Decide which of the given units would be the most appropriate to use for
a) the height of a building: kilometres, metres or centimetres?
b) the mass of a pen: grams, tonnes or kilograms?
c) the capacity of a paddling pool: millilitres or litres?

The length of the missing side (hypothenuse) is equal to 5

"Information available from the question"

Opposite side of the triangle(y) = 3

Adjacent side of the triangle (z)= 4

Hypothenuse side of the triangle = x

Pythagorean Theorem

This formula is used to find the missing side of a right angle triangle if two sides are given.

[tex]x^{2} =y^2+z^2[/tex]

Let's substitute the values into the formula and solve for the hypothenuse

[tex]x^{2} =3^2+4^2[/tex]

[tex]x^{2}[/tex] = 9 + 16

[tex]x^{2}[/tex] = 25

[tex]x=\sqrt{25}[/tex]

x = 5

The length of the missing side (hypothenuse) is equal to 5.

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The grandfather's age if he is 10 years more than thrice Kapil's age is

3x +10.

A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.

Variables are the name given to these symbols because they lack set values.

In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.

Given:

Kapil's age is m years.

His Grandfather is 10 years more than thrice Kapil's age.

Thrice Kapil's age = 3x

and, 10 years more than thrice Kapil's age = 3x + 10

Then, the age of Grandfather is

= 3x+ 10

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D) 110 = 16 + 10h

C) 16 = 110 – h

Step-by-step explanation:

Think about it. She NEEDS $110 but she only has $16. So now it's $110=$16 {or C}.

She can EARN the rest {H} by working her hours.

The rational function that is graphed below include the following: A. f(x) = 1/(x - 1)(x - 5).

In Mathematics, a rational function simply refers to a type of function  which is expressed as a fraction. This ultimately implies that, a rational function is composed of two (2) main parts and these include the following:

In order to graph any rational function, you should determine the values for which it is undefined. This ultimately implies that, a function is considered as undefined when the value of the denominator is equal to zero, which represents vertical asymptote lines.

Therefore, when x = 1, the rational function become undefined;

f(x) = 1/(x - 1)(x - 5)

f(x) = 1/(1 - 1)(x - 5)

f(x) = 1/0 (undefined).

Also, when x = 5, the rational function is undefined;

f(x) = 1/(x - 1)(x - 5)

f(x) = 1/(x - 1)(5 - 5)

f(x) = 1/0 (undefined).

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Answer:

36π cm^2

Step-by-step explanation:

area= πr^2

= 36π cm^2

The graph of y = G(x) consists of a semicircle and three line segments. The function G is defined and differentiable on the closed interval [-7, 5] and satisfies G(0) = 5.

A) G(3) = 4.5 and G(-2) = 4

B) The x-coordinates of the points of inflection are x = -3, x = 0 and x = 4. This is because the graph has three separate linear segments, each with a point of inflection at the junction between them.

The graph of y = G(x) consists of a semicircle and three line segments. The function G is defined and differentiable on the closed interval [-7, 5] and satisfies G(0) = 5.

A) To find G(3) and G(-2), we need to identify the y-coordinate of each point on the graph. The y-coordinate of G(3) is 4.5 and the y-coordinate of G(-2) is 4.

B) To find the x-coordinates of each point of inflection of the graph of y = G(x) on the interval -7 < x < 5, we need to identify the points where the graph changes direction. These points are located at the junction between each of the three linear segments. Therefore, the x-coordinates of the points of inflection are x = -3, x = 0 and x = 4.

the complete question is :

The Function G Is Defined And Differentiable On The Closed Interval [-7,5] And Satisfies G(0)=5. The Graph Of Y = G(X), The Derivative Of G, Consist A Semicircle And Three Line Segments, As Shown In The Figure Above. (A) Find G(3) And G(-2). (B) Find The X-Coordinate Of Each Point Of Inflection Of The Graph Of Y =G(X) On The Interval -7 < X < 5. Explain your reasoning.

