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Answer:

2 root 5

6 root 5

are the same

Step-by-step explanation:

Answer:

[tex]2\sqrt{5} \\6\sqrt{5}[/tex]

are the same

Step-by-step explanation:

Answer:

320.041 - 47.96 = 272.081

Step-by-step explanation:

I need more information on what you want me to do.

Do you want me to:

Multiply 320.041 by 47.96?

Subtract 47.96 from 320.041?

Multiply the difference between 320.041 and 47.96 by 47.96?

Multiplying 320.041 by 47.96 gives 152,399.6896.

Subtracting 47.96 from 320.041 gives 272.08.

Multiplying the difference between 320.041 and 47.96 by 47.96 gives 13049.0048.

The radius of the pond should be modified to 19.72ft to be able to maintain the original volume of the pond.

The original shape of the pond is the shape of a cylinder and the formula tye can be used to calculate the volume of a cylinder = πr²h

The volume of the original pond is calculated as follows;

π = 3.14

Radius = 18 ft

height = 36ft

Vol = 3.14×18×18×36

= 36,624.96ft³

The radius of the modified pond is calculated as follows; Volume = 36,624.96ft³

height = 30ft

radius = ?

That is;

36,624.96 = 3.14×r²× 30

r² = 36,624.96/94.2

= 388.8

r = √388.8

= 19.72 ft

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The relative frequency of the two frequency table is completed as below

                               less than 2 years    2 or more years      row total

college degree           0.26                         0.74                     1.00

no coll degree             0.70                          0.30                     1.00

The relative frequency table is filled by comparing the values as below

                               less than 2 years    2 or more years      row total

college degree              5/19                       14/19                     1.00

no coll degree                16/23                     7/23                     1.00

The row total

5 + 14 = 19 so we have 5/19 (0.26) and 14/19 (0.74)

16 + 7 = 23 o we have 16/23 (0.70) and 7/23 (0.30)

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If an annuity pays 5.5% compounded monthly, then the "equal-monthly-deposit" to have $100000 in 10 years is $627.

In order to calculate the "monthly-deposit" needed to accumulate $100,000 in 10 years at 5.5% compounded monthly, we use the formula for the future value of an annuity:

Which is : FV = P × [(1 + r)ⁿ - 1]/r,

where:

FV is "future-value" = $100000,

P = monthly deposit

r = monthly interest rate (5.5%/12 = 0.00458)

n = number of months (10 years × 12 months per year = 120 months)

Substituting the values,

We get,

⇒ 100000 = P × [(1 + 0.00458)¹²⁰ - 1]/0.00458,

⇒ P = 100000 × 0.00458 / [(1 + 0.00458)¹²⁰ - 1],

⇒ P ≈ $627,

Therefore, an equal monthly deposit is approximately $627.

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Answer:

[tex]f(-1) = -2\\[/tex]

[tex]f(0)=0[/tex]

[tex]f(1)=2[/tex]

Step-by-step explanation:

f(x)=2x

1) f(-1) = 2(-1) = -2

2) f(0) = 2(0) = 0

3)  f(1) = 2(1) = 2

1. The monthly payment for Loan A is roughly $516.40.

2. The total interest for Loan A is roughly $1590.4

We've been given the formula: PMT = (P(r/n)) / [1 - (1 + r/n)^-nt] to calculate the monthly payment loan.

If we should insert the figures given to the formula, it should be

PMT = (17000(0.059/12)) / [1 - (1 + 0.059/12)^(-12*3)]

PMT = 516.40

To calculate  total interest for loan A, we use the formula  (PMT x n x t) - P.

If we insert the figure provided, it should be;

(598.87 x 12 x 3) - 17000

=  $1590.4

The above answer is in response to the question below as seen in the picture;

Suppose that you decide to borrow $17,000 for a new car. Installment loan A: 3 years at 5.9%. Use PMT = (p(r/n))/ [1 - (1 + r/n)^-nt]

Find the monthly payment and the total interest for loan A. The monthly payment for Loan A is $..............

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The predicted value of Variable 2 when Variable 1 = 2 is 82.

How to calculate the value :-

The graph shows that the data has a diminishing exponential trend.

We can utilize the trendline tool in a spreadsheet program like Excel to discover the equation of the exponential function that matches the data. Using the trendline feature, we obtain the following equation:

Variable number 2 = 120.28 * 0.8555Variable number one

We can now use this equation to estimate the value of Variable 2 when Variable 1 = 2:

82 Variable 2 = 120.28 * 0.85552

When Variable 1 = 2, the anticipated value of Variable 2 is 82, rounded to the closest whole number.

