Find the equation of the line shown.
y
10
9
8
5
4
3
2
1
O
1 2 3 4 5 6 7 8 9 10
X

By using differentials the error in the volume estimation is 7.29 cubic centimeters.

The volume of a cube (V), in cubic centimeters, is equal to the cube of the side length (L), in centimeters, whose formulas are:

V = L³

Now we proceed to estimate the volume differential by using first derivatives:

dV = 3 · L² · dL

Where dL is the length differential, in centimeters.

If we know that L = 9 cm and dL = 0.03 cm, then the error in the computed volume of the cube is:

dV = 3 · (9 cm)² · (0.03 cm)

dV = 7.29 cm³

The error in the volume estimation is 7.29 cubic centimeters.

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The approximate length and width of this rectangle to the nearest tenth are 15.6 feet and 31.2 feet respectively.

Mathematically, the area of a rectangle can be calculated by using this formula:

A = LW

Where:

A represents the area of a rectangle.

W represents the width of a rectangle.

L represents the length of a rectangle.

Making length (L) the subject of formula, we have:

L = A/W

Substituting the given parameters into the formula, we have;

3x = 489/6x

3x × 6x = 489

18x² = 489

x² = 489/18

x² = 27.2

x = √27.2

x = 5.2

Now, we can determine the length and width of this rectangle as follows:

Width = 6x

Width = 6 × 5.2

Width = 31.2 feet.

Length = 3x

Length = 3 × 5.2

Length = 15.6 feet.

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The value of percent of the decimal .065 is 6.5 %.

We are provided with the value .065 .

The ratio or a number expressed as a fraction of 100 is referred to as percentage. It is  denoted using the percent sign % .

We have, .065 . We need to convert this value in the percentage. certain steps need to be followed to convert this value in the percentage. These steps are mentioned below;

.065

Multiply this above mentioned value by 100 to convert it into percent.

.065 × 100

= 6.5 %

So, percent of the decimal value is  6.5 %.

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Mayumi took 4.5 laps by riding her bike around the park

Distance of each lap around the park = 2/3 miles

Distance covered by Mayumi = 3 miles

Fractions: The components of a whole or group of items are represented by fractions. A fraction consists of two components. The numerator is the figure at the top of the line. It specifies the number of equal portions of the whole or collection that are taken.

Laps took by Mayumi:

Distance covered by Mayumi on her bike/Distance of each lap around the park

= 3/(2/3)

= 3*3/2

= 9/2 or 4.5 laps

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Answer:

SAS

Step-by-step explanation:

SAS is side, angle, side so two sides are congruent and one angle is congruent.

If you look at the picture the side that is shared by both triangles is equal.(side)

The two sides with the line through them means they're equal.

(side)

The picture shows the two angles are equal.

(angle)

=SSA or SAS

Answer: 5.13

Step-by-step explanation:

1) Set up the equation

3.8(1.35)

2) Solve

5.13

The sequence(s) of translations and reflections that were performed to show given two figures are congruent:

- Translate triangle ABC down and then reflect across vertical line.

- Reflect triangle ABC across vertical line and then translate down.

- ΔABC ≅ ΔDEF

In this question, we have been given a triangle and its image.

We need to select all sequence of translations and reflections that performed to show given figures in each pair are congruent.

From figure, we can see that the image of vertex A is vertex D, the image of vertex B is vertex E and the image of vertex C is vertex F.

In we translate the triangle ABC down and then reflect across vertical line then the image would be DEF.

We can do the same transformation by reflecting triangle ABC across the vertical line and then translating it down.

From above, we can conclude that, ΔABC ≅ ΔDEF

Therefore, the sequence(s) of translations and reflections that were performed to show given two figures are congruent:

- Translate triangle ABC down and then reflect across vertical line.

- Reflect triangle ABC across vertical line and then translate down.

- ΔABC ≅ ΔDEF

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Answer:7 6/10 is the answer if you turn a fraction into a decimal like so

7.5=7.5, 7 6/10=7.6, 7 2/5=7.4, 7.02=7.02 i hope i helped

Step-by-step explanation:

Answer:  [tex]7\frac{6}{10}[/tex] is closest to 8.

