Find the sum of the first 36 terms of the following series, to the nearest integer. 9,12,15

Answer:

6887

Step-by-step explanation:

given

x + \(\frac{1}{x}\) = 83 ( square both sides )

(x + \(\frac{1}{x}\) )² = 83² = 6889 ← expand factor on left using FOIL

x² + 2( x × \(\frac{1}{x}\) ) + \(\frac{1}{x^2}\) = 6889

x² + 2(1) + \(\frac{1}{x^2}\) = 6889 ( subtract 2 from both sides )

x² + \(\frac{1}{x^2}\) = 6887

Answer:

She spends 2 hours driving.

Step-by-step explanation:

The formula given is:

\(d = rt\)

In which d is the distance traveled, r is the rate of speed, and t is the amount of time spent traveling.

Grace drives her truck a distance of 80 miles at a steady speed of 50 miles per hour.

This means that \(d = 80, r = 50\)

To the nearest hour, how many hours does she spend driving?

We have to find t. So

\(d = rt\)

\(50t = 80\)

\(t = \frac{80}{50}\)

\(t = 1.6\)

Rounding to the nearest hour

She spends 2 hours driving.

You need to multiply by 5 instead of 6 because each pair of opposite faces on a cuboid has the same area, so by considering one face from each pair, you ensure that you don't count any face twice.

When calculating the total surface area of a cuboid, you need to understand the concept of face pairs.

A cuboid has six faces, but each face has a pair that is identical in size and shape.

Let's break down the reasoning behind multiplying by 5 instead of 6 in the given scenario.

To find the surface area of a cuboid, you can add up the areas of all its faces.

However, each pair of opposite faces has the same area, so you avoid double-counting by only considering one face from each pair. In this case, you have five pairs of faces:

(1) top and bottom, (2) front and back, (3) left and right, (4) left and back, and (5) right and front.

By multiplying the average area of a pair of faces by 5, you account for all the distinct face pairs.

Essentially, you are considering one face from each pair and then summing their areas.

Since all the pairs have the same area, multiplying the average area by 5 gives you the total surface area.

When dividing 150 by 4 (to find the average area of a pair of faces), you are essentially finding the area of a single face.

Then, by multiplying this average area by 5, you ensure that you account for all five pairs of faces, providing the total surface area of the cuboid.

Thus, multiplying by 5 is necessary to correctly calculate the total surface area of the cuboid by accounting for the face pairs while avoiding double-counting.

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Answer

=12/13

Step-by-step explanation:

I have done it before:)

The coordinates of the vertices for the image of the pre image is translated 4 units right are: ’(-1, 2), B’(5, 3), and C’(1, 0).

Translation on the coordinate plane is sliding a point or figure in any direction without any changes in size or shape.

During translation, the coordinates of the vertices of a figure or point change, and they slide left or right, up, or down without changing size or shape.

Given the question above, we need to find the coordinates of the vertices for the image of the pre image that are translated 4 units right.

So,

\(\rightarrow\sf \boxed{\boxed{-5+4=1=\bold{(-1,2)}}}\)

\(\rightarrow\sf \boxed{\boxed{1+4=5=\bold{(5,3)}}}\)

\(\rightarrow\sf \boxed{\boxed{-3+4=1=\bold{(1,0)}}}\)

Thus, the coordinates of the vertices for the image of the pre image is translated 4 units right are: ’(-1, 2), B’(5, 3), and C’(1, 0).

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The 3-year-old boy is more unusually tall for his age and gender than the 10-year-old girl.

A z-score calculates how many standard deviations an observation is from the mean. An observation is said to be above the mean if the z-score is positive, while it is said to be below the mean if the z-score is negative.

For the 3-year-old boy, the z-score is:

z = (43 - 38) / 2 = 2.5

The z-score for the 10-year-old girl is:

z = (57 - 54.5) / 2.5 = 1

The 3-year-old boy has a higher z-score than the 10-year-old girl, indicating that he is more unusually tall for his age and gender. This is due to his height, which is higher than the average for his age group 38 inches .

Therefore, the 3-year-old boy is more unusually tall for his age and gender than the 10-year-old girl.

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Answer:

The other leg is 4 m long, and the hypotenuse is 5 m long

Step-by-step explanation:

Recall that the longest side of a right angle triangle is its hypotenuse, and that the legs and hypotenuse must verify the Pythagorean identity:

\(hyp^2=leg_1^2+leg_2^2\)

so, we know that the other two sides have consecutive integers for lengths. That is: if one is "x" in length, the other one must be "x+1"

So we can assume that the largest of this is the hypotenuse: "x+1"

Not, they must verify the Pythagorean identity:

\(hyp^2=leg_1^2+leg_2^2\\(x+1)^2=x^2+3^2\\x^2+2\,x+1=x^2+9\\2\,x+1=9\\2\,x=8\\x = 4\)

then, the other side is of length 4 m, and finally the hypotenuse is of length 4+1 = 5 m

There is no change in its slope as initial and final slope is 1.

What is slope?

In arithmetic, the slope or gradient of a line may be a variety that describes each the direction and therefore the abruptness of the line.