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Answer:

$5111.76

Step-by-step explanation:

compounded daily means 365 times interest is compounded per year, so

A=4156x[tex](1+\frac{0.0345}{365}) ^{365x6}[/tex] ≈ 5111,76

Answer:

Original Number is 37

Step-by-step explanation:

Let

x = First digit

y = Second digit

x + y = 10

∴y = 10 - x

Original Number = 37

3 + 7 = 10

When reversed:

New Number is 36 more than the original Number:

37 + 36 = 73

∴New Number = 73

The measurements in millimeters of each folded leaflet are 210 mm by 99 mm.

millimetre (mm), also spelled millimetre, unit of length equal to 0.001 metre in the metric system and the equivalent of 0.03937 inch in the imperial system.

When an A4 sheet of paper is folded in thirds, it yields three equal sections with widths of 210/3 = 70 mm and heights of 297 mm. As a result, each folded leaflet will be 210 mm by 99 mm (since 297/3 = 99).

As a result, each folded leaflet measures 210 mm by 99 mm in millimetres.

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The functions y = 2 (1/5)^x - 5 and y = 4^x are compared as follows

                                  y = 2 (1/5)^x - 5             y = 4^x

Initial value:               2                                    1

base function:        1/5 = decay function       4 = growth function

Translation:             5 units down                    no transformation

A decay function is a mathematical function used in various fields such as physics, engineering, economics, and machine learning, to model the reduction or decline of a value over time.

It is a type of function that decreases at a rate proportional to its current value, so that it approaches zero as time progresses.

Decay function are exponential functions with the base function as

This is the opposite of growth function which has values greater than 1

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The absolute amount of the difference between the measured and real value, divided by the actual value, is multiplied by 100 to determine the percent inaccuracy.

1. Divorce the measured value from the true value.

2. Calculate the result's absolute value.

3. Subtract the true value.

4. Increase by 100.

A measure of how closely a measured value matches an actual value is called percent error. By taking the absolute difference between the measured and real values, dividing by the actual values, and multiplying by 100, it is determined. We may determine the percentage difference between our measured value and the real value using this calculation. For instance, the error would be 20% if the real value was 10 and the measured value was 8. It is determined in the following manner step by step: first, deduct the measured value from the real value, then calculate the absolute value of the outcome. Multiply by 100 after dividing the result by the actual value. Percent Error = |Measured Value - Actual Value| Actual Value x 100 is the formula for this problem.

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If today were January 1, 2023, then 80 days from today would be March 22, 2023. Keep in mind that the actual date that is 80 days from today will depend on the current date.

To determine the date that is 80 days from today, you can add 80 days to the current date.

As of my knowledge cutoff date of September 2021, the current date is irrelevant for today. However, I can tell you how to calculate the date that is 80 days from any given date.

Assuming you want to calculate 80 days from today's date, you would add 80 days to today's date. For example, if today were January 1, 2023, then 80 days from today would be:

January 1, 2023 + 80 days = March 22, 2023

So, if today were January 1, 2023, then 80 days from today would be March 22, 2023. Keep in mind that the actual date that is 80 days from today will depend on the current date.

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Answer:

A. 1809.6 cm²

Step-by-step explanation:

The formula for the surface area of a sphere is:

Surface Area = 4πr^2

where r is the radius of the sphere.

Substituting the given value of radius, r = 12cm, we get:

Surface Area = 4π(12)^2

= 4π(144)

= 576π

≈ 1809.6 cm² (rounded to the nearest tenth)

Therefore, the answer is (a) 1809.6 cm²

Answer:

[tex] \frac{5}{6} + \frac{5}{8} = \frac{4 \times 5 + 3 \times 5}{24} = \frac{20 + 15}{24} = \frac{35}{24} = 1 \frac{11}{24} [/tex]

Answer: 11.2 inch

Step-by-step explanation:

The maximum height of the rocket is 256 feet and the time it takes the rocket to reach this height is 4 seconds.

The rocket will be in the air for 8 seconds.

Option C is the correct answer.

A function has an input and an output.

A function can be one-to-one or onto one.

