square root 7 squared

Answer:

Step-by-step explanation: The speed of reaction to differences between forecasts and actual results. is the answer i think

Answer:

there isnt m and n are right next to eachother in the alphabet

Step-by-step explanation:

Answer:

=1

yes because if you switch the x and y and solve youd get the other equation

Step-by-step explanation:

Answer:

f(1/3x+2)

Step-by-step explanation:

Answer:

i think d

Step-by-step explanation:

Answer:

y=5/3x

Step-by-step explanation:

Hope this Helps!

If not I am sorry.

\(2^{10}.2^8.2^6.2^4.2^2.2^{-1}.2^{-3}.2^{-5}.2^{-7}.2^{-9}\) = 32

We need to compute \(\bold{2^{10}.2^8.2^6.2^4.2^2.2^{-1}.2^{-3}.2^{-5}.2^{-7}.2^{-9}}\) .

This is the product of exponential numbers with same bases.

We use rules of exponents:

Using the first rule we can rewrite

\(2^{10}.2^8.2^6.2^4.2^2.2^{-1}.2^{-3}.2^{-5}.2^{-7}.2^{-9}\)

as,

\(2^{10+8+6+4+2}.2^{-1-3-5-7-9} = 2^{10+8+6+4+2}.2^{-(1+3+5+7+9)}\)

Using the second rule,

\(2^{10+8+6+4+2}.2^{-(1+3+5+7+9)} = \frac{2^{10+8+6+4+2}}{2^{1+3+5+7+9} }\)

                                            \(=\frac{2^{30}}{2^{25}}\)

                                            \(\bold{= 2^5 = 32}\)                        

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Step-by-step explanation:

So what type of maths help do you want

lim x→5+ (x + 1)/(x - 5)

= lim x→5+ [(x - 5) + 6]/(x - 5)

= lim x→5+ [(x - 5)/(x - 5)] + (6/(x - 5))

= 1 + ∞

= ∞

Therefore, the infinite limit of lim x→5+ (x + 1)/(x - 5) is ∞.

lim x→1 (2 - x)/(x - 1)²

= lim x→1 -(x - 2)/(x - 1)²

= lim x→1 -1/[(x - 1)/(x - 2)]²

= -∞

Therefore, the infinite limit of lim x→1 (2 - x)/(x - 1)² is -∞.

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The probability of the horse winning the race is 11/13, which is approximately 0.846 or 84.6%

To find the probability of the horse winning the race, we need to use the odds against the horse. The odds against the horse winning are given as 2:11, which means that for every 2 chances the horse loses, it wins 11 times.
We can find the probability of the horse winning by dividing the number of times it wins by the total number of outcomes. In this case, the total number of outcomes is the sum of the chances of winning and losing, which is 2+11 = 13.
So, the probability of the horse winning the race is 11/13. This can be simplified by dividing the numerator and denominator by their greatest common factor, which is 1. Therefore, the probability of the horse winning the race is 11/13.
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In this case the answer is very simple.

We must analyze all the statements to find the correct one.

Therefore, the correct statement would be:

c. All rectangles are quadrilaterals.

That is the solution.

The chance that the hospital will run out of sleeping pills on any given day is 0.5000 (or 0.5000 with four decimal places).

To calculate the chance that the hospital will run out of sleeping pills on any given day, we can use the normal distribution and Z-score.

First, let's calculate the Z-score using the formula:

Z = (X - μ) / σ

Where:

X = consumption rate per day (1,155 pills)

μ = average consumption rate per day (1,155 pills)

σ = standard deviation (81 pills)

Z = (1,155 - 1,155) / 81

Z = 0

Now, we need to find the probability associated with this Z-score. However, since the demand for sleeping pills can be considered continuous and not discrete, we need to calculate the area under the curve from negative infinity up to the Z-score. This represents the probability of not running out of sleeping pills.

We discover that the region to the left of a Z-score of 0 is 0.5000 using a basic normal distribution table or statistical software.

To find the probability of running out of sleeping pills, we subtract this probability from 1:

Probability of running out of sleeping pills = 1 - 0.5000

Probability of running out of sleeping pills = 0.5000

Therefore, on any given day, the hospital has a 0.5000 (or 0.5000 with four decimal places) chance of running out of sleeping tablets.

