It takes a turtle 3 hours to walk 1/2 miles. How many hours does it take to walk 6 mile?

Answer:

B

Step-by-step explanation:

using the recursive rule \(a_{n}\) = 3\(a_{n-1}\) and a₁ = 10, then

a₁ = 10

a₂ = 3a₁ = 3 × 10 = 30

a₃ = 3a₂ = 3 × 30 = 90

the first 3 terms are 10 , 30 , 90

Answer:

a) The expected value of the job satisfaction score for senior executives is:

= 4.01

b) The expected value of the job satisfaction score for middle managers is:

= 3.83

Step-by-step explanation:

a) Data and Calculations:

Job Satisfaction             Probability

Score  

                IS Senior Executives    IS Middle Managers

1                          0.06                             0.04

2                         0.09                             0.10

3                         0.03                             0.13

4                         0.42                             0.45

5                         0.40                             0.28

Low of 1 = very dissatisfied

High of 5 = very satisfied

Job Satisfaction     IS Senior Executives             IS Middle Managers

      Score       Probability  Expected Value   Probability  Expected Value

1                      0.06               0.06 (1 * 0.06)      0.04           0.04 (1 * 0.04)

2                     0.09               0.18 (2 * 0.09)      0.10            0.20 (2 * 0.10)

3                     0.03               0.09 (3 * 0.03)      0.13            0.39 (3 * 0.13)

4                     0.42               1.68 (4 * 0.42)       0.45           1.80 (4 * 0.45)

5                     0.40               2  (5 * 0.40)         0.28            1.40 (5 * 0.28)

Expected value                    4.01                                          3.83

The binomial expansion is solved and the error in Dakota's statement is the incorrect substitution of 36g^2h^2 for the correct expression

Given data ,

Dakota made a mistake because the third term of the expansion of (2g + 3h) should have been 36g2h2. The binomial theorem asserts that the expansion of (2g + 3h) is as follows:

( x + y )ⁿ = ⁿCₐ ( x )ⁿ⁻ᵃ ( y )ᵃ

Here, x = 2g and y = 3h. Since term numbers begin at 0, since we are seeking for the third term, r = 2.

So , on simplifying the equation , we get

= nC2 * (2g)⁽ⁿ⁻²⁾ * (3h)²

= (n! / (2! * (n - 2)!)) * (2g)⁽ⁿ⁻²⁾ * (3h)²

= ((n * (n - 1)) / 2) * (2g)⁽ⁿ⁻²⁾ * (3h)²

Hence , the correct expression for the third term of the expansion of (2g + 3h) is ((n * (n - 1)) / 2) * (2g)^(n - 2) * (3h)², where n is the exponent in the binomial expansion.

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The graph of the linear inequality  y > 5 / (-2x + 2) shows a solution of (0, 2.5)

The graph of an inequality in two variables is the set of points that represents all solutions to the inequality. A linear inequality divides the coordinate plane into two halves by a boundary line where one half represents the solutions of the inequality. The boundary line is dashed for > and < and solid for ≤ and ≥.

In the given inequality, y > 5 / (-2x + 2) can be represented on a graph using a graphing calculator.

Kindly find the attached graph below

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The value of y in simplest form for the point P = (1/2, y) lying on the unit circle is y = ± √(3)/2.

To find the value of y in simplest form for the point P = (1/2, y) lying on the unit circle, we can use the equation of the unit circle, which states that for any point (x, y) on the unit circle, the following equation holds: x^2 + y^2 = 1.

Plugging in the coordinates of the point P = (1/2, y), we get:

(1/2)^2 + y^2 = 1

1/4 + y^2 = 1

y^2 = 1 - 1/4

y^2 = 3/4.

To simplify y^2 = 3/4, we take the square root of both sides:y = ± √(3/4).

Now, we need to simplify √(3/4). Since 3 and 4 share a common factor of 1, we can simplify further: y = ± √(3/4) = ± √(3)/√(4) = ± √(3)/2.

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Answer:

#1  (0,-4)

#2  (5,0)

#3  (3,1)

Step-by-step explanation:

#1.  (-3, 2) (0, y)  slope = -2

slope = rise/run    therefore slope = -2/1  or down 2 and over 1

so from -3 to 0 you are going over 3 units (or 3 times)  Therefore to find y at x=0, you have to move three steps, or 3 times -2 = -6      so 2-6 = -4

so y intercept (b)  = -4 0r (0,-4)

#2   (-7,-4)  (x,0)  slope (m) = 1/3   -7+12=5    x=5

#3   (4,-3)   (x, 1)   slope (m) = -4   (4/-1)   Moving one unit in slope  means

-3=4=1 for Y and 4-1=3 for X    therefore the point is (3, 1)

Answer:

The mean number of hours will increase.

