Suppose there are two blocks of solid iron. One block is a cube, three inches on a side. The other block is a cube three miles on a side. Obviously, the large cube is many, many times greater volume than the small cube, and many, many times heavier. Is the large cube more dense than the small cube, or less dense?

The sum of the arithmetic series 12 + 22 + ... + 142 is 1078.

The sum of an arithmetic series can be found by multiplying the average of the first and last terms by the number of terms.

The following formula can be used to get the sum of an arithmetic series:

S = (n/2)(a + l)

where S is the sum of the series, n is the number of terms, a is the first term, and l is the last term.

In this case, we can see that a = 12, d = 10 (the common difference), and l = 142. We can find n by using the formula for the nth term of an arithmetic sequence:

an = a + (n-1)d

Setting this equal to l and solving for n, we get:

142 = 12 + (n-1)10

130 = 10(n-1)

n-1 = 13

n = 14

Now that we know n, we can use the formula for the sum of an arithmetic series to find S:

S = (n/2)(a + l)

S = (14/2)(12 + 142)

S = 7(154)

S = 1078

Therefore, the sum of the arithmetic series 12 + 22 + ... + 142 is 1078.

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Answer:

600

Step-by-step explanation:

75 x 8 = 600

Answer:

the answer is 600 silver paper clips

Step-by-step explanation:

So the question asks how many SILVER PAPER CLIPS are in 8 boxes. The questions adds 25 GOLD CLIPS just to throw you off. You do not do nothing with it, it just there to mess with your mind. Also it says 75 silver clips in EACH box and there are 8 boxes. So you multiply 75 with 8 and get 600 SILVER PAPER CLIPS

Answer:

-5x+(- 15 ) = 20

x=-7

Step by Step

-5x+(-15)= 20 becomes

-5-15=20 add 15 tp (15 and 20)

-5x=35 ( divide by 51

x=-7

The presence of multiplication in an equation shows a context of repeated addition of values of that equation.

Multiplication is defined as one of the major arithmetic operation that shows the repeated addition of values of which a final figure is gotten. The other arithmetic operations include the following:

When there is multiplication sign in a mathematical expression it shows the context that repeated addition is needed to arrive at the desired value.

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Linear Transformation ta : ℜn → ℜm can be represented in the form of a matrix A

(a). The dimension of the matrix 'a' will be mxn. Suppose we have a vector v in R^n, so we can represent it in the form of a column matrix,

\(v = $\begin{bmatrix} v_{1} \\ v_{2} \\ \vdots \\ v_{n} \end{bmatrix}$\)

and when we apply the linear transformation to vector 'v' the resultant vector will be of the form Ax, i.e., \(A$\begin{bmatrix} v_{1} \\ v_{2} \\ \vdots \\ v_{n} \end{bmatrix}$\).

It is given that the dimension of the domain is n and that of codomain is m, so A is an m x n matrix.

The dimension of the matrix A depends on the number of columns of the matrix A which is equal to the dimension of the domain (n), and the number of rows of matrix A which is equal to the dimension of the co domain (m).

Hence, we can say that the dimension of a is \(mxn\), i.e., the number of rows is equal to the dimension of codomain and the number of columns is equal to the dimension of the domain.

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False. The minimum of two independent exponential random variables is not necessarily exponential.

For two independent exponential random variables X and Y, with rate parameters λ1 and λ2 respectively, the minimum of X and Y is a random variable Z with the cumulative distribution function (CDF) given by

\(F_Z(z) = 1 - e^(-(λ1+λ2)z)\).

The survival function of Z is given by

\(S_Z(z) = e^(-(λ1+λ2)z)\).

Therefore, the probability density function of Z is

\(f_Z(z) = (λ1 + λ2)e^(-(λ1+λ2)z)\).

This is not an exponential distribution because the form of the probability density function is not of the form \(f(z) = λe^(-λz)\).

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2.37 x 10^4 is equivalent to 52.249556 lb. So on converting 2.37 X 10^4 g into pounds we get 52.249556.

Therefore the answer is 52.249556.

We know that 1 pound is equivalent to 453.59237 grams. We can use it to find the conversion factor.

To convert 2.37 x 10^4 g to lb, we need to use the following conversion factor:

1 lb = 453.59237 g

So, to convert 2.37 x 10^4 g to lb, we can use the following calculation:

2.37 x 10^4 g ÷ 453.59237 g/lb = 52.249556 lb

Therefore, 2.37 x 10^4 g is equivalent to 52.2496 lb (rounded to four decimal places).

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Answer:

G. 14:5 is the correct answer.

Step-by-step explanation:

a:b = 4:5

a:c = 2:7

so,

here in first ratio a = 4

in second ratio a = 2

making them equal:

Taking LCM of 2 and 4 = 4

so

a:c = 2/7 = (2×2)/(7×2) = 4/14

so,

a = 4

c = 14

b = 5

so ratio c : b = 14:5

Answer:

its -3

Step-by-step explanation:

my explanation is in your comments whoops

Over the course of 300 months, the monthly payment of $965.92 will gradually pay off the entire loan.

