The quadratic regression in this case is y = 126.01x2 - 312.04x + 888.88.
What do you mean by quadratic regression?An analysis tool called quadratic regression is implemented to identify the parabola equation that perfectly matches a given collection of data. Finding the equation of the straight line that most closely matches a collection of data is the goal of this sort of regression, which is an expansion of simple linear regression.
Step 1: Input the data sets into the graphing calculator.
Step 2: Choose "Scatter Plot" from the graphing calculator's interface.
Step 3: Choose "Quadratic Regression" from the graphing calculator's toolbar.
Step 4: The calculator will create the equation y=ax2+bx+c, where a, b, and c are constants.
Step 5: Round the constants to the hundredths place, and the best-suited quadratic model's equation will be: y = 0.06x2 - 3.12x + 4.00.
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which equation can be solved to find one of the missing side lengths in the triangle? triangle a b c is shown. angle a c b is 90 degrees and angle c b a is 60 degrees. the length of side c b is a, the length of c a is b, and the length of hypotenuse a b is 12 units.cos(60o)
The equation cos (60°) = a/12 can be used to find one of the missing side lengths in the triangle.
Trigonometric identities are equations that are true for all values of the angles in a right triangle. They express the relationships between the angles and sides of a triangle and are used to simplify trigonometric expressions or to prove that two expressions are equal.
One of the trigonometric identities is the SOH CAH TOA.
SOH: sin θ = opposite/hypotenuse
CAH: cos θ = adjacent/hypotenuse
TOA: tan θ = opposite/adjacent
Since angle CBA is 60°, the adjacent side is a, the opposite side is b, and the hypotenuse is 12 units, then:
cos θ = adjacent/hypotenuse
cos (60°) = a/12
Rearranging the equation, we can solve one of the missing side lengths, which is a.
a = 12cos(60°)
Hence, we can use the equation cos (60°) = a/12 to find the length of side a.
The problem seems incomplete, it must have been...
"Which equation can be solved to find one of the missing side lengths in the triangle? Triangle A B C is shown. Angle A C B is 90 degrees and angle C B A is 60 degrees. The length of side C B is a, the length of C A is b, and the length of hypotenuse A B is 12 units.
cos(60°) = 12/a
cos(60°) = 12/b
cos(60°) = b/a
cos(60°) = a/12"
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ANSWER ASAP OR MY MOM WILL BE MAD CUZ SHES ABOUT TO LOOK AT MY WORK IN MATH
25% of 84 is what value?
3
20
21
59
Imagine a lidless box with height h and a square base whose sides have length x. The box must have a volume of 117 ft^3. Estimate the value of x that produces the box with a minimum surface area.
The closest value of x that would produce the box with the minimum surface area would be 117 ft.
The volume of a lidless box with height h and a square base with sides of length x is given by V = x^2 * h.
To have a volume of 117 ft^3, we have:
x^2 * h = 117
The surface area of a lidless box is given by:
A = 2x^2 + 4xh
We want to minimize this surface area while still keeping the volume of the box at 117 ft^3. To do this, we need to find an expression for h in terms of x, and then minimize A in terms of x.
From the volume equation, we can solve for h:
h = 117 / x^2
Substituting this expression into the surface area equation, we get:
A = 2x^2 + 4x * (117 / x^2)
= 2x^2 + 466 / x
Now, we can use calculus to find the minimum of A in terms of x.
The derivative of A with respect to x is:
dA/dx = 4x - 466 / x^2
Setting dA/dx equal to zero, we find the critical points:
4x - 466 / x^2 = 0
4x = 466
x = 116.5
We now need to check if x = 116.5 is a local minimum or maximum.
To do this, we need to examine the second derivative of A with respect to x:
d^2A/dx^2 = -932 / x^3
Since the second derivative is negative, this means that A has a local minimum at x = 116.5.
Hence, the value of x that produces the box with a minimum surface area is approximately 116.5 ft.
