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Question 10

The value of f(2) is 40.5

The given function is f(x) = 1/x + 5[tex]x^3[/tex], and we need to find the value of f(2).

To do this, we substitute x=2 into the function and simplify:

f(2) = 1/2 + 5([tex]2^3[/tex])

= 1/2 + 5(8)

= 1/2 + 40

= 40.5

Therefore, the value of f(2) is 40.5.

The function f(x) has two parts: 1/x and 5[tex]x^3[/tex]. The first part of the function, 1/x, is a decreasing function that approaches zero as x gets larger. The second part of the function, 5[tex]x^3[/tex], is an increasing function that grows rapidly as x gets larger.

When we substitute x=2 in the function f(x), we get f(2) = 1/2 + 5([tex]2^3[/tex]) = 40.5. This means that at x=2, the value of the function is 40.5.

This result tells us that the function f(x) has a positive value at x=2. Moreover, since the second part of the function grows faster than the first part, the value of the function f(x) will increase as x gets larger. This means that as x increases, the value of f(x) will increase more and more rapidly.

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Answer: 30.6 km away

Step-by-step explanation:

The main thing this problem requires is Pythagoras' theorem. So set the problem up by marking the airport as (0,0) on a graph. Then move 19 units to the right, and 24 units down and make a point. Now you have the two short lengths of a right-angle triangle, so all that's left is to solve for the hypotenuse. So using the formula [tex]a^{2} + b^{2} = c^{2}[/tex] you would end up with [tex]19^{2} + 24^{2} =c^{2}[/tex]. Then you get: 361+576=[tex]c^{2}[/tex]

solve for c and you get about 30.6 km!

Hope this helps!

Answer:

Do you wish for the mistake to be pointed out? If so, can you please provide the dot plot so I can answer this question?

Step-by-step explanation:

The rule for this translation. and the coordinates of the image point are  (x, y) = (x + 4, y - 5); (7, -6)

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

translated to the right 4 units and down t units

Mathematically, this can be expressed as

(x, y) = (x + 4, y - 5)

Given that

A = (3, -1)

And, we have

(x, y) = (x + 4, y - 5)

This means that

A' = (3 + 4, -1 - 5)

Evaluate

A' = (7, -6)

So, the image point is A' = (7, -6)

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Question

ABC is translated 4 units to the right and 5 units down. Answer the questions to find the coordinates of A after the translation.

A = (3, –1)

The distribution of the weight of one dozen eggs is approximately normally distributed with a mean of 68 grams and a standard deviation of 4.2 grams.

The distribution of the weight of one dozen eggs is also approximately Normally distributed. The mean of the distribution is the same as the mean of the individual eggs, which is 68 grams.

The standard deviation of the distribution is the square root of the sum of the variances of the individual eggs and the sample size, which is:

= 2.2 * ✓12

= 4.2 grams.

Therefore, the distribution of the weight of one dozen eggs is approximately normally distributed with a mean of 68 grams and a standard deviation of 4.2 grams.

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398.223 redondeado a la decena más cercana es 400.

Redondear un número a la decena más cercana implica determinar a qué decena se acerca más. En este caso, estamos redondeando el número 398.223.

Para hacer esto, observamos el dígito en la posición de las decenas, que es el 9 en 398.223. El dígito a la derecha de la posición de las decenas es el lugar de las centésimas, que en este caso es 8.

Para redondear a la decena más cercana, seguimos la regla general de redondeo: si el dígito en el siguiente lugar de valor más bajo (en este caso, el lugar de las centésimas) es 5 o mayor, redondeamos hacia arriba el dígito en el lugar de valor objetivo (en este caso, las decenas). Si el dígito es menor que 5, redondeamos hacia abajo.

En nuestro caso, el dígito en el lugar de las centésimas (8) es mayor que 5, por lo que redondeamos hacia arriba el dígito en el lugar de las decenas (9) al número siguiente más alto. Por lo tanto, 398.223 redondeado a la decena más cercana se convierte en 400.

En resumen, redondear 398.223 a la decena más cercana nos da 400 porque el dígito en el siguiente lugar de valor más bajo (8) es mayor que 5.

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The solution is, simplification of the expression is; 71.19.

