Which numbered choice represents the solution to this system?

y=2x+4
-6x+3y=12

1) (2,8)
2) (-3,-2)
3) (0,4)
4) All are solutions.

An angle is produced at the point where two or more lines meet. Thus the value of LP required in the question is approximately 14.

Two lines are said to be perpendicular when a measure of the angle between them is a right angle. While parallel lines are lines that do not meet even when extended to infinity.

From the question, let the length of LP be represented by x.

Thus, from the given question, it can be deduced that;

LM ≅ PN = 20

KP = KN - PN

    = 30 - 20

KP = 10

LP = x

Also,

<MLP is a right angle, so that;

< KLP = < KLM - <PLM

         = 126 - 90

<KLP = \(36^{o}\)

So that applying the Pythagoras theorem to triangle KLP, we have;

Tan θ = \(\frac{opposite}{adjacent}\)

Tan 36 = \(\frac{10}{x}\)

x = \(\frac{10}{Tan 36}\)

  = \(\frac{10}{0.7265}\)

x = 13.765

Therefore the side LP ≅ 14.

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The option a "The chi-square test for independence" is correct.

In the given question we have to find, a test of a single population and is to determine if there is an association between two characteristics of that population.

The given options are

A) The chi-square test for independence

B) Pearson product moment test

C) The chi-square test for homogeneity

D) Goodness-of-fit test

E) Welch’s t test

As we know that;

When a categorical variable has more than two levels, a chi-square test can be performed. A one proportion z test may be performed if there are precisely two categories. There must be no overlap between those category variable's levels. To put it another way, every situation must fall into exactly one group.

So, the chi-square test for independence is correct answer.

Option (B) and (E) are two-sample tests.

(C) involves two attributes.

(D) Doesn't check association.

Hence all these are incorrect.

So the option a "The chi-square test for independence" is correct.

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Here, we are required to determine how many perfect cube divisors 160,000 has.

160,000 has three(3) perfect cube divisors namely;. 8, 8 and 125

To determine how many perfect cube divisors 160,000 has;

We first need to highlight the factors of 160,000 as follows;

(2 × 2 × 2) × (2 × 2 × 2) × 2 × 2 × (5 × 5 × 5) × 5

As such, the product of numbers in each bracket yield a perfect cube; the expression above then becomes;

2 × 2 × 5 × 8 × 8 × 125.

Therefore, 160,000 has three(3) perfect cube divisors namely;. 8, 8 and 125

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Answer:

260

Step-by-step explanation:

5×20=100

So 13 × 20

because 5 percent of the collection is 13 so it is 260.

Answer:

Kerri

calculate z scores z= (x - xbar)/stdev

Kerri = 1.7

Cade = .7

Vincent = 1

Step-by-step explanation:

The formula used to calculate the variance of a set of data is Variance = \(s^2\)=1n−1n∑i=1(xi−¯x\()^2\).(Option-A)

To calculate the variance, each data point is subtracted from the mean, squared, and then added together. This gives the sum of the squared deviations from the mean. This sum is then divided by the total number of data points to get the average squared deviation from the mean, which is the variance.

Variance is a measure of the spread or variability of a set of data. It is useful in statistical analysis to understand how much the data points differ from the mean, and to compare different sets of data. Lower variance values indicate that the data is more tightly clustered around the mean, while higher variance values indicate that the data is more spread out.(option-A)

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Answer:

36

Step-by-step explanation:

The shaded region will be the universal set excluding set A , set B and set C.

[A U B ]' = the region excluding the union of Set A and Set B.

C' = The region excluding the set c

[A U B ] ' ∩ C ' = Universal set excluding Set A , Set B and Set C.

The shaded region is given in the below image.

Hence, the shaded region will be the universal set excluding set A , set B and set C.

