(Laws of Exponents with Integer Exponents LC)

Create an equivalent expression for 17−7 • 175.

one over seventeen raised to the second power
one over seventeen raised to the power of negative two
172
−172

The expression represents the probability that both students chosen are sophomores is C( 6 , 1 ) * C ( 5 , 1 ) / C ( 20 , 2 ) .

Given :

The requested probability can be computed as the ratio between the number of ways to choose two sophomores in alternate positions [tex]N_s[/tex] and the total number of possible choices [tex]N_t[/tex] .

p = [tex]N_s[/tex] / [tex]N_t[/tex]

There are 6 sophomores and 14 freshmen to choose from each separate set. There are 20 students in total .

We'll assume the positions of the selections are NOT significative, i.e. student A/student B is the same as student B/student A.

To choose 2 sophomores out of the 6 available, the first position has 6 elements to choose from, the second has now only 5.

C( 6 , 1 ) * C ( 5 , 1 ) ways .

The total number of possible choices is C ( 20 , 2 )

Probability = C( 6 , 1 ) * C ( 5 , 1 ) / C ( 20 , 2 )

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Full question :

Six sophomores and 14 freshmen are competing for two alternate positions on the debate team. Which expression represents the probability that both students chosen are sophomores? StartFraction (6 C 1) (5 C 1) Over 20 C 2 EndFraction StartFraction (6 P 1) (5 P 1) Over 20 P 2 EndFraction StartFraction (20 C 6) (19 C 5) Over 20 C 2 EndFraction StartFraction (20 P 6) (19 P 5) Over 20 P 2 EndFraction

The vertex of a parabola is the point at which the parabola changes direction, the vertex of y =-x² + 4 is (0, 4).

The equation for a parabola in standard form is y = ax² + bx + c. To find the vertex of y = -x² + 4, we need to use the formula x = -b/2a. In this equation, a is -1, and b is 0, so x = 0. Therefore, the vertex of y = -x² + 4 is (0, 4).

To find the vertex of a parabola, we can use the formula x = -b/2a. In this formula, a is the coefficient of x², and b is the coefficient of x. Therefore, to find the vertex of a parabola, we need to find the coefficients of x² and x and then plug them into the formula. This formula will give us the x-coordinate of the vertex, and we can then use the equation of the parabola to find the y-coordinate of the vertex. In the case of y = -x² + 4, the coefficient of x² is -1 and the coefficient of x is 0. Plugging these values into the formula, we get x = 0. We can then use the equation of the parabola to find the y-coordinate of the vertex, which is 4. Therefore, the vertex of y =-x² + 4 is (0, 4).

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Kim could start contributing to her employer-sponsored 401 K for retirement and 529 plans for her son's college education.

401(k) is an employer sponsored retirement benefits plan where the employer and employee contribute a percent of the employee's benefits or gross income every payday in order that the funds can be used to to generate further wealth by a way of investment for the benefit of the employees upon retirement.

529 plan on the other hand,is a college savings plan wherein parent,guardian or even the beneficiary(the would college student) saves money at interval with hope of funding the costs of college education

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The median is the middle score in the set.

To find the median, start by arranging all of the data points from smallest to largest.

In an odd-numbered set, the median will be the number in the very middle of the list.

In an even-numbered set, you will need to calculate the average of the two middle numbers.

To do this:

Step 1: Take the two middle numbers of the even-numbered set

Step 2: Add the two numbers together

Step 3: Divide the total by 2

As an example, consider this set of numbers: 5, 9, 11, 9, 7. First, you arrange them in numerical order (5, 7, 9, 9, 11). Since you have an odd number of scores, the number in the third position of the data set is the median which, in this case, is 9 (5, 7, 9, 9, 11).

To calculate the median for an even number of scores, imagine that your research revealed this set of data: 2, 5, 1, 4, 2, 7. Your first step is to put them in numerical order (1, 2, 2, 4, 5, 7). The two middle scores are 2 and 4, so you should add them together (2+4=6) and then divide 6 by 2, which equals 3. In this data set, the median score is 3.

The median is calculated by arranging the scores in numerical order, dividing the total number of scores by two, then rounding that number up if using an odd number of scores to get the position of the median or, if using an even number of scores, by averaging the number in that position and the next position.

