Answer:
See below
Step-by-step explanation:
Best way to do this is to convert the equation to vertex form and that will tell you several points you can graph:
\(y=x^2-4x-1\\y+5=x^2-4x-1+5\\y+5=x^2-4x+4\\y+5=(x-2)^2\\y=(x-2)^2-5\)
Here, we can see that the vertex of the parabola is (2,-5) and that the axis of symmetry is x=2. You can also quickly get the y-intercept since plugging in x=0 gets you (0,-1). Finding a few more points should be pretty simple from here on out since your equation is more condensed.
Find the equation of the exponential function represented by the table belowFind the equation of the exponential function represented by the table below:
x y
0 4
1 12
2 36
3 108
The equation of the exponential function is\(4 * 3^{x}\).
What is exponential function?
An exponential function is of the form:
\(f(x) = a^{x}\)
here "a" is a constant called the base, and "x" is the variable. The base "a" is typically a positive real number, but it can also be a negative number or a complex number. The function is called exponential because the variable "x" appears in the exponent.
We can see that as "x" increases by 1, "y" is multiplied by a constant factor of 3. This suggests that the exponential function has a base of 3. To find the equation, we can use the general form of an exponential function:
\(y = a * b^{x}\)
where "a" is the initial value or y-intercept, and "b" is the base.
We can use the given values of (x,y) to form a system of equations:
\(a * 3^{0} = 4\)
\(a * 3^{1} = 12\)
\(a * 3^{2} = 36\)
\(a * 3^{3} = 108\)
Simplifying each equation, we get:
a = 4
3a = 12
9a = 36
27a = 108
Solving for "a", we get:
a = 4
Substituting this value of "a" into the equation, we get:
\(y = 4 * 3^{x}\)
So the equation of the exponential function represented by the table is y \(= 4 * 3^{x}.\)
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what do public opinion researchers analyze to estimate the opinions of large populations? select an answer and submit. for keyboard navigation, use the up/down arrow keys to select an answer. a the demographics of the individuals of the population b polls conducted on small samples from those populations c social media activity of the selected population d polls distributed to most individuals from the population that is being analyzed
Public opinion researchers analyze polls conducted on small samples from those populations to estimate the opinions of large populations. The correct answer is b.
They use various sampling techniques to ensure the sample is representative of the population, and then analyze the results to make inferences about the opinions of the larger group. Survey sampling, as used in statistics, is the process of choosing a sample of constituents from a target population to perform a survey. The word "survey" can be used to describe a wide range of observational methods or procedures.
Most frequently, a questionnaire meant to assess people's traits and/or opinions is employed in survey sampling. The topic of survey data collecting is various methods of contacting sample participants after they have been chosen. Sampling is done to cut down on the expense and/or labor required to survey the complete target population. Therefore option b. is the correct answer.
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hii pls help asap ty
Answer: 0.45 :)
Step-by-step explanation:
divide y by x
I'm considering the line with the equation y equals x + 9 I need to find a line parallel to it which passes through -2 negative 4 and perpendicular which also passes through negative two negative 4
a) y = x - 2
b) y = -x -6
Explanation:\(\begin{gathered} \text{The equation:} \\ \text{y = x + 9} \\ \text{This equation is a staright line and has a slope} \end{gathered}\)a) parallel line that passes through (-2, -4)
For a line to be parallel to another line, the slope of both lines must be equal
y = x + 9
comparing with equation of line:
y = mx + b
mx = x
m = 1
Slope of first line = 1
slope of the 2nd line = 1
For the 2nd line, it passes through (-2, -4)
x = -2, y = -4
y = mx + b
-4 = 1(-2) + b
-4 = b - 2
-4 + 2 = b - 2 + 2
-2 = b + 0
b = -2
The equation parallel to y = x + 9 becomes:
y = x + (-2)
y = x - 2
b) For a line to be perpendicular to another line, the slope of one line will be thenegative reciprocal of the other line.
slope of 1st line = 1
reciprocal of the line = 1/1 = 1
negative reciprocal = -1
point (-2, -4)
y = mx + b
-4 = -1(-2) + b
-4 = 2 + b
-4 -2 = b
b = -6
The equation perpendicular to the line y = x + 9:
y = -1(x) + (-6)
y = -x -6
(Expected rate of return and risk) B. J. Gautney Enterprises is evaluating a security. One-year Treasury bills are currently paying 4.8 percent. Calculate the investment's expected return and its standard deviation. Should Gautney invest in this security? Probability 0.20 Return - 4% 4% 7% 0.45 0.15 0.20 10% (Click on the icon in order to copy its contents into a spreadsheet.) ...) a. The investment's expected return is%. (Round to two decimal places.)
