Staff
Americans eat 7 billion hot dogs between Memorial Day and Labor Day. If all these hot dogs were laid end to end they
would circle the earth 21.5 times. If the circumference of the Earth is approximately 24,860 miles, and one mile is
5,280 feet, find the length (in inches) of each hot dog. (Round your answer to the nearest tenth)

Answer:

(-2,-2)

Step-by-step explanation:

x^2 + y^2 = 9

A circle has an equation of the form

(x-h)^2 + (y-k)^2 = r^2

where the center is at ( h,k) and the radius is r

The circle is centered at (0,0) and has a radius 3

The only point entirely within the circle must have points less than 3

(-2,-2)

(1) This series consists of terms of an arithmetic sequence:

179 - 173 = 6

173 - 167 = 6

and so on, so that the n-th term in the series is (for n ≥ 1)

a(n) = 179 - 6 (n - 1) = 185 - 6n

Then the sum of the first 53 terms is

[tex]\displaystyle\sum_{n=1}^{53}(185-6n) = 185\sum_{n=1}^{53}1-6\sum_{n=1}^{53}n[/tex]

[tex]\displaystyle\sum_{n=1}^{53}(185-6n) = 185\times53-6\times\frac{53\times54}2[/tex]

[tex]\displaystyle\sum_{n=1}^{53}(185-6n) = \boxed{1219}[/tex]

(2) This series has terms from a geometric sequence:

-12 / 6 = -2

24/(-12) = -2

-48/24 = -2

and so on. The n-th term is (again, for n ≥ 1)

a(n) = 6 (-2)ⁿ⁻¹

and the sum of the first 19 terms is

[tex]\displaystyle\sum_{n=1}^{19}6(-2)^{n-1} = 6\left(1 + (-2) + (-2)^2 + (-2)^3 + \cdots+(-2)^{19}\right)[/tex]

Multiply both sides by -2 :

[tex]\displaystyle-2\sum_{n=1}^{19}6(-2)^{n-1} = 6\left((-2) + (-2)^2 + (-2)^3 + (-2)^4 + \cdots+(-2)^{20}\right)[/tex]

Subtracting this from the first sum gives

[tex]\displaystyle(1-(-2))\sum_{n=1}^{19}6(-2)^{n-1} = 6\left(1 -(-2)^{20}\right)[/tex]

and solving for the sum, you get

[tex]\displaystyle3\sum_{n=1}^{19}6(-2)^{n-1} = 6\left(1 -(-2)^{20}\right)[/tex]

[tex]\displaystyle\sum_{n=1}^{19}6(-2)^{n-1} = 2\left(1 -(-2)^{20}\right)[/tex]

[tex]\displaystyle\sum_{n=1}^{19}6(-2)^{n-1} = 2\left(1 -(-1)^{20}2^{20}\right)[/tex]

[tex]\displaystyle\sum_{n=1}^{19}6(-2)^{n-1} = 2\left(1 -2^{20}\right) = 2-2^{21} = \boxed{-2,097,150}[/tex]

Answer:

(-7, 3)

General Formulas and Concepts:

Algebra I

Point-Slope Form: y - y₁ = m(x - x₁)

Step-by-step explanation:

Step 1: Define

Identify

y - 3 = 4(x + 7)

↓ Compare to Point-Slope Form

Point (-7, 3)

Slope m = 4

Answer:  13.46 km/h

Step-by-step explanation:

7 1/2 hr= 450 min

6057/450= 13.46

Answer:

14

Step-by-step explanation:

The a value is from the center to the maximum

We want from minimum to max so we need 2 times the amplitude

a = 7

2 *7 = 14

Answer:

30 degrees.

Step-by-step explanation:

Let the acute angle be x.

Then as the 2 acute angles in a right triangle sum to 90 degrees,

x = 90 - 60

= 30.

We used the information we know to give us this equation.

90°+60°+x=180°

We add 90° and 60° to give 150°

150°+x=180°

Answer:

p = 1

Step-by-step explanation:

7 = 8 - p

7 + p = 8

p = 8-7

p = 1

Answered by Gauthmath

Step-by-step explanation:

1/5=1/5×1000=200

1/2 of 200

1/2×200=100

Answer:

54

Step-by-step explanation:

Surface area of a cube = 6a²

Where,

a = edge = 3

Surface area of a cube = 6a²

= 6 * (3)²

= 6 * (3 * 3)

= 6 * 9

= 54

Therefore,

The Surface area of the cube = 54

Answer:

Solution given:

we have formula

a²+b²=(a+b)(a-b)

now

4x²-9

(2x)²-3²

using formula

(2x+3)(2x-3)

other expression is 2x-3.

Answer:

( 2x - 3 )

Step-by-step explanation:

4x² - 9 is a perfect square meaning it can be factored into 2 expressions,

( 2x + 3 ) ( 2x - 3 )

Answer:

Volume of cylinder

= π r² h

OAmalOHopeO

Answer:

The volume of the cylinder would be approximately 392.5 ft^3

Step-by-step explanation:

Just like the volume formulas for a cuboid, the formula for a cylinder is: Vol = (Circle Area)(Height). Since we already have the height value, let's move onto the circle area.

The formula for the area of a circle is: πr^2. The problem only gave us the value for the diameter (10), so to get the radius value, we just need to divide the diameter by 2, and we get a value of 5 ft as our radius. Next, we just need to square root it. So 5 x 5 = 25. Then, we multiply it by π. Because the problem is asking for an approximate answer, we can just assume that π is 3.14. And that gets us a value of 78.5 ft^2 for the area of the circle.

