Tim wants to buy soda. He can choose a 6-pack of 0.355-liter cans or a 2-liter bottle. Which statement is true?
The 6-pack contains 0.130 liters more soda.
The 2-liter bottle contains 0.130 liters more soda.
The 2-liter bottle contains 0.645 liters more soda.
The 6-pack contains 0.645 liters more soda.

This is closed under addition because the sum of the polynomial produces another polynomial.

A polynomial is an expression that involves the addition, subtraction and multiplication of variables.

Polynomials will be closed under an operation if the operation produces another polynomial.

(3x⁴ + 5x - 7) + (2x - (2x)² + 4x - 1) + [(-8x)⁻² - (3x)³ + 7]

= 3x⁴ - 27x³ - 4x² + 9x - 1 + (-8x)⁻²

This is closed under addition because the sum of the polynomial produces another polynomial.

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The statement about both functions that is true is: B. The y-intercept of f(x) is greater than the y-intercept of g(x).

The y-intercept of a function is the output value (y) of the function when the input value (x) is zero. On a graph, it would be the value of y-coordinate of the point where the line cut across the y-axis.

From the table given for function g, the value of y when x is zero is 3. The y-intercept for g(x) is 3.

From the graph given for function f, the value of the point at which the line intercepts the y-axis is 6. Therefore, the y-intercept for f(x) is 6.

Therefore, the statement about both functions that is true is: B. The y-intercept of f(x) is greater than the y-intercept of g(x).

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Answer:

C. 15 cm

Step-by-step explanation:

The formula to find the area of a circle is: π × r²

But since we need to solve for the radius, we use the formula:

[tex]r = \sqrt{ \dfrac{ A }{ \pi } \phantom{\tiny{!}}}[/tex]

r = radius

A = area

π = 3.14

Now we substitute the information given in the text into the equation

[tex]r = \sqrt{ \dfrac{ A }{ \pi } \phantom{\tiny{!}}}[/tex]

Substitute values into the equation

[tex]r = \sqrt{ \dfrac{ 706.5 }{ 3.14 } \phantom{\tiny{!}}}[/tex]

Divide 706.5 by 3.14

[tex]r = \sqrt{ 225 }[/tex]

Take the square root of 225

[tex]r = {15 }[/tex]

So, the radius of the pie is 15 cm

Answer:

Step-by-step explanation:

1.  12/3x = 1/2

4/1x = 1/2

4/1x = 1/2 / 4/1

1/2 x 1/4 ,  x = 1/8.

2).    x / 2.5 = 1. 75/ 1

cross multiply to get

x = 2.5 x 1.75

x = 4.375

Equation in slope intercept form

Now

Answer:

27

Step-by-step explanation:

a + b = 7

a - b = 3

2a = 10

a = 5

b = 7 - 5

b = 2

3⁵ / 3² = 3³ using law of indices

3³ = 27.

Answer:

27

Step-by-step explanation:

a + b = 7

a - b = 3

2a = 10

a = 5

b = 7 - 5

b = 2

3⁵ / 3² = 3³ using law of indices

3³ = 27

Answer:

8:20 or if you want it simplified 2:5

Step-by-step explanation:

Answer:

the postulate that proves these two triangles congruent is AAA or angle angle angle.

Using an exponential function, it is found that the equation is:

[tex]f(1.8868) = 60(0.5)^{1.8868}[/tex]

Which means that approximately 16.22 mg remain.

A decaying exponential function is modeled by:

[tex]A(t) = A(0)(1 - r)^t[/tex]

In which:

In this problem, the equation is:

[tex]f(h) = m(0.5)^h[/tex]

We work with a 50 mg Cobalt-60 sample, hence m = 60, and considering a half-life of 5.3 years, in 10 years we have h = 10/5.3 = 1.8868. Hence the equation is:

[tex]f(1.8868) = 60(0.5)^{1.8868} = 16.22[/tex]

Approximately 16.22 mg remain.

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Answer:

Here I graphed it for you.

Step-by-step explanation:

Answer:

10. s = 1.50x

11. s = 28x + 5

Step-by-step explanation:

10. s (money); so multiply x (the amount of pencils) by the price which is 1.50. Which is equal to 112.50.

