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10. Rebecca goes to a bank with $2000 she has saved over the summer. The bank advertises a 3% interest rate when opening a savings account. The bank compounds the money daily with an exponential formula of A(t) = Pe^rt, where P represents the initial amount deposited, e is Euler's constant (approximately 2.71828), r is the rate in decimal form, and t is the total time. Rebecca wants to know how much money will be in her savings account after 10 years.

P = 2000

e = Euler's constant (2.71828)

r = 0.03

t = 10

A(t) = Pe^rt

A(10) = 2000 * 2.71828^ 0.03*10

A(10) = 2000 * 2.71828^ 0.3

A(10) = 2699.71707036 ≈ $2700

The initial amount and rate of change given a table for a linear function are $65 and $86, respectively

The table of linear function represents the given parameter

On the table, we have the following points

(x, y) = (6, 476) and (10, 736)

The rate of change is calculated as

Rate = (y2 - y1)/(x2 - x1)

So, we have

Rate = (736 - 476)/(10 - 6)

Evaluate

Rate = 65

This means that the rate of change is $65

The initial amount is calculated as

y = m(x - x1) + y1

Where

m = 65

So, we have

y = 65(x - x1) + y1

Using one of the points, we have

y = 65(x - 6) + 476

Set x = 0

So, we have

y = 65(0 - 6) + 476

Evaluate

y = 86

Hence, the initial amount and rate of change given a table for a linear function are $65 and $86, respectively

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The sum of the numbers as a product of their GCF is 5 x ( 5 + 7 ).

Given,

25 + 35.

We need to find its GCF and another sum.

It is the greatest factor common to both 25 and 35.

Example: 8 and 24

- 4 x 2 = 8

- 4 x 6 = 24

4 is the GCF.

Find the GCF of 25 and 35.

5 x 5 = 25

5 x 7 = 35

5 is the GCF of 25 and 35.

Now,

25 + 35 = 60

5 x ( 5 + 7 ) = 5 x 12 = 60

The sum of the numbers as a product of their GCF is 5 x ( 5 + 7 )

Thus,

The sum of the numbers as a product of their GCF is 5 x ( 5 + 7 ).

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The difference between the distances flown by these birds is 150 Km.

According to the statement

We have to find that the rate of each birds speed in kilometers per hour.

So, For this purpose, we know that the

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

From the given information:

We have the graph given within the question to understand it please see the image below.

We have to search out the difference within the distances flown by these two birds after 3 hours of flight.

According to the question -

The slope of the road is -

m = 400/5 = 80

The y - intercept of the road is 0.

Therefore  c = 0.

Therefore, the equation of the road are -

y = 80x

The distance covered by Bird 1 is

D[1] = initial distance + 80 x 3 = 250 + 240 = 490 Km.

And

The distance covered by Bird 2 is

D[2] = initial distance + 80 x 3 = 400 + 80 x 3 = 400 + 240 = 640 Km.

Then

difference between the distances flown by these birds is D[2] - D[1] = 640 - 490 = 150 Km.

Therefore, The difference between the distances flown by these birds is 150 Km.

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Answer:

46

Step-by-step explanation:

(-7/5) is the multiplicative inverse of the number - 5/7.

The answer to the question is (b/a), which is the multiplicative inverse of the fraction number that is (a/b).

So, according to the question:

The reciprocal of (-5/7) is (-7/5).

As a result, (-7/5) is the right response to a multiplicative inverse.

The reciprocal of the supplied integer can be used to establish a number's multiplicative inverse. The denominator must not be 0 in order for a multiplicative inverse to exist. And the result of the multiplication should be 1.

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The average rate of change is 1.625.

The average rate of change in height for chuck can be found as follows:

The average rate of change is a measure of how much the function changed per unit, on average, over that interval.

Therefore,

average rate of change = change in y / change in x

Therefore,

(10, 51)(18, 64)

average rate of change = y₂ - y₁ / x₂ - x₁

x₁ = 10

x₂ = 18

y₁ = 51

y₂ = 64

Therefore,

average rate of change = 64 - 51 / 18 - 10

average rate of change = 13 / 8

average rate of change = 1.625

Therefore, the average rate of change is 1.625.

