and symbols.Sarah and Angela have a collection of pennies and nickels in their piggy banks. Which girl has more coins in her bank? Explain how you know using numbers and symbols.
Answers
which expression is equivalent to ^3 square root 216x^3 y^6 z^12 ?
6xy^2 z^4
18xy^3 z^6
36xy^2 z^4
72xy^3 z^6
Answers
hope it helps
Answer:
Option A.
Step-by-step explanation:
The given expression is
[tex]\sqrt[3]{216x^3y^6z^{12}}[/tex]
We need to find the simplified form of the given expression.
It can be rewritten as
[tex]\sqrt[3]{6^3x^3y^6z^{12}}[/tex]
Using the properties of exponents, we get
[tex](6^3x^3y^6z^{12})^{\frac{1}{3}}[/tex] [tex][\because \sqrt[n]{x}=x^{\frac{1}{n}}][/tex]
[tex](6^3)^{\frac{1}{3}}(x^3)^{\frac{1}{3}}(y^6)^{\frac{1}{3}}(z^{12})^{\frac{1}{3}}[/tex] [tex][\because (ab)^x=a^xb^x][/tex]
[tex]6^{\frac{3}{3}}x^{\frac{3}{3}}y^{\frac{6}{3}}z^{\frac{12}{3}}[/tex] [tex][\because (x^m)^n=x^{mn}][/tex]
[tex]6^{1}x^{1}y^{2}z^{4}[/tex]
[tex]6xy^{2}z^{4}[/tex]
Hence, the correct option is A.
A circle has center O(−3, 1) and radius 10. Which of the following points is on the circle?
A. V(−3, −4)
B.X(5, −2)
C.Y(−6, 0)
D.Z(5, 7)
Answers
1. common equation of circle is (x-a)²+(y-b)²=r², where a,b - coordinates of the centre, r - radius of the circle.
2. using point O and radius: (x+3)²+(y-1)²=100 - the equation of the circle.
3. substituting point V,X,Y and Z into the equation of the circle:
V: (-3+3)²+(-4-1)²=100 - false;
X: (5+3)²+(-2-1)²=100- false;
Y: (-6-3)²+(0-1)²=100 - false;
Z: (5+3)²+(7-1)²=100 - true.
Answer: D.
A pair of diamond earrings has been marked up 50% and is now selling for $198.00. How much were the earrings before the mark-up?
Answers
Final answer:
The original price of the diamond earrings before a 50% markup that led to a final selling price of $198.00 was $132.00.
Explanation:
The question asks us to find the original price of the diamond earrings before a 50% markup that resulted in a final selling price of $198.00. To solve this, we use the markup formula, which is Final Price = (Original Price) × (1 + Markup Percentage). Here, the Final Price is $198.00 and the Markup Percentage is 50%, or 0.50 when expressed as a decimal.
First, we rearrange our formula to solve for the Original Price:
Original Price = Final Price ÷ (1 + Markup Percentage). Plugging in the given values, we have: Original Price = $198.00 ÷ (1 + 0.50) = $198.00 ÷ 1.50.
Doing the computation: Original Price = $132.00. Therefore, the earrings were priced at $132.00 before the 50% markup.
how do you find a meadian?
Answers
Final answer:
The median is a number that measures the center of the data. To find the median, arrange the data in ascending order and determine the middle value. If the data has an even number of values, the median is the average of the two middle values.
Explanation:
The median is a number that measures the center of the data. It separates the data into two halves, with half the values being smaller or equal to the median and the other half being larger or equal to it. To find the median, you need to arrange the data in ascending order and then determine the middle value.
If the data has an even number of values, the median is the average of the two middle values.
The speed limit is posted in most areas, but, if not, the ___________ speed limit will be in effect.
Answers
When no specific speed limit is posted, the default speed limit applies. These defaults are set by local or state law and can vary. Drivers must adhere to these limits and drive safely for conditions.
