Evaluate the expression

z + 3x4
A. 27

B. 32

C. 56

D. 1,304

Solution is y(t) = ((c1e2t − c2e2t) (1 0) + (c1e8t + c2e8t) (0 1))

The differential equations of the given system are: y1′=5y1+3y2y2′=3y1+5y2 The solutions to these equations are:y1(t)=c1e2t+c2e8t y2(t)=−c1e2t+c2e8tNow,

let's rewrite the solution in the vector form y(t) = c1y1 vector(t) + c2y2 vector(t).The vector form of y1(t) and y2(t) is as follows: y1 vector(t) = (1 0) (c1e2t) + (0 1) (c2e8t)y2 vector(t) = (-1 0) (c1e2t) + (0 1) (c2e8t)

Therefore, the solution in the vector form y(t) = c1y1 vector(t) + c2y2 vector(t) is as follows: y(t) = c1((1 0) (c1e2t) + (0 1) (c2e8t)) + c2((-1 0) (c1e2t) + (0 1) (c2e8t))y(t) = (c1e2t − c2e2t) (1 0) + (c1e8t + c2e8t) (0 1)y(t) = ((c1e2t − c2e2t) (1 0) + (c1e8t + c2e8t) (0 1))

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Answer:

Step-by-step explanation:

To factor 25x^6 + 10x^3 + 12, we can first factor out the greatest common factor of the three terms which is 1, then use a substitution:

Let's substitute y = x^3. Then, the expression becomes:

25y^2 + 10y + 12

We can now try to factor this quadratic expression. However, since the discriminant (b^2 - 4ac) of this quadratic equation is negative (10^2 - 4*25*12 = -440), this expression cannot be factored using real numbers.

Therefore, the final answer for the factoring is:

25x^6 + 10x^3 + 12 = (unfactorable)

Answer:

Step-by-step explanation:

Therefore, the difference in the price of 300 cm of ribbon between shop A and shop B is £1.20.

In mathematics, an equation is a statement that two expressions are equal. It usually contains one or more variables, which are typically represented by letters, and may contain constants and mathematical operations such as addition, subtraction, multiplication, division, exponents, and roots. An equation can be true or false depending on the values of the variables. Solving an equation means finding the values of the variables that make the equation true.

Here,

To find the difference in price between the two shops, we need to first calculate the cost per centimeter of ribbon for each shop:

Shop A: £1.68 / 140 cm = £0.012 per cm

Shop B: £1.72 / 215 cm = £0.008 per cm

Now, we can calculate the cost of 300 cm of ribbon at each shop:

Shop A: 300 cm x £0.012 per cm = £3.60

Shop B: 300 cm x £0.008 per cm = £2.40

The difference in price between the two shops for 300 cm of ribbon is:

£3.60 - £2.40 = £1.20

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Answer: 1 hour and 20 minutes

Step-by-step explanation:

We can use the formula:

time = distance / speed

Let's call the distance of the journey "d".

When the train is travelling at 40 km/h, it takes 3 hours to complete the journey. So we have:

3 = d / 40

Solving for "d", we get:

d = 3 x 40 = 120 km

Now we want to know how long it will take for the train to complete the same journey at 90 km/h. We can use the formula again:

time = distance / speed

Plugging in the values we know:

time = 120 / 90

Simplifying, we get:

time = 4/3 hours or 1 hour and 20 minutes

Therefore, the train will take 1 hour and 20 minutes to complete the journey at 90 km/h.

Required answer :-

Step-by-step explanation:

A train travelling at 40km/h takes 3 hours for a journey. So, Speed will be 40 km/hr

Time will be 3 hours.

Speed = Distance/time

Distance = Speed × time

Distance = 40 × 3

Distance = 120 km.

Now, we have to find that how long will it take the train to complete the same journey, travelling at 90km/h.

Now, Speed will be 90 km/hr

Distance = Speed × time

Time = Distance/speed

Time = 120/90

Time = 4/3 hours

1 hour = 60 minutes

4/3 × 60

4 × 20

80 minutes

1 hour 20 minutes.

Therefore, The train will take 1 hour 20 minutes to complete the journey, travelling at 90km/h.

James bought a total of 7 yards of ribbon for his craft project.

To begin with, let's first convert the length of the ribbon from feet to yards. There are 3 feet in a yard. So, to convert 2.1 feet to yards, we need to divide it by 3.

2.1 feet ÷ 3 = 0.7 yards

So, each piece of ribbon is 0.7 yards long.

Now, let's calculate the total length of ribbon James bought by multiplying the length of each piece of ribbon by the total number of ribbons he bought.

