In MODE, (second line), fix the number of decimal places to be 2. Then the slope and the y-intercept values of the LinReg line will round to the nearest hundredth. Find the LinReg line of best fit for the National Health Expenditures data. Then predict national health expenditures for 2010. (Hint: You may have to expand the calculator window to include the year 2010 on your screen.)
Answers
The equation of line is y = 92x – 182631. The slope is 92 and the y-intercept is the negative 182631. And the health expenditure in 2010 will be 2289.
What is the equation of a line passing through two points?Suppose the given points are (x₁, y₁) and (x₂, y₂), then the equation of the straight line joining both two points is given by
[tex]\rm (y - y_1) = \left [ \dfrac{y_2 - y_1}{x_2 - x_1} \right ] (x -x_1)[/tex]
In MODE, (second line), fix the number of decimal places to be 2.
Then the slope and the y-intercept values of the Lin Reg line will round to the nearest hundredth.
(x₁, y₁) → (1997, 1093)
(x₂, y₂) → (2002, 1553)
Then we have
y – 1093 = [(1553 – 1093) / (2002 – 1997)] (x – 1997)
y – 1093 = [460 / 5] (x – 1997)
y – 1093 = 92 (x – 1997)
y = 92x – 182631
If x = 2010, then the value of y will be
y = 92 × 2010 – 182631
y = 184920 – 192631
y = 2289
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Related Questions
find the volume of the composite figure & round to the nearest tenth if needed!!
please answer correctly...
25 points!!
Answers
Answer:
(2*2*1.5*1/3)+(2*1.5*4)= 14
Step-by-step explanation:
To find the area of a pyramid, you use the equation of 1/3 *lwh. When we place the values in there, we get 2*2*1.5*1/3, which is equal to 2. Then we solve the bottom part. Since it is a rectangular prism, we use the equation of lwh. When we insert the values, we get 2*1.5*4, which is equal to 12. Now, we take these two values of 2 and 12 and we combine them, giving us our final answer of 14.
william used 15 cm of tape to wrap 3 presents, Find the length of tape to wrap for 1 present?
Answers
Refer to the attached image
Answers
Answer: [tex]\boldsymbol{2(x-2)(5x+7)}[/tex]
========================================================
Work Shown:
[tex](4x^2-16)+3(2x-4)(x+1)\\\\4(x^2-4)+3*2(x-2)(x+1)\\\\4(x-2)(x+2)+3*2(x-2)(x+1) \ \text{ ... difference of squares rule}\\\\2*2(x-2)(x+2)+3*2(x-2)(x+1)\\\\2(x-2)(2(x+2)+3(x+1))\\\\2(x-2)(2x+4+3x+3)\\\\\boldsymbol{2(x-2)(5x+7)}\\\\[/tex]
The answer has been confirmed with WolframAlpha which is basically a calculator app, but does a ton more than any average calculator.
The CAS (computer algebra system) in the app GeoGebra is another tool I use all the time.
Yet another way to confirm the answer is to graph the original expression and the answer as separate functions. You should find they produce the exact same curve. One curve perfectly overlaps the other. This visually verifies the two expressions are the same thing, just written a different way of course.
Let me know if you have any questions about any step. The basic idea I did was to pull out the GCF and then combine like terms.
Use the Multiplication Law of Exponents to explain why 5^3*5^-3 = 1
(URGENT PLEASE)
Answers
The multiplication law states that
a^m×a^n=a^m+nSo
5³×5-³=15^(3-3)=15⁰=11=1Answer:
1 = 1
Step-by-step explanation:
5^3*5^-3 = 1We all know the law of exponents,the one we'll use to solve this is the multiplication law:
x^y * x^z = x^y+zIf the bases are equal or two numbers then the powers are equal too.Solved:
[tex]5^3 \: * \: 5^{-3} = 1[/tex][tex]5 {}^{3 + ( - 3)} = 1[/tex][tex]5 ^{0} = 1[/tex]x^0 = 1
[tex]1 = 1 \: ( \rm \: Proved)[/tex]Alternate method:
5^3*5^-3 = 15^3*1/5^3 = 15^3 and 5^3 cancels, which results to
1 = 1The following set of random numbers represents 20 simulations of three daily
flights from New York to Los Angeles, with 0, 1, 2, or 3 representing a late
departure and 4, 5, 6, 7, 8, or 9 representing an on-time departure. In how
many of the simulations was there an on-time departure for all three flights?
