Into how many parts should you divide 30?

The transformations have been performed on the graph of f(x) = 3√x to obtain the graph of g(x)=1/4x+3√x+3+6 are respectively,

C. stretch the graph away from the x-axis

E. translate the graph to the left  

G. translate the graph up

Function is a relation between a set of inputs and a set of outputs which are permissible. In a function, for particular values of x we will get only a single image in y. It is denoted by f(x).

Given that,

Two functions,

f(x) = 3√x,

g(x)=1/4x+3√x+3+6

Graph is attached,

the steps of transformation are,

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Answer:  

compress the graph closer to the x-axis

translate the graph up

translate the graph to the left

Step-by-step explanation:

I took the test on k12 trust me.

The range of ants to eat is 20,000-1,00,000 ants.

The difference between the highest and lowest values for a particular data collection is the range in statistics. For instance, the range will be 10 - 2 = 8 if the provided data set is 2, 5, 8, 10, and 3.

As a result, the range may alternatively be thought of as the distance between the highest and lowest observation. The range of observation is the name given to the outcome. Statistics' range reflects the variety of observations.

The answer is given below:

If each ant is of 1 mg:

1g = 1000 mg = 1000 ants

100g = 100000 mg = 100000 ants

=> Maximum 105 ants

Now if one ant is of 5 mg:

1g = 1000mg = 1000/5 = 200 ants

100g = 20000 ants

Minimum 20,000 ants

Hence the range of ants to eat is 20,000-1,00,000 ants.

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Answer: Each part of 20.49 cm.

Step by step explanation:

Data :

In this problem we have to divide the piece of wood that is 102.45 cm, with 5 equal parts:

[tex]\bf \: \cfrac{ 102.45 }{5} = \boxed{ \bf20.49 \: cm}[/tex]

Rpt: Each part of 20.49 cm.

Answer: 20.49

Step-by-step explanation:

102.45/5=20.49

A linear function rule to model the distance in feet {d} the car has traveled any number of seconds {t} after passing the timing device is

d = 92t.

Given is that a car moving at a constant speed passed a timing device at t = 0 s. After 9s, the car has traveled 828 ft.

We can write the linear function as -

y = mx

Now, we can write the slope as -

{m} = (828/9) = 92

So -

d = 92t

Therefore, a linear function rule to model the distance in feet {d} the car has traveled any number of seconds {t} after passing the timing device is

d = 92t.

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The other side of this equation so it's true for all values of x: 1/2(6x - 10) - x = 2x - 5, and the other side of this equation so it's true for no values of x: 1/2(6x - 10) - x = 2x-5 = 2x+3.

A mathematical equation is a formula that uses the equals sign to represent the equality of two expressions.

Given that, find the other side of this equation so it's true for all values of x:

1/2(6x - 10) - x

= 6x/2 - 10/2 -x

= 3x-5-2

= 2x-5

Now for, equation so it's true for no values of x:

1/2(6x - 10) - x =

Distribute the parentheses:

1/2(6x - 10) - x =

= 3x -5 -x

= 2x -5

We need to other side to be of the form 2x - constant where the constant is not equal to 5.

2x-5 = 2x+3

Subtract 2x from each side.

-5 =3

This is not true so there is no solution.

Hence, the other side of this equation so it's true for all values of x: 1/2(6x - 10) - x = 2x - 5, and the other side of this equation so it's true for no values of x: 1/2(6x - 10) - x = 2x-5 = 2x+3.

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The reflection points of (-7, 8) across the x-axis and y-axis are (-7, -8) and (7, 8).

A reflection is a type of transformation that involves flipping a shape, known as the preimage, over a line, known as the line of reflection, to produce a new shape (called the image). You can picture what would happen if you flipped the form over the line in order to graph a reflection.

Given:

A point (-7, 8).

Reflection rule about the x-axis:

(x , y) → (x, -y)

So, (-7, 8) → (-7, -8)

Reflection rule about the y-axis:

(x , y) → (-x, y)

So, (-7, 8) → (7, 8)

Therefore, all the required values are given above.

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The magnitude and direction of the force C are 93.853 pounds-force and  281.237°, respectively.

In this problem we find the case of a system at equilibrium and formed by 3 vectors, of which we must determine the magnitude and direction of a force must be determined. Vectors are described by two features: (i) Magnitude, (ii) Direction.

