Step-by-step Answer:
One of the properties of a least-squares regression line (line of best fit) is that the line always passes through the point (xbar, ybar).
Assuming the given "line of best fit" is a least-squares line, then we are given
a slope m=1.885 passing through (x0,y0)=(3.448,12.318).
Applying the standard point-slope formula:
(y-y0) = m (x-x0)
we get
y-12.318 = 1.885(x-3.448)
Expand and simplify,
y=1.885x -1.885*3.448 + 12.318, or
y=1.885(x) + 5.81852
(numbers to be rounded as precision dictates).
To find the y-intercept of the line of best fit, substitute the mean x and y values and the slope into the equation y = mx + b and solve for b. In this case, the y-intercept is 5.820.
Explanation:To calculate the y-intercept of the line of best fit when you know the slope and the mean values of the x-coordinates and y-coordinates, you can use the formula for the equation of a line, which is y = mx + b, where m is the slope and b is the y-intercept.
Given:
Slope (m): 1.885Mean of x-coordinates: 3.448Mean of y-coordinates: 12.318We can substitute the means into the line equation:
12.318 = 1.885(3.448) + b
Now solve for b:
12.318 = 6.49836 + b
b = 12.318 - 6.49836
b = 5.81964
Therefore, the y-intercept b to three decimal places is 5.820.
The equation (x + 6)^2 + (y + 4)^2 = 36 models the position and range of the source of a radio signal. Describe the position of the source and the range of the signals
Answer:
position: (-6, -4)
range: 6
Step-by-step explanation:
The equation is that of a circle centered at (-6, -4) with a radius of √36 = 6. We presume that the "position" is that of the circle's center, and the "range" is the radius of the circle.
___
The standard form equation of a circle with center (h, k) and radius r is ...
(x -h)^2 +(y -k)^2 = r^2
Matching parts of the equation, we find ...
h = -6, k = -4, r = √36 = 6.
The source of the radio signal is at the point (-6, -4), and the range of the signals is within a circular area with a radius of 6 units.
The equation given, (x + 6)² + (y + 4)² = 36, is a mathematical representation of a circle in a Cartesian plane. This equation indicates that the source of the radio signal is at the center of the circle, which is the point (-6, -4).
The number 36 on the right side of the equation is the square of the radius of the circle, which implies that the radius of the circle is 6 units. Hence, the range of the signals emitted from the source is limited to a circular area with a radius of 6 units around the point (-6, -4).
The Environmental Protection Agency is attempting to revive 3 acres of contaminated soil by replacing the top 24 inches of the soil. Trucks with a hauling capacity of 28 cubic yards of soil are hired to remove the contaminated soil. How many full truckloads of contaminated soil will be hauled away?
Answer:
346 trucks are needed
Step-by-step explanation:
We know that one acre equals 43560 feet ^ 2
In this case the area is 3 acres. So:
[tex]3\ acres * \frac{43,560\ ft^2}{1\ acre} = 130,680\ ft^2[/tex]
We know that 1 foot equals 12 inches. So:
[tex]24\ in * \frac{1\ ft}{12\ in} = 2\ ft[/tex]
So the volume of the contaminated area is:
[tex]V = 2* 130,680\ ft^3\\\\V = 261,360\ ft^3[/tex]
In a cubic yard there are 27 cubic feet. So:
[tex]28\ yard^2 * \frac{27\ ft^3}{1\ yard^3} = 756\ ft^3[/tex]
Finally if we have a volume of [tex]261,360\ ft ^ 3[/tex] and each truck can transport [tex]756\ ft ^ 3[/tex] then the amount of trucks x we need is:
[tex]x = \frac{261,360\ ft ^ 3}{756\ ft ^ 3} = 346\ trucks[/tex]
2(3y − 1)(y − 3) is the factored form of
Answer:
6 y² - 20 y + 6
Step-by-step explanation:
Multiply step by step the terms inside the brackets:
3y * y
3y * -3
-1 * y
-1 * -3
add those up to get 3y² - 10 y + 3
multiply all terms of the result by 2
Answer:
6y^2 - 20y + 6.
