Michael bought 160 hot dogs for an eating competition. He spent $240 in all. How much did each hot dog cost?

Answer:

[tex]Number = 2.71 * 10^{-7}[/tex]

Step-by-step explanation:

Given

[tex]Number = 0.0000002711[/tex]

Required

Write, using scientific notation

The scientific notation is written in the form:

[tex]Form = a * 10^n[/tex]  Where n is an integer and [tex]1 \leq a \leq 10[/tex]

To start with; Represent the given number as fraction

[tex]Number = \frac{2711}{10000000000}[/tex]

Represent the denominator as an exponent

[tex]Number = \frac{2711}{10^{10}}[/tex]

This can be rewritten in form of:

[tex]Number = 2711 * 10^{-10}[/tex]

Remember that: [tex]Form = a * 10^n[/tex]  Where n is an integer and [tex]1 \leq a \leq 10[/tex]

This implies that; we need to adjust 2711 to a number between 1 and 10;

This gives:

[tex]Number = 2.711 * 1000 * 10^{-10}[/tex]

Write 1000 as an exponent

[tex]Number = 2.711 * 10^3 * 10^{-10}[/tex]

Apply law of indices

[tex]Number = 2.711 * 10^{3-10}[/tex]

[tex]Number = 2.711 * 10^{-7}[/tex]

The question requires 2 numbers after the decimal point;

So, 2.711 will be approximated to 2.71

[tex]Number = 2.71 * 10^{-7}[/tex]

Hence;

[tex]0.0000002711[/tex]  is equivalent to [tex]2.71 * 10^{-7}[/tex]

Answer: -3/2

Step-by-step explanation:

To find its distance away from 0, then just find its opposite.

On the number line if you graph 3/2,  its opposite will be -3/2

Answer:

Step-by-step explanation:

Answer:

The angles of rotation coincide as follows:

DEF  is  45°

GHI is  115°

JKL  is  210°

Step-by-step explanation:

Answer:

15 rubber bands per day

Step-by-step explanation:

Answer:

Domain : (-∞,∞)

Range : (1 , ∞)

Answer:

[tex]b  =  (q,r , 5q-2\sqrt{26} )[/tex]

Step-by-step explanation:

From the question we are told that

The vector given is  

               [tex]a = (5,0,-1)[/tex]

  Also  [tex]comp_a b =  2[/tex]

Generally

       [tex]comp_a b  =  \frac{a \cdot b}{|a|}[/tex]

Here  [tex]|a|[/tex] is the magnitude of  a which is mathematically represented as

      [tex]|a| =  \sqrt{5^2  + 0^2  +(-1)^2 }[/tex]

=>     [tex]|a| =  \sqrt{26}[/tex]

b is vector which we will assume to have the following parameters

     [tex]b  =  (q , r , x)[/tex]

So

        [tex]comp_a b =  \frac{(5,0,-1) \cdot (q,r,x)}{\sqrt{26} } =  2[/tex]

=>     [tex]\frac{5q + 0 -x}{\sqrt{26} } = 2[/tex]

=>     [tex]x =  5q-2\sqrt{26}[/tex]

Hence the vector be can be mathematically represented as

      [tex]b  =  (q,r , 5q-2\sqrt{26} )[/tex]

This means that the vector b is more than one value  since it is made up of variable

This means that if

   [tex]q = 1\\r=1\\x =1[/tex]

Then

    [tex]b  =  (1,1,5-2\sqrt{26} )[/tex]

A quantity has magnitude but not position, that's why in this the vector [tex]b =(0,0, -2\sqrt{26}).[/tex]

If[tex]a =(5,0,-1)[/tex] Our goal is to determine a vector b that will allow comp to work properly [tex]_{a}b = 2.[/tex]

Allow the vector to flow naturally  [tex]b =(x, y,z)[/tex]

Recalling

comp[tex]_{a}b =\frac{a.b}{|a|}[/tex]

Therefore,

comp [tex]_{a}b= 2 \\\\[/tex]

[tex]\to \frac{a.b}{|a|}= 2\\\\[/tex]

[tex]\to \frac{(5,0,-1)\cdot (x,y,z)}{ |(5,0,-1)|} =2\\\\\to \frac{5x+0-z}{5^2+0+(-1)^2}=2\\\\ \to \frac{5x-z}{\sqrt{26}}= 2 \\\\\to 5x-z = 2\sqrt{26}\\\\ \to z=5x-2\sqrt{26}\\\\[/tex]

As a result, the vector b can be expressed as,

[tex]\to b =(x,y,z) =(x, y, 5x-2\sqrt{26}) \\\\[/tex]

As a result, this aforementioned form can be found in an endless number of vectors.

