Find the sum of the first 6 terms of the following sequence. Round to the
nearest hundredth if
necessary.
12,
4
3
Sum of a finite geometric series:
Sn =
-
1-r

Lenght of Tsing Ma Bridge in Hong Kong is, 1,377 meters

Given that;

The Mackinac Bridge in Michigan is 1158 meters long.

And,  The Tsing Ma Bridge in Hong Kong is 97 meters longer than the Golden Gate Bridge in California.

Let the length of Golden Gate Bridge = x

Then, Lenght of Tsing Ma Bridge in Hong Kong = x + 97

Since, Together, all three bridges have a length of 3815 meters.

Hence, We get;

1158 + x + (x + 97) = 3815

1255 + 2x = 3815

2x = 2,560

x = 1,280 meters

Thus, Lenght of Tsing Ma Bridge in Hong Kong = x + 97

                                                                         = 1280 + 97

                                                                        = 1,377 meters

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The total amount paid to harry in past week, is 299.28.

We know that,

Amount is the sum or the total value.

For example, if A purchase 2 kg rice at the price of 40 rs/kg, the amount will be 40×2= 80 rs.

Given that,

The amount paid to Harry for 1 hour = $8.60

Since, Harry worked for 33 hours,

So, The amount paid to Harry for 33 hours = 8.60×33=283.8

Harry gets half times more amount than hourly rate and also gets bonus for last 3 days

So for last 3 days the extra amount paid to Harry

= 3×1/2×8.60+3×1/10×8.60

= 12.9+2.58

=15.48

So the total amount paid to harry = 283.8+15.48=299.28

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complete question:

Harry is paid £8.60 per hour for the first 30 hours he works each week. After 30 hours he is paid 1 and a half times the hourly rate.

Last week Harry worked 33 hours. He was also paid a bonus of 1/10 of his earnings

Calculate how much in total Harry was paid last week

Answer:

There is nothing to write about my brother

Step-by-step explanation:

There is a scientific notation moment when shrek had to hit the griddy and said "i said right foot creep"

An experience that I had outside the academia was when I worked as a marketing coordinator for a small start-up company.

A product launch event had been planned by the team for several weeks, and everything appeared to be going according to plan. However, we learned the day before the event that our keynote speaker, who was an important component of it, had unexpectedly become unwell and would not be able to attend.

I had to evaluate the situation as the marketing coordinator and decide right away. Either we could cancel the event or we could locate a another speaker.

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a) From Carmen's results, the experimental probability of landing on black is given as follows: 6/25.

b) The theoretical probability of landing on black is given as follows: 1/5.

c) The correct statement is the second statement, as the number of trials increases, the two probabilities get closer.

A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.

In 25 trials, 6 resulted in black, hence the experimental probability is given as follows:

p = 6/25.

Two out of 10 regions of the spinner are black, hence the theoretical probability is given as follows:

p = 2/10 = 1/5.

The problem is given by the image presented at the end of the answer.

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The transformations of the given functions is vertical shift 2 units down.

Given that, the function is f(x)=-eˣ to f(x)=-eˣ-2.

To find the transformation, compare the function to the parent function and check to see if there is a horizontal or vertical shift, reflection about the x-axis or y-axis, and if there is a vertical stretch.

Parent Function: f(x)= −eˣ

Horizontal Shift: None

Vertical Shift: Down 2 Units

Reflection about the x-axis: None

Vertical Compression or Stretch: None

Therefore, the transformations of the given functions is vertical shift 2 units down.

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The required maximum value of C is 16, and it occurs when x = 3 and y = 2.

To find the maximum value of C = 4x + 2y subject to the restraints x > 2, x < 5, y > 1, and y < 6, we can use the method of Lagrange multipliers.

First, we set up the Lagrangian function L as follows:

L = 4x + 2y - λ₁(x - 2) - λ₂(x - 5) - λ₃(y - 1) - λ₄(y - 6)

where λ1, λ2, λ3, and λ4 are Lagrange multipliers.