Step-by-step explanation:

The mean is the sum of all the values in a data set divided by the number of values in that data set.

First, find the mean of the original data set without the additional value. There are 22 values.

So, the mean of the original data set is approximately 7.27 hours.

Next, add the additional data point to the sum of the number of hours, and divide by the new number of values in the data set, 23, to find the new mean.

So, the mean of the data set with the additional value is approximately 8.26 hours.

Since 8.26 > 7.27, the effect of the additional value is that the mean number of hours will increase.

Answer:

28 i think

Step-by-step explanation:

The correct answer is Confidence interval lower bound: 32.52 cm,Confidence interval upper bound: 37.48 cm

To calculate the confidence interval for the true mean height of the loaves, we can use the t-distribution. Given that the sample size is small (n = 10) and the population standard deviation is unknown, the t-distribution is appropriate for constructing the confidence interval.

The formula for a confidence interval for the population mean (μ) is:

Confidence Interval = sample mean ± (t-critical value) * (sample standard deviation / sqrt(sample size))

For the first situation:

n = 15

Confidence level is 95% (which corresponds to an alpha level of 0.05)

x = 35 (sample mean)

s = 2.7 (sample standard deviation)

Using RStudio or a t-table, we can find the t-critical value. The degrees of freedom for this scenario is (n - 1) = (15 - 1) = 14.

The t-critical value at a 95% confidence level with 14 degrees of freedom is approximately 2.145.

Plugging the values into the formula:

Confidence Interval = 35 ± (2.145) * (2.7 / sqrt(15))

Calculating the confidence interval:

Lower Bound = 35 - (2.145) * (2.7 / sqrt(15)) ≈ 32.52 (rounded to 2 decimal places)

Upper Bound = 35 + (2.145) * (2.7 / sqrt(15)) ≈ 37.48 (rounded to 2 decimal places)

Therefore, the lower bound of the confidence interval is approximately 32.52 cm, and the upper bound is approximately 37.48 cm.

For the second situation:

n = 37

Confidence level is 99% (which corresponds to an alpha level of 0.01)

x = 82 (sample mean)

s = 5.9 (sample standard deviation)

The degrees of freedom for this scenario is (n - 1) = (37 - 1) = 36.

The t-critical value at a 99% confidence level with 36 degrees of freedom is approximately 2.711.

Plugging the values into the formula:

Confidence Interval = 82 ± (2.711) * (5.9 / sqrt(37))

Calculating the confidence interval:

Lower Bound = 82 - (2.711) * (5.9 / sqrt(37)) ≈ 78.20 (rounded to 2 decimal places)

Upper Bound = 82 + (2.711) * (5.9 / sqrt(37)) ≈ 85.80 (rounded to 2 decimal places)

Therefore, the lower bound of the confidence interval is approximately 78.20 cm, and the upper bound is approximately 85.80 cm.

For the third situation:

n = 1009

Confidence level is 90% (which corresponds to an alpha level of 0.10)

x = 0.9 (sample mean)

s = 0.04 (sample standard deviation)

The degrees of freedom for this scenario is (n - 1) = (1009 - 1) = 1008.

The t-critical value at a 90% confidence level with 1008 degrees of freedom is approximately 1.645.

Plugging the values into the formula:

Confidence Interval = 0.9 ± (1.645) * (0.04 / sqrt(1009))

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Answer: J = 33

Step-by-step explanation:

the corner of the triangle is 90 degrees so

90 + 57 = 147

Now the rest is 33 degrees.

Since it'll equal to 180 degrees.

Answer:

It's 33 degree

explanation:

Two triangles are similar so

angle K is equal angleQ=90DEGREE

ANGLE J=AngleP=33

Answer:

1)  695.3 m²

2)  8 ft

3)  172.0 in²

Step-by-step explanation:

To find the area of a regular polygon, we can use the following formula:

\(\boxed{\begin{minipage}{5.5cm}\underline{Area of a regular polygon}\\\\$A=\dfrac{s^2n}{4 \tan\left(\dfrac{180^{\circ}}{n}\right)}$\\\\\\where:\\\phantom{ww}$\bullet$ $n$ is the number of sides.\\ \phantom{ww}$\bullet$ $s$ is the side length.\\\end{minipage}}\)

Given the polygon is an octagon, n = 8.

Given each side measures 12 m, s = 12.