11. s (money); multiple x (the amount of shoes) by the price, 28, which equals 84. Then add 5 for the shipping. This equals 89.

Answer:3 jeans and 11 shirts with 15 dollars leftover

Step-by-step explanation:

3x25=75

11x10=110

110+75=185

200-185=15

25x4 will make the leftover money higher, so 3 and 11

Answer:

12000

Step-by-step explanation:

Using this information, you can make a ratio: 12.2/50 = x/48744

By simplifying this ratio you get that 50x = 594676. Dividing both sides by 50 you get about 11900, which you can round up to 12000

Answer:

11,894 women

Step-by-step explanation:

ratio of women to employees = 12.2 : 50

Let x = number of women employees to 48744 employees

12.2 : 50 = x : 48744

⇒ 12.2 / 50 = x / 48744

⇒ 0.244 = x / 48744

⇒ x = 0.244 · 48744

⇒ x = 11893.536

⇒ x = 11894 (nearest whole number)

Therefore, there are approximately 11,894 women in a company with a total of 48,744 employees

Answer:

Hope it helps u

Step-by-step explanation:

1.7

1.749

1.75

1.775

1.796

1.84

Answer:

the order would go 1.7, 1.749, 1.75, 1.775, 1.796, then 1.84.

Step-by-step explanation:

becuase if you ignore how long the numbers are, and focus on numerical order like 1, 2, 3, and apply that to this, this becomes the order.

Answer:

A.

Step-by-step explanation:

πr^2 h/3

Hope this helps!

Answer:

41,246.046 which could be rounded to .05 cents at the end.

Step-by-step explanation:

[tex]20700(1.09)^8[/tex]

we use this equation since we are working with interest, and we are compounding interest twice per year, for 4 years or 8 times.

hope this helps, please rate and mark as brainelst.

Answer:

C. work backwards

Step-by-step explanation:

I did it

Using an exponential function, it is found that 4 mg of the substance would still be left after 32 days.

A decaying exponential function is modeled by:

[tex]A(t) = A(0)(1 - r)^t[/tex]

In which:

In this problem, considering that the initial amount if of 64 mg, and we are working with half-lifes, the equation is given by:

[tex]A(t) = 64(0.5)^t[/tex]

32 days is 32/8 = 4 half-lifes, hence the amount remaining in mg is given by:

[tex]A(4) = 64(0.5)^4 = 4[/tex]

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The difference between the amount in two cards of Sandra after 4 years will be $125.58 approx.

If n is the number of times the interested is compounded each year, and 'r' is the rate of compound interest annually, then the final amount after 't' years would be:

[tex]a = p(1 + \dfrac{r}{n})^{nt}[/tex]

For this case, Sandra has got 2 credit cards p and q. Calculating the final amount both card will have after 4 years:

Initial amount = p = $726.19

The rate of interest is r = 10.19% = 10.19/100 = 0.1019 (converted percent to decimal)

Years for which amount is compounded = 4 years, Thus, t = 4

The interest is compounding semiannually, that means twice per year, thus, n = 2

Thus, the final amount in card p after 4 years would be:

[tex]a = p(1 + \dfrac{r}{n})^{nt}\\\\a = 726.19(1+0.1019/2)^{2 \times 4} \\\\a= 726.19 \times (1.05095)^8 \approx 1080.70\: \rm (in \: dollars)[/tex]

Initial amount = p = $855.20

The rate of interest is r = 8.63% = 8.63/100 = 0.0863 (converted percent to decimal)

Years for which amount is compounded = 4 years, Thus, t = 4

The interest is compounding monthly, that means twelve times per year, thus, n = 12

Thus, the final amount in card q after 4 years would be:

[tex]a = p(1 + \dfrac{r}{n})^{nt}\\\\a = 855.20(1+0.0863/12)^{12 \times 4} \\\\a= 855.20\times (1.0071916)^{48} \approx 1206.28\: \rm (in \: dollars)[/tex]

Clearly card q has more amount than card p at the end of 4 years.

