simplify
[tex]\frac{3\sqrt{7}+6\sqrt{2} }{4\sqrt{2}+2\sqrt{7} }[/tex]

An example of how you can report your analysis in APA style is

A one-way ANOVA was conducted to compare the effects of three conditions (High, Moderate, and Low) on the dependent variable. The results showed no significant difference between the groups, F(2, 12) = 1.77, p = .212. Therefore, we fail to reject the null hypothesis, as the p-value is greater than the typical alpha level of .05.

To put out a good APA report, ensure you know the independent and dependent variable. The information provided in the picture did not explicitly state the variables that was being tested. For example, "A one-way ANOVA was conducted to compare the effects of stress levels (independent variable) on the academic performance (dependent variable).

Secondly, you should know the significant level that helps you judge whether or not to reject the hypothesis.

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The inequality 1 - 3x > 4( 2x - 6 ) is equivalent to x < 25 / 11

To solve the inequality 1 - 3x > 4( 2x - 6 ), we can start by simplifying the right-hand side:

4( 2x - 6 ) = 8x - 24

When we insert this into the original inequality, we get:

1 - 3x > 8x - 24

Adding 3x to both sides, we get:

1 > 11x - 24

Adding 24 to both sides, we get:

25 > 11x

Dividing both sides by 11, we get:

x < 25 / 11

Therefore, the inequality 1 - 3x > 4( 2x - 6 ) is equivalent to x < 25 / 11

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ACF is a 30º-60º-90º triangle because of the following:

1) Based on a theorem, in a 30°-60°-90° triangle the sides are in the ratio 1 : 2 : [tex]\sqrt{3}[/tex]

1 → short leg

2 → hypotenuse

[tex]\sqrt{3}[/tex] → long leg

Side length of the hexagon is the short leg of the triangle. It is 1.

r1 is the radius of the incircle in a regular hexagon. 2(r1) is the diameter of the incircle. It is also the hypotenuse of the right triangle. It is 2.

Using Pythagorean theorem.

[tex]a^2 + b^2 = c^2[/tex]

[tex]1^2 + b^2 = 2^2[/tex]

[tex]b^2 = 2^2 - 1^2[/tex]

[tex]b^2 = 4 - 1[/tex]

[tex]b^2 = 3[/tex]

[tex]\sqrt{b^2} = \sqrt{3}[/tex]

[tex]b = \sqrt{3}[/tex]

The scale factor from the drawing to the actual tower is 1 in : 5 ft

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

In his drawing, 2 in. represents 10 ft on the actual tower.

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

Scale factor = Drawing : Actual

Substitute the known values in the above equation, so, we have the following representation

Scale factor = 2 in : 10 ft

Divide

Scale factor = 1 in : 5 ft

Hence, the scale factor = 1 in : 5 ft

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The answer is (C) This is not a functional relationship.

A functional relationship is a relationship between two variables in which each input (independent variable) maps to exactly one output (dependent variable).

In other words, for every value of x, there is only one corresponding value of y that satisfies the equation.

Here we have

The equation x² + y² = 10  

The equation x²+ y² = 10 represents a circle with a center at the origin and a radius of √10.

Since a circle passes through multiple points with the same x-coordinate or y-coordinate, it cannot be represented as a function.

Hence, the relationship shown in the equation is not a functional relationship.

Therefore,

The answer is (C) This is not a functional relationship.

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Complete Question:

Which of the following best describes the relationship shown in the equation x² + y² = 10

A. It cannot be determined if this is or is not a functional relationship.

B. This is a functional relationship.

C. This is not a functional relationship.

Claude would have to rotate the wheel 54 times to complete a 100m unicycle race. And the unicycle moves 1.884 meters when the wheel turns once.

How to solve the question?

A) To determine how far the unicycle moves when the wheel turns once, we need to find the circumference of the wheel.

The formula for the circumference of a circle is:

C = πd

where C is the circumference, π (pi) is a mathematical constant equal to approximately 3.14, and d is the diameter of the circle.

So, in this case, the circumference of the unicycle wheel is:

C = πd = 3.14 x 60cm = 188.4cm

To convert centimeters to meters, we need to divide by 100:

188.4cm ÷ 100 = 1.884m

Therefore, the unicycle moves 1.884 meters when the wheel turns once.

B) To determine how many times the wheel must rotate to travel 100m, we need to divide the distance by the distance covered in one revolution of the wheel, which is the circumference.