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Given that f(x)=-x^2+6x-1

f(1) = - 1^2 + 6(1) - 1

= -1 + 6 -1

= 4

f(3) = -3^2 + 6(3) - 1

= -9 + 18 -1

= 8

Hence

a. f(1) + f(3) = 4 + 8

= 12

b. f(1) - f(3) = 4 - 8

= -4

The answer is all real numbers for x

because simplifying, you get both sides are equal

Answer:

0.24 to 2dp

Step-by-step explanation:

The equation of the path of the parabola is y = a(x - 13)² + 27

Given data ,

To represent the path of Al's toss, we can assume that the path is a parabolic trajectory.

The equation of a parabola in vertex form is given by:

y = a(x - h)² + k

where (h, k) represents the vertex of the parabola

Now , the balloon was released from the 10-yard line and landed at the 16-yard line, we can determine the x-values for the vertex of the parabola.

The x-coordinate of the vertex is the average of the two x-values (10 and 16) where the balloon was released and landed:

h = (10 + 16) / 2 = 13

Since the height of the balloon reached 27 yards, we have the vertex point (13, 27)

Now, let's substitute the vertex coordinates (h, k) into the general equation:

y = a(x - 13)² + k

Substituting the vertex coordinates (13, 27)

y = a(x - 13)² + 27

To determine the value of 'a', we need another point on the parabolic path. Let's assume that the highest point reached by the balloon is the vertex (13, 27).

This means that the highest point (13, 27) lies on the parabola

Substituting the vertex coordinates (13, 27) into the equation

27 = a(13 - 13)² + 27

27 = a(0) + 27

27 = 27

Hence , the equation representing the path of Al's toss is y = a(x - 13)² + 27, where 'a' can be any real number

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The solutions to the equation are x = -1, x = -8, and x = 1/2.

The equation 4x³ + 32x² + 42x - 16 = 0 can be divided throuh by 2 as follows:

2x³ + 16x² + 21x - 8 = 0

We can test each of these possible roots by substituting them into the equation and seeing if we get 0. When we substitute -1, we get 0, so -1 is a root of the equation. We can then factor out (x + 1) from the equation to get:

(x + 1)(2x² + 15x - 8) = 0

We can then factor the quadratic 2x² + 15x - 8 by grouping to get:

(x + 8)(2x - 1) = 0

This gives us two more roots, x = -8 and x = 1/2.

Therefore, the solutions to the equation are x = -1, x = -8, and x = 1/2.

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Using the simplex method, the optimal solution for the given linear program is z = 14, with x1 = 0 and x2 = 5. There are no alternative optimal solutions.

To solve the linear program using the simplex method, we start by converting the problem into standard form with all constraints in the form of inequalities and non-negative variables. The initial tableau for the problem is as follows:

 |   x1  |   x2  |   s1   |   s2   |   b   |

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

z |  -3   |   6   |   0    |   0    |   0   |

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

s1|   5   |   7   |   1    |   0    |   35  |

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

s2|  -1   |   2   |   0    |   1    |   2   |

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

Next, we perform the simplex iterations to improve the objective function value. After performing the necessary row operations, we arrive at the final tableau:

 |   x1  |   x2  |   s1   |   s2   |   b   |

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

z |   0   |   1   |  3/2   |  -1/2  |   14  |

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

s1|   0   |   0   |   4    |   3    |   5   |

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

s2|   1   |   0   |  -1/2  |   5/2  |   3   |

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

From the final tableau, we can see that the optimal solution is z = 14, with x1 = 0 and x2 = 5. The decision variable x1 is at its lower bound, indicating that it is non-basic. Therefore, there are no alternative optimal solutions in this case.

In summary, the optimal solution for the given linear program is z = 14, with x1 = 0 and x2 = 5. There are no alternative optimal solutions.

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Answer:

Step-by-step explanation:

so use the properties of powers, recall that powers like \(x^{2^{2} }\) is the same as \(x^{2} *x^{2}\) which can also be written as  \(x^{2*2}\) = \(x^{4}\).

I want to make this clearer.

