he graph of a linear function is shown.

A coordinate plane with a straight line passing through (negative 4, 2), (0, 0), and (4, negative 2).
Which word describes the slope of the line?

positive
negative
zero
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The linear equation for the given table is y = 10*x - 8.

A general linear equation in the slope-intercept form is:

y = m*x + b

where m is the slope and b is the y-intercept.

The y-intercept is the value of y when x = 0, on the table we can see the pair (0, -8), then the y-intercept is -8.

y = m*x - 8

Using another pair from the table, like (1, 2), we can replace these values in the above linear equation:

2 = m*1 - 8

2 + 8 = m

10 = m

Then the linear equation is:

y = 10*x - 8

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The difference between the three variances, Var(x), Var(y), and Var(x + y), can be determined analytically in the context of the bus ridership example.

In the given context, let's consider two variables: x represents the ridership on line l2, and y represents the ridership on line l1. The statement mentions that intuitively, l1 and l2 are not independent, meaning they are related in some way.

To determine the difference between the variances, we need to calculate the variances of x, y, and the sum of x and y, which is x + y.

Var(x): This represents the variance of the ridership on line l2. It quantifies the spread or variability in the data points of x. To calculate Var(x) analytically, you can use the formula: Var(x) = E[(x - μx)^2], where E represents the expectation (mean) operator and μx represents the mean of x.

Var(y): This represents the variance of the ridership on line l1. Similar to Var(x), it quantifies the spread or variability in the data points of y. Var(y) can be calculated using the same formula as Var(x): Var(y) = E[(y - μy)^2], where μy represents the mean of y.

Var(x + y): This represents the variance of the sum of ridership on both lines l1 and l2. It measures the combined variability of the two variables. To calculate Var(x + y), you can use the formula: Var(x + y) = E[(x + y - μ(x + y))^2], where μ(x + y) represents the mean of the sum of x and y.

By analytically calculating the three variances, Var(x), Var(y), and Var(x + y), you can compare them to understand their differences and the relationship between the ridership on line l1 and line l2.

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Answer:

x=37/20

Step-by-step explanation:

4(2x-7)+3(3x-1)=3(2-x)

8x-28+9x-3=6-3x

17x+3x=6+31

20x=37

Answer:

x = \(\frac{71}{3}\)

Step-by-step explanation:

1. Simplify/distribute each side.

\(4(2)(-7)+3(3)(-1)=3(2-x)\)

\(4(2)(-7)+3(3)(-1)=(3)(2)+(3)(-x)\)

\(-56+-9=6+-3x\)

2. Flip the equation around.

\(-3x+6=-65\)

3. Subtract 6 to balance the equation.

\(-3x+6-6=-65-6\)

\(-3x=-71\)

4. Divide each side by 3. We know they are in the same fact family.

\(\frac{-3x}{-3} = \frac{-71}{3}\)

Podemos utilizar la función arcoseno para encontrar los valores del ángulo (t) en los que se cumple la ecuación. Sin embargo, ten en cuenta que puede haber múltiples soluciones dentro de un ciclo. Por lo tanto, debemos encontrar los valores del ángulo que se encuentran en el intervalo [0, 2π] y satisfacen la ecuación.

t1 = (30/2π) arcsin(89/99)

t2 = π - (30/2π) arcsin(89/99)

Para escribir la ecuación trigonométrica que describe tu altura sobre el suelo en función del tiempo, podemos utilizar una función seno. La función seno tiene un periodo de 2π, lo que significa que se repite cada 2π unidades de tiempo.

Dado que el viaje tarda 30 segundos en completar una revolución completa, el periodo de la función seno será 30 segundos. Además, necesitamos considerar el desplazamiento vertical de la función seno, que en este caso es 1 pie.

Entonces, la ecuación que describe tu altura sobre el suelo a los t segundos después de que comienza el viaje es:

h(t) = 99 sin((2π/30) t) + 1

Para encontrar los dos momentos dentro de un ciclo en los que te encuentras exactamente a 90 pies del suelo, debemos resolver la ecuación:

99 sin((2π/30) t) + 1 = 90

Restamos 1 a ambos lados de la ecuación:

99 sin((2π/30) t) = 89

Luego, despejamos el ángulo:

sin((2π/30) t) = 89/99

Finalmente, podemos utilizar la función arcoseno para encontrar los valores del ángulo (t) en los que se cumple la ecuación. Sin embargo, ten en cuenta que puede haber múltiples soluciones dentro de un ciclo. Por lo tanto, debemos encontrar los valores del ángulo que se encuentran en el intervalo [0, 2π] y satisfacen la ecuación.

t1 = (30/2π) arcsin(89/99)

t2 = π - (30/2π) arcsin(89/99)

Los momentos dentro de un ciclo en los que te encuentras exactamente a 90 pies del suelo son t1 y t2, donde t1 y t2 están en el intervalo [0, 30].

