Evaluate each expression.
3^4
2^5​

The correct answer for this question is 30 students

Sure hope this helps you :)

Answer:

EEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEE

Answer:

A

Step-by-step explanation:

Answer:

$17.17! I really hope this helped kiddo :3

Answer:

$321.6915

Step-by-step explanation:

original price= $399.00

20% off $399 is $319.2

$319.2-$15.00=$304.2

0.75% of 304.2 is 2.2815

5% of 304.2 is 15.21+2.2815=17.4915+304.2=321.6915

hope this helps

A percentage is a way to describe a part of a whole. The final cost of the television is $321.69.

A percentage is a way to describe a part of a whole. such as the fraction ¼ can be described as 0.25 which is equal to 25%.

To convert a fraction to a percentage, convert the fraction to decimal form and then multiply by 100 with the '%' symbol.

Given that a 55" flat screen television is regularly priced at $399.00. Now, It is on sale for 20% off. Therefore, the cost of the flat screen is,

Cost after discount = $399 - 20% of $399

= $399 - 0.20($399)

= $319.2

The cost after the application of the coupon of $15.00 off on any purchase over $100.00. Therefore, the new cost will be,

New Cost = $319.20 - $15.00

                 = $304.2

Since the tax on the cost is 5.75%, therefore, the cost after the application of the tax is,

Cost after the tax = $304.2 + 5.75% of $304.2

                             = $304.2 + 0.00575($304.2)

                             = $321.69

Hence, the final cost of the television is $321.69.

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Answer:

872.52

Step-by-step explanation:

Answer:

Given that in a walking competition, Marlinda was 15m ahead of Sandra Evliani, and Marlinda steps 1m each time Sandra Elviani's foot steps 0.8m, to determine how many steps does Sandra Elviani have to make to match Marlinda, the following calculation must be performed:

Since Sandra Elviani walks 0.8 meters for every 1 meter that Marlinda walks, and that she has an advantage of 15 meters in the competition, it is impossible that at that rate Sandra can reach her. This is so because for each step of Marlinda, Sandra will be 0.2 meters behind her, increasing the distance (1-0.8).

The total number of workers that were studied can be found to be 139,340,000.

The percent of workers unemployed would be 5. 4 %.

Percentage of unemployed men is 5. 6 % and unemployed women is 5. 1%.

Number of employed workers :

= 74,624,000 + 64, 716, 000

= 139,340,000

Percentage unemployed :

= ( 4, 209,000 + 3,314,000 ) / 139,340,000

= 5. 4 %

Percentage of unemployed men :

= 4,209,000 / 74,624,000

= 5.6 %

Percentage of unemployed women:

= 3,314,000 / 64, 716, 000

= 5. 1 %

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The full question is:

a. How many workers were studied?

b. What percent of the workers were unemployed?

c. Compare the percent unemployed for the men and the women.

Answer:

B -5/6

Step-by-step explanation:

Answer:

534 is the mean.

Step-by-step explanation:

to calculate the mean you add all the numbers together (for example this set of numbers):

785, 585, 465, 409, 495, 465

=3204

then divide the number of numbers that you added together , (in this case 6)

3204/6

=

534

Answer: it is neither

Answer:

See below

Step-by-step explanation:

Question is unclear

could be (11-2)^3  = 9^3 = 729

could be  11 - 2^3 = 11 - 8 = 3       Pick the one you want !

The value of length BC is 18.9

Cosine Rule states that the square of the length of any side of a given triangle is equal to the sum of the squares of the length of the other sides minus twice the product of the other two sides multiplied by the cosine of angle included between them.

Therefore,

c² = a² + b² - 2abcosC

To find the length BC we use cosine rule.

c² = 13² + 7² - 2(13)(7)cos140

c² = 218 - 182cos140

c² = 218-(-139.42)

c² = 218+139.2

c² = 357.2

c = √357.2

c = 18.9

Therefore, the length of BC is 18.9

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In the triangle, the value of the side BC is 18.9cm to 1 decimal place

The side BC can be found using the cosine formula, Remember that Cosine Rule states that the square of the length of any side of a given triangle is equal to the sum of the squares of the length of the other sides minus twice the product of the other two sides multiplied by the cosine of angle included between them.

The cosine formula states that

c² = a² + b² - 2abcosC

To find the length BC we use cosine rule.

c² = 13² + 7² - 2(13)(7)cos140

c² = 218 - 182cos140

c² = 218-(-139.42)

c² = 218+139.2

c² = 357.2

c = √357.2

c = 18.9

In conclusion, the value of  the length of BC is 18.9cm

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Answer:

14(120)t

Step-by-step explanation:

hopes this helps

Answer:

Step-by-step explanation:

Correct choice is C

A²+B²= C²

31²+ 21²= z²

961+441 = z²

1402= z²

z= 37.443290454

Answer:

Step-by-step explanation:

Perimeter is the sum of side lengths

Let's find the sides first

Perimeter is

Answer: 2^4*3^5*19

Step-by-step explanation:

You also need to divided by 2 four times, then divided by 3 five times, then the final one is divided by 19.