Here, we have,

the given expression is:

(5/2)^4/2 * (3/2)^6

=(5/2)^2 * (3/2)^6

as we know that, 4/2 = 2.

now, we have,

(5/2)^2 * (3/2)^6

=5²/2² ^ 3⁶/2⁶

= 5² * 3⁶ / 2² * 2⁶

=5² * 3⁶  / 2 ^ (2+6)

=5² * 3⁶  / 2 ^8

=25 * 729/ 256

=18225/ 256

=71.19

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Ans4863

Step-by-step explanation:

Hüseyin concluded: "I was able to map quadrilateral EFGH onto quadrilateral EJGK using a sequence of rigid transformations and dilations, so the figures are similar."  The error that he make is option A: Huseyn  used a vertical stretch, so the quadrilaterals aren't similar.

Hüseyin's transformations is one that keeps the EFGH's shape and proportions, so EJGK is similar to EFGH. Similar figures have congruent angles and proportional sides.

The error is seen when he uses vertical stretch, that is violating similarity condition of quadrilaterals EFGH and EJGK. A vertical stretch would alter the proportions of the sides and angles in quadrilateral EFGH, making it non-similar to that of  EJGK.

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Answer:

Let x be the amount invested at 9% and y be the amount invested at 6%

.According to the problem:

x + y = 11,335 ----(1) (the total amount  invested is $11,335)0.09x - 0.06y = 865.35 ----(2) (the interest earned from the amount invested at 9% exceeds the interest earned from the amount invested at 6% by $865.35)

We can use these two equations to solve for x and y.

Multiplying equation (1) by 0.06, we get

:0.06x + 0.06y = 680.10 ----(3)

Subtracting equation (3) from equation (2), we get:

0.03x = 185.25

x = 6,175

Substituting x = 6,175 into equation (1), we get:

y = 5,160

Therefore, $6,175 is invested at 9% and $5,160 is invested at 6%.

Step-by-step explanation:

Answer:3

Step-by-step explanation:

subtract 3 from 3 and repeat on the other side of the equal sign. So 6 minus 3 equals 3.

The value of the car 4 years after it was purchased is  $16,270.86.

Depreciation is when the value of an asset declines with the passage of time as a result of wear and tear.

The equation that would be used to determine the value of car with the passage of time would be an exponential equation.

Value of the car after t years = [tex]p(1 -r)^{\frac{t}{3}[/tex]

Where:

Value of the car after 4 years  = [tex]41,000(1 -0.5)^{\frac{4}{3}[/tex] = $16,270.86

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The reduced row echelon form of the matrix is:

[tex]\left[\begin{array}{ccc}-1144/259&\\-321/259\\25/74\end{array}\right][/tex]

Given the matrix below

[tex]\left[\begin{array}{ccc}7&-1&-3 |-63\\0&-6&-2 |-20\\0&1&1 | 6\end{array}\right][/tex]

Divide the first row by 7:

[tex]\left[\begin{array}{ccc}1&-1/7&-3/7 |-9\\0&-6&-2 |-20\\0&1&1 | 6\end{array}\right][/tex]

Add 1/7 times the first row to the second row:

[tex]\left[\begin{array}{ccc}1&-1/7&-3/7 |-9\\0&-37/7&-17/7 |-107/7\\0&1&1 | 6\end{array}\right][/tex]

Add 3/7 times the second row to the first row:

[tex]\left[\begin{array}{ccc}1&0&-16/37 |-296/37\\0&-37/7&-17/7 |-107/7\\0&1&1 | 6\end{array}\right][/tex]

Add 17/37 times the second row to the third row:

[tex]\left[\begin{array}{ccc}1&0&-16/37 |-296/37\\0&-37/7&-17/7 |-107/7\\0&0&20/37 | 25/37\end{array}\right][/tex]

Multiply the third row by 37/20:

[tex]\left[\begin{array}{ccc}1&0&-16/37 |-296/37\\0&-37/7&-17/7 |-107/7\\0&0&1 | 25/74\end{array}\right][/tex]

Add 3/7 times the third row to the second row:

[tex]\left[\begin{array}{ccc}1&0&-16/37 |-296/37\\0&-37/7&0 |-321/259\\0&0&1 | 25/74\end{array}\right][/tex]

Add 16/37 times the third row to the first row:

[tex]\left[\begin{array}{ccc}1&0&0 |-1144/259\\0&-37/7&0 |-321/259\\0&0&1 | 25/74\end{array}\right][/tex]

Multiply the second row by -7/37:

[tex]\left[\begin{array}{ccc}1&0&0 |-1144/259\\0&1&0 |321/259\\0&0&1 | 25/74\end{array}\right][/tex]

This is the reduced row echelon form of the given matrix.