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Answer:

x = 10

Step-by-step explanation:

Answer:

-7/18

Step-by-step explanation:

Multiply both the numerator and denominator of each fraction by the number that makes its denominator equal the LCD. This is basically multiplying each fraction by 1.

( -1/2 × 9/9) + (1/9 × 2/2) = ?

Complete the multiplication and the equation becomes:

-9/18 + 2/18 = ?

Then:

-9+2/18 = -7/18

Therefore:

-1/2 + 1/9 = -7/18

Answer:

vhdvbhahshsh

shsljjhsishhgdddndhd

a and b are vertically opposite angle ...

☘☘☘...

The measured height in feet of the base to its highest peak is 18045.5 feet

The given parameter is

Length of the base to its highest peak = 5500 meters

As a general rule

1 meter = 3.281 feet

So, we have:

Length of the base to its highest peak = 5500 * 3.281 feet

Evaluate the product

Length of the base to its highest peak = 18045.5 feet

Hence, the measured height in feet of the base to its highest peak is 18045.5 feet

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The unit price of the pair of gloves is $6.59

The package contains 4 pairs of insulated gloves costs ​$26.36.

The unit price of the pairs of gloves can be found as follows:

Unit price is the price at which a single quantity of a product is being sold.

Therefore, the unit price is the price of a single pair of gloves.

Hence,

unit price of the pair of gloves = total price / number of pairs of gloves

where

Therefore,

unit price of the pair of gloves = 26.36 / 4

unit price of the pair of gloves = $6.59

Therefore, the unit price of the pair of gloves is $6.59

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Answer

5.6967 rounded up will be 5.697.

Step-by-step explanation:

Answer:

$37.12

Step-by-step explanation:

Total cost = $3.50(350/33) = $37.12

According to the given statement;

If ​P(A)=0.9​, ​P(B)​=0.1, and A and B are​ independent, ​ P(A and​ B)=0.09

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a proposition is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty. The likelihood that an event will occur increases with its probability. A straightforward illustration is tossing a fair (impartial) coin. Since there are no other possible outcomes and the coin is fair, the odds of both the outcomes, "heads" and "tails," are equally likely to occur. As a result, the probability of either outcome is half.

According to the given value;

P(A) = 0.9

P(B) = 0.1

A and B independent;

We know that independent

P(A∩B) = P(A) · P(B)

             = (0.9)*(0.1)

             =0.09

P(A∩B) =0.09

hence, If ​P(A)=0.9​, ​P(B)​=0.1, and A and B are​ independent, ​ P(A and​ B)=0.09

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The possible endpoints are: (i) A(x, y) = (6, - 2) and B(x, y) = (3, 5), (ii) A(x, y) = (4, 4) and B(x, y) = (6, - 4).

In this problem we know the location of the midpoint and the line segment ratio. There are two posibilities according to the definition of line segment ratio:

AX / BX = 2 / 3   (1)

BX / AX = 2 / 3   (2)

And now we solve for each case:

Case 1

X(x, y) = A(x, y) + (2 / 5) · [B(x, y) - A(x, y)]

X(x, y) = (3 / 5) · A(x, y) + (2 / 5) · B(x, y)

(4.8, 0.8) = (3 / 5) · A(x, y) + (2 / 5) · B(x, y)

(4.8, 0.8) = 0.6 · A(x, y) + 0.4 · B(x, y)

(4.8, 0.8) - 0.6 · A(x, y) = 0.4 · B(x, y)

(12, 2) - 1.5 · A(x, y) = B(x, y)

B(x, y) = (12, 2) - 1.5 · A(x, y)

Now we proceed to check each choice:

A(x, y) = (6, - 2)

B(x, y) = (12, 2) - 1.5 · (6, - 2)

B(x, y) = (3, 5)    TRUE

A(x, y) = (6, 2)

B(x, y) = (12, 2) - 1.5 · (6, 2)

B(x, y) = (3, - 1)   FALSE

A(x, y) = (8, 1)

B(x, y) = (12, 2) - 1.5 · (8, 1)

