\( {( \sqrt{3} )}^{x + y}  = 9 \\ {( \sqrt{2} )}^{x - y}  = 32\)



find the value of 2x + y.​

Answer:

-7y > 161

7y < -161

y < -23

7y > -161

y > -23

So, your answer is: -7y > 161 is equal to y < -23, and 7y > -161 is equal to y>-23.

Let me know if this helps!

The number of regions created when constructing a Venn diagram with three overlapping sets is 8.

In a Venn diagram, each set is represented by a circle, and the overlapping regions represent the elements that belong to multiple sets.

When three sets overlap, there are different combinations of elements that can be present in each region.

For three sets, the number of regions can be calculated using the formula:

Number of Regions = 2^(Number of Sets)

In this case, since we have three sets, the formula becomes:

Number of Regions = 2^3 = 8

So, when constructing a Venn diagram with three overlapping sets, there will be a total of 8 regions formed.

Each region represents a unique combination of elements belonging to different sets.

These regions help visualize the relationships and intersections between the sets, providing a graphical representation of set theory concepts and aiding in analyzing data that falls into multiple categories.

Therefore, the correct answer is 8.

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12) There were about 557 principals in attendance. 13) Option A: The college will have about 480 students who prefer cookies. 14) Option C: bar graph, title favorite sport and the x axis labeled sport and the y axis.

The relationship between two quantities that are measured on the same scale and in the same units is known as a percentage. The relative size or magnitude of one thing in comparison to another is represented by proportions, which are frequently stated as ratios, fractions, or percentages. For instance, if there are 8 girls and 12 boys in a class, the girl-to-boy ratio is 8:12, or 2:3, which indicates that there are 3 guys for every 2 girls. Statistics, geometry, and physics are just a few of the mathematical and scientific disciplines that use proportions. Proportions are frequently used in statistics to describe the distribution of a population or a sample.

12) For the number of principals in conference we set up a proportionality with total people as follows:

We know that, 52 principals out of 70 people thus:

52/70 = x/750

Now,

x = (52/70) * 750

x = 557.14

Hence, we can predict that there were about 557 principals in attendance at the conference.

13) Given that, out of 225 students 27 prefer cookies thus,

27/225 = 0.12

That is 12% students like cookies.

Now, for the total number of students we have:

0.12 * 4000 = 480

Thus, option A: The college will have about 480 students who prefer cookies.

14) For the collected data the best representation is option C: bar graph with the title favorite sport and the x axis labeled sport and the y axis labeled number of students, with the first bar labeled basketball going to a value of 17, the second bar labeled baseball going to a value of 12, the third bar labeled soccer going to a value of 27, and the fourth bar labeled tennis going to a value of 44.

15) For the given description of the line plot the median is:

For Bus 47 = 16

For Bus 18 = 13

The faster bus is Bus 47, with a median of 16.

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Answer: One solution, I think

Step-by-step explanation: If you combine like terms, x=4

Answer:

W double u or v

Step-by-step explanation:

In triangle $abc$, let angle bisectors $bd$ and $ce$ intersect at $i$. the line through $i$ parallel prove that  $AB < AM < AN < AC$.

To solve this problem,  use the angle bisector theorem and some geometric properties of triangles. Let's begin.

Given: Triangle $ABC$ with angle bisectors $BD$ and $CE$ intersecting at $I$. The line through $I$ parallel to $BC$ intersects $AB$ and $AC$ at $M$ and $N$, respectively. Also, $AB < AC$.

to prove: $AB < AM < AN < AC$.

Proof:

Angle Bisector Theorem:

According to the angle bisector theorem,

$frac{BD}{DC} = frac{AB}{AC} quad$ (1)

Parallel Lines:

Since line $MI$ is parallel to $BC$,

$angle MIB = angle IBC quad$ (2)

Angle Bisector Property:

From the angle bisector property,

$frac{AB}{BD} = frac{AC}{DC}quad$ (3)

Combining Equations (2) and (3):

$frac{AB}{BD} = frac{AC}{DC} =frac{AB}{MI} quad$ (4)

Using Equations (1) and (4):

$frac{BD}{DC} = frac{AB}{MI}$

From Equation (5):

$frac{AB}{MI} + 1 = frac{AB}{BD} + 1$

Simplifying Equation (6):

$frac{AB + MI}{MI} = frac{AB + BD}{BD}$

Using Equation (7):

$frac{AM}{MI} = frac{AB}{BD} quad$ (8)

Comparing Equations (1) and (8):

$frac{AB}{AC} = frac{AB}{BD} = frac{AM}{MI}$

Since $AB < AC$, it follows that $frac{AB}{AC} < 1$. Thus, $frac{AM}{MI} < 1$.

From Equation (10),  $AM < MI$.

Using the same logic,  prove $MI < AN$.

Finally, since $AM < MI < AN$, it follows that $AB < AM < AN < AC$, as required.

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Type I error is We conclude that the mean is not 34 years when it really is 34 years. The correct option to this question is C.

