A culture initially contains 400 bacteria. If the number of bacteria doubles every 3 hours, how many bacteria will there be at the end of 15 hours?

The general solution is given by: y = c1cos(5x) + c2sin(5x) + 1/25(- cos(ln(sec5x))) + 5xsin(5x)

The most general solution to the original nonhomogeneous differential equation can be found by adding the homogeneous solution and the particular solution together. That is,

y = y_h + y_p

= c1cos(5x) + c2sin(5x) + 1/25(- cos(ln(sec5x))) + 5xsin(5x)

This is the most general solution to the original nonhomogeneous differential equation. We can use the arbitrary constants c1 and c2 to find specific solutions for different initial conditions. The general solution is given by:

y = c1cos(5x) + c2sin(5x) + 1/25(- cos(ln(sec5x))) + 5xsin(5x)

This is the final answer. Note that we have used the terms "general solution" and "arbitrary constants" in our answer, as instructed.

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Answer:

I believe it's C.

Step-by-step explanation:

The correct equation of p is C. p(x) = x(x - 3)^2(2x + 7)^2. This is because the given polynomial has a zero of multiplicity 2 at x = 3, a zero of multiplicity 1 at x = 0, and a zero of multiplicity 2 at x = -7/2. Therefore, the equation of the polynomial can be written as p(x) = k(x - 3)^2(x)(2x + 7)^2, where k is some constant. Since the leading coefficient of the polynomial is 1, k = 1. Thus, we get the equation p(x) = x(x - 3)^2(2x + 7)^2.

It is option C and not A, B, or D because:

Option A, p(x)= x(x - 3)(2x + 7)^2, has only one factor of (x - 3), but the given polynomial has a factor of (x - 3) squared.

Option B, p(x) x^2(x - 3)(2x + 7), has an extra factor of x^2 that is not present in the given polynomial.

Option D, p(x)= x(x - 3)^2(2x + 7), is very close to the correct answer, but it is missing the factor of (x) that is present in the given polynomial.

Thus, the correct equation of p is C, p(x) = x(x - 3)^2(2x + 7)^2, which includes all the necessary factors and satisfies the given conditions.

Hope this helps you! I'm sorry if it doesn't. If you need more help, ask me! :]

Answer: ty

Step-by-step explanation:

Brainliest pls:)

Answer:

7 marbles

Step-by-step explanation:

For every 6 marbles, 2 marbles appear as red.

This pattern would repeat thrice as 6x3 = 18, and then the first 2 marbles (one blue and red) will be counted to make 20 marbles.

So total marbles will be 3x2 in the 18 marble set and 1 in the final 2 marbles.

so 3x2 + 1 = 6+1 = 7

We get 7 marbles as red if we continue in this pattern.

Answer:

Your anser is u = 6

Step-by-step explanation:

[tex]\frac{6}{7} =\frac{8}{u+5}[/tex]

Cross multiply.

[tex]6*(u+5) =7*8\\\\6u+30=56\\\\6u=56-30\\\\6u=36\\\\u=6[/tex]

The family needs 15 cubic feet of sand to fill the mold completely.

The volume of the square pyramid sand castle mold can be calculated as V = (1/3) * b² * h, where b is the length of one edge of the square base and h is the height from the base to the apex.

In this case, b = 3 feet and h = 5 feet.

Plugging these values into the formula, we get:

V = (1/3) * 3² * 5

V = 15 cubic feet

Therefore, the family needs 15 cubic feet of sand to fill the mold completely.

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Cami's trophy rack has a volume of 2904 cubic inches.

In mathematics, volume is the amount of space within a particular 3D object. For example, an aquarium is 3 feet long, 1 foot wide, and 2 feet high. To find volume, multiply length with width and height. This is 3x1x2, or 6. To calculate the volume of Cami's trophy rack, you need to multiply the length, width, and height of the rack. Looking at the drawing provided, you can see that the shelf is 8 inches high, 11 inches wide and 33 inches long.

So the volume of the trophy rack is:

V = 8x11x33

V = 2904 cubic inches

Therefore, the Cami Trophy Rack has a volume of 2904 cubic inches. 

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Complete question is: Cami was building a shelf to put her trophies on. The drawing of her shelf is shown below.