Amortization is the act of paying off a debt or loan over a set period through scheduled, recurring payments. It entails dividing the principal into equal installments, with a portion of each payment going towards the interest and the remainder going towards the outstanding principal.

In this case, Heather McIntosh took out a 25-year loan for $190,000 with an interest rate of 5.5 percent.

To begin with, she paid a down payment of $25,000. We must first calculate the principal amount, which is the amount borrowed minus the down payment, to calculate the monthly payment.
Principal = $190,000 - $25,000 = $165,000
The interest rate is stated as an annual rate, so we must convert it to a monthly rate.
Monthly interest rate = 5.5% / 12 = 0.004583
Using the formula for calculating monthly payments, we can calculate the monthly mortgage payment:
Monthly payment = P [ r (1 + r)^n ] / [ (1 + r)^n – 1]
P = principal amount ($165,000)
r = monthly interest rate (0.004583)
n = number of monthly payments (25 years x 12 months/year = 300)
Monthly payment = $965.92
To figure out how much of each payment goes towards interest and principal, we can use an amortization schedule.

At first, the majority of each payment will go towards paying off the interest, while the remaining amount will go towards the principal. Over time, as the principal balance decreases, more of each payment will go towards paying down the principal balance and less towards interest. This is how amortization works.

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Answer:

please dont use the r slur :)) and if you care so much about your grades, heres an idea!! study on your OWN and dont rely on others

Step-by-step explanation:

The theorem that explains why ∠4 ≅ ∠8 is the Alternate Interior Angles Theorem. The same side interior angles pair are ∠3 and ∠5, and ∠4 and ∠8.

Alternate Interior Angles theorem states that if two parallel lines are intersected by a transversal, then the alternate interior angles formed are congruent.

The same-side interior angles are the angles that are on the same side of the transversal and inside the two parallel lines. In the given diagram, the same-side interior angle pairs are ∠3 and ∠5, and ∠4 and ∠8.

All the angle pairs formed by the intersection of the two parallel lines and the transversal are

Corresponding angles are ∠1 and ∠5, ∠2 and ∠6, ∠3 and ∠7, ∠4 and ∠8

Alternate interior angles are ∠3 and ∠5, ∠4 and ∠8

Alternate exterior angles are ∠1 and ∠7, ∠2 and ∠6

Vertical angles are ∠3 and ∠4, ∠5 and ∠6, ∠1 and ∠2, ∠7 and ∠8

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The expression that can be used to find the perimeter of the rectangle is  2(5x- 2) 2(3x + 1); 62 . Correct option is : c.

The formula for the perimeter of a rectangle is P = 2L + 2W, where L is the length and W is the width. To find the expression for the perimeter, we substitute the given expressions for L and W:

P = 2(5x - 2) + 2(3x + 1)

P = 10x - 4 + 6x + 2

P = 16x - 2(when x = 4)

To find the value of the perimeter when x = 4, we substitute x = 4 into the expression and simplify:

P = 16(4) - 2 = 62 centimeters

Therefore, the correct answer is option: c .

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Therefore, the degree of the resulting polynomial is m + n when two polynomials of degree m and n are multiplied together.

What is polynomial?

A polynomial is a mathematical expression consisting of variables and coefficients, which involves only the operations of addition, subtraction, multiplication, and non-negative integer exponents. Polynomials can have one or more variables and can be of different degrees, which is the highest power of the variable in the polynomial.

Here,

When two polynomials are multiplied, the degree of the resulting polynomial is the sum of the degrees of the original polynomials. In other words, if the degree of the first polynomial is m and the degree of the second polynomial is n, then the degree of their product is m + n.

This can be understood by looking at the product of two terms in each polynomial. Each term in the first polynomial will multiply each term in the second polynomial, so the degree of the resulting term will be the sum of the degrees of the two terms. Since each term in each polynomial has a degree equal to the degree of the polynomial itself, the degree of the resulting term will be the sum of the degrees of the two polynomials, which is m + n.

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Answer:

1. 5x(n-7)

2. 4÷(p-6)

3. 14+(7xn)            (n is "a number")

Answer: 60%

Step-by-step explanation:

First you have 1,080 satisfied out of 1,800.

Then you divide 1,080/ 1,800.

When you divide you get .6

Finally move the decimal 2 places to the right and you get 60 which is 60%.

The Given statement "If a distribution is normal, then it is not possible to randomly select a value that is more than 4 standard deviations from the mean"  is a true statement.

A normal distribution is a bell-shaped curve that represents how data is spread out around an average value. About 99.99% of the data in a normal distribution falls within 4 standard deviations from the average.

This means that it is very rare to find a data point that is more than 4 standard deviations away from the average. Therefore, if a distribution is normal, it is not possible to randomly select a value that is more than 4 standard deviation from the mean.

