What is the following product?

Answer:

78

Step-by-step explanation:

Wrong theories the passageway

Answer:

Cost of living is the amount of money needed for fixed expenses such as housing, food, taxes, and health care, as well as variable expenses. Big cities tend to have a higher cost of living than smaller cities.

Answer:

Step-by-step explanation:

Purplemath

To simplify with exponents, don't feel like you have to work only with, or straight from, the rules for exponents. It is often simpler to work directly from the definition and meaning of exponents. For instance:

Simplify a6 × a5

The rules tell me to add the exponents. But I when I started algebra, I had trouble keeping the rules straight, so I just thought about what exponents mean. The " a6 " means "six copies of a multiplied together", and the " a5 " means "five copies of a multiplied together". So if I multiply those two expressions together, I will get eleven copies of a multiplied together. That is:

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Simplifying Expressions on MathHelp.com

Simplifying Expressions

a6 × a5 = (a6)(a5)

= (aaaaaa)(aaaaa)

= aaaaaaaaaaa

= a11

Thus:

a6 × a5 = a11

Simplify the following expression:

\mathbf{\color{green}{\dfrac{6^8}{6^5}}}

6

5

6

8

​

The exponent rules tell me to subtract the exponents. But let's suppose that I've forgotten the rules again. The " 68 " means I have eight copies of 6 on top; the " 65 " means I have five copies of 6 underneath.

\dfrac{6 \cdot 6 \cdot 6 \cdot 6 \cdot 6 \cdot 6}{6 \cdot 6 \cdot 6 \cdot 6 \cdot 6}

6⋅6⋅6⋅6⋅6

6⋅6⋅6⋅6⋅6⋅6

​

How many extra 6's do I have, and where are they? I have three extra 6's, and they're on top. Then:

= \dfrac{6 \cdot 6 \cdot 6}{1} = \mathbf{\color{purple}{6^3}}=

1

6⋅6⋅6

​

=6

3

Unless the instructions also tell you to "evaluate", you're probably expected to leave numerical exponent problems like this in exponent form. If you're not sure, though, feel free to add "= 216", just to be on the safe side.

Simplify the following expression:

\mathbf{\color{green}{\dfrac{\mathit{t}^{10}}{\mathit{t}^8}}}

t

8

t

10

​

How many extra copies of t do I have, and where are they? I have two extra copies, on top:

\dfrac{t^{10}}{t^8} = \dfrac{t \cdot t \cdot t \cdot t \cdot t \cdot t \cdot t \cdot t \cdot t \cdot t}{t \cdot t \cdot t \cdot t \cdot t \cdot t \cdot t \cdot t}

t

8

t

10

​

=

t⋅t⋅t⋅t⋅t⋅t⋅t⋅t

t⋅t⋅t⋅t⋅t⋅t⋅t⋅t⋅t⋅t

​

= \dfrac{t \cdot t}{1} = \mathbf{\color{purple}{\mathit{t}^2}}=

1

t⋅t

​

=t

2

Once you become comfortable with the "how many extras do I have, and where are they?" reasoning, you'll find yourself not needing to write things out and cancel off the duplicate factors. The answers will start feeling fairly obvious to you.

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Simplify the following expression:

\mathbf{\color{green}{\dfrac{5^3}{5^9}}}

5

9

5

3

​

This question is a bit different, because the larger exponent is on the term in the denominator. But the basic reasoning is the same.

How many extra copies of 5 do I have, and where are they? I have six extra copies, and they're underneath:

\dfrac{5^3}{5^9} = \dfrac{5 \cdot 5 \cdot 5}{5 \cdot 5 \cdot 5 \cdot 5 \cdot 5 \cdot 5 \cdot 5 \cdot 5 \cdot 5}

5

9

5

3

​

=

5⋅5⋅5⋅5⋅5⋅5⋅5⋅5⋅5

5⋅5⋅5

​

= \dfrac{1}{5 \cdot 5 \cdot 5 \cdot 5 \cdot 5 \cdot 5} = \mathbf{\color{purple}{\dfrac{1}{5^6}}}=

5⋅5⋅5⋅5⋅5⋅5

1

​

=

5

6

1

​

Note: If you apply the subtraction rule, you'll end up with 53–9 = 5–6, which is mathematically correct, but is almost certainly not the answer they're looking for.