Step-by-step explanation:
2(3y − 1)(y − 3)
= 2 [ 3y(y - 3) - 1(y - 3)]
= 2 (3y^2 - 9y - y + 3)
= 2(3y^2 - 10y + 3)
= 6y^2 - 20y + 6.
Juan drew a right triangle with leg lengths of 6 centimeters and 8 centimeters. He wants to draw another right triangle that is similar to the first one. Which could be the lengths of the legs?
The lengths of the legs of a similar triangle to the one Juan drew, which has leg lengths 6cm and 8cm, could be 12 cm and 16 cm because the sides of similar triangles are proportional.
Explanation:Juan's right triangle has leg lengths of 6 centimeters and 8 centimeters. To find a similar right triangle, we need ratios of corresponding sides to be equivalent or proportional. As these are right triangles, we can use the Pythagorean theorem which states that a² + b² = c². If the original triangle has sides 6 cm and 8 cm, then triangle with proportional sides could have sides that are multiple of these dimensions, such as 12 cm (which is 6cm x 2) and 16 cm (which is 8cm x 2). So, one example of a similar triangle could have leg lengths of 12 cm and 16 cm.
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For which values of x, rounded to the nearest hundredth, will x 2 − 9 | | | | − 3 = log3 x?
Answer:
2.3 and 3.6
Step-by-step explanation:
Final answer:
To solve the equation x^2 - 9|||-3 = log3 x, simplify both sides of the equation and then find the values of x that satisfy the equation.
Explanation:
To find the values of x that satisfy the equation, we can start by simplifying both sides of the equation.
On the left side, we have x^2 - 9|||-3. To simplify this, we first evaluate the absolute value of -3, which is 3. Then we have x^2 - 9(3), which simplifies to x^2 - 27.
On the right side, we have log3 x.
Setting the two sides equal to each other, we have x^2 - 27 = log3 x.
To solve this equation, we can graph both sides and find the intersection points, or we can use numerical methods like iteration or Newton's method to find the approximate solutions.
Which of the following equations represents Exponential Decay?
y=−3x+5
y=3(0.8)x
y=−3x−5
y=0.8(3)x
Answer:
y=3(0.8)x
Step-by-step explanation:
An exponential function is a function of the form;
[tex]y=ab^{x}[/tex]
The explanatory variable x is the exponent, a is the initial value and b the base of the exponential function.
The function is said to be an exponential decay function if the base is between 0 and 1;
0<b<1
Therefore, y=3(0.8)^x is the required function. The values of y become smaller as x increases.
A certain country's consumer price index is approximated by a(t) = 100e0.024t, where t represents the number of years. use the function to determine the year in which costs will be 50% higher than in year 0.
Answer:
[tex]\boxed{\text{Year 17}}[/tex]
Step-by-step explanation:
[tex]a(t) = 100e^{0.024t}[/tex]
Data:
a(t) = 150
a(0) = 100
Calculations :
[tex]\begin{array}{rcll}150 & = & 100e^{0.024t} & \\\\1.50 & = & e^{0.024t} & \text{Divided each side by 100}\\0.4055 & = & 0.024t & \text{Took the ln of each side}\\t & \approx & \mathbf{17} & \text{Divided each side by 0.024}\\\end{array}[/tex]
[tex]\text{The consumer price index will be 50 \% higher in } \boxed{\textbf{year 17}}[/tex]
The function f(x) is the total amount spent at a store, when purchasing x items that are $5 each and the items are not taxable.
What is the practical domain for the function f(x)?
A. all positive integers that are multiples of 5
B. all whole numbers
C. all positive integers
D. all real numbers
Answer:
B
Step-by-step explanation:
The domain is all possible values of x. Here, x is the number of $5 nontaxable items. So x must be an integer, and it can't be negative. It is possible for x to be 0. So x is all whole numbers.
The practical domain for the function f(x) which represents the total amount spent at a store is all whole numbers. Option B is correct.
What is domain of function?Domain of a function is the set of all the possible input values which are valid for that function.