Substitute the values of n and s into the formula for area and solve for A:

\(\implies A=\dfrac{(12)^2 \cdot 8}{4 \tan\left(\dfrac{180^{\circ}}{8}\right)}\)

\(\implies A=\dfrac{144 \cdot 8}{4 \tan\left(22.5^{\circ}\right)}\)

\(\implies A=\dfrac{1152}{4 \tan\left(22.5^{\circ}\right)}\)

\(\implies A=\dfrac{288}{\tan\left(22.5^{\circ}\right)}\)

\(\implies A=695.29350...\)

Therefore, the area of a regular octagon with side length 12 m is 695.3 m² rounded to the nearest tenth.

\(\hrulefill\)

The sum of an interior angle of a regular polygon and its corresponding exterior angle is always 180°.

If the exterior angle of a polygon measures 40°, then its interior angle measures 140°.

To determine the number of sides of the regular polygon given its interior angle, we can use this formula, where n is the number of sides:

\(\boxed{\textsf{Interior angle of a regular polygon} = \dfrac{180^{\circ}(n-2)}{n}}\)

Therefore:

\(\implies 140^{\circ}=\dfrac{180^{\circ}(n-2)}{n}\)

\(\implies 140^{\circ}n=180^{\circ}n - 360^{\circ}\)

\(\implies 40^{\circ}n=360^{\circ}\)

\(\implies n=\dfrac{360^{\circ}}{40^{\circ}}\)

\(\implies n=9\)

Therefore, the regular polygon has 9 sides.

To determine the length of each side, divide the given perimeter by the number of sides:

\(\implies \sf Side\;length=\dfrac{Perimeter}{\textsf{$n$}}\)

\(\implies \sf Side \;length=\dfrac{72}{9}\)

\(\implies \sf Side \;length=8\;ft\)

Therefore, the length of each side of the regular polygon is 8 ft.

\(\hrulefill\)

The area of a regular polygon can be calculated using the following formula:

\(\boxed{\begin{minipage}{5.5cm}\underline{Area of a regular polygon}\\\\$A=\dfrac{s^2n}{4 \tan\left(\dfrac{180^{\circ}}{n}\right)}$\\\\\\where:\\\phantom{ww}$\bullet$ $n$ is the number of sides.\\ \phantom{ww}$\bullet$ $s$ is the side length.\\\end{minipage}}\)

A regular pentagon has 5 sides, so n = 5.

If its perimeter is 50 inches, then the length of one side is 10 inches, so s = 10.

Substitute the values of s and n into the formula and solve for A:

\(\implies A=\dfrac{(10)^2 \cdot 5}{4 \tan\left(\dfrac{180^{\circ}}{5}\right)}\)

\(\implies A=\dfrac{100 \cdot 5}{4 \tan\left(36^{\circ}\right)}\)

\(\implies A=\dfrac{500}{4 \tan\left(36^{\circ}\right)}\)

\(\implies A=\dfrac{125}{\tan\left(36^{\circ}\right)}\)

\(\implies A=172.047740...\)

Therefore, the area of a regular pentagon with perimeter 50 inches is 172.0 in² rounded to the nearest tenth.

Answer:

1.695.29 m^2

2.8 feet

3. 172.0477 in^2

Step-by-step explanation:

1. The area of a regular octagon can be found using the formula:

\(\boxed{\bold{Area = 2a^2(1 + \sqrt{2})}}\)

where a is the length of one side of the octagon.

In this case, a = 12 m, so the area is:

\(\bold{Area = 2(12 m)^2(1 + \sqrt{2}) = 288m^2(1 + \sqrt2)=695.29 m^2}\)

Therefore, the Area of a regular octagon is 695.29 m^2

2.

The formula for the exterior angle of a regular polygon is:

\(\boxed{\bold{Exterior \:angle = \frac{360^o}{n}}}\)

where n is the number of sides in the polygon.

In this case, the exterior angle is 40°, so we can set up the following equation:

\(\bold{40^o=\frac{ 360^0 }{n}}\)

\(n=\frac{360}{40}=9\)

Therefore, the polygon has n=9 sides.

Perimeter=72ft.

We have

\(\boxed{\bold{Perimeter = n*s}}\)

where n is the number of sides in the polygon and s is the length of one side.

Substituting Value.

72 feet = 9*s

\(\bold{s =\frac{ 72 \:feet }{ 9}}\)

s = 8 feet

Therefore, the length of each side of the polygon is 8 feet.

3.