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The SAS Similarity Theorem asserts that two triangles are similar if two sides in one triangle are proportionate to two sides in another triangle and the included angle in both is congruent.

The side-angle-side (SAS) theorem is one such example. Triangles are congruent if their two sides and included angles are equivalent to those of another triangle's two sides and included angle. SAS similarity analysis: When the ratio of two sides' lengths in one triangle equals the ratio of sides' lengths in another triangle, and the included angles are also equal, the two triangles are said to be comparable.

Area of triangle =

[tex]1/2 X b X h\\b= 10\\h=5\\A = 1/2 X 10X 5\\A = 25 unit sq.[/tex]

and also by heron's formula

Area = [tex]\sqrt{s(s - a)(s - b)(s - c) }[/tex]

and, here s = half the perimeter,

[tex](a + b + c)/2.[/tex]

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Answer:

x=13

Step-by-step explanation:

the bottom line is 11 the top line is 6 the difference is 5 hence we use the the formula 12 5 13 i mean the pythogrious formula

Standard deviation of 13 denotes a high value. This indicates observed data values are dispersed in relation to mean value.

Standard deviation expresses the amount of scatter of a set of values.

It is an estimation that implies how far each data value apart from the mean value. A high deviation scores denotes that the data are dispersed around the mean value. A low value indicates that all data value is close in relation to the mean value.

As per the statistical rules, any standard deviation value above or equal to 2 is considered as high. So, this value is high. According to the fourth-grade test for insurance policy, score 13 is equivalent to the 84th percentile. And as per the fifth-grade test score 13 is equivalent to the 98 percentiles.

In accordance with the empirical assumption of normal distribution, this higher value of standard deviation implies most of the data will be dispersed in relation to the mean value.

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Answer:

This data has a positive correlation.

Step-by-step explanation:

As the x-values increase, the y-values increase. Therefore, there is a positive correlation. (positive/positive = positive)

We can conclude that under the AAS congruency condition, we can prove that △WXY ≅ △YZX.

Two triangles are said to be congruent if all three corresponding sides and all three corresponding angles have the same size.

You can move, flip, twist, and turn these triangles to produce the same effect.

When relocated, they are parallel to one another.

So, we know that;
Shared side XZ by △WXZ and △YZX.

Right angles exist between WXZ and XZY.

∠XYZ and ∠XYZ have the same values.

Now that we have the parameters, we can infer that XZ is congruent to itself according to the reflexive property of congruence, and as a result, both triangles have a congruent side.

Second, since WXZ and XZY are right angles, it follows that they are equal and hence congruent.

The last piece of information is that XWZ and XYZ are congruent.

In conclusion, the triangles are congruent according to the AAS Congruency since we have two corresponding angles and one corresponding side that are equal but the corresponding side is not with the included angles.

Therefore, we can conclude that under the AAS congruency condition, we can prove that △WXY ≅ △YZX.

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Answer:

12x plus 9x

Step-by-step explanation:

Answer:

the second

Step-by-step explanation:

so first you now that slope is y=mx+b with b=y, so with this we go (0,-3) down the the slope is 2 so we go up two right one the the opposite down two left then do that a couple of times and you have your line. since Y is less than the coloring goes down. HOPE THIS HELPS

The cost of 1 oz in dollars if 10 oz cost $0.95 is $0.095

Based on the given concept; we can solve by using ratio

Cost of 10 oz = $0.95

Cost of 1 oz = x

Equate the ratio of number of oz to cost in dollars

10 : 0.95 = 1 : x

10/0.95 = 1/x

cross product

10 × x = 0.95 × 1

10x = 0.95

divide both sides by 10

x = 0.95/10

x = $0.095

In conclusion, 1 oz cost $0.095

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Answer:

99%

Step-by-step explanation:

10% = 0.1

Take 550 times 0.1 = $55

So, 10% of $550 is $55

Because it is a discount, so we subtract it

550 - 55 - $495

Then we know it marks up by 10%

10% of 495 is $49.50

495 + 49.50 = $544.50

Then take 544.50 divided by 550, then times 100% = 99%

Answer: 3.5

Step-by-step explanation:

To solve for x in a square, you need to find the value of x that makes the square equal to zero. In this case, the square is given by (6x-21), so we can solve for x by setting this expression equal to zero and then solving for x.