Total yards of ribbon = length of one ribbon × number of ribbons

Total yards of ribbon = 0.7 yards × 10

Total yards of ribbon = 7 yards

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Complete Question:

For his craft project, James bought 10 pieces of ribbon that were each 2.1 feet long. How many total yards of ribbon did James buy?

The value of the integral in cylindrical coordinates is -81π/2.

We have the following integral

∫ from 3 to -3 ∫ from 0 to √(9-x^2) ∫ from 20 to 11+x^2+y^2 dz dy dx

Converting to cylindrical coordinates, we have:

x = r cos(theta)

y = r sin(theta)

z = z

Also, from the equation of the cone, we know that r^2 = x^2 + y^2 = 9. Thus, we have

r = 3

Substituting these values, we get

∫ from 0 to 2π ∫ from 0 to 3 ∫ from 20 to 11+r^2 dz r dr dtheta

Evaluating the z integral, we get:

∫ from 0 to 2π ∫ from 0 to 3 (11+r^2-20) r dr dtheta

= ∫ from 0 to 2π ∫ from 0 to 3 (r^3-9r) dr dtheta

= ∫ from 0 to 2π [ (1/4) r^4 - (9/2) r^2 ] |_0^3 dtheta

= ∫ from 0 to 2π (81/4 - 81/2) dtheta

= -81π/2

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The percentage of 27 miles in 23 miles is 117.39%.

Percentage is a way of expressing a fraction or a portion of a whole number in relation to 100. It is denoted by the symbol "%". A percentage is calculated by dividing the part (numerator) by the whole (denominator) and multiplying the result by 100. A percentage can also be used to represent a rate or a percentage change over time.

In this case, we are asked to find what percentage of 23 miles is 27 miles. The part is 27 miles and the whole is 23 miles. Therefore, the percentage is:

% = part/whole = 27/23 x 100 = 117.39%

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Let's use variables to represent the number of $1000 and $500 bills used.

Let x be the number of $1000 bills used.

Then 16 - x is the number of $500 bills used.

The total amount paid is the sum of the values of the bills used:

$1000(x) + $500(16 - x) = $3200

Simplifying and solving for x:

$1000x + $8000 - $500x = $3200

$500x = $4800

x = 9.6

We can't have a fraction of a bill, so we'll round down to 9 $1000 bills.

Then the number of $500 bills used is:

16 - x = 16 - 9 = 7

Therefore, 9 $1000 bills and 7 $500 bills were used to pay the $3200 restaurant bill.

The cost of petrol for the trip to UWC is R1.2384.

In general, cost refers to the amount of resources (usually money) that must be expended to produce or acquire something. It can be thought of as the value of the resources that are given up in order to obtain something else.

To calculate the cost of petrol for the trip to UWC, we need to know the distance traveled and the amount of fuel consumed.

Let's assume that the distance from Andrew's home to UWC is 20 kilometers (km). Then, the amount of fuel consumed for the trip is:

[tex]Fuel consumed = (0.0052 k/100 km) * 20 km = 0.00104 k[/tex]

where k stands for liters of petrol.

To convert the amount of fuel consumed to liters, we need to multiply by 100, since the fuel consumption rate is given in liters per 100 km:

[tex]Fuel consumed = 0.00104 k * 100 = 0.104 liters\\Fuel consumed = 0.00104 k * 100 = 0.104 liters[/tex]

Now we can calculate the cost of petrol for the trip:

[tex]Cost of petrol = (0.104 liters) * (R11.90/liter) = R1.2384[/tex]

Therefore, the cost of petrol for the trip to UWC is R1.2384.

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Answer:

  x = y = z = (√6)/3 cm ≈ 0.8165 cm

Step-by-step explanation:

You want the dimensions of the cuboid with the largest volume and a total surface area of 4 cm².

For a fixed surface area, the figure with the largest volume is a regular figure. In this case, it is a regular cuboid, or cube.

The total surface area of a cube with edge length s is ...

  A = 6s²

Then the edge length of the desired cube is found from ...

  4 = 6s²

  s² = 2/3 = 6/9 . . . . . . divide by 6; write with square denominator

  s = √(6/9) = (√6)/3

The dimensions of the box are ...

  x = y = z = (√6)/3 cm ≈ 0.8165 cm

The null hypothesis is rejected whenever "there is a low probability that the obtained results could be due to random error." The correct answer is Option B.

The null hypothesis is a statistical hypothesis used to test the difference between two sample data groups. The null hypothesis is the hypothesis that the sample statistics are not significantly different. Any significant differences between the sample data are seen as supporting the alternative hypothesis.

