What expressions that are equivalent to 4(9u)

x is rational, because it can be expressed as the ratio of two integers (d-b) and (a-c).

Let's multiply both sides of the given equation by cx+d to eliminate the denominator:

ax + b = cx + d

ax - cx = d - b

x(a-c) = d - b

x = (d - b)/(a - c)

Since a, b, c, and d are integers and a ≠ c, (a-c) is also an integer. Therefore, x is rational, because it can be expressed as the ratio of two integers (d-b) and (a-c).

Note that this is a special case of the more general result that if p(x) and q(x) are polynomials with integer coefficients and q(x) ≠ 0 for some real number x, and if p(x)/q(x) is an integer, then p(x) is divisible by q(x).

In this case, q(x) = cx + d, which is nonzero because a ≠ c, and p(x) = ax + b - (cx + d) = (a-c)x + (b-d). Since p(x) is an integer and q(x) is an integer except possibly at x = -d/c, it follows that p(x) must be divisible by q(x), and hence x = (d-b)/(a-c) is rational.

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The ratio of orange water made by Zakiya is 3:1.

The ratio is defined as the relation between two amounts. It is a quantitative relation which shows the amount of value contains within other value. The ratio will be written by taking amount of yellow wate rin numerator and amount of red water in denominator.

So, the ratio of yellow water to red water will be represented as 3:1. The ratio indicates 3 units of yellow water is contained in the 1 unit of red water.

Therefore, the final ratio of yellow water to red water is 3:1.

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The area of the parallelogram in the diagram given is: 1,330 in.²

Area of a parallelogram = (base × height)

Given the following dimensions of the parallelogram:

Base = 38 in.

Height = 35 in.

Area of the parallelogram = 38 × 35

Area of the parallelogram = 1,330 in.²

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The formula to calculate the confidence interval is given by: \(CI = X \pm Z^* \cdot \frac{\sigma}{\sqrt{n}}\) Here, X = sample mean, σ = population standard deviation, n = sample size, and Z = z-value corresponding to the level of confidence.

Constructing the 99% confidence interval:We have X = $62,000, σ = $23,000, and n = 65.The z-value for a 99% confidence interval can be found using a standard normal distribution table or a calculator.Using the calculator, we get: Z = 2.576 (rounded off to three decimal places)Now, we can substitute these values in the formula:

\(CI = X \pm Z^* \cdot \frac{\sigma}{\sqrt{n}}\)

= $62,000 ± 2.576*($23,000/√65)CI

= $62,000 ± $7,999.16

The lower limit of the interval is given by:

$62,000 - $7,999.16

= $54,000.84T

he upper limit of the interval is given by:

$62,000 + $7,999.16

= $69,000.16

Therefore, the 99% confidence interval for the average bonus that all employees working for financial companies in New York City received last year is ($54,000.84, $69,000.16).

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Answer:4 words per minute.

Step-by-step explanation:32 divided by 8 is 4.

Answer:

  D.  plain quadrilateral

Step-by-step explanation:

This is a vocabulary question.

__

A parallelogram is a quadrilateral (4-sided plane figure) with both pairs of opposite sides parallel. A rhombus is a special case of a parallelogram in which the sides have equal lengths.

A trapezoid is quadrilateral with exactly one pair of parallel sides. An isosceles trapezoid is one that has equal-length non-parallel sides.

__

The given figure has no parallel sides, so is none of the above. It is a ...

  plain quadrilateral

To evaluate the integral using a parametric description of the circle, we can parameterize the circle using trigonometric functions.

Let's denote the circle as C, with radius r centered at the origin. We can describe the circle using the parameter θ, which represents the angle in the counterclockwise direction from the positive x-axis to a point on the circle.

The parametric equations for the circle C are:

x = rcos(θ)

y = rsin(θ)

By substituting these parametric equations into the integral, we can set up the integral over the circle C. The integral could involve a function f(x, y) that needs to be evaluated over the circle C. The integral can be written as:

∫∫f(x, y) dA

where dA represents the area element. To evaluate this integral, we need to express dA in terms of the parameter θ and compute the limits of integration based on the range of θ that corresponds to the circle C.

The explanation paragraph would then provide more details on how to set up the integral, determine the limits of integration for θ, and compute the area element dA in terms of θ. It would also mention that depending on the specific function f(x, y) and the desired computation, additional techniques such as changing variables or using appropriate coordinate transformations may be required to evaluate the integral over the circle C.

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Step-by-step explanation:

1 and 2 are  'none'

5 and 6 are 'vertical '

The area of a triangle with sides a = 20, b = 15, and c = 25 is 150.

The sides of the triangle are given as a = 20, b = 15, and c = 25.

We will use Hero's formula to find the area of this triangle.

It is a three-face polygon that consists of three edges and three vertices.

We use Heron's formula to find the area of a triangle with 3 sides:

Herons formula:

Area of a triangle =  \(\sqrt{s(s-a)(s-b)(s-c)}\\\)

Where a, b, and c are sides of a triangle.

And s = semi perimeter of a triangle.

s = \(\frac{a+b+c}{2}\)

If the sum of two sides of a triangle is greater than the third side of a triangle then the sides of a triangle are true.

