Write a function describing the relationship of the given variables.

A, varies directly with, r, and when r = 4, A = 8

A=______

The measure of PQ in the given triangle is 24.

What is triangle?

PQ = ST

7x-2 = -2x+32

7x + 2x = 32 + 2

9x = 34

x = 34/9

The measure of PQ:

PQ = 7x-2

= 7(34/9) - 2

= (238 - 18) / 9

= 24.4

PQ ≅ 24

Hence, the measure of PQ in the given triangle is 24.

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The graph of the proportional relationship represented by the equation y = 7.5x is The graph is a line that goes through points (0, 0) and (1, 7.5)

A linear function consists of functions where the variables has exponents of 1.

The graph of linear functions is a straight line graph and the relationship is expressed in the form.

y = mx + c

definition of variable to suit the problem

y = output variable

m = slope

x = input variable

c = y intercept

considering the given equation y = 7.5x.

c = 0

hence the graph passed through (0, 0)

substituting x = 1 gives y = 7.5 hence (1, 7.5) is another point

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The correct answer is c) iii only as statement 1 and statement 2 are false.

What do mean and standard deviation tell us?

In statistics, the measurement of variability known as the standard deviation (SD) is frequently utilized. It demonstrates how different things are from the norm (mean). While a high SD shows that the data are dispersed throughout a wide range of values, a low SD suggests that the data points tend to be close to the mean.

What is relationship between mean and standard deviation?

The standard deviation is a measure that summarizes how far away from the mean each observation is. The positive would exactly balance the negative if the discrepancies themselves were totaled together, making their aggregate equal to zero. The squares of the discrepancies are then added as a result.

What is median?

The value that, when a dataset is arranged, falls exactly in the middle is the median. It is a measure of central tendency that distinguishes between the values' lowest and maximum 50%. Depending on whether you have an odd or an even number of data points, the processes for calculating the median change.

Statement 1: False, it only works if distributiion is syummetric, for non- symmetric distribution, median is not unbiased estimator population in mean.

Statement 2: False standard deviation is not equal to IQR, and is heavily influenced by sample mean and outliers.

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Answer:

see attachment

Step-by-step explanation:

Answer:

2sin²0 + 2sin0 - 1/2 = 0

(2sin0 + 1)(sin²0 - 1/2)= 0

2sin0 + 1 = 0 or sin²0 - 1/2 = 0

2sin0 = -1 or sin0 = ±1/√2

Answer:

increase of 100%

Step-by-step explanation:

50 cents to 1 dollar is an increase.

The percent increase can be calculated by dividing the increased amount by the original amount.

$1.00 - $0.50 = $0.50 increase

% increase = 100%

ABCD is a rhombus and side AE Is congruent to EC. Then triangle AEB is congruent to CEB.

A rhombus is one type of parallelogram and has 4 sides and 4 vertices.

Every side is equal in length and opposite angles are equal.

Given that the side AE is congruent to EC of rhombus.

That means, AE ≅ EC.

And the diagonals of rhombus bisects each other.

Both the triangle AEB and triangle CEB share the same side which is BE.

That means BE ≅ BE, by the reflexive property.

And the sides AB and BC are the sides of rhombus.

So, AE ≅ BC.

Therefore, if ABCD is a rhombus and side AE Is congruent to EC. Then triangle AEB is congruent to CEB.

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Answer:

A. 20

Step-by-step explanation:

300 ÷ 2.5= 120

So

50÷2.5 = 20

The circumference of the circle with the dimensions radius = 6 and π = 3.14 is 37.68

The circumference of a circle refers to the line that bounds a circle or other two-dimensional figure.

Circumference of a circle = 2πr

Where,

Circumference of a circle = 2πr

= 2 × 3.14 × 6

= 37.68

Therefore, the circumference of the circle is given by 37.68

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Since the time is 0.24 hour. Yes, it takes less than a quarter of an hour to fill the container

Given: A container is a hemisphere of radius 30cm

Sand fills the container at a rate of 4000 cm³ per minute

A hemisphere is half a sphere. Thus:

The volume of a hemisphere = 1/2 × 4/3 πr³ = 2/3 πr³

The volume of a hemisphere = 2/3 × π × 30 = 56548.67 cm³

Rate = Volume / Time

Time = Volume/Rate

Time =  56548.67 /4000 = 14.14 minutes

In hours: Time = 14.14/60 = 0.24 hour

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Answer:

The answer to your question is,

B) It isn’t true that corresponding cross-sections have the same area.