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\(\huge\text{$m\angle O=\boxed{11^{\circ}}$}\)

Since we know that all angles in a triangle add up to \(180^{\circ}\), we can solve for \(x\) and substitute it back into \((x-5)^{\circ}\) to find \(m\angle O\).

\(\begin{aligned}m\angle N+m\angle O+m\angle P&=180\\(5x-8)+(x-5)+(6x+1)&=180\end{aligned}\)

Remove the parentheses and combine like terms.

\(\begin{aligned}5x-8+x-5+6x+1&=180\\(5x+x+6x)+(-8-5+1)&=180\\12x-12&=180\end{aligned}\)

Add \(12\) to both sides of the equation.

\(\begin{aligned}12x-12&=180\\12x&=192\end{aligned}\)

Divide both sides of the equation by \(12\).

\(\begin{aligned}x=16\end{aligned}\)

Now that we have the value of \(x\), we can substitute it back into \((x-5)^{\circ}\) to find \(m\angle O\).

\(\begin{aligned}m\angle O&=(x-5)\\&=16-5\\&=\boxed{11}\end{aligned}\)

Answer:

2

Step-by-step explanation:

it may not be right because i guessed

The original price 1. $ 88.

Suppose the value of which a thing is expressed in percentage is "a'

Suppose the percent that considered thing is of "a" is b%

Then since percent shows per 100 (since cent means 100), thus we will first divide the whole part in 100 parts and then we multiply it with b so that we collect b items per 100 items(that is exactly what b per cent means)

Given;

The cost of the product was reduced by 20%, leaving $ 70.4 as the final price.

Cost of phone after 80% off= $70.40

So, now we will do a cross-multiplication;

If the percent is 80% =70.40

Let, the original price 100% = x

80x = 70.40. 100

80x = 7040

X = 7040: 80

X = 88

Therefore, the 100 percent value of phone will be $88

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Answer:

An introduction of sets and its definition in mathematics. The collection of well-defined distinct objects is known as a set. ... The word well-defined refers to a specific property which makes it easy to identify whether the given object belongs to the set or not.

To determine whether the geometric series ∑(n=0 to ∞) (√(1/7))^n is convergent or divergent, we can examine the common ratio (r) of the series.

The given series has a common ratio of (√(1/7)). For a geometric series to be convergent, the absolute value of the common ratio (|r|) must be less than 1.

In this case, |√(1/7)| = √(1/7) ≈ 0.377, which is less than 1. Therefore, the geometric series is convergent.

To find the sum of the geometric series, we can use the formula for the sum of an infinite geometric series:

Sum = a / (1 - r),

where 'a' is the first term and 'r' is the common ratio.

In this case, the first term 'a' is (√(1/7))^0 = 1, and the common ratio 'r' is √(1/7).

Substituting these values into the formula, we have:

Sum = 1 / (1 - √(1/7)).

To simplify this expression, we can rationalize the denominator:

Sum = 1 / (1 - √(1/7)) * (1 + √(1/7)) / (1 + √(1/7)).

Multiplying the numerators and the denominators, we get:

Sum = (1 + √(1/7)) / (1 - (1/7)).

Simplifying further:

Sum = (1 + √(1/7)) / (6/7).

Finally, multiplying the numerator by 7, we obtain the sum of the geometric series:

Sum = 7(1 + √(1/7)) / 6.

Therefore, the sum of the given geometric series is 7(1 + √(1/7)) / 6.

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Step-by-step explanation:

Disagree.

If each shirt is originally x dollars, then the new price is 0.8x.  So the total cost is 1.6x, down from the original 2x.

So the discount is (2x − 1.6x) / 2x × 100% = 20%.