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The first five terms of the given sequence are:

C: 18, 30, 42, 54, 66

The formula for the nth term of an arithmetic sequence is expressed as:

aₙ = a + (n - 1)d

where:

a is first term

d is common difference

n is number of term

The formula for the sequence is 12x + 6. Thus:

First term = 12(1) + 6 = 18

Second term = 12(2) + 6 = 30

Third term = 12(3) + 6 = 42

Fourth term = 12(4) + 6 = 54

Fifth term = 12(5) + 6 = 66

Thus, the sequence is : 18, 30, 42, 54, 66

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Answer:

-8x+35=19

-8(2)+35=19

-8×2= -16

-16+35=19.

Answer:

x=2

Step-by-step explanation:

19=-8x+35

subtract 35 from 19

-16=8x

divide -16 by -8

x=2

Answer:

i would say about 33 books in total from tuesday to wednesday

Step-by-step explanation:

The labeling of bases and height in a trapezium is not fixed and can vary based on the context or problem. It doesn't matter where they are on the trapezium, as long as they are clearly defined and consistent within the given situation.

In a trapezium (or trapezoid), the labeling of the bases and height is not fixed or standardized. It can vary depending on the context or the specific problem being considered. However, there are a few general guidelines to keep in mind when labeling a trapezium.

Bases: The trapezium has two parallel sides, often referred to as the "top base" and the "bottom base." The bases are usually labeled based on their relative lengths or position in the trapezium. The longer parallel side is commonly referred to as the "top base," while the shorter parallel side is referred to as the "bottom base." However, this is not a strict rule and can vary depending on the problem or preference.

Height: The height of a trapezium is the perpendicular distance between the bases. It is generally labeled as a vertical line segment connecting the bases. The placement of the height is not fixed, and it can be drawn from any point on the top base to any point on the bottom base, as long as it forms a perpendicular line. The height is usually labeled with the symbol "h" or sometimes "x" or "y" depending on the context.

It's important to note that the labeling of the bases and height is primarily for communication and clarity. As long as the labeling is consistent and clearly defined within the given problem or context, it does not have to conform to any specific arrangement or be in a rectangular shape. The key is to ensure that the labels are clearly understood and can be used to calculate the desired quantities or solve the problem at hand.

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Answer:

0.666 miles

Step-by-step explanation:

2 miles divide 3

=0.666

The term "isometric" has the Greek roots "isos," which means "same," and "metron," which means "measure." The definition of an isometric transformation is one in which the original figure and its transformed equivalent have the same shape, size, and orientation.

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The sale price of the shoe is given as follows:

P3,436.

The sale price of the shoe is obtained applying the proportions in the context of the problem.

The initial price is of:

P 4,295.

The shoe is sold at a discount of 20%, meaning that the sale price is 80% of the initial price, and the value is given as follows:

0.8 x 4295 = P3,436.

The problem asks for the selling price of the shoe.

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Answer:

Step-by-step explanation:

b

Answer:

which means  each day kathy swims ≥ 6 laps

Step-by-step explanation:

Answer:

The answer is "\(\bold{\theta= 70.53^{\circ}}\)"

Step-by-step explanation:

The given value:

\(8x+8y+8z = 1\ and \ 8x-8y+8z = 1\)  

When the normal vectors are in the plane:  

\(n_1 = < 8,8,8 > \ and \ n_2 = < 8, -8, 8>:\)

Because the two variables really aren't proportional to each other and the wings are not parallel.  

Let us just find that two vectors' dot product.

\(n_1 \cdot n_2 =<8,8,8> < 8,—8,8>\\\\ = 64-64+ 64 \\\\ = 64 \neq 0\)

Therefore, we won't find that angle between both the given planes as parallel.

\(\cos \theta = \frac{n_1 \cdot n_2}{|n_1||n_2|}\\\\\cos \theta =\frac{64}{\sqrt{192} \sqrt{192}}\\\\\cos \theta =\frac{64}{8\sqrt{3} 8\sqrt{3}}\\\\\cos \theta = \frac{1}{3}\\\\ \theta = 70.53^{\circ}\)

It is required to know the orientation of one plane relative to the other.

The angle between the planes is 70.5°.

The given planes are

8x + 8y + 8z = 1

8x − 8y + 8z = 1

Parallel

\(\dfrac{8}{8}=\dfrac{8}{-8}=\dfrac{8}{8}\\\Rightarrow 1\neq -1\neq 1\)

The planes are not parallel.