Next, we take the partial derivatives of L with respect to x, y, λ1, λ2, λ3, and λ4, and set them equal to zero:

∂L/∂x = 4 - λ₁ - λ₂ = 0

∂L/∂y = 2 - λ₃ - λ = 0

∂L/∂λ₁ = x - 2 = 0

∂L/∂λ₁ = 5 - x = 0

∂L/∂λ₃ = y - 1 = 0

∂L/∂λ₄ = 6 - y = 0

Solving these equations simultaneously, we get:

λ₁ = 1, λ₂ = 3, λ₃ = 1, λ₄ = 1, x = 3, y = 2

Therefore, the maximum value of C is:

C = 4x + 2y = 4(3) + 2(2) = 16

So, the maximum value of C is 16, and it occurs when x = 3 and y = 2.

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Answer: the real zero of this equation is 5/3.

The solution of the equation is x=0.08813 or 3.90664.

We have,

2x² / 3  + 9[tex]x^{1/3[/tex] = -4

Now, solving the equation for x

2x² + 27[tex]x^{1/3[/tex] = -12

Now, taking cube on both side we get

(2x² + 27[tex]x^{1/3[/tex] )³= -12³

Now, simplifying we get

19683x = -1728 -864x² -144[tex]x^4[/tex]-8[tex]x^6[/tex]

So, x=0.08813 or 3.90664

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The amount it would cost to put a new floor in the closet is $76.00

From the question, we are to calculate how much it would cost to put a new floor in the closet

From the given information,

A closet in the house is 2 yards by 1 yard.

To determine how much it would cost to put a new floor in the closet,

First,

We calculate the area of the closet

Area of the closet = 2 yard × 1 yard

Area of the closet = 2 square yards

Now,

From the given information,

The flooring costs $38.00 per square yard

Thus,

The amount it would cost to put a new floor in the closet is

2 × $38.00

= $76.00

Hence,

The amount it would cost is $76.00

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The 95% confidence interval for the mean is [3.23, 8.76].

The confidence of interval of the mean is calculated as follows;

Confidence interval = σ ± (t-value  x   μ)

where;

The standard error is calculated as follows:

μ = std / √n

μ = 5 / √15

μ = 1.29

Based on this value we will check the distrbution table, for the t-value of 95% confidence;

=  2.145.

Confidence interval = σ ± (t-value  x   μ)

= 6 ± (2.145 x 1.29)

= [3.23, 8.76]

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1560 g.

To convert 1.56 kg to g, we can use the conversion factor 1 kg = 1000 g:

1.56 kg = 1.56 x 1000 g = 1560 g

Therefore, the answer is 1560 g.

Answer: Y = 6.5

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

If the standard error is 33.64, the size of the margin of error at 95% confidence is 65.93. So, correct option is D.

The margin of error (ME) can be calculated using the formula:

ME = z* (standard error)

where z is the z-score from the standard normal distribution corresponding to the desired level of confidence. For 95% confidence, z is 1.96.

Substituting the values given in the problem, we have:

ME = 1.96 * 33.64 = 65.93

Therefore, correct option is D.

This means that if we take multiple random samples of size 121 from the population, and calculate the sample mean and confidence interval for each sample, we can expect the true population mean to fall within 65.93 units above or below the sample mean, 95% of the time.

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The Area of Maria's canvas is 30 ft.

Area of Maria's canvas, we need to know the length of the other side of the rectangle. We can use the Pythagorean theorem to find this length. Let's call it SA.

According to the problem statement, the base edge ST measures 4 ft, and the diagonal AT measures 8.5 ft. Using the Pythagorean theorem, we have:

[tex]AT^2 = ST^2 + SA^2\\8.5^2 = 4^2 + SA^2\\72.25 = 16 + SA^2\\56.25 = SA^2\\SA = \sqrt{56.25}\\SA = 7.5\ ft[/tex]

Now we know that the length of the canvas is 7.5 ft, and the width is 4 ft. Therefore, the area of Maria's canvas is:

Area = length x width

Area = 7.5 ft x 4 ft

Area = 30 square feet

Therefore, the area of Maria's canvas is 30 square feet.