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The predicted value of Variable 2 when Variable 1 = 2 is 82.

How to calculate the value :-

The graph shows that the data has a diminishing exponential trend.

We can utilize the trendline tool in a spreadsheet program like Excel to discover the equation of the exponential function that matches the data. Using the trendline feature, we obtain the following equation:

Variable number 2 = 120.28 * 0.8555Variable number one

We can now use this equation to estimate the value of Variable 2 when Variable 1 = 2:

82 Variable 2 = 120.28 * 0.85552

When Variable 1 = 2, the anticipated value of Variable 2 is 82, rounded to the closest whole number.

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Answer:

Step-by-step explanation:

[tex]H_o: p = 0.5,H_1:p\neq 0.5[/tex]

[tex]p(\text{buttered side down})=\frac{19}{51}[/tex]

[tex]\pi _o=0.5\\n=51[/tex]

[tex]z=\frac{p-\pi _o}{\sqrt{\frac{\pi _o(1-\pi _o)}{n} } } =\frac{\frac{19}{51}-0.5 }\sqrt{{\frac{0.5(1-0.5)}{51} } }[/tex]

≈ [tex]-1.82[/tex]

a = 0.01    [tex]z_a/z=2.58\\|z| < |z_[ay}}_2|[/tex]

Thus, it cant reject H₀

The toast will land with the buttered side down 50% of the time.

{Hypothesis test}

According to given information the P-value is approximately 0.016.

In statistical hypothesis testing, the p-value is the probability of obtaining a test statistic as extreme as or more extreme than the observed results, under the assumption that the null hypothesis is true.

To find the P-value for this hypothesis test, we need to use a t-distribution with degrees of freedom equal to n-1 = 14-1 = 13. Since the test statistic is t = -2.645, we need to find the area under the t-distribution curve to the left of t.

Using a t-table or calculator, we can find that the area to the left of t = -2.645 with 13 degrees of freedom is approximately 0.008. This is the probability of observing a t-value less extreme than -2.645, assuming the null hypothesis is true.

Since this is a two-tailed test (we are testing whether the true mean is less than or greater than 18.00 Mbps), we need to double the one-tailed P-value to get the two-tailed P-value. Therefore, the P-value is approximately 0.016 (i.e., 2 x 0.008).

So, the P-value is approximately 0.016.

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If the TV consumes 150 watts per hour and electricity costs (18 cents)/(1 kilowatt-hour), it would cost Lee $1.62 to operate his TV for a month of 30 days.

To calculate the cost of operating Lee's TV for a month of 30 days, we need to determine the total amount of electricity used by the TV in that period.

First, we need to calculate the total number of hours Lee watches TV in a month:

2 hours/day x 30 days = 60 hours

Next, we need to calculate the total electricity consumed by the TV:

150 watts/hour x 60 hours = 9,000 watt-hours or 9 kilowatt-hours (kWh)

Now, we can calculate the cost of operating the TV for a month:

9 kWh x $0.18/kWh = $1.62

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If the TV consumes 150 watts per hour and electricity costs (18 cents)/(1 kilowatt-hour), it would cost Lee $1.62 to operate his TV for a month of 30 days.

To calculate the cost of operating Lee's TV for a month of 30 days, we need to determine the total amount of electricity used by the TV in that period.

First, we need to calculate the total number of hours Lee watches TV in a month:

2 hours/day x 30 days = 60 hours

Next, we need to calculate the total electricity consumed by the TV:

150 watts/hour x 60 hours = 9,000 watt-hours or 9 kilowatt-hours (kWh)

Now, we can calculate the cost of operating the TV for a month:

9 kWh x $0.18/kWh = $1.62

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Answer:

x = 2

Step-by-step explanation:

3x + 2 = 8

Subtracting both sides by 2 we get,

=> 3x + 2 - 2= 8 - 2

=> 3x = 6

=> x = 6/3

=> x = 2

Answer:

Color Probability

Red         1/11

Blue 3/11

Green 7/11

Step-by-step explanation:

The total number of counters in the bag is 1+3+7=11. The probability of selecting a red counter is 1/11, because there is only one red counter in the bag. The probability of selecting a blue counter is 3/11, because there are three blue counters in the bag. Similarly, the probability of selecting a green counter is 7/11, because there are seven green counters in the bag.

Answer:

The angle of C is 118.6

Step-by-step explanation:

The index of refraction of the second material is 1.27.