11 inches

33 inches

8 inches

What is the volume of Cami's trophy shelf? (in cubic inches)

The tοtal interest paid οver the full 40 years the Jacksοns have a lοan fοr the hοuse is apprοximately $137,986.85.

Tο sοlve this prοblem, we can use the fοrmula fοr a fixed-rate mοrtgage payment:

[tex]P = (Pv\times r) / (1 - (1 + r)^{(-n))[/tex]

Where:

Pv = present value οf the mοrtgage

r = mοnthly interest rate

n = tοtal number οf payments

a) Mοnthly payment οn the οriginal 5.75% mοrtgage:

Pv = $150,000

r = 5.75% / 12 = 0.004792

n = 30 years × 12 mοnths per year = 360

[tex]P = (150,000 \times 0.004792) / (1 - (1 + 0.004792)^{(-360))[/tex]

P ≈ $875.25

Therefοre, the mοnthly payment οn the οriginal 5.75% mοrtgage was apprοximately $875.25.

b) Remaining balance after 10 years:

Using an οnline amοrtizatiοn calculatοr οr fοrmula, we can find that the remaining balance after 10 years is apprοximately $111,138.77.

c) Interest paid during the first 10 years:

Using the same amοrtizatiοn calculatοr οr fοrmula, we can find that the tοtal interest paid during the first 10 years is apprοximately $54,316.57.

d) Mοnthly payment οn the refinance 4.375% mοrtgage:

Pv = $111,138.77

r = 4.375% / 12 = 0.003646

n = 30 years × 12 mοnths per year = 360

[tex]P = (111,138.77\times 0.003646) / (1 - (1 + 0.003646)^{(-360))[/tex]

P ≈ $554.62

Therefοre, the mοnthly payment οn the refinance 4.375% mοrtgage is apprοximately $554.62.

e) Tοtal interest paid οver the 30 year term οf the refinance:

Using the same amοrtizatiοn calculatοr οr fοrmula, we can find that the tοtal interest paid οver the 30 year term οf the refinance is apprοximately $82,670.28.

f) Tοtal interest paid οver the full 40 years:

Tο find the tοtal interest paid οver the full 40 years, we can add up the interest paid during the first 10 years and the interest paid οver the 30 year term οf the refinance:

Tοtal interest = $54,316.57 + $82,670.28

Tοtal interest = $137,986.85

Therefοre, the tοtal interest paid οver the full 40 years the Jacksοns have a lοan fοr the hοuse is apprοximately $137,986.85.

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Answer:

The answer is 4/17

Step-by-step explanation:

The probability of occurring not more than two flood events in a particular year at that location is approximately 0.546.

The given distribution is λxe-λx! where λ is the expected number of flood events in a year. In order to calculate the probability of not more than two flood events in a particular year at that location.

The expected number of flood events in a year is given by: λ = (5 flood events) / (2 years) = 2.5 flood events per year

The given distribution is:λxe-λx! = 2.5xe-2.5x!

We need to find the probability of occurring not more than two flood events in a particular year at that location.

Therefore, the required probability is:P(x ≤ 2) = P(x = 0) + P(x = 1) + P(x = 2)Here, P(x) represents the probability of x flood events.

The probability of x flood events can be calculated using the Poisson distribution formula:

P(x) = λxe-λx!Substitute λ = 2.5 and x = 0 in the above formula to get:P(0) = (2.5)0e-2.5 / 0! = e-2.5 ≈ 0.082Substitute λ = 2.5 and x = 1 in the above formula to get:P(1) = (2.5)1e-2.5 / 1! = 2.5e-2.5 ≈ 0.206Substitute λ = 2.5 and x = 2 in the above formula to get:P(2) = (2.5)2e-2.5 / 2! = 3.125e-2.5 ≈ 0.258Step 5

Now, add the above probabilities to find the required probability:P(x ≤ 2) = P(0) + P(1) + P(2)≈ 0.082 + 0.206 + 0.258 = 0.546Therefore, the probability of occurring not more than two flood events in a particular year at that location is approximately 0.546.

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The amount of fertilizer needed for the garden is 508600 grams.

In the middle of the garden is a pond that is approximately circular with a diameter of 40 m. Therefore, the fertilizer will not be applied in the pond area.

The villagers will only apply the fertilizer in the garden area. The recommended rate of application of the fertiliser is 25 g/m².