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Answer:

m = 476

Step-by-step explanation:

m + 310 = 786

(Subtract 310 from both sides.)

m = 786 - 310

(Subtract 310 from 786 to get 476)

m = 476

Answer:

  30.0 ft

Step-by-step explanation:

You want the length of a pole whose shadow is 20 ft long when the angle of elevation of the sun is 62° and the pole is tilted 8° away from the sun.

Referring to the attached diagram, we see that the interior angle at B of triangle ABC is 90° -8° = 82°. This makes the interior angle at A ...

  A = 180° -82° -62° = 36°

The law of sines tells us side lengths are proportional to the sines of the opposite angles:

  c/sin(C) = a/sin(A)

  c = a×sin(C)/sin(A) = 20×sin(62°)/sin(36°) ≈ 30.043 . . . feet

The length of the pole is about 30.0 feet.

Answer:

  C. 10

Step-by-step explanation:

You want to know the bin size in a histogram with bin boundaries 10.5, 20.5, 30.5, ....

The size of the bin is the difference between its boundary values. Here, all of the bins are the same size:

  20.5 -10.5 = 10

The bin size is 10.

__

Additional comment

The bin boundaries are typically chosen so that no data value can fall on the boundary, but must be unambiguously allocated to one bin or another. When the data values are integers, it is not uncommon to have the bin boundary be halfway between two integers.

Here, the boundary being 20.5 means a score of 20 will be counted in the bin to the left, and 21 will be counted in the bin to the right.

The boundary value shown at the right edge of the graph is not 100.5, as we might expect. However, we can reasonably assume that a test score of 100 would be counted in the bin with upper boundary 100, without any ambiguity.

Answer: 10

Step-by-step explanation:

The size of each value marker

Answer:

632.83mm²

Step-by-step explanation:

Applying Pythagorean theorem to triangle SOH

SH² = SO² + OH²

SH = [tex]\sqrt{(15.4)^2+(7.2)^2}=17mm[/tex]

Since the base of the pyramid is a regular pentagon, angle OAH
is 108°/2 = 54°.

AH = 7.2/tan 54° = 5.23mm

So AB = 2AH = 10.46mm

The area of triangle SAB is:

A1 = 1/2 × SH × AB = 1/2 × 17 × 10.46 = 88.91mm²

The area of all triangles is

A2 = 5 × A1 = 5 × 88.91 = 444.55mm²

The area of the base is:

A3 = (perimeter × apothem)/2 = (5 × 10.46 × 7.2)/2 = 188.28mm²

The surface area of the pyramid is:

A2 + A3 = 444.55 + 188.28 = 632.83mm²

Step-by-step explanation:

the surface area is the sum of the base area (pentagon) and the 5 side triangles (we only need to calculate one and then multiply by 5, as they are all equal).

these side triangles are isoceles triangles (the legs are equally long).

the usual area formula for a pentagon is

1/2 × perimeter × apothem

the apothem is the minimum distance from the center of the pentagon to each of its sides.

in our case this is 7.2 mm.

how to get the perimeter or the length of an individual side of the pentagon ?

if the apothem of a pentagon is given, the side length can be calculated with the formula

side length = 2 × apothem length × tan(180/n)

where 'n' is the number of sides (5 in our case). After getting the side length, the perimeter of the pentagon can be calculated with the formula

perimeter = 5 × side length.

so, in our case

side length = 2 × 7.2 × tan(180/5) = 14.4 × tan(36) =

= 10.4622124... mm

perimeter = 5 × 10.4622124... = 52.31106202... mm

area of the pentagon = 1/2 × perimeter × apothem =

= 1/2 × 52.31106202... × 7.2 = 188.3198233... mm²

now for the side triangles.

the area of such a triangle is

1/2 × baseline × height

baseline = pentagon side length

height we get via Pythagoras from the inner pyramid height and the apothem :

height² = 7.2² + 15.4² = 51.84 + 273.16 = 289

height = 17 mm

area of one side triangle =

1/2 × 10.4622124... × 17 = 88.92880543... mm²

all 5 side triangles are then

444.6440271... mm²

and the total surface area is then

444.6440271... + 188.3198233... = 632.9638504... mm²

≈ 632.96 mm²

There is enough data to indicate that Jordanian children are at risk of anemia.