Step-by-step explanation:

They have the same areas and the same heights. but the corresponding cross-section is not the same

{The top of the first figure is a point, but the second one is a flat}

I hope this helps :)

Answer:

B)  It isn’t true that corresponding cross-sections have the same area.

Step-by-step explanation:

Cavalieri's principle

If two three-dimensional figures have the same height and the same cross-sectional area at every point along that height, they have the same volume.

From inspection of the given diagram:

The cross-sectional area at every point along the height is not the same in both figures.

To prove parallelograms is a parallelograms we have show that, diagonals cut each other in half, and one angle adds to both following angles .

One particular type of quadrilateral that is created by parallel lines is a parallelogram. A parallelogram can have any angle between its adjacent sides as long as its opposite sides are parallel.

The sum of all the sides' lengths determines a rhombus' perimeter. A rhombus's perimeter is equal to four times the length of each side because all of its sides are equal. A diamond's perimeter is given in 4x units, for instance, if one of its sides is x units.

P=4a

The two opposing side pairs must be parallel, the two opposite side pairings must coincide, the two opposite angle pairs must coincide, the diagonals must cut each other in half, the first angle must add to both the following angles, and one set of opposing sides must be both parallel AND congruent. These are the six basic properties of parallelograms.

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Answer:

x = 8

y = 2

Step-by-step explanation:

Answer:

To find the dimensions of a rectangle

Step-by-step explanation:

perimeter=302

let width=x

length=x+47

p=2(L+W)

302=2(x+x+47)

302=2(2x+47)

302=4x+94

subtracting 94 from the other side we have

302-94=4x

208=4x

x=52

length=99

width=52

Answer:

Step-by-step explanation:

X^-3=1/343

X^-3=1/7^3

X^-3=7^-3

Since the powers are equal, the bases should also be equal.

Therefore, X=7

By using the concept of vector, it can be calculated that

28) First option is correct

29) Fourth option is correct

What is vector?

Anything that has both magnitude and direction and follow the vector addition law is called vector.

28) The vectors are

[tex]\vec{v} = -2i-5j,[/tex]

[tex]\vec{w} = -3i+j[/tex]

[tex]\vec{v}. \vec{w} = (-2i-5j).( -3i+j) = 6 - 5 = 1\\|\vec{w}|^2 = (-3)^2+(1)^2 = 9 + 1 = 10\\\vec{v_1} = \frac{1}{10}( -3i+j) = \frac{-3}{10}i+\frac{1}{10}j[/tex]

[tex]\vec{v_2} = (-2i-5j) - (-\frac{3}{10}i - \frac{1}{10}j)\\\vec{v_2}= (-2+\frac{3}{10})i+(-5 - \frac{1}{10}j)\\\vec{v_2}=-\frac{17}{10}i - \frac{51}{10}j\\[/tex]

First option is correct

29) P = (1, 2) and Q = (-6, -1)

Position vector = (-6-1)i + (-1-2)j = -7i - 3j

Fourth option is correct

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Median won't change, however Mean will fall by 180.

By summing all the numbers in a data collection and dividing by the total number of values in the set, one may get the mean (average) of the data set. When a data collection is sorted from least to largest, the median represents the midpoint value.

African elephants total 555 in number.

Elephants had a 3800 kg average mass.

Elephants had a 3600 kg median mass.

Lola, the elephant that was the smallest, weighed 2700 kg.

Later, Lola became really ill and lost a lot of weight, reaching a mass of 1800 kg.

What effect will Lola's weight loss have on the mean and median as well as Currently, the median is 3600 and the lowest is 2700.

now 2700 becomes 1800

so Median remains the same as 3600

No change in Median

The mean mass of the elephants was  3800 kg

=> total weight = 5 x 3800 = 19000 kg

2700 kg becomes 1800 kg

Hence new total mass = 19000 - 2700 + 1800 = 181000 kg

New Mean = 18100/5   = 3620  kg

Mean reduced by 3800 - 3620  = 180 kg

No change in Median weight

Mean reduced by 180 kg

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Answer: 68

Step-by-step explanation:

Angles in a triangle add to [tex]180^{\circ}[/tex], meaning that [tex]m\angle TRS +m\angle TSR=136^{\circ}[/tex].

Furthermore, since [tex]\triangle TSR[/tex] is isosceles, [tex]m\angle TRS=m\angle TSR[/tex].

Therefore, [tex]m\angle TSR=68^{\circ}[/tex].

