the line of best is y = 0.20x + 5.43 and it will take 7.5 min to get to work in week 10.
What is the line of best fit?A mathematical notion called the line of the best fit connects points spread throughout a graph. It's a type of linear regression that uses scatter data to figure out the best way to define the dots' relationship.
\(\rm m = \dfrac{n\sum xy-\sum x \sum y}{n\sum x^2 - (\sum x)^2}\)
\(\rm c = \dfrac{\sum y -m \sum x}{n}\)
The question is incomplete.
The complete question is in the picture, please refer to the attached picture.
We have the data shown in the picture.
Let's suppose the line of best is:
y = mx + c
We can calculate the value of m and c using the formula.
m = 0.20
c = 5.43
The line of best will be:
y = 0.20x + 5.43
Plug x = 10 in the line of best fit:
y = 0.20(10) + 5.43
y = 7.43 ≈ 7.5 min
Thus, the line of best is y = 0.20x + 5.43 and it will take 7.5 min to get to work in week 10.
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what is the explicit formula for this sequence? -7,-3,1,5,…
Answer:
\(a_n=4n-11\)
Step-by-step explanation:
The common difference is \(d=4\) with the first term being \(a_1=-7\), so we can generate an explicit formula for this arithmetic sequence:
\(a_n=a_1+(n-1)d\\a_n=-7+(n-1)(4)\\a_n=-7+4n-4\\a_n=4n-11\)
Which data set does the box-and-whisker plot represent?
Answer:
2nd choice
Step-by-step explanation:
Which ratio is equivalent to 1:1
Answer:
the answer is 1
because 1 is not multiple in our self
What is the area of rhombus ABCD? Enter your answer in the box. Do not round at any steps.
Answer:
Area of the rhombus ABCD = 16 square units
Step-by-step explanation:
Area of a rhombus = \(\frac{1}{2}(\text{Diagonal 1})(\text{Diagonal 2})\)
From the graph attached,
Diagonal 1 = Distance between the points A and C
Diagonal 2 = Distance between the points B and D
Length of a segment between (x₁, y₁) and (x₂, y₂) = \(\sqrt{(x_2-x_1)^{2}+(y_2-y_1)^2 }\)
Diagonal 1 (AC) = \(\sqrt{(4-0)^2+(-1+1)^2}\) = 4 units
Diagonal 2(BD) = \(\sqrt{(2-2)^2+(3+5)^2}\) = 8 units
Now area of the rhombus ABCD = \(\frac{1}{2}(\text{AC})(\text{BD})\)
= \(\frac{1}{2}\times 4\times 8\)
= 16 units²
Therefore, area of the given rhombus is 16 units².
What is the area of KDL to the nearest tenth of a square inch? Use special right triangles to help find the height. Show
your work
Answer:
8
Step-by-step explanation:
This is a 45-45 traingle which mean that the two sides that aren't the hyptonouse are equal (because their angles are equal)
We will let x equal the length of one of the sides
we have
x²+x²=(4√2)²
2x²=32
x²=16
x=4
this means that the length of the two missing sides are 4
Now using the area of a traingle formula we can solve for the area
A=.5*b*h
.5*4*4=8
.5*4*4
2x(x-5) -x (3 + 2x) = 26
help me pls
Answer:
x = -2
Step-by-step explanation:
\(2x(x-5)-x(3+2x) = 26\\2x^{2} -10x-3x-2x^{2} = 26\\-13x=26\\x=\frac{26}{-13} \\=-2\)
Its basically the order of operations, from left to right , evaluate brackets (if possible), then multiplication or division, lastly followed by addition or subtraction.
2x2-10x-3x-2x2=26
Eliminam opusele
reducem termenii
-13x=26
imparte ambele parti
x=-2
Step-by-step explanation:
Use the equation below to find y, if m=9, x=5, and b=6.
y=mx+ b
y = 1
X
?
Which best describes why these two figures are similar or not similar?
Answer:
first one top left
Step-by-step explanation:
Langston estimated the temperature to be 45°F . The thermometer showed the actual temperature to be 50°F. Complete the steps below to find the percent error of Langston’s estimate.
The percentage error is 11.1%
What is percentage error?Percentage error is simply the difference between the exact and the estimated values as a percentage
The given parameters are:
Estimate = 45Actual = 50The percentage error is then calculated as:
\(\% E = \frac{50 - 45}{45} \times 100\%\)
Evaluate the difference
\(\% E = \frac{5}{45} \times 100\%\)
So, we have:
\(\% E = \frac{500}{45} \%\)
\(\% E = 11.1\%\)
Hence, the percentage error is 11.1%
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(a) Solve the following system using the Gauss-Jordan method. 2xy +3z=0 x+y+3z=3 x - 2y = -3
The system can be solved using Gauss-Jordan method in a few steps.