Using the circumference we calculated above, we can divide the total distance by the distance covered in one revolution:

100m ÷ 1.884m/revolution ≈ 53 revolutions

Therefore, Claude must rotate the wheel approximately 53 times to travel 100m. Since he cannot rotate the wheel partially, we must round up the number of revolutions to the nearest whole number, which is 54.

In conclusion, Claude would have to rotate the wheel 54 times to complete a 100m unicycle race.

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Answer:

$21.00 / 3 hours = $7.00/hour

($7.00/hour)(10 hours) = $70.00

Answer:

if she probably earns $21.00 per hour.It may be 21.00×10 which is $210.thats my own answer

Answer:

48 + 12 is equivalent to 60.

The margin of error is 0.35

According to Amelia's results, 42% of students prefer coffee in the morning.

If the margin of error is ±0.072, between 689 and 978 students at the school prefer coffee.

How do we calculate for the percentage and margin of error?

To calculate percentages;

total coffee takers/ total number of students surveyed x 100.

TCT= 63  TSS = 150 which then becomes 63/150x 100 = 42

To calculate the margin of error;

TCT/TSS - ME  and TCT/TSS + ME, which becomes

63/150 + 0.072 = 0. 49

63/150 - 0.072 = 0.35

Next, we calculate the highest and lowest number by saying;

0.49 x total number of students in the school  1,981 =

0. 35 x total number of students in the school  1,981 =

The above answer is in response to the full question below;

There are a total of 1,981 students enrolled at Amelia's high school. Amella surveyed 150 of the students regarding their morning drink preference. Her results are recorded in the table.

Drinks                               number

Milk                                     45

Juice                                   18

Coffee                                 63

Smoothie                            11

Others                                 13

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Answer:

drop down 1: 42%

drop down 2: 689

drop down3 : 975

Step-by-step explanation:

Step-by-step explanation:

Each year the truck retains 85 % of its value   ( 85% + 15% = 100%)

45000 * .85 * .85 * .85 * .85   = $ 45 000 *  .85^4 = $ 23490.28

Answer:

The value of the truck would be $23,490.28 after 4 years.

Step-by-step explanation:

Main concepts:

Concept 1. Percentages

Concept 2. Depreciation

Concept 3. Distributive property

Concept 4. Repeated multiplication as a power

Concept 1. Percentages

A percentage is effectively a unit.  In the same way that 25¢ is the same as 0.25 US dollars, 15% is the same as 0.15 (unit-less number).

A common task is to find a percentage of a quantity.  For example, finding 25% of 40.  Mathematically, the word "of" here means multiply, so 25% of 40 means "25% * 40".  But, since a percentage can be converted to a regular unit-less number, this is also the same as "0.25 * 40" which is 10.  So, 25% of 40 is 10.

Concept 2. Depreciation

To depreciate means that the value of the thing decreases.  In this question, the value of the truck depreciates by 15% (per year), so its value would decrease by whatever 15% of its current value is.

15% of $45,000 is 0.15 * $45,000 = $6,750 (this is the amount that the value decreases by during the first year)

To find the value after 1 year, we need to subtract this from the original value.  We'll label this equation 1:

Common mistake: It is a common mistake for people to continue subtracting $6,750 for years 2, 3, and 4 thinking that this is subtracting another 15%.  However, each year, the 15% depreciation is based on the new value of the truck, so during the second year, the truck started at a value of $38,250 (from the end of the first year), and 15% of $38,250 will be different from 15% of $45,000.

15% of $38,250 is 0.15 * $38,250 = $5,737.50 (this is the amount that the value decreases by)

To find the value after 2 year, we need to subtract this from the value at the end of year 1.  We'll label this equation 2:

Concept 3. Distributive property

In Equation 1 above, the left side of the equation can be factored by using the distributive property in reverse, and factoring out "$45,000":

$45,000 - $6,750 is the same as

$45,000 * ( 1 - 0.15 ) = $38,250    -- Equation 1a

This expression illuminates what is happening to the value if we change the numbers inside the parentheses into percentages

$45,000 * ( 100% - 15% )

Notice that in the parentheses, we start with 100% (whatever 100% is), and we're subtracting 15%.

