The sum of the series below is 10,900. how many numbers, n, are in the series? 19 20.5 22 23.5 ... 181

hi

we have an aroithmetic serie of first term 1 and  pace  2

so sum of 12 first terms, namming  1 as  S1 and  12th term as  S12

S12 =  1 + 2*11 = 23

formula of summ :      number of term *  (  final term + first term) / 2

So sum of terms  from S1 +S12 =    12   ( S12 +S1 )  / 2  =  12 * ( 23+1) /2

12*  12=  144

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The value of x when y =2 is 8

The inverse proportion to the square of x represented as:

k = yx^2

Where

k represents the constant of proportion

When y = 2, x = 8.

So, we have:

k =2 * 8^2

k =128

Substitute k = 128 in k = yx^2

So, we have:

yx^2 = 128

When y = 2, we have:

2x^2 = 128

Divide by 2

x^2 = 64

Take the square roots

x = 8

Hence, the value of x when y =2 is 8

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Using the z-distribution, considering the standard 95% confidence level, the margin of error is of 0.0486 = 4.86%.

A confidence interval of proportions is given by:

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

The margin of error is:

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which:

In this problem, we have a 95% confidence level, hence[tex]\alpha = 0.95[/tex], z is the value of Z that has a p-value of [tex]\frac{1+0.95}{2} = 0.975[/tex], so the critical value is z = 1.96.

The sample size and the estimate are given by:

[tex]n = 350, \pi = \frac{240}{350} = 0.6857[/tex]

Hence the margin of error is:

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

[tex]M = 1.96\sqrt{\frac{0.6857(0.3143)}{350}}[/tex]

M = 0.0486 = 4.86%.

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Answer:

99% - 0.06

95% - 0.05

90% - 0.04

Step-by-step explanation: i got it right

The statement that is true about Sheila's savings plan is that; C.

Sheila must save $60 per month to achieve her goal.

The price of bathroom remodeling is $ 810.

After 13 months , she has saved $ 510

This means that she has a $300 shortage to cover in 5 months.

This means that she need to save :

$300/5  = $60 / month in order to achieve her goal

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Answer: C

Step-by-step explanation: edge

The width of the delivery box is 9 inches.

Given that  volume of delivery box is 756 cubic inches,length is 6 inches less than twice the width, height is 2 inches less than width.

let width be x

Length = 2x- 6

Height = x - 2

Width = x

We can find the value of x by putting values one by one and then we will be able to get the value of  x which is width.

Because the delivery box is cuboid in shape so the volume is equal to product of length,breadth and height.

When x=7: Volume=7 x (7 - 2) x (2x7 - 6) = 7 x 5 x 8 = 280

When x=9,Volume will be 9 x (9 - 2) x (2x9 - 6) = 9 x 7 x 12 = 756

Therefore, the width of the delivery box is 9 inches.

Hence the width of the delivery box is 9 inches.

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The algebraic equation to represent the given situation is as follows,

y = 4 + 2x

What is an algebraic equation?

The term "algebraic equation" refers to a formulation of the equality of two expressions using the algebraic operations of addition, subtraction, multiplication, division, raising to a power, and extraction of a root on a set of variables.

An expression that includes variables, constants, and algebraic operations is known as an algebraic expression in mathematics (addition, subtraction, etc.).

Forming the Algebraic Equation

Number of book present on the shelf initially = 4

It is given that 2 books are added per minute to the shelf.

If x is the number of minutes, then the books added will be 2x.

If y is the total number of books present on the shelf, then the algebraic equation is given as,

y = Number of books initially present on the shelf  + 2x

⇒ y = 4 + 2x

Thus, y = 4 + 2x is the required algebraic equation.

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Answer:

w = ±[tex]\sqrt{1/2}[/tex] or w= ±[tex]\sqrt{2}[/tex]

Step-by-step explanation:

if we say some variable y = w^2, we can rewrite the equation to:

2y^2 - 5y + 2 = 0

this can be factored into (2y-1)(y-2) = 0

putting w^2 back in the place of y, that's (2w^2 - 1)(w^2 - 2) = 0

The equation is a fourth degree polynomial, so there are four roots, or four values of w that will cause the equation to equal 0.