Following is the step-by-step solution for the given system of equations
.2xy + 3z = 0 ...(1) x + y + 3z = 3 ...(2) x - 2y = -3 ...(3)
Using equations (1), (2) and (3), we can write the following matrix equation and use Gauss-Jordan method to solve the system.
[2xy 3z | 0][x y z | 3][x - 2y 0 | -3]
Subtracting equation (1) from (2),
we get
x + y + 3z - 2xy - 3z = 3 - 0
=> x + y - 2xy = 3 ...(4)
Adding equation (3) to (4), we get
2x - y - 2xy = 0
=> 2x - y(1+2x) = 0
=> y = 2x / (1+2x)
Substituting this value of y in equation (4),
we get
x + 2x / (1+2x) - 2x(2x / (1+2x)) = 3
=> x + 2x / (1+2x) - 4x^2 / (1+2x) = 3
=> (1+2x)(3x + 2) - 4x^2 = 3(1+2x)
=> 3x^2 - 4x + 3 = 0
Using quadratic formula,
we get
x = [4 ± sqrt(16 - 4*3*3)] / 6x
= [4 ± 2] / 6
=> x = 1 or x = 1/3
Substituting x = 1 in equation (4), we get y = 2/3 and using this in equation (2), we get z = 1.
Substituting x = 1/3 in equation (4), we get y = 1/5 and using this in equation (2), we get z = 8/5.
Hence, the solution of the system of equations is (x, y, z) = (1, 2/3, 1) or (1/3, 1/5, 8/5).
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Is TUV~WXV? Explain.
carter has two consecutive numbers with a sum of 49. what is the smaller number?
A. 23
b. 24
C. 25
D. 26
Answer:
A.23 is the answer
Step-by-step explanation:
49-26=23
49-25=24
49-24=25
Solve the system of linear equations by graphing. y=-3x + 1 y = x- 7
Answer:
(2,-5)
Step-by-step explanation:
Use the distributive property to rewrite each expression in its equivalent form.
1. 4(x + 3)
2. -7(4 - y)
3. 6(3x + 5y -4)
4. 9a-3/3
Rewrite each linear expression by factoring out the greatest common factor.
5. 64x + 24
6. -5y -35
HELPP I NEED TO SUMBIT SOON
write the system x′=e3tx−9ty 8sin(t)x′=e3tx−9ty 8sin(t), y′=8tan(t)y 8x−3cos(t)y′=8tan(t)y 8x−3cos(t) in the form ddt[xy]=p(t)[xy] f⃗ (t).
To write the system in the form ddt[xy]=p(t)[xy] f⃗ (t), we need to express the derivatives x′ and y′ in terms of xy. We can do this by multiplying the first equation by 8sin(t) and the second equation by 8x - 3cos(t):
8sin(t)x′ = 8sin(t)e^(3t)x - 72sin(t)ty
(8x - 3cos(t))y′ = 8tan(t)(8x - 3cos(t))y
Now we can add these two equations and simplify:
8sin(t)x′ + (8x - 3cos(t))y′ = 8sin(t)e^(3t)x - 72sin(t)ty + 8tan(t)(8x - 3cos(t))y
ddt[xy] = (8sin(t)e^(3t) - 72sin(t)t + 8tan(t)(8x - 3cos(t)))xy
So the system in the desired form is ddt[xy] = (8sin(t)e^(3t) - 72sin(t)t + 8tan(t)(8x - 3cos(t)))xy f⃗ (t).
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PLEASE HELP!!! This table shows the profit for a company (in millions of dollars) in different years. The quadratic regression equation that models these data is y=-0.34x^2+4.43x +3.46. Using the quadratic regression equation, what was the predicted profit in year 4?
Answer:
15740000 million dollars in profit in year 4
Step-by-step explanation:
Now since you didn't provide the table, im going to have to assume the years are going to be the X while the Y is going to be profit.
Using the equation you provided y=-0.34x^2+4.43x +3.46, we can simply put 4 as our x value (since x represents years) and we would get 15.74. Now you have to remember to convert it into millions to show the profit so 15.74 times 1,000,000 would be 15740000 million dollars
the administration team compiled test results for those who had been tested for strep throat in a random sample of 400 sick patients who had been tested. the following relative frequency table shows the data. positive negative total has the flu 54% 6% 60% does not have the flu 8% 32% 40% total 62% 38% 100% based on the data, what is the ratio of false positives to true positives? 6 over 32 8 over 6 8 over 54
The ratio of false positives to true positives is 8 over 54.
