melonie is 3 times older than her cousin their total of there ages are 36 how old is melonies cousin

The correct value of 2f(a-1) is 2a^2 - 12a + 10.

To find the value of 2f(a-1), we need to substitute (a-1) into the function f(x) and then multiply the result by 2.

Given: f(x) = x^2 - 4x

Substituting (a-1) into the function:

f(a-1) = (a-1)^2 - 4(a-1)

Expanding and simplifying:

f(a-1) = (a^2 - 2a + 1) - (4a - 4)

f(a-1) = a^2 - 2a + 1 - 4a + 4

f(a-1) = a^2 - 6a + 5

Now, we multiply the result by 2:

2f(a-1) = 2(a^2 - 6a + 5)

Expanding:

2f(a-1) = 2a^2 - 12a + 10

Therefore, the value of 2f(a-1) is 2a^2 - 12a + 10.

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We can be 95% confident that the true proportion of correct responses made by touch therapists is between 0.383 and 0.555.

What is the probability?

Probability is the study of the chances of occurrence of a result, which are obtained by the ratio between favorable cases and possible cases.

a. If the touch therapists made random guesses, the probability of guessing correctly would be 1/2 or 0.5. Therefore, we would expect the proportion of correct responses to be 0.5.

b. The best point estimate of the therapists' success rate is the sample proportion, which is the number of correct responses divided by the total number of trials:

sample proportion = number of correct responses / total number of trials

= 145/309

= 0.469

Therefore, the best point estimate of the therapists' success rate is 0.469 or 46.9%.

c. To construct a 95% confidence interval estimate of the proportion of correct responses made by touch therapists, we can use the formula:

confidence interval = sample proportion ± (critical value) × (standard error)

where the critical value depends on the desired confidence level and the degrees of freedom, and the standard error is a measure of the variability in the sample proportion.

For a 95% confidence interval with 308 degrees of freedom (309 trials minus 1), the critical value is 1.96. The standard error can be calculated as:

standard error = sqrt[(sample proportion) × (1 - sample proportion) / n]

= sqrt[(0.469) × (1 - 0.469) / 309]

= 0.044

Therefore, the 95% confidence interval estimate of the proportion of correct responses made by touch therapists is:

confidence interval = 0.469 ± (1.96) × (0.044)

= (0.383, 0.555)

We can be 95% confident that the true proportion of correct responses made by touch therapists is between 0.383 and 0.555.

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Answer:

10.1

Step-by-step explanation:

I just put in a calculator and got the answer.

Answer:

a

Step-by-step explanation:

Answer:

Step-byHow do I calculate the mean?

The mean can be calculated only for numeric variables, no matter if they are discrete or continuous. It's obtained by simply dividing the sum of all values in a data set by the number of value

-step explanation:

46+57+66+63+49+52+61+68= 462/8 the total number of observation

the answer 57

The amount of money in Marianna's annuity after 6 years will be approximately $300,516.

To calculate the amount of money in Marianna's annuity after 6 years, we can use the formula for compound interest on an annuity:

A = P * ((1 + r/n)^(n*t) - 1) / (r/n)

Where:

A = the final amount in the annuity

P = the regular contribution (each quarter) = $10,000

r = annual interest rate = 8% = 0.08

n = number of compounding periods per year = 4 (since it's compounded quarterly)

t = number of years = 6

Plugging in the values:

A = 10000 * ((1 + 0.08/4)^(4*6) - 1) / (0.08/4)

Calculating this expression:

A ≈ 10000 * ((1.02)^24 - 1) / 0.02

A ≈ 10000 * (1.601032449136241 - 1) / 0.02

A ≈ 10000 * 0.601032449136241 / 0.02

A ≈ 10000 * 30.05162245681205

A ≈ 300,516.22

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Answer:

304200

Step-by-step explanation:

To find the value of P6, use the savings annuity formula

PN=d((1+r/k)N k−1)r/k.

From the question, we know that r=0.08, d=$10,000, k=4 compounding periods per year, and N=6 years. Substitute these values into the formula gives

P6=$10,000 ((1+0.08/4)6⋅4−1)/(0.08/4).

Simplifying further gives P6=$10,000 ((1.02)24−1)/(0.02) and thus P6=$304,218.62.

Rounding as requested, our answer is 304200.

Yes, the range of a elementary matrix is the same as its column space, but there is one subtlety.

what is elementary matrix?

A matrix is a collection of numbers arranged in rows and columns. The dimensions of a matrix are defined as the sum of the number of rows and columns, where m and n are the number of rows and columns, respectively.

explanation:

The short answer is, yes, the range of a matrix is the same as its column space, but there is one subtlety.

Given some number  m , we can view this number either as a constant, or as a means to define a linear function,  f(x)=mx . In a similar vein, we can view a matrix  M  either as an array of numbers (boring), or as a means to defines a linear function  f(x)=Mx .