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Fred’s fish tank is shown below how many cubic feet of water will he need to fill in his fish tank l=8.3ft W=11.5ft H=6
Answer:
611.05
Step-by-step explanation:
To find the number of cubic feet of water needed to fill Fred's fish tank, we need to calculate the volume of the tank. The volume of a rectangular prism (such as a fish tank) can be found by multiplying the length, width, and height together. Using the given measurements, the volume of Fred's fish tank would be:
8.3 ft * 11.5 ft * 6 ft = 611.05 cubic ft
So, Fred will need 611.05 cubic ft of water to fill his fish tank.
solve 10 + x ≥ 14. then graph the solution.
Answer:
x ≥ 4
Step-by-step explanation:
Just treat the equation like you would a regular algebraic equation.
10 + x ≥ 14
10 + x - 10 ≥ 14 - 10
x ≥ 4
As for graphing it, I'm not really sure if you want a proper graph or a number line.
For a number line, put a closed dot on a 4
is 12,15,18 a phythagorean triple?
Answer:
Below
Step-by-step explanation:
Put the numbers into the pythagorean theorem to see if true
12^2 + 15^2 = 18^2 ??????
144 + 225 = 324 ?????
369 = 324 ?????? <========= not true ....not a triple
Andrea is buying some new shirts and sweaters. She is able to buy 6 shirts and 7 sweaters for $212 or she is able to buy 10 shirts and 8 sweaters for $258. How much does a shirt cost? How much does a sweater cost?
Answer:
Sweater: $26
Shirt: $5
Step-by-step explanation:
Systems of Equations:We can set up two linear equations to form a systems of equations which will allow us to solve for the price of a shirt and sweater.
The first step we want to take is assigning the shirt and sweater to an unknown, so I'll just refer to the price of a shirt as: [tex]S_h[/tex] with the little subscript "h" and I'll refer to the price of a sweater as: [tex]S_w[/tex] with the little subscript "w".
Now the next main thing to understand is we can calculate the total price of something by multiplying the price of an individual item by the quantity. So if I buy an apple for $10, but I buy 10 of them, then the total price would be 10 * 10 or $100. So when Andrea buys 6 shirts, the price of that can be represented as: [tex]6S_h[/tex] and when Anrea buys 7 sweaters the price of that can be represented as: [tex]7S_w[/tex], adding these together should equal 212, since it gives us that buying 6 shirts and 7 sweaters costs a total of $212.
Using this logic with the other case where she buys 10 shirts and 8 sweaters for $258, we can set up the two equations:
[tex]6S_h + 7S_w=212\\10S_h+8S_w=258[/tex]
From here we can use substitution to solve this equation. So let's solve for the [tex]S_h[/tex] on the top equation.
[tex]6S_h+7S_w=212[/tex]
Froom here subtract [tex]7S_w[/tex] from both sides and then divide by 6
[tex]S_h=\frac{212-7S_w}{6}[/tex]
Now we can plug this into the second equation:
[tex]10(\frac{212-7S_w}{6})+8S_2=258[/tex]
Simplifying the division and multiplication on the left side we get:
[tex]\frac{1060}{3}-\frac{70}{6}S_w+8S_w=258[/tex]
From here we can combine the like terms
[tex]\frac{1060}{3}-\frac{22}{6}S_w=258[/tex]
we can simplify the fraction a bit more
[tex]\frac{1060}{3}-\frac{11}{3}S_w=258[/tex]
Now subtract 1060/3 from both sides
[tex]\frac{-11}{3}S_w=\frac{-286}{3}[/tex]
Now divide both sides by -11/3
[tex]S_w=26[/tex]
Now from here we can substitute this back into any equation to solve for the shirt price. Let's use the equation where we solved for the price of the shirt but we just needed to know the price of the sweater.
[tex]S_h=\frac{212-7S_w}{6}[/tex]
Now let's plug in 26 for the sweater price.
[tex]S_h=\frac{212-7(26)}{6}[/tex]
Simplify this and we get:
[tex]S_h=5[/tex]
and now we know the shirt and sweater price!