The largest prime factor of 309² - 147² is, 19.

The highest number that divides exactly into two more numbers, is called  Greatest common factors.

Given that;

The expression is,

⇒ 309² - 147²

Now, We can simplify as;

⇒ 309² - 147²

⇒ (309 - 147) (309 + 147)

⇒ 162 × 456

⇒ 2 × 3 × 3 × 3 × 3 × 2 × 2 × 2 × 3 × 19

Thus, The largest prime factor of 309² - 147² is,

⇒ 19

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The experimental probability that an arrangement will contain at least one yellow balloon is 0.767. Then the correct option is C.

Given that:

Each balloon arrangement in Ethan's class has four balloons in it. The likelihood of each balloon being red, blue, or yellow is equal. To represent this possibility, Ethan made a spinner.

ybrr, bybb, rbbb, rrry, rbbb, rryy, yybb, ryry, ryyr, rbyr, ryyr, rryy, rrrr, yrby, bbyy, byyr, byyr, byyb, rbby, ybry, rryy, rbrr, rybb, bbbr, rrbr, ybry, ryrr, rryb, rrrb, rryr

The experimental probability that an arrangement will contain at least one yellow balloon is calculated as,

P = 23 / 30

P = 0.767

Thus, the correct option is C.

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Answer:

Step-by-step explanation:

You would scale up the recipe to make a greater portion to accomodate for 75 crepes.

The the coefficient of variation for set a is 15.7% and the coefficient of variation for set b is 22.3%.

The formula for calculating the coefficient of variation is:

CV = (standard deviation / mean) x 100%

where standard deviation is a measure of the spread of the data around the mean. The CV expresses the standard deviation as a percentage of the mean.

To calculate the CV for set a, we first need to find the mean and standard deviation of the data set. The mean can be calculated by adding all the values and dividing by the number of values.

Mean = (3.97 + 3.47 + 3.99 + 4.30 + 3.16 + 3.07 + 4.24 + 2.94 + 3.56 + 3.43 + 3.06 + 3.34 + 4.35 + 3.57) / 14 = 3.65

The standard deviation can be calculated using a calculator or a spreadsheet software such as Microsoft Excel. For this set, the standard deviation is 0.574.

CV = (0.574 / 3.65) x 100% = 15.7%

To calculate the CV for set b, we need to first remove the dollar sign from each value and then find the mean and standard deviation.

Mean = ($24,800 + $30,000 + $22,300 + $20,400 + $19,000 + $32,200 + $23,000 + $23,000 + $24,000 + $27,200 + $34,900) / 11 = $25,727.27

The standard deviation can be calculated using a calculator or spreadsheet software. For this set, the standard deviation is $5,746.38.

CV = ($5,746.38 / $25,727.27) x 100% = 22.3%

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The correct answer is 3/2. In this case, x = 3/2, and its square, (3/2)^2 = 9/4, is rational. x satisfies the given condition.option (c)

To explain further, we need to understand the properties of rational and irrational numbers.

A rational number can be expressed as a fraction of two integers, while an irrational number cannot be expressed as a fraction and has non-repeating, non-terminating decimal representations.

In the given options, (a) √5102.0 (£) and (b) √2 are both irrational numbers.

Their squares, (√5102.0)^2 and (√2)^2, would also be irrational, violating the given condition. On the other hand, (d) 4/5 is rational, and its square, (4/5)^2 = 16/25, is also rational.

Option (c) 3/2 is rational since it can be expressed as a fraction. Its square, (3/2)^2 = 9/4, is rational as well.

Therefore, (c) 3/2 is the only option where x is rational, but its square is irrational, satisfying the condition mentioned in the question.

In summary, the number x that satisfies the given condition, where x^2 is irrational but x is rational, is (c) 3/2.option (c)

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The value of x will be -7. The expression is solved using the identity.

Exponents can also be written as logarithms. The other number is equal to a logarithm with a number base. It's the exact inverse of the exponent function.

Given expression;

\(\rm log_2(\frac{1}{128}) = x\)

The expression is solved using the identity as;

\(\rm log_e1 = x\\\ e^x=1\)

Apply the identity;

\(\rm log_2(\frac{1}{128}) = x \\\\ 2^x = \frac{1}{128}\\\\ 2^x = \frac{1}{2^7} \\\\ 2^x = 2^{-7} \\\\ x = -7\)

Hence the value of x will bed -7.