Let the given sides be:

a = 20, b = 15 and c = 25.

(20 + 15) > 25

(20 + 25) > 15

(15 + 25) > 20 so the given sides are true.

Now,

Semi perimeter of the triangle:

s = (a+b+c) / 2

s = (20+15+25) / 2

s = 60 / 2

s = 30

Putting s = 30 in the area of the triangle.

we get,

Area of the triangle = \(\sqrt{s(s-a)(s-b)(s-c)}\\\)

Area of the triangle = \(\sqrt{30(30-20)(30-15)(30-25)}\\\\\sqrt{30\times10\times15\times5}\\\\\sqrt{22500}\\\\150\)

Thus, the area of a triangle is 150.

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To construct a histogram of the estimates and compare it to the above estimates, follow these steps:
1. Compile the data and organize it into groups or bins.
2. Assign each group a height or frequency, usually the number of occurrences in the group.
3. Represent each group by drawing a bar with the corresponding height.
4. Connect the tops of the bars to form a histogram.

Comparing the histogram to the above estimates, if the histogram is similar in shape and spread, then the estimates are consistent.

The best estimate of the random modifier without examining the value is the mode of the data, which is the value that occurs most often.

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The probability that both Event A (the first die is 4 or less) and Event B (the second die is even) will occur is 1/3.

To find the probability that both Event A and Event B will occur, we need to calculate the individual probabilities of each event and then multiply them together.

Event A: The first die is 4 or less.

There are 6 possible outcomes for the first die (numbers 1 to 6), and out of those, 4 outcomes (numbers 1, 2, 3, and 4) satisfy the condition. Therefore, the probability of Event A is 4/6, which simplifies to 2/3.

Event B: The second die is even.

For a fair six-sided die, there are 3 even numbers (2, 4, and 6) out of a total of 6 possible outcomes. Therefore, the probability of Event B is 3/6, which simplifies to 1/2.

To find the probability that both events will occur, we multiply the probabilities of Event A and Event B:

Probability of both events occurring = Probability of Event A * Probability of Event B

P = (2/3) * (1/2)

P = 2/6

P = 1/3

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The equivalent multiplier of 2.08% increase is 1.0208

To convert a given percentage into multiplier, first either add or subtract the percentage from 100 and, then convert it to a decimal.

Here given that the,

Percentage increase = 2.08%

Thus to find, an increase of 2.08% is equivalent to multiplier is ,

(100 + 2.08) / 100

= 102.08 / 100

= 1.0208

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Answer:

2. given

5. substitution

Step-by-step explanation:

that the perimeter is 12 is simply a given fact. in the same way as the shape of the object is defined as square.

nothing was calculated, this information is simply there at the beginning, is "given" to us.

step 5 simply takes step 3 and substitutes all sides by the same side, as (per definition) all sides in a square are equal. so, every side can stand in for every other side.

Step-by-step explanation:

a) 4x 12+n = There are no like terms )

b) (4x12) +n = There are no like terms )

c) 4x (12+ n)  = 4nx+48x

d) 4+ (12 x n) =12nx+4

( I hope this was helpful ) >;D

Answer:

Step-by-step explanation:

\([(6^{2}+8^{2})^{\frac{1}{2}}]^{3} = [(36+64)^{\frac{1}{2}}]^{3}\\\\= [(100)^{\frac{1}{2}}]^{3}\\\\= 10^{3}\\\\= 1000\)

Answer:

0.16666666666667.

Step-by-step explanation:

Answer: -2 1/2

Step-by-step explanation:

First term = a = -40

Common ratio = 2nd term / First term = 20 / -40 = -1/2

5th term = ar⁴

5th term = -40 × (-1/2)⁴

5th term = -40 × 1/16

5th term = -2 1/2

Answer:

2.1 m

Step-by-step explanation:

The gutter is in the shape of a cylinder.

Its volume is 20 liters and its diameter is 11 cm (0.11 m).

Its radius is half of its diameter => r = 0.055 m.

The volume in cubic metres:

1 litre = 0.001 cubic metres

20 litres = 20 * 0.001 = 0.02 cubic metres

The volume of a section of guttering is given as:

\(V = \pi r^2h\)

where h = length of the guttering

Therefore:

\(0.02 = \pi * 0.055^2 * h\\\\0.02 = 0.009503h\\\\h = 0.02 / 0.009503\\\\h = 2.10 m\)

The length of the section of guttering is 2.1 m long.

Answer:

11.5 inches

Step-by-step explanation:

Just subtract the .5 inch from 12. The max of variance that it can have.

Answer:

S > R + Q

Step-by-step explanation:

Locations:

P = 0.30

Q = 1.10

R = 2.80

S = 4.40

Statements:

A. P + Q > R

B. P > S - Q

C. S > R + Q

Find the correct statement:

P + Q > R

0.30 + 1.10 > 2.80

1.40 > 2.80

This statement is incorrect

P > S - Q

0.30 > 4.40 - 1.10

0.30 > 3.30

This statement is incorrect

S > R + Q

4.40 > 2.80 + 1.10

4.40 > 3.90

This statement is correct

Therefore, the correct statement is S > R + Q

Hope this helps!