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The ordered pairs representing the amount of money left after playing variable number of games is :

(Number of games played, Amount of money left)

(0, 8)

(1, 6)

(2, 4)

(3, 2)

(4, 0)

Ordered pairs gives a tabular description of data as the values of two or more variables change.

Here, the amount Gabe has before playing a game is $8 and the cost per game is $2 .

Hence, the amount he has left decreases by $2 for every increase in number of games played.

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Answer: the awnser is b

Step-by-step explanation:

The illustration of p - q and p + (-q) using a number line is added as an attachment

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

p - q

Also, we have

p + (-q)

The above expressions mean that

To add two numbers (positive and negative), we can start from a point p, and then count backwards on the number line in q terms

Using the above as a guide, we have the following:

The illustration using a number line is added as an attachment

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Jodi will need 10 half-cup measurements of flour to make 2 batches of cookies.

To double the recipe, Jodi needs to multiply the amounts of each ingredient by 2.

The original recipe calls for 2½ cups of flour. Doubling this amount gives:

2½ cups * 2 = 5 cups of flour

We may divide the total amount of flour required (5 cups) by the quantity in each 12-cup measurement to get the number of 1-1/2 cups Jodi needs.

5 cups / ½ cup = 10

Therefore, Jodi will need 10 half-cup measurements of flour to make 2 batches of cookies.

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Answer:

The correct answer is b) f^-1(n)= 4/-n-1 +1.

b

Step-by-step explanation:

I think parentheses are missing :

y = -4/(n-1)  - 1       switch n and y   then solve for y

n = -4/(y-1) - 1         add 1 to both sides of the equation

n+1 = - 4/(y-1)         multiply through by y -1

(y-1)(n+1) = - 4         divide through by (n+1)

y -1   = - 4/ (n+1)      add 1 to both sides

y = - 4/ (n+1 )  + 1     <=====this is the inverse function  y = -4/(n-1) -1

   equivalent to   4 / (-1-n)  + 1        by putting the ' - ' in the denominator

The minimum number of tickets the agent must sell to have a 95% chance of selling at least one prize-winning ticket is 368 tickets

To unravel this issue, we are able to utilize the concept of likelihood. Let's begin with discovering the likelihood of not offering any prize-winning tickets with one ticket:

- The likelihood of not winning with one ticket is 499/500 (since there's as it were one winning ticket out of 500).

- The likelihood of not winning with n tickets is (499/500)[tex]^n[/tex](since the probabilities are autonomous and we duplicate them together).

Presently, we need to discover the least number of tickets the specialist must offer to have a 95% chance of offering at the slightest one prize-winning ticket. In other words, we need to discover the least esteem of n such that:

- The likelihood of not winning with n tickets is less than or rises to 5% (or 0.05).

- This can be identical to (499/500)[tex]^n[/tex]≤ 0.05.

We will illuminate for n utilizing logarithms:

- Take the normal logarithm of both sides:

ln[(499/500)[tex]^n[/tex]] ≤ ln(0.05).

- Utilize the logarithmic property of types to bring down the example:

n ln(499/500) ≤ ln(0.05).

- Fathom for n by partitioning both sides by ln(499/500) and taking the ceiling work (since n must be an entire number):

n = ceil[tex][ln(0.05) / ln(499/500)].[/tex]

Employing a calculator, we get 

n = ceil[tex][ln(0.05) / ln(499/500)][/tex]≈ 368

In this manner, the specialist must offer at the slightest 368 tickets to have a 95% chance of offering at the slightest one prize-winning ticket. 

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i) The capacities of different vessels which completely fill P vessel with exact number of fillings are:

(ii) The capacities of different vessels which completely fill Q vessel with exact number of fillings are:

One vessel of 18 I

Two vessels of 9 I each

Three vessels of 6 I each

Six vessels of 3 I each

Nine vessels of 2 I each

Eighteen vessels of 1 I each

(iii) The common capacities of vessels which completely fill P as well as Q vessels with exact number of fillings are:

Two vessels of 6 I each

Three vessels of 4 I each

Six vessels of 2 I each

Twelve vessels of 1 I each

(iv) The greatest capacity of vessel that completely fills P as well as Q vessels with exact number of fillings is 6 I.

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Answer:

Company policies help employees to carry out their daily operations. - Yes, part of internal control accounting.

Bank reconciliation needs to be prepared for verification. - Yes, part of internal control accounting.

The organization's financial data in the computer should be in password-protected files. - Yes, part of internal control accounting.