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Answer:

A. From 2005 to 2009, both assets and liabilities decrease.

Step-by-step explanation:

I just took the test and it was correct

From 2005 to 2009, both Assets and Liabilities decreased.

We have - A table showing the assets and liabilities of smith family in year 2005 and 2009.

We have to estimate, whether the smith family has acquired more assets or liabilities from the year 2005 to 2009.

Assets are the items that an individual own in order to extract some economic benefit from it in the future.

Liability includes the money, services or items that you owe to other person. Example : Loan, mortgage etc.

In the question given -

In the year 2005 :

In the year 2009 :

Hence, it can be seen from the above figures that - From 2005 to 2009, both Assets and Liabilities decreased.

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It is possible to translate the parent function f(x) = x using various transformations including vertical and horizontal translations. Each transformation will result in
the graph intersecting the x- or y-axis at a different point.

Function is an operation that takes an input, performs some processing on it, and returns a result. It is a set of instructions that performs a specific task. Functions are typically used to perform repetitive tasks, like finding the sum of two numbers, adding two strings together, or finding the maximum of a list of numbers. Functions are essential to programming and can be used to make code more organized, reusable, and efficient.


The function f(x) = x is the parent function for linear equations. This equation is generally used to graph a line with a slope of 1 and a y-intercept of (0, 0). In order to translate this parent function, different transformations are applied to it.

A vertical translation down 4 units would be represented by the equation f(x) = x - 4. This transformation would shift the graph of the parent function down 4 units on the y-axis. This would result in the graph intersecting the y-axis at the point (0, -4).

A horizontal translation right 4 units would be represented by the equation f(x) = x + 4. This transformation would shift the graph of the parent function right 4 units on the x-axis. This would result in the graph intersecting the x-axis at the point (4, 0).

A horizontal translation left 4 units would be represented by the equation f(x) = x - 4. This transformation would shift the graph of the parent function left 4 units on the x-axis. This would result in the graph intersecting the x-axis at the point (-4, 0).

Finally, a vertical translation up 4 units would be represented by the equation f(x) = x + 4. This transformation would shift the graph of the parent function up 4 units on the y-axis. This would result in the graph intersecting the y-axis at the point (0, 4).

In conclusion, it is possible to translate the parent function f(x) = x using various transformations including vertical and horizontal translations. Each transformation will result in the graph intersecting the x- or y-axis at a different point.

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Answer:

To find the number of integral solutions for x in the given inequality, we can first solve the inequality to find the range of values that x can take on. To do this, we need to isolate the x term on one side of the inequality, so let's start by subtracting 9 from both sides of the inequality:

-69 ≤ 7x + 9 ≤ 49

-9 ≤ 7x ≤ 40

Next, we can divide both sides of the inequality by 7 to isolate the x term:

-9/7 ≤ x ≤ 40/7

The result of this calculation is a range of values for x, but we are looking for the number of integral solutions, which means we need to find the number of whole numbers that x can take on within this range. In this case, we can see that the range of possible values for x is from -1 to 5, and there are 5 whole numbers within this range (-1, 0, 1, 2, 3, 4, 5), so there are 5 integral solutions for x in this inequality.

In general, to find the number of integral solutions for x in an inequality of the form a ≤ bx + c ≤ d, where a, b, c, and d are constants, you can follow these steps:

1.Solve the inequality to isolate the x term on one side, by subtracting c from both sides and then dividing both sides by b. This will give you the range of possible values for x.

2.Count the number of whole numbers within this range to find the number of integral solutions for x.

Step-by-step explanation:

Answer:

\(\Huge \boxed{\text{13.66$\%$}}\)

Step-by-step explanation:

To find the rate, we need to use the following formula:

\(\LARGE \boxed{ \boxed{\text{Rate = $\frac{\text{Portion}}{\text{Base}}$$\times$100}}}\)

Where "Portion" is the part of the whole and "Base" is the whole.

Now, let's plug in the given values:

\(\large \text{Rate = $\frac{\text{50}}{\text{366}}$$\times$100 = 13.66 (Rounded to the nearest tenth of a percent)}\)

Therefore, the rate is 13.66% (rounded to the nearest tenth of a percent).

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Answer:

Nolan's account balance would be $1800 after 4 years

Step-by-step explanation:

Simple Interest

Interest is calculated only on the original principal of a loan or on the balance of an account.

Unlike compound interest where the interest earned in the compounding periods is added to the new principal, simple interest only considers the principal to calculate the interest.