Finally, we just need to multiply the area and the height of the cylinder. So 78.5 x 5 is approx. 392.5 ft^3. Since we don't need to round to the nearest tenths place, we can just leave it alone.

Since I didn't use the exact value of π, the real answer may be a little off of what we got, but if you want to extra precise, you can go ahead and use the actual value of π.

Answer:

range{-5,4)

Step-by-step explanation:

3(-1)-2= -5

3(2)-2=4

Answer:

42.78⁹, 137.22⁹.

Step-by-step explanation:

sine Ф=0.6792

Angle Ф in the first quadrant = 42.78 degrees.

The sine is also positive in the second quadrant so the second solutio is

180 - 42.78

= 137.33 degres.

Answer:

i might be wrong but this is what i put

Step-by-step explanation:

In question 3 it was comparing three triangles where now it is using the triangles to find the area of a square instead of proving that they are the same.

Answer:

[tex]\frac{-1}{30} a - \frac{1}{6}[/tex]

Step-by-step explanation:

Answer:

I think the answer is C.

Answer:

a) 81-6

b) 10.4

Step-by-step explanation:

a) assuming that the VAT is 20% of the 68 pounds,

you calculate 120% of 68 (convert percentage to decimal)

= 1,20 * 68 = 81.6 pounds

or

calculate 20% of 68 pounds and add the answer to 68 pounds:

(0.2 * 68) + 68 = 81.6 pounds

b) 20% of 52

first convert the percentage to decimals:

0.2 * 52 = 10.4 pounds

Answer:

3

Step-by-step explanation:

Answer:

7.8391

Step-by-step explanation:

Answer:

Step-by-step explanation:

The key to solving this equation is knowing how to "undo" a natural log. Just like square roots are "undone" by squaring, and cubing "undoes" a cubed root, raising a natural log to the base of e, Euler's number, undoes a natural log. Because this is an equation you have to raise both sides of it to the base of e:

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

That leaves us on the left with simply

x + 3

On the right we have a constant. e is not a variable, it is a number. You can find its value on your calculator. Solving for x:

[tex]x=e^5-3[/tex] and

[tex]e^5=148.4131591[/tex], so

x = 148.4131591 - 3 and

x = 145.4132, the first choice listed.

Answer:

A.

Step-by-step explanation:

85.9 > 85.31 > 85 > 84.52

Dallas, Fort Worth, San Antonio, Austin

Answer:

The 65,000 salary

Step-by-step explanation:

Because the 30,000 salary after 5 years would be 31,500.

30,000+300=30,300

30,300+300=30,600

30,600+300=30,900

30,900+300=31,200

31,200+300=31,500

The 65,000 paying company

65,000x1.05=68,250

68,250x1.05=71.662.5

71,662.5x1.05=75,245.625

75,245.625x1.05=79,007.90625

79,007.90625x1.05=82,958.3015625

her salary after 5 years would be 82,958.3015625

Answer:

-6

Step-by-step explanation:

A parabola is vertex form is written as

y = a(x-h)^2 +k  where (h,k) is the vertex

Substituting in the vertex

y = a(x-5)^2 +5

We know a point on the parabola so we can find a

-1 = a( 6-5)^2 +5

-1 =a(1)^2+5

-1 = a +5

Subtract 5 from each side

-1-5 = a

-6 =a

Answer:

29

Step-by-step explanation:

all in all it is 180 so 61 + m (which is 90 because it is a right angle)=151

then 180-151=29

Answer:

Three times a number minus two times a number

3x-2x

=x

Answer:

Choice C.

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

Step-by-step explanation:

When converting to

[tex]y = mx + b[/tex]

We are left with:

[tex]y = - 2x + 3[/tex]

Which fits both the x-intercept and y-intercept.

Answer:

B) To the left five units, down three units

Answer:

( B ) To the left five units, down three units.

The value of x for the given equation [tex]log_{8}[/tex](16) + 2[tex]log_{8}[/tex](x) = 2 will be 2 so option (B) must be correct.

The exponent indicates the power to which a base number is raised to produce a given number called a logarithm.

In another word, a logarithm is a different way to denote any number.

Given the equation

[tex]log_{8}[/tex](16) + 2[tex]log_{8}[/tex](x) = 2

We know that,

xlogb = log[tex]b^{x}[/tex]

So,

2[tex]log_{8}[/tex](x) = logx²

For the same base

logA + logB = log(AB)

So,

[tex]log_{8}[/tex](16) + [tex]log_{8}[/tex](x)² = 2

[tex]log_{8}[/tex](16x²) = 2

We know that

[tex]log_{a}[/tex](b) = c ⇒ b = [tex]a^{c}[/tex]

so,

[tex]log_{8}[/tex](16x²) = 2 ⇒ 8² = 16x²

x = 2 hence x = 2 will be correct answer.

For more about logarithm

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Answer:rrrrrrrr

rrrrrrrrrr

Step-by-step explanation:

rrrrrrrrrrrrrrr

The equation for the scenario is x + x+1 + x+2 = 117 and largest number is 40.

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

Let x be the first number:

The other numbers are:

x+1, x+2

The sum of three consecutive numbers is 117:

x + x+1 + x+2 = 117

3x + 3 = 117

3x = 114

x = 38

x+ 1 = 38+1 = 39

x+2 = 38+2 = 40

Thus, the equation for the scenario is x + x+1 + x+2 = 117 and largest number is 40.

Learn more about the linear equation here:

brainly.com/question/11897796

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Answer:

m∠DAB+m∠ADC=180

115+ 29 + m∠ADB=180

m∠ADB=180 - 115 -29

= 36°