The function f(x) represents the total amount spent at a store. The purchasing number of x items which are $5 each and the items which are not taxable is represented by x.
Thus, this function can be given as,
f(x)=5x
Now the domain of a function is the set of all the possible input values which are valid for that function. Thus, for this case the domain is,
-∞<x<∞
(-∞,∞)
For the practical domain, the numbers should be whole number to avoid negative amount value and integer amount.
Hence, the practical domain for the function f(x) which represents the total amount spent at a store is all whole numbers. Option B is correct.
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WILL MARK BRAINLEST
The graph shows two lines, A and B.
A graph is shown with x- and y-axes labeled from 0 to 6 at increments of 1. A straight line labeled A joins the ordered pair 0, 6 with the ordered pair 6, 3. Another straight line labeled B joins the ordered pair 0, 0 with the ordered pair 6, 6.
Part A: How many solutions does the pair of equations for lines A and B have? Explain your answer. (5 points)
Part B: What is the solution to the equations of lines A and B? Explain your answer. (5 points)
Answer:
Part A) The system has one solution
Part B) The solution is the point (4,4)
Step-by-step explanation:
step 1
Find the equation of the line A
we have
(0,6) and (6,3)
Find the slope
m=(3-6)/(6-0)
m=-0.5
Find the equation of the line into slope intercept form
y=mx+b
we have
m=-0.5
b=6 -----> the point (0,6) is the y-intercept
substitute
y=-0.5x+6 ------> equation A
step 2
Find the equation of the line B
we have
(0,0) and (6,6)
Find the slope
m=(6-0)/(6-0)
m=1
Find the equation of the line into slope intercept form
y=mx+b
we have
m=1
b=0 -----> the line represent a direct variation
substitute
y=x ------> equation B
step 3
Find how many solutions does the pair of equations for lines A and B have
we have
y=-0.5x+6 ------> equation A
y=x ------> equation B
Solve the system of equations by graphing
Remember that the solution of the system of equations is the intersection point both lines
using a graphing tool
There is one point of intersection
therefore
The system has one solution
see the attached figure
step 4
What is the solution to the equations of lines A and B?
we know that
The solution of the system of equations is the intersection point both lines
The intersection point is (4,4)
therefore
The solution is the point (4,4)
so
x=4,y=4
A spinner has five equal sections that are numbered 1 through 5.
In which distributions does the variable X have a binomial distribution?
Select EACH correct answer.
When the spinner is spun three times, X is the sum of the numbers the spinner lands on.
When the spinner is spun multiple times, X is the number of spins until it lands on 5.
When the spinner is spun four times, X is the number of times the spinner does not land on an odd number.
When the spinner is spun five times, X is the number of times the spinner lands on 1.
Answer:
Step-by-step explanation:
X has a binomial distribution when the probability of X is the same for each spin.
When the spinner is spun four times, X is the number of times the spinner does not land on an odd number.
When the spinner is spun five times, X is the number of times the spinner lands on 1.
Answer with explanation:
Total number of sections in the spinner = 1 to 5=5 in all
For, a Distribution to be a Binomial Distribution,
Number of trials should be fixed.
All trials should be Independent of one another.
Only two outcomes are Possible one is called Success and Other is failure.
Probability of each Outcome should remain constant irrespective of number of trials.
Probability of getting either of 1,2,3,4,or 5 when the spinner is spun once
[tex]=\frac{1}{5}[/tex]
Option C
When the spinner is spun four times, X is the number of times the spinner does not land on an odd number.
Probability of Failure ={1,3,5}=Getting odd number on spinner
[tex]=\frac{3}{5}[/tex]
Probability of Success={2,4}=Getting even number on spinner
[tex]=\frac{2}{5}[/tex]
Number of trials is fixed and each trial is independent of another.
Option D
Total Number of Trials= 5
Probability of Success = When the Spinner is spun and it Lands on 1
Probability of Failure = When the Spinner is spun and it does not Land on 1
When the Spinner is spun five times ,Probability of each Outcome,that is either of 1,2,3,4,or 5 is constant which is [tex]\frac{1}{5}[/tex]
⇒⇒When the spinner is spun five times, X is the number of times the spinner lands on 1.