It simply indicated the relationships between the input and the output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

y = -16t² + 128t _____(1)

This can be assumed as an equation of a parabola.

i.e

y = ax² + bx

so,

a = -16 and b = 128

To find the maximum height of the rocket, we need to find the vertex of the parabola.

The vertex is given by the formula.

t = -b/2a

t = -128/(2 x -16)

t = 4

Substitute t = 4 in (1).

y = -16 x 4² + 128 x 4

y = 256 feet

So,

The maximum height of the rocket is 256 feet.

When the rocket is on the ground.

y = 0

-16t² + 128t = 0

t (-16t + 128) = 0

t = 0 or -16t + 128 = 0

t = 0 and -16t = 128

t = 0 and t = -8 (rejected)

Since the rocket is launched at t = 0,

The rocket will be in the air for 8 seconds.

i.e

8 - 0 = 8

Therefore,

The maximum height is 256 feet and it will be in 4 seconds.

The rocket will be in the air for 8 seconds.

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Answer:

x=166

Step-by-step explanation:

180-14= 166

x=166

The number of packages of hot dogs is 4 hot dogs.

The number of packages of hamburgers is 5 hamburgers.

In order to write a system of linear equations to describe this situation, we would assign variables to the number of packages of hot dogs and number of packages of hamburgers respectively, and then translate the word problem into algebraic equation as follows:

Since Mrs Vahey bought a total of 9 hot dogs or hamburgers, the linear equation to represent this is as follows:

x + y = 9

Additionally, hot dogs are $1.50 and hamburgers are $4, and she spent a total of $26;

1.50x + 4y = 26

Next, we would use an online graphing calculator to plot the above system of linear equations in order to determine the solution (point of intersection) as shown in the graph attached below.

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The questions for grade 7 math worksheets are typically prepared by math teachers, curriculum specialists, and educational publishers.

These professionals use their knowledge of math concepts and pedagogy to create questions that are appropriate for the grade level and aligned with educational standards.

Additionally, they may use feedback from students and other teachers to refine the questions and ensure they are effective for teaching and learning. It is important for the questions to be clear, accurate, and challenging in order to help students develop their math skills and prepare for more advanced concepts.

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The total number of signatures on a petition doubles each week. In the sixth week, there are 192 signatures on the petition therefore the number of signatures which were on the petition in the first week is 3.

This is referred to as twice as large as usual or is made up of two standard units or things.

Since the petition doubled every week then:

3 × 2 = 6 × 2 = 12 ×2 = 24 ×2 = 48×2 = 96×2 =192 thereby making the number of signatures on the petition in the first week as 3.

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A rectangle is a rhombus =Sometimes

A parallelogram is a rectangle = Always

A quadrilateral is a pentagon = Never

Parallelogram is a quadrilateral that has two pairs of parallel sides.

In a parallelogram, opposite sides and angles are equal.

The adjacent angles add up to 180 degrees.

We have,

A rhombus has four equal sides and its opposite angles are equal.

A rectangle is a rhombus if the rectangle becomes a square.

So,

We can say that a rectangle is sometimes a rhombus.

A parallelogram is always a rectangle.

But not all rectangle is a parallelograms.

A quadrilateral has four sides.

A pentagon has 5 sides.

So,

A quadrilateral is never a pentagon.

Thus,

A rectangle is sometimes a rhombus.

A parallelogram is always a rectangle.

A quadrilateral is never a pentagon.

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Answer: B: 113.04cm^2

Step-by-step explanation:

Due to the fact that there are an unlimited number of values that are either more than or less than the variable x.

Rationales are intelligent, independent, and capable of both stubbornness and skepticism. Rationales typically spend a lot of time and effort trying to comprehend the manner in which the universe of ideas works.

Every number that can be stated as a percentage or as a portion of a whole integer is considered rational. (For instance, -7, 2/3, and 3.75) Irrational numbers are those that can't be stated as a ratio of two integers or a fraction. They cannot be expressed in any finite way.

