7.2 puzzle time did you hear about the smog worksheet 8th grade answer key
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Any constructed vertical line that can only ever cross a graph once is considered to be a function. It is not a function if any points on the graph allow a vertical line to pass through them more than once.

To find the average rate of change per year for each loan over a certain interval, we can use the formula:

average rate of change = (change in amount owed) / (change in time)

We can calculate the change in amount owed by subtracting the initial amount from the final amount. For each loan, we'll consider the following time intervals:

Loan A: from t = 0 to t = 1

Loan B: from t = 1 to t = 2

Loan C: from t = 2 to t = 3

We can then calculate the average rate of change per year for each loan as follows:

Loan A:

average rate of change = (a(1) - a(0)) / (1 - 0)

= (1.12a(0) - a(0)) / 1

= 0.12a(0)

Therefore, the average rate of change per year for Loan A over the interval from t = 0 to t = 1 is 0.12 times the initial amount owed.

Loan B:

average rate of change = (b(2) - b(1)) / (2 - 1)

= (1.24b(1) - b(1)) / 1

= 0.24b(1)

Therefore, the average rate of change per year for Loan B over the interval from t = 1 to t = 2 is 0.24 times the amount owed at t = 1.

Loan C:

average rate of change = (c(3) - c(2)) / (3 - 2)

= (1.306c(2) - c(2)) / 1

= 0.306c(2)

Therefore, the average rate of change per year for Loan C over the interval from t = 2 to t = 3 is 0.306 times the amount owed at t = 2.

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Therefore, the average rate of change per year for Loan A over the interval from t = 0 to t = 1 is 0.12 times the initial amount owed.

Therefore, the average rate of change per year for Loan B over the interval from t = 1 to t = 2 is 0.24 times the amount owed at t = 1.

Therefore, the average rate of change per year for Loan C over the interval from t = 2 to t = 3 is 0.306 times the amount owed at t = 2.

Every vertical line that has been drawn but cannot cross a graph more than once is referred to as a function. It is not considered to be a function for any graph points to allow a vertical line to pass through them more than once.

To find the average rate of change per year for each loan over a certain interval, we can use the formula:

average rate of change = (change in amount owed) / (change in time)

We can calculate the change in amount owed by subtracting the initial amount from the final amount. For each loan, we'll consider the following time intervals:

Loan A: from t = 0 to t = 1

Loan B: from t = 1 to t = 2

Loan C: from t = 2 to t = 3

We can then calculate the average rate of change per year for each loan as follows:

Loan A:

average rate of change = (a(1) - a(0)) / (1 - 0)

= (1.12a(0) - a(0)) / 1

= 0.12a(0)

Therefore, the average rate of change per year for Loan A over the interval from t = 0 to t = 1 is 0.12 times the initial amount owed.

Loan B:

average rate of change = (b(2) - b(1)) / (2 - 1)

= (1.24b(1) - b(1)) / 1

= 0.24b(1)

Therefore, the average rate of change per year for Loan B over the interval from t = 1 to t = 2 is 0.24 times the amount owed at t = 1.

Loan C:

average rate of change = (c(3) - c(2)) / (3 - 2)

= (1.306c(2) - c(2)) / 1

= 0.306c(2)

Therefore, the average rate of change per year for Loan C over the interval from t = 2 to t = 3 is 0.306 times the amount owed at t = 2.

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Answer:  I'm gonna go with letter A.

A. y ≥ –3

C. x ≥ –3

Step-by-step explanation:  It's either letter A or letter C.

A.

y ≥ –1

Answer:

Step-by-step explanation:

The zero of a function is also known as the x-intercept of a function. The x-intercept of a function exists where y = 0. So we will begin by setting each of those lines = 0:

4x - 20 = 0     and     -1/2x + k = 0 and then solve each for x:

4x = 20 so

x = 5 and

-1/2x = -k and

1/2x = k so

x = 2k. Now we set the 2 x expressions equal to each other and solve for k:

5 = 2k so

k = 5/2

The value of the K in the given equation is 5/2.

The zero of a function is also known as the x-intercept of a function.