Similarly, in Equation 2, the left side of the equation can be factored by using the distributive property in reverse, and factoring out "$38,250":

$38,250 - $5,737.50 is the same as

$38,250 * ( 1 - 0.15 ) = $32,512.50   -- Equation 2a

Notice that in the parentheses, we again start with 100% (whatever 100% is), and we're subtracting 15%.

Concept 4. Repeated multiplication as a power

Quick recap from Equation 1a & Equation 2a:

For year 1, Equation 1a:  $45,000 * ( 1 - 0.15 ) = $38,250

For year 2, Equation 2a:  $38,250 * ( 1 - 0.15 ) =  $32,512.50

However, note the equivalence in bold above.  This means that we can replace the $38,250 in the "Year 2" equation with the entire left side of the equation from Year 1.

Thus, for Year 2, the equation become:

$45,000 * ( 1 - 0.15 ) * ( 1 - 0.15 ) =  $32,512.50

While the value at the end of year 3 could be written

$32,512.50 * ( 1 - 0.15 )

notice that the left side again starts with the value that ended the year before.  With another substitution, for Year 3, the equation becomes:

$45,000 * ( 1 - 0.15 ) * ( 1 - 0.15 ) * ( 1 - 0.15 ) =  Value at end of year 3

Continuing the pattern, we need the value at the end of the year before, times ( 1 - 0.15 ) to get the value for the end of the following year.  

$45,000 * ( 1 - 0.15 ) * ( 1 - 0.15 ) * ( 1 - 0.15 ) * ( 1 - 0.15 ) =  Value at end of year 4.

Notice that each year, we're multiplying by another factor of ( 1 - 0.15 )

Recall that multiplying by the same number or expression repeatedly can be simplified with an exponent.  For example, five 2s multiplied together: 2*2*2*2*2 can be written as [tex]2^5[/tex].  

Therefore, the value of the truck at the end of year 2 can be written as

[tex]\$45,000 * (1-0.15)^{2}[/tex]

The value of the truck at the end of year 3:  [tex]\$45,000 * (1-0.15)^{3}[/tex]

The value of the truck at the end of year 4:  [tex]\$45,000 * (1-0.15)^{4}[/tex]

Side note: the value of the truck at the end of any year "n" is [tex]\$45,000 * (1-0.15)^{n}[/tex]

So, to answer the question, and find the value of the truck in 4 years, we just need to evaluate [tex]\$45,000 * (1-0.15)^{4}[/tex]

[tex]\$45,000 * (1-0.15)^{4}=[/tex]

[tex]=\$45,000 * (0.85)^{4}[/tex]

[tex]=\$45,000 * 0.52200625[/tex]

[tex]=\$23,490.28125[/tex]

Rounded to the nearest penny, the value of the truck would be $23,490.28 after 4 years.

The total selling price of the 300 toys bought at a cost of $24 per unit with a mark up of 25% is $9,000.

The mark up refers to the percentage added on the cost of a retail item.

The mark up increases the cost price to determine the selling price.

The difference between the selling price and the cost price is the profit margin.

The number of toys bought by the store = 300

The unit purchase cost = $24

The total cost = $7,200 (300 x $24)

The mark up = 25%

The selling price for 300 = $9,000 ($7,200 x 1.25)

The selling price per unit = $30 ($9,000 ÷ 300)

Thus, after marking up the items by 25%, the total selling price is $9,000.

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Using the TI-83, 83+, 84, 84+ Calculator to calculate these probabilities

Go to 2nd DISTR, and select item 2: normalcdf

The syntax is: normalcdf (lower bound, upper bound, mean, standard deviation)

a) P(1100 <= X <= 1500)

     = normalcdf(1100, 1500, 1252, 129)

     = 0.8534

b) P(X < 1125)

   = normalcdf(-1E99, 1125, 1252, 129)

   = 0.1624

c) P(X > 1200)

   = normalcdf(1200, 1E99, 1252, 129)

  = 0.6566 = 65.66%

d) P(X < 1000)

   = normalcdf(-1E99, 1000, 1252, 129)

   = 0.0254 = approx 3rd percentile

Answer:

[tex] \sqrt{ \frac{196 {a}^{16} }{ {a}^{14} } } = \sqrt{196 {a}^{2} } = 14 |a| [/tex]

He would have $13,409 in the account after four years .

We have the information from the question:

Money saver's Bank offers a savings account that earns 8.5% interest compounded continuously.

And, Goran deposits is $2300.

