Convert 0.2194 to a fraction.
Give your answer in its simplest form.​

Answer:

After Multiplying them.

we get 0 as an answer.

The exponential model that calculates the concentration of bacteria after x weeks can be represented by the equation B(x) = 2.1 million * (3^x), the concentration after 1.6 weeks would be approximately 14.87 million bacteria per milliliter.

This equation assumes that the concentration triples each week, starting from the initial concentration of 2.1 million bacteria per milliliter.

To estimate the concentration after 1.6 weeks, we can substitute x = 1.6 into the exponential model. B(1.6) = 2.1 million * (3^1.6) ≈ 14.87 million bacteria per milliliter. Therefore, after 1.6 weeks, the estimated concentration of bacteria in the river would be approximately 14.87 million bacteria per milliliter.

The exponential model B(x) = 2.1 million * (3^x) represents the concentration of bacteria after x weeks, where the concentration triples each week. By substituting x = 1.6 into the equation, we estimate that the concentration after 1.6 weeks would be approximately 14.87 million bacteria per milliliter.

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Answer:

a - one dart on 3 one dart on 5

b- one dart on 3 one dart on 9

c- 3 darts on 9

d- 4 darts on 7

e-

Answer:

Answer x = 9   y = 4

-2x + 8y = 14

-2x - 2y = -26      

0  + 10y = 40

y = 4

-2x + 8(4) = 14

-2x = 14 - 32 = -18

x = 9

Answer:b

Step-by-step explanation:

The equation for the perpendicular bisector of line segment XY is 2x + y = 7, the correct option is A.

The standard equation of a line is given by

y = mx+c

Here m is the slope and c is the y intercept

The slope can be determined by

m = (y₂ -y₁)/(x₂ -x₁)

The line segment XY  has the points  X(5, 7) and Y(–3, 3).

The slope of the line is,

m = ( 3 - 7) /( -3 - 5)

m = -4 / -8

m = 1 /2

The product of the slope of a line and a line perpendicular to it is -1.

( 1/2) * m' = -1

m' = -2

As it is a bisector , the midpoint of X and Y will be the point on the line.

Midpoint of XY is ( ( 5 -3)/2 , (7+3)/2 )

Midpoint of XY is ( 1 , 5)

The equation of the perpendicular bisector of line segment XY is,

y = -2x +c

5 = -2 + c

c = 7

So, the equation is,

y = -2x +7

2x +y = 7

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Answer:

Step-by-step explanation:

Let M and S be the numbers of Math and Science books, respectively.  Let T be Steve's Total money he has to play with.

We are told that if Steve splurges (as he should) on nothing but science books. he has $6 left.

We can write this as:  7S = T - 6  [The number of science books, S, times $7 each, leaves Steve with only $6 (T - 6).]

We also find that if he buys the same number of math books, he'll need $8 more.  Zounds.  But we can write this as:  9M = T + 8  But since we know he is buying the same number as science, we can also write this as 9S = T + 8    [The same number as he bought for science, S, times $9, Steve needs another $8].

We have two equations and two unknows (S and T), so lets see if we can solve for these variables.

7S = T - 6

9S = T + 8

Let's rearrange the first:  T = 7S + 6

Now use that  vale of T in the second equation:  

9S = T + 8

9S = (7S + 6) + 8

2S = 14

S = 7  That's 7 Science books.  It's also the value of M, 7 math books, since the problem states if he bought the same number as science books.

Now use S = 7 to find T, the total money Steve has [after coffee and doughnuts].

7S = T - 6

7*7 = T - 6

T = 49 + 6

T = $55

----

Let's see if $55 works for both the science and math book options:

1.  7 Science books:  $7/(S book)*(7 books) = $49  [He has $6 left]

2.  7 Math books:  $9/(M book)*(7 books) = $63  [He needs $8 more]

These results match the problem statements.

Steve has $55 (T).  He can buy either  7 science books or 6 math books:

Math:  6*($9) = $54  with $1 left, or

Science:  7*($7) = $49 with $6 left.

I suggest 6 Science books ($42) and 1 Math book ($9) for a total of $51, and still have $3 for coffee.  We aren't told if these books are all different from one another.  If they aren't, then Steve needs to ponder why he needs duplicated books.