The x-intercept of a function exists where y = 0. So we will begin by setting each of those lines = 0:

4x - 20 = 0     and  

-1/2x + k = 0 and then solve each for x:

The substitution method is the algebraic method to solve simultaneous linear equations. As the word says, in this method, the value of one variable from one equation is substituted in the other equation.

4x = 20 so

x = 5 and

-1/2x = -k and

1/2x = k so

x = 2k. Now we set the 2 x expressions equal to each other and solve for k

5 = 2k so

k = 5/2

Therefore the value of the K in the given equation is 5/2.

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Answer: -30

Let's call the original number "x". Then, we can write the equation as follows:

-3/10 x + 1 = 10

To find the original number, we can isolate x by subtracting 1 from both sides and then multiplying both sides by 10/3:

-3/10 x = 9

x = (9 * 10)/(-3)

x = -30

So, the original number is -30.

Answer: The hypotheses of this test are:

Null hypothesis: The average weight of the product on the line is equal to the specified value of 16 ounces.

Alternative hypothesis: The average weight of the product on the line is different from the specified value of 16 ounces.

Step-by-step explanation:

Answer: C

Step-by-step explanation:

make the two functions equal to each other

10x + 5 = 7.5x + 25

2.5x = 20

x = 8

Answer is C

Answer:i think its 115 degres

Step-by-step explanation:

Answer:

2/5

Step-by-step explanation:

you switch the numbers from the equation

Okay so 550/10 is 55. So he went down 55 feet per minute. Or in otherwords, -55 (negative 55). Its negative because your going down.

Heart if it did help!

Answer:

Step-by-step explanation:

Average number of feet = Entire descent ÷ total time taken

                                       = 550 ÷ 10 = 55 per minute

                                       = -55

Negative sign denotes  he is descending.

=======================================================

Explanation:

n = diagram number

m = number of matches for diagram n

The given figures show that we have this info so far

\(\begin{array}{|c|c|} \cline{1-2}n & m\\\cline{1-2}1 & 3\\\cline{1-2}2 & 5\\\cline{1-2}3 & 7\\\cline{1-2}\end{array}\)

In other words, we have this sequence of values to represent the number of matches: 3, 5, 7

Each time we generate a new figure, we add 2 matches to the far right side. One match being horizontal and the other vertical.

This shows the common difference of this arithmetic sequence is d = 2.

The starting term is \(a_1 = 3\).

Let's find the nth term.

\(a_n = a_1 + d(n-1)\\\\a_n = 3 + 2(n-1)\\\\a_n = 3 + 2n-2\\\\a_n = 2n+1\\\\\)

Then we can determine the 50th term.

\(a_n = 2n+1\\\\a_{50} = 2(50)+1\\\\a_{50} = 100+1\\\\a_{50} = 101\\\\\)

There are 101 matches in the 50th diagram of the pattern.

Answer:

B) 2/12 basically 1/6 but not simplified

Step-by-step explanation:

so the probability of flipping heads is 1/2

The probality of rolling a number LESS than 3 is 2/6 becuase there are only 2 numbers less then 3 on a 1-6 cube.

now multiply them

1/2*2/6

2/12

so B

Answer:

third option

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = - 2x - 5 ← is in slope- intercept form

with slope m = - 2

Given a line with slope m then the slope of a line perpendicular to it is

\(m_{perpendicular}\) = - \(\frac{1}{m}\) = - \(\frac{1}{-2}\) = \(\frac{1}{2}\) , then

y = \(\frac{1}{2}\) x + c ← is the partial equation

To find c substitute (- 1, 1) into the partial equation

1 = - \(\frac{1}{2}\) + c ⇒ c = 1 + \(\frac{1}{2}\) = \(\frac{3}{2}\)

y = \(\frac{1}{2}\) x + \(\frac{3}{2}\) ← equation of perpendicular line

(a) The relative rate of growth of x can be defined as the derivative of x concerning time, dx/dt. and (b) The relative rate of growth of y, 1/y * dy/dt, is related to the relative rate of growth of x, 1/x * dx/dt, by the equation 1/y * dy/dt = a/x * dx/dt.