The magnitude is obtained by Pythagorean theorem:

F = √(x² + y²)

The direction is determined by inverse trigonometric functions:

θ = tan⁻¹ (y / x)

Besides, the system can be described physically by Newton's laws and mathematically by vector sum:

F₁(x, y) + F₂(x, y) + F₃(x, y) = (0, 0)

First, determine the vector associated to force C:

F₃(x, y) = - F₁(x, y) - F₂(x, y)

F₃(x, y) = - (- 92 · cos 45°, 92 · sin 45°) - (54 · cos 30°, 54 · sin 30°)

F₃(x, y) = - (- 46√2, 46√2) - (27√3, 27)

F₃(x, y) = (46√2, - 46√2) - (27√3, 27)

F₃(x, y) = (46√2 - 27√3, - 46√2 - 27)

Second, calculate the magnitude of force C:

F₃ = √[(46√2 - 27√3)² + (- 46√2 - 27)²]

F₃ ≈ 93.853

Third, determine the direction of force C:

θ = tan⁻¹ [(- 46√2 - 27) / (46√2 - 27√3)]

θ ≈ 281.237°

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Answer:

  F₃ = 94 lb at 78.8° below the +x axis

Step-by-step explanation:

You want the magnitude of force F₃ that makes the sum of forces be zero.

As you have already noted, the sum of forces is zero when the system is at equilibrium.

  F₁ +F₂ +F₃ = 0

  F₃ = -(F₁ +F₂)

The forces F₁  and F₂ can be added by adding their horizontal and vertical components.

  F₁ = 92(cos(135°), sin(135°)) ≈ (-65.0538, 65.0538)

  F₂ = 54(cos(30°), sin(30°)) ≈ (46.7654, 27)

Then the sum of forces is ...

  F₁ +F₂ ≈ (-18.2884, 92.0538) . . . . . sum of corresponding parts

As we noted above, F₃ is the opposite of the sum, so is ...

  F₃ = (18.2884, -92.0538)

The magnitude is found using the Pythagorean theorem:

  |F₃| = √(18.2884² +(-92.0538)²) ≈ √8808.3677 ≈ 93.8529

The magnitude of F₃ is about 94 lb.

The components of F₃ tell you the force is in the 4th quadrant. The ratio of the x- and y-components is the tangent of the angle:

  θ = arctan(y/x) = arctan(-92.0538/18.2884) = arctan(-5.03345)

  θ ≈ -78.763°

In the first attachment, the sum of forces F₁ +F₂ is shown by the black arrow. The direction of F₃ will be the opposite of that arrow's direction, so will be down to the right, about 78.8° below the +x axis. The second attachment shows the magnitude and direction of F₃, where 0° is the direction of the +x axis.

__

Additional comment

For finding the magnitude of the sum of two forces, the Law of Cosines is another way to do it. To use that, you need to know the angle between the two forces. That's the angle at lower right inside the triangle shown in the first attachment. It is 75°. Then the magnitude is ...

  |F₃| = √(54² +92² -2·54·92·cos(75°)) ≈ √8808.37 ≈ 93.853 . . . . lb

This math can be simpler than working with the x- and y-components of the forces.

The angle of F₃ is another matter. Finding that requires solving the force triangle for one of the other interior angles, then adding the angles in the appropriate way.

For example, the angle at the origin can be found from the Law of Sines as ...

  α = arcsin(92/93.853·sin(75°)) ≈ 71.237°

Adding this to the angle of the red vector (30°) gives the resultant angle relative to the +x axis of 101.237°. The direction of F₃ is opposite this, so is ...

  101.237° -180° = -78.763° . . . . as above

As you can see from the attachments, a vector calculator or spreadsheet is a useful tool for finding sums of forces from their magnitude and direction.

Just to be clear, the conversion between polar and rectangular forms is ...

  (x, y) = r(cos(θ), sin(θ))

  r = √(x² +y²)

  θ = arctan(y/x) . . . . . with attention to quadrant

Spreadsheets and some calculators have an ATAN2(x, y) function that takes the signs into account when it computes the angle. When working with angles, make sure the calculator's angle mode is set to degrees or radians appropriately. (Spreadsheets usually use radians.)