Answers
The number of simulations in which was there was an on-time departure for all three flights is; 6
How to carry out number simulations?
We are given;
Number of Simulations = 20
Numbers that represent late departure = 0, 1, 2 or 3
Numbers that represent On-time departure = 4, 5, 6, 7, 8 or 9.
Now, the 20 simulations as seen online are;
339 931 317 444 432 858 194 192 649 709
742 626 702 258 955 880 505 854 774 132
To know the number of simulations that were on-time departure, we need to find the ones that don't include 0, 1, 2 or 3.
Looking at the simulations, the ones that represent on-time departure are 444, 858, 649, 955, 854, 774.
Thus, there are 6 simulations in which was there an on-time departure for all three flights
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Which of the following are solutions to the equation below?
Check all that apply.
4x²-12x+9 = 5
□ A. x = -√5 + ³/2
B. x= √√4-3
C. X= -√√4-3
D. x = √5 + 1/2
3
N|W
□ E. x= -√5 +3
2
□ F. X=
√√5+3
2
Answers
The solutions of the given equation are x= (√5+3)/2 & x= (-√5+3)/2
What is sridharacharya formula ?
If ax²+bx+c = 0 is a quadratic equation ,where a,b,c are real numbers, Then the solution is x = (-b±√(b²-4ac))/2a , where a≠0
Which are the solutions of the equation ?The given equation is, 4x²-12x+9 = 5
So, 4x²-12x+9 = 5
⇒ 4x²-12x+9-5 = 0
⇒ 4x²-12x+4 = 0
Comparing this equation with ax²+bx+c = 0 we get,
a = 4, b = -12, c = 4
Applying sridharacharya formula we get,
x = (-(-12)±√((-12)²-4×4×4))/(2×4)
= (12±√(144-64)/8
= (12±√80)/8
= (3±√5)/2
The values of x are (√5+3)/2 & (-√5+3)/2
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If 10% off is 20 what is 23% off?
Answers
The person who answered is correct
if you do all you'll get brainliest
Drive-In movie theatres are outdoor movie venues where people park facing a large screen and watch a movie from their own car. Daisy’s Drive-In charges $14.00 for a vehicle and an additional $4.00 per person in the car. Donald’s Drive-In charges $26.00 for a vehicle and an additional $2.00 per person in the car.
Write two equations that represent the 2 drive-in theatres.
Daisy’s Drive-In:
Donald’s Drive-In:
Graph the system of equations. Label the x and y axis and give the graph a title. Label each line.
What is the point of intersection on your graph? What does this mean in context of the problem? Answer in complete sentences.
Compare and contrast the theatre options. When will Daisy’s be a better deal? When will Donald’s be a better deal? Explain how you know. Answer in complete sentences.
Answers
Daisy’s: y = 4x + 14
Donald’s: y= 2x + 26
The point of intersection is (6, 38)
This point refers to how many of passengers it will take for both equations to have have the same cost output.
Daisy’s deal is better if you have less than 6 passengers. We can tell because the line for the equation is lower than Donald’s line. Donald’d deal will be better if you have more than 6 passengers since the line is lower than daisy’s deal.