The null hypothesis is that the true mean hemoglobin level for Jordanian children is greater than or equal to 12 g/dl, and the alternative hypothesis is that it is less than 12 g/dl.

Using the P-value method:

The test statistic for the one-sample t-test is given by:

t = (x - μ) / (s / √n)

where x is the sample mean, μ is the population means (here, μ = 12), s is the sample standard deviation, and n is the sample size.

Substitute the given values,

t = (11.3 - 12) / (1.6 / √50) = -2.98

Using a t-distribution table with 49 degrees of freedom (df = n - 1), find that the p-value for this test is approximately 0.002.

Since the p-value is less than the significance level of α = 0.05, we reject the null hypothesis and conclude that there is sufficient evidence to support the claim that Jordanian children are at risk of anemia.

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Step-by-step explanation:

5 000 gm = 5 kg

784kg  - 5kg=  779 kg  more than average

Answer:

Step-by-step explanation:

To create a magic square with -6,-5,-4,-3,-2,-1,1,2, we need to arrange these numbers in a 3x3 grid such that each row, column, and diagonal add up to the same sum.

Here's one possible solution:

diff

Copy code

-6 1 2

-4 -5 9

8 -3 -2

To check if this is a magic square, we can calculate the sum of each row, column, and diagonal:

Rows:

(-6 + 1 + 2) = -3

(-4 - 5 + 9) = 0

(8 - 3 - 2) = 3

Columns:

(-6 - 4 + 8) = -2

(1 - 5 - 3) = -7

(2 + 9 - 2) = 9

Diagonals:

(-6 - 5 - 2) = -13

(2 - 5 + 8) = 5

All of these sums are equal to 0, so this is indeed a magic square.

Answer:

3 years

Step-by-step explanation:

1. Find 5 percent of 50.

5 percent of 50 is 2.5.

However, we are talking about money so we will say 2.50.

2. Add to 50 until you reach your desired number.

50 + 2.50 = 52.50

52.50 +2.50 = 55

55+2.50 = 57.50

Finally we have reached 57.50. It took us 3 equations to get there and therefore took 3 years.

Below are the true and false results for the number sentence;

1. 6x = 48 when x = 6 is false

2. 6x = 48 when x = 8 is True

3. x/2 ≥ 3 when x = 6 is True

4. x/2 ≥ 3 when x = 8 is True

5. x < 8 when x = 6 is true

6. x < 8 when x = 8 is False

7. 5x ≤ 30 when x = 6 is True

8. 5x ≤ 30 when x = 8 is False

The solution to the number sentence are;

1. 6 x 6 = 36, not 48.

2. 6 x 8 = 48

3. 6/2 = 3. therefore it fits the equal or greater sign

4. 8/2 = 4. it fits the greater or equal sign

5. if x is 6, 6 is less than 8. which makes the number sentence true

6. if x is 8, it is therefore not less than 8 but equal.

7. 5 x 6 is 30. Therefore 30 is not less than 30 but equal

8. 5 x 8 is 48. 48 is not less than or equal to 30

The answers provided are in reference to the questions below;

In each row of the table, select True or false if the number substituted for x results in a true or false number sentence

                                                            True                     False

6x = 48 when x = 6

6x = 48 when x = 8

x/2 ≥ 3 when x = 6

x/2 ≥ 3 when x = 8

x < 8 when x = 6

x < 8 when x = 8

5x < 30 when x = 6

5x < 30 when x = 8

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The profession that would earn that amount more than a bank teller is Office Clerk.

The profession that would earn $1,151,700 in 30 years is Bookkeeper.