The solution of the expression ( 7⁻²  x  7⁵ x  7⁻³ ) is equal to 1.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that the expression is ( 7⁻²  x  7⁵ x  7⁻³ ). The expression will be solved as below,

E = ( 7⁻²  x  7⁵ x  7⁻³ )

E = 7⁽ ⁻²⁺⁵⁻³⁾

E = 7⁽⁻⁵⁺⁵⁾

E = 7⁰

E =1

Hence, the solution of the expression ( 7⁻²  x  7⁵ x  7⁻³ ) is equal to 1.

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The true diameter of the Venus given the angular diameter of 0.018 is about 39.7 million km.

An angular distance used to describe how big a sphere or circle seems from a certain point of view is known as the angular diameter, angular size, apparent diameter, or apparent size. It is known as the visual angle in the vision sciences and as the angular aperture in optics (of a lens). The angular diameter may also be thought of as the angle that a camera or eye must spin around in order to view from one side of an apparent circle to the other.

Given that the angular diameter of Venus is 0.018 degrees.

The true diameter of the planet is calculate using the following formula:

diameter = distance (angular diameter / 57.3)

Substitute the value of distance = 38.5 million and angular diameter = 0.018 degrees.

diameter = 38.5 * 10^6 (0.018 / 57. 3)

diameter = 39. 7 million

Hence, the true diameter of the Venus given the angular diameter of 0.018 is about 39.7 million km.

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Answer: The relationship between the variables x and y in the given data points is linear.

Step-by-step explanation: A linear relationship is one in which the change in the y-value (output) is always the same for a given change in the x-value (input), regardless of the starting point. In other words, the slope of the line is constant.

In this case, the slope of the line can be calculated by finding the difference in y-values for a given difference in x-values between two points. We can pick any two points, for example:

(X: -6, Y: 12) and (X: 6, Y: 20)

The slope can be calculated by:

m = (20 - 12) / (6 - (-6)) = 8/12 = 2/3

This means that for every 1 unit increase in x, y increases by 2/3 units.

This is a linear relationship.

In contrast, in an exponential relationship, the y-value increases (or decreases) at a constantly increasing (or decreasing) rate as the x-value increases.

The tangent of the given angle shown above would be = 1.43. That is option C.

The formula that is used to calculate the tangent of the given angle ;

Tan θ = opposite/adjacent

Where the opposite = 60ft

the adjacent = 42ft

Tan θ = 60/42

= 1.43°

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Answer:

Check: 198+214+764 = 1176 total rooms

==========================================================

Explanation

I'll define these variables:

We have these given facts:

Fact 1 allows us to form the equation c = p+16

Fact 2 allows us to form the equation m = 4p-28

Fact 3 leads to the equation p+c+m = 1176

Let me know if you have any questions about how I formed the equations.

---------------------

The system of equations is:

[tex]\begin{cases}c = p+16\\m = 4p-28\\p+c+m = 1176\\\end{cases}[/tex]

Notice how the first two equations have the variable p on the right hand side, and no other variable. We'll use this to apply substitution and solve for p.

p+c+m = 1176

p+(p+16)+m = 1176 ... replace c with p+16

p+(p+16)+(4p-28) = 1176 ... replace m with 4p-28

6p-12 = 1176

6p = 1176+12

6p = 1188

p = 1188/6

p = 198

Use this value of p to find the other variables.

c = p+16 = 198+16 = 214

m = 4p-28 = 4*198-28 = 764

---------------------

Summary:

We found that p = 198, c = 214, and m = 764.

As a check,

198+214+764 = 1176 total rooms

The answer is confirmed.

[tex]{\Large \begin{array}{llll} y=ab^x \end{array}} \\\\[-0.35em] ~\dotfill\\\\ \begin{cases} x=5\\ y=7 \end{cases}\implies 7=ab^5 \\\\[-0.35em] ~\dotfill\\\\ \begin{cases} x=0\\[1em] y=\frac{1}{4} \end{cases}\implies \cfrac{1}{4}=ab^0\implies \cfrac{1}{4}=a(1)\implies \cfrac{1}{4}=a \\\\\\ \stackrel{\textit{substituting on the 1st equation}}{7=\left( \cfrac{1}{4} \right)b^5\implies 28=b^5}\implies \sqrt[5]{28}=b~\hfill \boxed{y\approx \cfrac{1}{4}(1.9473)^x}[/tex]

Answer:

24

Step-by-step explanation:

36 * 1/3 = 12

36 - 12 = 24

Answer:

24

Step-by-step explanation:

36/3 = 12

2/3 of 36 = 24

The standard deviation of the sampling distribution of sample means will be 0.097.