The answers to the above asked questions can be computed as,

(a) The derivative dx/dt denotes the instantaneous rate of change of x concerning time. x grows exponentially over time in the setting of a power law relationship. As a result, the derivative dx/dt may be thought of as x's relative rate of growth since it shows how rapidly x increases at a given point in time about its current value.

(b) To demonstrate the link between the relative rates of increase of y and x, we may use the time derivative of the power law equation:

d/dt(y) = d/dt(kx^a)

Using the chain rule and the fact that dx/dt = a * x^(a-1) (which can be derived by taking the derivative of the power law equation concerning x), we can simplify this expression:

d/dt(y) = a * k * x^(a-1) * dx/dt

Now, we can rearrange this equation to express the relative rates of growth of y and x:

d/dt(y) / y = a * dx/dt / x

This equation states that the relative rate of growth of y (i.e., how quickly y grows relative to its current value) is proportional to the relative rate of growth of x (i.e., how quickly x grows relative to its current value), with a proportionality constant equal to the power law equation's exponent an. This is an example of an allometric equation, which illustrates how two variables' relative rates of growth are connected.

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The equation of the straight line is y = -2x - 4, the value of x₁ is -1 and the value of y₁ is -2.

To find the equation of a straight line given its slope and one point, we use the point-slope form of the equation:

−y − y₁​ = m(x−x₁ )

where m is the slope of the line, and (x₁, y₁) is the given point.

In this case, m = -2 and the point is (-1, -2). So we have:

x₁ = -1

y₁ = -2

m = -2

Substituting these values into the point-slope form, we get:

y−(−2)=−2(x−(−1))

Simplifying and rearranging terms, we get the equation of the line:

y + 2 = -2x - 2

y = -2x - 4

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Answer:

Unsolvable

Step-by-step explanation:

If you have any questions about the way I solved it, don't hesitate to ask me in the comments below =)

Step-by-step explanation:

An object moving along the x-axis is said to exhibit simple harmonic motion if its position as a function of time varies as

x(t) = x0 + A cos(ωt + φ).

The object oscillates about the equilibrium position x0.  If we choose the origin of our coordinate system such that x0 = 0, then the displacement x from the equilibrium position as a function of time is given by

x(t) = A cos(ωt + φ).

A is the amplitude of the oscillation, i.e. the maximum displacement of the object from equilibrium, either in the positive or negative x-direction.  Simple harmonic motion is repetitive.  The period T is the time it takes the object to complete one oscillation and return to the starting position.  The angular frequency ω is given by ω = 2π/T.  The angular frequency is measured in radians per second.  The inverse of the period is the frequency f = 1/T.  The frequency f = 1/T = ω/2π of the motion gives the number of complete oscillations per unit time.  It is measured in units of Hertz, (1 Hz = 1/s).

The velocity of the object as a function of time is given by

v(t) = dx(t)/dt = -ω A sin(ωt + φ),

and the acceleration is given by

a(t) = dv(t)/dt = -ω2A cos(ωt + φ) = -ω2x.

Answer:

there's nothing there..

Step-by-step explanation:

Answer:

i need the question to answer though

Step-by-step explanation:

Answer:

Buy Two tshirts and a pair of pants....

Step-by-step explanation:

Total purchase -

$9.85 + $56.00 = $65.85

Shipping charges is 20%  -

65.85 * 0.2 = 13.17

Total (including shipping) = $79.02

If you purchace two t shirts and a pair of pants then you dont have to pay for the shipping therefore,

Total purchase will be -

$9.85 + $56.00 + $9.85 = $75.70

Puchasing 2 tshirts will be $3.32 cheaper....

Answer:

You should buy a second t-shirt.

Step-by-step explanation:

The total without shipping comes out to $65.85. Add the 20% shipping by multiplying .20 by the total, $65.85, and you get $65.85 plus $13.17, the total being $79.02. Now, if you added another shirt for $9.85, your total comes out to $75.70, which barely qualifies for free shipping. In other words, yes, you should purchase a second shirt because you would actually save money, almost $4.

