two different points on a number line are both 3 units from the point with coordinate -4. The solution to which equation gives the coordinates of both points

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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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!

In multiplication when bases are same, the powers are added. So the answer after simplifying is d) -24a^3b^7

Product of  (3a^2b^4)*(-8ab^3)

Multiplication is one of the four basic arithmetic operations, alongside addition, subtraction, and division. Multiplication essentially means the repeated addition of groups of equal sizes. While solving multiplication problems, one-digit numbers can be multiplied in a simple way by using the multiplication tables, but for larger numbers, we split the numbers into columns using their respective place values, like ones, tens, hundreds, thousands, and so on.

The multiplication formula is expressed as, Multiplicand × Multiplier = Product; where:

Multiplicand: The first number (factor).

Multiplier: The second number (factor).

Product: The final result after multiplying the multiplicand and multiplier.

(3a^2b^4)*(-8ab^3)= -24a^3b^7

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(-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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Answer:26

Step-by-step explanation:

x - .35x = 16.90

x(1 - .35) = 16.90

x(.65) = 16.90

x = 16.90/.65

x = $26

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:

2*10^-4

Step-by-step explanation:

0.02*0.01

Answer:

$37.12

Step-by-step explanation:

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

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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125 and 216 are two perfect cubes

Answer

5.6967 rounded up will be 5.697.

Step-by-step explanation:

Answer:

46

Step-by-step explanation:

Answer:

11000

Step-by-step explanation:

I=(PxRxT)/100

I=(10000x20x1)/100x2

I=200000/200

I=1000

TA=10000 + 1000

Total Interest = 11000

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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The surface area of the given cuboid is 48ft².

The formula for the Surface area of a cuboid: 2(lw + wh +lh)

Now, substitute values in the formula as follows:

Therefore, the surface area of the given cuboid is 48ft².

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The only possible equation of the drawn line is: y - 2 = 1/2(x + 4)

The rest options are not equations of the drawn line.

The equation, y - b = m(x - a), is the point-slope form of any given line where m is the slope of the line and any point on the line is given as (a, b).

Slope (m) = rise/run.

Find the slope (m) of the graph at the right.

Slope (m) = rise/run = 1 units/2 units

Slope (m) = 1/2.

Any possible equation of the line should have a slope of 1/2.

y - 2 = 1/2(x - 4), y - 2 = 1/2(x + 4), and y - 4 = 1/2(x - 2) are the only equations that has a slope of 1/2.

Using a point on the line, say (0, 3), substitute x = 0 and y = 3 into each of the three equations to check if the equation is true.

y - 2 = 1/2(x - 4)

3 - 2 = 1/2(0 - 4)

1 = -2 [not true]

y - 2 = 1/2(x + 4)

3 - 2 = 1/2(0 + 4)

1 = 2 [not true]

y - 4 = 1/2(x - 2)

3 - 4 = 1/2(0 - 2)

-1 = -1 [true]

Therefore, the only possible equation of the drawn line is: y - 2 = 1/2(x + 4)

The rest 4 equations are not equations of the drawn line.

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Answer:

x = 10

Step-by-step explanation:

a and b are vertically opposite angle ...

☘☘☘...

From the given geometry, it can be concluded that line 'a' and 'b' are parallel.

What do you mean by geometry?

Geometry is a discipline of mathematics concerned with the study of the sizes, forms, locations, angles, and dimensions of objects.

The area of mathematics that studies the characteristics, measurement, and spatial relationships of points, lines, planes, and figures.

From the geometry, the angles 19 and 22 are consecutive converse exterior angles when line 'a' and 'b' is cut through a transversal 'e'. And their sum is 180°. So, lines 'a' and 'b, are parallel.

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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 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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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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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.

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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