A null hypothesis is often expressed as "no difference," "no correlation," or "no significant effect." For example, the null hypothesis for an experiment comparing two groups of people could be "there is no difference between the two groups." When the null hypothesis is rejected, it means that the results of the experiment are statistically significant, and the alternative hypothesis is supported.

Therefore, the null hypothesis is rejected whenever there is a low probability that the obtained results could be due to random error.

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The signof function is defined as follows:

def signof(num):
   if num > 0:
       return 1
   elif num == 0:
       return 0
   else:
       return -1

In the above code snippet, we have defined a function named signof which receives an integer argument named num. The if condition checks if the num is greater than 0, if yes, the function will return 1 as it is positive. Else if the num is equal to 0, then it will return 0, as per the requirement. Otherwise, it will return -1 as the number is negative. This code snippet will give the required output as per the requirement of the problem statement.

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Answer:

Step-by-step explanation:

150

The three consecutive entries in Pascal's Triangle that are in the ratio 3:4:5 occur in the 14th row.

The ratio 3:4:5 can be expressed as 3x, 4x, and 5x, where x is a constant. Using this ratio, we can find the values of the entries in the 14th row of Pascal's Triangle.

Starting from the left, the entries in the 14th row are 1, 13, 78, 286, 715, 1287, 1716, 1716, 1287, 715, 286, 78, 13, and 1.

We can see that the ratio of the 5th, 6th, and 7th entries (715, 1287, and 1716) is 3:4:5. Therefore, the answer is the 14th row.

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[tex]0.000000778\implies \stackrel{ \textit{rounded up} }{0.000000800} ~\hfill 0.00000000155\implies \stackrel{ \textit{rounded up} }{0.00000000200} \\\\[-0.35em] ~\dotfill\\\\ 0.\underset{ 6~zeros }{\underline{000000}}800\implies 8.00\times 10^{-6}\implies \boxed{8\times 10^{-6}} \\\\\\ \underset{ 8~zeros }{0.\underline{00000000}200}\implies 2.00\times 10^{-8}\implies \boxed{2\times 10^{-8}} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\cfrac{\stackrel{ \textit{dust particle} }{8\times 10^{-6}}}{\underset{ \textit{grain of pollen} }{2\times 10^{-8}}}\implies \cfrac{8}{2}\times\cfrac{10^{-6}}{10^{-8}}\implies 4\times10^{-6}10^{8}\implies 4\times 10^2\implies \boxed{400}[/tex]

The linear function that models the data is y=3/5x - 2/5 which has the form y=mx+b, where m is the slope and b is the y-intercept.

This can be written in the form y = mx + b where m and b are constants and x is a variable. The graph of a linear function is a straight line that goes through the origin.

To calculate the linear function, we must first calculate the slope. The slope is the numerical change in y (rise) divided by the numerical change in x (run).

Subtracting the y-values for x=-9 and x=-8, we get

-29/5 - (-26/5) = -3/5.

Similarly, subtracting the x-values for x=-9 and x=-8, we get

-9 - (-8) = -1.

Now, -3/5 / -1, we get the slope, m, of 3/5.

Next, we must calculate the y-intercept, b.

To do this, we can use either of the points given.

Using the points (x=-9, y=-29/5), we can substitute the x and y values into the linear equation, y=mx+b.

-29/5 = 3/5(-9) + b, which can be simplified to

-29/5 = -27/5 + b.

Adding 27/5 to both sides, we get b = -2/5.

Therefore, the linear function that models the data is y=3/5x - 2/5.

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Answer:

D

Step-by-step explanation:

First, yes, it is a function. Functions are defined as having one output per input, and given a number on this graph, we can find only one output.

Domain is the range of x-values in a graph. The domain here is from [tex]-\pi[/tex] to [tex]\pi[/tex].

Range is the range of y-values in a graph. The range here is from -1 to 1.

This graph has three intercepts at [tex](-\pi ,0)(0,0)(\pi ,0)[/tex].

Symmetry: This graph has rotational symmetry, meaning it can be rotated about a point to map onto itself. Here, we can rotate it 180 degrees about the origin to map onto itself.

Although I can't see the final two points for answer D, answer A is similar but the symmetry portion is wrong, leading me to believe that it must be D.

Let me know if this helped by hitting thanks or brainliest! If not, comment below and I'll get back to you ASAP.

Answer:

yes

Step-by-step explanation:

Answer:

140 sandwiches

Step-by-step explanation:

56/4=14 which is 10% of the sandwiches sold

14*10=140

Answer:

140 sandwiches.