According to the Anxiety and Depression Association of America (ADAA), approximately 8.7% of all adults suffer from a specific phobia, such as high bridges or old elevators. An experiment consists of selecting adults at random and asking them if they suffer from any kind of phobia. Is there any evidence to suggest the ADAA claim is false? Justify your answer. Because the probability that 35 people are selected before the first person with a phobia is chosen is 0.0453, there _____ evidence that the claim about the probability of people having a phobia being 8.7% is false.
The probability of 35 people being selected before the first person with a phobia being chosen does not provide sufficient evidence to suggest that the ADAA claim is false. To determine if the ADAA claim is false, we would need to perform a statistical hypothesis test to compare the sample proportion of adults with phobias to the ADAA estimate of 8.7%. This would involve collecting data on a random sample of adults, calculating the sample proportion of adults with phobias, and comparing it to the ADAA estimate of 8.7%.
If the sample proportion is significantly different from 8.7%, we can conclude that there is evidence to suggest that the ADAA claim is false. However, without performing a statistical hypothesis test, we cannot make a conclusion about the validity of the ADAA claim based solely on the probability of 35 people being selected before the first person with a phobia is chosen.
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line ab is shown on the grid a is the point (0,3) b is the point (6,6) work out the coordinates of the midpoint of the line ab
Answer:
(3, 4.5)
Step-by-step explanation:
x = [tex]\frac{0 + 6}{2}[/tex] = 3
y = [tex]\frac{3+6}{2}[/tex] = 4.5
During the time interval 4 St ≤ 8, the rate at which the number of wolves in a forest is changing, in wolves per week, can be modeled by the function
E(t) = 31 cos(0.11t?), where t is measured in weeks.
What is the rate at which the number of wolves in the
forest is changing at timet = 7? You may use a
calculator and round to the nearest thousandth. Indicate units of measure.
For the function E(t) = 31 cos (0.11t), the rate at which the number of wolves in the forest is changing at time t = 7 is 22.2549.
What is a function?
In mathematics, a function is a unique arrangement of the inputs (also referred to as the domain) and their outputs (sometimes referred to as the codomain), where each input has exactly one output and the output can be linked to its input.
The function to model the rate at which the number of wolves in a forest is changing is E(t) = 31 cos (0.11t)
Here t is the time measured in weeks.
The time value is given as t = 7
Substitute the value of t in the equation -
E(t) = 31 cos (0.11t)
Apply the arithmetic operation of multiplication -
E(7) = 31 cos (0.11 × 7)
E(7) = 31 cos (0.77)
E(7) = 31 × 0.7179
E(7) = 22.2549
Therefore, the rate value is obtained as 22.2549.
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Is the following statement true or false? the mean of a random sample equals the mean of the population from which it was drawn.
The claim that the average of a random sample is the same as the average of the population from which it was taken is False.
Is the sample mean the same as the population mean?The sample mean will, of course, differ from the population means. The sample mean, however, is a fair estimation of the population mean if the sample is a simple random sample.
Thus, neither the sample mean nor the population mean is statistically greater or lower. The sample mean will always have a mean that is identical to the mean of the original non-normal distribution. In other words, the population mean is the same as the sample mean.
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class 10r sat a test
the mean mark was 70%
there are thirty students in class 10r, 20 of whom are boys
the mean mark for the boys in the test was 62%
work out the mean of the girls
Answer:
15% tell me if im wrong
Step-by-step explanation:
simplify!!
(-2x^2-3x+4)+(-4x^2+x-2)
Answer:
number b is the write answer
Step-by-step explanation:
-2x²-3x+4-4x²+x-2
-2x²-4x²-3x+x+4-2
-6x²-2x+2
(a) The displacement (in centimeters) of a particle s moving back and forth along a straight line is given by the equation
s = 2 sin(t) + 3 cos(t),
where t is measured in seconds. (Round your answers to two decimal places.)
[1, 2]
[1, 1.1]
[1, 1.01]
[1, 1.001]
(b) Estimate the instantaneous velocity of the particle when
t = 1.