Two piecewise functions are shown below. What is the value of
6f (-2) + 3g (1)?
f(x) =
0-7
O-25
1/3
O 18
{
-3x
*+2'
if x < -2
³, if x ≥-2
(2|x-1| +3,
-5√x+3-1,
g(x) =
={
if x ≤ 1
if x > 2
Answers
Step-by-step explanation:
I am not sure what your problem here is.
you understand the inequality signs ?
anyway, to get
6×f(-2) + 3×g(1)
we can calculate every part of the expression separately, and then combine all the results into one final result.
f(-2)
we look at the definition.
into what category is -2 falling ? the one with x<-2, or the one with x>=-2 ?
is -2 < -2 ? no.
is -2 >= -2 ? yes, because -2 = -2. therefore, it is also >= -2.
so, we have to use
1/3 x³
for x = -2 that is
1/3 × (-2)³ = 1/3 × -8 = -8/3
g(1)
again, we look at the definition.
into what category is 1 falling ? the one with x > 2 ? or the one with x <= 1 ?
is 1 > 2 ? no.
is 1 <= 1 ? yes, because 1=1. therefore it is also <= 1.
so we have to use
2×|x - 1| + 3
for x = 1 we get
2×0 + 3 = 3
6×f(-2) = 6 × -8/3 = 2× -8 = -16
3×g(1) = 3× 3 = 9
and so in total we get
6×f(-2) + 3×g(1) = -16 + 9 = -7
how many ounces of a 16% alcohol solution must be mixed with 2 ounces of a 20% alcohol solution to make a 17% alcohol solution?
Answers
Answer:
x = 6
Step-by-step explanation:
.16x + 2 * .02 = (x + 2) * .17
.16x + .4 = .17x + .34
.06 = .01x
6 = x
Ali had 3 times as many marbles as cho does. After cho gives 4 marbles to Ali, Ali has 18 more marbles than cho does. How many more marbles does cho have in the beginning
a. 5
b. 9
c. 10
d. 15
Answers
Answer:
d. 15
Step-by-step explanation:
Let A and C be the initial number of marbles Ali and Cho have, respectively.
We are told that:
A = 3C [Ali had 3 times as many marbles as cho does]
We then discover that
C-4 = A-18 [After cho gives 4 marbles to Ali, Ali has 18 more marbles than cho does]
How many more marbles does cho have in the beginning?
We have 2 equations and 2 unknowns (A and C). That means we can likely rearrange one of the equations and isolate one unknown on the left, and then use that in the second equation.
The first equation already has one of the unknowns isolated (A) so I'll use that in equation 2.
Eq. 1: A = 3C
Eq. 2: C-4 = A-18
Use the definition of A from Eq. 1 (=3C) to replace A in Eq. 2:
Eq. 2: C-4 = A-18
C-4 = (3C)-18 [Replace A with 3C, as promised in E1q. 1]
-2C = -14
C=7
If C = 7, then from Eq. 1, A = 21
In the beginning, Ali has 21 marbles and Cho has 7.
Cho has 15 more marbles than Ali in the beginning.
a. 5
b. 9
c. 10
d. 15
What is the common difference of the following arithmetic sequence?
{15,11,7,3,...}
Answers
Answer:
Solution : AP = 19 , 15 , 11 , 7 , 3.....
Common difference ( d ) = 15 - 19 = -4.
Answer:
The common difference is -4.
Step-by-step explanation:
Subtract a term from the next term.
11 - 15 = -4
The common difference is -4.
On a coordinate plane, 2 dashed lines are shown. The first straight line has a negative slope and goes through (0, 1) and (2, 0). Everything below and to the left of the line is shaded. The second straight line has a positive slope and goes through (negative 1, 0) and (0, 2). Everything above and to the left of the line is shaded. A point is shown at (negative 3, 1).
Which system of inequalities with a solution point is represented by the graph?
y > 2x – 2 and y < Negative one-halfx – 1; (3, 1)
y > 2x – 2 and y < Negative one-halfx + 1; (–3, 1)
y > 2x + 2 and y < Negative one-halfx – 1; (3, 1)
y > 2x + 2 and y < Negative one-halfx + 1; (–3, 1)
Answers
Answer:
Using the concepts of coordinate system and equation of line, we find that y ≥ (1/3)x + 3 and 3x-y > 2 are represented by the graph.