Explanation:In most areas, when specific traffic speed limit signs are not posted, what's known as the default speed limit applies. These default speed limits are not posted on signs and instead are set by local or state law. It's important to stay aware of these limits in different areas, as they can vary. For instance, in many cities, the default speed limit is 25 mph unless otherwise posted. However, it should be noted that these default limits may not protect you from being pulled over if the police deem your speed unsafe for the current conditions. Thus, it's recommended to always drive at a speed that is appropriate for the conditions, even if you are technically within the speed limit.
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The graph of the function f(x) = ax2 + bx +c (where a, b, and c are real and nonzero) has two x-intercepts. Explain how to find the other x-intercept if one x-intercept is at (-b/a2 +3,0)
Answers
The method to find the other x-intercept for the function f(x) = ax² + bx + c is given in the explanation below the answer.
The other x-intercept is; ((-b/2a - 3), 0)
We are given the equation of the function;
f(x) = ax² + bx + c
where a, b and c are real numbers and non - zero
Now, this is a quadratic equation that has 2 roots and it means there will be two x-intercepts.
Also, in quadratic equations, the formula to find the x-coordinate of the line of symmetry of the graph is;
x = -b/2a
The line of symmetry divides the graph curve into 2 equal parts at the vertex. This means the two x - intercepts will be the same distance from the x-coordinate of the vertex or line of symmetry but on opposite sides.
Thus, if one x-intercept is at ((-b/2a + 3), 0), then the other coordinate using the line of symmetry reason above is; ((-b/2a - 3), 0)
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Liza is playing a game in which she earns 3 points for each correct response but loses 2 points for each incorrect response. She missed the first 3 questions. Right now she just hopes to break even. Which statement is true?
To break even, Liza must answer 3 questions correctly to cancel out the 3 she answered incorrectly.
To break even, Liza must answer 2 questions correctly to give her 6 points, because she now has –6 points and the result would be a score of 0.
To break even, Liza must answer 6 questions correctly to give her 6 points, because she now has –6 points and the result would be a score of 0.
To break even, Liza must answer 1 question correctly, because she needs 3 points to cancel out the 3 questions she answered incorrectly.
Answers
have a nice day!!
The price of a condominium is $102,000. The bank requires a 5% down payment and one payment and one point at the time of closing. The cost of the condominium is financed with a 30-year fixed-rate mortage at 8.5%? Find the required down payment.
Answers
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Julia has to measure an object.she does not have a ruler. Tell what Julia could do to solve her problem.
Answers
enter a positive value for n that makes this statement true:1×n is less than 1 but greater than 0
Answers
N=0.5
1x0.5=0.5 which is less than 1 but greater than 0
The possible value of n is,
⇒ n = 1/2
What is Multiplication?
To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.
Given that;
The statement is,
1×n is less than 1 but greater than 0
Now, We can write as;
⇒ 0 < 1 × n < 1
Simplify as;
⇒ 0 < n < 1
Thus, The possible value of n is,
⇒ n = 1/2
⇒ n = 0.5
Thus, The possible value of n is,
⇒ n = 1/2
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Simplify the expression fraction with numerator of the square root of negative twenty five and denominator of the quantity five minus two times i plus the quantity one minus three times i
Answers
[tex] \frac{\sqrt{-25}}{(5-2i)+(1-3i)}[/tex]
You should keep in mind that square root of -1 is equal to i. i is called the imaginary unit.
Let us simplify this expression:
[tex]\frac{\sqrt{-1}\cdot \sqrt{25}}{6-5i}= \frac{5i}{6-5i} [/tex]
To simplify this further we can multiply numerator and denominator with 6+5i to elimante imaginary numbers from denominator.
[tex]\frac{5i}{6-5i}\cdot \frac{6+5i}{6+5i} = \frac{5i(6+5i)}{6^2-(5i)^2}= \frac{30i-25}{36+25}= \frac{-25+30i}{61} [/tex]
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Answers
A = 1/2 · (3+2) · 3 = 1/2 · 5 · 3 = 7.5 units²
The answer is 7.5 units².
On Wednesday Rachel hid 1.50 in a box. On Thursday she added $18 to the box. On Friday she took half the money out the box. How much money remains in the box ?