The displacements are 2.84 cm, 2.77 cm, 2.83 cm and 2.83 cm respectively.
Instantaneous velocity of the particle at t =,1 is 0.72 cm/s.
How to calculate displacement and velocity?a. To find the displacement of the particle at various times t, we can simply plug the given value of t into the equation s = 2 sin(t) + 3 cos(t) and evaluate:
[1, 2]: s = 2 sin(1) + 3 cos(1) = 2.84 cm
[1, 1.1]: s = 2 sin(1.1) + 3 cos(1.1) = 2.77 cm
[1, 1.01]: s = 2 sin(1.01) + 3 cos(1.01) = 2.83 cm
[1, 1.001]: s = 2 sin(1.001) + 3 cos(1.001) = 2.83 cm
b. To find the instantaneous velocity of the particle when t = 1, we need to find the derivative of the equation for displacement with respect to time, which will give us the velocity. The derivative is given by:
v(t) = ds/dt = 2 cos(t) - 3 sin(t)
Plugging in t = 1 into this equation, we find:
v(1) = 2 cos(1) - 3 sin(1) = 0.72 cm/s
So, the instantaneous velocity of the particle at t = 1 is approximately 0.72 cm/s.
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If f(x) = 2x³ + x² - 3x + 4 , what is f'(2) ?
Answer:
f'(2) = 25
Step-by-step explanation:
differentiate f(x) using the power rule
[tex]\frac{d}{dx}[/tex] ( a[tex]x^{n}[/tex] ) = na[tex]x^{n-1}[/tex] and [tex]\frac{d}{dx}[/tex] ( constant) = 0
f(x) = 2x³ + x² - 3x + 4
f'(x) = 3× 2x² + 2x - 3 = 6x² + 2x - 3 , then
f'(2) = 6(2)² + 2(2) - 3
= 6(4) + 4 - 3
= 24 + 1
= 25
HELLLLP MEEEE PLEASEE
Answer:
34 R 12
Step-by-step explanation:
I will add an explanation later, because I do not have time, I have to go somewhere.
It'll be added in at least 1 day AT MOST.
determine if ST is parallel to PR
Answer:
Step-by-step explanation:
Picture?
You didn’t give enough info. Are you able to provide more information? Or a picture?
The equation 3x -4y=3
The equation 3x -4 =12
The equation 3x +4y=12
Answer:
The point (4,0) lies on the line.
All the other answers are not applicable for this situatino.
Step-by-step explanation:
En una empresa de papas fritas una máquina automática debe llenar las bolsas manteniendo una determinada cantidad de gramos, sin embargo, en algunas ocasiones los paquetes de papas pueden pesar más o menos del peso establecido. Se revisaron 2500 bolsas de los últimos días, en las cuales 2100 bolsas tuvieron el peso correcto, 275 tuvieron un peso menor y 125 tuvieron un peso mayor
The Percentage of bags with correct weight will be 84%
How to calculate the percentage?A percentage simply has to do with the a value or ratio which can be stated as a fraction of 100. It should be noted that when we want to we calculate a percentage of a number, we simply divide it and then multiply the value that is gotten by 100.
From the information, the following can be gotten:
Total number of bags = 2500
Bags with correct weight = 2100
Bags with lower weight = 275
Bags with higher rate = 125
Percentage of bags with correct weight will be:
= 2100 / 2500 × 100
= 84%
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Write each expression as a fraction and then reduce the fraction
[tex](1 + {a }^{3} ) \div (1 + a)[/tex]
[tex]\textit{difference and sum of cubes} \\\\ a^3+b^3 = (a+b)(a^2-ab+b^2) ~\hfill a^3-b^3 = (a-b)(a^2+ab+b^2) \\\\[-0.35em] ~\dotfill\\\\ (1+a^3)\div (1+a)\implies \cfrac{1+a^3}{1+a}\implies \cfrac{1^3+a^3}{1+a} \\\\\\ \cfrac{~~\begin{matrix} (1+a) \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~(1^2 - (a)(1)+a^2)}{~~\begin{matrix} 1+a \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}\implies 1^2 - (a)(1)+a^2\implies \boxed{a^2-a+1}[/tex]
In 1976, a certain model of car cost $5,000. What would be the cost of that car in 1983 dollars? Express your answer rounded to the nearest cent.