Answer:

19

Step-by-step explanation:

A' represents everything out A

B' represents everything out B

C' represents everything out C

So only the outside is left hope this helps

Answer:

-0.03

Step-by-step explanation:

\(3^{-3}=\frac{1}{3^3}\\=-\frac{1}{3^3}\\3^3=27\\=-\frac{1}{27}\\= -0.03\)

The coordinates of the vertex B' is (2,3)

Given,

The vertices of triangle ABC are

A = (-4,4)

B = (-2,3)

C = (-5,2)

and, reflected across the y-axis to produce the image of triangle A'B'C'

To find the coordinate of the vertex B'

Now, According to the question

For reflection across y-axis, the rule is:

(x, y) → (-x, y)

So, the image of B is:

(-2, 3) → (-(-2), 3)

(-2,3) → (2, 3)

Hence, The coordinates of the vertex B' is (2,3)

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We can clearly see that the area must be more than \($\frac{8 \pi}{3}$\), and the only such answer is \(3 \pi\).

Part of what Spot can reach is \($\frac{240}{360}=\frac{2}{3}$\) of a circle with radius 2, which gives him \($\frac{8 \pi}{3}$\). He can also reach two\($\frac{60}{360}$\)parts of a unit circle, which combines to give \($\frac{\pi}{3}$\). The total area is then \($3 \pi$\).

A circle is a two-dimensional closed shape in which the set of all points in the plane is equidistant from a particular point known as the "centre."

A Sphere is a three-dimensional object, whereas a Circle is a two-dimensional figure. All points in a circle are the same distance from its center along a plane, whereas all points in a sphere are equidistant from the center along any of the axes.

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For a two-factor independent-measures research study with 2 levels of factor A and 3 levels of factor B, a total of 6 separate samples or groups would be needed.

In a two-factor independent-measures research study, each combination of levels of the two factors (A and B) constitutes a separate condition or treatment group. In this case, there are 2 levels of factor A and 3 levels of factor B, resulting in 2 x 3 = 6 possible combinations of levels.

To obtain valid and independent measurements, each combination or condition should be represented by a separate sample or group. This means that for each combination of levels of factors A and B, we would need a distinct group of participants or subjects. Therefore, a total of 6 separate samples or groups would be needed to conduct the study.

Having separate samples for each combination of factor levels allows for the comparison of the effects of each factor independently as well as their interaction. By varying the levels of both factors and observing the responses in each group, researchers can assess the main effects of each factor and investigate any potential interaction effects between the two factors.

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The bearing is the angle measured clockwise from the north direction to a specified direction. To find the bearing of Town Y from Town B, we use the given information that Town B is located south 38 degrees east from Town Y. By subtracting this angle from 180 degrees, we find that the bearing is 142 degrees.

To determine the bearing, we need to find the angle between the north direction and the direction from Town B to Town Y.

Since Town B is located south of Town Y, the bearing will be a southern direction. The bearing angle can be calculated as 180 degrees minus the given angle, which is 38 degrees.

Therefore, the bearing of Town Y from Town B is 180 - 38 = 142 degrees.

In conclusion, the main answer is that the bearing of Town Y from Town B is 142 degrees.

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That is a parabola.

All domain of a parabola are, (-∞,∞).

The range would be, (-∞, 0]

Question seem incorrect because 60%,50% and 20% sum up to more than a 100% therefore we've made a little correction

Answer:

0.8

Step-by-step explanation:

Probability = number of favorable outcomes/number of outcomes

Given that 30% are entertained by reading books

50% are entertained by watching TV

20% are entertained by reading books and watching TV

The probability that a person will be entertained by books or TV =

30/100+50/100= 3/10+5/10

=8/10

=0.8

Complex numbers are represented on a cartesian coordinate system with a horizontal real axis and a vertical imaginary axis.

Any number that can be expressed as a+bi, where i is the imaginary unit and a and b are the real numbers, is a complex number. The number is made up of two parts: real part (a) and imaginary part (b).

Just like we can use the number line to visualize a set of real numbers, we can use the complex plane to visualize a set of complex numbers. The complex plane consists of two number lines intersecting at a right angle at the point (0,0)(0,0)left parenthesis, 0, comma, 0, right parenthesis.

The horizontal number line (what we know as the xxx-axis on a Cartesian plane) is the real axis. The imaginary axis is the vertical number line (the yyy-axis on a Cartesian plane).A point in the complex plane can represent every complex number.

For example, consider the number 3-5i3−5i3, minus 5, i. This number, also expressed as 3+(-5)i, has a real part of 3 and imaginary part of -5. The location of this number on the complex plane is the point that corresponds to 3 on the real axis and -5 on the imaginary axis.

So the number 3+(-5) corresponds with the point (3,-5). In the general complex number, a+bi corresponds to the complex plane's point(a,b).

Hence, complex numbers are represented on a cartesian coordinate system with a real horizontal axis and an imaginary vertical axis.

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