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In a normal distribution, x = -5 and z = -3.14 means that x = -5 is 3.14 standard deviations to the left of the mean

From the question, we have the following parameters that can be used in our computation:

Distribution = Normal

z = -3.14

z = -5

In a standard normal distribution, which has a mean of 0 and a standard deviation of 1, a z-score of -3.14 indicates that the value is 3.14 standard deviations below the mean.

Since x is given as -5, we know that this value is 3.14 standard deviations below the mean value, which can be determined by multiplying the standard deviation by the z-score.

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The amount of paint needed if the dimensions are doubled is; 8 ounces.

The quantity of sugar which the rectangular prism would hold if the dimensions are doubled is; 120 cups of sugar.

Recall,

Area of a rectangular prism = 2 (lw + lh + wh) and

Volume of a rectangular prism = l × w × h.

Hence, when the dimensions are doubled;

New Area = 2 × 4 (lw + lh + wh) = 4 × initial area.

Therefore, the quantity of paint needed is; 4 × 2 ounces = 8 ounces of paint.

Also, when the dimensions are doubled;

New Volume = 2l × 2w × 2h = 8 lwh.

New Volume = 8 × initial volume = 8 × 15 cups = 120 cups of sugar.

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Time taken to walk across 100 yard field is 60 minutes.

Speed is the unit rate in terms of distance travelled by an object and the time taken to travel the distance.

Speed is a scalar quantity as it only has magnitude and no direction.

Given that,

Speed of Slauson = 5 ft./min

That is, in 1 minute, Slauson can walk 5 feet.

We have to find the time taken to walk 100 yard.

1 yard = 3 feet

100 yard = 300 feet

Speed = Distance / Time

Time = Distance / Speed

Time = 300 / 5 = 60 minutes

Hence it will take 60 minutes to walk across a 100 yard field.

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The number of each kind of package that were shipped include the following:

Standard-Delivery: = 61

Express Delivery: = 61

The total number of packages that was delivered in a day = 138.

The total cost for the delivery for a day = $669.00

The charges for each standard-delivery package = $2.50

The charges for express-delivery package = $8.50

The total charges for both = $11

The charges for Standard-Delivery

= 2.50/11 × 669.00

= 1672.5/11

= $152.1

The number of Standard-Delivery that was shipped = 152.1/2.5 = 61

The charges for Express Delivery:

= $669.00-$152.1

= $516.9

The number of Express Delivery that was shipped;

=516.9/8.5 = 61.

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Answer:

y is the dependent variable and it is the total amount of money that she has saved.  

X is the dependent variable and it is the number of months that she has saved.

Step-by-step explanation:

y = 15x + 50

This is what the equation would look like.  If you tell me how many months she has saved, I can tell you how much is in her account.

The equation of line is y = 35x + 10 and Juan followed the instructions

The solution is Option A. Yes, his free throws can be represented by

y = 35x + 10

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given data ,

Let the equation of line be represented as A

Now , the value of A is

Let the first point be P ( 1 , 45 )

Let the second point be Q ( 2 , 80 )

Now , the slope of the line is m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Substituting the values in the equation , we get

Slope m = ( 80 - 45 ) / 2 - 1

Slope m = 35

Now , the equation of line is y - y₁ = m ( x - x₁ )

Substituting the values in the equation , we get

y - 45 = 35 ( x - 1 )

On simplifying the equation , we get

y - 45 = 35x - 35

Adding 45 on both sides of the equation , we get

y = 35x + 10

Hence , the equation of line is y = 35x + 10

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The complete question is :

Juan recorded the total number of free throws he attempted during practices. His results are shown in the table.

Number of practices = { 1 , 2 , 3 , 4 }

Number of throws attempted = { 45 , 80 , 115 , 150 }

Juan's coach told him to attempt 10 free throws before the first practice and then 35 free throws each practice. Did Juan follow his coach's instructions?

A) Yes, his free throws can be represented by y = 35x + 10.

B) Yes, his free throws can be represented by y = 45x.

C) No, his free throws can be represented by y = 35x.

D) No. his free throws can be represented by y = 45x.

Answer:

13

Step-by-step explanation:

11+2^2 -2

= 11+4-2

= 15-2

= 13