Whether or not you've been taught about negative exponents, when they say "simplify", they mean "simplify the expression so it doesn't have any negative or zero powers". Some students will try to get around this minus-sign problem by arbitrarily switching the sign to magically get " 56 " on top (rather than below a "1"), but this is incorrect.

Let's move on to expressions that are a bit more complex.

Simplify the following expression:

\mathbf{\color{green}{\dfrac{5\mathit{x}^5}{3\mathit{x}^3}}}

3x

3

5x

5

​

I mustn't forget that the "5" and the "3" are just numbers. Since 3 doesn't go evenly into 5, I can't cancel the numbers.

And I mustn't try to subtract the numbers, because the 5 and the 3 in the fraction "\frac{5}{3}

3

5

​

" are not at all the same as the 5 and the 3 in rational expression "\frac{x^5}{x^3}

x

3

x

5

​

". The numerical portion \frac{5}{3}

3

5

​

 stays as it is.

For the variables, I have two extra copies of x on top, so the answer is:

\dfrac{5x^5}{3x^3} = \dfrac{5 \cdot x \cdot x \cdot x \cdot x \cdot x}{3 \cdot x \cdot x \cdot x}

3x

3

5x

5

​

=

3⋅x⋅x⋅x

5⋅x⋅x⋅x⋅x⋅x

​

= \dfrac{5 \cdot x \cdot x}{3}=

3

5⋅x⋅x

​

= \mathbf{\color{purple}{\dfrac{5\mathit{x}^2}{3} = \dfrac{5}{3}\mathit{x}^2}}=

3

5x

2

​

=

3

5

​

x

2

Either of the purple highlighted answers should be acceptable: the only difference is in the formatting; they mean the same thing.

Simplify (–46x2y3z)0

This is simple enough: anything to the zero power is just 1.

(–46x2y3z)0 = 1

Simplify –(46x2y3z)0

The parenthetical portion still simplifies to 1, but this time the "minus" is out in front of the parentheses; that is, it's out from under the power, so the exponent doesn't touch it. So the answer in this case is:

–(46x2y3z)0 = –1

Final answer:

The expression using only positive exponents is [tex]1/k^3[/tex].

Explanation:

To simplify the expression [tex]k^0 * k^-3[/tex] and write it using , we need to apply the laws of exponents.

The expression can be broken down into two parts.

Therefore,

[tex]k^0 = 1[/tex] (anything raised to the power of 0 is 1).

[tex]k^-3 = 1/k^3[/tex] (negative exponent indicates reciprocal).

Therefore,

[tex]k^0 * k^-3[/tex] [tex]= 1 * 1/k^3[/tex]

[tex]= 1/k^3.[/tex]

Answer: 49929 years ago

Step-by-step explanation:

Radiocarbon dating is a method that provides objective age estimates for carbon-based materials that originated from living organisms

To calculate the time, we will use exponential formula

R% = e^ -kt

Where t = number of years

0.25/100 = e^- 0.00012t

Log both sides with natural logarithm

Ln0.0025 = lne^-0.00012t

-5.9915 = -0.00012t

t = 5.9915/0.00012

t = 49928.9 years

Approximately t = 49929 years

The whale died approximately 49,929 years ago.

To determine how long ago the whale died, we use the fact that its vertebrae contain roughly 0.25% as much carbon-14 as they originally did when the whale was alive. This suggests the carbon-14 has decayed, following its known decay rate.

The carbon-14 decay formula is:

N(t) = N0 × [tex]e^{-kt}[/tex]

where:

Given that N(t)/N0 = 0.0025, we solve for t:

1. Divide both sides by N0:

0.0025 = [tex]e^{(-0.00012 * t)}[/tex]

2. Take the natural logarithm of both sides:

ln(0.0025) = -0.00012 × t

3. Solve for t:

t = ln(0.0025) / -0.00012

t = −5.991464547/−0.00012

Calculating this, we get:

t ≈ 49928.87 ≈ 49,929 years

Therefore, the whale died approximately 49,929 years ago.