Interval should we restrict cosine so as to obtain a one-to-one function, so that the resulting inverse is a function will be 0 ≤ x ≤π.

The standard trig functions repeat themselves means they are periodic. Therefore, multiple input values of the function, the same output value appeaed. This makes inverse functions impossible to construct. To solve equations involving trig functions, it is imperative for inverse functions to exist. Thus, mathematicians have to restrict the trig function to create these inverses.

To define an inverse function, the original function must be one-to-one. For a one-to-one correspondence to exist. (a) each value in the domain must correspond to exactly one value in the range, and (b) each value in the range must correspond to exactly one value in the domain. The second is not but the first restriction is shared by all functions. The sine function, for example, does not satisfy the second restriction, since the same value in the range corresponds to many values in the domain.

Sine function is not one to one. To define the inverse functions for sine and cosine, the domains of these functions are restricted. The restriction that is placed on the domain values of the cosine function is 0 ≤ x ≤ π . This restricted function is called Cosine. Note the capital ^ C deg in Cosine.

Graph of restricted cosine function. The inverse cosine function is defined as the inverse of the restricted Cosine function Cos -1 (cos x) = x ≤ π Therefore

Graph of inverse cosine function.

y = Cos ^ - 1 * x where 0 <= y <= π and - 1 ≤ x ≤1

Identities for the cosine and inverse cosine:

cos(Cos ^ - 1 * x) = x

- 1 ≤ x ≤1

Cos ^ - 1 * (cos x) = x

0 ≤ x ≤π

The inverse sine function's development is similar to that of the cosine. The restriction that is placed on the domain values of the sine function is

- π/2 ≤ x ≤ π/2

Graph of inverse sine function.

- π/2 ≤ x ≤ π/2

The graphs of the functions y = cos x and y = cos - 1 x are reflections of each other about the line y = x The graphs of the functions y = sin x and y = Sin - 1 xare also reflections of each other about the line y = x.

Interval should we restrict cosine so as to obtain a one-to-one function, so that the resulting inverse is a function will be 0 ≤ x ≤π.

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To determine the location of the maximum tensile bending stress with respect to the neutral axis, you need to find the point where the distance (y) is maximum.

To calculate the maximum tensile bending stress, you need to know the moment of inertia of the cross-sectional shape and the distance from the neutral axis to the point of interest.

The formula to calculate the maximum tensile bending stress (σ) is:

σ = (M * y) / I

where:

- M is the bending moment applied to the material

- y is the distance from the neutral axis to the point of interest

- I is the moment of inertia of the cross-sectional shape

Please provide the values for the bending moment (M), the moment of inertia (I), and the cross-sectional shape to calculate the maximum tensile bending stress and determine its location with respect to the neutral axis.

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Answer:

450 x (1 + 0.5) ^ X = Phone subscribers

Step-by-step explanation:

Since a telecommunications company in a small town had 450 phone subscribers before they introduced a plan for newly joining members, and the company recorded an approximate 50% increase each month in the number of new phone subscribers, where they had one new subscriber at the start of the plan, to determine the number of phone subscribers x months after the plan was launched, the following function must be considered and solved:

450 x (1 + 0.5) ^ X = Phone subscribers

So, for example, in 3 months, the number of subscribers would be the following:

450 x (1 + 0.5) ^ 3 = 1,518.75

Thus, in 3 months, the company would have 1,518 subscribers.

Answer:-9

Step-by-step explanation:

that is the answer

The mean of X - 6 is 1/2 and the variance is 145/12. To find the probability distribution, we need to determine the cumulative distribution function and differentiate it to obtain the probability density function (PDF).

First, let's find the cumulative distribution function (CDF) of X - 6. Since X has a continuous uniform distribution on the interval [0, 1], the CDF of X is given by:

F(x) = P(X <= x) = ∫[0, x] f(t) dt

where f(t) is the probability density function of X.

For the continuous uniform distribution on [0, 1], the probability density function (PDF) f(t) is constant within the interval and zero outside the interval. Thus, f(t) = 1 for 0 ≤ t ≤ 1 and f(t) = 0 otherwise.