Rejecting the null hypothesis when it is in fact true is a Type I mistake. It entails drawing conclusions about outcomes that are statistically significant when, in fact, they were just the consequence of chance or unrelated causes.

The significance level you select (alpha or ) determines the likelihood that you will make this mistake. You determined that figure at the start of your research to determine the statistical likelihood of getting your results (p-value).

The typical significance level is 0.05 or 5%. If the null hypothesis is accurate, your results only have a 5% chance or less of occurring.

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Answer:

135

Step-by-step explanation:

\(\dfrac{x}{3}-8=37 \\\\\\\dfrac{x}{3}=45 \\\\\\x=45\cdot 3=135\)

Hope this helps!

A decile rank is a single number on a scale of 1 to 10, which corresponds to a percentage.

On a scale from 1 to 10, decile rank is a single number that represents a percentage, typically ten percentage points. A decile of one would indicate the top 10%, whereas a decile of five may indicate the top 50%. This kind of ranking may be applied to evaluate investments' quality or school rankings.

The decile rank is a comparison rank in which accomplishments are compared to those of related objects. For instance, in mutual funds, each fund would be ranked according to how it performed in comparison to other funds. Therefore, a decile rank of two would typically indicate that the mutual fund had a rate of return that was in the top 20%. It could be viewed as a more advantageous investment than a mutual fund.

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Answer: $7.25 at part-time job

$9.00 every time lawn mowed

so he would get 33.33 day so we will just say 33 times to get 300 dollars if he gets $9 for mowing. And 41.37 hours to get $300 and he would have to use x and y graph to find the boundary line.

Step-by-step explanation:

Answer:

xz=cb            = 45/60 = .75

zy=ab            = 30/40 = .75

xy=ac             = 37.5/50 = .75

Step-by-step explanation:

all lines when put into ratio format show .75 scale factor big to little triangle side lengths.

wAnswer:

e

Step-by-step explanation:

The probability of the event not happening is 5/83.

Here, probability refers to the likelihood of a given event occurring and that the inequality f(x) > 3g(x) holds for all x > 0.

If the probability of an event happening is 88/83, then the probability of the event not happening is 1 minus the probability of the event happening. This can be expressed as:

1 - 88/83

To simplify this expression, we can first find a common denominator for 1 and 88/83, which is 83/83:

83/83 - 88/83

-5/83

Therefore, the probability of the event not happening is 5/83.

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Answer:

All the ones without the equal signs.

x + 2

2x² - 1/2x

2x²

x/2

Step-by-step explanation:

An expression is the ones without equal signs and equations do.

Answer:

1, 3, 5, 6 (estimate)

Step-by-step explanation:

expressions do not have an equal sign (=).

a. From fastest to slowest, the speeds of the balls at the right ends of the tracks will depend on the curvature of the tracks.

If the tracks are of equal length but have different curvatures, the ball on the track with the least curvature will have the highest speed, followed by the ball on the track with the next least curvature, followed by the ball on the track with the most curvature.

b. From longest to shortest, the tracks in terms of the times for the balls to reach the ends will depend on the curvature of the tracks. If the tracks are of equal length but have different curvatures, the track with the most curvature will have the longest time for the ball to reach the end, followed by the track with the next most curvature, followed by the track with the least curvature.

c. From greatest to least, the tracks in terms of the average speeds of the balls will depend on the curvature of the tracks. If the tracks are of equal length but have different curvatures, the track with the least curvature will have the highest average speed, followed by the track with the next least curvature, followed by the track with the most curvature.

All the balls will have the same average speed on all three tracks if the track lengths are equal, but will have different speeds at the end of each track due to the different curvatures.

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Answer:

49% of the lights are on!

One common algorithm to merge k sorted lists into one sorted list with a time complexity of O(n LG k) is the "k-way merge" algorithm.

The algorithm's steps are:Create a min-heap and fill it with the first item from all k input lists.There will be k maximum elements in the min-heap.

But the min-heap is not completely full:

Add the minimum element to the output list after removing it from the min-heap.

Add the subsequent element from the list from which the minimal element was removed to the min-heap if it still contains items.

Get the output list back.Below is an analysis of this algorithm's time complexity:

The min-heap initialization process requires O(k) time.

Each element is added to and deleted from the min-heap exactly once after visiting each of the k input lists precisely once.

Hence, O represents the total number of operations carried out on the min-heap (n LG k).

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Answer:

9/4

Step-by-step explanation:

you can use photomath for questions like these :P

Answer:

2 1/4

Step-by-step explanation:

3/4 x 3 = 9/4 = 2 1/4

Hope that helps!

Answer:find the area i gaurntee once you do that you will start to get the problem

Step-by-step explanation:

Answer:

Volume of the cuboid = 1000cm³

Volume of the cuboid = length x breadth x height

= 25 x 5 x 8

= 1000cm³

Answer: 1000

Step-by-step explanation:

V = lenght×breadth×heighthe

V = 25×5×8

V = 1000

The function g(n) can be approximated by a growth rate of O(n log(n)).