Answer:

Step-by-step explanation:

∠A + ∠B  = 90°  {given they are complementary}

5x+ 15 + 30 = 90

5x + 45 = 90

5x = 90 - 45

5x = 45

x = 45/5

x = 9

Answer:

$299.90

Step-by-step explanation:

Add the $34.56 back to the $265.34

Answer:

54/3=18 so Brad is 18 and Corey is 36

36 + 18 = 54

Step-by-step explanation:

If Corey is 2 times older then you divide by that number which is 2 + 1 so you divide by 3.

Hope this helps can I have brainliest

Answer:

68

Step-by-step explanation:

Answer:

28.26

Step-by-step explanation:

If you find the area by using the eqaution A=pi*raduis*2 you can then divide it by 4

Answer:

4y^2 + 14y + 34

I hope this helps :)

Answer:

C

Step-by-step explanation:

Answer:

The solution is given by s=9 because it makes the value of 3s+12 equal to 21.

Step-by-step explanation:

If you replace s with 9 you will get 21

Answer:

b. The solution is given by s = 3 because it makes the value of 3 s + 12 equal to 21.

Explanation:

I took the test and got it right.

Step 1: Substitute s for 3. You get 3(3) + 12 = 21.

Step 2: 3(3) + 12 = 21 is converted to 9 + 12 = 21.

Step 3: 9 + 12 equals 21.

Answer:  ±7

Step-by-step explanation:

Solution of the expression are,

⇒ ± 7

Mathematical expression is defined as the collection of the number variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The expression is,

⇒ √ 49

Now, We can simplify as;

⇒ √49

⇒ √ 7 × 7

⇒ ± 7

Thus, Solution of the expression are,

⇒ ± 7

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Answer:

We are 99% confident interval for the population proportion of passing test scores between ( 0.5987  and 0.9413 )

Step-by-step explanation:

Given -

n = 40

Population proportion = [tex]\widehat{(p)}[/tex] = [tex]77\%[/tex] = .77

1 - [tex]\widehat{(p)}[/tex] = 1 - .77 =.23

[tex]\alpha[/tex] = 1 - confidence interval = 1 - .99 = .01

[tex]z_{\frac{\alpha}{2}}[/tex] = [tex]z_{\frac{.01}{2}}[/tex] = 2.58

99% confidence interval for the population proportion of passing test scores=

[tex]\widehat{(p)}\pm z_{\frac{\alpha}{2}} \sqrt{\frac{\widehat{(p)} (1 - \widehat{p})}{n}}[/tex]

= [tex].77\pm z_{\frac{.01}{2}} \sqrt{\frac{{(.77)} (.23)}{40}}[/tex]

= [tex].77\pm 0.1713[/tex]

= [tex](.77 + 0.1713 , .77 - 0.1713)[/tex]

= ( 0.5987 , 0.9413 )

FInd the height of the box by dividing the volume by 7 x 5 ( length x width)

Height = 105 / 35

Height = 3cm

There are 6 sides to a box.

Surface area = 2 x length x width + 2 x length x height + 2 times height x width

SA = 2*7*5 + 2*7*3 + 2*5*3

SA = 70 + 42 + 30

SA = 142 cm^2

Answer:

2 inch

Step-by-step explanation:

The radius is the fixed distance from the center of a circle to any point on its circumference. The radius of a circle always equals half of its diameter, so to find the diameter, multiply the radius by two. ( 1 x 2= 2 inch)

The radius of a circle is 1/2 inch with a diameter of 1 inch.

The circumference of a circle is the distance around the circle which is 2πr.

The diameter of a circle is the largest chord that passes through the center of a circle it is 2r and the radius of a circle is half if the diameter which is r.

Given, A circle has a diameter of 1 inch.

As we know the radius of a circle is half of the diameter,

∴ A circle with a diameter of 1 inch will have a radius of 1/2 inch.