The cost of car in the year 1983 is 2845
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
The CPI (consumer price index) is a measure of the overall change in prices of goods and services over a certain period of time. It is given by:
CPI = (cost of market basket in a given year / cost of market basket in base year) * 100
Given that:
CPI = 56.9 in 1976, cost of market basket in a given year = x, cost of market basket in base year = $5000
Hence:
56.9 = (x/ 5000) * 100
x = 2845
The cost of car is 2845
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Which graph shows the solution to the system of linear equations?
y = 2x − 2
4x − 2y = 4
Coordinate plane with one line that passes through the points 0 comma negative 2 and 1 comma 0.
Coordinate plane with one line that passes through the points 0 comma negative 1 and 1 comma 1 and another line that passes through the points 0 comma negative 2 and 1 comma 0.
Coordinate plane with one line that passes through the points 0 comma 1 and 1 comma 2.
Coordinate plane with one line that passes through the points 0 comma negative 2 and 1 comma 0 and another line that passes through the points 0 comma 1 and 1 comma 2.
The solution of the system of equations can be seen in the image at the end, the system has infinite solutions.
Which graph shows the solution of the system of equations?Here we have the system of linear equations below:
y = 2x - 2
4x - 2y = 4
To find the solution graphically, we need to graph both of the equations on the same coordinate axis and find the point where the lines intersect.
The graph can be seen in the image below, and there you can see only one line, that is because both of the equation of our system represent the same line, and thus, the system has infinite solutions.
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The population of 6 different states is shown below. Order the populations from the source to the target in order of GREATEST to LEAST value.
Florida: 1.98 x 10^7
Arizona: 6,730,000
Washington: 7.06 x 10^6
New York: 19,700,000
California: 3.88 x 10^7
Massachusetts: 6.74 x 10^6
Ordering the populations of the 6 different states, written in scientific notations, in order of the greatest to the least value is as follows:
California: 3.88 x 10^7Florida: 1.98 x 10^7New York: 19,700,000Washington: 7.06 x 10^6Massachusetts: 6.74 x 10^6Arizona: 6,730,000.What is scientific notation?Scientific notation is the standard way of writing very long or short numbers in their shorthand forms.
A number is written in scientific notation when a number between 1 and 10 is multiplied by a power of 10, with the following parts: coefficient, base, and exponent.
For instance, New York's population is 19,700,000 and can be written in scientific notation as 1.97^7.
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Find the slope of the line described by the table.
M =
The slope of the line describes by the table is 0.1.
What are lines and their slopes?We know lines have various types of equations, the general type is
Ax + By + c = 0, and the equation of a line in slope-intercept form is
y = mx + b.
Where slope = m and b = y-intercept.
the slope is the rate of change of the y-axis with respect to the x-axis and the y-intercept is the (0,b) where the line intersects the y-axis at x = 0.
The table represents Bike ride, where x represents the number of minutes in 'x' and y represents the number of kilometers.
We know, slope(m) = (y₂ - y₁)/(x₂ - x₁).
Slope(m) = (1.0 - 0.5)/(10 - 5).
Slope(m) = 0.5/5.
Slope(m) = 0.1
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The number of households in the U.S. that own homes is 79.4 million, or 63.5% of all households. Find the total number of households to the nearest hundredth of a million.
Answer:
125 million
Step-by-step explanation:
[tex]79.4 \times \frac{100}{63.5} = 125.03[/tex]
Three friends are participating in a relay race where they each need to eat a hotdog as fast as they can. The first friend, Monica, starts eating as soon as the timer starts. When she finishes eating the hot dog, her team earns one point. Then, the next friend, Richard, starts eating the second hotdog. As soon as he finishes eating, the team earns another point. Finally, Andrew starts eating the third hotdog. As soon as he finishes eating the team earns their third point.