Step-by-step explanation:
Equation of line passes through points (a, b) and (c, d) is given by:
y-b = [(d-b) / (c-a)] / (x-a)
Given that the first solid line (≤ or ≥) has a positive slope and goes through (0, 3) and (3, 4).
y-3 = [(4-3) / (3-0)] / (x-0)
y-3 = x / 3
y - (1/3)x = 3
Also, everything above the line is shaded, i.e. the inequality represents the first graph: y ≥ (1/3)x + 3
The second dashed line (< or >) has a positive slope and goes through (0, - 2) and (1, 1).
y+2 = [(1+2) / (1-0)](x-0)
y+2 = 3x
3x-y = 2
Everything to the right of the line is shaded.
i.e. inequality represents the second graph: 3x-y > 2
Hence, the system of linear inequalities is represented by the graph :
y ≥ (1/3)x + 3
3x-y > 2
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Answer:
D
Step-by-step explanation:
Got it right on edge 2022
Toby has $31 to buy t-shirts for his bowling team. each t-shirt costs $5. how many t-shirts can he buy?
Answers
Answer:
6 because 30 divided by 5 is 6 so he would have 1$ change
Answer:
Toby can buy 6 T-shirts with 1 extra dollar leftover
Step-by-step explanation:
Hook me up with a 5 star and a thanks :)
Which graph represents the following system of inequalities?
Answers
Answer:
D
Step-by-step explanation:
On graphing the 3 equations, we find that the central area (triangle) formed by the 3 inequalities is the solution.
Answer:
D
Step-by-step explanation:
When graphing inequalities:
< or > : dashed lines≤ or ≥ : solid line< or ≤ : shading under the line> or ≥ : shading above the lineGiven inequalities:
[tex]\begin{cases}y > \dfrac{1}{2}x-1\\\\y\leq -x+1\\\\y > -2x-1 \end{cases}[/tex]
From inspection of the given graphs, the red dashed line is the first inequality as it is the only inequality with a positive slope.
The blue sold line is the second inequality, as it is the only inequality with the sign that suggest a solid line.
Therefore, by process of elimination, the green dashed line is the third inequality.
Using the inequality signs and their definitions for shading, find the graph that has:
Shading above the red dashed lineShading below the blue solid lineShading above the green dashed lineThe only graph that matches these conditions is graph D
Expand and simplify x(x + 2)(x + 4)
Answers
Answer:
Step-by-step explanation:
Comment
Expand the second and 3rd factors first. Then worry about the x.
Solution
x(x + 2)(x + 4)
first: x * x = x^2
Outside: 4*x = 4x
Inside: 2*x = 2x
Last: 2*4 = 8
Combine
x^2 + 4x + 2x + 8
x^2 + 6x + 8
Now is the time to worry about the extra x
x(x^2 + 6x + 8)
remove the brackets.
x*x^2 + x*6x + 8*x
Combine
Answer: x^3 + 6x^2 + 8x
Summer looked at the formula for the Pythagorean Theorem, a2 + b2 = c2, she said that it didn’t matter which sides of a right triangle were a, b, and c. Is she correct?
Answers
Answer:
Summer is incorrect
Step-by-step explanation:
It definitely matters which side is side "c". Side "c" must be the hypotenuse (the side across from the right angle).
The other two sides are the legs (sides touching the right angle), and either leg can be "a" or "b", but the hypotenuse must be "c".
Take the equation, a² + b² = c², and subtract c² from both sides:
[tex]a^{2} +b^{2} -c^{2} =0[/tex]
It won't matter which leg is "a" or "b", because of the commutative property of addition. Note that "a²" and "b²" are added together, and due to the commutative property of addition, we can add in either order and get the same result.
However, since the c² term is connected by subtraction, and subtraction doesn't have a commutative property, it can't be subtracted in any order. Meaning which side it is is important.
What is 21% of 456? Calculate the percentages. Make sure to show all your work!