\(x^{3^{3} }\) = \(x^{3}\)  * \(x^{3}\) * \(x^{3}\)  = \(x^{3*3*3}\) =\(x^{27}\)

I'm not sure if that's making it clearer or not.

so for your question  of  \((8x^{6}) ^{2/3}\)  we can rewrite it to look like the above multiplication of powers

\(8x^{6*(2/3)}\)

\(\frac{6}{1}\) * \(\frac{2}{3}\) = \(\frac{12}{3}\)  = 4

\(8x^{4}\)

The first step in simplifying is to apply that outer exponent of \(\frac{2}{3}\) to each factor inside the parentheses.

      \(\left(8\cdot x^6\right)^{2/3} = \left(8\right)^{2/3} \cdot \left(x^6\right)^{2/3}\)

Now using the concept that \((a)^{m/n} = \sqrt[m]{a^n}\) for positive real numbers a and integers m and n, we can evaluate the first part:

       \((8)^{2/3} = \sqrt[3]{8^2} = \sqrt[3]{64} =4\)

For the second part, we use the power-to-a-power rule, that says \((a^m)^n = a^{m\cdot n}\):

    \(\left(x^6\right)^{2/3} = x^{6\cdot \frac{2}{3}} = x^4\)

Putting that all together, we have

    \(\left(8 x^6\right)^{2/3} = \left(8\right)^{2/3} \cdot \left(x^6\right)^{2/3} = 4x^4\)

The first four nonzero terms of the Taylor series for f(x) centered at a = 2 are: 3, (x-2), 0, 0.

To find the first four nonzero terms of the Taylor series for f(x) centered at a = 2, we can use the definition of the Taylor series expansion:

f(x) = f(a) + f'(a)(x-a)/1! + f''(a)(x-a)^2/2! + f'''(a)(x-a)^3/3! + ...

First, let's find the values of f(a), f'(a), f''(a), and f'''(a) at a = 2:

f(2) = 1 + 2 = 3

f'(2) = 1

f''(2) = 0

f'''(2) = 0

Now, we can substitute these values into the Taylor series expansion:

f(x) = 3 + 1(x-2)/1! + 0(x-2)^2/2! + 0(x-2)^3/3!

Simplifying, we get:

f(x) = 3 + (x-2) + 0 + 0

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Answer:

Below

Step-by-step explanation:

Losing 27 % of value each year means it retains 73% each year

  we need to multiply 20 000 x  .73 x .73 x .73     ....  .73     (twelve times )

                  or   re-written as   20 000 * .73^12 = value =$ 458.04

The equation of the sphere passing through P(1,2,3) and Q(4,5,6) with its center at the midpoint of PQ is (x - 7/2)^2 + (y - 7/2)^2 + (z - 9/2)^2 = 27/2.

Given points are p(1,2,3) and q(4,5,6). We need to find the equation of the sphere passing through these points with its center at the midpoint of PQ. The midpoint of PQ is (x, y, z). We know that the center of the sphere lies at the midpoint of PQ.

So, we have:(1+x)/2 = 4-x/2 ...(i)

(since midpoint of PQ is (x,y,z), and P is (1,2,3) and Q is (4,5,6))

Substitute in eqn (i)

=> 1+x = 8 - x

=> x = 7/2

Similarly, we get:

y = 7/2

z = 9/2

Hence, the center of the sphere is C(7/2, 7/2, 9/2).

We know that the general equation of a sphere is given by

(x - h)^2 + (y - k)^2 + (z - l)^2 = r^2

where (h, k, l) is the center and r is the radius of the sphere. To find the radius, we use the distance formula. Let the radius be r.

Distance between P(1, 2, 3) and Q(4, 5, 6) is given by

√[(4 - 1)^2 + (5 - 2)^2 + (6 - 3)^2] = √27

Hence, the radius of the sphere is r = √27/2.

Let the equation of the sphere be (x - 7/2)^2 + (y - 7/2)^2 + (z - 9/2)^2 = 27/2. So, the equation of the sphere passing through P(1,2,3) and Q(4,5,6) with its center at the midpoint of PQ is

(x - 7/2)^2 + (y - 7/2)^2 + (z - 9/2)^2 = 27/2.