We are given that;

Angle= 59°

Randomized Variables 1 = 1.47θ1 = 59°θ2 = 69°

Now,

To find n2, we can rearrange Snell’s law as:

n2 = n1 sin θ1 / sin θ2

Plugging in the given values, we get:

n2 = 1.47 sin 59° / sin 69°

n2 = 1.47 (0.857) / (0.934)

n2 = 1.27 (rounded to two decimal places)

Therefore, by the expression the answer will be 1.27

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The building is 246 feet tall.

Two or more triangles will always be referred to as similar if on comparing their corresponding properties, some common relations holds. Some of the relations are relations between their length of sides, relations among their internal angles etc.

To determine the height of the building, we have;

height of pole = 7 ft

total length of the building's shadow = 167 ft

the length of the shadow of the pole = 4.75 ft

Let the height of the building be represented by h. On comparison, we have;

4.75/ 167 = 7/h

4.75h = 167 x 7

         = 1169

h = 1169/ 4.75

  = 246.11

The building is 246 ft. tall.

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The inverse of f(x) = [tex](4x-9)^{1/2[/tex] when the variables of x and y are switched is [tex]F(x)^{-1}[/tex] =  [tex]\frac{x^{2}+9 }{4}[/tex]

Inverse of a function is a function which can be reversed into another function. It is also a function that undoes the action of the another function.

How to determine this

When f(x) = (4x-9)^1/2

To determine the inverse, [tex]f(x)^{-1}[/tex]= y

y = (4x-9)^1/2

y = [tex]\sqrt{4x-9}[/tex]

By squaring both sides

y^2 = 4x - 9

By swapping the variables

x^2 = 4y - 9

Subtracting 9 from both sides

x^2 +9 = 4y

divide through by 4

[tex]\frac{x^{2}+9 }{4}[/tex] = 4y/4

y = [tex]\frac{x^{2}+9 }{4}[/tex]

Therefore [tex]F(x)^{-1}[/tex] = [tex]\frac{x^{2}+9 }{4}[/tex]

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Answer: F=32

Step-by-step explanation:formula: F = Celsius*9/5+32

so plug the zero for Celsius, in this case, 0*9/5+32 = 32

You would need approximately 23.077 pounds of whole apples to make 18 pounds of peeled and cored apples with a 78% yield percentage.

Explanation:

To find out how many pounds of whole apples are needed to make 18 lbs of peeled and cored apples with a yield percentage of 78%, we can use the following formula:

Pounds of whole apples needed = (Pounds of peeled and cored apples needed) / Yield percentage

Plugging in the values we have:

Pounds of whole apples needed = 18 lb / 0.78Pounds of whole apples needed = 23.077 lb (rounded to three decimal places)

Therefore, you would need approximately 23.077 pounds of whole apples to make 18 pounds of peeled and cored apples with a 78% yield percentage.

The area of the field, given that it is a trapezium, would be 7, 986 m ² .

The field is in the shape of a trapezium which means that the area of the field can be found by the formula :

= ( a + b ) / 2 x height

Side a = 102 m

Side b = 140 m

height = 66 m

The area of the field is therefore:

= ( 102 + 140 ) / 2 x 66

= 121 x 66

= 7, 986 m ²

In conclusion, the area of the field is 7, 986 m ².

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Answer: 0

Step-by-step explanation:

[tex]log_{3} log_{5} log_{2} 32[/tex]

Let's evaluate    

[tex]log_{2}32[/tex]   this is the same as

[tex]2^{x}=32[/tex]       2*2*2*2*2=32  

or

you can think of it as 2 to the what power is 32

so x=5

now substitute that in for [tex]log_{2}32[/tex]

[tex]log_{3} log_{5} 5[/tex]

Now evaluate   [tex]log_{5}5[/tex]

5 to the what power is 5

=1

substitute into [tex]log_{3} log_{5} 5[/tex]

[tex]log_{3} 1[/tex]

3 to the what power is 1

=0

Anything to the 0 power is 1 (it's a rule)

The probability that the coin reads heads or tails and the dices number is less than or equal to 6 is 1/3 or approximately 0.333.