Answers
Answer:
21% of 456 = 0.21 x 400 + 0.21 x 50 + 0.21 x 6 = 95.76
Step-by-step explanation:
The function gives the mass, m, of a radioactive substance remaining after h half-lives. Cobalt-60 has a half-life of about 5.3 years. Which equation gives the mass of a 50 mg Cobalt-60 sample remaining after 10 years, and approximately how many milligrams remain?
Answers
The equation is [tex]f(t)=50(0.5)^{\frac {10}{5.3}}[/tex] and approximately 13.52 milligram remains
How to determine the equation?The missing information in the question is:
[tex]f(t)=m(0.5)^{\frac th}[/tex]
When the mass is 50 mg, it means that:
m = 50
So, we have:
[tex]f(t)=50(0.5)^{\frac th}[/tex]
When 10 years remain in the life of the substance, it means that:
t = 10
So, we have:
[tex]f(t)=50(0.5)^{\frac {10}h}[/tex]
The half life is 5.3. So, we have
[tex]f(t)=50(0.5)^{\frac {10}{5.3}}[/tex]
Evaluate the equation
f(t) = 13.52
Hence, the required equation is [tex]f(t)=50(0.5)^{\frac {10}{5.3}}[/tex] and approximately 13.52 milligram remains
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Answer:c
Step-by-step explanation:
Dixie lives in a $67,000 wood house in the country whose contents are valued at $12,000. She wants to know her monthly property insurance premium. Use the table above to calculate her monthly property insurance premium.
Answers
Without the table indicating the stated premium rates and applicable discounts, the monthly property insurance cannot be computed. Hence, on the assumption that the rate is 2.5% and the discount applicable is 7.5% the premium per month will come to $152.24
What is Property Insurance?
The simple definition of Property Insurance is, it is an insurance policy that covers a policyholder for the structure of a building and its contents against stated or agreed perils.
What is the calculation for the above?Given (based on assumption) that the applicable annual rate is 2.5%
and that:
Value of Wooden House = $67,000Value of the contents of the House = $12,000Applicable discount = 7.5% of premium/annumHence annual premium will be:
= (67,000 + 12000) * (2.5/100) * 0.925
Annual Premium Payable = $1,826.89.............A
Recall that we are asked to derive the monthly Insurance premium.
This is thus given as: Answer in A/12
→ 1,826.89/12
= $152.24
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The graphs below have the same shape. What is the equation of the red
graph?
Answers
Answer:
g(x) = x^2+4
Step-by-step explanation:
The graph of f(x) = x^2 is translated up 4 units to become g(x) = x^2+4
Solve for X
2x+ 17
3x-4
Answers
Answer:
x = 21
Step-by-step explanation:
3x - 4 = 2x + 17 because of alternate angles
3x - 2x = 17 + 4
x = 21
Two similar triangles are shown below:
Two triangles are shown. The sides of the triangle on the left are marked 6, 4, 3. The sides of the triangle on the right are marked as 3, 2 and 1.5. For the triangle on the left, the angle between sides marked 4 and 6 is labeled as w, marked by a double arc, and the angle between the sides marked 6 and 3 is labeled as x, marked by a single arc. The third angle is marked by a triple arc. For the triangle on the right, the angle between sides marked 3 and 1.5 is labeled as y and the angle between the sides marked 2 and 3 is labeled as v, marked by a double arc. The angle between the sides 2 and 1.5 is labeled as z, marked by a triple arc, and it is also the angle on the top vertex of this triangle.
Which two sets of angles are corresponding angles?
∠w and ∠v; ∠x and ∠y
∠w and ∠y; ∠x and ∠v
∠w and ∠z; ∠x and ∠v
∠w and ∠z; ∠x and ∠y
Answers
Two sets of angles are corresponding angles will be ∠w = ∠v and ∠x = ∠y. Then the correct option is A.
What is the triangle?A triangle is a three-sided polygon with three angles. The angles of the triangle add up to 180 degrees.