Answer:

[tex]W=\frac{A}{L}[/tex]

Step-by-step explanation:

Divide both sides of the equation by [tex]L[/tex].

Answer:

86

Step-by-step explanation:

If you did 1,022 divided by 12, you would get something crazy like 85.16666666666. So round up.

Answer:

Quotient: 66

Remainder: 1

Step-by-step explanation:

133/2 = 66.5

66.5 =

66 + 0.5 =

66 + 1/2 = 66 1/2

1/2 * 2 = 1  ==> Remainder: 1

Whole number : 66

Quotient: 66

Remainder: 1

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The top 18 percent of scores fall within two standard deviations of the mean.

Publicly recognized refers to something that is well-known or acknowledged by the public or by a large segment of the population. This could include a famous person, a popular business, or an important event or achievement. Public recognition is often seen as an indicator of success, as it shows that the person or thing being recognized has achieved something noteworthy or has had a positive influence on the public. Examples of publicly recognized things include awards, honors, and other achievements.

Assuming a normal distribution, a student needs to score at least two standard deviations above the mean to be publicly recognized. This is because the top 18 percent of scores fall within two standard deviations of the mean. This can be expressed mathematically as:
P(x > μ + 2σ) = 0.18
where μ is the mean and σ is the standard deviation.

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Answer:

y=1, x=1

Step-by-step explanation:

no need for step by step cause i know

The required anti derivative of given function is  -(ky^2)/2 + 77ky.

Anti-differentiation or integration is the converse interaction to separation. For instance, if f (x) = 2x, we realize that this is the subordinate of f(x) = x^2.

We have,

dy/dx +ky - 77k = 0

dy/dx = -ky + 77k

Integrate with respect to x

∫dy/dx =  ∫(-ky + 77k)

∫dy/dx = -∫ky +∫77k

y = -(ky^2)/2 + 77ky

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The required antiderivative is   [tex]y=e^{-(kx+c)} +77[/tex]

What is antiderivative?

In calculus, a differentiable function F whose derivative is identical to the original function f is known as an antiderivative, inverse derivative, primitive function, primitive integral, or indefinite integral of a function f. F' = f can be used to represent this.

[tex]\frac{dy}{dx} = 77k - ky\\\\dx=\frac{dy}{77k-ky} \\\\dx = \frac{dy}{77-y} \times \frac{1}{k} \\\\kdx = \frac{dy}{77-y} \\\\-\frac{dy}{y-77} =kdx\\\\log(y-77)=-(kx+c)\\\\y=e^{-(kx+c)} +77[/tex]

Hence, The required antiderivative is   [tex]y=e^{-(kx+c)} +77[/tex]

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Answer:

Step-by-step explanation:

d. 0 to 4 seconds, None, 4 to 6 seconds.

Based on the data in the table, the speed of the car is increasing for the interval of time from 0 to 4 seconds. After 4 seconds, the speed remains constant at 23 mph for the remainder of the time period. Therefore, the speed is not decreasing at any point in the given time interval.

The value of y that satisfies the equation is 41.

What is the arithmetic operation?

Arithmetic operations involve the study of numbers, the operation of numbers that are useful in all the other branches of mathematics. It basically comprises operations such as Addition, Subtraction, Multiplication, and Division.

To solve this equation for y, you can divide both sides by 4:

4y/4 = 164/4

This simplifies to:

y = 41

Hence, the value of y that satisfies the equation is 41.

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well, as you already know, to check if a function is EVEN, we simply check what's f( -x ), if f( -x ) = f( x ), then voila!!.  and if f( -x ) = -f( x ), then oddly enough, is an ODD function.

well, let's plug in " -x " to see what we get anyway

[tex]f(x)=-5x^2 + |2x|\implies \boxed{f(x)=-5x^2 + 2x} \\\\[-0.35em] ~\dotfill\\\\ f(-x)=-5(-x)^2 + |2(-x)|\implies f(-x)=-5(-x)(-x) + |-2x| \\\\\\ f(-x)=-5(+x^2) +2x\implies \boxed{f(-x)=-5x^2 + 2x}~\hfill \stackrel{\textit{\LARGE Even}}{f(-x)=f(x)}[/tex]

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

The value of x is 6.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

4(x + 11/3) = 9(2/3)

Divide both sides by 4.

x + 11/3 = 29/3

Subtract 11/3 on both sides.

x = 29/3 - 11/3

x = (29 - 11) / 3

x = 18/3

x = 6

Thus,

The value of x is 6.

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