Answer:

q energy flows inside the crust causes magma to rise.

Step-by-step explanation:

i took test

The correct statement about the flow of thermal energy inside earth, energy flows inside the crust causes magma to rise.

Thermal energy refers to the energy contained within a system that is responsible for its temperature.

Given that, flow of thermal energy inside the earth,

Heat flow is the movement of heat (energy) from the interior of Earth to the surface.

Thermal energy inside earth can be explained in statement, Energy flow inside the crust causes magma to rise.

Hence, The correct statement about the flow of thermal energy inside earth, energy flows inside the crust causes magma to rise.

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True. The variance and standard deviation both quantify how far spaced apart a set of data is from the mean. They cannot be used to calculate the dispersion around the median or mode, or any other center-of-mass metric.

The variance and standard deviation both quantify how far spaced apart a set of data is from the mean. They can therefore be used to calculate the difference between the highest and lowest values in a data set. The standard deviation, which is the square root of the variance, is used to calculate how far away from the mean each result is on average. The average of the squared deviations between each data point and the mean is the variance. The variance and standard deviation cannot be used to quantify the dispersion of data around other measures of center, such as the median or mode, because they only measure the dispersion of data around the mean.

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Answer:

Step-by-step explanation;

54+8p+4=90

58+8p=90

8p=90-58

8p=32

p=32/8

thus,p=4

8p+4=8×4+4=32+4=36

Answer:

Graph of polynomial of 2nd degree,i.e,X^2

Step-by-step explanation:

Answer:

3.125 miles

Step-by-step explanation:

5 × 0.625 = 3.125 miles

Answer:

it’s years

Step-by-step explanation:

The total amount of money left with Ram is Rs. 105

According to the given information:

Amount Ram had = Rs.200

Amount Ram spent= 1/4th of 200

Amount Ram gave to his friend = 1/2th of 90

To find: money left out for Ram.

Let the value of money left with Ram be x

Hence,

Step 1: Amount Ram had =200

Step 2: After spending 1/4th he is left with = 200*1/4 = 50

Step 3: Actual amount he has after spending the money = 200-50 = 150

Step 4: The amount is given to his friend = 90*1/2 = 45

Step 5: The actual amount left with Ram (x) = [step3] -[step4]

                                                                      x  = 150-45

                                                                       x = 105

Therefore the amount available with Ram after spending and giving his friend is Rs. 105.

Here we have to make a note of the original amount that the question specifies. The questions always have a trick to confuse the solvers, so make sure that while reading the question, mark the important aspects such as the amount Ram previously, the amount he spent, and later the amount he gave to his friend.

Always note the value that is given numerically and try to solve it chronologically or maintain the order of the question. Also, specify the steps properly so that the evaluator does not use much time to understand the solution.

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Step-by-step explanation:

equate the equation to zero

x³-6x+11x-6=0

if we replace x with 1

it will result to zero

1³-6+11-6=0

using long Division

as shown in the picture

obtain

x²-5x+6

using factorisation

x²-5x+6

(x²-2x)-(3x+6)

x(x-2)-3(x-2)

x=2

x=3

x=1

The provided options (x = -2, x = -1, x = 3, x = 2) are not asymptotes for the given function.

An asymptote of a function is a line that the graph of the function approaches but never touches. In the given function Y = (4x - 2)/(x^2 - 3x). The vertical asymptotes occur when the denominator of the fraction equals zero, so we set x^2 - 3x = 0 and solve for x:
x(x - 3) = 0
x = 0 or x = 3
The vertical asymptotes occur at x = 0 and x = 3.
The horizontal asymptote occurs when the degree of the numerator is less than or equal to the degree of the denominator. In this case, the degree of the numerator is 1 and the degree of the denominator is 2, so the horizontal asymptote occurs at y = 0.
   4x - 2
x^2 - 3x | 4x - 2

- 4x + 12
-14x - 2
To determine the asymptote of the given function Y = (2/cos(y-20)), we need to identify the values of y for which the denominator (cos(y-20)) becomes zero. For cosine, this occurs when its argument is an odd multiple of π/2.