Let's calculate the CDF of X - 6:

F(x - 6) = P(X - 6 ≤ x) = P(X ≤ x + 6)

Since X has a uniform distribution on [0, 1], if x + 6 < 0 or x + 6 > 1, then P(X ≤ x + 6) = 0. Otherwise, if 0 ≤ x + 6 ≤ 1, then P(X ≤ x + 6) = x + 6.

Therefore, the CDF of X - 6 is given by:

F(x - 6) =

{

0, if x + 6 < 0,

x + 6, if 0 ≤ x + 6 ≤ 1,

1, if x + 6 > 1

}

To obtain the probability density function (PDF) of X - 6, we differentiate the CDF with respect to x:

f(x - 6) = d/dx (F(x - 6))

Differentiating the CDF in the respective intervals gives us:

f(x - 6) =

{

0, if x + 6 < 0 or x + 6 > 1,

1, if 0 ≤ x + 6 ≤ 1,

0, otherwise

}

So, the PDF of X - 6 is a step function with a value of 1 over the interval [0, 1] and zero outside this interval.

Now, let's find the mean and variance of X - 6.

The mean of X - 6 can be calculated as follows:

E(X - 6) = ∫(-∞, ∞) x f(x - 6) dx

Since the PDF of X - 6 is zero outside the interval [0, 1], we can integrate over this interval:

E(X - 6) = ∫[0, 1] x dx

E(X - 6) = [x^2/2] [0, 1]

E(X - 6) = 1/2

Therefore, the mean of X - 6 is 1/2.

To find the variance of X - 6, we can use the formula:

Var(X - 6) = E[(X - 6)^2] - [E(X - 6)]^2

To calculate E[(X - 6)^2], we integrate over the interval [0, 1]:

E[(X - 6)^2] = ∫[0, 1] (x - 6)^2 dx

E[(X - 6)^2] = ∫[0, 1] (x^2 - 12x + 36) dx

E[(X - 6)^2] = [x^3/3 - 6x^2 + 36x] [0, 1]

E[(X - 6)^2] = (1/3 - 6 + 36) - (0/3 - 0 + 0)

E[(X - 6)^2] = 1/3 - 6 + 36

E[(X - 6)^2] = 37/3

Now, we can calculate the variance:

Var(X - 6) = E[(X - 6)^2] - [E(X - 6)]^2

Var(X - 6) = 37/3 - (1/2)^2

Var(X - 6) = 37/3 - 1/4

Var(X - 6) = (148 - 3)/12

Var(X - 6) = 145/12

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\( \huge \tt \color{pink}{A}\color{blue}{n}\color{red}{s}\color{green}{w}\color{grey}{e}\color{purple}{r }\)

\( \large\underline{ \boxed{ \sf{✰\:Note }}}\)

\( \rule{70mm}{2.9pt}\)

\({ \boxed{✠ \: \underline{ \boxed{ \sf{\: P(A) = \frac{Number \: of \: favourable \: outcomes}{Total \: number \: of \: favourable \: outcomes} }}} \: ✠}}\)

\( \rule{70mm}{2.9pt}\)

✛ Here ✛

\( \qquad \sf \:➛ \: x = \frac {4 }{20} \\ \qquad \sf \:➛ \: x = \frac { \cancel4 }{ \cancel{20}} \\ \qquad \sf \:➛ \: x = 0.2min\)

\( \rule{70mm}{2.9pt}\)

★ Hence probabllty that the news and weather report is NOT on P(A)

\( \qquad \qquad{ \boxed{✟\: \underline{ \boxed{ \sf{\:0.2min\green ✓ }}} \:✟ }}\)

\( \rule{70mm}{2.9pt}\)

Hope it helps !

The value of a lies between 90.8209 and 91.0116 is 91. Then the correct option is C.

Inequality is simply a type of equation that does not have an equal sign in it. Inequality is defined as a statement about the relative size as well as is used to compare two statements.

The inequality is given as

9.53 < √a < 9.54

On squaring both sides, we have

  9.54² > a > 9.53²

91.0116 > a > 90.8209

Thus, the value of a lies between 90.8209 and 91.0116 is 91. Then the correct option is C.

