What are the exact solutions of x2 - 5x-7= 0, where
Ox=
O
x=
X
H
-5± √3
2
5+√3
2
-5± √53
2
5± √53
2
X=
-b± √b²-4ac7
2a

When selecting 2 letters from the set {A, B, C, D}, considering that the order matters, we can use the concept of permutations to calculate the number of possible arrangements.

The number of ways to arrange 2 letters from a set of 4 can be calculated using the formula for permutations:

P(n, r) = n! / (n - r)!

Where n is the total number of items (in this case, 4) and r is the number of items being selected (in this case, 2).

Using this formula, the number of ways to arrange 2 letters from A, B, C, D is:

P(4, 2) = 4! / (4 - 2)!

= 4! / 2!

= (4 x 3 x 2 x 1) / (2 x 1)

= 24 / 2

= 12

Therefore, there are 12 possible ways to arrange 2 letters selected from A, B, C, D when considering that the order matters.

~~~Harsha~~~

Answer:

Step-by-step explanation:

When selecting 2 letters from the set {A, B, C, D} and considering that the order matters, we can determine the number of possible arrangements using the concept of permutations.

The number of ways to arrange 2 letters from a set of 4 can be calculated using the formula for permutations:

P(n, r) = n! / (n - r)!

where P(n, r) represents the number of permutations of r objects chosen from a set of n objects.

In this case, we have n = 4 (the total number of letters) and r = 2 (the number of letters to be selected).

Using the formula, we can calculate:

P(4, 2) = 4! / (4 - 2)!

       = 4! / 2!

       = (4 × 3 × 2 × 1) / (2 × 1)

       = 24 / 2

       = 12

Therefore, there are 12 different ways to arrange 2 letters chosen from the set {A, B, C, D} when the order matters.

Let x, xr , xr² be the terms of GP.

After the increase, the terms are : x+xr , xr+xr , xr²+xr

or in simplified manner : x(1+r), 2xr, xr (r+1) .

For these terms to be in Harmonic Progression, their reciprocals should be in Arithmetic Progression .

Thus,

Arithmetic mean of first and last terms should be equal to the middle term.

First term = 1/[x(1+r)] ; Middle term= 1/(2xr) ; Last term = 1/[xr(r+1)]

Assume,

A = Arithmetic mean of first and last term

A= [1/[x(1+r)]+[1/[xr(r+1)] /2

A= (1/2)[(r+1)/(xr(1+r))]

A= (1/2)(1/xr)

A= 1/(2xr)

A = Middle term

Thus, the reciprocals are in AP.

Hence x(1+r), 2xr, xr(r+1) in HP.

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Answer:

Perimeter:[tex]4x+10[/tex] feet
Area:[tex]x^{2}+5x+6[/tex] feet

Step-by-step explanation:

The perimeter is equal to 2*width +2*length. The width is x+2 and the length is x+3, therefore the perimeter is equal to 2x+4+2x+6 which equals 4x+10.
The area is equal to width*length
(x+3)(x+2)=[tex]x^{2}+2x+3x+6=x^{2}+5x+6[/tex]

(a) The expected value of playing the game is 0.

(b) Heather can expect to break even in the long run.

To find the expected value of playing the game, we need to calculate the weighted average of the possible outcomes.

Expected value calculation:

The probability of selecting each ball is the same since Heather replaces the ball in the bag each time.

The probability of selecting any particular number is 1/8.

Expected value = (Probability of outcome 1 × Value of outcome 1) + (Probability of outcome 2 × Value of outcome 2) + ... + (Probability of outcome 8 × Value of outcome 8)

Expected value = (1/8 × 1) + (1/8 × 2) + (1/8 × 5) + (1/8 × 6) + (1/8 × 8) + (1/8 × 10) + (1/8 × (-13)) + (1/8 × (-13))

Expected value = (1/8) + (2/8) + (5/8) + (6/8) + (8/8) + (10/8) + (-13/8) + (-13/8)

Expected value = 26/8 - 26/8

Expected value = 0

Since the expected value of playing the game is 0 On average, she neither gains nor loses money over multiple plays of the game.

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The angle opposite to side BC in triangle ABC is approximately 38.213 degrees.

We have,

To find the angle opposite to side BC in triangle ABC, we can use the Law of Cosines.

The Law of Cosines states that in a triangle with sides of lengths a, b, and c, and the angle opposite to side c being denoted as C, the following equation holds:

c² = a² + b² - 2ab x cos(C)

In this case,

Side a is BC with length 12, side b is AC with length 20, and side c is AB with length 11. We want to find the angle C, which is opposite to side BC.

Plugging the given values into the Law of Cosines equation:

11² = 12² + 20² - 2 x 12 x 20 x cos C

121 = 144 + 400 - 480 x cos C

121 = 544 - 480 x cos C

480 x cos C = 544 - 121

480 x cos C = 423

cos C = 423/480

Now, we can find the angle C by taking the inverse cosine (arccos) of (423/480):

C = arccos(423/480)

Using a calculator, we find that C is approximately 38.213 degrees.

Therefore,

The angle opposite to side BC in triangle ABC is approximately 38.213 degrees.

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The length AC in the kite is 8.7 cm.

A kite is a quadrilateral that has two pairs of consecutive equal sides and

perpendicular diagonals. Therefore, let's find the length AC in the kite.

Hence, using Pythagoras's theorem, let's find CE.

Therefore,

7² - 4² = CE²

CE = √49 - 16

CE = √33

CE = √33

Let's find AE as follows:

5²- 4² = AE²

AE = √25 - 16

AE = √9

AE = 3 units

Therefore,

AC = √33 + 3

AC = 5.74456264654 + 3

AC = 8.74456264654

AC = 8.7 units

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AnswerTherefore, Jennifer traveled for 2 hours.

Step-by-step explanation:

Let x be the time Jennifer traveled.

Kristin traveled for 2 hours at 33 km/h, so she had traveled 66 km when Jennifer started traveling.

After x hours, Jennifer had traveled 45x km.

The total distance between them was 156 km.

So, we have:

66 km + 45x km = 156 km

Simplifying the equation, we get:

45x km = 90 km

x = 2 hours

Therefore, Jennifer traveled for 2 hours.

The confidence interval using a margin of error of 0.07 is (0.85,0.99)

Sample proportion = 0.92

Margin of error = 0.07

Lower bound of the confidence interval = Sample proportion - Margin of error

Lower bound = 0.92 - 0.07 = 0.85

Upper bound of the confidence interval = Sample proportion + Margin of error

Upper bound = 0.92 + 0.07 = 0.99

Confidence interval = [Lower bound, Upper bound]

Confidence interval = [0.85, 0.99]

Therefore, the confidence interval for the proportion of math majors who found the curriculum challenging is approximately 0.85 to 0.99.

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Applying the properties of the diagonal of a rectangle, the value of x is calculated as: x = 37.

A rectangle is a quadrilateral that has two equal diagonals which bisect each other, to form equal segment. Rectangle RSTW has two diagonals RT and SW, therefore:

2(RZ) = SW

Given the following:

RZ = 2x + 7

SW = 5x - 23

Plug in the values:

2(2x + 7) = 5x - 23

4x + 14 = 5x - 23

4x - 5x = -14 - 23

x = 37

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Step-by-step explanation:

Unclear what you are asking

here is one possibility

3^2  - 4^5

9    - 1024 = - 1015

Here is another possibility

(3^(2-4) )^5    =  = (3^(-2))^5 =   3 ^-10 =    1/59049      

Hello!

men = 10/26 = 5/13

women = 2/29

P = 5/13 x 2/29 = 10/377

Note that his is solved using the principle of Combination, and there are 771, 891, 120 different ways to form the groups for the first division soccer league tournament in Mexico.

Let 's compute the number of ways to form the groups using combinations.

First group - 5 teams

C(18, 5) = 18! / (5! * (18-5)!) = 8568

Second group - 5 teams

C(13, 5) = 13! / (5! * (13-5)!) = 1,287

Third group - 4 teams

C(8, 4) = 8! / (4! * (8-4)!) = 70

Fourth group - 4 teams

C(4, 4) = 4! / (4! * (4-4)!) = 1

Now, applying the product rule

Total ways =  8568 x 1,287 x 70 x 1 = 771891120

Therefore, there are 771, 891, 120  different ways to form the groups for the first division soccer league tournament in Mexico.

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Translation

In how many ways is it possible to form the groups of the first division soccer league tournament? Let's remember that 18 teams participate in the first division of soccer in Mexico, and for the league tournament, two groups of five teams and two groups of 4 teams are formed. It is suggested that when solving it, the number of teams that have been considered for the first group be subtracted, then for the second group and so on for each group. Finally apply the product rule to find the different shapes.​

Question One:A positive z-score indicates that the raw score is above the mean, while a negative z-score indicates that the raw score is below the mean.

Question Two: , the raw score is relatively lower than the mean.

If a raw score corresponds to a z-score of 1.75, it tells us that the raw score is 1.75 standard deviations above the mean of the distribution. In other words, the raw score is relatively higher than the mean. The z-score provides a standardized measure of how many standard deviations a particular value is from the mean.

A positive z-score indicates that the raw score is above the mean, while a negative z-score indicates that the raw score is below the mean.

Question Two:

If a raw score corresponds to a z-score of -0.85, it tells us that the raw score is 0.85 standard deviations below the mean of the distribution. In other words, the raw score is relatively lower than the mean. The negative sign indicates that the raw score is below the mean.