There are 12 possible outcomes in the table where the coin reads heads or tails and the dice roll is less than or equal to 6. These are:

Coin Toss: H, Die Roll: 1

Coin Toss: H, Die Roll: 2

Coin Toss: H, Die Roll: 3

Coin Toss: H, Die Roll: 4

Coin Toss: H, Die Roll: 5

Coin Toss: H, Die Roll: 6

Coin Toss: T, Die Roll: 1

Coin Toss: T, Die Roll: 2

Coin Toss: T, Die Roll: 3

Coin Toss: T, Die Roll: 4

Coin Toss: T, Die Roll: 5

Coin Toss: T, Die Roll: 6

Out of these 12 outcomes, 6 have the coin reading heads and 6 have the coin reading tails. So, the probability that the coin reads heads or tails and the dice number is less than or equal to 6 is:

P(heads or tails and dice number <= 6) = P(heads and dice number <= 6) + P(tails and dice number <= 6)

= 6/36 + 6/36

= 12/36

= 1/3

Therefore, the probability is 1/3 or approximately 0.333.

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The function is positive and increasing.

Given is an exponential function y = √4x,

So, since all the value of the function will be above x-axis therefore, the function is positive.

Now,

Differentiating the function,

y' = d(√4x)/dx

y' = 1/2 × [tex]4x^{-1/2[/tex]

y' = 1/2√4x

y' = 1/4√x

Since, y' > 0, therefore, the function is increasing.

Now,

For functions with exponential growth, we have the following end behavior.

The end behavior on the left (as x → -∞), it has a horizontal asymptote at y = 0,

The end behavior on the right (as x → ∞), y→ ∞.

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Answer:

Step-by-step explanation: length of a rectangle is 4 meters less than 3 times the width so we can write L = 3W-4

The formula for the perimeter of a rectangle: P = 2L+2W

Now plug the numbers: P = 2(3W-4)2W

                                        24 = 6W - 8 +2W

                                         24 = 8W - 8

                                         32 = 8W

                                          W = 4

The equation of the line that passes through the point (-1, 1) and is parallel to a line that passes through (3, 6) and (1, -2) is: [tex]$y = 4x + 5$[/tex].

The slope of a line is a measure of its steepness, and is calculated as the change in the y-coordinate divided by the change in the x-coordinate.

In this case, the line passing through the points (3, 6) and (1, -2) has a slope of [tex]$\frac{6 - (-2)}{3 - 1} = \frac{8}{2} = 4$[/tex].

Therefore, the line that passes through the point (-1, 1) and is parallel to the given line has the same slope of 4.

To find the equation of the line passing through (-1, 1) and having a slope of 4, we need to use the point-slope formula.

The point-slope formula is given by: [tex]$y - y_1 = m(x - x_1)$[/tex] where [tex]$(x_1, y_1)$[/tex] is a point on the line, and m is the slope of the line. In this case, [tex]$(x_1, y_1)$[/tex] is (-1, 1) and m is 4, so the equation of the line is:

[tex]$y - 1 = 4(x - (-1))$[/tex]

[tex]$y - 1 = 4x + 4$[/tex]

[tex]$y = 4x + 5$[/tex]

Therefore, the equation of the line that passes through the point (-1, 1) and is parallel to a line that passes through (3, 6) and (1, -2) is: [tex]$y = 4x + 5$[/tex].

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The equation of the line that passes through the point (-1, 1) and is parallel to a line that passes through (3, 6) and (1, -2) is: [tex]$y = 4x + 5$[/tex].

The slope of a line is a measure of its steepness, and is calculated as the change in the y-coordinate divided by the change in the x-coordinate.

In this case, the line passing through the points (3, 6) and (1, -2) has a slope of [tex]$\frac{6 - (-2)}{3 - 1} = \frac{8}{2} = 4$[/tex].

Therefore, the line that passes through the point (-1, 1) and is parallel to the given line has the same slope of 4.

To find the equation of the line passing through (-1, 1) and having a slope of 4, we need to use the point-slope formula.

The point-slope formula is given by: [tex]$y - y_1 = m(x - x_1)$[/tex] where [tex]$(x_1, y_1)$[/tex] is a point on the line, and m is the slope of the line. In this case, [tex]$(x_1, y_1)$[/tex] is (-1, 1) and m is 4, so the equation of the line is:

[tex]$y - 1 = 4(x - (-1))$[/tex]

[tex]$y - 1 = 4x + 4$[/tex]

[tex]$y = 4x + 5$[/tex]

Therefore, the equation of the line that passes through the point (-1, 1) and is parallel to a line that passes through (3, 6) and (1, -2) is: [tex]$y = 4x + 5$[/tex].

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The converted acceleration in feet per hour per second is 13200 feet per hour per second

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

Acceleration = 2.5 miles per hour per second

From the question, we have

(1 mile = 5,280 feet)

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

Acceleration = 2.5 * 5,280 feet per hour per second

Evaluate the products

So, we have

Acceleration = 13200 feet per hour per second

Hence, the acceleration = 13200 feet per hour per second

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