The term range refers to the set of outputs that  f()  can return, and is typically defined as a property of functions, not numbers.

The column space, on the other hand, is typically defined as a property of the matrix itself. And since the column space is the set of all possible linear combinations (aka span) of the columns of  M , this can be written as  {Mx|x∈R} , which is the very range of  f  above.

Hence,  the range of a elementary matrix is the same as its column space, but there is one subtlety.

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Answer:

B (39)

Step-by-step explanation:

Multiply the Number of Packs of Dog Food by 39.

3 x 39 = 117

4 x 39 = 156

5 x 39 = 195

Solution :

Given :

Sample mean, \($\overline x = 714.2$\)

Sample size, n = 40

Standard deviation, s = 83.2

∴ The null hypothesis is \($H_0 : \mu = 703.5$\)

   Alternate hypothesis is \($H_a : \mu > 703.5$\)

Test statistic :

\($z = \frac{\overline x - \mu}{s / \sqrt n}$\)

\($z = \frac{714.2-703.5}{83.2 / \sqrt {40}}$\)

z = 0.813

Now at α = 0.05, for a right tailed,

\($z_{critical} = 1.645$\)

Since, \($z < z_{critical}$\) , we fail to reject the null hypothesis.

Answer:600?

Step-by-step explanation:

The graph of the feasible region is attached

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

\(\left\{ \begin{array}{lr} y + 7x \ge 10 \\ 8y + 2x \ge 20 \\ y + x \ge 4 \\ y + x\le 10 \\ x \ge 0 \\ y \ge 0\end{array}\)

To plot the graph of the feasible region, we plot each inequality in the domain x ≥ 0 and y ≥ 0

Using the above as a guide, the graph is attached

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Answer:

fluid ounces

Step-by-step explanation:

A fluid ounce is a unit of volume typically used for measuring liquids. Various definitions have been used throughout history, but only two are still in common use: the British Imperial and the United States customary fluid ounce.

Answer:*

Step-by-step explanation:

Let's represent the number with the variable "x". According to the given property, we can write the following equation:

3(x + 4) < 7x

Now, let's solve this inequality to find the range of numbers that satisfy the property.

3x + 12 < 7x

Subtract 3x from both sides:

12 < 4x

Divide both sides by 4 (since the coefficient of x is 4):

3 < x

So, the range of numbers that satisfy the given property is x > 3.

Therefore, any number greater than 3 will satisfy the condition. For example, 4, 5, 6, 7, 8, etc.Step-by-step explanation:

Step-by-step explanation:

\(1) \: \: 2x - 2y + z = 3 \\ 2x = 3 + 2y - z \\ x = \frac{3 + 2y - z}{2} \\ \\ 2) \: \: \: not \: any \: \: \: x \: \: \: available \: \: \\ \\ 3) \: \: x + 3y + 2z = - 21 \\ x = - 21 - 3y - 2z\)

Answer:

x= -5

Step-by-step explanation:

5y-z= -31, add z and 31 to both sides

5y+31 = z, substitute z in the other two given equations

2x - 2y+z=3

2x-2y +5y+31 = 3, combine like terms and subtract 31 from both sides

2x+3y = -28

x+ 3y + 2z = -21

x+3y +2(5y+31) = -21, distribute 2 over the addition parenthesis

x+3y +10y+62 = -21, combine like terms and subtract 62 from both sides

x+13y = -83

Now we have 2 equations  with 2 variables x and y to solve

2x+3y = -28

x+13y = -83

Because we need to find x then from the first equation we can write that

3y = -2x-28, subtract 2x from both sides and the divide both sides by 3

y = (-2x-28)/3, substitute this in the second equation

x + [13(-2x-28)/3] = -83 , distribute 13 . over the subtraction parenthesis

(3x/3)+[(-26x - 364) /3= -83, find the common denominator

3x+[(-26x - 364) = -83*3 , cross multiply

3x -26x = -249 +364, add 364 to both sides

- 23x = 115, divide both sides by (-23)

x= -5

The value of x from the diagram is 18degrees

An angle is a line where two or more lines meet.

The magnitude of two lines is known to be parallel if they have the same magnitude.

From the diagram shown, we can see that line BC is parallel to line ED

This shows that the following are true:

If the two angles are supplementary, then:

8x + 2x  = 180

10x = 180

x = 180/10

x = 18 degrees

Hence the value of x is 18degrees

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The angle relationships formed in the diagram are as follows;

When parallel lines are cut by a transversal, angle relationships can be formed such as corresponding angles, alternate interior angles, alternate exterior angles, vertically opposite angles, linear angles, etc.

Therefore, let's find the angles relationship formed in the diagram as follows:

∠1 and ∠5 are corresponding angles.

∠4 and ∠7 are corresponding angles

Corresponding angles are the angles which are formed in matching corners or corresponding corners with the transversal when two parallel lines are intersected by any other line.

