For a pair of similar triangles, if the ratio of their corresponding sides is 1/4, what is the ratio of their areas? A. 1/64
B. 1/16
C. 1/4
D. 1/2

b.)The number of people that has pizza would be = 22.

c.) The number of people that has salad or fruit = 6.

To calculate the number of people that had pizza, the following steps should be taken as follows:

The total number of people that are at the restaurant = 45 people.

For question b.)

From the given table, total number of people that had pizza = 22

That is;

The number of people that are pizza and fruit = 12-(6+3) = 3

The number of people that are pizza and yogurt = 5

The number of people that are pizza and ice cream = 22-(5+3) = 14

The total number of people that are pizza = 14+5+3 = 22

For question c.)

The total number of people that ate salad or fruit = 6 people.

Learn more about addition here:

https://brainly.com/question/30458444

#SPJ1

Answer:

  2048

Step-by-step explanation:

You want the value of a10 = 4(2^(10 -1)).

If you don't have powers of 2 memorized, you can put this expression into your calculator or spreadsheet to get it evaluated. You will need parentheses around the exponent.

  4(2^(10-1)) = 4(2^9) = 4(512) = 2048

The value of the expression is 2048.

__

Additional comment

This looks like an instance of the equation for the n-th term of a geometric sequence:

  an = a1·r^(n -1)

where a1 = 4, r = 2, and n = 10.

This is why we have assumed that the "-1" is part of the exponent, and that you simply want the value of the right-side expression.

If this equation means something else, then it needs to be written differently. For example, if a10 means 'a' to the 10th power, it needs to be written as a^10, and we need to be told we're solving for 'a'.

<95141404393>

Answer:

36 m

Step-by-step explanation:

Perimeter = 2L + 2w = 99

2(L + w) = 99

L = length = 8x

w = width = 3x

2(8x + 3x) = 99

16x + 6x = 99

22x = 99

x = 99/22 = 4.5

L = 8x = 8(4.5) = 36

The probability of selecting a defective compact disk from a randomly chosen label produced by the company is 0.0428 or 4.28%. The correct option is d.

To find the probability of a randomly selected label produced by the company containing a defective compact disk, we need to consider the probabilities of each manufacturer's defective compact disks and their respective supply percentages.

Let's calculate the probability:

1. Manufacturer I produces 36% of the compact disks, and 3% of their disks are defective. So, the probability of selecting a defective disk from Manufacturer I is (36% * 3%) = 0.36 * 0.03 = 0.0108.

2. Manufacturer II produces 54% of the compact disks, and 5% of their disks are defective. The probability of selecting a defective disk from Manufacturer II is (54% * 5%) = 0.54 * 0.05 = 0.0270.

3. Manufacturer III produces 10% of the compact disks, and 5% of their disks are defective. The probability of selecting a defective disk from Manufacturer III is (10% * 5%) = 0.10 * 0.05 = 0.0050.

Now, we can find the total probability by summing up the probabilities from each manufacturer:

Total probability = Probability from Manufacturer I + Probability from Manufacturer II + Probability from Manufacturer III
                 = 0.0108 + 0.0270 + 0.0050
                 = 0.0428

Therefore, the probability that a randomly selected label produced by the company will contain a defective compact disk is 0.0428. Hence, the correct option is (d) 0.0428.

To know more about probability, refer to the link below:

https://brainly.com/question/30034780#

#SPJ11

The general solutions to the Diophantine equation 18x + 735y = 3 can be expressed as follows:

x = 245 - 49k

y = -6 + 2k

To find the general solutions to the Diophantine equation 18x + 735y = 3, we need to determine the values of x and y that satisfy the equation. One approach to solving such equations is by using the extended Euclidean algorithm. By applying this algorithm, we can find the greatest common divisor (gcd) of the coefficients 18 and 735, which is 3 in this case. Since 3 divides both 18 and 735, the equation has solutions.