The profession that will earn  $828,600 over a 20-year career is Truck Driver.

The profession that earns $136,200 more than a fire fighter over a period of 30 years is Electrician

The 15 year difference between bank teller and office clerk is:

= ( 30, 850 x 15 ) - ( 27, 260 x 15 )

= $ 53, 850

The earnings of a Bookkeeper in 30 years is:

= 38, 390 x 30

= $ 1, 151, 700

The earnings of a Truck driver in 20 years is :

= 41, 430 x 20

= $ 828, 600

The difference between earnings of Fire fighter and Electrician over 30 years is:

= ( 52, 570 x 30 ) - ( 48, 030 x 30 )

= $ 136, 200

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Comparing the percent of water, we can see that Tristan's mix has a higher percent of water, which means it will be more watery so  Tristan's mix will be more watery than Yaritza's mix.

To determine whose mix will be more watery, we need to compare the percent of water in each mix.

The higher the percent of water, the more watery the mix will be.

Tristan's mix has a total of 7 + 3 = 10 cups of liquid

The percent of water in Tristan's mix is: (7 cups of water / 10 cups of liquid) x 100% = 70%

Yaritza's mix has a total of 2 + 1 = 3 cups of liquid (water + powdered lemon mix).

The percent of water in Yaritza's mix is: (2 cups of water / 3 cups of liquid) x 100% = 66.7%

Comparing the percent of water, we can see that Tristan's mix has a higher percent of water, which means it will be more watery.

Therefore, Tristan's mix will be more watery than Yaritza's mix.

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Answer:

[tex]y = \frac{ - 1}{2} *\sqrt{x-1} - 5[/tex]

Step-by-step explanation:

The standard equation of a square root function with vertex at point (h,k) is given by:

[tex]y = a \times \sqrt{x - h} + k[/tex]

where (h,k) is the vertex and "a" is a coefficient that determines the vertical stretch and direction of the square root function.

We know that the vertex of our square root function is (1, -5), so we can substitute those values into the equation to get:

y = [tex] a*\sqrt{x-1} - 5[/tex]

Now, we need to find the value of "a". To do that, we will use the fact that the square root function passes through point (5, -7). Substituting these coordinates into the equation, we get:

[tex]-7 = a*\sqrt(5-1) - 5[/tex]

-2 = 4a

[tex]a = \frac{ - 1}{2} [/tex]

Now that we know the value of "a", we can substitute it into our equation to get the final equation of the square root function:

[tex]y = \frac{ - 1}{2} *\sqrt{x-1} - 5[/tex]

Therefore, the equation of the square root function with a vertex at (1, -5) and passing through (5, -7) is

[tex]y = \frac{ - 1}{2} *\sqrt{x-1} - 5[/tex]

Answer:

[tex]f(x) = -\sqrt{x-1} - 5[/tex]

Step-by-step explanation:

The standard form of a square root function is:

[tex]f(x)=a\sqrt{x-h}+k[/tex]

where "a" is a scaling factor determining the vertical stretch or compression of the function, and (h, k) is the vertex.

Given the vertex is (1, -5), substitute h = 1 and k = -5 into the equation:

[tex]f(x) = a\sqrt{x - 1} - 5[/tex]

Substitute the point (5, -7) that the function passes through to find the stretch factor "a":

[tex]\begin{aligned}-7 &= a \sqrt{5 - 1} - 5\\-7 &= a \sqrt{4} - 5\\-7 &= 2a - 5\\-7 +5&= 2a - 5+5\\-2&= 2a\\\dfrac{-2}{2}&=\dfrac{2a}{2}\\-1&=a\\a &= -1\end{aligned}[/tex]

Substitute the value of "a" back into the equation:

[tex]f(x) = -\sqrt{x-1} - 5[/tex]

Therefore, the equation of the square root function with a vertex at (1, -5) and passes through the point (5, -7) is:

[tex]\boxed{f(x) = -\sqrt{x-1} - 5}[/tex]