The investment's expected return is 5.95%.
Is the investment's expected return favorable for Gautney?The expected return of an investment is calculated by multiplying the probabilities of each possible return by their respective returns and summing them up. In this case, Gautney Enterprises has provided the probabilities and returns for the investment. By applying the formula, we find that the expected return is 5.95%.
To calculate the standard deviation, we need to determine the variance first. The variance is computed by taking the difference between each possible return and the expected return, squaring those differences, multiplying them by their respective probabilities, and summing them up. Once we have the variance, the standard deviation is simply the square root of the variance. The standard deviation measures the degree of risk associated with an investment.
In this scenario, the expected return of the investment is 5.95%, but we need to consider the standard deviation as well to assess the risk. If the standard deviation is high, it indicates a greater level of uncertainty and potential volatility in returns. A low standard deviation implies a more stable investment.
Without the specific values for each return and their respective probabilities, we cannot calculate the exact standard deviation. However, Gautney Enterprises should compare the calculated expected return and the associated standard deviation to their risk tolerance and investment objectives. If the expected return meets their desired level of return and the standard deviation aligns with their risk appetite, they may consider investing in this security.
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Explain how to solve a system of linear equations using the substitution method:)
Step-by-step explanation:
step 1 :first solve one linear equation for y in terms of x
step 2: then substitute that expression for y in the other linear equation
step 3 :solve this and you have the x-coordinate of the intersection
step 4: then plug in a to either equation to find the corresponding y -coordinate
Place the correct function type in the table to show whether the situation could be modeled with a linear or an exponential function. Response area with 5 blank spaces Situation Linear or Exponential? A competition eliminates one-fourth of the participants per round. Blank space 1 empty A pizzeria charges a base price for pizza and then $1.50 for each additional topping. Blank space 2 empty A tutor charges $40 per hour of tutoring. Blank space 3 empty An animal population doubles every 3 months. Blank space 4 empty An electrician charges $125 per house call and then $65 per hour of work. Blank space 5 empty Answer options with 2 options. Answer Options Linear Exponential
The correct function type for each situation:
1) A competition eliminates one-fourth of the participants per round. - exponential
2) A pizzeria charges a base price for pizza and then $1.50 for each additional topping. - linear
3) A tutor charges $40 per hour of tutoring. - linear
4) An animal population doubles every 3 months. - exponential
5) An electrician charges $125 per house call and then $65 per hour of work. - linear
We know that, in order to determine whether fundtion is linear or exponential we chaeck the relationships in the way the y-values change when the x-values increase by a constant amount:
In case of a linear function, the y-values have equal differences.
And in an exponential function, the y-values have equal ratios.
1) A competition eliminates one-fourth of the participants per round.
This is an exponential function.
2) A pizzeria charges a base price for pizza and then $1.50 for each additional topping.
This situation could be modeled with a linear function.
3) A tutor charges $40 per hour of tutoring.
This situation could be modeled with a linear function.
4) An animal population doubles every 3 months.
This situation could be modeled with an exponential function.
5) An electrician charges $125 per house call and then $65 per hour of work.
This situation could be modeled with a linear function.
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Find the complete question below.
suppose Yolanda places $2,500 in an account that pays 8% interest compounded each year assume that no withdrawals are made from that account follow the instructions below do not do any rounding
Answer:2,127.33
Step-by-step explanation:
Use guess and check to find an anti-derivative
F(x)
for
f(x)=sin(x)cos(x)
. Explain why you chose particular guesses, and how you checked them.
When finding an antiderivative using the method of guess and check, it is important to use a guess that is based on the original function and the rules of differentiation.
One approach to finding an antiderivative of a function is the method of guess and check. This involves making an educated guess for the antiderivative and then verifying it by taking the derivative of the guess and comparing it to the original function.