The extended Euclidean algorithm also yields two integers s and t such that 18s + 735t = 3. In this case, s = -49 and t = 2. We can express x and y in terms of s and t:

x = (735/3)s + (18/3)t = 245s + 6t

y = (-18/3)s + (735/3)t = -6s + 245t

Simplifying the expressions, we get:

x = 245 - 49s

y = -6 + 2s

Here, s can take any integer value, which means we can choose an arbitrary integer k and substitute it for s to obtain the general solutions for x and y. Thus, the general solutions to the Diophantine equation are given by:

x = 245 - 49k

y = -6 + 2k

Learn more about Diophantine equation

brainly.com/question/30709147

#SPJ11

To find the battery life of the latest model 10 months from now, we need to calculate the cumulative increase in battery life over the 10-month period.

The battery life of each model increases by 4% compared to the previous model. Therefore, the battery life of the second model is [tex]\displaystyle 100\% + \dfrac{4}{100} = 104\%[/tex] of the first model's battery life. Similarly, the battery life of the third model is [tex]\displaystyle 104\% + \dfrac{4}{100} = 108.16\%[/tex] of the second model's battery life, and so on.

Using this pattern, the battery life of the latest model 10 months from now can be calculated as follows:

[tex]\displaystyle 632.0 \, \text{minutes} \times \left(1 + \dfrac{4}{100}\right)^{10}[/tex]

Simplifying this expression, we get:

[tex]\displaystyle 632.0 \times \left(1.04\right)^{10}[/tex]

Calculating this expression, we find that the latest model's battery life 10 months from now is approximately 1057.1 minutes.

Therefore, the correct answer is A) 1057.1.

[tex]\huge{\mathfrak{\colorbox{black}{\textcolor{lime}{I\:hope\:this\:helps\:!\:\:}}}}[/tex]

♥️ [tex]\large{\underline{\textcolor{red}{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}[/tex]

Since Jeffrey deposits the $450 at the end of every quarter, the type of annuity is an Ordinary Annuity.

An ordinary annuity is a type of annuity where the payment occurs at the end of the period and not at the beginning like Annuity Due.

The ordinary annuity can be computed as follows using an online finance calculator.

Quarterly deposits = $450

Investment period = 4 years and 6 months (4.5 years)

Compounding period = semi-annually

N (# of periods) = 18 (4.5 years x 4)

I/Y (Interest per year) = 5.3%

PV (Present Value) = $0

PMT (Periodic Payment) = $450

P/Y (# of periods per year) = 4

C/Y (# of times interest compound per year) = 2

PMT made = at the of each period

Results:

FV = $9,073.18

Sum of all periodic payments = $8,100 ($450 x 4.5 x 4)

Total Interest = $973.18

Thus, the annuity is not an Annuity Due but an Ordinary Annuity.

Learn more about annuities at https://brainly.com/question/30100868.

#SPJ4

The transformation represented by the rule (x, y) → (y, -x) is a rotation of 90° clockwise about the origin.

To understand the transformation, let's consider a point (x, y) in a coordinate plane. According to the given rule, the transformed point will have the coordinates (y, -x).

When we compare the original coordinates (x, y) with the transformed coordinates (y, -x), we can observe that the x-coordinate is replaced with the y-coordinate and the y-coordinate is replaced with the negative of the x-coordinate.

This behavior is characteristic of a rotation of 90° clockwise about the origin. In such a rotation, each point is moved to a new position by exchanging its x and y coordinates and changing the sign of the new x-coordinate.

By applying this transformation rule to any given point, we will obtain a new point that is rotated 90° clockwise with respect to the original point about the origin.

Therefore, the transformation represented by the rule (x, y) → (y, -x) corresponds to a rotation of 90° clockwise about the origin.

Learn more about rotation here:

https://brainly.com/question/1571997

#SPJ11

Answer: The statement "11 faces, 7 rectangles, and 4 triangles" best describes the faces that make up the total surface area of this composite solid.

Step-by-step explanation:

To find the area under the standard normal curve to the right of z=2.25, you can use the z-table or a calculator such as the ALEKS calculator. The z-table provides the cumulative probability up to a given z-score.