Perpendicular

\(8\times 8+8\times -8+8\times8=64\neq 0\)

The planes are not perpendicular as dot product is not 0.

Finding angle

\(\theta=\cos^{-1}\dfrac{8\times 8+8\times -8+8\times8}{\sqrt{8^2+8^2+8^2}\sqrt{8^2+(-8)^2+8^2}}\\\Rightarrow \theta=\cos^{-1}\dfrac{1}{3}\\\Rightarrow \theta=70.53^{\circ}\)

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By looking at the behavior of the derivative we can conclude that the graph of the function is:

if you divide "1" into two equal parts, each part would be 0.5. If you divide it into four equal parts, each part would be 0.25.

The concept of "1" in mathematics typically represents a whole unit or a single entity. However, your question about how many parts "1" equals to requires clarification. If you are referring to dividing a whole into parts, then "1" can be divided into any number of parts, as long as each part is equal.

For instance, if you divide "1" into two equal parts, each part would be 0.5. If you divide it into four equal parts, each part would be 0.25, and so on. In this context, "1" can be divided into an infinite number of parts, depending on the desired level of precision or subdivision.

On the other hand, if you are referring to expressing "1" as a fraction or a ratio, it can be written as 1/1 or 1:1, indicating that there is one part in total, and that one part is the whole itself.

In this case, "1" is not divided into multiple parts but represents the entirety of a single unit.

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Answer:

25.9 m

Step-by-step explanation:

Add them all together.

Answer:

Step-by-step explanation:

\(\bf \left( \dfrac{-11}{2} * +3 \right) -2*\left(\dfrac{11}{4}x-\dfrac{5}{2} \right) =\left( \dfrac{-33}{2} \right) - 2*\dfrac{11}{4}x - (-2) * \dfrac{5}{2}\\\\\\\)

                                                   \(\bf = \dfrac{-33}{2}-\dfrac{11}{2}x + \dfrac{10}{2}\\\\\\ = \dfrac{-33-11x+10}{2}\\\\\\ = \dfrac{-23-11x}{2}\)

Answer:

18.22

Step-by-step explanation:

Answer:

66.5 in or 5.5 ft (rounded)

Step-by-step explanation:

Answer:

5 ft    6 1/2 inches

Step-by-step explanation:

6 1/4 ft

1/4 ft is 3 inches

6 ft 3 inches

Subtract 8 1/2 inches

6 ft  3 inches

-      8  1/2 inches

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

borrow from the ft  ( 1 ft = 12 inches)

5 ft  3+12 inches

-      8  1/2 inches

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

5 ft  15 inches

-      8  1/2 inches

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

5 ft    6 1/2 inches

Answer:

-4 + 32i

Step-by-step explanation:

use the distributive property to multiply

remember: i^2 = 1

(4 - 6i)(-4 + 2i)

-16 + 8i + 24i - 12i^2

-16 + 32i - 12(- 1)

-16 + 32i +12

-4 + 32i

Answer:

4 - (6 * i)) * ((-4) + (2 * i)) =

-4 + 32 i

Step-by-step explanation:

The trigοnοmetric equatiοn we can use tο find x is x = 30 tan(25)

Assuming the cοnveyοr belt is leaning against the building in a straight line, we can use trigοnοmetry tο find x.

Here, θ is the angle between the grοund and the cοnveyοr belt, and x is the distance frοm the base οf the building tο where the cοnveyοr belt tοuches the grοund.

Using trigοnοmetry, we knοw that:

tan(θ) = οppοsite/adjacent

In this case, the οppοsite side is x and the adjacent side is 30 feet, sο we can write:

tan(25) = x/30

Sοlving fοr x, we get:

x = 30 tan(25)

Sο the trigοnοmetric equatiοn we can use tο find x is:

x = 30 tan(25)

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Answer:

30 : 11

Step-by-step explanation:

Length : Width

    7.50 :  2. 75

    750  : 275

30 x 25 : 11 x 25

       30 : 11

Answer:

2nd one is the best division