Step-by-step explanation:

[tex]7\frac{6}{10} =\frac{70}{10} +\frac{6}{10} = \frac{76}{10} = 7.6[/tex]

[tex]7\frac{2}{5} = \frac{35}{5} +\frac{2}{5} =\frac{37}{5} =7.4[/tex]

7.02 < 7.4 < 7.5 < 7.6

7.02 < [tex]7\frac{2}{5}[/tex] < 7.5 < [tex]7\frac{6}{10}[/tex]

Answer:

525 miles is that was what was being asked

Step-by-step explanation:

sorry I don't know the quest but the car can travel a total of 525 miles with 15 gallons in the tank

15 times 35=525

A number that contains both positive and negative integers, including zero, is called an integer. There are no fractional or decimal parts in it. Here are a few instances of integers: -5, 0, 1, 5, 8, 97, and 3,043

Integers, as opposed to fractions or decimals, are all whole numbers plus their antipodes. For instance, numbers include -3, -2, -1, 0, 1, 2, 3,... On a number line, positive numbers are those to the right of zero. Negative numbers are those to the left of 0

An integer, pronounced "IN-tuh-jer," is a whole number that can be positive, negative, or zero and is not a fraction. Integer examples include: -5, 1, 5, 8, 97, and 3,043.

False. An integer is a whole number.

False. For instance, 1/2 is not a whole number but is a rational number.

False. For instance, -3 is not a whole number but is an integer.

True. Rational numbers include all integers.

Answers:

False

False

False

True

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Answer:

261 500

Step-by-step explanation:

450x670-80x500
301500-80x500

301500-40000

261500

Answer:

it's 0

Step-by-step explanation:

i hope this helps you

The 14.2 cm correct 1 decimal place is 14.2 after rounding to the nearest 0.1 or the tenth place.

Rounding is a technique to reduce a large number to a smaller, more approachable figure which is very similar to the actual. Rounding numbers can be achieved in a variety of ways.

It is given that:

14.2 cm correct 1 decimal place

14.2

Rounded to the nearest 0.1 or

the Tenths Place.

Rounded to the nearest tenth place. The 2 in the tenth place rounds down to 2 or stays the same because the digit to the right in the hundredth place is 14.2

Thus, the 14.2 cm correct 1 decimal place is 14.2 after rounding to the nearest 0.1 or the tenth place.

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The expression given: 7/6 x 3  can be calculated to get 7/2

This is a basic math operation that helps to determine the product of two or more numbers.

The numbers given here include a whole number and a fraction

A fraction refers  to classification of numbers to be represented as having a stroke dividing the two groups of numbers.

The numbers on top is referred to as numerators while the numbers below is referred to as the denominator

in the question the fraction is 7/6: The numerator is 7 while the denominator is 6

= 7/6 * 3

= 7/2

= 3.5

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The number 4,300,000,000 in scientific notation is 4.3x10⁹.

What is a number?

A number is a quantitative entity that may be used to tally, measure, and name things. The natural numbers 1, 2, 3, 4, and so on are the original instances. Number words can be used to represent numbers in language. Individual numbers can be represented more generically by symbols known as numerals; for example, "5" is a numeral that represents the number five. Because only a small number of symbols can be memorized, fundamental numerals are often structured in a numeral system, which is a systematic method of representing any number. The most prevalent numeral system is the Hindu-Arabic numeral system, which allows any number to be represented using a combination of 10 fundamental numeric symbols known as digits.

The number 4,300,000,000 in scientific notation is 4.3x10⁹.

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We have that the tangents which meet at the same point outside the circle have the same length:

Then, in this case:

Now that we have all the measures, we find the perimeter just by adding them:

6 + 6 + 9 + 9 + 12+ 12 = 54

Answer: the perimeter of the figure is 54

The probability that I, Sharon, and Robert are chosen is 0.0012

What is the formula for calculating combinations?

The equation  [tex]^{n}C_{r}=\frac{n!}{(n-r)! r!}[/tex] will be used to calculate combinations, where n is the overall number of things and r is the number of items that are being chosen at a time.

The total number of employees=18

The Boss must choose 3 employees to attend the conference.

The number of possible ways to choose 3 employees from the total of 18 employees is [tex]^{18}C_{3}[/tex] .

The equation  [tex]^{n}C_{r}=\frac{n!}{(n-r)! r!}[/tex] will be used to calculate combinations,.

So, [tex]^{18}C_{3}=\frac{18!}{(18-3)! 3!}[/tex]

    [tex]^{18}C_{3}=\frac{18!}{(15)! 3!}[/tex]  

    [tex]^{18}C_{3}=\frac{18 \times 17 \times 16 \times 15}{3 \times 2}[/tex]

     [tex]^{18}C_{3} =816[/tex]

The probability that I, Sharon, and Robert are chosen is  [tex]\frac{1}{816}[/tex] = 0.0012

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The probability that I, Sharon, and Robert are chosen is 0.0012

What is the formula for calculating combinations?

