What i the quotient of 3. 12\time 10^83. 12×10
8
and 2. 6 \time 10^52. 6×10
5
expreed in cientific notation?

Answer:

-168

Step-by-step explanation:

8 × -7 × 3

-56 × 3

-168

For the given expression 2t² is the impulse response, and the given system is linear and the system is unstable

Given, y(t) = 2t{t-4 x(T) dt.
a) To find impulse response, let x(t) = δ(t).Then, y(t) = 2t{t-4 δ(T) dt = 2t.t = 2t².

Let h(t) = y(t) = 2t² is the impulse response.
b) A system is said to be linear if it satisfies the two properties of homogeneity and additivity.

A system is said to be linear if it satisfies the two properties of homogeneity and additivity. For homogeneity,

let α be a scalar and x(t) be an input signal and y(t) be the output signal of the system. Then, we have

h(αx(t)) = αh(x(t)).

For additivity, let x1(t) and x2(t) be input signals and y1(t) and y2(t) be the output signals corresponding to x1(t) and x2(t) respectively.

Then, we have h(x1(t) + x2(t)) = h(x1(t)) + h(x2(t)).

Now, let's consider the given system y(t) = 2t{t-4 x(T) dt.

Substituting x(t) = αx1(t) + βx2(t), we get y(t) = 2t{t-4 (αx1(t) + βx2(t))dt.

By the linearity property, we can write this as y(t) = α[2t{t-4 x1(T) dt}] + β[2t{t-4 x2(T) dt}].

Hence, the given system is linear.
c) A system is stable if every bounded input produces a bounded output.

Let's apply the bounded input to the given system with an input of x(t) = B, where B is a constant.Then, we have

y(t) = 2t{t-4 B dt} = - 2Bt² + 2Bt³.

We can see that the output is unbounded and goes to infinity as t approaches infinity.

Hence, the system is unstable. Therefore, the system is linear and unstable.

Thus, we have found the impulse response of the given system and checked whether the system is linear or not. We have also checked whether the system is stable or unstable. We found that the system is linear and unstable.

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Answer:

10.29 (rounded = 10.30)

Step-by-step explanation:

X = a^2 + b^2 = c^2

X = 9^2 + 5^2 = c^2

X = (81) + (25) = c^2

X = 106 = c^2

X = √106 = c^2

X = 10.295630141 = c^2

X = 10.03 = c^2 (10.03 is 10.295630141 rounded to the nearest tenth)

Answer:

$77

Step-by-step explanation:

i just take 55 x 0.14 which is 7.7 then i moved the decimal 1 place to the right.

Answer:

I believe the answer it 62.70

although I am not completely sure

Step-by-step explanation:

14% of 55 = 7.7

7.7 + 55 = 62.7

= $62.70

Answer:

3rd option

Step-by-step explanation:

The zeros ( where the graph crosses the x- axis ) are x = 3 and x = 7

The corresponding factors are then (x - 3) and (x - 7)

The equation is then

f(x) = a(x - 3)(x - 7) ← a is a multiplier

To find a substitute any point on the graph into the equation.

Using (8, 15 ) , then

15 = a(8 - 3)(8 - 7) = a(5)(1) = 5a ( divide both sides by 5 )

3 = a

Thus

f(x) = 3(x - 3)(x - 7)

The center of the circle is (-4, 11), and the radius of the circle is r = 3.

An equation of the circle with center (h,k) and radius r is

\((x - h)^{2} + (y - k)^{2} = r^{2}\)

So, comparing \((-4-x)^{2} + (-y+11)^{2} = 9\) that is \((x-(-4))^{2} + (y-11)^{2} = 9\)

with the above equation of a circle, we get:    

h = −4, k = 11 and r = 3

Therefore, the center of the circle is (−4,11) and the radius of the circle is r=3.

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Complete question:

Find the center and radius of the circle represented by the equation below.

\((-4-x)^{2} + (-y+11)^{2} = 9\)

Answer:

the answer is 589.4

Step-by-step explanation:

In doing this equation you do the order of operations:

(2.1 x 104)= 218.4

(3.5 x 106)= 371

you then add the answers together to get:

218.4 + 371 = 589.4

If the variables are not quantitative we cannot do the arithmetic required in the formulas for r.