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Answer:

300 g. of chocolate.

75 g. of flour

3 people.

Step-by-step explanation:

These are proportion problems.  I'll just give you the first formula.

[tex]\frac{200}{4} =\frac{x}{6} \\\\(200)(6)=4x\\1200=4x\\x=300[/tex]

Can you do the rest? I'll be waiting in the comments.

:)

The algebraic expression for the cost of entering a state park and camping for n nights, with an entry fee of $6.00 and a nightly fee of $7.50, is Cost = $6.00 + ($7.50 times n).

The algebraic expression to represent the cost in dollars of entering a state park and camping for n nights, when the state park charges a $6.00 entry fee plus $7.50 per night of camping, is calculated as follows:

Cost = Entry fee + (Cost per night times Number of nights)

Here, the entry fee is $6.00, and the cost per night is $7.50. Therefore, the expression becomes:

Cost = $6.00 + ($7.50 times n)

Where n represents the number of nights spent camping.

====================================================

Explanation:

The number 4 shows up 14 times

The number 3 shows up 6 times

This is a total of 14+6 = 20 times we get a 3 or a 4 on the dice

This is out of 64 total rolls

Use a calculator to find that 20/64 = 0.3125

Move the decimal point over 2 spots to the right to get 31.25%

Lastly, round this to the nearest whole number percent to get 31%

Keep in mind that this only works for experimental probability. Theoretical probability is going to be different.

Answer:

31 percent on edgunity

Step-by-step explanation:

Answer:

You mean that if we have two pairs of points, (x1, y1) and (x2, y2)

we can find the slope of the line that conects those two points as:

a = (y2 - y1)/(x2 - x1)

remember that a linear equation has the shape:

y(x) = a*x + b

Now let's prove it:

for our case we have that

y1 = a*x1 + b

y2 = a*x2 + b

we can isolate be in both equtaions and get:

b = y1 - a*x1

b = y2 - a*x2

this means that:

y1 - a*x1 = y2 - a*x2

then:

a*x2 - a*x1 = y2 - y1

a*(x2 - x1) = y2 - y1

a = (y2 - y1)/(x2 - x1)

Which is the thing we wanted to get.

The subtraction of y-values and x-values to find the slope of a line is based on measuring the rate of change of y (rise) per unit change in x (run). This concept is fundamental in determining and understanding the steepness of a line on a graph.

To understand why we subtract y-values and x-values to find the slope, let's look at the formula for the slope of a line, m = (y2 - y1) / (x2 - x1). Here, 'm' represents the slope of the line, the y values (y2 and y1) represent points on the vertical axis, and the x values (x2 and x1) represent points on the horizontal axis.

When we say 'slope', we mean how steep a line is. That steepness is determined by how much y changes (the rise) for a certain amount of change in x (the run). By subtracting y-values and x-values from each other, we are able to accurately measure this change, and therefore calculate the slope of the line.

Graphically, if we consider two points on a straight line, the slope of the line (m) can be seen as how much the line rises (the difference in y-values) for each unit it runs horizontally (the difference in x-values).

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Answer: The mistake caused the perimeter to increase by 4 inches

The mistake caused the area to increase by 13 square inches

Step-by-step explanation: The original dimensions have been given as 5 inches by 7 inches. If this measurement had been correctly used, the perimeter was supposed to be;

Perimeter = 2(L + W)

Perimeter = 2(5 + 7)

Perimeter = 2(12)

Perimeter = 24 inches

Also the area was supposed to be;

Area = L x W

Area = 5 x 7

Area = 35 square inches

However, Sam accidentally printed a photo that is 6 inches by 8 inches, therefore the effect would be as follows;

Perimeter = 2(L + W)

Perimeter = 2(6 + 8)

Perimeter = 2(14)

Perimeter = 28 inches

And the Area would be

Area = L x W

Area = 6 x 8

Area = 48 square inches

From the calculations so far, the mistake would cause the perimeter to increase by 4 inches (28 inches - 24 inches).

Also the area would likewise increase by 13 inches (48 inches - 35 inches).