To solve the equation (6x-21) = 0, we can use basic algebraic techniques. First, we can add 21 to both sides of the equation to get (6x-21) + 21 = 21. Then, we can use the distributive property to expand the left-hand side of the equation as follows:

(6x-21) + 21 = 21

6x - 21 + 21 = 21

6x = 21

Finally, we can divide both sides of the equation by 6 to find the value of x that makes the square equal to zero:

6x = 21

x = 21 / 6

x = 3.5

Therefore, the value of x that makes the square (6x-21) equal to zero is x = 3.5.

Answer:

don't know the answer

Step-by-step explanation:

but thanks for the points bookie

Answer:

x = 14.4

Step-by-step explanation:

[tex]\frac{30}{18} =\frac{24}{x}[/tex]

30x = 18*24

30x = 432

x = 14.4

The value of x in the triangle is,

⇒ x = 14.4

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

Given that;

A triangle is shown in figure.

Now, We can formulate by definition of proportion as;

⇒ 30 / 24 = 18 / x

⇒ x = 18 × 24 / 30

⇒ x = 14.4

Thus, The value of x in the triangle is,

⇒ x = 14.4

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The most important step in financial planning is to create a budget.

What is financial planning?

The process of setting and achieving long-term financial goals is called financial planning. It involves evaluating one's current financial resources, setting financial objectives, and devising a plan to achieve those objectives. It also entails developing savings, managing debt, and creating a budget.

According to the given question:

Financial planning is crucial because it enables individuals and families to better manage their finances and ensure that they will be able to achieve their desired objectives. Additionally, it aids individuals in making sound financial decisions and preventing costly errors.

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The sum of these numbers is indeed 131 + 133 + 135 = 399. Therefore, the three consecutive odd numbers are 131, 133, and 135.

What are consecutive numbers ?

Numbers that follow each other continuously in the order from smallest to largest are called consecutive numbers. For example: 1, 2, 3, 4, 5, 6, and so on are consecutive numbers.

Here we will use algebra to find three consecutive integers whose sum is 399. We start by assigning X to the first integer. Since they are consecutive, it means that the 2nd number will be X + 1 and the 3rd number will be X + 2 and they should all add up to 399. Therefore, you can write the equation as follows:

(X) + (X + 1) + (X + 2) = 399

To solve for X, you first add the integers together and the X variables together. Then you subtract three from each side, followed by dividing by 3 on each side. Here is the work to show our math:

X + X + 1 + X + 2 = 399

3X + 3 = 399

3X + 3 - 3 = 399 - 3

3X = 396

3X/3 = 396/3

X = 132

Which means that the first number is 132, the second number is 132 + 1 and the third number is 132 + 2. Therefore, three consecutive integers that add up to 399 are 132, 133, and 134.

132 + 133 + 134 = 399

Since, 132 + 133 + 134 equals 399 as displayed above.

Hence ,The sum of these numbers is indeed 131 + 133 + 135 = 399. Therefore, the three consecutive odd numbers are 131, 133, and 135.

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There are four factors that should be taken into consideration when creating a financial plan.

The process of figuring out how a corporation will be able to afford to meet its strategic goals and objectives is known as financial planning. Typically, a business develops a financial plan right away after establishing its vision and goals.

You can reach your financial objectives with the help of financial planning, whether they are to purchase a home for your family, save money for your children's school, have a comfortable retirement, or take a dream vacation. Additionally, it gets you ready for crises and unanticipated circumstances like getting sick, losing your job, or needing home renovations.

4 things to think about when creating your financial plan:

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Step-by-step explanation:

13 cups = ? pints

there are 2 cups per pint so:

13/2 = 6.5

13 cups = 6.5 or [tex]6\frac{1}{2}[/tex] pints

The value of x° and y° are 48.5° and  38.6°.

What is the cosine law?

The square of the length of any one side of a triangle is equal, by the cosine rule, to the total of the squares of the lengths of the other two sides, multiplied by the cosine of the angle they are a part of.

The length of sides of the triangle are 10, 12, and 16.

Assume that AB = c = 10, BC = a = 16, and AC = b = 12

m∠B = x° and m∠C = y°.