The answer is true.

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Answer: $30

Step-by-step explanation:

should be $30 spent in total

Answer:

1) 6.6 × 10^5   2) 3.65 × 10^-3   3) 9 × 10^-3   4)  8.1 × 10^2

Step-by-step explanation:

I think that's what it is.

A conditional statement is written in the if-then form. The hypothesis is the first or "if" part while the conclusion is the "then" or then part. Thus, the conditional statement would be

If a person lives in Ohio, then the person lives in the United states

To form the converse of the conditional statement, the hypothesis and conclusion are interchanged. It becomes

If a person lives in the United states, then they live in Ohio

what grade level is this

Answer:

20

Step-by-step explanation:

The ratio of red : yellow is 3 : 4 = 3x : 4x ( x is a multiplier )

If 3 red counters are removed then

red : yellow = 3x - 3 : 4x = 3 : 5

Expressing in fractional form

\(\frac{3x-3}{4x}\) = \(\frac{3}{5}\) ( cross- multiply )

5(3x - 3) = 12x

15x - 15 = 12x ( subtract 12x from both sides )

3x - 15 = 0 ( add 15 to both sides )

3x = 15 ( divide both sides by 3 )

x = 5

Then

number of yellow counters = 4x = 4 × 5 = 20

The parts of the ellipse are:

In this case, we have:

• Vertices,: (3, 2) and (3, -6) → the vertices lie over the vertical line x = 3 → , the ellipse has the form of the ellipse at the ,right, in the graph,,

• Endpoints of minor axis,: (0, -2) and (6, -2).

In this case, the general equation of the ellipse is:

Where:

• (h, k) are the coordinates of the center of the ellipse,

• a and b are the legs.

From the graph at the right, we see that the equations for:

• the vertex are:

We see that h = 3. Summing the equations and solving for k and a, we get:

So we have a = 4 and k = -2.

• the endpoints of the minor axis are:

Solving for b and replacing the value h = -3, we get:

So we have b = 3.

The four parameters of the ellipse are:

• (h, k) = (3, -2),

• a = 4

• b = 3.

Replacing these values in the general equation of the ellipse, we get:

Answer

Answer:

g(10)=92

Step-by-step explanation:

g(x)=10x-8

To find g(10), substitute x with 10

g(10)=10(10)-8

g(10)=100-8

g(10)=92

I hope this helps!

If f is differentiable on an open interval, f is concave down on that interval if f' is decreasing. This means that the slope of the tangent lines to the function f is getting smaller as we move along the interval, indicating a downward curving graph.

To determine whether a function f is concave down on an open interval, we need to analyze the behavior of its derivative, denoted as f'. Concave down refers to a function that curves downward or is "concave" in shape.

If f' is decreasing on the open interval, it means that the slope of the tangent lines to the function f is getting smaller as we move along the interval. This indicates that the graph of f is curving downward, resembling a concave shape.

Therefore, among the given options, option d ("f' is decreasing on that interval") accurately describes the condition for a function f to be concave down on an open interval. It is important to note that this relationship holds true when f is differentiable on the interval, allowing for the existence of a derivative f'.

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

To factor each expression, we apply the given concepts, that is, greatest common factor, difference of squares and perfect squares.

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

Expression 1:

The expression is:

\(2a^3 + 4a^2 + 8a\)

First, we find the gcf of the numbers 2, 4 and 8, which is 2.

Of the exponents, the gcf between 3, 2 and 1 is 1, so:

\(2a^3 + 4a^2 + 8a = 2a(\frac{2a^3}{2a} + \frac{4a^2}{2a} + \frac{8a}{2a}) = 2a(a^2 + 2a + 4)\)

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

Expression 2:

The expression is:

\(6y^4 - 294y^2\)

The gcf of 6 and 294 is 6.

The gcf of the exponents 2 and 4 is 4.

Thus:

\(6y^4 - 294y^2 = 6y^2(\frac{6y^4}{6y^2} - \frac{294y^2}{6y^2}) = 6y^2(y^2 - 49)\)

Then, applying the difference of squares:

\(y^2 - 49 = (y - 7)(y + 7)\)

Thus, the factored expression is:

\(6y^2(y^2 - 49) = 6y^2(y - 7)(y + 7)\)

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

Expression 3:

The expression is:

\(5x^2 + 50x + 125\)

The gcf of the coefficients, 5, 50 and 125 is 5, so:

\(5(\frac{5x^2}{5} + \frac{50x}{5} + \frac{125}{5}) = 5(x^2 + 10x + 25)\)

Applying the perfect square, we get that:

\(x^2 + 10x + 25 = (x + 5)^2\)

Tus, the factored expression is:

\(5(x^2 + 10x + 25) = 5(x+5)^2\)

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Answer:

paro paro g

Step-by-step explanation:

fly high butterfly