Solution:

A regular pentagon has five sides of equal length. If the perimeter of the pentagon is 50 in, then each side has a length = \(\bold{\frac{perimeter}{n}=\frac{50}{5 }= 10 in.}\)

The area of a regular pentagon can be found using the following formula:

\(\boxed{\bold{Area = \frac{1}{4}\sqrt{5(5+2\sqrt{5})} *s^2}}\)

where s is the length of one side of the Pentagon.

In this case, s = 10 in, so the area is:

\(\bold{Area= \frac{1}{4}\sqrt{5(5+2\sqrt{5})} *10^2=172.0477 in^2}\)

Drawing: Attachment

Step-by-step explanation:

Pythagoras theorem

16²=7²+a²

a²=16²-7²

a²= 256 -49

a²=207

a=√207

a=14.38

a≈14.4 in. (approx)

Answer:

Step-by-step explanation:

As it is a right angle triangle, we can use Pythagorean theorem to find a

base² + altitude² = hypotenuse²

7² + a² = 16²

49 + a² = 256

       a² = 256 - 49

       a² = 207

     a = √207

a = 14.4 in

Answer: 6y = 7x - 40

Step-by-step explanation:

The variable h, which is a row vector with eight equally spaced elements, is h = linspace(68, 12, 8).

To create the variable h as a row vector with eight equally spaced elements, we can use the linspace function in MATLAB or Octave. The linspace function takes three arguments: the starting value, the ending value, and the number of elements in the vector.

Here's how to create the variable h with the desired specifications:

This will create a row vector h with eight equally spaced elements ranging from 68 to 12. The output will be:

The elements in the vector are not integers because we asked for eight equally spaced elements between 68 and 12.

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Answer:

Step-by-step explanation:

To differentiate the function y = x^4 - x, we will use the power rule of differentiation. The power rule states that if f(x) = x^n, then the derivative of f(x) is f'(x) = nx^(n-1).

So, for y = x^4 - x, we can find the derivative as follows:

y' = 4x^3 - 1

So, the derivative of the function y = x^4 - x is y' = 4x^3 - 1.

Answer:

I only know the second part sorry

9.35

Step-by-step explanation:

3(9)÷4+2.6=

27÷4+2.6=

6.75+2.6=

9.35

Answer:

Option A. 283 cm²

Step-by-step explanation:

to find the area of the shaded sector, we use the formula:

 \(\frac{\text{angle given}}{360^\circ}\times \text{area of the circle}\)

where area of the circle = πr²

∴ for the given circle,

\(\text{Area of the sector}=\frac{\text{given angle}}{360^\circ} \times \pi r^2\)

                            =  \(\frac{100}{360}\times 3.14\times 18\times 18\)

                            = \(\frac{100}{360}\times 1017.36\)

                            = 282.6

                            ≈ 283 cm²

The approximate area of the shaded sector is 283 cm².

Answer:

A) 41%

Step-by-step explanation:

the complement of at least one balloon being hit is no balloons being hit

thus, if "at least one balloon is hit" is false, "no balloons are hit" is true

1 - probability something is false  = probability it is true

1 - probability no balloons are hit = probability at least one balloon is hit

probability no balloons are hit = P(A and B and C and D and E), where each event is a balloon is not hit

probability a balloon is hit = 1/10 = 0.1

probability a ballon is not hit = 1 - probability a balloon is hit = 1-0.1 = 0.9

P(A and B) = P(A) * P(B)

P(A and B and C and D and E) = 0.9*0.9*0.9*0.9*0.9 = 0.9^5 = 0.59049 = probability no balloons are hit

1 - probability no balloons are hit = probability at least one balloon is hit = 1-0.59049 = 0.40951 ≈41%

Answer:

i believe the answer is 15 milliliters

Step-by-step explanation:

Answer:

Figure it out yourself

Step-by-step explanation:

The  volume of rectangular prism is 90 unit³.

We can consider the 1 block = 1 unit.

Length of prism = 5 unit

width of prism = 6 unit

Height of prism = 3 unit

So, Volume of rectangular prism

= l w h

= 5 x 6 x 3

= 90 unit³

Thus, the volume of rectangular prism is 90 unit³.

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The option A is correct because the value of the statement is 6+3/n-8.

According to the statement

we have given that the statement and we have to write the statement in the numerical form.

So, For this purpose

we know that the given statement is

"Six more than the quotient of three and a number, decreased by eight".

In this statement "Six more than" indicates the sum between the quotient and 6.

And "The quotient of three and a number" indicates a fraction where the numerator is 3 and the denominator is , a number.

"Decreased by eight" indicates a subtraction between the quotient an 8 units".