One of them is [tex]b =(0,0, -2\sqrt{26}).[/tex]

Find out more about the vector here:

brainly.com/question/13322477

Answer:

16

Step-by-step explanation:

A = 2; S = 4

3A + 2.5S =

= 3(2) + 2.5(4)

= 6 + 10

= 16

Answer:

1/-3

Step-by-step explanation:

Answer:

2.5

Step-by-step explanation:

multiply -5 by -1/2

Answer:

[tex]\huge\boxed{\mathrm{Range = 1.05}}[/tex]

Step-by-step explanation:

Given Data:

2.45 , 3.50 , 2.89 , 2.99

Arrange it in ascending order.

2.45 , 2.89 , 2.99 , 3.50

Range = Highest No - Lowest No.

Range = 3.50 - 2.45

Range = 1.05

Answer:

Range=largest value-smallest value

Range=2.99-2.45

Range=0.54

Step-by-step explanation:

hope it is helpful for you

if it is please follow

Answer:

Recede

Step-by-step explanation:

Famished means extremely hungry

Recede means go or move back or further away from a previous position

Answer:

Recede

Step-by-step explanation:

So let's look at the meanings of these two words.

Recede: To go or move back backward; become more distant.

Famished: Severely suffering from hunger.

So now you can see that recede is the word that makes more sense in the blank.

Far away on the horizon, we saw the tiny figures of a lonely traveler and his mule Recede into the sunset.

Hope this Helps!

Answer:

[tex]=2(2x-5)(x+1)[/tex]

Step-by-step explanation:

So we have the trinomial:

[tex]4x^2-6x-10[/tex]

First, factor out a 2:

[tex]=2(2x^2-3x-5)[/tex]

Now, factor within the parentheses.

To do so, we want to find two numbers. When multiplied, these two numbers must equal (a)(c) and when added, they must equal b

(a)(c) is 2(-5) or -10 and b is -3. So, we want two numbers that when multiplied together gives -10 and when added gives -3.

-5 and 2 works. Therefore:

[tex]=2(2x^2-3x-5)[/tex]

Replace -3x with 2x and -5x:

[tex]=2(2x^2+2x-5x-5)[/tex]

Factor out a 2x for the first two terms. And factor out a negative 5 for the remaining two:

[tex]=2(2x(x+1)-5(x+1))[/tex]

Grouping:

[tex]=2(2x-5)(x+1)[/tex]

And we're done!

Answer:

The third one, 104,000,027,571

Step-by-step explanation:

The first and second ones are not the answers because the problem does not say one hundred forty billion.

The last one is not the answer because the problem doesn't say two hundred seventy thousand.

Thus leaving the third one, which fits the description of the number.

Answer:

The answers are all real numbers where x<2 or x>2. We can use a symbol known as the union, ∪,to combine the two sets. In interval notation, we write the solution:(−∞,2)∪(2,∞). In interval form, the domain of f is (−∞,2)∪(2,∞).

Round each number to the nearest hundred.

 212 = 200.

 314 = 300.

How much more marbles does Peck have?

 314 - 212 = 102.

That is your answer. Hope this helps!

Answer:

100 more marbles

Step-by-step explanation:

So first let's round the numbers to the nearest hundred. So 212 rounds to 200, and 314 rounds to 300. Then we do 300-200 and get 100. SO the answer is 100.

━━━━━━━━━━━━━━━ ♡ ━━━━━━━━━━━━━━━  

Of the United States, true, you are in the south.

Texas is a southern state of the USA.

Of the world, false, you are more north than south, and also you are around the middle north of the world.

The pictures I attached are maps of the USA and the world.

As you can see in the USA map, Texas is one of the states are are the lowest.

But if you look at the world map, Texas is not very south.

━━━━━━━━━━━━━━━ ♡ ━━━━━━━━━━━━━━━  

Answer:

[tex]-\frac{7}{6}[/tex]

Step-by-step explanation:

I hope this helps!

Answer:

-7/6

Step-by-step explanation:

-1/3=-2/6

-2/6-5/6=-7/6

Answer:

[tex]f(-1) = \frac{5}{2}[/tex]

[tex]f(0) = 5[/tex]

[tex]f(2) = 20[/tex]

Step-by-step explanation:

Given

[tex]f(x) = 5(2^x)[/tex]

Required

Determine f(-1); f(0) and f(2)

Solving f(-1)

In this case, we simply take x as;

[tex]x = -1[/tex]

Substitute -1 for x in [tex]f(x) = 5(2^x)[/tex]

[tex]f(-1) = 5(2^{-1})[/tex]

Apply law of indices

[tex]f(-1) = 5 * \frac{1}{2}[/tex]

[tex]f(-1) = \frac{5}{2}[/tex]

Solving f(0)

In this case, we simply take x as;

[tex]x = 0[/tex]

Substitute 0 for x in [tex]f(x) = 5(2^x)[/tex]

[tex]f(0) = 5(2^0)[/tex]

[tex]f(0) = 5(1)[/tex]

[tex]f(0) = 5[/tex]

Solving f(2)

In this case, we simply take x as;

[tex]x = 2[/tex]