\(\text{Given that,}\\\\\\f(x) = 9x^3 -x^2 +2 \\\\f(2) = 9(2^3) - 2^2 +2\\\\~~~~~~~ = 9(8) -4 +2 \\\\~~~~~~~= 72 -2 \\\\~~~~~~~=70\)

It’s probably too late but

Point M is now at (7,1)

Answer: 18

Step-by-step explanation:

The calculated value of the expected number of spin is 216

From the question, we have the following parameters that can be used in our computation:

Yellow or purple outcomes = 12

P(Yellow or purple) = 1/18

using the above as a guide, we have the following:

Yellow or purple outcomes = P(Yellow or purple) * Expected number of spin

So, we have

1/18 * Expected number of spin = 12

Rewrite as

Expected number of spin = 12 * 18

Evaluate

Expected number of spin = 216

Hence, the expected number of spin is 216

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Answer:

x = 2 , y = 0 , z = 3

Step-by-step explanation:

Cramer's rule is a rule through which we can find the solution of linear equation.

we have the three linear equations as

x+2y+3z=11

2x+y+2z=10

3x+2y+z=9

AX=B  

A: coefficient matrix

X= unknown vectors(x,y,z)

D = values of the linear equation (11 , 10 , 9)

now we find the determinant of the given linear equation

determinant of the matrix will be

A = \(\left[\begin{array}{ccc}1&2&3\\2&1&2\\3&2&1\end{array}\right]\)  = 1(1-4) - 2(2-6) + 3(4 - 3)

                    = 1(-3) - 2(-4) + 3(1)

                    = -3+8+3 = 8

also D\(\neq 0\)

so the determinant is Non zero we can apply Cramer's rule

we will be replacing the first column of the coefficient matrix A with the values of D

by replacing the first column we will get the value of the variable 'x'

Dx =  \(\left[\begin{array}{ccc}11&2&3\\10&1&2\\9&2&1\end{array}\right]\)   = 11(1-4) -2(10-18) + 3(20-9) = -33+16+33 = 16

x = \(\frac{Dx}{D}\)  = \(\frac{16}{8}\) = 2

similarly

Dy = \(\left[\begin{array}{ccc}1&11&3\\2&10&2\\3&9&1\end{array}\right]\) = 1(10-18) -11(2-6) + 3(18 -30) = -8 +44 -36 = 0

y = \(\frac{Dy}{D}\) = 0

Dz= \(\left[\begin{array}{ccc}1&2&11\\2&1&10\\3&2&9\end{array}\right]\) = 1(9 - 20) -2(18 - 30) + 11(4 -3) = -11 +24 +11 = 24

z = \(\frac{Dz}{D}\) = \(\frac{24}{8} = 3\)

so we have the solution as

x = 2 , y = 0 , z = 3

Therefore the solution for the given linear equations is (2,0,3).

Answer:

The total Cost of 2 candies is $6.00.

Step-by-step explanation:

We are told that f(x) represents the cost of candy, and that x represents the number of candies.

f(2) means that x=2, which is 2 candies; f(2) = 6 means that the cost of 2 candies is $6.

Answer:

The total cost of 2 candies is $6.00.

Step-by-step explanation:

I aced the test.

The account balance at the end of the month is $-1.04.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that Josiah's monthly bank statement showed the following deposits and withdrawals: $94.57, -−$87.78, -−$16.36, -−$64.92, $10.73 If Josiah's balance in the account was $62.72 at the beginning of the month.

The balance after the end of the withdrawal and deposits will be,

Account balance = $62.72 + $94.57−$87.78−$16.36−$64.92 + $10.73

Account balance = $-1.04

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In the future, you should post all possible answer choices to have a complete post. However, there's enough information to get the answer.

The original set has points in the form (x,y)

The first point is (x,y) = (-49,7) making x = -49 and y = 7. When we find the inverse, we simply swap the x and y values. The inverse undoes the original function and vice versa. So if (-49, 7) is in the original function, then (7, -49) is in the inverse. The rest of the points follow the same pattern.

We end up with this answer

{ (7, -49), (8, -56), (9, -63), (10, -70) }

Three shoppers are in the elevator of a department store. the anticipated number of stops the lift makes sometime recently the three customers have all cleared out the lift is 21/4, or 5.25 stops on normal.

E(X) = ∑ x P(X = x) where the summation is over all conceivable values of X, and P(X = x) is the likelihood that X takes on the esteem x.

