A rectangular prism with a volume of 4 cubic units is filled with cubes with side lengths of 1/3 cubic units

Answer:

Part a) A'B'=15 units, B'C'=12 units, A'C'=21 units

Part b) The graph in the attached figure

Step-by-step explanation:

Part a) calculate the length of each side of the dilated image

we know that

To calculate the length of each side of the dilated image, multiply the scale factor by the original length

we have

scale factor=1.5

so

A'B'=AB*1.5=10*1.5=15 units

B'C'=BC*1.5=8*1.5=12 units

A'C'=AC*1.5=14*1.5=21 units

Part b) draw the new image and label it a'b'c

The graph in the attached figure

Answer:

the son is 30 and the daughter is 15

Step-by-step explanation:

the mom is 55 in 15 years

100-55=45

45-30=15

15x2=30

Answer:

15 and 5

Step-by-step explanation:

Mother's current age:  40

daughter's age:  d

son's age:  s

son is 2x as old as daughter:  s = 2d

Then, 15 years from now, the sum of their ages will be:

(40 + 15) + (2d + 15) + (d + 15) = 100

or

55 + 15 + 15 + 3d = 100

85 + 3d = 100, or 3d = 15, or d = 5.

Then the son's age is 3(5) = 15 and the daughter's is 5.

Answer:

x=3

Step-by-step explanation:

[tex]45-\frac{90}{x} = 15[/tex]

Minus 45 from both sides

[tex]-\frac{90}{x}=-30[/tex]

Multiply both sides x

[tex]-90=-30x[/tex]

Divide both sides by -30

[tex]3=x[/tex]

Answer:

3

Step-by-step explanation:

To eliminate the x on the denominator, multiply all terms by x

45x - 90 = 15x ( subtract 45x from both sides )

- 90 = - 30x ( divide both sides by - 30 )

3 = x ⇒ x = 3

Answer:

x = 95

Step-by-step explanation:

Using the rule of logarithms

• [tex]log_{b}[/tex] x = n ⇔ x = [tex]b^{n}[/tex]

Given

[tex]log_{5}[/tex](x + 30) = 3, then

x + 30 = 5³ = 125 ( subtract 30 from both sides )

x = 95

Answer:

U think the answer is C.

Answer:

Number of ways of selecting two students is 15

Step-by-step explanation:

number of ways of selecting n out of r  is given by

[tex]n_{C_{r} } =\frac{n!}{r!(n-r)!}[/tex]

It is given that there are 6 seniors on student council.

2 students are selected for district meeting

So we have  [tex]n= 6[/tex] and [tex]r=2[/tex]

number of ways of selecting two students =[tex]6_{C_{2} } [/tex]

                                                                       =[tex]\frac{6!}{2!(6-2)!}[/tex]

                                                                       =[tex]\frac{6!}{2!4!}=15[/tex]

So we have number of ways of selecting two students is 15

It’s is 35968.1 since you need to find the radius since area=pie time the radius squared, so divide 214 by 2 to get 107 then multiply pie time 107 to the second power to get 35968.1

B) it is 450 dollars

Answer:   C: 480

Step-by-step explanation:

trust me its this answer not the other guys

The answer is:

- First inequality:  The fourth number line.

- Second inequality: The second number line.

- Third inequality: The first number line.

- Fourth inequality: The third number line.

To be able to match each inequality to the number line that represents its solution, we need to solve each inequality.

So, solving we have:

- First inequality:

[tex]\frac{7x}{9}>-\frac{14}{3}\\\\x>-\frac{14}{3}*\frac{9}{7}>-\frac{126}{21}>-6 \\\\x>-6[/tex]

Therefore, the solution for the first inequality is the x greaters than 6, and the solution matchs with the fourth number line.

- Second inequality:

[tex]-\frac{75x}{4}>\frac{225}{2}\\\\\frac{75x}{4}<-\frac{225}{2}\\\\x<-\frac{225}{2}*\frac{4}{75}<-6[/tex]

Therefore, the solution for the first inequality is the x less than 6, and the solution matchs with the second number line.

- Third inequality:

[tex]\frac{x}{4}\leq -\frac{3}{2}\\\\x\leq -\frac{3}{2}*4\leq -\frac{12}{2}=-6[/tex]

Therefore, the solution for the first inequality is the x less or equals than 6, and the solution matchs with the first  number line.