The equation y - 20 = (2n+1)π/2, where n is an integer. Adding 20 to both sides gives y = (2n+1)π/2 + 20. Since there is no specific value of x involved in this function, we can conclude that there are no vertical asymptotes in the form x = some constant value.

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Since each trait is inherited independently, we can multiply the probabilities together. The probability of obtaining A/a; B/b; C/c; D/d offspring is (1/2) * (1/2) * (1/2) * (1/2) = 1/16.

The probability of obtaining A/a; B/b; C/c; D/d offspring can be calculated by multiplying the probabilities of each individual trait. Since each trait is inherited independently, we can multiply the probabilities together.

The probability of obtaining A/a offspring is 1/2 (A is dominant and a is recessive).

The probability of obtaining B/b offspring is 1/2 (B is dominant and b is recessive).

The probability of obtaining C/c offspring is 1/2 (C is dominant and c is recessive).

The probability of obtaining D/d offspring is 1/2 (D is dominant and d is recessive).

Therefore, the probability of obtaining A/a; B/b; C/c; D/d offspring is (1/2) * (1/2) * (1/2) * (1/2) = 1/16.

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The probability which represents the likelihood of randomly selecting a card that is a heart or a 7 from a well-shuffled standard deck is 4/13.

To calculate the probability of selecting a card that is either a heart or a 7 from a standard deck of 52 cards, we need to determine the number of favorable outcomes (cards that are hearts or 7s) and the total number of possible outcomes (all the cards in the deck).

Let's break it down:

Number of favorable outcomes:

- There are 13 hearts in a deck (one for each rank).

- There are four 7s in a deck (one for each suit, including the 7 of hearts).

- However, we need to subtract one card (the 7 of hearts) from the count since it has already been counted as a heart.

So, the number of favorable outcomes is 13 + 4 - 1 = 16.

Total number of possible outcomes:

- There are 52 cards in a deck.

Therefore, the probability of selecting a card that is either a heart or a 7 is:

Probability = Number of favorable outcomes / Total number of possible outcomes

          = 16 / 52

          = 4 / 13

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The selection depends on individual needs, preferences, and the intended use of the tiny house.

a) To find the amount of space inside each house, we need to calculate the volume for each design.

House on the left:

Volume = length x width x height = 2.5 m x 18 m x 2.8 m = 126 m³

Triangular house:

Volume of a triangular prism = (base area x height) / 2

Base area = (1/2) x base x height = (1/2) x 4 m x 10 m = 20 m²

Volume = (20 m² x 7 m) / 2 = 70 m³

b) When comparing the environmental impacts of each house, several factors need to be considered:

Positive impacts:

1. Material usage: Tiny houses use fewer materials, reducing resource consumption and waste generation.

2. Energy efficiency: Smaller living spaces require less energy for heating, cooling, and lighting, leading to lower energy consumption.

3. Land utilization: Tiny houses can be built on smaller plots of land, preserving green spaces and reducing urban sprawl.

Negative impacts:

1. Construction materials: Although tiny houses use less material overall, the environmental impact depends on the types of materials used. Sustainable and eco-friendly materials should be prioritized.

2. Water and waste management: Adequate provisions for water supply and waste disposal should be implemented to minimize environmental impacts.

3. Transportation: The transportation of tiny houses to their locations can contribute to carbon emissions if not done efficiently.

c) The choice of design for a tiny house depends on personal preferences and priorities. However, considering the provided information:

The house on the left offers a larger interior space of 126 m³, providing more room for living and storage. It may be suitable for individuals or couples who desire more space and functionality within their tiny house.

The triangular house has a smaller interior volume of 70 m³ but offers a unique design and aesthetic appeal. It may be preferred by individuals who prioritize a distinctive architectural style or who are looking for a minimalist and cozy living space.

Ultimately, the selection depends on individual needs, preferences, and the intended use of the tiny house. Factors such as lifestyle, desired amenities, and personal values regarding sustainability and resource conservation should be considered when making the final decision.

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The particular antiderivative that satisfies the given condition is: C(x) = (4/9)x^4 - (9/8)x^3 + K1x + 2000

To find the particular antiderivative (or integral) of the given derivative \(C''(x) = 4x^2 - 3x\)  that satisfies the condition C(0) = 2000, we need to integrate the given function twice.