The conceivable values of X are 3, 4, and 5, The likelihood that X = k for k ≥ 3 is the likelihood that the three customers will have all left the lift after k stops, which is 7/8 times the Probability that they have not all cleared out after k - 1 stops. That's, P(X = k) = (7/8) P(X = k-1)

Utilizing this recursive relationship, ready to compute the probabilities of X taking on each conceivable esteem: P(X = 3) = 7/8

P(X = 4) = (7/8)(1/8) = 7/6

P(X = 5) = (7/8)(7/64) = 49/512

P(X = 6) = (7/8)(49/512) = 343/4096

Presently we are able to utilize the equation for anticipated esteem to discover E(X): E(X) = ∑ x P(X = x)

= 3(7/8) + 4(7/64) + 5(49/512) + 6(343/4096) + ...

= ∑ (3/2)\(^{k}\) (7/8)\(^{k}\)

= (7/8) (3/2) / (1 - 3/2)

= (7/8) (3/2) / (1/2)

= 21/4

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Not performing qualitative tests in duplicate can introduce certain risks and potential issues:

False positives: Without duplicate testing, there is a higher risk of obtaining false positive results. False positives occur when a test incorrectly indicates the presence of a particular characteristic or condition. Duplicate testing helps verify the accuracy and reliability of the results, reducing the chances of false positives.

False negatives: Similarly, not performing qualitative tests in duplicate increases the risk of false negatives. False negatives occur when a test fails to detect a characteristic or condition that is actually present. Duplicate testing provides an additional opportunity to identify any missed detections and reduces the likelihood of false negatives.

Variability and uncertainty: Qualitative tests can be subject to variability due to factors such as sample preparation, test conditions, or interpretation. Duplicate testing helps assess the consistency and reproducibility of the results, providing a measure of confidence and reducing uncertainty.

Quality control issues: Duplicate testing is an essential component of quality control protocols. It helps ensure the reliability and accuracy of the testing process and minimizes the potential for errors or inconsistencies. Not performing duplicate tests can compromise the overall quality control procedures, leading to compromised data and unreliable conclusions.

Validation and reproducibility: Duplicate testing is often required for validation purposes and to demonstrate the reproducibility of results. It helps establish the robustness and reliability of the testing method. Without duplicate testing, it becomes more challenging to validate and reproduce the results, which can undermine the credibility of the findings.

In summary, not performing qualitative tests in duplicate increases the risks of false positives, false negatives, variability, uncertainty, quality control issues, and challenges in validation and reproducibility. Duplicate testing plays a crucial role in ensuring the accuracy, reliability, and validity of qualitative test results.

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Answer:

here are a total of 14 + 15 + 9 + 11 = 49 donuts.

The probability of selecting a maple donut is the number of maple donuts divided by the total number of donuts:

P(maple donut) = 14/49

So the probability of selecting a maple donut is 14/49, which can also be written as a fraction in simplest form: 2/7.

In the given scenario, with the known value of Bo, there is no need for a variance stabilizing transformation. The assumption of constant variance for the error term can be satisfied without any further transformation.

In the simple linear regression model, where Yi = Bo + Bixi + €i, with the assumption that var(€i) = σ²r², and Bo ∈ R is known, we can use a variance stabilizing transformation known as the Fisher transformation.

The Fisher transformation is typically used to stabilize the variance when dealing with proportions or variables bounded between 0 and 1. However, in this case, since Bo is known and not estimated, we don't need to perform any variance stabilizing transformation. The known value of Bo helps to eliminate any variability associated with the intercept term, making the assumption of constant variance for the error term (€i) unnecessary.

Therefore, in this scenario, there is no need for a variance stabilizing transformation because Bo is known, and the assumption of constant variance can be satisfied without any further transformation.

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Answer:

2,196;    549;     131.76;     8;     175.68;      1339.56

Step-by-step explanation:

2,196 is the biggest number, so use that as the first number.

.25x2196=549

.06x2196=131.76

.08x2196=175.68

2196-(549+131.76+175.68)=1339.56

With regards to University Admissions, Limited spaces, entrance requirements, prerequisites, quotas, and holistic selection processes can contribute to learners not being accepted into universities.

There are several reasons why learners with excellent matric results may not be accepted into universities.

Firstly, limited spaces in popular courses can lead to intense competition. Secondly, universities may have specific entrance requirements, such as interviews or additional tests, which not all applicants meet.

Also, certain courses may have prerequisites or specific quotas for certain demographics.