To understand the meaning of a z-score, it is helpful to consider the concept of standard deviation. The standard deviation measures the average amount of variability or spread in a distribution. A z-score allows us to compare individual data points to the mean in terms of standard deviations.

In the case of a z-score of -0.85, we can conclude that the raw score is located below the mean and is relatively lower compared to the rest of the distribution. The negative z-score indicates that the raw score is below the mean and is within the lower portion of the distribution. This suggests that the raw score is relatively smaller or less than the average value in the distribution.

By using z-scores, we can standardize and compare values across different distributions, allowing us to understand the position of a raw score relative to the mean and the overall distribution.

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The value of x for which the two lines are parallel is given as follows:

x = 60º.

We have two parallel lines that are cut by a transversal, and the two angles are between the parallel lines and on the same side of the transversal, meaning that they are consecutive interior angles.

Consecutive interior angles are supplementary, meaning that the sum of their measures is of 180º, hence the value of x can be found as follows:

x + 2x = 180

3x = 180º

x = 180º/3

x = 60º.

The figure is given by the image presented at the end of the answer.

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The equation line is y= 1/50x.

We have a graph from which we can take two points as

(100, 2) and (200, 4).

So, the slope of line

= (change in y)/ (change in x)

= (4-2)/ (200- 100)

= 2/ 100

= 1/50

Now, the equation line is

(y - 2)= 1/50 (x - 100)

y-2 = 1/50 x - 2

y= 1/50x

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Answer:

Here is an example of a dot plot (in text, did as best as I could to represent it) that matches the description you provided:

Number of Minutes Spent on Math Homework Problem

 |

10|    o

9| o

8|

7|       o

6|

5|          o

4|

3|             o

2|

1|                o

0|___________________

  1  2  3  4  5  6  7  8  9  10

  Students

This dot plot shows the number of minutes spent on a math homework problem by ten students. The mean amount of time is represented by the dot at the y-value of 9, and the MAD (Mean Absolute Deviation) is represented by the spread of the data around the mean.

Answer:

Multiplicative identity for any real number is 1.

Step-by-step explanation:

The expression that we need to solve is 4*45 + 2*123 , and that is equal to 426.

Here we want to calculate the quadruple of the decimal part by adding twice the integer part of the following decimal number: 123.45​

The decimal part of this number is 45

The integer part of this number is 123.

Then the expression that we need to solve is:

4*45 + 2*123 = 426

That is the value of the mathematical sentence.

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Answer:

-84x^7

Step-by-step explanation:

The product of (4x)(-3x³)(-7x³) is -84x^8.

To calculate the product, we multiply the coefficients together and add the exponents of the variables:

4 * (-3) * (-7) = 84

x^1 * x^3 * x^3 = x^(1+3+3) = x^7

Combining the coefficient and the variable, we get -84x^7.

The probability that a sample of size n = 62 is randomly selected with a mean between 189.7 and 213 is approximately 0.9702.

To find the probability that a single randomly selected value is between 189.7 and 213, we can use the standard normal distribution.

Step 1: Calculate the z-scores for the given values using the formula:

  z = (x - μ) / σ

  For 189.7:

  z1 = (189.7 - 189.7) / 96.7 = 0

  For 213:

  z2 = (213 - 189.7) / 96.7 ≈ 0.2417

Step 2: Utilize a standard typical conveyance table or number cruncher to find the probabilities comparing to the z-scores.

  P(189.7 < X < 213) = P(0 < Z < 0.2417) ≈ 0.0939

Therefore, the probability that a single randomly selected value is between 189.7 and 213 is approximately 0.0939.

To find the probability that a sample of size n = 62 is randomly selected with a mean between 189.7 and 213, we use the central limit theorem. Under specific circumstances, the testing dispersion of the example mean methodologies a typical conveyance

Step 1: Calculate the standard error of the mean (σ_m) using the formula:

  σ_m = σ / sqrt(n)

  σ_m = 96.7 / sqrt(62) ≈ 12.2878

Step 2: Convert the given qualities to z-scores utilizing the equation:

  z = (x - μ) / σ_m

  For 189.7:

  z1 = (189.7 - 189.7) / 12.2878 = 0

  For 213:

  z2 = (213 - 189.7) / 12.2878 ≈ 1.8967

Step 3: Utilize a standard typical conveyance table or mini-computer to find the probabilities relating to the z-scores.

  P(189.7 < M < 213) = P(0 < Z < 1.8967) ≈ 0.9702

Therefore, the probability that a sample of size n = 62 is randomly selected with a mean between 189.7 and 213 is approximately 0.9702.

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total angles of the triangle = 180°

∠BAC + ∠ABC + ∠ACB = 180°

40° + 90° + ∠ACB = 180°

130° + ∠ACB = 180°

∠ACB = 180° - 130°

∠ACB = 50°

∠ACB and ∠ECD is opposite angles. So, that two angles are equal.

∠ACD = ∠ECD = 50° (B)

That's it :)

Step-by-step explanation:

50°

abc is right angle and

a is 40°

b is 90°

c is 50°

so angle acb is vertical opposite to angle ecd and it is equal

Answer:

17.5

Step-by-step explanation:

You can find the mean of a data set by adding all numbers in the data set together and dividing by the amount of numbers in the given data set.

In this case, your data set is:

15 , 16 , 17 , 23 , 11 , 19 , 20 , 15 , 18 , 22 , 15 , 19   (12 numbers).

Firstly, add all the numbers together: [tex]15 + 16 + 17 + 23 + 11 + 19 + 20 + 15 + 18 + 22 + 15 + 19 = 210[/tex]

Next, divide 210 (total sum) with the amount of terms in total (12):

[tex]\frac{(210)}{(12)} = 17.5[/tex]

17.5 is already in the tenth digit place value, and so you do not need to round.

17.5 is your answer.

~

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Answer:f(x) = (x-10)^2-49

f(x) = (x-10+7)(x-10-7)

f(x) = (x-3)(x-17)

The zeros of the function are 3 and 17.

Step-by-step explanation:

The probability of 12 women jurors being chosen is approximately 0.000342 or 0.0342%.

To calculate the probability of selecting 12 women jurors out of a pool of 26 men and 29 women, we need to consider the total number of possible combinations and the specific combination of interest.

The total number of ways to choose 12 individuals from a pool of 55 (26 men + 29 women) is given by the combination formula:

C(55, 12) = 55! / (12! * (55-12)!) = 22579284062370.

The number of ways to choose 12 women from a pool of 29 is given by the combination formula:

C(29, 12) = 29! / (12! * (29-12)!) = 7726160.

Therefore, the probability of selecting 12 women jurors is the ratio of the number of ways to choose 12 women to the total number of possible combinations:

P(12 women jurors) = C(29, 12) / C(55, 12) ≈ 7726160 / 22579284062370 ≈ 0.000342.

Hence, the probability of 12 women jurors being chosen is approximately 0.000342 or 0.0342%.

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A full circle has [tex]360^{\circ}[/tex].

[tex]\dfrac{4}{9}\cdot 360^{\circ}=160^{\circ}[/tex]

The mark angle is [tex]160^{\circ}[/tex].

The perimeter of the trapezoid is 106 meters.

The area of the trapezoid is 1360 square meters.

To calculate the perimeter and area of an isosceles trapezoid, we need to use the given measurements:

The length of the minor base (34 m), the height (20 m), and the length of the oblique side (29 m).

First, let's calculate the length of the major base (the other parallel side). In an isosceles trapezoid, the major base and minor base have the same length.

So, the length of the major base is also 34 m.

The perimeter of a trapezoid is the sum of all its sides. In this case, the perimeter can be calculated as follows:

Perimeter = length of minor base + length of major base + 2 × length of oblique side

Perimeter = 34 m + 34 m + 2 × 29 m

Perimeter = 34 m + 34 m + 58 m

Perimeter = 106 m

To calculate the area of the trapezoid, we can use the formula:

Area = (sum of the lengths of the bases) × height / 2

Area = (34 m + 34 m) × 20 m / 2

Area = 68 m × 20 m / 2

Area = 1360 m²

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The possible price for the items if the store sells $600 is (c) $40

From the question, we have the following parameters that can be used in our computation:

The supply-demand graph

If the store sells $600, then there is a supply worth of $600

The equation of the supply line is calculated as

y = mx + c

Where

c = y = 0

i.e. c = 100

So, we have

y = mx + 100

Using another point on the graph, we have

30m + 10 = 400

So, we have

m = 13

This means that

y = 13x + 100

For a supply of 600, we have

13x + 100 = 600

So, we have

13x = 500

Divide by 13

x = 38.4

Approximate

x = 40

Hence, the possible price for the items is (c) $40

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