The equation   [tex]^{n}C_{r}=\frac{n!}{(n-r)! r!}[/tex]    will be used to calculate combinations, where n is the overall number of things and r is the number of items that are being chosen at a time.

The total number of employees=18

The Boss must choose 3 employees to attend the conference.

The number of possible ways to choose 3 employees from the total of 18 employees is [tex]^{18}C_{3}[/tex]   .

The equation  [tex]^{n}C_{r}=\frac{n!}{(n-r)! r!}[/tex]    will be used to calculate combinations,.

So,

[tex]^{18}C_{3}=\frac{18!}{(18-3)! 3!}^{18}C_{3}=\frac{18!}{(15)! 3!}^{18}C_{3}=\frac{18 \times 17 \times 16 \times 15}{3 \times 2}[/tex]

[tex]^{18}C_{3}=816[/tex]

The probability that I, Sharon, and Robert are chosen is  = 0.0012

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Answer: to solve this equation, multiply both sides of the equation by 2.

Step-by-step explanation: by multiplying both sides of the equation by 2, you are effectively eliminating the fraction on the left, making the answer x = 16.

Answer:

f(3) = -11

f(-5) = 37

Step-by-step explanation:

f(x) = -6x + 7

We want to find f(3) and f(-5)

To do so we substitute the input with any x in the equation and evaluate.

f(3) = -6x + 7

==> substitute all x's with the input, 3

f(3) = -6(3) + 7

==> multiply -6 and 3

f(3) = -18 + 7

==> add -18 and 7

f(3) = -11

f(-5) = -6x + 7

==> substitute all x's with the input -5

f(-5) = -6(-5) + 7

==> multiply -6 and -5

f(-5) = 30 + 7

==> add 30 and 7

f(-5) = 37

Answer:

2-33i

Step-by-step explanation:

(2 − 5i)(3 + 7i) − (4 + 3i)   |Set up equation|

6+14i-15i-35i-(4+3i)         |Multiply the numbers in the parentheses together using the distributive property|

6-1i-35i-(4+3i)                       Subtract like terms

6-36i-(4+3i)                           Subtract like terms

6-4-36i+31                          Open parentheses and put like terms together

2-33i                                    Answer

Hope this helped!

Answer:

Pues hablemos primero de lo que sucede antes de apagar la luz y usemos como ejemplo el viaje de un solo fotón.

Un fotón proveniente de un bombillo de luz blanca se dispara en línea recta hacia la pared. El material que cubre la pared, en este caso la pintura, tiene ciertas propiedades físicas y la energía del fotón es absorbida por un electrón de algún átomo de esa superficie. Ocurre una excitación del electrón, el cual ahora tiene más energía de la que normalmente tiene en su estado fundamental, y para regresar a su estado fundamental emite parte de esa energía como un nuevo fotón, este último de menor energía (frecuencia) que el anterior. La frecuencia dependerá del material y esa nueva frecuencia es la que da color a la pared. La luz blanca está compuesta por fotones de distintas frecuencias. Los de baja frecuencia son absorbidos y lo que se emite es en forma de calor, lo cual no puedes ver con tus ojos. Los de alta frecuencia tienen suficiente energía para que la energía que se re-emite sea visible y posiblemente sea re-emitida, cada vez con menos energía. Uno habla de que la luz “rebota” en el objeto. (Aunque “rebotar” no es necesariamente la acción correcta, voy a usar el término para simplificar).

Ahora digamos que ese fotón que “rebotó” en la pared rebota en otra pared y otra pared. Ese fotón es solo visible si en ese rebotar llega a tu ojo antes de que su energía sea demasiado baja. No podemos ver el calor ni las microondas que son fotones de baja energía. Al final la energía se va a convertir en calor, el cual es invisible al ojo humano.

Ese es el trayecto de un solo fotón. El bombillo produce un flujo de fotones en todas direcciones. Hay que recordar que esos fotones viajan a la velocidad de la luz. Cuando el bombillo se apaga, se interrumpe el flujo de fotones. Si se movieran a la velocidad del agua en una manguera, verías el flujo rebotando por varios segundos hasta que los fotones que más han rebotado desaparecen de tu vista por aquello de la baja frecuencia energética. Pero al viajar a la velocidad de la luz, el tamaño de la habitación se hace irrelevante y nuestra experiencia es prácticamente instantánea.