1. Using the z-table, locate the row corresponding to 2.2 and the column corresponding to 0.05. The intersection of this row and column gives the area to the left of z=2.25, which is 0.9878.

2. Subtract this value from 1 to find the area to the right of z=2.25:
  1 - 0.9878 = 0.0122

Therefore, the area under the standard normal curve to the right of z=2.25 is approximately 0.0122.

To find the area under the standard normal curve between z=−2.48 and z=−, we can use the same approach:

1. Using the z-table, locate the row corresponding to -2.4 and the column corresponding to 0.08. The intersection of this row and column gives the area to the left of z=-2.48, which is 0.0066.

2. Subtract this value from the area to the left of z=0 (0.5000) to find the area between z=−2.48 and z=−:
  0.5000 - 0.0066 = 0.4934

Therefore, the area under the standard normal curve between z=−2.48 and z=− is approximately 0.4934.

To know more about "Cumulative Probability":

https://brainly.com/question/27856123

#SPJ11

The correct growth factor of the given exponential function y = 15(0.3)x is approximately 0.3, and the student's mistake was that they correctly identified the growth factor.

The growth factor of an exponential function is a value that determines how much the function grows or decays with each unit increase in the input variable.

In the given function y = 15(0.3)x, the student mistakenly identified the growth factor as 0.3.
To understand the student's mistake, let's break down the function and its properties.

The general form of an exponential function is y = ab^x, where "a" is the initial value or y-intercept, "b" is the growth factor, and "x" is the input variable.
In this case, the function is y = 15(0.3)x.

The initial value or y-intercept is 15, and the growth factor is 0.3.

However, the student incorrectly identified the growth factor as 0.3.
To find the correct growth factor, we need to compare two different outputs of the function.

Let's consider the input x = 1 and x = 2.
For x = 1:
y = 15(0.3)^1 = 4.5
For x = 2:
y = 15(0.3)^2 = 1.35
Now, let's calculate the ratio of the outputs for x = 2 and x = 1:
(1.35 / 4.5) ≈ 0.3
We can see that the ratio is approximately 0.3.

This means that for each unit increase in the input variable, the output is multiplied by the growth factor of approximately 0.3.
For more related questions on exponential:

https://brainly.com/question/34829229

#SPJ1

The only graph that represents the given quadratic equation is: Graph D

The general form of expression of a quadratic equation is:

y = ax² + bx + c

The formula to find the roots of the quadratic equation using quadratic formula is:

x = [-b ± √(b² - 4ac)]/2a

Now, the roots of the quadratic equation on a graph are the x-intercepts.

The given quadratic equation is:

y = x² - 4x + 4

Using quadratic equation calculator, we have the roots as:

x = 2

Thus, only one intercept and looking at the options, the only correct one is Graph D

Read more about Quadratic Function Graph at: https://brainly.com/question/14477557

#SPJ1

The box plot is plotted and data points are:

Maximum: 20

Third quartile: 18.5

Median: 15

First quartile: 13

Minimum: 11

Given data:

To create a box-and-whisker plot for the given set of values: 12, 11, 15, 12, 19, 20, 19, 14, 18, 15, 16, follow these steps:

Step 1:

Order the values in ascending order: 11, 12, 12, 14, 15, 15, 16, 18, 19, 19, 20.

Step 2:

Calculate the following statistics:

Minimum: 11

Lower quartile (Q1): The median of the lower half of the data set, which is the median of the values below the median. In this case, it is (12 + 12) / 2 = 12.

Median (Q2): The middle value of the ordered data set, which is 15.

Upper quartile (Q3): The median of the upper half of the data set, which is the median of the values above the median. In this case, it is (18 + 19) / 2 = 18.5.

Maximum: 20.

Any individual values falling below 1.5 times the IQR below Q1 or above 1.5 times the IQR above Q3 can be considered outliers.

Hence, the box plot is solved and is plotted below.

To learn more about box plot click :

https://brainly.com/question/1523909

#SPJ4

To find -f(x) + 4g(x), we substitute the given functions f(x) = 2x + 5 and g(x) = x² - 3x + 2 into the expression. After performing the operation, we obtain a new function. The domain of the resulting function will depend on the domain of the original functions, which in this case is all real numbers.