B(x, y) = (0, 0.5)  FALSE

A(x, y) = (2.4, 0.4)

B(x, y) = (12, 2) - 1.5 · (2.4, 0.4)

B(x, y) = (8.4, 1.4)  FALSE

A(x, y) = (4, 4)

B(x, y) = (12, 2) - 1.5 · (4, 4)

B(x, y) = (6, - 4)     TRUE

A(x, y) = (1.8, - 1.2)

B(x, y) = (12, 2) - 1.5 · (1.8, - 1.2)

B(x, y) = (9.3, 3.8)  FALSE

Case 2

X(x, y) = B(x, y) + (2 / 5) · [A(x, y) - B(x, y)]

X(x, y) = (2 / 5) · A(x, y) + (3 / 5) · B(x, y)

(4.8, 0.8) = (2 / 5) · A(x, y) + (3 / 5) · B(x, y)

(4.8, 0.8) = 0.4 · A(x, y) + 0.6 · B(x, y)

(4.8, 0.8) - 0.4 · A(x, y) = 0.6 · B(x, y)

(12, 2) - 0.667 · A(x, y) = B(x, y)

B(x, y) = (12, 2) - 0.667 · A(x, y)

Now we proceed to check each choice:

A(x, y) = (6, - 2)

B(x, y) = (12, 2) - 0.667 · (6, - 2)

B(x, y) = (8, 3.334)             FALSE

A(x, y) = (6, 2)

B(x, y) = (12, 2) - 0.667 · (6, 2)

B(x, y) = (8, 0.667)             FALSE

A(x, y) = (8, 1)

B(x, y) = (12, 2) - 0.667 · (8, 1)

B(x, y) = (6.664, 1.333)      FALSE

A(x, y) = (2.4, 0.4)

B(x, y) = (12, 2) - 0.667 · (2.4, 0.4)

B(x, y) = (10.399, 1.733)     FALSE

A(x, y) = (4, 4)

B(x, y) = (12, 2) - 0.667 · (4, 4)

B(x, y) = (9.332, - 0.668)   FALSE

A(x, y) = (1.8, - 1.2)

B(x, y) = (12, 2) - 0.667 · (1.8, - 1.2)

B(x, y) = (10.8, 2.8)            FALSE

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Answer:

2*10^-4

Step-by-step explanation:

0.02*0.01

The equation of a line which is perpendicular to [y = (4x - 11)] and passes through the point (-2, 1) will be [(4y + x) = 2].

As per the question statement, a line is perpendicular to [y = (4x - 11)] and passes through the point (-2, 1).

We are required to determine the equation of the above mentioned line.

Now, we know that, the standard equation of a line goes as [y = (mx + c)] where, "m" is the slope of the line while "c" is the y-intercept.

Comparing [y = (4x - 11)] to the standard form, we can identify that (m = 4), i.e., slope of the given line is 4.

Since the products of the slopes of two perpendicular lines is (-1), and considering the slope of our required line to be "m₁", we can say that,

[tex]4*m_{1}=(-1)\\ or,m_{1}=\frac{-1}{4}[/tex]...[since our required line is perpendicular to [y = (4x - 11)]

                        and slope of [y = (4x - 11)] is 4]

That is, slope of our required line is [tex](\frac{-1}{4})[/tex].

Another concept we need to know about forming the equation of a line is that, the equation of a line can be written as  [tex][(y-y_{1})=m(x-x_{1})][/tex], if the line passes through the point (x₁, y₁).

Here, our concerned line passes through the point (-2, 1) and has a slope of [m =  [tex](\frac{-1}{4})[/tex]].

Therefore, equation of our concerned line can be written as

[tex](y-1)=(\frac{-1}{4})[x-(-2)]\\or,(y-1)=(\frac{-1}{4})(x+2)\\or,(y-1)=(\frac{-x}{4})+(\frac{-1}{4}*2)\\ or,(y-1)=(\frac{-x}{4})+(\frac{-1*2}{4})\\or,(y-1)=(\frac{-x}{4})+(\frac{-1}{2})\\or,y=(\frac{-x}{4})+1+(\frac{-1}{2})\\or,y=(\frac{-x}{4})+(1-\frac{1}{2})\\or, y=(\frac{-x}{4})+\frac{1}{2}\\or,4y=(-x)+2\\or,4y+x=2[/tex]

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Answer:

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

Let the weekly salary is x.