Cosine law:

c² = a² + b² - 2ab cos C  ....(i)

b² = a² + c² - 2ac cos B  ....(ii)

a² = b² + c² - 2bc cos A  ....(iii)

Putting a = 16, b = 12, c = 10, and C = y° in law (i)

10² = 16² + 12² - 2×16×12 cos y

100 = 256 + 144 - 384 cos y

384 cos y = 300

cos y = 300/384

y = 38.6°

Putting a = 16, b = 12, c = 10, and B = x° in law (ii)

12² = 16² + 10² - 2×16×10 cos x

144 = 256 + 100 - 320 cos x

320 cos x = 212

cos x = 212/320

x =48.5°

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Step-by-step explanation:

We're asked to find the simplified form of,

[tex]\longrightarrow S=\underbrace{1^2+3^2+5^2+7^2+\,\dots}_{\textrm{$n$ terms}}[/tex]

The n'th term of the sequence [tex]1^2,\ 3^2,\ 5^2,\ 7^2,\,\dots[/tex] is [tex](2n-1)^2.[/tex] So,

[tex]\longrightarrow S=1^2+3^2+5^2+\,\dots\,+(2n-1)^2[/tex]

We know the following sum,

[tex]\longrightarrow 1^2+2^2+3^2+\,\dots\,+n^2=\dfrac{n(n+1)(2n+1)}{6}[/tex]

This is expression for the sum of squares of first 'n' natural numbers. In case of '2n' natural numbers,

[tex]\longrightarrow 1^2+2^2+3^2+\,\dots\,+(2n)^2=\dfrac{2n(2n+1)(4n+1)}{6}[/tex]

We separate odd squares and even squares in the LHS.

[tex]\begin{aligned}\longrightarrow\ \ &\Big(1^2+3^2+5^2+\,\dots\,+(2n-1)^2\Big)&\\+\ \ &\Big(2^2+4^2+6^2+\,\dots\,+(2n)^2\Big)&=\dfrac{2n(2n+1)(4n+1)}{6}\end{aligned}[/tex]

We can take 4 common from the sum of even squares.

[tex]\begin{aligned}\longrightarrow\ \ &\Big(1^2+3^2+5^2+\,\dots\,+(2n-1)^2\Big)&\\+\ \ &4\Big(1^2+2^2+3^2+\,\dots\,+n^2\Big)&=\dfrac{2n(2n+1)(4n+1)}{6}\end{aligned}[/tex]

Now the sums in LHS are, as written above,

[tex]1^2+3^2+5^2+\,\dots\,+(2n-1)^2=S[/tex]

[tex]1^2+2^2+3^2+\,\dots\,+n^2=\dfrac{n(n+1)(2n+1)}{6}[/tex]

So,

[tex]\longrightarrow S+\dfrac{4n(n+1)(2n+1)}{6}=\dfrac{2n(2n+1)(4n+1)}{6}[/tex]

[tex]\longrightarrow S=\dfrac{2n(2n+1)(4n+1)}{6}-\dfrac{4n(n+1)(2n+1)}{6}[/tex]

[tex]\longrightarrow S=\dfrac{2n+1}{6}\Big[2n(4n+1)-4n(n+1)\Big][/tex]

[tex]\longrightarrow S=\dfrac{2n+1}{6}\Big[4n^2-2n\Big][/tex]

[tex]\longrightarrow S=\dfrac{2n(2n-1)(2n+1)}{6}[/tex]

[tex]\longrightarrow\underline{\underline{S=\dfrac{n}{3}\,(4n^2-1)}}[/tex]

This is the expression for the sum of squares of first 'n' odd natural numbers.

We will use the concept of Probability in this question. The probability that Hannah will win both games is 0.42.

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty. The likelihood that an event will occur increases with its probability. A straightforward illustration is tossing a fair (impartial) coin. Since there are no other conceivable outcomes and the coin is fair, the odds of both the possibilities, "heads" and "tails," are equally likely to occur. As a result, the probability of either occurrence is half.

The probability she will win the game of chess is 0.6.

The probability she will not win  the game of chess is 0.4[1-0.6]

The probability that she will win the game of backgammon is 0.7.

The probability that she will not win the game of backgammon is 0.3.[1-0.7]

To find the probability of winning of two games

    P(A∩B)=P(A)×P(B)

   ⇒P(Hannah)=0.6×0.7

    ∴Probability of winning both games=0.42.