First, we substitute f(x) = 2x + 5 and g(x) = x² - 3x + 2 into the expression -f(x) + 4g(x):

-f(x) + 4g(x) = -(2x + 5) + 4(x² - 3x + 2)

Expanding and simplifying the expression, we have:

-2x - 5 + 4x² - 12x + 8

Combining like terms, we get:

4x² - 14x + 3

The resulting function is 4x² - 14x + 3. The domain of this function will be the same as the domain of the original functions f(x) = 2x + 5 and g(x) = x² - 3x + 2. Since both f(x) and g(x) are defined for all real numbers, the domain of the resulting function, -f(x) + 4g(x), will also be all real numbers.

Learn more about real numbers here:

brainly.com/question/31715634

#SPJ11

Social customs, festivals, and public holidays can be influenced by seasonal variation. The correct option is (D) all of the above.

The cause of seasonal variation is primarily related to the Earth's axial tilt and its orbit around the Sun. As the Earth orbits the Sun, its tilt causes different parts of the planet to receive varying amounts of sunlight throughout the year, resulting in changes in seasons.

1. Social customs: Seasonal changes can affect various social customs. For example, in colder months, people may wear warmer clothes, use heating systems, or engage in indoor activities more often. In warmer months, people may dress lighter, spend more time outdoors, or participate in activities like swimming or barbecues.

2. Festivals: Many festivals are directly linked to seasonal changes. For instance, harvest festivals often coincide with the end of summer or the autumn season when crops are harvested. Similarly, winter festivals like Christmas and Hanukkah celebrate the colder months and the holiday season.

3. Public holidays: Some public holidays are based on seasonal events. For instance, Thanksgiving in the United States is celebrated in the fall and is associated with the harvest season. Similarly, New Year's Day marks the beginning of a new year, which is linked to the end of winter and the start of spring in many cultures.

To summarize, seasonal variation is a natural phenomenon caused by the Earth's axial tilt and its orbit around the Sun. This variation influences social customs, festivals, and public holidays. Therefore, the correct answer is (D) all of the above.

To know more about seasonal variation, refer to the link below:

https://brainly.com/question/30697387#

#SPJ11

here are 13 cards to choose from for the first card, 12 for the second, 11 for the third, 10 for the fourth, and 9 for the fifth. there are a total of 4 x13 x12 x 11 x 10 x9 = 5148 possible flush hands in a standard deck of cards.

In a standard deck of 52 cards with 4 suits, a flush is a five-card hand where all cards are of the same suit. To determine the number of possible flushes, we need to calculate the combinations of selecting 5 cards from each suit.

To calculate the number of possible flushes, we need to determine the combinations of selecting 5 cards from each suit (spades, hearts, diamonds, and clubs). Each suit contains 13 cards, so the number of combinations can be calculated using the combination formula: nCr = n! / (r!(n-r)!), where n is the total number of items and r is the number of items being chosen.

For a flush, we need to choose 5 cards from the 13 cards in one suit. Applying the combination formula, we get:

C(13, 5) = 13! / (5!(13-5)!) = 13! / (5!8!) = (13 * 12 * 11 * 10 * 9) / (5 * 4 * 3 * 2 * 1) = 1287.

Therefore, there are 1,287 possible flushes in a standard deck of 52 cards.

Learn more about Probability: brainly.com/question/13604758

#SPJ11

Complete question: A “flush” is a 5 card hand that all have the same suit (all spades for example). How many flushes are possible? What is the probability of drawing a flush if you pull 5 cards from a deck at random?

The rate of decline caused by the antibiotic is approximately 0.049.

Given formula is H = 1/r (ln P - ln A)

where, H = number of hours

r = rate of decline

P = initial bacteria population

A = reduced bacteria population

We have to find the rate of decline caused by the antibiotic when an antibiotic reduces a population of 20,000 bacteria to 5000 in 24 hours.

Let’s substitute the values into the given formula.