The graph below shows the points the team has (y) in relation to the time in minutes (x):
Use this information to answer the following questions:
How many points does the team have 1 minute into the competition?
How many points does the team have 5 minutes into the competition?
After how many minutes, does the team have 3 points?
The required solutions are as follows,
(a) The team has zero points in 1 minute of the competition.
(b) The team has two points in 5 minutes of the competition.
(c) After 8 minutes, the team has 3 points.
The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Here,
From graph,
As at 0 seconds the race started and Monia finished eating a hot dog at 3 minutes. so 1 to 2.9 minutes of race point is zero.
Scorecard with time is given as
1 to 2.9-minute score = 0
3 to 4.9-minute score = 1
5 to 7.9 minutes score = 2
after 8 minutes score = 3
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find the value of [tex](a-\frac{1}{a} )^2[/tex] and [tex](a-\frac{1}{a} )[/tex], when [tex]a^{2} +\frac{1}{a^2}=18[/tex]
Answer:
To find the value of (a - 1/a)^2 and (a - 1/a), we can start by squaring the given equation:
a^2 + 1/a^2 = 18
(a^2 + 1/a^2)^2 = 18^2
a^4 + 2 + 1/a^4 = 324
a^4 + 1/a^4 = 322
Now, to find (a - 1/a)^2, we can square the difference of a and 1/a:
(a - 1/a)^2 = a^2 - 2 + 1/a^2
We can substitute the value of a^4 + 1/a^4 = 322 into this equation:
(a - 1/a)^2 = 322 - 2
(a - 1/a)^2 = 320
To find (a - 1/a), we can take the square root of (a - 1/a)^2:
(a - 1/a) = √320
And, a^2 + 1/a^2 = 18, we can solve for a,
a^4 - 18a^2 + 1 = 0
(a^2 - 1)(a^2 - 18) = 0
a^2 = 1 or a^2 = 18
a = 1 or a = ±√18
So, in this case, the value of (a - 1/a)^2 is 320 and (a - 1/a) is √320.
Step-by-step explanation:
please help me will give u extra points :)
•
(5, 9), open (5), close (9), is the interval graph. This interval is inequitable because: 5 < x ≤ 9
What is meant by inequality?Inequality is the absence of an equality link between two expressions or values. So inequality emerges from an imbalance. A relationship that compares two numbers or other mathematical expressions in an unequal way is known as an inequality.It is most frequently used to compare the sizes of two numbers on the number line. The equals sign in the equation-like statement 5x 4 > 2x + 3 has been replaced by an arrowhead. This is a prime instance of inequality. This indicates that the left half, 5x 4, is larger than the right part, 2x + 3, in the equation.Therefore,
a) Letter A is erroneous since it implies that the graph should have two shaded areas, but this particular graph only has one.
b) Letter B is erroneous because the graph shows that there must be a parenthesis before point 5 because it is open, and point 9 must come after a because it is shaded.
c) The letter c is also wrong because it implies there are two shaded portions in the graph when there is only one.
The complete question is:
Which compound inequality can be represented by the graph below?
A) x < 5 or x ≥ 9
B) 5 ≤ x < 9
C) x ≤ 5 or x > 9
D) 5 < x ≤ 9
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A tank is full of water. Find the work W required to pump the water out of the spout. (Use 9.8 m/s2 for g. Use 1000 kg/m3 as the weight density of water. Assume that a = 4 m, b = 4 m, c = 18 m, and d = 3 m.)
W = __________ J
Answer:
Find the work required to pump the water out of the spout. (Use 9.8 m/s 2 for g. Use 1000 kg/m 3 as the weight density of water.
Step-by-step explanation:
Enter the exact value in terms of
π
.
Answer:
calculate = 3.14159
Step-by-step explanation:
convert to degrees 189°
positive angle
[tex] 3\pi \: positive \: angle[/tex]