- Fourth inequality:

[tex]\frac{2x}{3}>-\frac{16}{3}\\\\x>-\frac{16}{3}*\frac{3}{2}>-\frac{48}{6}>-8\\\\x>-8[/tex]

Therefore, the solution for the first inequality is the x greater than 6, and the solution matchs with the third number line.

Have a nice day!

It is positive . Every time it’s to the right it’s positive when it’s to the left it’s negative and when the points are all over the place it’s no Trend

Answer: Positive trend

Step-by-step explanation: In this scatter plot, notice that we can draw a line of best fit to represent the data. This means that we have a trend. Notice the x-values increase while the y-values increase which means we have a positive correlation between x and y.

Therefore, this scatter plot represents a positive trend.

Image provided.

Answer: First consider the case that ‘just’ 5 persons are seated around a round table.

Clearly, ‘just’ 5 persons can be seated around a round table in (5 - 1)! = 4! = 24 ways.

Now, one vacant chair is to be inserted among them.

Say, for a particular sitting arrangement ‘ABCDE’; there are 5 scopes available for inserting the vacant chair - between A and B, between B and C, between C and D, between D and E & between E and A.

So, there are 5*24 = 120 ways available that 5 persons can sit around a round table with 6 chairs.

Step-by-step explanation:

First consider the case that ‘just’ 5 persons are seated around a round table.

Clearly, ‘just’ 5 persons can be seated around a round table in (5 - 1)! = 4! = 24 ways.

Now, one vacant chair is to be inserted among them.

Say, for a particular sitting arrangement ‘ABCDE’; there are 5 scopes available for inserting the vacant chair - between A and B, between B and C, between C and D, between D and E & between E and A.

So, there are 5*24 = 120 ways available that 5 persons can sit around a round table with 6 chairs.

Answer:

1 x 1,000,000 + 9 x 100,000 + 4 x 10,000 + 8 x 1,000 + 4 x 100 + 4 x 10 + 7 x 1

Hope I helped : )

Step-by-step explanation:

The place value chart can help us to write a number in expanded notation.

When we put 1,948,447 into the place value chart, we can recognize that our number is equal to 1 million + 9 hundred thousands + 4 ten thousands + 8 thousands + 4 hundreds + 4 tens + 7 units.

Answer:

a = 5 and b = 2

Step-by-step explanation:

y = ab^x

If x is the number of double periods, then b is the rate of growth (2), and a is the initial height (5).

a = 5 and b = 2

14/16

Then reduced it would be

7/8 you leave 16 and add 11 to 3 and get that number

Since the denominators are the same, add the numerators. 3 + 11 = 14 so the new fraction is 14/16. Divide the numerator and the denomintor by 2 (because 2 goes into both evenly) to get 7/8

Hope this helps!

[tex]x2y + z = 9 \\ \\ 1. \: x + 2y + z + - 2y = 9 + - 2y \\ x + z = - 2y + 9 \\ 2. \: x + z + - z = - 2y + 9 + - z \\ x = - 2y - z + 9 \\ \\ \\ x + y - z = 5 \\ \\ 1. \: x + y - z + - y = 5 + - y \\ x - z = - y + 5 \\ 2. \: x - z + z = - y + 5 + z \\ x = - y + z + 5 \\ \\ \\ 3x - y + 2z = 12 \\ 1. \: 3x - y + 2z + y = 12 + y \\ 3x + 2z = y + 12 \\ 2. \: 3x = y - 2z + 12 \\ 3. \: \frac{3x}{3} = \frac{y - 2z + 12}{3} \\ x = \frac{1}{3} y + \frac{ - 2}{3} z + 4[/tex]

ANSWER

x=-3, y=6

EXPLANATION

The given equation is

[tex] - 3 + yi = x + 6i[/tex]

We can rewrite this equation as:

[tex]x - yi = - 3 - 6i[/tex]

The two complex number equations are equal therefore their corresponding parts are also equal.

Comparing the real number parts,

[tex]x = - 3[/tex]

Comparing the complex number part,

[tex] - y = - 6[/tex]

y=6.