Therefore, let's find the fertilizer required for the garden.

area of the garden to be fertilized = area of trapezium - area of a circle

area of the garden to be fertilized = 1 / 2 (a + b)h - πr²

area of the garden to be fertilized = 1 / 2 (124 + 196)135 - 3.14(20)²

area of the garden to be fertilized = 1 / 2 (320)(135) - 1256

area of the garden to be fertilized = 43200 / 2 - 1256

area of the garden to be fertilized = 21600 - 1256

area of the garden to be fertilized = 20344 m²

Therefore,

1 m² = 25 grams

20344 m² = ?

Hence,

amount of fertiliser needed  = 20344 × 25 = 508600 grams

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The probability of at most one accident in the next 2 hours is 82.15%.

Let X be the number of car accidents in the next 2 hours, and Y be the number of motorcycle accidents in the next 2 hours. Both X and Y follow Poisson distributions, with rates of λX = 0.12 = 0.2 and λY = 0.052 = 0.1, respectively.

To find the probability that there will be at most one accident (either car or motorcycle) in the next 2 hours, we need to find the probability of the events {X + Y = 0} and {X + Y = 1}:

P(X + Y ≤ 1) = P(X + Y = 0) + P(X + Y = 1)

To find these probabilities, we can use the joint Poisson distribution of X and Y:

P(X = i, Y = j) = e^-(λX+λY) * (λXᵃ /a!) * (λYᵇ / b!)

where a and b are non-negative integers.

For X + Y = 0, we have:

P(X + Y = 0) = P(X = 0, Y = 0) = e⁻⁽⁰ ²⁺⁰ ¹⁾  * (0.2⁰ / 0!) * (0.1⁰ / 0!) = e⁻⁰ ³ ≈ 0.7412

For X + Y = 1, we have:

P(X + Y = 1) = P(X = 0, Y = 1) + P(X = 1, Y = 0) = e⁻⁽⁰ ²⁺⁰ ¹⁾ * (0.2⁰/ 0!) * (0.1¹/ 1!) + e⁻⁽⁰ ²⁺⁰ ¹⁾  * (0.2¹/ 1!) * (0.1⁰ / 0!) = 20.20.1*e⁻ ⁰ ³ ≈ 0.0803

Therefore, the probability of there being at most one accident (either car or motorcycle) in the next 2 hours is:

P(X + Y ≤ 1) ≈ 0.7412 + 0.0803 ≈ 0.8215

So the probability of there being at most one accident in the next 2 hours is about 82.15%.

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0.67032

The given data is that car accidents and motorcycle accidents on a stretch of road occur independently and are described by the Poisson distribution at a rate of 0.1 and 0.05 per hour respectively. It is required to find the probability that there will be at most one accident in the next 2 hours.The number of car accidents along the stretch of the road in the next 2 hours is a Poisson distribution with a mean of 0.1 x 2 = 0.2. Similarly, the number of motorcycle accidents in the next 2 hours is a Poisson distribution with a mean of 0.05 x 2 = 0.1.The probability that there will be at most one accident in the next 2 hours is:P(at most one accident in the next 2 hours)=P(no accident in the next 2 hours)+P(one accident in the next 2 hours)= e^(-0.2) (0.2)^0 / 0! + e^(-0.2) (0.2)^1 / 1! + e^(-0.1) (0.1)^0 / 0! + e^(-0.1) (0.1)^1 / 1!= 0.67032Therefore, the probability that there will be at most one accident in the next 2 hours is 0.67032.

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Answer:

Step-by-step explanation:

D.The value of B is equal to -1

The hight above the first floor to second floor is 15 ft , for this we have Trigonometry angles.

Angles determined by the ratios of the trigonometric functions are known as trigonometric angles.

The trigonometric functions in mathematics are real functions that connect the right-angled triangle's angle to the ratios of its two side lengths.

Given h = 60 ft, we have to find p

Sin 15° = p/h

0.25 = p/60

p = 15 ft

So, the hight above the first floor to second floor is 15 ft.

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The value of the test statistic is -1.75.

To test the claim that the percentage of uninsured patients is under the expected percentage of 32%, we can use a one-sample z-test. The null hypothesis is that the true percentage of uninsured patients is equal to 32%, while the alternative hypothesis is that the true percentage is less than 32%.

Using the sample data, we can calculate the sample proportion of uninsured patients as 40/160 = 0.25. We can then calculate the standard error of the sample proportion as sqrt[(0.32 x 0.68)/160] = 0.0385.