Quantitative order:

Therefore, if the variables are not quantitative we cannot do the arithmetic required in the formulas for r.

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Answer:

Step-by-step explanation:

is it

-f(x)=9x+5 or positive?

9(8)+5=72+5

f(8)=77

9(-10)+5=-90+5

f(-10)=-85

9(0)+5=5

f(0)=5

think of f(x) is y instead and whatever is in the parenthesis just plug into the equation for x

Answer:

3/1

Step-by-step explanation:

you just start at the point where the line intersects the corner

Answer:

8.2 cm

Step-by-step explanation:

The given shows us that we will be using CAH from SOH CAH TOA where

cos theta = adjacent / hypotenuse

in this case it will be

. cos 47 = h / 12

we want h to be the subject so we will multiply both sides by 12

. h = cos 47 * 12

. h = 8.184

now all you have to do is round to 1d.p

. h = 8.2cm

The value of cos θ is equal to 1/3 when sec θ= √6/2.

Since we are given the value of secant of theta, we can use the relationship between secant and cosine to find the value of cosine of theta.

Let's start by recalling the definitions of secant and cosine functions. The secant of an angle is defined as the reciprocal of the cosine of that angle.

In other words, secθ = 1/cosθ

Conversely, the cosine of an angle is defined as the reciprocal of the secant of that angle.

cosθ = 1/secθ

We are given that secθ= √6/2

We can use this value to find cosθ= 1/secθ

cosθ = 1 / (√6/2)

To simplify this expression, we can multiply both the numerator and denominator by 2/sqrt(6).

cosθ = ((2/√6) / (√6/2) * (2/√6))

cosθ = (2/√6) / 1

cosθ = (2/√6 * √6/√6)

cosθ = 2/6 = 1/3

Therefore, the value of cosθ is equal to 1/3 when secθ = sqrt(6)/2.

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The price of the rechargeable drill in the home improvement stores is P(m) = 1.2m + 4, where m is the manufacturing total cost.

P(m) = 1.2m + 4

P(m) = 1.2(manufacturing cost) + 4

P(m) = 1.2m + 4

The manufacturer of tools charges $4 more than its manufacturing cost for a rechargeable drill to a chain of home improvement stores. Following that, the chain sells each drill for 120 percent of what it paid the manufacturer.. Therefore, the price of the rechargeable drill in the home improvement stores can be represented by the function P(m), where m is the manufacturing cost of the drill. The equation P(m) = 1.2m + 4 shows that the price of the rechargeable drill in the home improvement stores is equal to 1.2 times the manufacturing cost plus $4. This equation indicates that the manufacturer of tools charges $4 more than its manufacturing cost and the home improvement stores then increase the price of the drill by 20% of the price they paid to the manufacturer. Therefore, the total cost of the rechargeable drill in the home improvement stores is 1.2m + 4, where m is the manufacturing cost of the drill.

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Hello,

\( \frac{1}{4} \times- \frac{1}{2} = \frac{1 \times (-1)}{4 \times 2} = - \frac{1}{8} \)

The correct sequence of project phases is Definition - Planning  - Performance. The correct answer is B.

This is the typical order of project phases in a traditional project management approach. It starts with the definition phase, where the project's goals, the scope, and the requirements are established.

Then comes the planning phase, where the project plan is developed, including the allocation of resources, scheduling, and budgeting.

Finally, the performance phase begins, during which the project activities are executed, monitored, and controlled to ensure the successful project completion.

Therefore the sequence of project phase is  Definition - Planning  - Performance The correct answer is B.

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Answer:

below⬇⬇⬇⬇⬇⬇

Step-by-step explanation:

since the table mostly gives us the answer, i think its:

\(\frac{100}{x}\)=\(\frac{200}{22.4}\)

⬆⬆⬆⬆that's your answer <3333

Answer:

Step-by-step explanation:

100 / x    = 200/22.4

cross multiplication

200x = 22.4 x 100

200x = 2,240

divide by 200

x = 11.2

It makes sense since 100 is half of 200 then 11.2 is half of 22.4

The decimal fοrm οf the mixed fractiοn 33 2/3, apprοximated tο the nearest tenth, is 33.67.