The student's question pertains to a survey on students' opinions about a new school mascot. The survey results showed varying levels of support and opposition, which are crucial for decision-making in educational policy. This demonstrates the real-world application of mathematics in understanding public opinion through statistics.

The student's question deals with a survey conducted by student government members to understand the school community's stance on the new school mascot. This survey follows a systematic sampling method by asking every 15th student entering the school. The outcome showed that 57% oppose, 37% are in favor, and 6% have no opinion regarding the new mascot. Such a poll is useful for making decisions related to public policy and ensuring that actions consider community preferences.

Another key component is understanding the methodology behind this survey. If we consider a similar scenario where 600 students are surveyed with 480 opposing new legislation (as mentioned in one of the examples), we could calculate the percentage opposing the legislation and use this to propose actions or influence decision-making processes regarding school policies.

In the context of educational institutions, conducting polls or surveys is a practical way to involve student bodies in decision-making processes, reflecting a democratic practice in school governance. This kind of statistical analysis forms a crucial part of mathematics in the real world, particularly within the fields of statistics and probability.

Answer:

x = 2 ± (i)√5  (Answer b)

Step-by-step explanation:

x²-4x+9=0 can be solved in a variety of ways; the first two that come to mind that are also appropriate are (1) completing the square and (2) using the quadratic formula.

Completing the square is fast here:

Rewrite x²-4x+9=0 as   x²-4x                    +9=0

Identify the coefficient of the x term:  it is -4

Take half of that, obtaining -2

Square this result, obtaining 4

Add 4 to   x²-4x                    +9=0, in the blank space in the middle, and then subtract 4:      x²-4x +4          -4         +9=0

Rewrite           x²-4x +4 as the square of a binomial:

                          (x - 2)² - 4 + 9  = 0  →    (x - 2)²  = -5

Take the square root of both sides:       x - 2  = ±√(-5)  =  ± (i)√5

Then x = 2 ± (i)√5

Answer:

y=6

Step-by-step explanation:

The complete question is as follows:-

The levels of mercury in two different bodies of water are rising. In one body of water, the initial measure of mercury is 0.05 parts per billion (ppb) and is rising at a rate of 0.1 ppb each year. In the second body of water, the initial measure is 0.12 ppb and the rate of increase is 0.06 ppb each year. Which equation can be used to find y, the year in which both bodies of water have the same amount of mercury?

An equation can be used to find y, the year in which both bodies of water have the same amount of mercury will be given as below:-

0.05 + 0.1y  =  0.12 + 0.06y

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

Here, we want to find y which is the heat in which the amount of mercury in each of the water bodies is the same.

Now for the first water body:

Initial is 0.05 ppb and after y years, we have a rise of 0.1  x  y = 0.1y ppb

So the amount of mercury in ppb after y years would be;

0.05 + 0.1y

For the second water body;

Initial is 0.12 and a rise of 0.06 ppb per year for y years. The rise would be

0.06  x  y = 0.06y

So the total amount of mercury here is

0.12 + 0.06y

So to find y which is the year the amount of mercury in each water body is the same, we simple equate both and that would be;

0.05 + 0.1y = 0.12 + 0.06y

Therefore an equation can be used to find y, the year in which both bodies of water have the same amount of mercury is 0.05 + 0.1y  =  0.12 + 0.06y

To know more about equations follow

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Answer: Figure 2

Step-by-step explanation: A translation of the blue shaded shape would be figure 2

Answer:

392

Step-by-step explanation:

Squares get really big very quickly, so you don't want to use any bigger numbers. The biggest total of the squares would be from

using

1 and 28

1+28

2=1+784=785

2 and 27=4+729=733

142+14

2=196+196=392

The greater the difference between the two numbers, the bigger one of the numbers is going to be.

Therefore use two numbers with the smallest difference between them which will be

14 and 14

The minimum value of sum of their square is 392.

A mathematical statement consisting of an equal symbol between two algebraic expressions with the same value is known as an equation.

Let the Bigger no. = x

Let the Smaller no. = y

x - y = 28 (given)

(x - y)^2 = 28^2

x^2 + y^2 - 2xy = 784

x^2 + y^2 = 784 + 2xy

Let the value of x = 14 and y = -14 (By trial and error)

Hence, the minimum value of sum of squares will be 14^2 + 14^2 = 392.