According to the Question
Results of a strep throat test performed on a sample of 400 ill people are displayed in the table's data. People who have the flu and those who don't are separated into two categories. The patients are then separated into groups based on whether they tested positive or negative for strep throat within each of these categories.
We must first define what a true positive and a false positive are in order to calculate the ratio of false positives to true positives. A patient who tests positive for strep throat but does not actually have the illness is said to have a false positive. The 8% of patients in this instance who tested positive for strep throat but did not have the flu would fall under that category. A patient who tests positive for strep throat and truly has the illness is said to have a true positive. That would be the 54% of patients who tested positive for both the flu and strep throat in this instance.
We divide the percentage of false positives (8%) by the percentage of true positives (54%), which gives us the ratio of false positives to true positives.
As a result, the ratio becomes 8% / 54%, or 8/54.
It's critical to remember that this ratio is dependent on the sample and test performed and may not be the same for different populations or testing methodologies.
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3x – 15 = 39
=
What does x equal
Answer:
X=18
Step-by-step explanation:
To isolate X you need to get rid of the -15 to do that you can add 15 on both sides of the equation resulting in 3x=54 now you need to divide both sides by 3 to get x on its own which is X=18.
A Home Depot, Inc. coupon bond that pays interest of $60 annually has a par value of $1,000, matures in 10 years, and is selling today at an $84.52 discount from par value. The yield to maturity on this bond is ________.
Group of answer choices
9.45%
6%
8.12%
7.22%
A Home Depot, Inc. coupon bond that pays interest of $60 annually has a par value of $1,000, matures in 10 years, and is selling today at an $84.52 discount from par value. The yield to maturity on this bond is 7.22%.
The yield to maturity (YTM) on a bond is the total return anticipated on a bond if it is held until maturity. To calculate the YTM, we need to determine the discount rate that equates the present value of the bond's future cash flows (interest payments and the final principal payment) with its current market price.
In this case, the coupon bond has an annual interest payment of $60, a par value of $1,000, matures in 10 years, and is selling at an $84.52 discount from par value.
To calculate the yield to maturity, we can use a financial calculator or a spreadsheet software, or we can make an estimate using trial and error. In this case, I'll use the trial and error method.
Let's assume a yield to maturity (YTM) of 7%. We can calculate the present value of the bond's future cash flows using this yield:
Present value of interest payments = $60 / (1 + 0.07) + $60 / (1 + 0.07)^2 + ... + $60 / (1 + 0.07)^10
Present value of principal payment = $1,000 / (1 + 0.07)^10
Next, we can sum up the present values of the interest payments and the principal payment:
Present value of bond = Present value of interest payments + Present value of principal payment
Now, we can compare the present value of the bond with its current market price. If the calculated present value is close to the market price, then the assumed yield is the yield to maturity. If not, we can try a different yield and repeat the calculations until we find a yield that matches the market price.
In this case, the bond is selling at an $84.52 discount from par value, so the market price is $1,000 - $84.52 = $915.48.
Let's plug in the yield of 7% and calculate the present value of the bond:
Present value of interest payments = $60 / (1 + 0.07) + $60 / (1 + 0.07)^2 + ... + $60 / (1 + 0.07)^10 ≈ $421.55
Present value of principal payment = $1,000 / (1 + 0.07)^10 ≈ $508.54
Present value of bond = $421.55 + $508.54 ≈ $930.09
The calculated present value of the bond is $930.09, which is higher than the market price of $915.48.
To find the correct yield to maturity, we can try a slightly higher yield. Let's assume a yield of 7.5% and repeat the calculations:
Present value of interest payments = $60 / (1 + 0.075) + $60 / (1 + 0.075)^2 + ... + $60 / (1 + 0.075)^10 ≈ $416.23
Present value of principal payment = $1,000 / (1 + 0.075)^10 ≈ $496.58
Present value of bond = $416.23 + $496.58 ≈ $912.81
The calculated present value of the bond is now $912.81, which is closer to the market price of $915.48.
By continuing this process of trial and error, we can find that the yield to maturity on this bond is approximately 7.22%.
The yield to maturity is the rate of return an investor can expect to receive if they hold the bond until maturity and reinvest all coupon payments at the same yield. In this case, the yield to maturity is approximately
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Dora says that only one triangle can be constructed with two given side lengths and one given angle measure. Is Dora correct? Explain.