First, we integrate C''(x) to find C'(x):

\(C'(x) = ∫ (4x^2 - 3x) dx\)

To find the antiderivative of \(4x^2\), we use the power rule for integration: the power of x increases by 1 and is divided by the new power. Similarly, the antiderivative of -3x is \(-(3/2)x^2\).

\(C'(x) = ∫ (4x^2 - 3x) dx = (4/3)x^3 - (3/2)x^2 + K1\)

Here, K1 is the constant of integration. Next, we integrate C'(x) to find C(x):

\(C(x) = ∫ (C'(x)) dx = ∫ ((4/3)x^3 - (3/2)x^2 + K1) dx\)

To find the antiderivative of \((4/3)x^3\), we again use the power rule for integration. Similarly, the antiderivative of \(-(3/2)x^2\) is \(-(3/2)(1/3)x^3\).

The constant of integration K1 will also be integrated with respect to x, resulting in another constant of integration, K2.

\(C(x) = (1/3)(4/3)x^4 - (1/2)(3/2)x^3 + K1x + K2\)

Simplifying further, we have:

\(C(x) = (4/9)x^4 - (9/8)x^3 + K1x + K2\)

Now, we can apply the initial condition C(0) = 2000 to find the particular solution for K2:

\(C(0) = (4/9)(0)^4 - (9/8)(0)^3 + K1(0) + K2 = 2000\)

Since all the terms involving x become zero when x = 0, we have:

K2 = 2000

Therefore, the particular antiderivative that satisfies the given condition is: \(C(x) = (4/9)x^4 - (9/8)x^3 + K1x + 2000\)

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For  students at Walden University,

a)

i) Expected college GPA for these students is 2.20.

ii) expected college GPA for these students is 1.10.

b) The relationship between Y and X1 for those students with X2 = 500 is E(Y) = 1.2 + 0.5X1.

Here we have to use regression analysis

Part a

(i) For students with high school GPA = 4.0 and college board score = 800, the expected college GPA is:

E(Y) = 0.20 + 0.50(4.0) + 0.002(800) = 2.20

Therefore, the expected college GPA for these students is 2.20.

(ii) For students with X1 = 3.0 and X2 = 300, the expected college GPA is:

E(Y) = 0.20 + 0.50(3.0) + 0.002(300) = 1.10

Therefore, the expected college GPA for these students is 1.10.

b)

To show that the relationship between Y and X1 for those students with X2 = 500 is E(Y) = 1.2 + 0.5X1, we need to use the given equation E(Y) = 0.20 + 0.50X1 + 0.002X2 and substitute X2 = 500 into it:

E(Y) = 0.20 + 0.50X1 + 0.002(500)

E(Y) = 1.20 + 0.50X1

Therefore, the relationship between Y and X1 for those students with X2 = 500 is E(Y) = 1.2 + 0.5X1.

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Answer:

The dog is 16 years old.

Step-by-step explanation:

X/4 + 6 = X/8 + 8

X/4-X/8 = 8-6

0.125X = 2

X = 2/0.125

X = 16

Answer:

16 years old

Step-by-step explanation

Dividing the dog’s age by 4 and adding 6

D÷4  + 6

dividing the dog’s age by 8 and adding 8

D÷8  + 8

equating both

D÷4  + 6 = D÷8 + 8

=> D÷4 - D÷8  = 2

multiplying by 8 both sides

=> 2D - D = 16

=> D = 16

hence, the dog is 16 years old

The minimum and maximum amounts that the artist received for her products this week are $225 and $275, respectively.

Let's define a variable to represent the amount the artist received for her products this week.

Let the variable be x

The absolute value equation that represents the scenario is:

| x - 250 | = 25

We have to solve the equation

Let there are two possibilities , one where x - 250 is positive and one where x - 250 is negative.

When x - 250 is positive:

If x - 250 is positive, then the equation becomes:

x - 250 = 25

Adding 250 to both sides:

x = 275

If x - 250 is negative:

If x - 250 is negative, then the equation becomes:

-(x - 250) = 25

Multiplying both sides by -1 to remove the negative sign:

x - 250 = -25

Adding 250 to both sides:

x = 225

So, the solutions to the absolute value equation are x = 275 and x = 225.