The Gaussian Distribution is another name for it. The most significant continuous probability distribution is this one. Because the curve resembles a bell, it is also known as a bell curve.

Assume that an investigation of primary school understudies reports that the mean age at which youngsters start perusing is 5.9 years with a standard deviation of 0.8 years.

The standard deviation of the sampling distribution of sample means is given as,

⇒ 0.8 / √68

⇒ 0.8 / 8.246

⇒ 0.097

The standard deviation of the sampling distribution of sample means will be 0.097.

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Answer:

20%

Step-by-step explanation:

To answer this question we have to 5% of 400, this will give us the number of managers!

1) 5% of 400

This gives us the answer!

Have a lovely day :)

It would be wiser for the couple to stay in the old apartment and save $1400.

In mathematics, multiplication is a method of finding the product of two or more numbers. It is one of the basic arithmetic operations, that we use in everyday life.

here, we have,

Explanation:

If they stay until the end of the lease, total money that will be paid out is $1000 x 6 = $6000,

If they leave, they'll have to forgo $1000.

If they move to their new apartment, they'll pay $900 x 6 = $5400

total expenditure if they move to the new place at the end of the six months period will be, the $1000 that will not be refunded back to them on the old apartment, plus this new $5600 for six month's rent in this new apartment, and that will be a total of $6400.

It would be wiser for the couple to stay in the old apartment and save $1400.

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A polynomial function is a function in an equation, such as the quadratic equation, cubic equation, etc.

A polynomial is an expression in mathematics that solely uses the operations of addition, subtraction, multiplication, and powers of positive-integer variables. It consists of indeterminates and coefficients.

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The value of x is obtained as follows:

x = 2.83.

The volume of a rectangular prism, with dimensions length, width and height, is given by the multiplication of these dimensions, as follows:

Volume = length x width x height.

Considering the dimensions in this problem, and the volume of 34 cubic meters, the equation is given as follows:

x(2x - 3)(3x - 4) = 34.

x(6x² - 17x + 12) = 34

6x³ - 17x² + 12x - 34 = 0.

Which is a cubic equation with coefficients given as follows:

a = 6, b = -17, c = 12, d = -34.

Using a calculator, the real solution are given as follows:

x = 2.83.

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The measure of each acute angle [tex]30^{0}[/tex]

If you need to see the algebra, the acute angles in a right triangle are complementary, adding to 90 degrees:

x + 2x = 90

3x = 90

x = 30

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If a baker will supply 22 jumbo cinnamon rolls to a cafe at a price of $3.46 each.   the equilibrium point is: 20 rolls and the price is $4.86.

The equilibrium point is where the supply and demand curves intersect, representing the price and quantity where the market is in balance.

Let's call the number of rolls the baker supplies x.

At the original price of $3.46 each, she supplies 22 rolls.

When offered $3.16, she will supply 2 fewer rolls, so she supplies x = 22 - 2 = 20 rolls.

We can use the demand equation to find the corresponding quantity demanded for each price:

p = D(x) = -0.25x + 6.56

D(22) = -0.25 * 22 + 6.56 = 4.56

D(20) = -0.25 * 20 + 6.56 = 4.86

The intersection of the two points (22, 4.56) and (20, 4.86) gives us the market equilibrium quantity and price.

So the equilibrium point is:

x = 20 rolls

p = $4.86 each.

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a) The point estimate of the population mean is given as follows: 3.2.

b) The standard error of the sample mean is given as follows: 0.16.

c) The interpretation of the 95% confidence interval is that we can be 95% confidence that the mean number of children that females would like to have is between 3.04 and 3.36. (option D).

d. It is not plausible that the population mean is of 2, as 2 falls outside of the confidence interval. (option A).

The point estimate of the confidence interval is given by half the sum of the bounds, hence:

(3.04 + 3.36)/2 = 3.20.

The standard error of the sample mean is half the difference between the bounds, hence:

(3.36 - 3.04)/2 = 0.16.

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Answer:

ive had this

Step-by-step explanation:

i remember having this its 35ft

Answer: 35ft

Step-by-step explanation: i did this before

The median of the data set is 75.80, rounded to two decimal places.

The mean of the data set can be calculated by adding up all the values and dividing by the number of values.