→≡Option C and D
Domain and Range...
The domain is the X values and the range is the y values.
The blue line starts at X 0 and Y 0 and moves up and to the right.
This means the range and domain are equal to or greater than 0.
The 3rd choice is the correct one.
What can you conclude from the diagram below?
Explanation:
E is the midpoint of ABF is the midpoint of CBEF is the midline of ΔABC, hence ║ACH is the midpoint of ADG is the midpoint of CDGH is the midline of ΔACD, hence ║AClength of EF = length of GH = 1/2 length of ACEFGH is a parallelogramΔEBF ~ ΔABCΔHGD ~ ΔACDarea relationships can be derived from the fact that the similar triangle scale factors are 1:2___
Similar relationships pertain to the diagonal BD and segments EH and FG. You can also conclude that area EFGH is half of area ABCD by considering the various triangles you get by connecting midpoints different ways.
Really need answer, don't understand what it want:
Answer:
y ≈ - 3.8
Step-by-step explanation:
Given the 2 equations
5x + 2y = 21 → (1)
- 2x + 6y = - 34 → (2)
To eliminate the terms in x , multiply (1) by 2 and (2) by 5
10x + 4y = 42 → (3)
- 10x + 30y = - 170 → (4)
Add (3) and (4) term by term
(10x - 10x) + (4y + 30y) = (42 - 170)
34y = - 128 ( divide both sides by 34 )
y ≈ - 3.8 ( to the nearest tenth )
The faces of triangular pyramid have a base of 5cm and a height of 11cm what is the lateral area of the pyramid
Answer:
55cm
Step-by-step explanation:
11 x 5 = 55, so the area of the pyrmid is 55cm.
Answer:You will have to multiply 55 x 5 because if the base if 5 cm and the height is 11 cm which equals to 55 and a pyramid has 5 faces, so the answer will be 220. I hoped this helped! :)
Step-by-step explanation:
Vector u has its initial point at (-7, 2) and its terminal point at (11, 5). Vector v has a direction opposite that of vector u, and its magnitude is three times the magnitude of u. What is the component form of vector v?
A. [tex]v= \ \textless \ -54, 63\ \textgreater \ [/tex]
B. [tex]v= \ \textless \ -162, -63\ \textgreater \ [/tex]
C.[tex]v= \ \textless \ -54, 21\ \textgreater \ [/tex]
D. [tex]v= \ \textless \ -162, 21\ \textgreater \ [/tex]
Here,
the initial point of vector u(x1,y1)=(-7,2)
the final point of vector u (x2,y2)=(11,5)
so the component of vector u(x,y)=(x2,y2)-(x1,y1)
=(11+7,5-2)=(18,3)
according to the question, the magnitude of vector is thrice the magnitute of vector u and is opposite ot the ditecrion of vector u.
so the component of vector v is -3(x,y)
=-3(18,3)=(-54,-9)
Please help me out!!!!!!!!
Answer:
(x-2)²+(y--2)²=9
Step-by-step explanation:
The center moves to the right by 2 so its x-2
The center moved down 2 so its y+2 or y--2
The radius is 3 so we square that to get what it equals (9)
Can the polynomial in the numerator of the expression x2-5x+7/x-9 be factored to derive (x − 9) as a factor?
Answer:
No.
Step-by-step explanation:
Because x²-5x+7, as x = 9 is 9²-5·9+7 = 81-45+7 ≠ 0
f(x) = x²-5x+7 is divisible by x-9 only if f(9) = 0.
Function 1: y = 4x + 5
Function 2: The line passing through the points (1, 6) and (3, 10).
Which of these functions has the greater rate of change?
Answer:
B
Hope this helps!
Answer:
B
Step-by-step explanation:
The rate of change is the slope. Function 1 has a slope of 4. Function 2 has a slope of:
m = Δy / Δx
m = (10 - 6) / (3 - 1)
m = 4 / 2
m = 2
So function 1 has the greater rate of change. Answer B.