Answer:

A : The height of the prism is is 10 cm

B : DFG is  a base

D : The appropriate unit of measure for the volume is cubic centimetres

Step-by-step explanation:

In the given right triangular prism, ADFG constitutes one of the bases, and the appropriate unit for volume is cubic centimeters. However, details about the height and the specific area of the base are not conclusively determined. (2 and 4 are correct)

Let's analyze each statement:

1. The height of the prism is 10 cm.

  - This statement is not necessarily true. The height of a right triangular prism is typically measured perpendicular to the base. The provided information about AC and AD doesn't directly determine the height.

2. ADFG is a base.

  - This statement is true. A base of the right triangular prism can be identified by the vertices, and ADFG forms one of the bases.

3. ADFG is a lateral side.

  - This statement is not true. ADFG is a base, not a lateral side.

4. The appropriate unit of measure for the volume is cubic centimeters.

  - This statement is true. Volume is measured in cubic units, and in this context, cubic centimeters is appropriate.

5. The area of the base is 45 square centimeters.

  - This statement is not necessarily true. The area of the base cannot be determined solely from the information given.

So, the true statements are 2 and 4.

Answer:

x² + y² = 144

Step-by-step explanation:

The general equation of a circle is given as

(x - a)² + (y-b)² = r²

where a and b are the center of the circle along the x and y axis respectively and r is the radius of the circle.

Hence a circle that has its center at the origin and has a diameter of 24 units, we can deduce that the values of a,b are 0,0. Also,

radius = diameter/2

= 24/2

= 12 units

Hence the standard equation of the circle

(x - 0)² + (y - 0)² = 12²

x² + y² = 144

Answer:

Honey the answer is 40.

It's correct cuz I had the same question sugar ^-^

Answer:

√85 or 9.22

Step-by-step explanation:

For this, you'd want to use the distance formula, which is just something you'd eventually memorize.

Distance = [tex]\sqrt{(x_{2}- x_{1})^{2} + (y_{2}- y_{1})^{2}}[/tex]

Then, you'd plug in the values. Something to keep in mind is the coordinate that is farther right will be ([tex]x_{2} ,y_{2}[/tex]), since [tex](x_{2}- x_{1})[/tex] is supposed to represent the change in x (and same with the y).

d = √( (7 - (-2))² + (9 - 7)²)

= √( (9²) + 2²)

= √(81 + 4)

= √85

= 9.22

I hope this helps!

The distance between point (7, 9) and point (-2, 7) is √85 units.

To find the distance between two points, you can use the distance formula:

[tex]\[d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\][/tex]

In this case, the coordinates of the two points are:

Point 1: (7, 9)

Point 2: (-2, 7)

Now, plug these coordinates into the distance formula:

[tex]\[d = \sqrt{(-2 - 7)^2 + (7 - 9)^2}\][/tex]

Simplify inside the square root:

[tex]\[d = \sqrt{(-9)^2 + (-2)^2}\][/tex]

[tex]\[d = \sqrt{81 + 4}\][/tex]

[tex]\[d = \sqrt{85}\][/tex]

So, the distance between point (7, 9) and point (-2, 7) is[tex]\(\sqrt{85}\)[/tex] units, which is an irrational number and cannot be simplified further as a whole number or fraction.

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Answer:

100 people

Step-by-step explanation:

The new population of the country at the end of the year considering all the conditions will remain at 100.

Arithmetic operators are four basic mathematical operations in which summation, subtraction, division, and multiplication involve.,

Summation = addition of two or more numbers or variable

Subtraction = Minus of any two or more numbers with each other called subtraction.

As per the given,

The population of the country at the beginning of the year = 100 people.

10 immigrated → 100 + 10 = 110

20 emigrated → 110 - 20 = 90

Birth rate is 15 → 90 + 15 = 105

Death rate is 5 → 105 - 5 = 100

Hence "The new population of the country at the end of the year considering all the conditions will remain at 100".

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Answer: A. 50 miles per hour

Step-by-step explanation:

in between the lines if you look at the number it goes 25,50,75,100 etc.

Answer:

It is translation

3

-5

in brackets