Step-by-step explanation:

To solve for f, we can rearrange the equation:

1975f = t1758 + Q2

First, we can isolate f by dividing both sides of the equation by 1975:

f = (t1758 + Q2) / 1975

So the final answer is:

f = (t1758 + Q2) / 1975

1. The balances for each type of investment at the end of the third year are:

2. The total gain from all of the investments combined is $4,150.39.

a. Treasury bond:

Balance = Principal * (1 + (interest rate/100))^time

Balance = $12,000.00 * (1 + (5.35%/100))³

Balance = $13,964.18

CD:

Balance = Principal * (1 + (interest rate/100))^time

Balance = $3,000.00 * (1 + (4.75%/100))³

Balance = $3,429.57

Stock plan:

Principal = 0.3 * $30,000.00 = $9,000.00

Year 1: Increase of 9%, so balance = $9,000.00 * (1 + (9%/100)) = $9,810.00

Year 2: Decrease of 5%, so balance = $9,810.00 * (1 - (5%/100)) = $9,319.50

Year 3: Increase of 7%, so balance = $9,319.50 * (1 + (7%/100)) = $9,973.02

Savings account:

Balance = Principal * (1 + (interest rate/100))^time

Balance = $6,000.00 * (1 + (3.90%/100))³

Balance = $6,783.62

b. Treasury bond: Gain = $13,964.18 - $12,000.00 = $1,964.18

CD: Gain = $3,429.57 - $3,000.00 = $429.57

Stock plan: Gain = $9,973.02 - $9,000.00 = $973.02

Savings account: Gain = $6,783.62 - $6,000.00 = $783.62

Total gain from all investments combined = $1,964.18 + $429.57 + $973.02 + $783.62 = $4,150.39

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You saved $30,000.00 and want to diversify your monies. You invest 40% in a Treasury bond for 3 years at 5.35% APR compounded annually. You

place 10% in a CD at 4.75% APR for 3 years compounded annually. 30% you invest in a stock plan and the remainder is in a savings account at

3.90% APR compounded annually. The stock plan increases 9% the first year, decreases in value by 5% the second year, and increases by 7% the

third year.

1. What are the balances for each type of investment at the end of the third year?

2. What is your total gain from all of the investments combined?

After considering all the given data we conclude that the measure of m∠E is 54.46° under the condition that ADEF is a right angled triangle.

We already know that ADEF is a right angled triangle having sides EF = 6 and FD = 4, we can apply the Pythagorean theorem to evaluate the length of the hypotenuse AD.
AD = √(6² + 4²)
= √52)
≈ 7.21
Now we can apply the sine function to find the measure of angle E.
sin(E) = opposite/hypotenuse = EF/AD
E = arcsin(EF/AD)
≈ 54.46°
Therefore,  m∠E  ≈ 54.46°.
The Pythagorean Theorem is considered a fundamental relation in the context of Euclidean geometry comparing the three sides of a right triangle.
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Answer:

[tex]573.9 \text{ in}^3[/tex]

Step-by-step explanation:

First, we can find the volume of the rectangular prism using the formula:

[tex]V_\square = l \cdot w \cdot d[/tex]

where [tex]l[/tex] is the prism's length, [tex]w[/tex] is its width, and [tex]d[/tex] is its depth.

Plugging the given dimensions into the formula:

[tex]V_\square = 8 \cdot 12 \cdot 6[/tex]

[tex]V _\square= 96 \cdot 6[/tex]

[tex]\boxed{V_\square = 576 \text{ in}^3}[/tex]

Next, we can find the volume of the half-sphere using the formula:

[tex]V_\circ = \dfrac{2}{3} \pi r^3[/tex]

where [tex]r[/tex] (or [tex]d/2[/tex]) is the half-sphere's radius.

Plugging the given diameter value into the formula:

[tex]V_\circ = \dfrac{2}{3} \pi (2/2)^3[/tex]

[tex]V_\circ = \dfrac{2}{3} \pi (1)^3[/tex]

[tex]\boxed{V_\circ=\dfrac{2}{3}\pi \text{ in}^3}[/tex]

Finally, we can find the volume of the composite figure by subtracting the volume of the half-sphere from the volume of the rectangular prism.

[tex]V = V_\square - V_\circ[/tex]

[tex]V = 576 \text{ in}^3 - \dfrac{2}{3}\pi \text{ in}^3[/tex]

We can evaluate this using a calculator.

[tex]\boxed{V\approx 573.9 \text{ in}^3}[/tex]

a) Approximately 778.7 grams of thorium 234 will be left after 0.5 years.

b) Approximately 2.1 years will have passed when 115 grams of thorium 234 are left.