If 5 pounds of beans cost $4, then how much does 50 pounds of beans cost?
Answer:
50 pounds of beans costs $40
A marketing class of 50 students evaluated the instructor using the following scale superior, good, average, poor or inferior. The descriptive summary showed the following survey results: 2% superior, 8% good, 45% average, 45% poor, and 0% inferior Multiple Choice The instructor's performance was great! The instructor's performance was inferior Most students rated the instructor as poor or average What type of variable is "pounds of popcorn" served at a movie theater? Multiple Choice Ratio Discrete Continuous
The variable "pounds of popcorn" served at a movie theater is a continuous variable that can take any value within a certain range. It is not restricted to specific discrete values or categories.
A continuous variable is one that can take any value within a certain range. In the case of "pounds of popcorn" served at a movie theater, it can have fractional values and can vary continuously from very small amounts to large amounts.
It is not restricted to specific discrete values or categories. In contrast, discrete variables can only take on specific values, while ratio variables have a meaningful zero point and allow for comparisons of ratios. Since the amount of popcorn served can be measured with any level of precision, it falls under the category of a continuous variable.
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(I NEED HELP URGENTLY, THIS IS DUE TOMORROW!)
The table represents a proportional relationship.
A. Find the constant of proportionality:
B: Write a equation to represent the relationship. Equation: y=
The constant of proportionality is 1/3, and the equation is y = (1/3)x represents the relationship.
What is the constant of proportionality?The value of the proportionality constant is determined by the type of proportion between the two specified values.
Proportional relationships are written in the form y = kx
where k is the constant of proportionality.
As per the given table, the constant of proportionality will be
k = (1 - 2/3)/(3-2)
k = (1/3)/1
k = 1/3
So, the equation is y = (1/3)x.
Thus, the constant of proportionality is 1/3, and the equation is y = (1/3)x represents the relationship.
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Carbon-14 has a half-life of 5730 years. How long will it take for 180 grams to decay to 100 grams?
Answer:
3185
(I'm not sure if it's correct, if it's wrong I apologize in advance.)
If the volume of a pyramid is 60 cubic inches and the area of the base is 36 square Inches, what is the height of the
pyramid?
7 in
5in
6in
4in
Answer:
No correct answer
Step-by-step explanation:
height = volume/ area
height= 69/36= 1.667in
5 in.
I just did this one, and this was the answer.
estimate the value of the square root of 40 to the nearest tenth
Answer:
The answer is √40 = 6.32455532033676.
Step-by-step explanation:
To check that the answer is correct, use your calculator to confirm that 6.32 is about 40.
I have found the area but I'm not sure how to find the perimeter.
Answer:
20+20+24+24=88
88/2=44
88+44=132
Step-by-step explanation:
If you split it so there is a rectangle and a triangle, you find the perimeter of the rectangle then divide it in half.
what would be the exact side length of a square with the area of 8 m2
Answer:
2*square root of 2
Step-by-step explanation:
The square root of 8 is equal to 2*square root of 2
Find the absolute maximum and minimum values of f on the set D.
f(x, y) = x2 + 8y2 − 2x − 16y + 1, D = {(x, y) | 0 ≤ x ≤ 2, 0 ≤ y ≤ 3 }
To find the absolute maximum and minimum values of f on the set D, we need to find the critical points and endpoints of the function f(x, y) on D.
First, we find the partial derivatives of f with respect to x and y:
∂f/∂x = 2x - 2
∂f/∂y = 16y - 16
Setting these partial derivatives to zero, we get:
2x - 2 = 0 => x = 1
16y - 16 = 0 => y = 1
So the critical point of f on D is (1,1).
Next, we check the endpoints of D:
f(0,0) = 1
f(0,3) = 73
f(2,0) = -13
f(2,3) = 121
So the absolute maximum value of f on D is 121 and occurs at the point (2,3), while the absolute minimum value of f on D is -13 and occurs at the point (2,0).
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More and more people are purchasing food from farmers' markets. As a consequence, a market researcher
predicts that the number of farmers' markets will increase by 15% each year. If there are 6,200 farmers' markets
this year, how many will there be in 10 years? (Round to the nearest whole number if necessary).
The exponential function is given by:
y = 6200(1.15)ˣ
Exponential function
Exponential function is in the form:
y = abˣ
where y, x are variables, a is the initial value of y and b is the multiplier
Let y represent the number of farmers after x years.
From the question:
a = 6200, b = 100% + 15% = 115% = 1.15
The exponential function is given by:
y = 6200(1.15)ˣ
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