To find the antiderivative of f(x) = sin(x)cos(x), we can start with a guess based on the product rule for differentiation: d/dx (uv) = u * dv/dx + v * du/dx
Since f(x) = sin(x)cos(x), we can write: d/dx (sin(x)cos(x)) = cos^2(x) + sin^2(x) = 1
This suggests that the antiderivative of f(x) = sin(x)cos(x) might be: F(x) = sin(x)sin(x) + C, where C is an arbitrary constant of integration.
To check our guess, we need to take the derivative of F(x) and compare it to the original function f(x): d/dx (sin(x)sin(x) + C) = cos(x)sin(x)
If our guess is correct, the derivative of F(x) should equal f(x). However, in this case, our guess does not match the original function f(x), so we need to make another guess. A second guess could be:
F(x) = -cos(x)cos(x) + C
Taking the derivative: d/dx (-cos(x)cos(x) + C) = -sin(x)cos(x)
This time, the derivative of F(x) does match the original function f(x), so our guess is correct and the antiderivative of f(x) = sin(x)cos(x) is:
F(x) = -cos(x)cos(x) + C.
Thus, In conclusion, when finding an antiderivative using the method of guess and check, it is important to use a guess that is based on the original function and the rules of differentiation. By checking the derivative of the guess and comparing it to the original function, we can determine whether or not our guess is correct.
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An advertising company is purchasing a new industrial-sized color printer. The company has been approved for a $75,000 loan at two different
banks. The terms of each loan are:
Offer 1: 4.99% annual simple interest, with a total account balance of $91,529.38 after a 53-month term
Offer 2: 3.5% annual interest compounded monthly for a 62-month term
Assuming no payments are made, what is the difference in the account balances at the end of the loan terms. Round your answer to the nearest
penny.
O $1,624.49
$1,686.87
$1,894.02
O $2,207.67
The difference in the account balances at the end of the loan terms is given as follows:
$1,686.87.
What is compound interest?The amount of money earned, in compound interest, after t years, is given by:
\(A(t) = P\left(1 + \frac{r}{n}\right)^{nt}\)
In which:
P is the principal, which is the value of deposit/loan/....r is the interest rate, as a decimal value.n is the number of times that interest is compounded per year, annually n = 1, semi-annually n = 2, quarterly n = 4, monthly n = 12.The parameters for the offer 2 are given as follows:
P = 75000, r = 0.035, n = 12, t = 62/12.
Hence the balance of the offer 2 is given as follows:
B = 75000 x (1 + 0.035/12)^(12 x 62/12)
B = $89,842.51.
The balance of Offer 1 is of $91,529.38, hence the difference in the balances is given as follows:
91529.38 - 89842.51 = $1,686.87.
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Solve the inequality: -2z - 3 < 5
Answer:
z>-4
Step-by-step explanation:
Answer:
z>4
Step-by-step explanation:
-2z-3<5
add 3 to 5: -2z < 8
divide by -2: z < -4
but since you divided by a negative number, you have to change the way the inequality is facing so the answer is z>-4
Which of the following is not a property of zero?
If you divide any number by zero, the answer will be zero.
Zero is neither positive nor negative.
If you add zero to a number, the answer will be that same number.
If you multiply any number by zero, the answer will be zero.
Answer:
If you divide any number by zero, the answer will be zero.
Step-by-step explanation:
You can't divide by zero. If you divide an number by zero on a calculator, it will come out as 'undefined'.
All other statements are true.
An integer that is positive is greater than zero, and a integer that is negative is less than zero. 0 is equal to 0, so it is neither positive or negative.
The sum of a number and zero will be that number. You are technically adding nothing.
\(4+0=4\)
The product of any number and zero is zero. This is the "Multiplication Property of Zero".
\(4*0=0\)
"If you divide any number by zero, the answer will be zero." should be the correct answer.
"If you divide any number by zero, the answer will be zero." should be the correct answer.
What is property of zero?
Addition property of zero:
The addition property of zero says that a number does not change when adding or subtracting zero from that number.
Multiplication property of zero:
The multiplication property of zero says that zero times any number is equal to zero.
Explanation for correct option:
If you divide any number by zero, the answer will be zero.
You can't divide by zero. If you divide an number by zero on a calculator, it will come out as 'undefined'.