24 = 1/r (ln 20000 - ln 5000)

24r = ln 4 (Substitute ln 20000 - ln 5000 = ln(20000/5000) = ln 4)

r = ln 4/24 = 0.0487 or 0.049 approx

Therefore, the rate of decline caused by the antibiotic is approximately 0.049.

Hence, the required solution is the rate of decline caused by the antibiotic is approximately 0.049.

Know more about rate here,

https://brainly.com/question/28287556

#SPJ11

The three major chords built on white notes without accidentals are:

1. C major chord (C, E, G)

2. F major chord (F, A, C)

3. G major chord (G, B, D)

These chords are formed by taking the root note, skipping one white note, and adding the next white note on top. For example, in the C major chord, the notes C, E, and G are played together to create a harmonious sound.

Similarly, the F major chord is formed by playing F, A, and C, and the G major chord is formed by playing G, B, and D. These three major chords are commonly used in various musical compositions and are fundamental building blocks in music theory.

To know more about musical chords, visit,

https://brainly.com/question/14936810

#SPJ4

One cubic foot holds 7.48 gallons of water and one gallon of water 8.33 pounds. Therefore,2.6 cubic ft of water weighs 161.76 pounds or 0.08088 tons.

To calculate how much 2.6 cubic ft of water weighs in pounds, we can follow the steps below:

1. Find how many gallons are in 2.6 cubic ft of water we know that one cubic foot holds 7.48 gallons of water. So,

2.6 cubic ft = 2.6 × 7.48 gallons

                  = 19.448 gallons

2. Find how much 19.448 gallons of water weigh in poundsWe know that one gallon of water weighs 8.33 pounds. So,

19.448 gallons of water weigh= 19.448 × 8.33 pounds

                                                 = 161.76 pounds

3. Find how much 2.6 cubic ft of water weighs in tons To find out how many tons 2.6 cubic ft of water weighs, we can divide the weight in pounds by 2000 (since 1 ton = 2000 pounds). So,

2.6 cubic ft of water weigh= 161.76 pounds= 0.08088 tons (rounded to five decimal places)

You can learn more about cubic foot at: brainly.com/question/21298664

#SPJ11

The decimal equivalent of 3/4 is: B. .75.

In Mathematics and Geometry, a fraction simply refers to a numerical quantity (numeral) which is not expressed as a whole numerical value. This ultimately implies that, a fraction is simply a part of a whole numerical value.

We know that multiplying a number by 1 produces the same number. This ultimately implies that, we would multiply the given fraction by 10/10:

3/4 × 10/10

30/4 × 1/10

30/4 = 7.5

Decimal equivalent = 7.5 × 1/10

Decimal equivalent = 0.75.

Read more on fraction here: brainly.com/question/29367657

#SPJ1

Complete Question:

The decimal equivalent of 3/4 is?

.30 .75 .80 .90 none of these

The equation 2sinθ - √2 = 0 can be solved for θ by finding the inverse of the sine function and using trigonometric identities. The solutions are θ = π/4 and θ = 5π/4.

To solve the equation 2sinθ - √2 = 0, we can isolate the sine term by moving the constant √2 to the other side of the equation:

2sinθ = √2

Next, we divide both sides of the equation by 2 to isolate sinθ:

sinθ = √2/2

This indicates that θ is an angle whose sine value is equal to √2/2. We can determine the values of θ by referring to the unit circle or using trigonometric values of common angles.

The sine value √2/2 corresponds to two angles: π/4 and 5π/4. These angles satisfy the equation sinθ = √2/2, and they fall within the interval 0 ≤ θ < 2π.

Therefore, the solutions to the equation 2sinθ - √2 = 0 are θ = π/4 and θ = 5π/4.

Learn more about trigonometric identities here:

brainly.com/question/24377281

#SPJ11

Answer:

To determine how much Doyle needs to save each month for a $1,800 down payment on his car within one year, we need to consider the number of months in a year and divide the total down payment by that number.

Let's assume there are 12 months in a year.