The test statistic can be calculated as (0.25 - 0.32)/0.0385 = -1.75.

To find the p-value associated with this test statistic, we can use a standard normal distribution table or a calculator to find the probability of a z-score less than -1.75. The p-value is approximately 0.04.

Since the p-value is less than the typical significance level of 0.05, we reject the null hypothesis and conclude that there is evidence to support the claim that the percentage of uninsured patients is under the expected percentage of 32%.

Therefore, the correct answer is -1.75, which is the calculated value of the test statistic.

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Answer:

Answer  = 21 Sacks

Step-by-step explanation:

First, we need to calculate how much flour the baker will use in 20 days:

Amount of flour used per day for 64 loaves = 64 loaves/day x 400 g/loaf = 25,600 g/day

Amount of flour used in 20 days = 25,600 g/day x 20 days = 512,000 g

Next, we need to convert the amount of flour used into kilograms:

512,000 g ÷ 1000 g/kg = 512 kg

Finally, we need to calculate the minimum number of 25 kg sacks the baker should order:

Number of 25 kg sacks = 512 kg ÷ 25 kg/sack ≈ 20.48

Since the baker cannot order a fraction of a sack, he will need to order at least 21 sacks to last him for 20 days.

Answer:

[tex]\frac{660}{4} = 165[/tex]  [tex]km/h[/tex]

The charged battery costs 16 dollars, which is denoted as -16. (negative number). The cost for  the savings for using a battery that can be recharged is +14(positive number).

A battery is an electrical energy storage instrument made up of one or more electrochemical cells connected to the outside world. The cathode and anode of a battery are the positive and negative terminals, respectively, when the battery is supplying electricity.                            The battery costs 16 dollars. You save 14 dollars each time you recharge the battery.  The cost of the rechargeable battery as a negative number is -16.The savings for using a battery that can be recharged is +14

The charged battery costs 16 dollars, which is denoted as -16. (negative number). Each refresh saves 14 dollars, which is symbolised as +14. (positive number). The charged battery costs 16 dollars, which is denoted as -16. (negative number). The cost for  the savings for using a battery that can be recharged is +14(positive number).

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Answer:

k=11/3

Step-by-step explanation:

Use distributive property.

3k+4=15

Subtract 4 from both sides.

3k=11

Divide 3 from both sides.

k=11/3

Answer: k=11/3 or 3.66

Step-by-step explanation:

3k+4=15 --Distribute 1/3 to 9k and 12.

3k=11 --Subtract 4 from both sides.

k=11/3 or 3.66

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Answer:

4.06 cm^2

Step-by-step explanation:

If you draw a line from the top vertex to intersect the base (which is 5.8 cm) at 90 degrees, the line is called the height. You need to calculate the height to determine the area.

So the triangle's height will divide the triangles into 2 smaller right triangles.

For the left right triangle, 2.5 will be hypotenuse

=> 2.5^2 = (height)^2 + (base1)^2

=> (height)^2 = 6.25 - (base1)^2

For the right right triangle, 4 will be hypotenuse

=> 4^2 = (height)^2 + (base2)^2

=> (height)^2 = 16 - (base2)^2

So

6.25 - (base1)^2 = 16 - (base2)^2

We have base1 + base2 = 5.8 => base1 = 5.8 - base2

Substitute

6.25 - (5.8 - base2)^2 = 16 - (base2)^2

6.25 - (33.64 - 11.6base2 + base2^2 = 16 - base2^2

base2^2 - base2^2 + 11.6base2 = 16 + 33.6 - 6.25

11.6base2 = 43.35

base2 = 43.35/11.6 = 3.74

since (height)^2 = 16 - (base2)^2

(height)^2 = 16 - (3.74)^2

height^2 = 2.0124

height = 1.42

so area = 1/2hb = 1/2(1.4)(5.8) = 4.06 cm^2

Answer:

735.1 square meters

Step-by-step explanation:

total surface area (TSA) of a cone can be calculated by using this mathematical expression:

Total surface area (TSA) of a cone = πr(l + r)

Total surface area (TSA) of a cone = πr(l + r)

Total surface area (TSA) of a cone = 3.142 × 6 × (33 + 6)

Total surface area (TSA) of a cone = 3.142 × 6 × (39)

Total surface area (TSA) of a cone = 735.1 square meters.