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Answer:

the answer is C

Step-by-step explanation:

i got it right.

The minimal approximation error A-A 2achievable by a rank-1 approximation A to A is

||A - A1||₂=0 where A is 2×2 matrix.

We have given a matrix A as seen in above figure or A = [ 5 15 ; 6 18 ; -1 -3 ; -4 -12 ; 2 6]

note here that C₂= 3C₁

where Cᵢ --> iᵗʰ column

v = [ 5 ; 6 ; -1 ; -4 ; 2]

||v||² = 82 => ||v|| = √82

and A At v = 820 v

and A At = [ 82 246 ; 246 738]

AAt [1;3] = 820[1;3]

=> v1 = 1/√10(1,3)^t

Then the best rank of 1 approx

= √820 /√80√10 [ 5 ; 6 ; -1 ; -4 ; 2] [ 1 3]

= A

Since , the rank of matrix A is one so, the minimal approx. value is ||A - A1||2 = 0

Hence, the minimal Approx. ||A - A1||2 = 0 .

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Complete question:

Consider the matrix A: A = [5 15] 6 18 -1 -3 -4 -12 [26] What is the minimal approximation error A-A 2 achievable by a rank-1 approximation A to A? Hint: Can you determine this without explicitly calculating the SVD?

The given series is a geometric series with the formula: ∑ (1 + 6)^n / 7^n (from n=1 to infinity) In a geometric series,

The convergence or divergence is determined by the common ratio (r). In this case, the common ratio r is (1 + 6) / 7, which simplifies to 1.

Since the absolute value of the common ratio |r| is equal to 1, the series is inconclusive regarding convergence or divergence. Therefore, we need to use another test.

Notice that (1+6)/7 = 7/6 > 1. This means that the terms of the series do not approach zero as n approaches infinity. Therefore, the series sigma^[infinity]_n=1 (1+6)^n/7^n diverges by the divergence test. Therefore, the series does not have a sum.

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(a) The product function, f(x), is the product of g(x) and h(x), given by f(x) = g(x) * h(x) = (4x² - 2) * 1.6.

(b) The rate-of-change function, f'(x), is the derivative of f(x), which can be found using the product rule.

(a) To find the product function, we multiply g(x) and h(x) together. g(x) is given as 4x² - 2 and h(x) is given as 1.6. Therefore, the product function f(x) is obtained by multiplying these two expressions: f(x) = (4x² - 2) * 1.6.

(b) To find the rate-of-change function, f'(x), we need to take the derivative of f(x). Using the product rule, the derivative of f(x) is given by:

f'(x) = g'(x) * h(x) + g(x) * h'(x).

The derivative of g(x) with respect to x is 8x, and the derivative of h(x) with respect to x is 0 since h(x) is a constant. Therefore, the rate-of-change function, f'(x), simplifies to:

f'(x) = (8x * 1.6) + (4x² - 2) * 0.

Simplifying further, we have:

f'(x) = 12.8x.

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The product function, f(x), is obtained by multiplying the given functions g(x) and h(x). The rate-of-change function, f'(x), represents the derivative of the product function with respect to x.

To find the product function, f(x), we simply multiply the given functions g(x) and h(x). Therefore, f(x) = g(x) * h(x) = (4x² - 2) * (1.6).

To find the rate-of-change function, f'(x), we need to take the derivative of the product function f(x) with respect to x. The derivative of a product of two functions can be calculated using the product rule of differentiation. Applying the product rule to f(x) = g(x) * h(x), we obtain f'(x) = g'(x) * h(x) + g(x) * h'(x).

However, since the given functions g(x) and h(x) are constants with respect to x, their derivatives are zero. Therefore, the rate-of-change function f'(x) simplifies to f'(x) = g'(x) * h(x) + g(x) * h'(x) = 0 * (1.6) + (4x² - 2) * 0 = 0.

In conclusion, the rate-of-change function f'(x) is equal to zero, indicating that the product function f(x) is a constant function with no change in value as x varies.

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