The formula is:

mean = (sum of all values) / (number of values)

For the given data set, mean = (59.8 + 61.4 + 69 + 71.2 + 78.7 + 83.5 + 89.6 + 94.1 + 84 + 75.2 + 79.7 + 83.6 + 74.8 + 74 + 83.3 + 73.8 + 90 + 68.3 + 71.7 + 74.2 + 69.3 + 68.5 + 71.3 + 78.5 + 73.2 + 91.4 + 78.7 + 56.4 + 73 + 65.6 + 69.9 + 73.8 + 80.1 + 78.7 + 75.8 + 66.7 + 79.7 + 66 + 73 + 85.3 + 72.1 + 78.5 + 79.9 + 75.6 + 71.3 + 69.6 + 58.6 + 64.3 + 63.2 + 79.9 + 70.1 + 80.4 + 88.2 + 79.4 + 74.6 + 65.2 + 70.6 + 77 + 73.2 + 81.5 + 83.3 + 77 + 82 + 78.5 + 75.4 + 78.5 + 73.6 + 86.8 + 74.4 + 65.2) / 60 = 6288.6 / 60 = 104.81

So, the mean of the data set is 104.81, rounded to two decimal places.

The median of the data set can be calculated by arranging the values in ascending order and finding the middle value. If there are an odd number of values, the median is the middle value. If there are an even number of values, the median is the average of the two middle values.

For the given data set, the median can be found as follows:

56.4 58.6 63.2 64.3 65.2 65.6 66 66.7 68.3 68.5 69 69.3 69.6 69.9 70.1 70.6 71 71.3 71.7 73 73 73.2 73.6 73.8 74 74 74.2 74.4 74.6 75.2 75.4 75.6 75.8 76.7 77 78 78.5 78.5 78.5 78.7 79 79.4 79.7 79.7 79.9 80.1 80.4 81.5 82 83 83.3 83.3 83.5 83.6 84 85.3 86.8 89.6 90 91.4 94.1

The median is 75.8.

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The required equation that represents the graph is j(x) =  (-x + 4)¹/². Option D is correct.

A parabola is a cross-section cut out of the cone and represented by an equation x = y².

here,
The given graph is of the left parabola,
-x = y²
When we translate the above expression 4 units right we get the graph,
So
-x + 4 = y²

put y = j(x)

-x + 4 = j(x)²
j(x) = [-x + 4]¹/²

Thus, the required equation that represents the graph is j(x) =  (-x + 4)¹/². Option D is correct.

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If a/2-b/3 = 1, then we can write:

2(a/2-b/3) = 2

Combining like terms, we have:

a - b/3 = 1

Multiply both sides by 3 to get:

3a - b = 3

Now, we can add b to both sides of the equation:

3a = b + 3

Finally, we can divide both sides by 3 to get:

a = (b + 3)/3

Now we can substitute this value of a into the original equation

2a + 3b = 2(b + 3)/3 + 3b = 2b/3 + 6/3 + 3b = 2b + 2 + 3b = 5b + 2

So 2a+3b = 5b + 2 in terms of b

Our assumption that m II  is intersected by a transversal n is wrong, thus none of the set of angles are supplementary to 108°.

A transversal in geometry is a line that intersects two other lines in the same plane at two different locations. It is possible to determine whether two or more other lines in the Euclidean plane are parallel by using transversals.

A line that crosses two lines in the same plane at two different geometric locations is referred to as a transversal. The angles that result from a transversal crossing of two lines in pairs can be successive internal angles, matching angles, or alternate angles.

The transversal angles. There are numerous angles created when a transversal splits two parallel lines. They are referred to as transversal angles.

Given, ∠1 = 70°

∠7 = 80°

Vertically opposite angles are equal.

∠1 = ∠3

⇒ ∠1 = ∠3 = 70°

As per the diagram, line 1 is intersected by line n.

Vertically opposite angles are equal.

∠5 = ∠7

=> ∠5 = ∠7 = 80°

Let m II l is intersected by a transversals n.

Then the pair of corresponding angles should be equal. i.e.,

∠1 = ∠5

= ∠3 = ∠7

but ∠1 = 70

and ∠5 = 80°

Therefore, our assumption that m II  is intersected by a transversal is wrong.

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Answer:

(t,v) =(5,61)

Step-by-step explanation:

re-write expression

v=61

t=5

a posible solution

then check the solution

then the ordered pair is the solution