Conclusion: The equation of the sphere passing through P(1,2,3) and Q(4,5,6) with its center at the midpoint of PQ is (x - 7/2)^2 + (y - 7/2)^2 + (z - 9/2)^2 = 27/2.

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Given that a sphere passes through P (1, 2, 3) and Q (4, 5, 6) with its center at the midpoint of PQ.

We need to find the equation of the sphere.

Step 1:

Find the center of the sphere.

We know that the center of the sphere lies at the midpoint of PQ.

The midpoint of PQ = $\frac{(P + Q)}{2}$

Midpoint of PQ = $\frac{(1 + 4, 2 + 5, 3 + 6)}{2}$

Midpoint of PQ = $(\frac{5}{2}, \frac{7}{2}, \frac{9}{2})$

Therefore, the center of the sphere is $(\frac{5}{2}, \frac{7}{2}, \frac{9}{2})$.

Step 2:

Find the radius of the sphere

Let the radius of the sphere be r.

Distance between P and Q is given by $\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2 + (z_2 - z_1)^2}$= $\sqrt{(4 - 1)^2 + (5 - 2)^2 + (6 - 3)^2}$= $\sqrt{9 + 9 + 9}$= $\sqrt{27}$= $3\sqrt{3}$

The radius of the sphere = $\frac{PQ}{2}$= $\frac{3\sqrt{3}}{2}$

Step 3:

Write the equation of the sphere

The equation of a sphere with center $(x_0, y_0, z_0)$ and radius r is given by $$(x - x_0)^2 + (y - y_0)^2 + (z - z_0)^2 = r^2$$

Therefore, the equation of the sphere passing through P(1, 2, 3) and Q(4, 5, 6) with its center at the midpoint of PQ is $$(x - \frac{5}{2})^2 + (y - \frac{7}{2})^2 + (z - \frac{9}{2})^2 = (\frac{3\sqrt{3}}{2})^2$$$$(x - \frac{5}{2})^2 + (y - \frac{7}{2})^2 + (z - \frac{9}{2})^2 = \frac{27}{2}$$

Hence, the equation of the sphere is $$(x - \frac{5}{2})^2 + (y - \frac{7}{2})^2 + (z - \frac{9}{2})^2 = \frac{27}{2}$$.

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Step-by-step explanation:

look at the photo..............

The inverse of the function f(x) = (1/9)x - 2 is  f⁻¹(x) = 9x + 18.

To find the inverse of the function f(x), denoted as  f⁻¹(x), we need to interchange the roles of x and f(x) and solve for the new variable.

Given that f(x) = (1/9)x - 2, we can proceed as follows to find  f⁻¹(x):

Replace f(x) with y

y = (1/9)x - 2

Swap x and y

x = (1/9)y - 2

Solve for y

x + 2 = (1/9)y

9(x + 2) = y

y = 9x + 18

Therefore, the inverse of the function f(x) is  f⁻¹(x) = 9x + 18.

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--The given question is incomplete, the complete question is given below " If f (x) = one-ninth x minus 2, what is f⁻¹(x)"--

Answer:

its 3.5

Step-by-step explanation:

since we need to replace x with 6 the equation is now 3(6) + 8y = -10.

next i would multiply  3&6 to 18 then subtract 8y to the other side like this

18 + 8y = -10

     - 8y         -8y

18= -10 -8y

then i would add -10 to 18 on that side

18= -10 -8y

+10   +10    

28 = 8y

then i divided

3.5 is my answer

There were 11679 applicants this year. We can now find the number of applicants this year as follows:Number of applicants this year = Number of applicants last year + Additional applicants= 11450 + 229= 11679

The given data can be represented in the following table:Number of applicantsLast Year11450This yearIncreased by 2%Let the number of applicants this year be xTherefore, the number of applicants this year will be the sum of the previous year's number of applicants and the percentage increase in the number of applicants.Number of applicants this year = (Number of applicants last year) + (Percentage increase in the number of applicants)Let's plug in the values:Number of applicants this year = 11450 + 2% of 11450Number of applicants this year = 11450 + (2/100) × 11450Number of applicants this year = 11450 + 229Number of applicants this year = 11679Therefore, there were 11679 applicants this year.