Main body:

formula for slope with two points form is =

y -y₁ =( y₂-y₁ /x₂-x₁ )(x - x₁)

according to question ,

points are (0,0) and (3,3)

y - 0 = (3-0/3-0)(x -0)

y = 3/3 *x

y = x

hence slope of line is 1.

Now points are (0,0) and (-3,-3).

y - 0 = (-3-0/-3-0)(x -0)

y =- 3/-3 *x

y = x

hence slope of line is 1.

So there is no change in its slope.

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Answer:

Dakota has 94 books, while Darius has 144.

Step-by-step explanation:

Given that Darius and Dakota are roommates, and together they have 238 books, if Darius has 50 more books than Dakota, to determine how many books does Dakota have the following calculation must be performed:

Dakota = X

Darius = X + 50

X + X + 50 = 238

2X + 50 = 238

2X = 238 - 50

X = 188/2

X = 94

Therefore, Dakota has 94 books, while Darius has 144.

DVD = $23.99

Sales tax = (23.99 x 0.07)

= 1,679 = $1.68

Answer:

Step-by-step explanation:

sp = 504

gain = 12%

in this case

sp =100%+12%=504

112%=504

1%=504/112 =4.5

100%=450

so cost =$450

Hope im correct, if i am im glad to be of service.

Answer: 0.701

Step-by-step explanation:

Formula :  \(EBM =z_{\alpha/2}\dfrac{\sigma}{\sqrt{n}}\) , where \(\alpha=\) significance level , \(\sigma =\) Population standard deviation, n= sample size.

As per given,  n= 22

\(\sigma = 2\)

Critical z- value for 90% confidence level : \(z_{\alpha/2}=1.645\)

Then,

 \(EBM =(1.645)\dfrac{2}{\sqrt{22}}\\\\=(1.645)\dfrac{2}{4.690416}\\\\\approx0.701\)

Hence ,  error bound (EBM) of the confidence interval with a 90% confidence level= ± 0.701

The probability of the area hit by the dart between the bigger square and the smaller square is equal to 0.7656.

As given in the question,

Total number of squares present = 2

Side length of the bigger square = 16 units

Side length of the smaller square = 14 units

Area of the bigger square = ( side length )²

                                           = ( 16 )²

                                           = 256 square units

Area of the smaller square = ( side length )²

                                           = ( 14 )²

                                           = 196 square units

Here favorable outcome is represented by small square and total outcome is represented by bigger square

Probability that the given dart hit the area between the square is

= 196 / 256

= 49/64

= 0.765625

≈ 0.7656

Therefore, the probability of the dart hitting the area formed by bigger square and smaller square is equal to 0.7656.

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Answer:

Step-by-step explanation:

For step explanation:

1. write the problem

2. distinguishing the neg sign

3. distributing 3

4. moving like terms next to each other through commutative property

5.  Combining like terms

6. getting rid of parentheses

The surface area of the cylinder is 408 square meters.

What is a cylinder?

In mathematics, a cylinder is a three-dimensional solid that maintains two parallel bases divided by a curved surface at a specific distance. The bases frequently have circular shapes, and an axis connects the centres of each base.

We know that surface area of a cylinder is given by the formula

Area (A) = 2πrh + 2πr²

We are given that the radius (r) is 5 meters and the height (h) is 8 meters.

So, on substituting the values, we get

⇒ Area of cylinder = (2 * 3.14 * 5 * 8) + (2 * 3.14 * 5 * 5)

⇒ Area of cylinder = 251.2 + 157

⇒ Area of cylinder = 408.2 square meters

⇒ Area of cylinder = 408 square meters

Hence, the surface area of the cylinder is 408 square meters.

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Answer:

Theory : A difference of two perfect squares,  A2 - B2  can be factored into  (A+B) • (A-B)

Proof :  (A+B) • (A-B) =

        A2 - AB + BA - B2 =

        A2 - AB + AB - B2 =

        A2 - B2

Note :  AB = BA is the commutative property of multiplication.

Note :  - AB + AB equals zero and is therefore eliminated from the expression.

Check :  1  is the square of  1  

Check :  c1   is not a square !!

Ruling : Binomial can not be factored as the difference of two perfect squares]

cos^2x=0

Step-by-step explanation:

The ratio 81:108 can be simplified to 9:13. To find the simplest form of the ratio, you can divide both numbers by the greatest common factor. The greatest common factor of 81 and 108 is 9, so you can divide both numbers by 9 to get the simplified ratio of 9:13.

The central angles for each category are approximately: Red: 100°, Blue: 150°, Green: 50° and Purple: 60°

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

To find the central angle of each category, we first need to calculate the total number of people:

Total = 20 + 30 + 10 + 12 = 72

Next, we can calculate the percentage of people who prefer each color:

Red: 20/72 = 0.278, or 27.8%

Blue: 30/72 = 0.417, or 41.7%

Green: 10/72 = 0.139, or 13.9%

Purple: 12/72 = 0.167, or 16.7%

To find the central angle for each category, we can multiply the percentage by 360°:

Red: 0.278 × 360° = 100.08°

Blue: 0.417 × 360° = 150.12°

Green: 0.139 × 360° = 50.04°

Purple: 0.167 × 360° = 60.48°

Therefore, the central angles for each category are approximately:

Red: 100°, Blue: 150°, Green: 50° and Purple: 60°

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The correct answers are 1st and 4th i.e translate 2 units down and reflect the triangle.