Lastly, the selection process also considers factors beyond academic performance, such as extracurricular activities or personal statements.

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Answer:

Step-by-step explanation:

when we find the volume of a cylinder we must know

the radius

the length of the cylinder-L

L^2=11^2+4^2

L^2= 144+16

L=√160

L=4√10 INCHES

                       = 3.14*16*4√10

                       = 3.14*64*2.23*1.41

                       = 632.192528

                       ≈632 CUBIC INCHES

a) An example of a polynomial of degree 5 for which x=1 is a critical number but not a local minimum nor a local maximum is:

P(x) = (x-1)^2(x-2)(x+1)(x+3)

To see why x=1 is a critical point but not a local minimum nor a local maximum, we can compute the first and second derivatives of P(x):

P'(x) = 2(x-1)(x-2)(x+1)(x+3) + (x-1)^2(x+1)(x+3) + (x-1)^2(x-2)(x+3) + (x-1)^2(x-2)(x+1)

P''(x) = 2(x-2)(x+1)(x+3) + 2(x-1)(x+1)(x+3) + 2(x-1)(x-2)(x+3) + 2(x-1)(x-2)(x+1) + 4(x-1)(x-2)(x+1)(x+3)

We can see that P'(1) = 0, so x=1 is a critical point. To determine whether it's a local minimum or maximum, we need to look at the sign of P''(1). However, computing P''(1) gives us:

P''(1) = 2(1-2)(1+1)(1+3) + 2(1-1)(1+1)(1+3) + 2(1-1)(1-2)(1+3) + 2(1-1)(1-2)(1+1) + 4(1-1)(1-2)(1+1)(1+3) = 16

Since P''(1) is positive, we know that x=1 is not a local maximum or a local minimum, but rather an inflection point.

b) To determine the intervals on which f(x) = (x-2)(x+3) is decreasing and increasing and find local minima and maxima, we can compute the first and second derivatives of f(x):

f'(x) = 2x+1

f''(x) = 2

We can see that f''(x) is always positive, so f(x) is always concave up. Therefore, any critical points of f(x) will be local minima. To find the critical points, we set f'(x) = 0:

2x+1 = 0

x = -1/2

So x=-1/2 is the only critical point of f(x). To determine whether it's a local minimum or not, we can look at the sign of f'(x) on either side of x=-1/2:

When x < -1/2: f'(x) < 0, so f(x) is decreasing.

When x > -1/2: f'(x) > 0, so f(x) is increasing.

Therefore, we know that x=-1/2 is a local minimum of f(x).

c) To determine the intervals on which f(x) = (x+1)(x-2)(x+3) is decreasing and increasing and find local minima and maxima, we can compute the first and second derivatives of f(x):

f'(x) = 3x^2-2x-7

f''(x) = 6x-2

To find the critical points of f(x), we set f'(x) = 0:

3x^2-2

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Answer: D

Step-by-step explanation:

The simplified expression is 0.

The fundamental identities are as follows:cot² (θ) + 1 = csc² (θ)

tan² (θ) + 1 = sec² (θ)

sin² (θ) + cos² (θ) = 1

Given expression, (1 + tan²(θ)/csc²(θ)) + sin²(θ) + (1/sec²(θ))

Now we need to simplify the given expression using the above-mentioned identities.

Substitute tan²(θ)/csc²(θ) with sec²(θ) in the first term, we get:

1 + tan²(θ)/csc²(θ) = 1 + (sec²(θ) - 1)/csc²(θ) = 1 + sec²(θ)/csc²(θ) - 1/csc²(θ) = csc²(θ) + sec²(θ) - 1/csc²(θ)

Now substitute 1/sec²(θ) with cos²(θ) in the given expression, we get:

csc²(θ) + sec²(θ) - 1/csc²(θ) + sin²(θ) + cos²(θ) = csc²(θ) + sec²(θ) + cos²(θ) + sin²(θ) - 1/csc²(θ) = (csc²(θ) + sec²(θ) + 1/csc²(θ)) - 1

The expression in the parentheses can be simplified using the identity:

csc² (θ) + sec² (θ) = 1/sin²(θ) + 1/cos²(θ) = (cos²(θ) + sin²(θ))/sin²(θ)cos²(θ)/cos²(θ) + sin²(θ)/sin²(θ) = 1/1 = 1

The expression simplifies to:1 - 1 = 0

The final simplified expression is 0.

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