The sοlutiοn(s) οn the graph are x = -4, 2.

In mathematics, a graph is a diagram οr visual representatiοn οf facts οr values that is οrdered. The pοints οn a graph are typically used tο depict the relatiοnships between twο οr mοre things. Graph theοry is the study οf graphs, which are mathematical structures that are used tο depict pairwise interactiοns between οbjects. A graph in this sense is made up οf vertices and edges.

A graph is an οrdered graphic οr visual representatiοn οf facts οr values in mathematics. The relatiοnships between twο οr mοre οbjects are οften shοwn by the pοints οn a graph.

The study οf graphs, which are mathematical representatiοns οf pairwise interactiοns between things, is knοwn as graph theοry. Vertices and edges make up a graph in this cοntext.

From the given graph we conclude following -

[tex]\frac{1}{4}x^2 = -\frac{1}{2}x + 2\\x^2 + 2x - 8 = 0\\x^2 + 4x - 2x - 8 = 0\\x(x + 4) - 2(x + 4) = 0\\(x + 4)(x - 2) = 0\\x = 2, -4[/tex]

On the graph, the solutiοns are the x-coοrdinates of the points of intersection

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Answer:

a) The circumference of the cylinder can be found using the formula C = 2πr, where r is the radius of the circular base. Rearranging the formula, we get r = C/2π. To find the circumference, we can use the formula for the curved surface area: A = 2πrh, where h is the height of the cylinder. Substituting the given values, we get:

660 = 2πr(10)

r = 33/π

Now we can find the circumference:

C = 2πr = 2π(33/π) = 66

Therefore, the circumference of the cylinder is 66 cm.

b) The radius of the cylinder is given by r = 33/π, which we already found in part a).

c) The area of one circular base can be found using the formula A = πr^2. Substituting the value of r from part b), we get:

A = π(33/π)^2 = 1089/π

Therefore, the area of one circular base is 1089/π cm^2.

d) The surface area of the cylinder consists of the curved surface area and two circular bases. The area of one circular base was found in part c), so we just need to add the curved surface area to twice the area of one circular base:

Surface area = 2A + 2πrh

Substituting the given values, we get:

Surface area = 2(1089/π) + 2π(33/π)(10) = 2187/π + 660

Therefore, the surface area of the cylinder is 2187/π + 660 cm^2.

Step-by-step explanation:

Answer:

C. (6r + 5)

Step-by-step explanation:

You would multiply (3r - 7) with (6r + 5) to get the value.

The Sun is approximately 9.2661 x 10^7 miles farther than the Moon from Earth.

The distance between the Sun and the Earth is approximately 9.29 x 10^7 miles, and the distance between the Moon and the Earth is approximately 2.389 x 10^5 miles.

To find how much farther the Sun is from the Earth than the Moon, we can subtract the distance between the Moon and the Earth from the distance between the Sun and the Earth:

9.29 x 10^7 miles - 2.389 x 10^5 miles = 9.2661 x 10^7 miles

Therefore, the Sun is approximately 9.2661 x 10^7 miles farther than the Moon from Earth.

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Answer:

a)

=2×5+2×6

=10+12

=22

Ans. GCF (10, 12) = 2

Answer:

0.85 m

Step-by-step explanation:

Model dimension : Real dimension

3 : 74

x : 21

[tex] \frac{21}{74} = \frac{x}{3} \\ x = 3 \times \frac{21}{74} \\ = \frac{63}{74} \\ = 0.851...[/tex]

Answer:

85.54 cm

Step-by-step explanation:

To find the height of the scale model, we need to use the scale ratio given: 3 : 74. This means that every 3 units on the model represent 74 units on the real building.

First, we need to determine the ratio of the heights. Let x be the height of the scale model. Then:

3 / 74 = x / 21

Solving for x, we get:

x = 21 * 3 / 74

x = 0.8554 m

To convert this to centimeters, we multiply by 100:

x = 85.54 cm

Therefore, the height of the scale model is 85.54 cm to 2 decimal places.

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Answer:

he pays 24,00 and he is left with 56000

Step-by-step explanation:

100% = 80000

30%  = X

100%X= 2400000

2400000/100= 24,000

80,000-24,000= 56,000

Answer:

the amount will give 69 percentage of nothing thanks