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4 years ago

There are (49)5 ⋅ 40 books at the library. What is the total number of books at the library?

Mathematics

2 answers:

Romashka-Z-Leto [24]4 years ago

8 0

it is 9,800 total books

dmitriy555 [2]4 years ago

5 0

There is a total of 9,800 books at the library because to find the total you need to multiply 49 by 5 by 40
so 49*5= 245
Finally you multiply 245 by 40 and you get a total of 9,800

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Select the recursive and explicit formula for the Arnold family 2 answers

MariettaO [177]

Answer: The first and last options are correct

Explanation:

The recursive formula is written in terms of the previous term of the sequence. From the information given,

the Arnold's are going to save a nickel on the first day of the month and double the amount each day of the month. Thus, the recursive formula would be

$A(n)\text{ = a}_{n\text{ - 1}}\text{ }\times\text{ 2}$

where

an - 1 defines a previous term

To write the explicit formula, we would apply the formula for finding the nth term of an arithmetic sequence which is expressed as

An = ar^(n - 1)

where

a is the first term of the sequence

n is the number of terms

r is the common ratio between consecutive terms

Thus,

r = 2 because the amount is doubling each day

n = number of days

a = value of 1 nickel = $0.05

By substituting these values into the formula,

the explicit formula is

A(n) = 0.05(2)^n - 1

7 0

1 year ago

Write an equation to describe the proportional relationship in this table. Explain your thinking and how you got your answer.

creativ13 [48]

Focus on the values in red outside the table (on the left and right sides). As the output increases by 4, the input increases by 1. This leads to the slope being rise/run = 4/1 = 4. The slope is the number just to the left of the x variable. So that's how they ended up with the equation y = 4x.

You can think of it as y = 4x+0, and note how it's in the form y = mx+b

m = 4 = slope

b = 0 = y intercept

The y intercept is the value of y when x = 0.

--------

Now because x = 0 and y = 0 pair up together, we can find the slope a different way: Pick any row other than the first row. Divide the y value over its paired x value. So let's say we pick on row two and we'd get a slope of y/x = 4/1 = 4.

Or we could pick on row three and get y/x = 8/2 = 4.

Picking on the fourth row gets us the slope to be y/x = 12/3 = 4. We end up with the same slope value each time. Again, this trick only works if (x,y) = (0,0) is on the line. Otherwise, you'll need to use the first method or use the slope formula.

For equations like this, we consider them a direct proportion. As x increases, so does y. As x increases by 1, y increases by 4. This is the same throughout the table.

----------

A real world example of this could be that x represents the number of sodas you buy, and if each soda is $4, then y = 4x represents the total cost of buying x number of sodas.

For instance, if you bought x = 10 sodas, then y = 4*x = 4*10 = 40 dollars is what you spend overall.

7 0

3 years ago

deposits \$700 into an account that pays simple interest at a rate of 6\% per year. How much interest will he be paid in the fir

Virty [35]

Answer:

$210

Step-by-step explanation:

pnr/100

700×6×5/100

$210

5 0

3 years ago

Expansion Numerically Impractical. Show that the computation of an nth-order determinant by expansion involves multiplications,

posledela

Answer:

number of multiplies is n!
n=10, 3.6 ms
n=15, 21.8 min
n=20, 77.09 yr
n=25, 4.9×10^8 yr

Step-by-step explanation:

Expansion of a 2×2 determinant requires 2 multiplications. Expansion of an n×n determinant multiplies each of the n elements of a row or column by its (n-1)×(n-1) cofactor determinant. Then the number of multiplies is ...

mpy[n] = n·mp[n-1]

mpy[2] = 2

So, ...

mpy[n] = n! . . . n ≥ 2

If each multiplication takes 1 nanosecond, then a 10×10 matrix requires ...

10! × 10^-9 s ≈ 0.0036288 s ≈ 0.004 s . . . for 10×10

Then the larger matrices take ...

n=15, 15! × 10^-9 ≈ 1307.67 s ≈ 21.8 min

n=20, 20! × 10^-9 ≈ 2.4329×10^9 s ≈ 77.09 years

n=25, 25! × 10^-9 ≈ 1.55112×10^16 s ≈ 4.915×10^8 years

_____

For the shorter time periods (less than 100 years), we use 365.25 days per year.

For the longer time periods (more than 400 years), we use 365.2425 days per year.

8 0

4 years ago

Solve for x round to the nearest tenth.

lesantik [10]

Answer:

x ≈ 15.9

Step-by-step explanation:

Using Pythagoras' identity in the right triangle

x² + 6² = 17²

x² + 36 = 289 ( subtract 36 from both sides )

x² = 253 ( take the square root of both sides )

x = $\sqrt{253}$ ≈ 15.9 ( to the nearest tenth )

3 0

3 years ago

Read 2 more answers