A mixed fractiοn is οne that is represented by bοth its quοtient and remainder. Sο, a mixed fractiοn is a cοmbinatiοn οf a whοle number and a prοper fractiοn. A fractiοn represents a piece οf a larger tοtal. Tο learn hοw tο determine the precise values οf mixed numbers, it is crucial tο cοnvert a mixed number tο a decimal. A mixed number can be cοnverted tο decimal fοrm using οne οf twο techniques:

the mixed number is changed intο an imprοper fractiοn.

by first changing the given mixed number's fractiοnal pοrtiοn tο decimal, then adding the whοle number pοrtiοn tο it.

Nοw the given fractiοn is 33 2/3.

This is a mixed fractiοn because it has a whοle number οf 33 and a fractiοn οf 2/3.

This mixed fractiοn can be cοnverted tο a decimal number by finding the value οf the fractiοn part οf the number and adding it tο the whοle number.

Sοlving fractiοnal parts,

2/3 = 0.66666 = 0.67 (Rοunding tο the nearest tenth)

Nοw add tο the whοle number.

33 + 0.67 = 33.67

Therefοre the decimal fοrm οf the mixed fractiοn 33 2/3 is 33.67.

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given:

To find 3/4 is a solution of the above given equation.

let us subsitute in value of x.

now,

we get the same answer for the equation.

Thus 3/4 is a solution of the given equaion.

The statistical decision based on the reported results of the hypothesis test is that the null hypothesis was rejected at the α = .05 significance level.

The t-value reported is 2.38, and the degrees of freedom are 21. This suggests that the test was likely a t-test with an independent samples design, where the sample size was n = 22 (since df = n - 1).

The p-value reported is less than .05, which indicates that the probability of obtaining the observed results, or results more extreme, under the assumption that the null hypothesis is true, is less than .05. Therefore, the null hypothesis is rejected at the .05 significance level in favor of the alternative hypothesis.

In conclusion, the statistical decision is that there is sufficient evidence to suggest that the population means are not equal, and the sample size was 22. However, we do not have information about the direction of the effect (i.e., whether the difference was positive or negative).

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The probability that their first child will be a phenotypically normal girl is 3/8 or 37.5%.

Lou Gehrig's disease, also known as amyotrophic lateral sclerosis (ALS), is typically considered as an autosomal recessive disease. This means that both copies of the gene responsible for the disease need to be inherited, one from each parent, in order for an individual to be affected by the disease.

Given that the woman and her husband are both carriers of the disease, they each have one copy of the mutated gene and one normal gene. The probability of passing on the mutated gene to their child is 1/2 for each parent since they are carriers.

To determine the probability of their first child being a phenotypically normal girl, we need to consider the inheritance pattern. Let's break it down:

Gender: The probability of having a girl is 1/2, as gender is determined by the combination of the father's sperm (containing either an X or a Y chromosome) and the mother's egg (containing an X chromosome).

Phenotypically normal: For the child to be phenotypically normal, they should inherit at least one normal gene from either parent. The probability of inheriting a normal gene from the mother is 1/2, and the same probability applies for inheriting a normal gene from the father.

Independence: The probability of having a girl and inheriting a normal gene are independent events, so we can multiply their individual probabilities to calculate the combined probability.

Therefore, the probability of having a phenotypically normal girl is:

Probability of being a girl × Probability of inheriting a normal gene

= (1/2) × (1/2)

= 1/4

However, we also need to consider the possibility of having a boy. The probability of having a phenotypically normal boy is also 1/4.

Adding the probabilities of having a phenotypically normal girl and a phenotypically normal boy, we get:

1/4 + 1/4 = 2/4 = 1/2        

Since the question specifically asks for the probability of having a phenotypically normal girl, we divide the probability of a phenotypically normal girl by the total probability of having a child:

(1/4) / (1/2) = 1/4 * 2/1 = 1/2 = 2/4 = 1/2

Therefore, the probability that their first child will be a phenotypically normal girl is 1/2 or 50%.