(a) To find the amount of thorium 234 left after 0.5 years, we can use the equation:

[tex]A_t = A_0 e^{(-10.498t)}[/tex]

where A₀ is the initial amount, which is 1000 grams, t is the time in years, and At is the amount after t years.

Substituting t = 0.5, we get:

[tex]At = 1000 e^{(-10.498\times0.5)} = 778.7 \ grams[/tex]

Therefore, approximately 778.7 grams of thorium 234 will be left after 0.5 years.

(b) To find the time at which 115 grams of thorium 234 will be left, we can use the same equation and solve for t:

[tex]A_t = A_0 e^{(-10.498t)[/tex]

Dividing both sides by A₀ and taking the natural logarithm of both sides, we get:

ln(At/A₀) = -10.498t

Substituting At = 115 grams and A₀ = 1000 grams, we get:

ln(115/1000) = -10.498t

Solving for t, we get:

t = (ln(115/1000)) / (-10.498) ≈ 2.1 years

Therefore, approximately 2.1 years will have passed when 115 grams of thorium 234 are left.

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right isosceles triangle.

Right Scalene Triangle

Angles

Acute angle:  An angle whose measure is less than 90 degrees.

Right angle:  An angle whose measure IS 90 degrees.  As a consequence, the two rays that form the angle are perpendicular.

Obtuse angle:  An angle whose measure is greater than 90 degrees.

Triangles (defined by side lengths)

Equilateral Triangle:  A triangle with all three sides congruent (all three sides have the same length)

Isosceles Triangle:  A triangle that contains two congruent sides (two sides with the same length).

Scalene Triangle: A triangle with three different length sides.

Triangles (defined by angle measures)

Acute Triangle:  A triangle whose angles are all acute angles

Right Triangle:  A triangle that contains one right angle.

Obtuse Triangle:  A triangle that contains one obtuse angle.

By angle

Our triangle has an angle that appears to be a right angle (the two sides look perpendicular).  This would be a Right Triangle (when classified by angles).

By side length

All three sides of this triangle are different in length.  This would be a Scalene Triangle (when classified by side length).

Combining the attributes:

This is both a Right Triangle and a Scalene Triangle.  Together, it is a Right Scalene Triangle.

Right Isosceles

To be a Right Isosceles Triangle, the triangle needs to be both a Right Triangle, and an Isosceles Triangle.

A Right triangle contains one right angle, and an Isosceles Triangle contains a pair of sides that are the same length.

While this triangle does contain a right angle, all three sides appear to be different length (scalene).

This is not a Right Isosceles Triangle.

Acute Isosceles

To be an Acute Isosceles Triangle, the triangle needs to be both an Acute Triangle, and an Isosceles Triangle.

An Acute Triangle contains all angles that are acute angles (less than 90 degrees), and an Isosceles Triangle contains a pair of sides that are the same length.

However, this triangle contains a right angle (equal to 90 degrees, not less than), so it cannot be an Acute Triangle, and this triangle does not contain a pair of sides that are the same length, so it cannot be an Isosceles Triangle.

This is not an Acute Isosceles Triangle.

Acute Scalene

To be an Acute Scalene Triangle, the triangle needs to be both an Acute Triangle, and a Scalene Triangle.

An Acute Triangle contains all angles that are acute angles (less than 90 degrees), and a Scalene Triangle has sides that are all different length.

While this triangle does have sides that are all different length, it contains a right angle, whose measure IS 90 degrees (not less than 90 degrees).  So it cannot be an Acute Triangle

This is not an Acute Scalene Triangle.

The implications of Constructivist approach in teaching mathematics is that it helps the students to develop a better way to comprehend the content of what they are being taught.

A constructive approach of teaching mathematics believes that students construct knowledge rather than just passively take in information.

A constructive approach of teaching also believes that students integrate new knowledge with existing knowledge to create a deeper understanding of the mathematics being taught to them.

Therefore, constructive approach of teaching can help the students to comprehend the content of what they are being taught.

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The required probability that a student is taking calculus or French, rounded to two decimal places, is 0.40.

The probability that a student is taking calculus or French is calculated by adding the number of students taking calculus and the number of students taking French and then subtracting the number of students taking both calculus and French. This gives us the number of students taking either calculus or French. We then divide this number by the total number of students, which is 100.

So, the number of students taking either calculus or French is 27 + 26 - 13 = 40.

The probability that a student is taking either calculus or French is 40 / 100 = 0.40 = 40%.

Therefore, the probability that a student is taking calculus or French, rounded to two decimal places, is 0.40.

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