The interest earned is calculated as follows:

I=P.r.t

Where:

I = Interest

P = initial principal balance

r = interest rate

t = time

Nolan has a savings account that pays r=5% = 0.05 with an initial balance of P=$1500. It's required to find the account's balance after t=4 years.

Substituting in the formula:

I = $1500 * 0.05 * 4

I = $300

The final balance is:

A = P + I = $1500 + $300 = $1800

Nolan's account balance would be $1800 after 4 years

The locus of the midpoints of all chords that can be drawn from a given fixed point \((a,b)\) on a circle with a radius of 6 units, is a circle of radius 3 units with center at a point whose x & y coordinates are shifted from the center of the given circle by \(\frac{a}{2}\) and \(\frac{b}{2}\) respectively.

Given: A circle of radius 6 units

To find: The locus of the midpoint of all chords that can be drawn from a given point on the circle.

To find the required locus, we need to know the following:

Let, without loss of generality, the given circle be centered at the origin. Even if it is not, we can shift the origin to the center of the given circle with coordinate transformation.

Then, the equation of the given circle is \(x^{2}+y^{2} =6^{2}\), that is, \(x^{2}+y^{2} = 36\)

Let the coordinates of the given fixed point be \((a,b)\)

Let the coordinates of any point on the circle be \((p,q)\) and let the coordinates of the midpoint of the chord joining the points \((a,b)\) and \((p,q)\) be \((h,k)\)

We have to find the locus of \((h,k)\)

Then, using the midpoint formula,

\((h,k)=(\frac{a+p}{2} ,\frac{b+q}{2})\)

On solving, we get,

\(p=2h-a,q=2k-b\)

Since \((a,b)\) and \((p,q)\) are both points on the given circle, they satisfy the equation of the circle, \(x^{2}+y^{2} = 36\)

Then,

\(a^{2} +b^{2} =36\)

\(p^{2} +q^{2} =36\)

Substituting \(p=2h-a,q=2k-b\) in \(p^{2} +q^{2} =36\), we have,

\((2h-a)^{2} +(2k-b)^{2} =36\)

\((2(h-\frac{a}{2}) )^{2} +(2(k-\frac{b}{2}))^{2} =36\)

\(4(h-\frac{a}{2})^{2} +4(k-\frac{b}{2})^{2} =36\)

\((h-\frac{a}{2})^{2} +(k-\frac{b}{2})^{2} =\frac{36}{4}\)

\((h-\frac{a}{2})^{2} +(k-\frac{b}{2})^{2} =9\)

\((h-\frac{a}{2})^{2} +(k-\frac{b}{2})^{2} =3^{2}\)

This is the locus of the point \((h,k)\)

Replace \((h,k)=(x,y)\) to get,

\((x-\frac{a}{2})^{2} +(y-\frac{b}{2})^{2} =3^{2}\)

This is the equation of a circle with center at \((\frac{a}{2} ,\frac{b}{2} )\) and radius 3 units.

Thus, we can conclude that the locus of the midpoints of all chords that can be drawn from a given fixed point \((a,b)\) on a circle with a radius of 6 units, is a circle of radius 3 units with center at a point whose x & y coordinates are shifted from the center of the given circle by \(\frac{a}{2}\) and \(\frac{b}{2}\) respectively.

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Answer: (1, √15) and (1, -√15)

Step-by-step explanation:

A circle centered at the point (a, b) of radius R can be written as:

(x - a)^2 + (y - b)^2 = R^2

In this case we have:

"A circle is centered at the origin (0,0) and has a radius of 4 units"

Then the equation for this circle is:

x^2 + y^2 = 4^2 = 16.

Now, we want to find the points where x = 1, then we can replace that value and solve the equation for y.

1^2 + y^2 = 16

1 + y^2 = 16

y^2 = 16 - 1 = 15

y = +-√15

Then the two points that have the x-coordinate equal to 1 are:

(1, √15) and (1, -√15)

The points on the circle which have an x-coordinate of 1 are:. (1,+√15) and (1,-√15)

The equation of a circle usually takes the form;

where a and b are x- and y- coordinates of the center of the circle.

In this scenario, the center is at the origin (0,0).

In essence, the points on the circle which have an x-coordinate of 1 can be evaluated as follows;

The points on the circle which have an x-coordinate of 1 are:. (1,+√15) and (1,-√15)

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Given:

The graph of a function is given.

To find:

The point that is the relative maxima on the interval x = –1 and x = 2 in the graph.

Solution:

Relative maxima: It is the maximum point of a function over a short interval.

From the given graph it is clear that the graph of the function over the interval x = –1 and x = 2 has a relative maxima at (0,0).

Clearly, (0,0) is represented by point a.

So, the point a is the relative maxima on the interval x = –1 and x = 2 in the graph.

Therefore, the correct option is A.