¿A donde va la luz? La luz no sale de la habitación sino que la calienta.

The figures are congruent and the corresponding sides are AC = KM, AB = KL and BC = LM

Congruent figures in geometry are identical in shape and size.

In other words, congruent figures are geometric figures that have the same shape and size.

If the figures are polygons, then they are congruent if all the corresponding sides and corresponding angles are congruent.

Therefore, the polygons above are triangles, they are congruent if the corresponding sides and angles are equal.

Therefore, the figures(triangles) are congruent by the following rules:

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Answer:

translates up 8 and 5 left

Step-by-step explanation:

To find the distance (x) it translate up, -3 + x = 5 where x = 8

To find the distance (x) it translate left, 2 + x = 7 where x = 5

Answer:

(x, y) → (x-5, y+8)

Step-by-step explanation:

A translation is a type of transformation that moves a figure up, down, left or right.

Calculate the change in the coordinates by subtracting the coordinates of point D from the coordinates of point D':

[tex]\implies (x_{D'}-x_D, y_{D'}-y_D)[/tex]

[tex]\implies (2-7, 5-(-3))[/tex]

[tex]\implies (-5, 8)[/tex]

Therefore, to map point D onto point D', move 5 units left and 8 units up.

Therefore, the translation rule that maps point D(7, -3) onto point D'(2, 5) is:

Answer:

Step-by-step explanation:

So, what you need to do is find out the formula for this question. And your answer will come out to be x=32

In order to determine the number of people in the sample for each age group, here are the steps:

1. Determine what proportion in the entire population the population of each group. To get the proportion, simply divide the population of each respective group by the entire population.

2. To get the number of samples for each group, multiply the proportion by 5,000 and round the answer to the nearest whole number.

Now, let's apply the steps above in each group.

Let's start with ages under 18.

Hence, we are expected to have 1,201 people aged under 18 in the sample.

For those aged 18 - 44,

Hence, we are expected to have 1,827 people aged 18-44 in the sample.

For those aged 45 - 64,

The expected number of samples for people aged 45-64 is 1,320.

Lastly, for aged 65 and over,

The expected number of samples for people aged 65 and over is 652.

To summarize, we have:

Age under 18 ⇒ 1,201 samples

18 - 44 ⇒ 1,827 samples

45 - 64 ⇒ 1,320 samples

65 and over ⇒ 652 samples

.

Answer:

8 years8 years

Explanation:

Let Eli's age be represented as x

Sydney's age = 11

half on Eli's age = x/2

7 more than half on Eli's age = x/2 + 7

If 7 more than half on Eli's age is Sydney's age, then;

x/2 + 7 = 11

Subtract 7 from both sides

x/2 + 7 - 7 = 11-7

x/2 = 4

Multiply both sides by 2;

x/2 * 2 = 4 * 2

x = 4 * 2

x = 8

Hence Eli is 8 years old

Given -

To Find -

Type of Triangle =?

Step-by-Step Explanation -

As we can see we have an obtuse angle in the triangle and also, the two sides are equal.

So,

It is an Obtuse angle triangle.

It is also an isosceles triangle

Final Answer -

B. Obtuse

E. Isoseceles

Answer:   Median = 5

=====================================================

Explanation

Given Table of Data

[tex]\begin{array}{|c|c|} \cline{1-2}\text{Size of the shoe} & \text{No. of pair sold}\\\cline{1-2}3 & 4\\\cline{1-2}4 & 18\\\cline{1-2}5 & 25\\\cline{1-2}6 & 12\\\cline{1-2}7 & 5\\\cline{1-2}8 & 1\\\cline{1-2}\end{array}[/tex]

The second column is the set of frequencies. Adding up those frequencies gets us

4+18+25+12+5+1 = 65

There are 65 total shoes.

Divide this in half

65/2 = 32.5

There are 32 values below the median, and 32 values above it. That's 32+32 = 64 values so far. When including the median value itself we have 32+1+32 = 65 values total. This only works when the sample size is odd.

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

What we'll do is add up the partial sums of the frequency values.

The goal is to get to a sum of 33, or larger, because the median is in the 33rd slot.

Adding the first two frequencies gets us 4+18 = 22. This is not 33 or larger, so we move on.

Adding the first three frequencies gets us 4+18+25 = 22+25 = 47 which is 33 or larger.

What this tells us is that the median corresponds to the third row of the table, since we added the first three frequencies to get to 33 or larger.

The median must be 5.