Now, According to the question:

Principle of the amount is = $2300

Rate of Interest is = 8.5% continuously

Time period = 4 years

We have to apply the formula :
[tex]A = Pe^R^T[/tex]

[tex]A=2300e^8^.^5^(^4^)[/tex]

A = 2300 × 5.83

A = $13,409

Hence, He would have $13,409 in the account after four years .

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Answer:

  (C)  x = 1 1/3, y = 2 1/3

Step-by-step explanation:

You want the graphical solution to the system of equations ...

The graph of the equations is attached.

We presume you want an "estimate" because your graphing tool does not have minor gridlines appropriately graduated. It is easy enough to see that the x-value is between 1 and 2, closer to 1, and the y-value is between 2 and 3, closer to 2.

An estimate of (x, y) = (1 1/3, 2 1/3) is not unreasonable, and is the exact solution.

The solution to the differential equation is A. y = sin⁻¹(√2 - cosx)

To find the solution of the differential equation dy/dx = sinx/cosy, passing through the point (π/4, π/4) we proceed as follows.

dy/dx = sinx/cosy

So, cosydy = sinxdx

Integrating both sides, we have that

∫cosydy = ∫sinxdx

siny = -cosx + c

At the point (π/4, π/4), we have that

siny = -cosx + c

sin(π/4) = -cos(π/4) + c

1/√2 = -1/√2 + c

c = 1/√2 + 1/√2

c = 2/√2

c = 2/√2 × √2/√2

c = 2√2/2

c = √2

So, substituting the value of c into the equation, we have that

siny = -cosx + c

siny = -cosx + √2

Taking inverse sine of both sides, we have that

sin⁻¹siny = sin⁻¹(-cosx + √2)

y = sin⁻¹(√2 - cosx )

The solution is A. y = sin⁻¹(√2 - cosx)

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Answer:

  about 17.7 mph

Step-by-step explanation:

You want the value of v that maximizes F(v) = 3600v/(22+0.07v²).

The derivative of F is ...

  [tex]F'(v)=\dfrac{3600(22+0.07v^2)-3600v(0.14v)}{(22+0.07v^2)^2}[/tex]

The derivative is zero at the maximum. This is the case when the numerator is zero:

  3600(22 +.07v² -.14v²) = 0

  .07v² = 22

  v = √(22/0.07) ≈ 17.728

Flow rate is maximized at a speed of about 17.7 miles per hour.

We can explain this  statement as describing an array of subsets of S whereby  each subset in the array  has a relationship to other subsets in a one way or another.

In mathematics, set A is a subset of a set B if all elements of A are also elements of B; B is then a superset of A.

\So we can say that a  proper subset is one that contains a few elements of the original set whereas an improper subset contains every element of the original set.

So in the scenario shown above, we can deduce that  for every pair of subsets Di and Dj in the array, there is another  third subset in the array  that contains both Di and Dj.

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Answer:

circumference of the circle is 25.13 cm

area of the circle is 50.27 square cm

Step-by-step explanation:

The formula for the circumference of a circle is C = 2πr.

Using this formula, we can find the circumference of the circle with radius 4cm:

C = 2πr

C = 2π(4)

C = 8π

C = 25.13

So the circumference of the circle is 25.13 cm (rounded)

The formula for the area of a circle is A = πr^2.

Using this formula, we can find the area of the circle with radius 4cm:

A = πr^2

A = π(4^2)

A = 16π

A = 50.27

So the area of the circle is 50.27 square cm (rounded)

The scenario that could be modelled with an exponential function would be; D) when Tim adds $10 to his savings account each week.

Noted that a continuous compounding function is an exponential function. So, we need to find the situation where the principal amount is invested for an infinitely long time.

A.) It is known that the amount is invested and a certificate of deposit is taken the amount will be invested for a fixed period of time. so this is not a continuous compound function.

B.) The amount put into the account and taken out of the account varies for each term. Thus, this is not a continuous function.

C.) As in Jaylon's account the money is reduced by $125 every month, therefore, at a certain point, it will become zero therefore, this is not a continuous compound function.

D.) Since Tim adds $10 to his saving account every month, and there is no time specified, also the account will be always positive therefore, it is continuous compound function.

Hence, the scenario that could be modelled with an exponential function is D.