Learn more about equations on:

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Answer:

A

Explanation:

Lillian is trying to find out how people feel about the new act Congress is trying to put through. I would go with A because the question is literally what she is trying to determine through the survey.

B, C, D are asking about certain things(issues) about the act or comparing it with other issues, and with A you get a broader answer. (or the question is straight to the point)

Answer:

* Hopefully this helps:) Mark me the brainliest:)!!!

4:8

2:4

1:2

16:32

Good luck!!!

The value of [tex]\(x\)[/tex] is [tex]\(14\)[/tex]. The correct option is [tex]\(14\)[/tex].

In a right triangle with a 45-degree angle, the sides are related by the special angles of 45-45-90 triangles. In such triangles, the sides are in the ratio [tex]\(1:1:\sqrt{2}\)[/tex].

Given that the height is [tex]\(7\sqrt{2}\)[/tex] and the hypotenuse is [tex]\(x\),[/tex] we can identify the relationship as follows:

[tex]\[ \text{Height} : \text{Base} : \text{Hypotenuse} = 1 : 1 : \sqrt{2} \][/tex]

So, the height is [tex]\(7\sqrt{2}\)[/tex], and the base would be [tex]\(7\sqrt{2}\)[/tex]as well, and the hypotenuse [tex](\(x\))[/tex] would be [tex]\(7\sqrt{2} \times \sqrt{2} = 7 \times 2 = 14\)[/tex].

Therefore, the value of [tex]\(x\)[/tex] is [tex]\(14\)[/tex], and the correct option is:

• [tex]\(14\)[/tex]

The correct answer is [tex]\boxed{14}[/tex]. The value of x is  [tex]\boxed{14}[/tex].

To determine the value of [tex]\( x \)[/tex], we need to consider the given options and the context of the question, which involves the square root of 2. The options provided are [tex]\( 7 \), \( 7\sqrt{2} \), \( 14 \), and \( 14\sqrt{2} \).[/tex]

Let's analyze the options:

1. [tex]\( 7 \)[/tex] is a straightforward integer.

2. [tex]\( 7\sqrt{2} \) is \( 7 \)[/tex] times the square root of 2, which is an irrational number approximately equal to [tex]\( 1.414 \)[/tex].

3.[tex]\( 14 \) is \( 7 \)[/tex] times [tex]\( 2 \)[/tex], which is a simple integer multiplication.

4. [tex]\( 14\sqrt{2} \) is \( 14 \)[/tex] times the square root of 2.

Given that the question is asking for the value of [tex]\( x \)[/tex] and the options involve multiples of [tex]\( 7 \)[/tex] and [tex]\( 14 \)[/tex], it is reasonable to suspect that the answer might involve the square root of 2, since it is the only mathematical operation present in all the options.

However, without additional context or a mathematical equation to solve for [tex]\( x \)[/tex], we cannot definitively determine which of these options is correct based solely on the information given. In mathematics, problems involving square roots typically require an equation or a geometric representation to provide a clear path to the solution.

Since the question does not provide an equation or additional context, we must rely on the principle that the most straightforward answer is often correct when dealing with multiple-choice questions. In this case, the simplest option that does not involve an irrational number is [tex]\( 14 \)[/tex].

Therefore, without further information, the most logical and simple choice is [tex]\( 14 \)[/tex], as it is a whole number and does not introduce the complexity of an irrational number like [tex]\( \sqrt{2} \)[/tex].

Thus, the final answer is [tex]\boxed{14}[/tex].

To make a line plot, plot all the numbers you see. Then plot how many of each number you see. For example, there are 4 one's in the data, so draw 4 x's above 1. I hope this helps!

The answer is:

The third option,

[tex]x^{2}+mx+m=(x+2)^{2}[/tex]

We are looking for an equation that establishes a relationship between the perfect-square trinomial and the givens notable products.

So, we are looking for a notable product that gives us a value of "m" that is the coefficient of the linear term (x) and it's also the constant term.

- Trying with the two first options, we have:

[tex](x+1)^{2}=x^{2}+2x+ 1\\\\(x-1)^{2}=x^{2}-2x+ 1[/tex]

We can see that for these first two options, the value of m has not the same value for the coefficient of the linear term and the constant term since m is equal 2 and the constant number is not 2.