We will use the concept of Probability in this question. The probability that Hannah will win both games is 0.42.

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To find y-intercept: set x = 0 and solve for y. The point will be (0, y).

To find x-intercept: set y = 0 and solve for x. The point will be (x, 0)

the X and Y Intercepts of a Line Using Algebra

When the equation is written in the slope-intercept form (y=mx +b) we can find the y-intercept by looking at the equation. The value of b is the y-intercept. This is because the y-intercept is when the x value equals 0. When x = 0, mx = 0, so when x = 0, y = b.

To find the x-intercept we set y = 0 and solve the equation for x. This is because when y=0 the line crosses the x-axis.

When an equation is not in y = mx + b form, we can solve for the intercepts by plugging in 0 as needed and solving for the remaining variable.

To find y-intercept: set x = 0 and solve for y. The point will be (0, y).

To find x-intercept: set y = 0 and solve for x. The point will be (x, 0)

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Answer:

45 million

Step-by-step explanation:

There will be approximately 45 million streams on the seventh day after the song's release.

To solve the problem, use the formula for exponential growth:

[tex]N(t) = N0 * (1 + r)^t[/tex]

where

N(t) is the number of streams at time t,

N0 is the initial number of streams,

r is the daily growth rate expressed as a decimal, and

t is the time elapsed in days.

In this case, N0 = 15 million, r = 0.2 (since the number of streams increases by 20% per day), and t = 7 (since we want to know the number of streams on the seventh day).

Plugin these values into the formula

[tex]N(7) = 15 * (1 + 0.2)^7\\N(7) = 15 * 1.2^7[/tex]

N(7) = 15 * 2.985984

N(7) = 44.78976

N(7) ≈ 45 million

Therefore, there will be approximately 45 million streams on the seventh day after the song's release.

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Write a function's inverse as y = f(x), then solve for x as a function of y to discover the inverse of the function.

Multiplying all of the terms on the equation's left and right sides by the fraction's denominator will remove a fraction from it. Try to solve for the variable. Isolate the fractional word initially. By multiplying both sides of the equation by the reciprocal of 4 / 7 (4/7), you can now eliminate the fractional coefficient.

A rational function in mathematics is any function that can be expressed as a rational fraction, which is an algebraic fraction in which the denominator and numerator are both polynomials. In particular, a polynomial term cannot contain any square roots of variables, fractional or negative powers on the variables, or variables in any fraction's denominator.

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Answer:

For a function to be continuous at a point, it must be defined at that point, its limit must exist at the point, and the value of the function at that point must equal the value of the limit at that point.

We can determine 3 terms in the expression 3×2y, 3 terms in the expression 2y2z and 3 terms in the expression z2×5

An expression is the symbolic form of representing a mathematical statement. In a word, description of a mathematical operation is expressed by a few terms and symbols. Expression has two component terms and symbols in where terms mean number, number accompanied by variables and variables. On the other hand, symbols mean addition, subtraction, division, multiplication, equal, inequal sign and so on.

In the question, we notice there are three expressions. The first one, 3 × 2y

3 is multiplied by 2y, here 3 is numbers and it is called constant, y is a variable and 2 is also a number but coefficient of y.

In the second expression, 2y2z, there are 3 terms, but number 2 is used in two times. In both cases, 2 is a coefficient of y and z respectively.

In the last, z2 × 5, we find there are 3 terms. 2 is a number called coefficient of variable z and 5 is constant.

we can say 2z is multiplied by 5.

hence, we find total 6 terms x, y, z, 2, 3 and 5.

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The price of a computer increase from £631 to £776. 13. The percentage change is 81.3%

As per the given data:

Old value of computer is £631

New value of computer is £776. 13

Percentage Change: Percentage Change is the difference coming after subtracting the old value from the new value and then divide by the old value and the final answer will be multiplied by 100.

The phrase percent change says the difference in the percent of the earlier and present quantity.

Percentage change formula is

Percentage Change [tex]=\frac{{New Value - Old Value} }{{Old Value}} \times 100[/tex]

If the result is positive, then it is an increase.

If the result is negative, then it is a decrease.

[tex]=\frac{631}{776.13} \times 100[/tex]

= 0.813 × 100

= 81.3%

Therefore the increase in percentage is 81.3%

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