Step-by-step explanation:

We know

56 tuna sandwiches were sold. This was 40% of the total number of sandwiches sold.

Work out the total number of sandwiches sold.

We Take

56 divided by 40, then time 100 = 140 Sandwiches

So, the total number of sandwiches sold is 140 sandwiches.

Answer:

Show that, the sum of an infinite arithmetic progressive sequence with a positive common difference

is +∞

Step-by-step explanation:

To show that the sum of an infinite arithmetic progressive sequence with a positive common difference is +∞, we can use the formula for the sum of the first n terms of an arithmetic sequence:

Sn = n/2 [2a + (n-1)d]

where a is the first term, d is the common difference, and n is the number of terms in the sequence.

Now, if we let n approach infinity, the sum of the first n terms of the sequence will also approach infinity. This can be seen by looking at the term (n-1)d in the formula, which grows without bound as n becomes larger and larger.

In other words, as we add more and more terms to the sequence, each term gets larger by a fixed amount (the common difference d), and so the sum of the sequence increases without bound. Therefore, the sum of an infinite arithmetic progressive sequence with a positive common difference is +∞.

We have that, using Euclid's algorithm, we find the inverse of 200 modules 1001 is -5 (or 1001+5).

To find the inverse of a module m using Euclid's algorithm, the steps are as follows:

1. Calculate the greatest common divisor (GCD) of a and m using the Euclidean algorithm.

2. Let a = GCD * s + m*t, where s is the inverse of a module m.

3. The GCD in terms of a and my is written as 1 = m-s*a.

4. Find s = -a, so the inverse of a module m is -a (or m+s).

For example, a = 2, m=17, so GCD = 1 = 17-8*2 and the inverse of 2 modulo 17 is -8 (or 17+8). Similarly, for a = 34, m= 89, the GCD = 1 = 89-34*2 and the inverse of 34 modulo 89 is -34 (or 89+34). Finally, for a = 200, m= 1001, the GCD = 1 = 1001-5*200 and the inverse of 200 modulo 1001 is -5 (or 1001+5).

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Based on the passage data, the most accurate statement describing the relationship between cultured yeast preparation conditions and fermented alcohol yield is: "Neither glucose concentration nor percentage yeast inoculate was positively correlated with fermented alcohol yield."

What this means is that increasing the concentration of glucose or percentage of yeast inoculate did not lead to more production of alcohol. The data in Table 1 shows that the maximum fermented alcohol yield was obtained in Broth A, which had 10% glucose and 8% yeast inoculation. Broth C, which had a higher concentration of glucose at 12%, did not result in a higher yield of alcohol. Similarly, Broth B, which had a higher percentage of yeast inoculate at 10%, did not lead to a higher yield of alcohol.

Therefore, it can be concluded that neither glucose concentration nor percentage of yeast inoculates was positively correlated with fermented alcohol yield.

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The probability that the jury makes the correct decision is approximately 0.7063.

To solve this problem, we need to find the probability that the jury makes the correct decision if the defendant is guilty. Let's break down the problem into smaller steps.

We know that the probability of a single juror making the correct decision is 0.80. If the defendant is guilty, then the probability of a juror making the correct decision is still 0.80. Therefore, the probability that a single juror makes the correct decision if the defendant is guilty is 0.80.

We can use the binomial distribution formula to determine the probability of at least 10 out of 12 jurors making the correct decision. The formula is:

P(X ≥ k) = 1 - Σ(i=0 to k-1) [n!/(i!(n-i)!) x [tex]p^i \times (1-p)^{(n-i)}[/tex] ]

where:

P(X ≥ k) is the probability of at least k successes

n is the total number of trials (in this case, 12 jurors)

p is the probability of success in a single trial (in this case, 0.80)

k is the number of successes we want to find the probability of (in this case, 10)

Plugging in the values, we get:

P(X ≥ 10) = 1 - Σ(i=0 to 9) [12!/(i!(12-i)!) x [tex]0.80^i \times (1-0.80)^{(12-i)}[/tex]]

Using a calculator or software, we can calculate this to be approximately 0.7063.

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Answer:

If the tires on Mavis’ car have to be replaced when they each have 160 000 km of wear, then the total distance Mavis can drive on a set of tires is:

4 tires * 160,000 km = 640,000 km

If Mavis drives 25,000 km in a year, she will need to replace her tires after:

640,000 km ÷ 25,000 km/year = 25.6 years

Since Mavis will need to replace her tires once every 25.6 years, the cost of the wear on her tires for a single year is:

$140.00/tire * 4 tires = $560.00

So the total cost of the wear on Mavis’ tires for a year in which she drives 25,000 km is $560.00.