If we unit all parts of the statements, we would have

6+3/n-8

So, From the given statement, The option A is correct because the value of the statement is 6+3/n-8.

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The expression in the form (x +a)² + b is shown below.

We have to expression given expression in the form (x +a)² + b.

1. x² + 12x

x² + 12x + 36 - 36

= (x +6)² - 36

2. x² + 3x - 2

x² + 2 . 3x /2 - 9/4 + 9/4 -2

(x+ 3/2)² - 17/4

3. x²+ 1/2 x

x² + 2 . 1/4 x + (1/2)² - (1/2)²

= (x+ 1/2)² - 1/4

4. x² - 2/9 x

=  x² + 2 . 2/20 x + 4/400 - 4/400

= (x+ 2/200)² - 1/100

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The perimeter of the figure with side length of 5 units is 50 units

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

Shape = rectangle

Smaller shapes = squares

Side lengths = 5 units

The perimeter of the figure is calculated as

Perimeter  = Number of visible sides * Side length of the square shape

In this case, we have

Number of visible sides = 10

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

Perimeter  = 10 * 5

Evaluate the products

Perimeter  = 50 units

Hence, the perimeter is 50 units

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Answer:

The answer to your problem is, 0.275 0.273 0.400 and 0.300

Step-by-step explanation:

My calculation ( May not be correct )

P ( low iron or LI )  \(\frac{165}{600}\) = 0.275

P ( low pH | LI ) = \(\frac{45}{165}\) = 0.273

P ( low pH ) = \(\frac{150}{600}\) = 0.400

P ( LI | Low pH ) = \(\frac{45}{150}\) = 0.300

Thus by making these calculations the answer to your problem is, 0.275 0.273 0.400 and 0.300

The origin is often used as the center of dilation. If you are dilating a figure centered at the origin, you can multiply the coordinates of the points in the preimage by the scale factor to determine the points in the image.

Given a scale factor of k, the transformation is given by

On our problem, we want to perform a dilation at (-2, 4) with a scale factor of 2, therefore, we have

After the dilation the coordinates are (-4, 8).

All real numbers, with the exception of -6 , are the solution to a rational equation. The quotient of two polynomials is the definition of a rational expression.

\($\frac{(x-2)(x+6)}{7(x+6)}=\frac{x-2}{7} \quad: \quad x \neq-6$\)

\($\frac{(x-2)(x+6)}{7(x+6)}=\frac{x-2}{7}$\)

Simplify

\($\frac{(x-2)(x+6)}{7(x+6)}: \quad \frac{x-2}{7}$\)

\($\frac{x-2}{7}=\frac{x-2}{7}$\)

Seven times both sides

\($\frac{x-2}{7} \cdot 7=\frac{x-2}{7} \cdot 7$\)

Simplify

\($x-2=x-2$\)

There is equality between the two sides.

For every x Verify Solutions, true

Search for ill-defined (singularity) points: \($x=-6$\)

Because -6, the equation is undefined.

\(x \neq -6\)

Therefore the correct answer is option C ) All real numbers except -6 .

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Answer:

75 Kilometers

Step-by-step explanation:

We have been given that the distance between two towns is 120 km.

We are also told that there are approximately 8 km in 5 miles. Let us find number of miles per km by dividing 5 by 8.

\text{Number of miles in 1 km}=\frac{5\text{ miles}}{\text{8 Km}}

\text{Number of miles in 1 km}=0.625\frac{\text{ miles}}{\text{ Km}}

Therefore, there are 0.625 miles in 1 km.

To convert our given distance into miles we will multiply our given distance by number of miles in 1 km.

\text{Number of miles in 120 km}=120\text{ km}\times \frac{0.625\text{ miles}}{\text{ km}}

\text{Number of miles in 120 km}=120\times 0.625\text{ miles}

\text{Number of miles in 120 km}=75\text{ miles}

Therefore, the distance between two towns is 75 miles.

Answer:

The answer is 75, I had this question a few days ago and I got it right

Answer:75

Answer:

What do you mean

Step-by-step explanation:

Answer:

x=72

y=54

Step-by-step explanation:

1st question. y=54 because it is a bisector of the 108 degree angles. (a polygon's interior angles add to number of sides minus 2 times 180)

There are two ys, so they add up to 108. A triangle's interior angles add to 180. 180-108 =72 x=72

2nd question, x is 72 ( it says x is the same measure) so 180-72=2y.

y still equals 54

Answer:

this is so easy

Step-by-step explanation:

3000* (15) (300) divided by 20 x 60 100ft  divided by 40