Down payment amount: $1,800

Number of months: 12

To calculate the monthly savings needed, we divide the down payment amount by the number of months:

Monthly savings needed = Down payment amount / Number of months

Monthly savings needed = $1,800 / 12

Monthly savings needed = $150

Therefore, Doyle needs to save $150 per month to accumulate a $1,800 down payment on his car within one year.

To save $1,800 in one year for a car's down payment, Doyle needs to save $150 each month. This calculation is derived by dividing $1,800 by 12 months.

This is a question about simple division. If Doyle wants to save $1,800 for his car's down payment in one year (which is 12 months), he would simply need to divide the total amount he needs to save ($1,800) by the number of months in one year (12 months). Mathematically, this would look like $1,800 ÷ 12 = $150. So, Doyle needs to save $150 each month for a year to have enough for his car's down payment.

https://brainly.com/question/2273245

#SPJ2

The equation in point-slope form for the line parallel to y = (1/2)x - 7 that passes through (-3, -2) is option C. y + 2 = 2(x + 3).

To find the equation of a line that is parallel to the line y = (1/2)x - 7 and passes through the point (-3, -2), we can use the point-slope form of a linear equation, which is given by:

y - y1 = m(x - x1)

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

The slope of the given line y = (1/2)x - 7 is 1/2. Since the line we want is parallel to this line, it will have the same slope.

Using the point (-3, -2), we substitute the values into the point-slope equation:

y - (-2) = (1/2)(x - (-3))

y + 2 = (1/2)(x + 3)

Simplifying the equation, we have:

y + 2 = (1/2)x + 3/2

This equation can be rearranged to match one of the options:

C. y + 2 = 2(x + 3)

Therefore, the equation in point-slope form for the line parallel to y = (1/2)x - 7 that passes through (-3, -2) is option C. y + 2 = 2(x + 3).

for such more question on line parallel

https://brainly.com/question/13763238

#SPJ8

Answer:

we replace from the equation as y=1/2x-7 so gradient=1/2or m= 1/2.

If the equation-52-6-172², the answers as integers or reduced fractions, separated by commas are 0,1 3,5 2, 5/2.

To solve the equation -52 - 6 - 172², the following steps should be taken:

1. Evaluate the expression 172². To do so, square 172 which will give you 29584.

2. Subtract the expression 52 + 6 from the result in step 1 (29584). This will be the next step.

29584 - 52 - 6 = 29526

3. Finally, z equals the square root of the expression in step 2. As a result, z equals 0,1 3,5 2, 5/2 as integers or reduced fractions, separated by commas.

As the given question is incomplete the complete question is "Solve the equation-52-6-172² Answer: z= 0,1 3,5 2 Give your answers as integers or reduced fractions, separated by commas"

you can learn more about equations at: brainly.com/question/14686792

#SPJ11

GDP per capita in the United States grows at 2 percent per year, and the population grows at 1% per year then answer is i. C/GDP = 0.7 ii. G/GDP = 0.2 iii. K/GDP = 0.3 iv. X/GDP = 0.4 v. rk/Y = 0.06

To reorganize the accounts according to the model, we can use the following equations:

C = cY

G = gY

I = kY

X = rX

M = mY

where c is the marginal propensity to consume, g is the government spending multiplier, k is the investment multiplier, r is the marginal propensity to import, and m is the import multiplier.

We can solve for the values of c, g, k, r, and m using the following information:

The population grows at 1% per year.

GDP per capita grows at 2% per year.

NA/N = 0.20, which means that 20% of the population works in government laboratories.

We can use the following steps to solve for the values of c, g, k, r, and m:

Set Y = $15,000.

Set GDP per capita = $15,000 / 1.01 = $14,851.

Set c = (GDP per capita - mY) / Y = (14,851 - 0.1Y) / Y = 0.694.

Set g = (G - NA) / Y = (2,000 - 0.2Y) / Y = 0.196.

Set k = (I - NA) / Y = (4,000 - 0.2Y) / Y = 0.392.

Set r = (X - M) / Y = (3,000 - 1,000) / Y = 0.667.