Step-by-step explanation:

source: trust me bro

The probability of selecting another black marble is 3/7. As a result, the probability of drawing two black marbles in a row without replacement

(a) P(two red marbles) with replacement:The probability of drawing a red marble from a jar with five red marbles and four black marbles is 5/9, as there are five red marbles and nine total marbles. As a result, the probability of selecting two red marbles in a row with replacement is:P(two red marbles with replacement) = (5/9) × (5/9) = 25/81without replacement:When the first marble is removed, there are now only eight marbles remaining in the jar. Because there are only four black marbles in the jar, the probability of drawing a red marble is now 5/8. Therefore, the probability of selecting two red marbles in a row without replacement is:P(two red marbles without replacement) = (5/9) × (5/8) = 25/72(b) P(two black marbles)with replacement:For the first draw, there are four black marbles in the jar and a total of nine marbles. Therefore, the probability of drawing a black marble on the first draw is 4/9. Since the first marble was not removed, there are now eight marbles in the jar, including three black ones, and there are a total of nine marbles. Therefore, the probability of selecting another black marble is 3/9 or 1/3.

The probability of drawing two black marbles in a row with replacement is:P(two black marbles with replacement) = (4/9) × (1/3) = 4/27without replacement:Since the first marble was removed, there are only eight marbles in the jar, and there are four black ones. Therefore, the probability of selecting a black marble is 4/8 or 1/2. When the first black marble is removed, there are only seven marbles left, including three black ones. Therefore, the probability of selecting another black marble is 3/7. As a result, the probability of drawing two black marbles in a row without replacement is:P(two black marbles without replacement) = (4/9) × (3/7) = 12/63(c) P(one red and one black marble)with replacement:When one red and one black marble are selected with replacement, there are nine marbles in the jar for each draw. The probability of selecting one red and one black marble in a row is:P(one red and one black marble with replacement) = 2 × (5/9) × (4/9) = 40/81without replacement:Since there are five red and four black marbles in the jar, the probability of selecting a red marble first is 5/9. Once the red marble has been drawn and removed, there are only eight marbles remaining, including four black ones. As a result, the probability of selecting a black marble is 4/8 or 1/2.

As a result, the probability of drawing one red and one black marble without replacement is:P(one red and one black marble without replacement) = (5/9) × (4/8) + (4/9) × (5/8) = 20/36 + 20/36 = 10/18 = 5/9(d) P(red on the first draw and black on the second draw)with replacement:There are nine marbles in the jar for each draw. The probability of selecting a red marble first is 5/9. When the red marble is returned to the jar, there are still nine marbles in the jar, but now there are only four black marbles. The probability of selecting a black marble on the second draw is 4/9. As a result, the probability of drawing a red marble first and a black marble second with replacement is:P(red on the first draw and black on the second draw with replacement) = (5/9) × (4/9) = 20/81without replacement:Since there are five red and four black marbles in the jar, the probability of selecting a red marble first is 5/9. Once the red marble has been drawn and removed, there are only eight marbles remaining, including four black ones. As a result, the probability of selecting a black marble is 4/8 or 1/2. As a result, the probability of drawing a red marble first and a black marble second without replacement is:P(red on the first draw and black on the second draw without replacement) = (5/9) × (4/8) = 5/18

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Answer:

(b+1)(5a+3)

Step-by-step explanation:

Notice how (b+1) appears on both sides. That means we can "factor it out" by moving it to the very left -

(b+1)

Now we know the form of the answer we can continue doing it.

For the next step, I take the terms 5a and 3 (what's left) and move them to the right as shown:

(b+1)(5a+3)

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Best regards

The area of the polygon is 80 units².

What is a Polygon?

A polygon is a plane figure made up of line segments connected to form a closed polygonal chain. The segments of a closed polygonal chain are called its edges or sides.

Dividing the polygon into parts marked in the attached figure so as to calculate the area easily.

For triangle, DEF

Area = [tex]\frac{1}{2} bh[/tex]

        = [tex]\frac{1}{2}[/tex] × 3 × 4

       = 6 units²

For triangle BCD

Area = [tex]\frac{1}{2}bh[/tex]

        = [tex]\frac{1}{2}[/tex] × 2 × 4

        = 4 units²

For trapezoid ABFG,

Area = [tex]\frac{1}{2} (a + b) h[/tex]

        = [tex]\frac{1}{2}[/tex] × (5.5 + 12) × 8

        = 70 units²

Hence, total area = 6 + 4 + 70

                             = 80 units².

Therefore, the total area of the polygon is 80 units².

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