1. Given the function: f(x)=√x+2+3 Fully explain the three transformations required to produce this function from the parent function.

Therefore, the formula for converting 35 liters to milliliters is 35000, with a conversion factor of 1000.

This is further explained below.

Generally,  The amount that is supplied in liters must be multiplied by 1000 in order to be converted to milliliters.

A conversion factor is a number that may be multiplied or divided to shift the units of measurement used for one set to another.

In situations when a conversion is required, the correct conversion factor that results in the same value must be used. For the purpose of converting inches to feet, for instance, the correct value for the conversion is 12 inches equaling 1 foot.

In conclusion, Therefore 35 liters to milliliters is given as 35000, conversion factor of 1000

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Answer:

1000ml and 1 liter

Step-by-step explanation:

Answer:

n=0.05

0.00036km

Step-by-step explanation:

a)

20:1

1:0.05

n=0.05

b)

1:25000

0.00036:9

0.00036km

Answer:

Step-by-step explanation:

no it isnt

The percentage by which population is growing each year is 2%

Percentage is a way to express a number as a fraction of 100. It is often used to represent ratios and proportions in a more convenient and understandable form, especially in financial and statistical contexts. For example, 50% means 50 per 100, or half of a given quantity. It is denoted using the symbol "%".

The formula for the population of the town as a function of time t is:

g(t) = 15,000(1.02)ⁿ

To find the percent growth rate, we need to determine the percent change in population from one year to the next. Let's consider the population at two different times, n and n+1 (i.e., one year later).

The population at time n is:

g(t) = 15,000(1.02)ⁿ

The population at time n+1 is:

g(t+1) = 15,000(1.02)ⁿ⁺¹

To find the percent change in population from t to t+1, we can divide g(t+1) by g(t) and express the result as a percentage:

(g(t+1)/g(t) - 1) x 100%

= ((15,000(1.02)⁽ⁿ⁺¹⁾)/(15,000(1.02)ⁿ) - 1) x 100%

= (1.02⁽ⁿ⁺¹⁾ - 1.02ⁿ) x 100%

= 1.02ⁿ x (1.02 - 1) x 100%

= 2%

Therefore, the population grows by 2% each year, which corresponds to option (D).

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Answer:

Step-by-step explanation:

The division of 6x⁴ + 11x³ + 13x² - 3x + 27 by 3x + 4 will have a quotient of 2x³ + x² +3x -5 and a remainder of 47 using the remainder theorem.

The remainder theorem states that if a polynomial say f(x) is divided by x - a, then the remainder is f(a).

We shall divide the 6x⁴ + 11x³ + 13x² - 3x + 27 by 3x + 4 as follows;

x⁴ divided by 3x equals 2x³

3x + 4 multiplied by 2x³ equals 6x⁴ + 8x³

subtract 6x⁴ + 8x³ from 6x⁴ + 11x³ + 13x² - 3x + 27 will give us 3x³ + 13x² - 3x + 27

3x³ divided by 3x equals x²

3x + 4 multiplied by x² equals 3x³ + 4x²

subtract 3x³ + 4x² from 3x³ + 13x² - 3x + 27 will give us 9x² - 3x + 27

9x² divided by 3x equals 3x

3x + 4 multiplied by 3x equals 9x² + 12x

subtract 9x² + 12x from 9x² - 3x + 27 will give us -15x + 27

-15x divided by 3x equals -5

3x + 4 multiplied by -5 equals -15x - 20

subtract -15x - 20 from -15x + 27 will result to a remainder of 47

using the remainder theorem, x = -4/3 from the the divisor 3x + 4

thus:

f(-4/3) = 6(-4/3)⁴ + 11(-4/3)³ + 13(-4/3)² - 3(-4/3) + 27 {putting the value -4/3 for x}

f(-4/3) = (1536/81) - (704/27) + (208/9) + (12/3) + 27

f(-4/3) = (1536 - 2112 + 1872 + 324 + 2157)/81 {simplification by taking the LCM of the denominators}

f(-4/3) = (5919 - 2112)/81

f(-4/3) = 3807/81

f(-4/3) = 47

Therefore, the quotient of after the division of 6x⁴ + 11x³ + 13x² - 3x + 27 by 3x + 4 is 2x³ + x² +3x -5 and there is the remainder of 47 using the remainder theorem.

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Answer: This refers to the number assigned to a unit within a building, where applicable. ... The first two digits refer to the floor level the unit is located on, while the numbers after the hyphen sign refer to the allotted number for the particular unit.