To further explain why g(n) can be represented by O(n log(n)), let's analyze the equation n log(n² + 1) + n² log(n) = O(g(n)).

We can simplify the equation by factoring out the dominant term, which in this case is n^2 log(n). The equation becomes:

n² log(n) * (1 + 1/(n² + 1)) = O(g(n))

Now, let's focus on the expression (1 + 1/(n² + 1)). As n approaches infinity, the term 1/(n² + 1) becomes negligible compared to 1. Thus, we can approximate the expression as:

(1 + 1/(n² + 1)) ≈ 1

Substituting this approximation back into the equation, we have:

n² log(n) * 1 = O(g(n))

Simplifying further, we get:

n² log(n) = O(g(n))

This shows that g(n) must have a growth rate at least as fast as n² log(n) in order for the equation to hold. Among the given options, option b) O(n log(n)) satisfies this condition. Therefore, g(n) can be represented by O(n log(n)).

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Answer:

c. 141.7 in

Step-by-step explanation:

multiply the length value by 39.37

The expression 2^7 times 19 can be simplified by first evaluating the exponential term, 2^7, which is equal to 128. Therefore:2^7 times 19 = 128 * 19We can then evaluate the product of 128 and 19 using multiplication. When we do that, we get:2^7 times 19 = 2432Therefore, the choice that is equivalent to the expression 2^7 times 19 is 2432

The solution set to the given inequalities from the graph in the form (x,y) is (-1, 2)

In mathematics, inequality arises when two mathematical expressions or two numbers are compared that are not equal. Generally, inequalities may be either numerical or algebraic, or a mixture of both.

Linear inequalities require at least one linear algebraic expression, here the polynomial is of one degree and is compared with another algebraic expression of a degree less than or equal to 1.

In the given question, we are to graph the following linear inequalities

x + y > 1

-x + y < 3

The solution set to the given inequalities by plotting their graph shows that (x,y) is (-1, 2)

The points in each shaded region of the graph are:

(0, 3)  The point is a solution to either inequality

(0, 1)   The point is a solution to one of the inequality

(-3, 0)  The point is  not a solution to either inequality

(-1, 2)   The point is a solution to either inequality

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Answer:

84/B

Step-by-step explanation:

Angle measure 51 is vertical

45+51+A=180

A=84

Answer:

x = 0.64, -3.14

Step-by-step explanation:

See attached screenshot for calculations, explanation and a graph too.

Note that the text box you need to input the answer into has very specific formatting when there are 2 answers.

Answer:

b

Step-by-step explanation:

it rigth ;0

The characteristics of the rectangular pyramid you mentioned are as follows:

What is rectangular pyramid?

Base Dimensions: The pyramid's base is shaped like a rectangle and measures 12 inches by 9 inches.

Height: The pyramid is 15 inches tall when measured from its base to its apex (highest point).

Slant Height: The Pythagorean theorem can be used to determine the pyramid's slant height. The hypotenuse of a right triangle made up of the height, one of the base's sides, and half of the base's length (6 inches) is the slant height. It is possible to determine the slant height as follows:

slant height =\(√(height^2 + (base length/2)^2)\)

= \(√(15^2 + 6^2)\)

= \(√(225 + 36)\)

= \(√261\)

≈ 16.155 inches (rounded to three decimal places).

Volume: The volume of a rectangular pyramid can be calculated using the formula:

volume = \((base area * height) / 3\)

The base area is calculated by multiplying the length and width of the base rectangle:

base area = length * width

=\(12 inches * 9 inches\)

= \(108 square inches\)

Plugging in the values:

volume = \((108 square inches * 15 inches) / 3\)

= 540 cubic inches

The rectangular pyramid's volume is 540 cubic inches as a result.

Add the areas of the base and the four triangular faces to determine the surface area of a rectangular pyramid.

In this situation, 12 inches by 9 inches, or 108 square inches, is the base area, which is calculated as length times width.

(Base length * Height) / 2 can be used to determine each triangle's area. The areas of the triangle faces are as follows since the base length is 12 inches:

Face 1: \((12 inches * 15 inches) / 2 = 180 square inches\)

Face 2: \((9 inches * 15 inches) / 2 = 135 square inches\)

Face 3: \((12 inches * 15 inches) / 2 = 180 square inches\)

Face 4: \((9 inches * 15 inches) / 2 = 135 square inches\)

Adding up all the areas:

surface area = base area + 4 * area of triangular faces

= 108 square inches + 4 * (180 square inches + 135 square inches)

= 108 square inches + 4 * 315 square inches

= 108 square inches + 1260 square inches

= 1368 square inches

Therefore, the surface area of the rectangular pyramid is 1368 square inches.

Therefore the true statements about the rectangular pyramid are:

The base dimensions are 12 inches by 9 inches.

The height of the pyramid is 15 inches.

The slant height is approximately 16.155 inches.

The volume of the pyramid is 540 cubic inches.

The surface area of the pyramid is 1368 square inches.

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