We are given that the number of applicants to a university last year was 11450. This year, the number of applicants grew by 2%. We are required to find the number of applicants this year.Let the number of applicants this year be x.We know that the percentage increase in the number of applicants is 2%. Therefore, the number of additional applicants is 2% of the number of applicants last year. We can calculate the number of additional applicants as follows:Additional applicants = 2% of the number of applicants last year= (2/100) × 11450= 229We can now find the number of applicants this year as follows:Number of applicants this year = Number of applicants last year + Additional applicants= 11450 + 229= 11679Therefore, there were 11679 applicants this year.

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The triangular face consists of a right triangle, so the prism itself is half of a 10x3x4 box. Such a box would have a volume of (10 ft)•(3 ft)•(4 ft) = 120 ft³. So the prism has a volume of 60 ft³.

The expression that can be used to find the percent of change between the gym's membership in 2012 and the current membership is ((Current Value - Initial Value) / Initial Value) \(\times\) 100.

To find the percent of change between the gym's membership in 2012 and the current membership, we can use the following expression:

Percent of change = ((Current Value - Initial Value) / Initial Value) \(\times\) 100

In this case, the initial value is 9,300 (membership in 2012), and the current value is 2,800 (current membership).

Substituting these values into the expression, we get:

Percent of change = ((2,800 - 9,300) / 9,300) \(\times\)100

Simplifying the expression further, we have:

Percent of change = (-6,500 / 9,300) \(\times\) 100

Therefore, the expression that can be used to find the percent of change between the gym's membership in 2012 and the current membership is ((Current Value - Initial Value) / Initial Value) \(\times\)100. This formula calculates the relative difference between the initial and current values and expresses it as a percentage.

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The event for which the probability can be calculated from the two events given is event B.

Given that:

Mean = 2.5 children per family

Standard deviation = 1.3 children per family

Here, for event B, the sample size is going to take 40.

So, the distribution can be formulated to be approximately normal distribution since the sample size is 40 which is greater than 30.

So, the mean is the same which is 2.5.

The standard deviation can be calculated as 1.3/√40.

So, event B can be calculated for the probability.

Hence the event is event B.

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The complete question is given below:

The distribution of the number of children per family in the United States is strongly skewed right with a mean of 2.5 children per family and a standard deviation of 1.3 children per family.

Event A: Randomly selecting a family from the United States that has 3 or more children.

Event B: Randomly selecting 40 families from the United States and finding an average of 3 or more children.

The probability of one of the two events can be calculated even though the distribution of the population is strongly skewed right. For which event can the probability be calculated?

The journal entries to record each of these five transactions are illustrated below.

1) Debit Accounts Receivable $2,965,700

  Credit Sales Revenue $2,965,700

2) Debit Sales Returns and Allowances $67,586

   Credit Accounts Receivable $67,586

3) Debit Cash $2,568,800

   Credit Accounts Receivable $2,568,800

4) Debit Allowance for Doubtful Accounts $42,560

   Credit Accounts Receivable $42,560

5) Debit Accounts Receivable $14,110

   Credit Allowance for Doubtful Accounts $14,110

In accounting, a journal entry is a formal record of a business transaction that shows the accounts affected and the amounts involved. In this case, we have five transactions related to accounts receivable for Carla Vista Co. Imports that need to be recorded using journal entries.

When a company sells goods on account, it records an increase in accounts receivable and an increase in revenue. In this case, the journal entry for the $2,965,700 in sales on account would be:

If a customer returns goods or receives an allowance, the company must reduce both its revenue and its accounts receivable. The journal entry for the $67,586 in sales returns and allowances would be:

When a company collects on its accounts receivable, it reduces the balance in its accounts receivable account and increases its cash balance. The journal entry for the $2,568,800 collected would be:

If a company determines that it is unlikely to collect on an accounts receivable balance, it may write it off as uncollectible. This reduces both its accounts receivable and its net income. The journal entry for the $42,560 write-off would be:

If a previously written-off accounts receivable is later collected, the company must reverse the write-off and record the collection as normal. The journal entry for the $14,110 recovery would be:

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