Step-by-step explanation:

Answer:

The answer is A because sixteen divide by two equals eight also two is common

We have to find the value of x for the given equation e^(−x^)−e^x =3. Here we can use a small trick to get the solution. We know that e^-x is the reciprocal of e^x. So we can replace e^-x with 1/e^x. Now we have the equation e^(−x^)−e^x =3 in the form e^x - 1/e^x = 3.

This is a quadratic equation in the form ax^2 + bx + c = 0. Here a = 1, b = 0, c = -3. We can solve this quadratic equation to get the value of x.

Given equation is e^(−x^)−e^x =3.We can replace e^-x with 1/e^x.Now the equation is e^(x) - 1/e^(x) = 3.

Let's take e^x as a variable and solve the equation:e^x - 1/e^x = 3Multiplying both sides by e^x, we get e^x * e^x - 1 = 3e^xNow e^(2x) - 3e^x - 1 = 0.

This is a quadratic equation in the form ax^2 + bx + c = 0. Here a = 1, b = -3, c = -1.

We can solve this quadratic equation using the quadratic formula which is given as:x = [-b ± sqrt(b^2-4ac)]/2a.

Substituting the values, we get:x = [-(-3) ± sqrt((-3)^2-4(1)(-1))]/2(1)x = [3 ± sqrt(13)]/2Hence the value of x is x = [3 ± sqrt(13)]/2.

We can solve the given equation e^(−x^)−e^x =3 using a small trick. We know that e^-x is the reciprocal of e^x. So we can replace e^-x with 1/e^x. Now we have the equation e^(−x^)−e^x =3 in the form e^x - 1/e^x = 3. This is a quadratic equation in the form ax^2 + bx + c = 0.

Here a = 1, b = 0, c = -3. We can solve this quadratic equation to get the value of x.We have, e^x - 1/e^x = 3Multiplying both sides by e^x, we get e^x * e^x - 1 = 3e^xNow e^(2x) - 3e^x - 1 = 0This is a quadratic equation in the form ax^2 + bx + c = 0. Here a = 1, b = -3, c = -1.

We can solve this quadratic equation using the quadratic formula which is given as:x = [-b ± sqrt(b^2-4ac)]/2aSubstituting the values, we get:

\(x = [-(-3) ± sqrt((-3)^2-4(1)(-1))]/2(1)x = [3 ± sqrt(13)]/2So the value of x is x = [3 ± sqrt(13)]/2.\)

Hence the solution of the equation e^(−x^)−e^x =3 is x = [3 ± sqrt(13)]/2.

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A parabola is the form of a quadratic function's graph because the vertex of a parabola is the location where the axis of symmetry of the curve crosses.

f(x) = ax^2 + bx + c, where a, b, and c are numbers and an is not equal to zero, is a quadratic function. A parabola is the form of a quadratic function's graph. Although the "width" or "steepness" of a parabola can vary as well as its direction of opening, they all share the same fundamental "U" form.

Regarding a line known as the axis of symmetry, all parabolas are symmetric. The vertex of a parabola is the location where the axis of symmetry of the curve crosses.

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Answer:

Move 1 to the left side of the equation by subtracting it from both sides. Subtract 1 from 43.

Hope I helped.  :)

- Valenteer

Answer: The one filled with wooden cubes.

Step-by-step explanation:

First, the box filled with spheres will have empty space, this is for how spheres are, so independent of the radius of the sphere, we will always have some empty space inside the box.

In the case of the cubes, this does not happen. Furthermore, the dimension of the box are 8cm by 8cm by 8cm, and the cubes have a sidelength of 1.6cm

We know that:

1.6cm*5 = 8cm

Then we can perfectly fill the box with the wooden cubes (such that there is no empty space like in the previous case).

Because this box has no empty space and is filled with the same material as the other box, we can conclude that this box will have a larger mass than the one filled with spheres.

And we know that:

density = mass/volume.

Both boxes have the same volume, but the box with cubes has a larger mass, then the box with cubes will have a larger density.

Answer:

In Mathematics, surds are the values in square root that cannot be further simplified into whole numbers or integers. Surds are irrational numbers. The examples of surds are √2, √3, √5, etc., as these values cannot be further simplified.

Step-by-step explanation:

Answer:

20 degrees

I know that it is acute, meaning it is less than 90. It is also less than 45 degrees, and is in the middle of 45 to 0 degree interval, so I say it is 20 degrees.

Answer:

4 ( x ) + ( y )

Step-by-step explanation:

.........

hmm yeah

Answer:

4*(4 + y)

Step-by-step explanation:

4*4 + 4y

16 + 4y

highest common factor is 4

4*(4+y)

Answer:

it's B 52

hope it helps. . ....