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To ensure the best test results, Anita should be provided with the following information before her spirometry:

1. Instructions for taking the test: Anita should be thoroughly explained about how the spirometry test works and what steps she needs to follow. This includes taking a deep breath and blowing as hard as she can into the spirometer mouthpiece. It is important to emphasize that she needs to repeat this procedure a few times and take deep breaths between each exhale.

2. Emphasize the importance of taking medication as prescribed: Anita should be reminded of the importance of taking her medications as prescribed, including on the day of the test. It is crucial for her to bring her medications to the test appointment.

3. Avoid certain foods and drinks: Anita should be informed to avoid consuming certain substances before the spirometry test, such as caffeine, alcohol, and heavy meals. These can potentially affect the accuracy of the test results.

4. Arrive early for the test: Anita should be advised to arrive early for the test to allow herself sufficient time to relax and calm down before the procedure. This can help ensure more accurate results.

The rationale behind providing these instructions and information is that spirometry is a lung function test that measures the amount and speed of air being breathed in and out. By following the instructions and guidelines, Anita can achieve optimal results, aiding in the diagnosis and assessment of lung conditions.

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Let's represent the cost of a cup of corn as 'c' and the cost of a taco as 't'.

From the first statement, we know that:

2c + 4t = 19 (equation 1)

From the second statement, we know that:

3c + 2t = 14.5 (equation 2)

We can solve this system of equations using elimination or substitution. Here, we'll use substitution.

Rearranging equation 2, we get:

3c = 14.5 - 2t

Dividing both sides by 3, we get:

c = 4.83 - 0.67t

Now we can substitute this expression for 'c' into equation 1:

2(4.83 - 0.67t) + 4t = 19

Simplifying, we get:

9.66 - 0.34t = 19

Subtracting 9.66 from both sides, we get:

-0.34t = 9.34

Dividing both sides by -0.34, we get:

t = -27.47 ≈ $-2.75

Since a negative price for a taco doesn't make sense, we made an error somewhere. Checking our calculations, we can see that we made a mistake in the expression for 'c'. It should be:

c = (14.5 - 2t)/3

Substituting this expression for 'c' into equation 1:

2[(14.5 - 2t)/3] + 4t = 19

Multiplying both sides by 3:

2(14.5 - 2t) + 12t = 57

Expanding and simplifying:

29 - 4t + 12t = 57

8t = 28

t = 3.5

Therefore, the tacos cost $3.50.

Answer:

are you okay?

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

It’s b

Answer:

-45x - 18

Step-by-step explanation:

distributive property

Answer:

x = 18/45 (or, in a decimal, 0.4). Someone correct me if I'm wrong. :)

Step-by-step explanation:

We have to use the distributive property here. That means that you multiply -5x by 9 and -2 by 9. So...

9*-5x = -45x

9*-2 = -18

-45x = -18

Now, divide both sides by 45...

-45x/45 = -18/45

x = 18/45 should be the answer.

By forming and solving equations, we know that the speed of the runner is 4 miles per hour.

So, we need to form an equation to get the speed of the runner:

'x' is the speed of the runner. Now, solve for x as follows:

Therefore, by forming and solving equations, we know that the speed of the runner is 4 miles per hour.

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Answer:

Step-by-step explanation:

y = 6X

so this is a direct variation , b/c as X goes up, so does Y

The equation that models the data is y = 6x

An equation contains one or more terms with variables connected by an equal sign.

Example:

2x + 4y = 9 is an equation.

2x = 8 is an equation.

We have,

To determine whether the data in the table represents a direct or inverse variation, we need to check whether the ratio of x to y is constant.

When we divide each y-value by its corresponding x-value, we get the ratios:

6/1 = 6

12/2 = 6

30/5 = 6

60/10 = 6

We see that the ratio of y to x is constant, which means that the data represents a direct variation.

To write an equation to model the data in the table, we can use the formula for direct variation, which is:

y = kx

where k is the constant of variation.

To find k, we can use any of the given data pairs.

