please help urgently! maths trigonometry

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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Answer:

C

Step-by-step explanation:

When we do 30=y/3 we get 90 because of the fraction symbol and its says in the problem 3 times as much so more not less so 3x30 equals 90 so we already take out A and B and when there is nothing but a simple equation like 30=3 we dived so it cant be D Ethier so its C

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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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The angles that is supplementary to <HAE is <IAE

Supplementary angles are simply described as a pair of angles whose sum is 180 degrees.

Some properties of supplementary angles are;

From the information given, we can see that;

<HAE is on a straight line with <IAE , making their sum to be 180 degrees

Then, <IAE is supplementary is <HAE

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Answer:

Step-by-step explanation:

Since they are in a row, add all the measurements

4 ft 10 in

5 ft 6 in             add ft with the ft and in with in

3 ft 3 in

12 ft 19 in        

There are too many inches.  So you can take away 12 of those inches and and turn it into 1 more foot.  That would make 13 ft.  You'd be left with 7 in.

12 ft + 1 ft    19 in - 12 in

13 ft 7in

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:

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}

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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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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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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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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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:

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 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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Answer:

The angle of C is 118.6

Step-by-step explanation:

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 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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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:

8,11,14,17

Step-by-step explanation:

3n + 5

When n = 1,

3(1) + 5

=> 3 + 5

=> 8

When n = 2,

3(2) + 5

=> 11

When n = 3,

3(3) + 5

=> 14

When n = 4,

3(4) + 5

=> 17

Answer:

104 square meters

Step-by-step explanation:

Make sure all the units are same and consistent!!

The shape of the shaded region = Trapezium

h = Perpendicular height of trapezium

  = 16 m

∴Area of shaded region = Area of trapezium

                                          = [tex]\frac{1}{2}[/tex] × (Sum of parallel sides) × h

                                          = [tex]\frac{1}{2}[/tex] × [(9 + 4) m] × (16 m)

                                         = [tex]\frac{1}{2}[/tex] × (13 m) × (16 m)

∴Area of shaded region = 104 [tex]m^{2}[/tex]

                                         = 104 square meters

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.

The hypothesis test conclude that the training program was successful in increasing students' math skills.

As the average exam score of students who participated in the program was significantly higher than the population mean.

Number of students participated = 36

Population mean µ = 70

and σ = 12

To determine whether the math program was successful in increasing students' math skills, we can conduct a hypothesis test.

The null hypothesis denoted as H₀,

There is no difference between mean exam scores of students who participated in math program and population mean µ = 70.

The alternative hypothesis denoted as H₁,

There is a difference between the mean exam scores of the two groups.

Mathematically, the hypotheses as follows,

H₀: µ = 70

There is no difference in the mean exam scores of students who participated in the math program and the population mean.

H₁: µ > 70

The mean exam scores of students who participated in the math program are greater than the population mean.

Use a one-sample t-test to test the hypotheses.

The formula for the t-test statistic is,

t = (X - µ) / (s / √n)

X is the sample mean = 73.6

µ is the population mean = 70

s is the sample standard deviation

s = 12 / √36

  = 2

and n is the sample size= 36

Substituting these values into the formula, we get,

t = (73.6 - 70) / (2 / √36)

 = 3.6 / (1/3)

 ≈10.8

To determine whether the t-value is significant,

Compare it to the critical t-value at a chosen significance level α. Assuming significance level of 0.05 and 35 degrees of freedom df=n - 1 .

Critical t-value to be approximately 1.69.

Since calculated t-value 10.8 is greater than the critical t-value 1.69.

Reject the null hypothesis .

Therefore, using hypothesis test conclude that there is sufficient evidence to suggest that the math program was successful in increasing students' math skills.

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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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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