Answer:

Step-by-step explanation:

See attachment.

The solutions are:

a) A ∪ B = {a, b, c, d, e, f, g, i, o, u, t}

b) A ∩ B = {e, f}

c) A′ = {a, h, i, j, k, l, o, t, u, v, z}

d) A - B = {b, c, d, g}

a) A ∪ B: The union of sets A and B is the set that contains all the elements from both A and B without repetition.

A = {b, c, d, e, f, g}

B = {a, e, f, i, o, u, t}

A ∪ B = {a, b, c, d, e, f, g, i, o, u, t}

b) A ∩ B: The intersection of sets A and B is the set that contains only the elements that are common to both A and B.

A = {b, c, d, e, f, g}

B = {a, e, f, i, o, u, t}

A ∩ B = {e, f}

c) A′: The complement of set A refers to all the elements in the universal set U that are not in set A.

A = {b, c, d, e, f, g}

U = {a, b, c, d, e, f, g, h, i, j, k, l, o, t, u, v, z}

A′ = {a, h, i, j, k, l, o, t, u, v, z}

d) A - B: The set difference between A and B is the set that contains the elements that are in A but not in B.

A = {b, c, d, e, f, g}

B = {a, e, f, i, o, u, t}

A - B = {b, c, d, g}

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There is a 0.5477 probability that a randomly selected customer will arrive less than 5 minutes after the previous customer during the 3 pm to 5 pm time period. (option a)

Given that the arrival rate of cars at the bank's drive-through window during the 3 pm to 5 pm time period is 15 customers per hour, we can calculate the average time between arrivals as follows:

Average time between arrivals = 1 / arrival rate

= 1 / 15

= 0.0667 hours (since there are 60 minutes in an hour, this is equivalent to 4 minutes)

Now, we need to find the probability of a customer arriving less than 5 minutes after the previous customer. Since the time between arrivals follows the exponential distribution, we can use the cumulative distribution function (CDF) of the exponential distribution to calculate this probability. The CDF gives us the probability of an event occurring within a certain time frame.

To find the probability of a customer arriving less than 5 minutes after the previous customer, we need to calculate the probability of an arrival occurring within a 5-minute time frame, which is equivalent to 0.0833 hours. So, we can substitute λ = 15 and x = 0.0833 in the formula for the CDF and get:

F(0.0833) = 1 - e¹⁵ˣ⁽⁻⁰°⁰⁸³³⁾

= 0.5477 (rounded to four decimal places)

Therefore, the answer is option (a) 0.5477.

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Here are the solutions to Problem 1:1. Sum of two vectors a and b can be computed by adding their respective components.

Given vectors area = (-5, 3, 2) and b = (3, -3, 5)

\(Therefore, their sum can be computed by adding their respective components as follows:a+b = (-5+3, 3+(-3), 2+5) = (-2, 0, 7)Therefore, a + b = (-2, 0, 7)2.\)

The difference between two vectors a and b can be computed by subtracting their respective components.

\(Given vectors area = (-5, 3, 2) and b = (3, -3, 5)\)

T\(herefore, their difference can be computed by subtracting their respective components as follows:a-b = (-5-3, 3-(-3), 2-5) = (-8, 6, -3)Therefore, a - b = (-8, 6, -3)3.\)

Scalar multiplication of a vector a with a scalar k can be computed by multiplying all its components with k.

\(Given vector is a = (-5, 3, 2)

Therefore, 2a = 2(-5, 3, 2) = (-10, 6, 4)Therefore, 2a = (-10, 6, 4)4.\)

The linear combination of two vectors a and b is given by the sum of their scalar multiplication with respective scalars. Given vectors are a = (-5, 3, 2) and b = (3, -3, 5)

\(Therefore, 3a + 4b = 3(-5, 3, 2) + 4(3, -3, 5)= (-15, 9, 6) + (12, -12, 20) = (-3, -3, 26)\)

\(Therefore, 3a + 4b = (-3, -3, 26)5.\)

The magnitude or length of a vector can be computed by taking the square root of the sum of the square of its components. Given vector is a = (-5, 3, 2)

\(Therefore, the magnitude or length of vector a = |a| = √((-5)² + 3² + 2²) = √(34) = 5.8301 (approx)\)

Therefore, |a| = 5.8301 (approx)Here is the solution to Problem 2:1. A unit vector in the same direction as a can be computed by dividing the vector a by its magnitude.

\(Given vector is a = (3, 0, 5)Therefore, the magnitude or length of vector a = |a| = √(3² + 0² + 5²) = √34\)

\(Therefore, a unit vector in the same direction as a = a/|a| = (3/√34, 0/√34, 5/√34) = (3/5.8301, 0, 5/5.8301)\)

\(Therefore, a unit vector in the same direction as a = (0.5145, 0, 0.8575) (approx)\)

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The unit vector in the same direction as a is approximately (0.5098, 0, 0.8498).

Given vectors a = (-5, 3, 2) and b = (3, -3, 5), we can compute the following:

a + b = (-5, 3, 2) + (3, -3, 5)

= (-5 + 3, 3 - 3, 2 + 5)

= (-2, 0, 7)

a - b = (-5, 3, 2) - (3, -3, 5)

= (-5 - 3, 3 + 3, 2 - 5)

= (-8, 6, -3)

2a = 2(-5, 3, 2)

= (-10, 6, 4)

3a + 4b = 3(-5, 3, 2) + 4(3, -3, 5)

= (-15, 9, 6) + (12, -12, 20)

= (-15 + 12, 9 - 12, 6 + 20)

= (-3, -3, 26)

|a| = magnitude of vector

\($a = \sqrt{((-5)^2 + 3^2 + 2^2)\)

\(= \sqrt{(25 + 9 + 4)\)

\(= \sqrt{(38)\)

Problem 2:

Given vector a = (3, 0, 5), we need to find a unit vector in the same direction.

To obtain a unit vector, we divide vector a by its magnitude:

Magnitude of vector

\(a = \sqrt{(3^2 + 0^2 + 5^2)\)

\(= \sqrt{(9 + 25)\)

\(= \sqrt{(34)\)

Unit vector in the same direction as

\(a = (3, 0, 5) / \sqrt{(34)\)

\(= (3/\sqrt(34), 0/\sqrt(34), 5/\sqrt(34))\)

Simplifying, the unit vector in the same direction as a is approximately (0.5098, 0, 0.8498).

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Using proportions, it is found that the number of marbles that Tom had is given by:

Then:

\(\frac{5}{6}\left(\frac{1}{24}x\right) = 5\)

\(\frac{5}{144}x = 5\)

\(x = 144\)

Hence, option D is correct.

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Answer:

D. Is your answer

Step-by-step explanation:

Answer:

I think the answer is 255cm squared

Step-by-step explanation:

If you look at the shape it has 2 shapes. A rectangle and a triangle.

17-10 to get the height of the triangle = 7

22-12 to get the base of the triangle = 10

The area to find a triangle is 1/2 * b * h

= (7 *10) / 2

= 35

To find the rectangle =

22 * 10

= 220

To find the area of the whole thing =

35 (triangle) + 220 (rectangle) = 255cm squared

Answer:

255 cm^

Step-by-step explanation:

If you cut your shape into a triangle and rectangle...or a trapezoid and a rectangle, then add the areas together.

Area of a rectangle is just length × width.



Area of a triangle is:

A = 1/2bh

Area of a trapezoid is:

A = 1/2(b1 + b2)

see image to see two different ways to cut the whole shape into two pieces. Then we calculate the total by adding the areas of the parts.

see image.

Della was crying because she doesn't have enough money to brought the present for her husband Jim.

Basically, the O Henry's story of "The gift of Magi" has the central them as Love. In this story, he sets up a contrasted picture in life- love among the ruins- the acute poverty in the family and the sacrifice of the greatest possessions of the family.

In this stage he defines how their possession has helped Jim and Della, that's the hero and heroine to conquer poverty they were in.

Now, the reason behind Della's cry was she had only one dollar and eighty seven cents and with this small amount she could not buy a good present for her dear husband.

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The age of the youngest of Elijah's neighbours given the information in the question is 11 years.

28 + x + y = 80

x + y = 80 - 28

x + y = 52 equation 1

x - y = 30 equation 2

Where:

x = age of the oldest neighbour

y = age of the youngest neighbour

Subtract equation 2 from 1

2y = 22

Divide both sides by 2

y = 11 years

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if the level of significance of a hypothesis test is raised from .01 to .05, then  the probability of a Type II error will decrease when the level of significance of a hypothesis test is raised from .01 to .05. (option a)

This change in the level of significance does not directly affect the probability of a Type II error. A Type II error occurs when we fail to reject the null hypothesis, even though it is false. This means that we have concluded that there is no relationship between the variables, even though there actually is one.

The probability of a Type II error depends on several factors, such as the sample size, the effect size, and the level of significance. In general, as the level of significance increases, the probability of a Type II error decreases.

This is because when we are more lenient in rejecting the null hypothesis, we are more likely to detect any real relationship that exists between the variables.

Therefore, the correct answer to your question is (a)

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