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Answer:

Should be D

Step-by-step explanation:

a) Sin(BAC) is equal to 3/5 in both drawings.

b) Angle BAC in the drawing where it is acute is at 38.7°.

c) Angle BAC in the drawing where it is obtuse is also at 38.7°.

a) In triangle ABC, we have angle BCA = 30°, AB = 15 mm, and BC = 24 mm. Let angle BAC be x. Then, using the law of cosines,

AC² = AB² + BC² - 2AB·BC·cos(BAC)

AC² = 15² + 24² - 2·15·24· × cos(30°)

AC² = 15² + 24² - 2·15·24· × (√(3)/2)

AC² = 561 - 120

AC² = 441

AC = √(441) = 21

Now using the law of sines to find sin(BAC):

sin(BAC) = sin(180°-30°-BAC) = sin(150°-BAC) = sin(30°+BAC)

sin(BAC) = sin(30°)cos(BAC) + cos(30°)sin(BAC)

sin(BAC) = (1/2)cos(BAC) + (√(3)/2)sin(BAC)

(2/5)sin(BAC) = (1/2)cos(BAC)

sin(BAC)/cos(BAC) = 4/5

tan(BAC) = 4/5

Therefore, sin(BAC) = 4/5 in both drawings.

b) Since sin(BAC) = 4/5 and AB = 15 use inverse sine to find angle BAC:

BAC = arctan(4/5) = 38.66°

So in the acute triangle, BAC is approximately 38.7°.

c) In the obtuse triangle:

AC² = AB² + BC² + 2AB·BC·cos(30°)

AC² = 15² + 24² + 2·15·24·(√(3)/2)

AC² = 1089

AC = √(1089) = 33

sin(BAC) = sin(180°-30°-BAC) = sin(150°-BAC) = sin(30°+BAC)

sin(BAC) = sin(30°)cos(BAC) + cos(30°)sin(BAC)

sin(BAC) = (1/2)cos(BAC) + (√(3)/2)sin(BAC)

(2/5)sin(BAC) = (1/2)cos(BAC)

sin(BAC)/cos(BAC) = 4/5

tan(BAC) = 4/5

BAC = arctan(4/5) = 38.66°

So in the obtuse triangle, BAC is also approximately 38.7°.

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The complete question:

There are two ways to draw a triangle ABC so that angle BCA = 30°, AB = 15 mm and BC= 24 mm. In one of the drawings below angle BAC is acute, and in the other it is obtuse. a) Show that sin(BAC) = 4/5 in both drawings. b) Work out angle BAC in the drawing where it is acute. c) Work out angle BAC in the drawing where it is obtuse. Give each angle to 1 d.p.

Volume of ice cream Cone = 753.6\(cm^{3}\)

A three-dimensional space's occupied volume is measured. It is typically quantified using a variety of imperial or US-standard units as well as SI-derived units. The definition of length and volume are connected.

According to the given information

Volume of toy ice cream Cone = Volume of Cone + Volume of Hemisphere

We are given that

Radius of cone = Radius of hemisphere = 6 cm

Height of cone = 8 cm

So

Volume of Sphere = \(\frac{1}{2}\) × \(\frac{4\pi r^{3} }{3}\)

                               = 1/2 × 4/3 × 3.14 × \(6^{3}\)

Volume of sphere = 452.16 \(cm^{3}\)

Volume of Cone = \(\frac{\pi r^{2}h }{3}\)

                            = 1/3 × 36 ×3.14 ×8

                            = 301.44 \(cm^{3}\)

So

The Volume of ice cream cone = 452.16 \(cm^{3}\) + 301.44 \(cm^{3}\)

                                                     = 753.6\(cm^{3}\)

Volume of ice cream Cone = 753.6\(cm^{3}\)

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Answer:

False

Step-by-step explanation:

This is not necessarily true because there are 2 types of these triangles, a 40-70-70 triangle or a 40-40-100 triangle. Since their angle measures are different, they are not similar.

Answer:

Its really blurry, what does it say?

Step-by-step explanation: