solve the following using the quadratic formula
10x^2-7x+5=0
a)-0.96 and -0.26
b)0.96 and -0.26
c)no solution
b)0.96 and 0.26

Step-by-step explanation:

\(thank \: you\)

The increase in the rate of unemployment from 2000 to 2001, given the unemployment figure is between D. 0. 46 % and 0. 49 %.

First, find the rate of unemployment in 2000 to be :

= Unemployment number / Total labor force x 100 %

= 3, 503, 917 / 25, 554, 417  x 100 %

= 13.71  %

The rate of unemployment in 2001 was :

= 3, 745, 300 / 26, 416, 800 x 100 %

= 14. 18 %

The increase in the rate of unemployment is:

= 14. 18 - 13. 71

= 0. 47 %

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The perimeter of DEFG will be 2(√10+√17).

The cοοrdinate system that is mοst frequently emplοyed in three-dimensiοnal systems is called spherical cοοrdinates οf the system, represented as (r,Ф,∅ ).

The surface area in three dimensiοns is calculated using the spherical cοοrdinate system. Radial distance, pοlar angles, and azimuthal angle are the three numbers that these cοοrdinates indicate. Additiοnally knοwn as spherical pοlar cοοrdinates.

A 2-dimensiοnal graph with an x-axis and a y-axis is given.

A parallelοgram DEFG is drawn οn it with cο-οrdinates (2,1), (3,4), (7, 5) and (6,2) respectively.

Sο the perimeter will be DE = √10

DG=√17

EF = √17

FG=√10

Sο the perimeter will be 2(√10+√17).

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The rates that are equivalent to this rate is 90 pages/hr

The rate is the number of pages Michael read in 1 hour.

If he read 135 pages in 1 1/2 hours then;

To determine the rate, we will have:

Divide both expressions:

135/x = 1.5/1

1.5x = 135

x = 135/1.5

x = 90

Hence the rates that are equivalent to this rate is 90 pages/hr

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The total number of games the team played last year was 80 (option C). In the first half of the year, the team won 60 percent of their games, indicating that they won 6 out of every 10 games played.

In the second half of the year, the team played 20 games and won 3 of them. This means that in the second half, they won only 3 out of 20 games, which is equivalent to winning 15 percent of their games.

To find the overall percentage of games won, we can calculate the weighted average of the two percentages. Since the team won 50 percent of their games overall, we can assign equal weights to the first and second halves of the year. Therefore, the average winning percentage for the team would be the midpoint between 60 percent and 15 percent, which is (60% + 15%) / 2 = 37.5%.

Let's assume the total number of games played last year was x. Since the team won 37.5% of the games, they won 0.375x games. We can set up an equation based on the information given:

0.375x = 50% of x

0.375x = 0.5x

0.5x - 0.375x = 0

0.125x = 0

x = 0 / 0.125

x = 0

However, we have arrived at an invalid result. It seems there is an error in the information provided or the calculations made.

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Answer:

8 1/3

Step-by-step explanation:

We want to find a number, x, that when divided by 10/3 equals 2.5.  We can write that as:

  x/(10/3) = 2.5

x = (2.5)*(10/3)    [MULTIPLY BOTH SIDES BY (10/3)

x = 25/3

x = 8 1/3             [

Answer:

5,424 ft.

Step-by-step explanation:

For every 1 foot the ski lift goes up by, it travels west 4 feet. So, because we know that the lift will be 1,356 feet higher at the top of the mountain, all we have to do is multiple 1,356 by 4.

1,356 * 4 = 5,424 ft.

I hope this helps. :)

Answer:

X= 6

Y=4

Step-by-step explanation:

10x-9x=24

10x-9(x-2)=24

10x-9x+18=24

x=24-18

x=6

Y=x-2

Y=6-2

Y=4

Answer:

4.994897396

Step-by-step explanation:

I am trying my best in mathematics and I think this is how to solve this question

AC=CB

line AC equals to line BC Square Plus line ab square

AC=13.5 square +8.2 square

AC=182.25 + 6.724

AC=24.949

I will win about $ 59.

This is a question of permutations and combinations.

We know that,

Probability of getting two non face cards = \(\frac{^{40}C_2}{{^{52}C_2}}\) = 10/17

Probability of not getting two non face cards = 1 - (10/17) = 7/17

Hence, we can write,

Money I will get = (7/17)*50*20 =  $ 411.764

Money I'll have to pay = (10/17)*30*20 = $ 352.94

We know that,

Money left with me = Money I will get - Money I'll have to pay

Hence, we can write,

Money left with me =   $ 411.764 - $ 352.94

Money left with me =  58.824 ≈ $ 59

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From the graph, we can see that the cost of 5lb of beans was $4, to get the cost of 50lb of beans, we will use the equality postulate as shown;

5lb = $4

50lb = x

Answer:

Step-by-step explanation:

The function that satisfies the given criteria can be constructed by combining three different equations to form three segments that fit together seamlessly. The general form of the function is:

f(z) = {P + Qcos(R(z-S))} + T

where P, Q, R, S, and T are constants to be determined.

The function has a local minimum at (5,1) and a local maximum at (9,6), which means that the middle segment of the function should be a cosine function that starts at a maximum and ends at a minimum. This can be achieved by setting the middle segment to:

P = 5.5 (the average of the local maximum and minimum)

Q = 5/2 (half the difference between the maximum and minimum)

R = π/2 (to make the function a cosine)

S = 7 (the midpoint between the two endpoints of the segment)

T = 0 (since this segment should start and end at 0)

Therefore, the function for the middle segment is:

f(z) = 5.5 + (5/2)cos(π/2(z-7))

The left and right segments of the function should be linear functions that connect the endpoints to the middle segment. To make the function start at (0,12), we can set the left segment to:

P = 12

Q = 0 (since we don't want any oscillations in this segment)

R = 0 (since this segment is a straight line)

S = 0 (since we want the function to start at 0)

T = 0 (since this segment should start at 12)

Therefore, the function for the left segment is:

f(z) = 12 - (12/5)z

To make the function end at (12,0), we can set the right segment to:

P = 0

Q = 0

R = 0

S = 12 (since we want the function to end at 0)

T = -3 (since this segment should end at 0 and we want the middle segment to start at 5.5)

Therefore, the function for the right segment is:

f(z) = -3z + 36

Putting all three segments together, we get:

f(z) = {12 - (12/5)z} 0 ≤ z < 5

f(z) = 5.5 + (5/2)cos(π/2(z-7)) 5 ≤ z < 9

f(z) = -3z + 36 9 ≤ z ≤ 12

Therefore, the values of P, Q, R, S, and T are:

P = 12

Q = 5/2

R = π/2

S = 7

T = 0 (for the middle segment)

T = 12 (for the left segment)

T = -3 (for the right segment)

Therefore, the answer is:

P = 12

Q = 5/2

R = π/2

S = 7

T = 0 (for the middle segment)

T = 12 (for the left segment)

T = -3 (for the right segment)

Answer:

  (P, Q, R, S) = (6.5, 5.5, π/4, -1.5)

Step-by-step explanation:

You want the values of the parameters P, Q, R, and S that makes the piecewise-defined function match the given graph. The function is ...

  \(f(x)=\begin{cases}P+Q\cos{\left(\dfrac{\pi}{5}x\right)}&0\le x < 5\\-2.5\cos{(R(x-5))}+3.5&5\le x < 9\\3-3\sin{\left(\dfrac{\pi}{3}(x-S)\right)}&9\le x \le12 \end{cases}\)

The value of Q in the function is half the difference between the maximum and minimum on the interval [0, 5). It is ...

  Q = (12 -1)/2 = 5.5

The value of P in the function is the average of the maximum and minimum on the interval [0, 5). It is ...

  P = (12 +1)/2 = 6.5

The value of R in the function is π divided by the difference between the interval ends. The interval applicable to R is [5, 9). R is ...

  R = π/(9 -5) = π/4

The value of S in the function is the average of the interval ends. It can be reduced by any multiple of twice the length of the interval. (The reason for that reduction would be to make the number have as small a magnitude as possible.) The interval applicable to S is [9, 12]. S is ...

  S = (9 +12)/2 -n·(2(12-9)) = 10.5 -6n

For n = 2, the value of S is ...

  S = 10.5 -12 = -1.5

Other possible values include 4.5 and 10.5. Your answer checker may have a preference for one or another of these values.

The parameters in the function are ...

  (P, Q, R, S) = (6.5, 5.5, π/4, -1.5)

__

Additional comment

Our description of the parameters in terms of the interval ends is based on the fact that each interval includes exactly 1/2 period of the trig function. For the sine function, the horizontal shift is based on the negative-going midline crossing, halfway between the extremes at the interval ends.

The attached graph provides confirmation that our choice of parameters is appropriate.

It is False that based only on the r and p values listed above you can come to the conclusion that age is a moderator of the bivariate relationship between the amount of texting and the number of accidents.

In the given scenario, it is not completely true that based only on the r and p values listed above, you can come to the conclusion that age is a moderator of the bivariate relationship between the amount of texting and the number of accidents.

Let's first understand what is meant by the term "moderator.

"Moderator: A moderator variable is a variable that changes the strength of a connection between two variables. If there is a statistically significant bivariate relationship between the amount of texting during driving and the number of accidents, scientists investigate whether this bivariate relationship is moderated by age.

Therefore, based on the values of r and p, it is difficult to determine if age is a moderator of the bivariate relationship between the amount of texting and the number of accidents.

As we have to analyze other factors also to determine whether the age is a moderator or not, such as the sample size, the effect size, and other aspects to draw a meaningful conclusion.

So, it is False that based only on the r and p values listed above you can come to the conclusion that age is a moderator of the bivariate relationship between the amount of texting and the number of accidents.

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Answer:

1,369 cm^2

Step-by-step explanation:

A square is a two-dimensional shape with four right angles and four equal sides.

This means each and every side is equal.

In this case, every side is 37 yards.

To find the area of a square, simply multiply a length of a side by itself.

Like this,

37⋅37 = 1,369.

Therefore, the area of the cornfield is 1,369 yards cm^2.

The equation that is approximately 13.52 milligram remains is f(x) = 50(0.5)⁽¹⁰/⁵°³)

Equation:

Equation also known as expression is the combination of numbers, variables and mathematical operators.

Given,

The function gives the mass, m, of a radioactive substance remaining after h half-lives. Cobalt-60 has a half-life of about 5. 3 years.

Here we need to find the equation gives the mass of a 50 mg Cobalt-60 sample remaining after 10 years, and approximately how many milligrams remain.

Here we know that, when the mass is 50 mg, it means that:

=> m = 50

So, the equation is written as,

=> f(x) = 50(0.5)⁽ᵃ/ᵇ⁾

Here they said that when 10 years remain in the life of the substance, it means that:

So, the value of t = 10 and the value of half life is 5.3

Then the equation is rewritten as,

=> f(x) = 50(0.5)⁽¹⁰/⁵°³⁾

To evaluate the equation

f(x) = 13.52

Therefore, the required equation is f(x) = 50(0.5)⁽¹⁰/⁵°³) and approximately 13.52  milligram remains

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The probability that a student who had a dog also had a cat would be = 7/25.

To calculate the possible outcome of the given event, the formula for probability should be used and it's given below as follows. That is;

Probability = possible outcome/sample space

possible outcome = 7

sample space = 7+2+3+13 = 25

Probability = 7/25

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If today were January 1, 2023, then 80 days from today would be March 22, 2023. Keep in mind that the actual date that is 80 days from today will depend on the current date.

To determine the date that is 80 days from today, you can add 80 days to the current date.

As of my knowledge cutoff date of September 2021, the current date is irrelevant for today. However, I can tell you how to calculate the date that is 80 days from any given date.

Assuming you want to calculate 80 days from today's date, you would add 80 days to today's date. For example, if today were January 1, 2023, then 80 days from today would be:

January 1, 2023 + 80 days = March 22, 2023

So, if today were January 1, 2023, then 80 days from today would be March 22, 2023. Keep in mind that the actual date that is 80 days from today will depend on the current date.

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Answer: 2/5

Step-by-step explanation:  Dividing two fractions is the same as multiplying the first fraction by the reciprocal (inverse) of the second fraction

Take the reciprocal of the second fraction by flipping the numerator and denominator and changing the operation to multiplication. Then the equation becomes

The, multiply the numerators and denominators and get 12/30, then simply by 6 and get 2/5

Answer:

Step-by-step explanation:

slope-intercept form of equation:  y = mx + b

where m is slope and b is y-intercept

If line y=ax+b passes through point (x₀,y₀) that means

that the equation y₀=ax₀+b is true

(2, 5)    ⇒   x=2,   y=5

m = 5

So:

              5 = 5×2 + b

               5 = 10 + b

               b = -5

Therefore equation in  slope-intercept form:

                                                                      y = 5x + (-5)

                                                                      y = 5x - 5                          

The equation of the line in slope-intercept form is y = 5x - 5.