- Trying with the third option, we have:

[tex](x+2)^{2}=x^{2}+2*(2*x)+2^{2}=x^{2} +4x+4[/tex]

Now, we can see that the value of m is the same for the coefficient of the linear term and the constant term, we can see that m is equal to 4.

So, the correct option is the third option, because

[tex]m=4[/tex]

[tex]x^{2} +mx+m=(x+2)^{2}=x^{2} +4x+4=x^{2} +mx+m[/tex]

Have a nice day!

The volume of the cylinder is defined (as usual) as the base area times the height. The base is a circle, so the base area is [tex]\pi r^2[/tex]

So, the volume is

[tex]h\pi r^2 = 15\cdot \pi \cdot 36 = 540\pi[/tex]

Answer:

[tex]

1696.46 {cm}^{3}

[/tex]

Step-by-step explanation:

[tex]V

=

π

{r}^{2}

h

\\ =

π

·

{6}^{2}

·

15

\\

≈

1696.46003

[/tex]

Answer:

Step-by-step explanation:

2, 3, 5

Answer:

Answers:2, 3, 5

Step-by-step explanation:

To find how many small cubes can fit inside a larger cube, you need to find the volume of both.

Once you have the volumes, divide the volume of the larger cube, by the volume of the smaller cube.

Volume = L x W x H

Small cube: Volume = 3/4 x 3/4 x 3/4 = 0.421875 cm^3

Large cube: Volume = 3 x 3 x 2 = 18 cm^3

Number of small cubes that can fit: 18 / 0.421875 = 42.67 Cubes.

Since you can't have a partial cube ( 0.67) round down to a whole number:

That means you can fit 42 cubes.

ANSWER

[tex]x = 75.5 \degree[/tex]

EXPLANATION

Lines WO and WX are tangents to the circle.

The angle subtended at the center, Z by minor arc XO is the angle subtended at the circumcenter by the same arc.

Therefore the central angle is 2x°.

The two radii ZX and ZO meets the tangents at right angles.

This implies that:

[tex]2x + 90 + 90 + 29 = 360 \degree[/tex]

Or

[tex]2x + 29 = 180 \degree[/tex]

[tex]2x = 180 - 29[/tex]

[tex]2x = 151[/tex]

Divide both sides by 2

[tex]x = \frac{151}{2} = 75.5[/tex]

The value of x using the quadratic equation is 0.00139. When adjusting exponential notations, move the decimal left or right, depending on whether the exponent is positive or negative. Verifying precision to a certain number of decimal places can be achieved by altering the increment and observing changes beyond the desired precision.

To find the value of x when using the quadratic equation, we have two potential solutions, which are x= -0.0024 and x= 0.00139. In practical applications, a negative result may not be viable, which indicates that x would equal to 0.00139. When dealing with exponential notation, moving the decimal to adjust for the exponent is necessary. For instance, 4.5 x 10¹ would become 0.45 when the decimal is moved one place to the left. Similarly, 1.6 x 10² would adjust to 160 by moving the decimal place to the right two places. Conversely, a negative exponent like in 2.4 x 10⁻² requires moving the decimal to the left twice to get 0.024. Understanding this concept is crucial when working with numbers written in scientific notation.

If we're verifying to three decimal places and see a change beyond the third decimal (such as with Ax=10⁻⁵ resulting in 1.00001), we can deduce that the initial three decimal places are indeed accurate. Hence, an answer like 1.00001 confirms that 1.000 is valid up to three decimal places. Additionally, using Newton's method can improve approximations, such as refining an initial estimate of the solution to tan x = x from about 4.5 to a more precise six decimal places.

Final answer:

To find the length of the wall on the new blueprint with a scale of 1 cm = 3 ft, a proportion can be used. The length of the wall on the new blueprint would be 0.75 ft.

Explanation:

To find the length of the wall on the new blueprint with a scale of 1 cm = 3 ft, we can use a proportion.

In the original blueprint with a scale of 1 cm = 4 ft, the length of the wall is 9 cm. Let's let x represent the length of the wall on the new blueprint.

Set up the proportion: 1 cm/4 ft = x cm/3 ft

Cross multiply: 1 * 3 = 4 * x

Solve for x: x = 3/4

Therefore, the length of the wall on the new blueprint would be 3/4 ft or 0.75 ft.