The difference is: 1206.28 - 1080.70 = 125.58 (in dollars)

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Answer:

Question (a)

Given equation:

[tex]8^{2x} = 32^{x+3}[/tex]

8 can be written as [tex]2^3[/tex]

32 can be written as [tex]2^5[/tex]

Therefore, we can rewrite the equation with base 2:

[tex]\implies (2^3)^{2x} = (2^5)^{x+3}[/tex]

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

Question (b)

To solve:

[tex](2^3)^{2x} = (2^5)^{x+3}[/tex]

Apply the exponent rule [tex](a^b)^c=a^{bc}[/tex] :

[tex]\implies 2^{3 \cdot 2x} = 2^{5(x+3)}[/tex]

[tex]\implies 2^{6x} = 2^{5x+15}[/tex]

[tex]\textsf{If }a^{f(x)}=a^{g(x)}, \textsf{ then } f(x)=g(x)[/tex] :

[tex]\implies 6x = 5x+15[/tex]

Subtract [tex]5x[/tex] from both sides:

[tex]\implies x = 15[/tex]

Answer:

19.6

Step-by-step explanation

= Sum of terms / number of terms

= ( 20 + 19 +18+ 20 +19 +22 ) / 5

= 19.6

The volume of the right rectangular prism is the amount of cubes in it

The formula to determine the volume of the right rectangular prism is V(n) = n

The question is incomplete; as the figure is not given.

So, I will provide a general solution

The volume of a one inch cube is:

[tex]V = 1^3[/tex]

[tex]V = 1[/tex]

Assume the number of one inch cubes used to fill the right rectangular prism is n.

Then the volume of the right rectangular prism would be:

[tex]V(n) = n * 1[/tex]

This gives

[tex]V(n) = n[/tex]

Hence, the general formula to determine the volume of the right rectangular prism is V(n) = n

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Answer: 47.28 miles

Step-by-step explanation: 5.91 times 8= 47.28

Answer:

A) 3

Step-by-step explanation:

12 * 2 = 24

8 * 3 = 24

24 = 24

Answer:

(0, 0) are the coordinates of the mid point

Step-by-step explanation:

[tex]coordinate \: of \: mid \: point \: = \\ ( \frac{x1 + x2}{2} \: \: \: \: \frac{y1 + y2}{2} ) \\ ( \frac{ - 3 + 3} {2} \: \: \: \: \: \: \: \frac{7 + - 7}{2} ) \\ ( \frac{0}{2} \: \: \: \: \: \: \: \: \frac{0}{2} ) \\ (0 \: \: \: \: \: \: \: \: \: \: \: 0)[/tex]

Answer:

the median is 55.6

Step-by-step explanation:

The average annual temperatures (°F) from 1991 to 2000 for Kentucky were 57.5, 55.1, 52.2, 55.6, 55.6, 54.4, 54.5, 58.3, 57.3, and 55.7.

We have to evaluate the measures of center.

Firstly, we will calculate the mean.

Mean = (Sum of all the observations)/ (Total number of observations)

Mean =  

=

= 55.62

Now, we will calculate mode.

Mode is a statistical term that refers to the most frequently occurring number found in a set of numbers.

Consider the data 57.5, 55.1, 52.2, 55.6, 55.6, 54.4, 54.5, 58.3, 57.3, and 55.7.

Mode = 55.6

Now, we will calculate the median.

Firstly, we will arrange in the ascending order.

52.2, 54.4, 54.4,55.1 ,55.6, 55.6, 55.7, 57.3, 57.5, 58.3

Since there are 10 terms.

Median = th observation

Median = 5th observation.

Since, the 5th observation is 55.6.

Therefore, the median is 55.6

The ninth term of the series [tex]80,60,45.....[/tex]  is [tex]50[/tex].

We need to determine the relationship between the consecutive terms of the series to evaluate the succeeding terms of the series.

How to find the terms in a series?

The difference between the first and second terms is [tex]60-80=-20[/tex].

The difference between the second and the third terms is [tex]45-60=-15[/tex]

So, the difference between the third and the fourth terms will be [tex]-10[/tex]. So, the fourth term will be [tex]45-10=35[/tex].

Similarly, the difference between the eighth and the ninth terms will be [tex]-15[/tex]. So, the ninth term will be [tex]35-(-15)=50[/tex].

Thus, the ninth term of the series is [tex]50[/tex].

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Answer: