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.

Let's see

[tex]\\ \rm\rightarrowtail 5x^2-9x+4=0[/tex]

[tex]\\ \rm\rightarrowtail 5x^2-5x-4x+4=0[/tex]

[tex]\\ \rm\rightarrowtail 5x(x-1)-4(x-1)=0[/tex]

[tex]\\ \rm\rightarrowtail (5x-4)(x-1)=0[/tex]

[tex]\\ \rm\rightarrowtail x=4/5,1[/tex]

The length of the colony is the product of 5. 3 × 10^3 and the length of the bacteria

The total length of the colony is 143.1 mm

The given parameters are:

Bacteria = 2.7 × 10^–2 mm.

Colony = 5. 3 × 10^3 of the bacteria

So, the length (L) of the colony is:

[tex]L = 5.3 * 10^3 * 2.7 * 10^{-2[/tex]

Rewrite as:

[tex]L = 5.3 * 2.7* 10^3 * 10^{-2[/tex]

Evaluate the products

[tex]L = 14.31* 10[/tex]

Evaluate the product

[tex]L = 143.1[/tex]

Hence, the total length of the colony is 143.1 mm

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Answer:

Step-by-step explanation:

Solution :

Hello:

an equation   for the line is : y =mx +b    (m: is a slope )

perpendicular to the line described by : y = 2/3 x -2

So : product for two slopes = -1   means : m×2/3=-1

m = -3/2

now : y = -3/2 x+b

but this line :

through the point (6,6) : 6 =(-3/2)(6)+b....... b=15

conclusion :

the equation is : y = -3/2x +15

Answer:

NP NP

Step-by-step explanation:

this is the only solution that works for the question

Answer:

True

Step-by-step explanation:

I always remember it, over then up

Answer:

2

Step-by-step explanation:

multiples of 12: 1, 2, 3, 4, 6, 12 (we don't use 1 in LCM)

Start with 2: 46/2 = 23, so the least common multiple is 2

The sound will travel fastest at an elevation of 500m,

Elevation      Temperature

500m              11.8°C (MAXIMUM)

1000m               8.5°C

1500m               5.3°C

2000m               2.0°C

Molecules at higher temperatures have more energy and they can vibrate faster and allow sound waves to travel more quickly because the more is the medium, the more quickly sound waves propagate.

So, when the temperature is maximum i.e. 11.8°C, the sound will travel fastest. The elevation corresponding to 11.8°C is 500m.

So, Sound will travel fastest at 500m elevation.

Therefore, At an elevation of 500m, the sound will travel fastest.

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Answer:

500 meters

Step-by-step explanation:

Answer: y = 32/7

Step-by-step explanation:

Solve the first equation for x by subtracting the 2y from the left side and getting: x = 1 - 2y.

Plug this in to the second equation: 2(1 - 2y) - 3y = -30 → 2 - 4y - 3y = -30 →

-7y = -32 → y = 32/7. Hope this helps!

Using separation of variables, it is found that the solution to the initial value problem is of y(x) = x² + 2.

In separation of variables, we place all the factors of y on one side of the equation with dy, all the factors of x on the other side with dx, and integrate both sides.

In this problem, the differential equation is given by:

[tex]\frac{dy}{dx} = 2x[/tex]

Then, applying separation of variables:

[tex]dy = 2x dx[/tex]

[tex]\int dy = \int 2x dx[/tex]

[tex]y = x^2 + K[/tex]

Since y(0) = 2, we have that the constant of integration is K = 2, and the solution is:

y(x) = x² + 2.

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The differential equation is y(x) = x² + 2.

Differential Equations In Mathematics, a differential equation is an equation that contains one or more functions with their derivatives.

The given equation is;

[tex]\rm \dfrac{dy}{dx}=2x[/tex]

Applying the variable separation method;

[tex]\rm \dfrac{dy}{dx}=2x\\\\\int\limits \, dy=\int\limits\, 2x. dx\\\\y = 2 \times \dfrac{x^{1+1}}{1+1} +c\\\\y = 2 \times \dfrac{x^{2}}{2} +c\\\\y = x^2+c[/tex]

The value of c when y( 0 ) = 2 is c =2.

Hence, the required differential equation is y(x) = x² + 2.

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Answer:

b no. is the correct answer

If [tex]P(x) = x^2-4x+4[/tex]  and x =2

   --> [tex]P(2) = 2^2-4(2)+4=4-8+4=0[/tex]

Hope that helps!

Answer:

side length = 4

Step-by-step explanation:

Let x = the side length

Area is x•x, which is x^2.

Perimeter is x+x+x+x, which is 4x.

x^2 = 4x

x^2 - 4x = 0

Factor.

x(x-4) = 0

x = 0 or x = 4

Discard 0 as an answer as it is not useful.

x = 4.

Area = 4^2 = 16

Perimeter = 4(4)= 16

The side length is 4.

Considering the confidence interval given, the likely difference is given by:

[tex]\frac{0.064 + (-0.014)}{2} = 0.025[/tex]

Given an interval (a,b), the point estimate is the mean of the bounds, that is:

p = (a + b)/2.

In this problem, the interval is (-0.014, 0.064), hence the expression for the likely difference is given by:

[tex]\frac{0.064 + (-0.014)}{2} = 0.025[/tex]

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Answer:

1

Step-by-step explanation:

5 + 4 - (8 x 3 – 22)* x 4

5 + 4 - (24 - 22) x 4

5 + 4 - 2 x 4

5 + 4 - 8

1

Answer:

16

Step-by-step explanation:

5+4- (8x3-22) ↑4 x4

         16

5+4 - (24-22) ↑4 x4

5+4- (2) ↑4 x4

2x2x2x2=16

hope that helps:)

Using the Poisson distribution, it is found that the probabilities are given by:

a) 0.1009 = 10.09%.

b) 0.8262 = 82.62%.

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by:

[tex]P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}[/tex]

The parameters are:

Item a:

The mean is of 7 customers for 60 minutes, hence, for 90 minutes = 1.5 x 60 minutes, the mean is given by:

[tex]\mu = 1.5 \times 7 = 10.5[/tex]

The probability of exactly 8 customers is of P(X = 8), hence:

[tex]P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}[/tex]

[tex]P(X = 8) = \frac{e^{-10.5}10.5^{8}}{(8)!} = 0.1009[/tex]

Item b:

Probability of at least one patient in 15 minutes, hence:

[tex]P(X \geq 1) = 1 - P(X = 0)[/tex]

For 15 minutes, the mean is given by:

[tex]\mu = 0.25 \times 7 = 1.75[/tex]

Then:

[tex]P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}[/tex]

[tex]P(X = 8) = \frac{e^{-1.75}1.75^{0}}{(0)!} = 0.1738[/tex]

[tex]P(X \geq 1) = 1 - P(X = 0) = 1 - 0.1738 = 0.8262[/tex]

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The geometric sequence can be represented explicitly or as recursions

The explicit formula of the geometric sequence is b(n) = 2 * 3^(n-1)

The sequence is given as:

2, 6, 18, 54, ....

Start by calculating the common ratio (r)

r = b2/b1

This gives

r = 6/2

Evaluate the quotient

r = 3

A geometric sequence is represented as:

b(n) = b1 * r^(n-1)

This gives

b(n) = 2 * 3^(n-1)

Hence, the explicit formula of the geometric sequence is b(n) = 2 * 3^(n-1)

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Answer:

40%

Step-by-step explanation:

2/5 is shaded

100 divided by 5 is 20

2x20=40

Answer:

rational

Step-by-step explanation:

Hope this helps!

If not I am sorry

let's keep in mind that that same/same = 1 always, so then we can say

[tex]\cfrac{spaghetti}{spaghetti}~~ = ~~\cfrac{hippopotamus}{hippopotamus}~~ = ~~\cfrac{meatballs}{meatballs}~~ = ~~\cfrac{dog}{dog}~~ = ~~\cfrac{0.\overline{55}}{0.\overline{55}}~~ = ~~\textit{\huge 1}[/tex]

well, "1" is a whole number

"1" is also an integer oddly enough

"1" can be written as a ration like 1/1, so is also rational.

Answer:

s so you're going to divide when you going to divide 95 why you take it to the other side it will become 95 * 450 equals to 42750 / 9 when we divide 42750 / 9 to give you 4750 that is your answe

Answer:

A = 253 sq ft

Step-by-step explanation:

see image. Section off the shape into rectangles. Sometimes you have to add to find the lengths of the sides. Sometimes you have to subtract. Area is length×width. see image.

Answer:

(3,0) reflection on x axis (3,0)

(3,0) reflection on y axis (-3,0)

Answer:

As Per Given Information

we have been asked to determine the consine ratio of ∠K .

[tex] \bf \: cos \: k = \cfrac{Base}{Hypotenuse} [/tex]

with respect to ∠K .

substitute the given value & let's solve it for k .

[tex] \longrightarrow\sf \: cos \: k \: = \cfrac{30}{50} \\ \\ \\ \longrightarrow\sf \: cos \: k \: = \cfrac{ 3\cancel0}{5 \cancel0} \\ \\ \\ \longrightarrow\sf \: cos \: k \: = \cfrac{3}{5} [/tex]

Therefore,

Your answer is (c) 3/5

Answer:

A. Line
<------------->

B. Angle
⦟

C. Line Segment
.___________.

Step-by-step explanation:

Have a great rest of your day
#TheWizzer

Answer:

17

Step-by-step explanation:

replace x with 5

3*5+2

next you use pemdas

you multiply before you add

3*5=15

15+2=17

Answer:

x = 4

y = -6

Step-by-step explanation:

5x + 2y = 8

8x + 4y = 8

-2(5x + 2y) = -2(8)

8x + 4y = 8

-10x -4y = -16

8x + 4y = 8

-10x -4y + 8x + 4y = -16 + 8

-2x = -8

x = 4

plug 4 into x so y = -6

Answer:

I think it's the fourth one.

Answer:

-(12+a)(a+2)

Step-by-step explanation:

this is to ez

The expression as a product is (a+12)(-a-2)

An expression in math is a statement having minimum of two numbers, or variables, or both and an operator connecting them.

Given that, is an expression, 25-(a+7)², we need to write it in product form, 25-(a+7)²

= 25 - (a²+49+14a)

= 25-a²-49-14a

= -a²-14a-24

Factorizing,

= -a²-12a-2a-24

= -a(a+12)-2(a+12)

= (a+12)(-a-2)

Hence, the expression as a product is (a+12)(-a-2)

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Answer:

[tex]6x^2+8x[/tex]

Step-by-step explanation:

Hey there!

In order to find the answer to this question, what you need to do is first find the area of the whole grey box as a whole (including the white box to)

The dimensions for this is 3x+2 and 4x

Now we know that to find area, we need to multiply length by height

So (3x+2)(4x) is what we have to solve to get the area

Now we simplify:

1. Distribute

2. [tex]12x^2+8x[/tex]

So now we know that the total area is [tex]12x^2+8x[/tex]

Now what we do is take out the area of the white box from the area of the grey box

Lets find the area of the white box:

l=3x   (l - length)

h=2x (h - height)

[tex]3x*2x=6x^2[/tex]

Now we have the area of both shapes

Since we have all the information we need to find the final answer, the following steps below will be using the information we found to find the final answer:

In order to find the final answer which is the area of the shaded region, we take out the area of the white region from the total area of the grey region (including the white region)

So now we can formulate this new equation:

[tex]12x^2+8x-6x^2= ta[/tex]

(ta= total area)

Now we simplify:

[tex]6x^2+8x\\[/tex] is going to be our final answer

So our final answer is [tex]6x^2+8x[/tex]

i think this should work good luck

Answer:

N = 9

Step-by-step explanation:

N^2 = 81

NxN = 81

N = 9 because 81/9 = 9 and if you don't trust me use a calculator