All other statements are true.
Explanations for other options:
An integer that is positive is greater than zero, and a integer that is negative is less than zero. 0 is equal to 0, so it is neither positive or negative.
The sum of a number and zero will be the same number. You are technically adding nothing.
The product of any number and zero is zero. This is the "Multiplication Property of Zero".
"If you divide any number by zero, the answer will be zero." should be the correct answer.
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The width of a rectangle is 3 feet less than twice the length. Find the length if the
perimeter is 84
Answer:
Your width is 5 feet and your length is 7!!!!!
Step-by-step explanation:
MARK AS BRAINLIEST
You have a job that pays $15 per
hour biweekly. If you work 30
hours per week each week, what
is your gross pay?
Answer:
$900
Step-by-step explanation:
60x15 because two weeks equals 60 hours in total.
Luesuon Help The perimeter of a rectangle is 48 feet and the length is 18 feet. What is the width? Define a variable for the unknown quantity. Write and solve an equation to answer the question. Let w= An equation to represent the situation is V = 48. So, w= The width is (Type integers or decimals.)
The equation for the perimeter of the rectangle is:
\(\begin{gathered} l\colon\text{length} \\ w\colon\text{width} \\ P=2l+2w \end{gathered}\)then an equation to find the widht is:
\(\begin{gathered} P=2l+2w \\ \Rightarrow P-2l=2w \\ \Rightarrow w=\frac{P-2l}{2} \end{gathered}\)Now, if P=48 and l=18, then we have the following:
\(\begin{gathered} w=\frac{48-2\cdot18}{2}=\frac{48-36}{2}=\frac{12}{2}=6 \\ w=6 \end{gathered}\)therefore, the width is 6 feet.
Need help due in 1 min!!
Simplify!!
Answer:
C. 3^9
Step-by-step explanation:
You would simply just add the exponents.
Answer:
3^9
Step-by-step explanation:
5+4=9
The complement in the following sentence is
My uncle drives a new car.
1. car
2. drives
3. new
Btw it's not new I tried but it said it was wrong, thanks!
Answer:
belve t would be drives
Step-by-step explanation:
Hope ths helps.
find the perimeter and area of quadrilateral abcd with vertices A (3,5) B (6,5) C (4,-1) D (1,-1)
Based on the coordinates of the vertices of the quadrilateral ABCD, the perimeter is 18.64 units and the area is 18.96 units².
What is the perimeter?First, find the distance between the points of the quadrilateral:
Distance formula is:
d = √( (x₂ - x₁)² + (y₂ - y₁)²)
Distance for AB:
= √( (6 - 3)² + (5 - 5)²)
= 3
Distance for BC:
= √( (4 - 6)² + (-1 - 5)²)
= 6.32
Distance of CD:
= √( (1 - 4)² + (-1 - (-1)²)
= 3
Distance of AD:
= √( (1 -3)² + (-1 -5)²)
= 6.32
Perimeter is:
= 6.32 + 6.32 + 3 + 3
= 18.64 units
The area of the quadrilateral would be:
= 3 x 6.32
= 18.96 units²
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The combined mass of a dog and a cat is 24kg. The dog is three times as heavy as the cat. Find the mass
Answer:
Cat = 6kg
Dog = 18kg
Step-by-step explanation:
Total mass combine = 24 g
dog = 3 x c
cat = c
the cat is 6kg and the dog is 18kg
The mass of the dog and cat are 18 kg and 6 kg respectively
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
Substituting the values in the equation , we get
Let the mass of the cat be = x
And , mass of dog = 3x
x + 3x = 24
On simplifying the equation , we get
4x = 24
Divide by 4 on both sides , we get
x = 6 kg
So , the mass of cat is 6 kg
And , the mass of dog is 18 kg
Hence , the equations are solved
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a rectangular plot of farmland will be bounded on one side by a river and on the other three sides by a​ single-strand electric fence. with m of wire at your​ disposal, what is the largest area you can​ enclose, and what are its​ dimensions?
To find the largest area you can enclose with a single-strand electric fence and m units of wire at your disposal, you need to optimize the dimensions of the rectangular plot.
Let's denote the length of the rectangular plot as L and the width as W. The perimeter of the plot can be calculated as P = L + 2W.
Since one side of the plot is already bounded by the river, we have L + W = m. Rearranging this equation, we get L = m - W.
To find the largest area, we need to maximize the function A = L * W. Substituting the value of L, we have A = (m - W) * W.
Expanding the equation, we have A = mW - W^2.
To find the maximum value of A, we take the derivative of A with respect to W and set it equal to zero: dA/dW = 0.
Differentiating, we get m - 2W = 0. Solving for W, we have W = m/2.
Substituting this value back into the equation for L, we have L = m/2.
Therefore, the dimensions of the largest area are L = m/2 and W = m/2.
To find the area, we substitute these values into the equation for A: A = (m/2) * (m/2) = m^2/4.
In conclusion, the largest area that can be enclosed is m^2/4, with dimensions L = m/2 and W = m/2.
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solve the following system of equations using the substitution method. –6x 2y = 8 y = 3x 4 question 9 options: a) no solution b) (0, 4) c) infinitely many solutions d) (8, 8)
The correct answer is option c) infinitely many solutions..
To solve the system of equations using the substitution method, we'll substitute the value of y from the second equation into the first equation and solve for x.
Given:
-6x + 2y = 8 ---(1)
y = 3x + 4 ---(2)
Substitute equation (2) into equation (1):
-6x + 2(3x + 4) = 8
Simplify:
-6x + 6x + 8 = 8
8 = 8
We obtained a true statement (8 = 8), which means the two equations are equivalent. This solution shows that the system has infinitely many solutions.
Therefore, the correct answer is option c) infinitely many solutions..
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a tank holds 4000 liters of water in which 100 grams of salt have been dissolved. saltwater with a concentration of 1 grams/liter is pumped in at 10 liters/minute and the well mixed saltwater solution is pumped out at the same rate. write initial the value problem for:
The mass of salt in the tank at time t.
dS/dt = 10 - S/400
S(0) = 100 grams
The solution is S(t) = 4000 - 3900\(e^{\frac{-t}{400}}\)
A tank holds water V(0) = 4000 liters in which salt S(0) = 100 grams.
So dS/dt = S(in) - S(out)
S(in) = 1 × 10 = 10 gram/liters
S(out) = S/V × 10 = 10S/V gram/liters
V = V(0) + q(in) - q(out)
V = 4000 + 10t - 10t
V = 4000 liters
dS/dt = 10 - 10S/V
dS/dt = 10 - 10S/4000
dS/dt = 10 - S/400
Now given; S(0) = 100.
Here, p(t) = 1/400, q(t) = 10
\(\int p(t)dt = \int\frac{1}{400}dt\)\(\int p(t)dt = \frac{1}{400}t\)
\(\mu=e^{\int p(t)dt}\)
\(\mu=e^{\frac{t}{400}}\)
So, S(t) = \(\frac{\int\mu q(t)dt+C}{\mu}\)
S(t) = \(\frac{\int e^{\frac{t}{400}} \cdot10dt+C}{e^{\frac{t}{400}}}\)
S(t) = \(e^{\frac{-t}{400}} \left({\int e^{\frac{t}{400}} \cdot10dt+C}\right)\)
S(t) = \(e^{\frac{-t}{400}} \left({10\times\frac{e^{\frac{t}{400}}}{1/400} +C}\right)\)
S(t) = \(e^{\frac{-t}{400}} \left({4000\times{e^{\frac{t}{400}} +C}\right)\)
Now solving the bracket
S(t) = 4000 + \(e^{\frac{-t}{400}}\)C.....(1)
At S(0) = 100
100 = 4000 + \(e^{\frac{-0}{400}}\) C
100 = 4000 + \(e^{0}\) C
100 = 4000 + C
Subtract 4000 on both side, we get
C = -3900
Now S(t) = 4000 - 3900\(e^{\frac{-t}{400}}\)
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The complete question is:
A tank holds 4000 liters of water in which 100 grams of salt have been dissolved. Saltwater with a concentration of 1 grams/liter is pumped in at 10 liters/minute and the well mixed saltwater solution is pumped out at the same rate. Write initial the value problem for:
The mass of salt in the tank at time t.
dS/dt =
S(0) =
The solution is S(t) =
si elsa tiene en el banco un capital de 9500 durante 900 dias al 6,5 de interes compuesto anual cual sera el interes o ganancia obtenida
Usando el interés compuesto, se encuentra que el interes obtenido es de 1609.
Interés compuesto:\(I(t) = P\left[\left(1 + \frac{r}{n}\right)^{nt} - 1\right]\)
En que:
I(t) es el interes obtenido después de t años. P es el capital. r es la taja de interes, en decimal. n es el número de veces que se capitaliza el interés por año.En este problema, los parámetros son:
\(P = 9500, t = \frac{900}{365} = 2.4658, r = 0.065, n = 1\)
Por eso:
\(I(t) = P\left[\left(1 + \frac{r}{n}\right)^{nt} - 1\right]\)
\(I(2.4658) = 9500\left[\left(1 + \frac{0.065}{1}\right)^{2.4658} - 1\right]\)
\(I(2.4658) = 1609\)
El interes obtenido es de 1609.
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The interest earned on the amount is 1,595.05.
Compound interest
The formula for calculating the compound interest is expressed as:
A = P(1+r)^t
A = 9500(1+0.065)^2.4658
A = 9500(1.065)^2.4658
A = 11,095.05
Interest = Amount - Principal
Interest = 11,095.05 - 9500
Interest = 1,595.05
Hence the interest earned is 1,595.05.
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Joan wants to make a dinner plan for next week. how many different arrangements are there for the 7 days?
Answer:
5040
Step-by-step explanation:
an illustration of permutations
The given parameter is:
number of days
dinners for 7 days
Substitute known values
What is the volume of this sphere?
Use 3.14 for pI and round to the nearest hundredth when
necessary.
Answer:
choice 3) 11,488.21 cm³
Step-by-step explanation:
r= 28/2 = 14
volume = 4/3πr3 = 4/3(3.14)(14³) = 11,488.21 cm³
Terry rides his bicycle mile in
6 minutes. If he continues at this rate,
how far will he travel in 21 minutes?
Answer:
3.5 miles assuming terry rode his bike 1 mile in 6 minutes
Step-by-step explanation:
Jen used 1/2 cup of cereal and 2/3 cup of nuts to make trail mix. Her mother asked if she used more cereal or more nuts in the mix. Which statement correctly compares the fractions?
1/2<2/3. 1/2= half of a whole and half of a whole is 1/2. 2/3 is over a half so it means that 2/3 is better then 1/2 since 1.5 is actually the half of 3. Jen should say that she used more nuts to make trail mix then using cup of cereal to make trail mix because 2/3 is greater then 1/2.
Simplify this expression.
–6w + (–8.3) + 1.5+ (–7w)
The simplified form of the expression -6w + (–8.3) + 1.5+ (–7w) is -13w - 6.8.
What is the simplified form of the expression?Given the expression in the question;
-6w + (–8.3) + 1.5+ (–7w)
To simplify, first remove the parenthesis
Note that;
- × + = -- × - = ++ × + = +-6w + × - 8.3 + 1.5 + × - 7w
-6w - 8.3 + 1.5 - 7w
Next collect and add like terms
-6w - 7w - 8.3 + 1.5
Add -6w and -7w
-13w - 8.3 + 1.5
Add -8.3 and 1.5
-13w - 6.8
Therefore, -13w - 6.8 is the simplified form.
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Which is most likely the correlation coefficient for the set of data shown?
–0.872
–0.191
0.191
0.872
The most likely correlation coefficient for the set of data shown is -0.872.
To determine the most likely correlation coefficient for the set of data, we need to examine the values provided: –0.872, –0.191, 0.191, and 0.872.
The correlation coefficient is a value between -1 and 1 that indicates the strength and direction of the linear relationship between two variables.
Since all the given values are positive (0.191 and 0.872) or negative (-0.191 and -0.872), we can conclude that the correlation coefficient is negative.
Out of the two negative values, -0.872 is closer to -1 than -0.191, so it is more likely the correlation coefficient for the given data set.
Therefore, the most likely correlation coefficient for the set of data shown is -0.872.
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PLEASE HELP!!! THIS IS FOR MATH
Answer:
the answer is D.........
Step-by-step explanation:
I dont really have a reason that just seem like the best answer..... I hope it's right