Given that the slope of the line is 5 and it passes through the point (2, 5), we can use the point-slope form of a linear equation to find the equation of the line.

The point-slope form is given by:

y - y1 = m(x - x1),

where (x1, y1) is the given point and m is the slope.

Substituting the values, we have:

y - 5 = 5(x - 2).

Now, let's simplify this equation:

y - 5 = 5x - 10.

Next, let's isolate y:

y = 5x - 10 + 5.

Simplifying further:

y = 5x - 5.

So, the equation of the line in slope-intercept form is y = 5x - 5.

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Answer:

3p - q = 3(2-5) - (8x3) = -9 - 24 = -33. Therefore, 3p-q=-33.

Let x and y be the two number. Then, we can write

From the first equation, we have

By substituting this result into the second equation, we obtain

which gives

we can rewrite this quadratic equation as follows

Then, we can apply the quadratic formula, that is,

which gives

Then, the 2 solutions for x are

Now, we can substitute these solutions into the equation x.y=684. For the first solution, we have

and for the second solution, we have

Therefore, the two numbers are 19 and 36

The given exponential function equation is A = P(1+r)t, where P represents the principal amount, A represents the final amount, r represents the annual interest rate, and t represents the time in years.a.

The independent variable is t (time in years) while the dependent variable is A (final amount).b. The growth factor can be obtained by dividing A by P. Therefore, Growth factor = A/PLet us assume P=100, r=20%, and t=1. Then we can find A as follows:A = P(1+r)tA = 100(1+0.2)1A = 100(1.2)A = 120Therefore, the growth factor is:A/P = 120/100 = 1.2If we assume P=150, r=5%, and t=2, thenA = P(1+r)t = 150(1+0.05)2= 150(1.1025)= 165.375The growth factor is:A/P = 165.375/150 = 1.1025

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The given linear system can be represented as a matrix equation:

A * X = B

where `A` is the coefficient matrix, `X` is the variable matrix, and `B` is the constant matrix.

The augmented matrix for the system is:

[-6 1 4 -2 | 1]

Using Gaussian elimination or row reduction, we can transform the augmented matrix to its row-echelon form:

[1 -1/6 -2/3 1/3 | -1/6]

[0 1 2/3 -1/3 | 1/6]

[0 0 0 0 | 0 ]

This row-echelon form implies that the system has a dependent variable since the third row consists of all zeros. In other words, there are infinitely many solutions to the system. The dependent variable, denoted as `x3`, can be expressed in terms of free parameters `s1` and `s2`.

Therefore, the set of solutions to the given linear system is:

x1 = -1/6 + (2/3)s1 - (1/3)s2

x2 = 1/6 - (2/3)s1 + (1/3)s2

x3 = s1

x4 = s2

where `s1` and `s2` are arbitrary real numbers that serve as parameters. These equations represent the general form of the solution, accounting for the infinite possible solutions.

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(a) Player Column's best response is given by:

BR_Column(p) = { L if p < 1/2, R if p > 1/2 (indifferent if p = 1/2)

(b) Where both players are indifferent between their available strategies.

(c)  The normal form representation of the game is above.

(d) No player can gain an advantage by deviating from this strategy.

This equilibrium results in an expected payoff of 0 for each player.

(a) To derive the best response functions, we need to find the strategies that maximize the payoffs for each player given the mixed strategy of the other player.

Player Row's best response function:

If Player Column chooses L with probability q, Player Row's expected payoff for choosing U is 0q + 2(1-q) = 2 - 2q.

If Player Column chooses R with probability 1-q, Player Row's expected payoff for choosing U is 0*(1-q) + 1*q = q.

Therefore, Player Row's best response is given by:

BR_Row(q) = { U if q < 1/3, D if q > 1/3 (indifferent if q = 1/3)

Player Column's best response function:

If Player Row chooses U with probability p, Player Column's expected payoff for choosing L is 0p + 2(1-p) = 2 - 2p.

If Player Row chooses D with probability 1-p, Player Column's expected payoff for choosing L is 0*(1-p) + (-1)*p = -p.

Therefore, Player Column's best response is given by:

BR_Column(p) = { L if p < 1/2, R if p > 1/2 (indifferent if p = 1/2)

Plotting the best response functions on a graph with p on the horizontal axis and q on the vertical axis will result in two line segments: BR_Row(q) is horizontal at U for q < 1/3 and horizontal at D for q > 1/3, while BR_Column(p) is vertical at L for p < 1/2 and vertical at R for p > 1/2.

The two segments intersect at the point (p, q) = (1/2, 1/3).

(b) To find the Nash equilibria, we look for the points where the best response functions intersect. In this case, the only Nash equilibrium is at (p, q) = (1/2, 1/3), where both players are indifferent between their available strategies.

Now let's move on to the rock-paper-scissors-lizard game:

(c) The normal form representation of the game can be written as follows:

    R    P    S    L

------------------------

R | 0,0 -1,1 1,-1 1,-1

P | 1,-1 0,0 -1,1 1,-1

S | -1,1 1,-1 0,0 -1,1

L | -1,1 -1,1 1,-1 0,0

(d) To find the Nash equilibria, we look for any strategy profiles where no player can unilaterally deviate to improve their payoff.

In this game, there are no pure strategy Nash equilibria since each strategy can be countered by another strategy with a higher payoff.

However, there is a mixed strategy Nash equilibrium where each player chooses their actions with equal probabilities: r = p = s = l = 1/4.

In this case, no player can gain an advantage by deviating from this strategy.

This equilibrium results in an expected payoff of 0 for each player.

In summary, the rock-paper-scissors-lizard game has a unique mixed strategy Nash equilibrium where each player randomly chooses their actions with equal probabilities.

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The smallest final thickness that can be obtained for the Cu- 30% Zn brass plate is approximately 2.0944 inches.

To calculate the smallest final thickness that can be obtained for a Cu- 30% Zn brass plate with an elongation greater than 36%, we need to consider the relationship between elongation and thickness.

Elongation is a measure of the material's ability to stretch or deform without breaking. It is typically expressed as a percentage increase in length compared to the original length. In this case, the elongation needs to be greater than 36%.

To calculate the smallest final thickness, we can use the formula:

Final thickness = Original thickness * (1 + Elongation/100)

Let's plug in the given values:

Original thickness = 1.54 inch
Elongation = 36%

Final thickness = 1.54 inch * (1 + 36%/100)
Final thickness = 1.54 inch * (1 + 0.36)
Final thickness = 1.54 inch * 1.36
Final thickness = 2.0944 inch (rounded to four decimal places)

Therefore, the smallest final thickness that can be obtained for the Cu-30% Zn brass plate is approximately 2.0944 inches.

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Based on the information you provided, it seems that a simple linear regression model was used to analyze the relationship between the size of a house (in square feet) and its selling price (in 1,000 dollars).

The dependent variable in this model was the price, while the independent variable was the size. The sample size used for this analysis was 8.

The correlation coefficient (r) measures the strength and direction of the linear relationship between two variables. In this case, the correlation coefficient would indicate how closely the selling price of a house is related to its size. The value of r can range from -1 to 1, with values closer to -1 or 1 indicating a stronger relationship, while values closer to 0 indicate a weaker relationship.

Without knowing the specific value of r, it is difficult to draw conclusions about the strength of the relationship between the size of a house and its selling price. However, in general, it is reasonable to assume that there is a positive correlation between these two variables - that is, as the size of a house increases, its selling price is likely to increase as well.

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Answer:

8.7

Step-by-step explanation:

a = side of a regular hexagon inscribed in a circle = radius of the circle

Area of a hexagon = (3√3 / 2)a² =  (3√3 / 2)4² = 41.57

Acircle = πr² = π4² = 50.27

Area of shaded region = Acircle - Ahexagon = 50.27 - 41.57 = 8.7

The parent function related t the function provided which is y = x² + 4 would be

O P(x) = x²

In mathematics, transformation refers to the process of changing the position, size, or shape of a geometric figure.

Transformations can be performed using a set of rules that define how the figure should be modified or moved.

The transformation in the given situation is a translation of the function 4 units in the upward direction. this results to the equation y = x² + 4.

The graph for y = x² + 4 is a curve but the movement made by the curve is a linear movement which is termed translation

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