We can easily deduce that the triangle A'B'C' is 2 units higher than the triangle ABC so if we want to map the both the triangles we have to make the triangle A'B'C' lower in the graph.

So, both the 1st and 4th points translate and reflect down the triangle A'B'C'  which will be mapped according to the triangle ABC.

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Answer: Hi! All of the answers and work are below. Please double check on your work just to make sure. Hope this helped! :)

Step-by-step explanation:

attached below :)

Answer:

3) D = 11.99

4) A = 113.09

5) C = 7.53

6) C = 53.40

7) A = 113.09

Step-by-step explanation:

3) D = C ÷ π

D = (37.68) ÷ π

D = 11.9

4) R = D ÷ 2

R = (12) ÷ 2 = 6

A = πr^2

A = π 6^2

A = 113.09

5) C = 2πr

C = 2π (1.2)

C = 7.53

6) R = D ÷ 2

R = (17) ÷ 2

R = 8.5

C = 2πr

C = 2π (8.5)

C = 53.40

7) A = πr^2

A = π 6^ 2

A = 113.09

Then, multiply this result by 100 to get the percentage. In this case, 120 is 80% of 150.

To use a double number line diagram to find what percent 120 is of 150, you need to create a diagram with two parallel lines. On the top line, mark 150 at one end and 100 at the other.

On the bottom line, mark 120 at one end and leave the other end blank. Then, draw diagonal lines connecting 120 on the bottom line to 150 on the top line and 100 on the top line to the blank end of the bottom line.

This creates two triangles. The height of the triangle with 120 is the percentage you're looking for.

To find this percentage, divide the length of the diagonal line connecting 120 and 150 by the length of the diagonal line connecting 100 and the blank end of the bottom line.

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Answer:

y = 3/2 x +1

For 20 hours is 31

Explanation:

The equation of a line with slope m and y-intercept b is

The two points that lie on the line of best fit are (6, 10) and (4, 7); therefore, the slope is

Therefore, our equation becomes

The y-intercept is found by putting in x = 4 and y = 7 in the equation

Solving for b gives

Hence the equation of the line is

With the equation of the line in hand, we now find the amount of money earned with 20 hours of babysitting.

Hence, the answers are

y = 3/2 x +1

For 20 hours is 31

Answer:

Your welcome

Step-by-step explanation:

Answer:

6 paintings

Step-by-step explanation:

so it would be 1,290/215 = 6

Answer:

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

C

Answer:

63 42

53

53

52

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By using property - 1,

m∠APD = m∠DPC = m∠BPC = m∠APB = 90°

Apply triangle sum theorem in ΔAPD,

m∠DAP + m∠APD + m∠DPA = 180°

52° + 90°+ m∠DPA = 180°

m∠DPA = 38°

By using property - 3,

m∠PDC = m∠DPA = 38°

m∠PAB = 52°

By using property - 2,

m∠ADC + m∠DCB = 180°

2(38°) + m∠DCB = 180°

m∠DCB = 104°

Therefore, m∠PCD = m∠PCB = \(\frac{104}{2}\) = 52°

m∠DAP = m∠BAP = 52°

Since, m∠ADC = m∠ABC = 76°

Therefore, mABP = m∠CBP = \(\frac{76}{2}=38^\circ\)

         Hence, m∠APD = m∠DPC = m∠BPC = m∠APB = 90°, m∠DPA = 38°, m∠PAB = 52°, m∠PCD = m∠PCB = 52°, m∠BAP = 52°, mABP = m∠CBP = 38°.

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Step-by-step explanation:

\(sin(1 \div 4a + 20) = \sqrt{3} \div 2 \\ sin(1 \div 4a + 20) =sin 60\)

1÷4a+20=60

1÷4a=4

a=1/160

Standard Deviation

The standard deviation for a sample of size n is given by:

Where xi represents each value of the sample, x(bar) is the mean of all the values, and n is the number of values of the sample.

For the convertible models, the values are:

25, 25, 24, 21, 21, 21, 20

The mean value is:

The calculations involved in this formula are too long to display here, so we show the result:

Following the same procedure for the sport models:

The second standard deviation is:

Answer:

3) 3 3/4

Step-by-step explanation:

A counter-example to the given conclusion is the difference between the numbers 15 and 25, where both are positive, but the difference gives a negative result.

Here we are shown some differences between positive numbers:

7 - 3 = 4

8 - 5 = 3

9 - 8 = 1

And the conclusion is:

"The difference of two positive numbers is always positive".

To find a counter-example we just need to find two positive numbers such that the difference between these two positive numbers gives a negative number as a result.

An example of that can be the numbers 15 and 25, if we take the difference we will get:

15 - 25 = -10

Here we can see that the difference between two positive numbers gives a negative number as an outcome, so this is our counter-example.

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