For example, we can use the first pair (x = 1, y = 6):

6 = k(1)

Solving for k, we get:

k = 6/1 = 6

Thus,

The equation that models the data is y = 6x

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Answer:

Addition = Justification 2

Division = Justification 4

Given = Justification 5

Distributive = Justification 1

Subtraction = Justification 3

Answer:

Addition property of order - Justification 4

Division property of order - Justification 5

Given - Justification 1

Distributive property - Justification 2

Subtraction property of order - Justification 3

Step-by-step explanation:

The first derivative of the function `g(u) = u(2u - 3)^3` is `g'(u) = 6u(2u - 3)^2 + (2u - 3)^3`. The second derivative of the function is `g''(u) = 12(u - 1)(2u - 3)^2`.

Given function: `g(u)

= u(2u - 3)^3`

To find the first derivative of the given function, we use the product rule of differentiation.`g(u)

= u(2u - 3)^3`

Differentiating both sides with respect to u, we get:

`g'(u)

= u * d/dx[(2u - 3)^3] + (2u - 3)^3 * d/dx[u]`

Using the chain rule of differentiation, we have:

`g'(u)

= u * 3(2u - 3)^2 * 2 + (2u - 3)^3 * 1`

Simplifying:

`g'(u)

= 6u(2u - 3)^2 + (2u - 3)^3`

To find the second derivative, we differentiate the obtained expression for

`g'(u)`:`g'(u)

= 6u(2u - 3)^2 + (2u - 3)^3`

Differentiating both sides with respect to u, we get:

`g''(u)

= d/dx[6u(2u - 3)^2] + d/dx[(2u - 3)^3]`

Using the product rule and chain rule of differentiation, we have:

`g''(u)

= 6[(2u - 3)^2] + 12u(2u - 3)(2) + 3[(2u - 3)^2]`

Simplifying:

`g''(u)

= 12(u - 1)(2u - 3)^2`.

The first derivative of the function `g(u)

= u(2u - 3)^3` is `g'(u)

= 6u(2u - 3)^2 + (2u - 3)^3`. The second derivative of the function is `g''(u)

= 12(u - 1)(2u - 3)^2`.

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The first derivative of g(u) is g'(u) = (2u - 3)³ + 6u(2u - 3)², and the second derivative is g''(u) = 12(2u - 3)² + 12u(2u - 3).

First, let's find the first derivative:

g'(u) = (2u - 3)³ * d(u)/du + u * d/dx[(2u - 3)³]

Using the chain rule, we can differentiate (2u - 3)³ and u as follows:

d(u)/du = 1

d/dx[(2u - 3)³] = 3(2u - 3)² * d(2u - 3)/du

= 3(2u - 3)² * 2

Plugging these values back into the equation for g'(u), we have:

g'(u) = (2u - 3)² + u * 3(2u - 3)² * 2

= (2u - 3)³ + 6u(2u - 3)²

Simplifying the expression, we have:

g'(u) = (2u - 3)³ + 6u(2u - 3)²

Now, let's find the second derivative:

g''(u) = d/dx[(2u - 3)³ + 6u(2u - 3)²]

Using the chain rule and product rule, we can differentiate each term:

d/dx[(2u - 3)³] = 3(2u - 3)² * d(2u - 3)/du

= 3(2u - 3)² * 2

d/dx[6u(2u - 3)²] = 6(2u - 3)² + 6u * d/dx[(2u - 3)²]

= 6(2u - 3)² + 6u * 2(2u - 3)

Plugging these values back into the equation for g''(u), we have:

g''(u) = 3(2u - 3)² * 2 + 6(2u - 3)² + 6u * 2(2u - 3)

= 6(2u - 3)² + 6(2u - 3)² + 12u(2u - 3)

= 12(2u - 3)² + 12u(2u - 3)

Simplifying the expression further, we have:

g''(u) = 12(2u - 3)² + 12u(2u - 3)

Therefore, the first derivative of g(u) is g'(u) = (2u - 3)³ + 6u(2u - 3)², and the second derivative is g''(u) = 12(2u - 3)² + 12u(2u - 3).

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