∠3 and ∠5 are alternate interior angles.

Alternate interior angles are the angles formed when a transversal intersects two coplanar lines.

∠1 and ∠8 are alternate exterior angles.

∠2 and ∠7 are alternate exterior angles.

Alternate exterior angles are the pair of angles that are formed on the outer side of the parallel lines but on the opposite side of the transversal.

∠3 and ∠6 are same interior angles. Same interior angles are supplementary angles.

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Answer:

Step-by-step explanation:

To create a magic square with -6,-5,-4,-3,-2,-1,1,2, we need to arrange these numbers in a 3x3 grid such that each row, column, and diagonal add up to the same sum.

Here's one possible solution:

diff

Copy code

-6 1 2

-4 -5 9

8 -3 -2

To check if this is a magic square, we can calculate the sum of each row, column, and diagonal:

Rows:

(-6 + 1 + 2) = -3

(-4 - 5 + 9) = 0

(8 - 3 - 2) = 3

Columns:

(-6 - 4 + 8) = -2

(1 - 5 - 3) = -7

(2 + 9 - 2) = 9

Diagonals:

(-6 - 5 - 2) = -13

(2 - 5 + 8) = 5

All of these sums are equal to 0, so this is indeed a magic square.

If c is the number of cookies that Josh bought and he ate 4 of them, then we would have to substract 4 from c, and the algebraic expression is:

Answer:

The statements that can be used to compare the characteristics of the functions are:

1. g(x) has the greatest maximum value.

2. All three functions share the same domain.

Explanation:

- The table shows the values of three functions - f(x), g(x), and h(x) - evaluated at different values of x.

- We cannot determine the domain of f(x) or h(x) from the given table but we can see that g(x) has a domain of all real numbers.

- We can see that g(x) has the highest maximum value among the three functions, which is 8.

- We cannot determine the range of f(x) or g(x) from the given table but we can see that h(x) has a range of all negative numbers.

- We cannot say anything about the domain or range of f(x) based on the given table.

- Therefore, the two statements that can be used to compare the characteristics of the functions are: g(x) has the greatest maximum value and all three functions share the same domain.

Answer:

2.16 cm

Step-by-step explanation:

5 through 11 = 6 hours

total of cms  = 13

13/6 = 2.16

Answer:

Answer is 6600.

Step-by-step explanation:

I hope it's helpful!

The value of 575 is greater than 500 thus the nearest thousand of 6575 will be 7000.

To round up or down tens place then we need to look at the unit place if it is less than 5 then we need to keep it as it and if it is greater than 5 then we need to round up the tens digit.

To round a thousand, we need to look at one hundred places if it is less than 500 we will keep the same, and if it is 500 or greater to it we will round up.

As per the given 6575 here 575 > 500

6575 → 7000

Hence"The value of 575 is greater than 500 thus the nearest thousand of 6575 will be 7000".

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The balance sheet attached shows the Total Assets to be $55.968M  and Total Liabilities and Capital to be $252M respectively.

1. Assets:

  a. Cash in Reserves:

The required reserves are 5.4% of checkable deposits.

Therefore, the required reserves amount to 5.4% of $92 million, which is:

(0.054 * $92 million) = $4.968 million.

This amount is considered a liability for the bank, but it is held as an asset in the form of cash reserves.

  b. Loans: The bank made a $28 million commercial loan and a $23 million mortgage loan. Therefore, the total loans amount to:

total loan =  $28 million + $23 million

                 = $51 million.

2. Liabilities:

  a. Checkable Deposits:

The bank received $92 million in checkable deposits.

  b. Required Reserves:

As mentioned above, the required reserves amount to $4.968 million.

3. Capital:

  The bank started with $155 million in capital.

Based on the above information, the bank's balance sheet would look as attached.

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9514 1404 393

Answer:

  290 ft

Step-by-step explanation:

The relevant trig relation is ...

  Sin = Opposite/Hypotenuse

  sin(65°) = d/(320 ft)

  d = (320 ft)sin(65°) ≈ 290 ft

The object is about 290 feet deep.

Answer:

\(\dfrac{17}{72}\)

Step-by-step explanation:

From the given information:

Total number of students, \(n(U)=72\)

The choices were: Chess(C), Swimming(S), and Football(F).

Everyone liked at least one sport except 7 kids, \(n( C \cup F \cup S)'=7\)

Chess is not an active sport; and

10 children liked Chess only, \(n( C \cap F' \cap S')=10\)

The probability that a randomly-chosen child from this group does not like active kinds of sport is the Probability that a student plays chess only or like no kind of sport at all.

\(P( C \cup F \cup S)'+P(C \cap F' \cap S')=\dfrac{n( C \cup F \cup S)'+n(C \cap F' \cap S')}{n(U)} \\=\dfrac{10+7}{72} \\=\dfrac{17}{72}\)

The subsets of real numbers are known as:

Best of Luck!