Karen finished watching a movie at 1:10 pm. The movie lasted 1 hour 38 minutes what time did Karen started watching the movie
well, the movie lasted 1:38 so.... and she finished it at 1:10pm.
1:10pm minus 1 hour? 12:10pm.
12:10 pm minus 10 and minus 28 minutes? 12:10 - 00:10 = 12:00pm, 12:00 - 00:28 minutes = 11:32am.
Answer: 11:32
Step-by-step explanation:
What is the volume of the space between the cylinder and the sphere?
500/3π cubic inches
500π cubic inches
250/3π cubic inches
750π cubic inches
250π cubic inches
Answer:
250/3π cubic inches
Step-by-step explanation:
we know that
The volume of the space between the cylinder and the sphere is equal to the volume of the cylinder minus the volume of the sphere
step 1
Find the volume of the cylinder
The volume of the cylinder is equal to
[tex]V=\pi r^{2} h[/tex]
we have
[tex]h=10\ in[/tex]
[tex]r=5\ in[/tex]
substitute
[tex]V=\pi (5)^{2} (10)[/tex]
[tex]V=250\pi\ in^{3}[/tex]
step 2
Find the volume of the sphere
The volume of the sphere is equal to
[tex]V=\frac{4}{3}\pi r^{3}[/tex]
we have
[tex]r=5\ in[/tex]
substitute
[tex]V=\frac{4}{3}\pi (5)^{3}[/tex]
[tex]V=(500/3)\pi\ in^{3}[/tex]
step 3
Find the difference
[tex]250\pi\ in^{3}-(500/3)\pi\ in^{3}=(250/3)\pi\ in^{3}[/tex]
he points A, B, C, and D are on a number line, not necessarily in that order. If the distance between A and B is 18 and the distance between C and D is 8, what is the distance between B and D ? (1) The distance between C and A is the same as the distance between C and B. (2) A is to the left of D on the number line. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient. EACH statement ALONE is sufficient. Statements (1) and (2) TOGETHER are NOT sufficient. Next Help End Review Review Screen
Answer:
Statements (1) and (2) TOGETHER are NOT sufficient.
Step-by-step explanation:
If the point order is DCAB or CDAB (or the reverse of either of these), then the BD distance will be 36±8 units. It cannot be determined.
__
If the point order is AD(BC) or A(BC)D, then the BD distance is the same as the CD distance, which is given as 8. In this scenario, point B and C lie at the same place on the number line.
__
So, we have 3 possible values of BD, even when both statements are used together. TOGETHER, the statements aren NOT sufficient.
someone please help me
i’ll give brainliest
Answer:
[tex]x^{1/4} y^{1/2}[/tex]
Step-by-step explanation:
When you have a power then a root like that, you have to divide the power by the root.
So, in this case, you have (x^2y^4) and a 8th root (8√).
So, you take your exponents from (x^2y^4) and divide them by the root (8), to get new powers of 2/8, or 1/4, and 4/8 or 1/2
As I already explained you in other questions, that leaves a fractional exponent that is equivalent to the regular exponent then rooted.
Answer is then: [tex]x^{1/4} y^{1/2}[/tex]
If the search item is the 500th item in the list, how many key comparisons does the sequential search make to find the search item?
Answer:
500
Step-by-step explanation:
A sequential search starts with the first item on the list, making a comparison with every item until the desired one is found. It takes 500 comparisons to find the 500th item.
Katie is going to rent an apartment and has to choose the number of bedrooms the apartment has, the type of parking she will use, and the length of the lease that she will sign. She has three options for the number of bedrooms (one, two, or three bedrooms), three options for the type of parking (street, assigned, or garage spots), and four options for the length of the lease (1, 6, 12, or 24 months.) How many possible combinations are there for the number of bedrooms, parking options, and the length of the lease that Katie could select?
How many possible combinations are there for the number of bedrooms, parking options, and the length of the lease that Katie could select?