Since both options end up with same amount, it can be shown as:

The matching choice is C.

The correct option is option C.

T(x) = 2.9(1.05)⁴ˣ ⁺ ⁵

Given the number of cities in a region is represented by the function:

C(x) = 2.9(1.05)ˣ

The approximate number of people per city is represented by the function P(x) = (1.05)³ˣ⁺⁵

we are asked to determine T(x), the approximate population in the region = ?

combine C(x) and P(x)

therefore, T(x) = C(x)P(x)

T(x) = 2.9(1.05)ˣ(1.05)³ˣ⁺⁵

During multiplication, when bases are same then powers are added.

T(x) = 2.9(1.05)³ˣ⁺ˣ⁺⁵

T(x) = 2.9(1.05)⁴ˣ⁺⁵

Hence we get the approximate function of T(x) as T(x) = 2.9(1.05)⁴ˣ⁺⁵

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What is the 10% of number in which the 14% is 160

Although "pct," "pct," and occasionally "pc" are also used as abbreviations, the percent symbol "%" is most usually used to denote it. A% is a number that has neither dimensions nor a defined unit of measurement.

being that,

14% × x = 160

14/100 × x = 160

x = 160 × 100/14

x = 1142.86

The current value is 1142.86.

10% of the total number must be located.

to say,

10% x 1142.86 = 10 / 100 x 1142.86

= 114.286

Consequently, 114.286 is the value of the 10% of the number.

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125 and 216 are two perfect cubes

The 10 students can be lined up for lunch in 3628800 ways.

Factorial of a number n is defined as the product of that number with every number less than or equal to the given number till 1.

The formula is given by:

n! = n(n-1)(n-2)(n-3(n-4)(n-5)(n-6)....3.2.1

We have,

n! = n(n-1)(n-2)(n-3)(n-4)(n-5)......3.2.1

We have to arrange for 10 students so n = 10.

Now,

10! = 10.9.8.7.6.5.4.3.2.1

Multiply each number.

10! = 3628800 ways

Therefore the 10 students can be lined up for lunch in 3628800 ways.

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Answer:

12, 12, and 12

Step-by-step explanation:

12 is an even integer, and 12 + 12 + 12 = 36, so it would be logical for 12 to be the unknown integer.

Answer-  A) 59,600 ; B) 4.12% per year.

Explanation

84,200 minus 24,600 is 59,600. This means the originally cost put into the account was 59,600.

Next we have to divide the amount of interest earn into the number of years that the amount was accumulated. 24,600 divided by 10 is 2460. This means that each year 2,460 were earned in interest. 59,600 divided into 2,460 is 0.0412751678. This rounds to .0412 If we move our decimal to a percentage this leaves us with 4.12% This means that annual interest on the investment is 4.12%

Hope this helps! Good Luck!

Answer: if my math is correct i think its b

Step-by-step explanation:

The correct option is option C that is the due amount which Tina needs to pay at the end of fourth month is $ 614.4.

What is algebra ?

Algebra is a branch of mathematics that deals with various symbols and the arithmetic operations such as division , multiplication , etc.

It is given that Tina needs to purchase a refrigerator as replacement for $1100.

The monthly periodic rate if balance is not paid by the second month = 1.2 %

The amount she paid by the second month = $500

The due amount is :

= 1100 - 500

= $600

This amount she decided to pay by end of fourth month or after two more months.

Let's assume the amount she had to pay now at the end of fourth month is x then it given by :

= 600 + ( 600 × [tex]\frac{1.2}{100}[/tex] × 2)

= 600 + ( 12 × 1.2 )

= 600 + 14.4

= $ 614.4

Therefore , the correct option is option C that is the due amount which Tina needs to pay at the end of fourth month is $ 614.4.

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Answer:

Hope this helps

Step-by-step explanation:

350*.06=21

annually 21*7=147

quarterly 21(4*7)=588

monthly 21(12*7)=1764