Substitute 2 for x in [tex]f(x) = 5(2^x)[/tex]

[tex]f(2) = 5(2^2)[/tex]

[tex]f(2) = 5(4)[/tex]

[tex]f(2) = 20[/tex]

Answer:

x=2 and y=1

Step-by-step explanation:

2x+y=5

x-y=1

buy adding both equations we get

3x=6

x=2  ( divide 3 on both sides)

put x=2 in any equation  

2-y=1

y=2-1

y =1

p2

Problem#2

Let say two complementary angles are A & B

difference of two complementary angles is 30°

=> A - B = 30

Sum of  two complementary angles is 90°

=> A + B = 90

Hence A = 60° , B = 30°

Problem#3

Total bill  = 30

$ 10 Bills = A

$ 20 Bills  = B

10 * A  + 20* B = 460

A + B = 30

A = 14 , B = 16

Problem#4

4x+2=y

2y−8x=10

The first step is to simplify the second equation into  

y=mx+b form.

2y−8x=10y  

y−4x=5

y=4x+5

Now, the two equations are:

y=4x+2

y=4x+5

Answer:

4% of x

Step-by-step explanation:

20% of x

y% of 20

Hope it is what you are looking for

Answer:

15mg/ml

Step-by-step explanation:

Percent mass per volume ( % m/v) is unit expression that tells us how many grams of a solute that we can find 100 ml of a particular solution.

In the above question, we are asked to express 1.5%w/v Bepotastine besilate (BEPREVE) ophthalmic solution as mg/mL

Step 1

1.5% w/v = 1.5 g of Bepotastine besilate (BEPREVE) in 100ml ophthalmic solution

Hence, if

100ml = 1.5g

1 ml = y g

We Cross Multiply

100ml × yg = 1 ml × 1.5g

yg = 1 ml × 1.5g/100ml

= 0.015g

Therefore, in 1 ml we have 0.15 g.

Step 2

Since we are asked to express as mg/ml

We convert 0.015g to mg

1 gram = 1000 milligrams

0.015 grams =

Cross Multiply

0.015grams × 1000 milligrams/ 1 gram

= 15 mg

Therefore, the concentration in mg/ml of 15% m/v of Bepotastine besilate (BEPREVE) ophthalmic solution is 15mg/ml

Answer:

$153.00

Step-by-step explanation:

A = $1,353.00

(I = A - P = $153.00)

Equation:

A = P(1 + rt)

Calculation:

First, converting R percent to r a decimal

r = R/100 = 4.25%/100 = 0.0425 per year.

Solving our equation:

A = 1200(1 + (0.0425 × 3)) = 1353

A = $1,353.00

The total amount accrued, principal plus interest, from simple interest on a principal of $1,200.00 at a rate of 4.25% per year for 3 years is $1,353.00.

Answer:

$153

Step-by-step explanation:

Simple Intrest = P ( money invested ) * R ( percentage ) * T ( year )

I = P * R * T / 100

I = 1200 * 4.25 * 3 = 15300 / 100 = $153

This is the easiest method for me and I hope it helps :)

Answer: Multiplying integers is very similar to multiplying whole numbers. A positive number times a negative number equals a negative number. A negative number times a negative number equals a positive number. A negative number times a positive number equals a negative number.

Answer:

$3 each

Step-by-step explanation:

Minus the $2 from $11 gives you $9. So $9÷3=$3 per candy bar.

Answer:

This can be because our number, 300,684, has only four digits different than zero.

Then we can write this number as:

300,684 = 300,000 + 600 + 80 + 4.

So we add only 4 terms.

So when we write a number in this form, we will have the same numbers of terms in the addition that the number of digits different than zero in our original number.

Answer:

  [0, 7]

Step-by-step explanation:

We want the height to be greater than or equal to 32 ft, so ...

  704 +16t -16t^2 ≥ 32

  t^2 -t -42 ≤ 0 . . . . . . . . . . . subtract 32, divide by -16

  (t -7)(t +6) ≤ 0

This inequality will be true for values of t between -6 and +7. Since we're only concerned with times t ≥ 0, the appropriate solution interval is ...

  0 ≤ t ≤ 7 . . . . [0, 7] in interval notation

Answer:

-0.74

Step-by-step explanation:

The computation of Z is shown below:

According to the question, data provided in the question is as follows

P(Z >  Z) = 0.23

Based on the above information, the calculation for Z is

Use the table of the standard normal distribution for z

By using this the Z value comes is -0.74

hence, in case of the standard normal distribution, the value of z is -0.74 and the same is to be considered

Answer:

Step-by-step explanation:

5        y

_   =   _

11       6

Cross multiply to get:

11y = 30

y = 2.7272

y = 2.7

Answer: Between about 31 and 33 dollars per month

Step-by-step explanation:

Answer:

m + 188 = 232

Step-by-step explanation:

sum → +

m + 188 = 232

Answer:

m + 188 = 232

Thats is an equation for your problem