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Answer:109

Step-by-step explanation:

h(t) = -16t^2 + 80t + 9.

compare with equation ax%5E2%2Bbx%2Bc=0

a=-16, b=80 c =9

time to go to height h = -b%2F2a

=(80/32)= 2.5 s

time to go maximum height is t = = = = 2.5 seconds.

The maximum height you can get by substituting this value t= 3.5 in the formula

h(t) = -16t^2 + 80t + 9

h(2.5) = -16*2.5^2 + 80*2.5 + 9.

h =109m

After 20 minutes the jello salad will have a temperature of 43.9 F.

We have,

Newton's Law of Cooling is given by the formula

T(t) = T(s) + (T(0) - T(s))[tex]e^{-kt[/tex]

So, T(t) = 68 + (50 - 68) [tex]e^{-(0.01457). 20[/tex]

T(t) = 68 + (-18) [tex]e^{-(0.2914)[/tex]

T(t) = 68 + (-18) (1.338299)

T(t) = 68 - 24.089382

T(t) = 43.910618

T(t) = 43.9F

Thus, After 20 minutes the jello salad will have a temperature of 43.9 F.

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The answers are :

a) The graph is translated upwards by 4 units.

b) The graph is translated downwards by 2 units.

Since, The modification of an existing graph or graphed equation to create a different version of the following graph is known as translation.

a) The graph of y = f(x) is shown.

The other function is y = f(x) + 4.

As it can be observed that the graph is translated from its parent function which is y = f(x) to function y = f(x) + 4.

The graph is shifted down by 4 units or translated upwards by 4 units.

b) Here , the graph of y = g(x) is shown.

The other function is y = g(x -2)

As we can observe that the graph is translated from its parent function which is y = g(x) to function y = g(x - 2).

The graph is shifted downwards by 2 units or translated downwards by 2 units.

Therefore , the answers are :

a) The graph is translated upwards by 4 units.

b) The graph is translated downwards by 2 units.

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The simple interest on the principal $3,960 over 3 years at 6% is $712.8.

Given that, Reagan invested $18,500 in a savings for 2 years and earned interest of $1,850 at a rate of 5%.

Here, simple interest = (18500×5×2)/100

= $1850

A person earned interest of $3,960 over 3 years at 6%.

Here, simple interest = (3960×6×3)/100

= $712.8

Therefore, the simple interest on the principal $3,960 over 3 years at 6% is $712.8.

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Parent function: y = x (linear)

Equation of the graph: y = x - 4

      This function is a linear equation and the parent linear function is;

       y = x.

      These equations are written in the form y = mx + b where m is the slope and b is the y-intercept. Our y-intercept is -4 and our slope is 1 using the method "rise over run" where we count units up for every unit right. This means our equation is;

     y = x - 4

The distributive pattern of 3 * 45 that can be expressed is:

3(40) + 3(5) = 135.

The Distributive Property is a fundamental property of arithmetic that explains how to simplify expressions that involve multiplication and addition or subtraction, for example:

a(b + c) can be expressed as a*b + a*c = ab + ac.

In the image given we have that 45 multiplied by 3 will give us 135. This can be written using the distributive pattern as:

3(45) = 3(40) + 3(5)

= 120 + 15

= 135

Therefore, 3(45) = 3(40) + 3(5)

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Answer:

y = -2/9 x + 56/9

Step-by-step explanation:

It will take approximately 2020.79 years for 70 grams of the radioactive element to remain 27.

The half-life of a radioactive element is the duration during which half of the initial quantity decays. Therefore, we can write:

[tex]t_{1/2} =0.693/k[/tex]

k is the decay constant

[tex]t_{1/2}[/tex] = half life

plugging in the values

1470 = 0.693 / k

k = 0.693 / 1470

k = 0.0004714

[tex]y = y_{0}e(-kt)[/tex]

where

y0 is the first amount,

y is the remnant after time

t has passed

plugging in the values

[tex]27 = 70e^{-0.0004714t}[/tex]

[tex]\frac{27}{70} = e^{-0.0004714t}[/tex]

taking the natural logarithm of both sides we obtain:

[tex]In\frac{27}{70} = In (e^{-0.0004714t})[/tex]

[tex]In\frac{27}{70} = -0.0004714t[/tex]

Solving for t, yields:

[tex](In\frac{27}{70})/( -0.0004714) = t[/tex]

Using a calculator, it can be determined that:

t = -0.9526 / -0.0004714

t ≈ 2020.79 years

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