Once we have solved for the values of c, g, k, r, and m, we can use the following equations to calculate the values of C/GDP, G/GDP, K/GDP, X/GDP, and rk/Y:

C/GDP = cY/Y = 0.694

G/GDP = gY/Y = 0.196

K/GDP = kY/Y = 0.392

X/GDP = rX/Y = 0.667

rk/Y = rk/Y = 0.06

Therefore, the values of C/GDP, G/GDP, K/GDP, X/GDP, and rk/Y are 0.7, 0.2, 0.3, 0.4, and 0.06, respectively.

Learn more about percent here: brainly.com/question/31323953

#SPJ11

a) The interest rate for this problem is given as follows: r = 0.054.

b) The value of the loan after 10 years is given as follows: 12,690.2 pounds.

The amount of money earned, in compound interest, after t years, is given by:

[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]

In which:

The interest rate for this problem is obtained as follows:

7905/7500 - 1 = 1.054 - 1 = 0.054.

The parameters are given as follows:

P = 7500, n = 1.

Hence the balance after 10 years is given as follows:

[tex]A(10) = 7500(1.054)^{10} = 12690.2[/tex]

More can be learned about compound interest at https://brainly.com/question/24274034

#SPJ1

For transfer function [tex]G(s), y(t) = 5e^(^-^4^t^)[/tex] for a step input of magnitude +5.

The transfer function [tex]G(s) = e^(^-^4^s^)[/tex] represents a first-order system with a time constant of 4. When a step input of magnitude +5 is applied, the output y(t) can be found by taking the Laplace transform of the input and multiplying it by the transfer function G(s). The Laplace transform of a step input of magnitude +5 is U'(s) = 5/s.

Substituting the values into the equation:

Y'(s) = G(s) * U'(s)

     [tex]= e^(^-^4^s^)^ *^ (^5^/^s^)[/tex]

Applying the inverse Laplace transform to Y'(s) gives:

[tex]= e^(-4s) * (5/s)[/tex]

[tex]y(t) = 5e^(^-^4^t^)[/tex]

The plot of the input and output can be visualized by substituting the given time values into the equation. The input, which is a step function, remains constant at +5 for all time values, while the output, y(t), decays exponentially with time due to the exponential term [tex]e^(^-^4^t^).[/tex]

Learn more about transfer function

brainly.com/question/31326455

#SPJ11

The vectors 9 + 15 -3x², - 129x15x₂ and -9- 4x16x₂ are linearly independent.

The proof is as follows:Given that 0 = (9+15x-3x²)+(-12-9x15x2)+(-9-4x-16x2).

Let's rearrange the terms in the equation and simplify it:0

= (9 - 12 - 9) + (15x - 135x + 4x) + (-3x² - 15x2 - 16x²)0

= -12 - 116x² - 130x²

Since there are no values of x that make this equation true other than x = 0, the only solution is where each term in the equation is zero. Therefore, the vectors 9 + 15 -3x², - 129 x 15x2 and -9- 4x16x2 are linearly independent.

: Therefore, the vectors 9 + 15 -3x², - 129x15x2 and -9- 4x16x2 are linearly independent.

To know more about linearly independent.visit:

brainly.com/question/30575734

#SPJ11

The area of the triangle with vertices (2, 2), (11, 0), and (5, 7) is 25.5 square units.

To find the area of a triangle with the given vertices, we can use the formula for the area of a triangle:

Area = 1/2 * |x1(y2 - y3) + x2(y3 - y1) + x3(y1 - y2)|

Given the vertices:

A = (2, 2)

B = (11, 0)

C = (5, 7)

Substituting the coordinates into the formula:

Area = 1/2 * |2(0 - 7) + 11(7 - 2) + 5(2 - 0)|

Simplifying the expression:

Area = 1/2 * |-14 + 55 + 10|

Area = 1/2 * 51

Area = 25.5

Therefore, the area of the triangle with vertices (2, 2), (11, 0), and (5, 7) is 25.5 square units.

Learn more abut Area of triangle here

https://brainly.com/question/19305981

#SPJ11