72
36
27
48
10
Answer:
36
Step-by-step explanation:
The total number of options is the product of the numbers of independent options: 3×3×4 = 36.
__
For each of the bedroom options, she can choose any parking option, so can have ...
1 br, street parking
2 br, street parking
3 br, street parking
1 br, assigned parking
2 br, assigned parking
3 br, assigned parking
1 br, garage spots
2 br, garage spots
3 br, garage spots
That is, 3×3 = 9 options. Any of these can be put with any of the four lease options, for a total of 9×4 = 36 options altogether.
The answer would be 36
Sydney needs 70cm of feinge for each scarf she makes. How many scarves can she make if she has 6 meters of fringe?
Answer:
8
Step-by-step explanation:
First Step
Convert meters to centimeters
For every meter there are 100 (centi)meters
6 meters ×100=600 cm
Second Step
Find how many scarves can be made
We have 600 cm of fringe
It takes 70 cm to make 1 scarf
Divide 70 into 600
600÷70=8.571
Rounding down we get 8
Please help me out with this!!!!! Help is much needed !
here the centre of circle(h,k) is (-2,4)
and its radius(r) is 6 uints.
now the equation of circle is,
(x-h)^2 +(y-k)^2 =r^2
or, (x+2)^2 + (y-4)^2=6^2
or, x^2 + 4x + 4+y^2 -8y+16=36
or, x^2 +y^2 + 4x -8y -16=o
What is the sum of the coefficients of the expression 3x^4 + 5x^2 + x?
9
7
8
6
Answer:
9
Step-by-step explanation:
coefficients = numbers in front of variables (x, x^2 etc)
so 5 + 3 + 1 = 9
In the expression 3x^4 + 5x^2 + x, the coefficients are 3, 5, and 1. Adding these values together gives a sum of 9.
Explanation:In the expression 3x^4 + 5x^2 + x, the coefficients are 3, 5, and 1 respectively. The term x is implied to have a coefficient of 1 though it is not written explicitly. We find the sum of the coefficients by simply adding all these values together. So the sum would be 3 + 5 + 1 = 9.
The term x is implied to have a coefficient of 1 though it is not written explicitly. We find the sum of the coefficients by simply adding all these values together.
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How do you do this problem?
Answer:
[tex]\boxed{x = 8}[/tex]
Step-by-step explanation:
1. Jump discontinuity
In the graph, you can see that the left-hand limit of g(x) as x⟶ 8 is 3 and the right-hand limit is -3.
When the left- and right-hand limits at x = 8 exist but are different, we say that g(x) has a jump discontinuity at [tex]\boxed{\textbf{x = 8}}[/tex].
2. Other discontinuities
At x = 10, the left-hand limit is ∞ and the right-hand limit is -∞. Both one-sided limits are infinite, so this is an infinite discontinuity.
At x= 1, both one-sided limits are equal, but g(1) does not exist,
At x= 4, the limits are equal, and g(4) = 3.
In each case, the holes can be removed by redefining g(x), so the holes are removable discontinuities.
Brianna and Maddie rode their bikes on Saturday. Maddy rode twice as much as Brianna. Together they rode for 162 minutes. How many minutes did each girl ride?
Answer: brianna rode for 54 minutes and maddie rode for 108 minutes.
Step-by-step explanation:
let the time for which brianna rode be = x
(since maddie rode twice as brianna then,)
let the time for which maddie rode be = 2x
(together they rode for 162 minutes. so,)
x + 2x = 162
3x = 162
x = 162/3
=>x = 54
=>2x = 54*2 = 108
hope it helps
What is the product of these numbers?
(1 + 2i)(2 + i)
1 − 5i
1 + 5i
0 − 5i
0 + 5i
Answer:
0 + 5i
Step-by-step explanation:
Multiply these the way you would any binomials, then replace i² with -1.
(1 +2i)(2 +i) = 1·2 +1·i +(2i)·2 +(2i)·i
= 2 + i + 4i + 2i² . . . . . the partial products
= 2 +5i -2 . . . . . . . . . . after replacement of i² = -1
= 0 +5i