Two similar triangles are shown below:
Then two sets of angles are corresponding angles will be
∠w = ∠v and ∠x = ∠y
Then the correct option is A.
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Two circles are concentric if they have the same center.
On a coordinate plane, a circle has center (4, 6) and has a radius of 2 units.
Which equation represents a circle that is concentric with the circle shown but has a radius that is twice as large?
(x – 4)2 + (y – 6)2 = 4
(x – 4)2 + (y – 6)2 = 16
(x – 6)2 + (y – 4)2 = 16
(x – 6)2 + (y – 4)2 = 4
Answers
The equation of the circle is (x - 4)² + (y - 6)² = 16. The correct option is the second option (x - 4)² + (y - 6)² = 16
Equation of a circleFrom the question, we are to determine the equation of the circle
The equation of circle is given by
(x - h)² + (y - k)² = r²
Where (h, k) is the center
and r is the radius
From the given information,
The two circles are concentric
∴ (h , k) = (4, 6)
But the other circle has a radius that is twice as large
∴ r = 2 × 2
r = 4
Thus,
The equation of the circle becomes
(x - 4)² + (y - 6)² = 4²
(x - 4)² + (y - 6)² = 16
Hence, the equation which represents a circle that is concentric with the circle shown but has a radius that is twice as large is (x - 4)² + (y - 6)² = 16. The correct option is the second option (x - 4)² + (y - 6)² = 16
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Name the property of equality or congruence that justifies going from the first statement to the second statement.
3x+x+7=23
4x+7=23
Answers
Answer:
Reflexive Property
PLEASE PLEASE HELP WILL MARK BRAINLIEST!!
Which choice is equivalent to the product below when x > 0?
A. x/9
B. 1/3
C. x/3
D. 1/9
Answers
The equivalent expression to given expression is 1/3.
What is Equivalent Expression?Equivalent expressions are defined as algebraic expressions which give the same resulting expression. An algebraic expression (or) a variable expression is defined as a combination of terms by the operations such as addition, subtraction, multiplication, division.
Here, given expression
[tex]\sqrt{2/x^2} X \sqrt{x^2/18}[/tex]
= [tex]\sqrt{2 X x^2/18x^2}[/tex]
= [tex]\sqrt{1/9}[/tex]
= 1/3
Thus, the equivalent expression to given expression is 1/3.
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Use substitution to solve the following system of equations
2x + 3y = 18 AND X = y - 6
Answers
Answer:
y=6,x=0
Step-by-step explanation:
here's an attachment with how to solve
Please Help!10.<ADC and <FDA are a linear pair. What is the reason?
Answers
Answer:
Linear pair of angles are formed when two lines intersect each other at a single point. Therefore, <ADC and <FDA are a linear pair.
Step-by-step explanation:
Graph the system of inequalities presented here on your own paper; then use your graph to answer the following questions:
Y > -4x-1
y<3/2x-1
Part A:
Describe the graph of the system; including shading and the types of lines graphed Provide a description of the solution area: (6 points)
Part B: Is the point (-1,1) included in the solution area for the system? Justify your answer mathematically
Answers
It is to be noted that the Graph of the indicated inequalities is herewith attached.
What is the graph of the system?As indicated above, this is a graph of a system of inequalities, where:
Y > -4x-1 and
y <3/2x-1
Is the point (-1,1) included in the solution area for the system?No. the point (-1, 1) is not included in the solution area for the system.
How do we justify this mathematically?
Step 1 - Plug in (-1, 1) in to the first equation. where y = -1 and x = 1.
Hence,
-1 > -4(1) -1
4 +1 < -1
4 < 0 (This is False)
Step 2 - Plug in (-1, 1) in to the second equation. where y = -1 and x = 1.
-1 < (3/2)(1) - 1
-1 < 1/2 (This is true).
Thus (-1, 1) is only partially included in the solution area.)
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Simplify x^5 •x^2 • x