If 0 is multiplied by anything, the result is 0, so we set 2w^2 - 1 = 0 and solve for w, which is ±√1/2, then set w^2 - 2 = 0 to get w = ±√2 as our roots

the four solutions are ±√1/2 and ±√2

(because the positive counts as one solution and the negative another solution)

We find that the function that could be a stretch of the exponential decay is [tex]f(x) = 2\cdot \left(\frac{1}{6} \right)^{x}[/tex]. (Correct choice: C)

Exponential functions are trascedent functions whose form is described below:

[tex]y = a\cdot r^{x}[/tex]     (1)

Where:

There are two conditions for a stretch factor and exponential decay: (i) a > 1, (ii) 0 < r < 1. Thus, we find that the function that could be a stretch of the exponential decay is [tex]f(x) = 2\cdot \left(\frac{1}{6} \right)^{x}[/tex]. (Correct choice: C)

The picture is missing and it cannot be found, but statement is still solvable as there is only one choice that responds the question.

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Answer: -7/5

​

Step-by-step explanation:

x = - 5cm^2 - 7m^2 + 35/ m (5c - 7), C = (cross out the equal sign) 7/5 and m = (cross out the equal sign) 0 and n = -7/5

Can send helicopter 3 but not helicopter 1 and 2.

What is distance formula?

Consider two points (x1, y1) and (x2, y2) in the two-dimension, then the distance between these two points is given by,

[tex]d=\sqrt{(x2-x1)^2+(y2-y1)^2}[/tex]

We will solve given problem as shown below:

Let fire have coordinate F (-3,-5)

Let Helicopter 1 have coordinate H1(1,4)

Let Helicopter 2 have coordinate H2(-2,3)

Let Helicopter 1 have coordinate H3(4, -2)

A. Distance between helicopter 1 and fire

[tex]=\sqrt{(1-(-3))^2+(4-(-5))^2}[/tex]

[tex]=\sqrt{16+81}[/tex]

[tex]=\sqrt{97}=9.8[/tex]

No, cannot send helicopter 1

B. Distance between helicopter 2 and fire

[tex]=\sqrt{(-3-(-2))^2+(-5-3)^2}[/tex]

[tex]=\sqrt{1+64}[/tex]

[tex]=\sqrt{65}=8.06[/tex]

No, cannot send helicopter 2

Distance between helicopter 3 and fire

[tex]=\sqrt{(4-(-3))^2+(-2-(-5))^2}[/tex]

[tex]=\sqrt{49+9}[/tex]

[tex]=\sqrt{58}=7.6[/tex]

Yes, can send helicopter 3

Hence, can send helicopter 3 but not helicopter 1 and 2.

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Answer:

The first chose is correct

Step-by-step explanation:

You can see in the first picture that graphed both of the triangles and then I followed the directions.  It is very, very helpful if you have tracing paper.  You can trace the original and then translate it three up.  For the 90 rotation, put a small + on the origin of your tracing paper, then move the tracing paper one one turn on the plus sign.  That would be 90 degrees.

Answer:

Step-by-step explanation:

Givens

line: 5y + 2x =  10

point (-2 , 5)

Discussion and Solution

You have to rearrange the given line to get the slope. It isn't nice, but it's not impossible.

5y + 2x = 10                            Subtract 2x from both sides

5y + 2x - 2x = -2x + 10           Simplify

5y = - 2x + 10                          Divide by 5

5y/5 = -2x/5 + 10/5                 Simplify

y = -0.4x + 2            

So the new equation is going to have a slope of - 0.4

So far what you have is

y =  - 0.4x + b

Now use the point to find the y intercept. What you should be thinking about the point is that when x = -2 then y = 5. Substitute that into the new equation.

5 = -0.4*-2 + b

5 = 0.8 + b                                Subtract 0.8 from both sides

5 - 0.8 = 0.8 - 0.8 + b               Simplify

4.2 = b

Answer

y = -0.4x + 4.2

Answer:

2^-6

Step-by-step explanation:

(1/8)^2 = (2^-3)^2 = 2^-6

Let's see

seven eighths means 7/8

So

Forty two eighths

Answer:

x = 6

Step-by-step explanation:

35 - 2x = 23

35 - 23 - 2x = 0

35 - 23 = 2x

12 = 2x

x = 6

35- 2x = 23

Subtract 35 from both sides.

Subtract 35 from 23 to get −12.

Divide both sides by −2.

Divide −12 by −2 to get 6.

The total amount in the investment account is $3031.00

The given parameters are

Principal, P = $2800

Rate, r = 5.5%

Time = 18 months i.e. 1.5 years

The amount is then calculated as:

A = P + PRT

This gives

A = 2800 + 2800 * 5.5% * 1.5

Evaluate

A = 3031

Hence, the total amount in the investment account is $3031.00

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Answer:

the 50th percentile = 66

The 25th percentile = 35

The 75th percentile = 85

Step-by-step explanation:

 We have 11 numbers ,so we are dealing with an odd set of values.

Also ,we notice that the numbers are already in order.

then

the 50th percentile of the set  27, 34, 35, 48, 48, 66, 75, 85, 85, 96, 99

is the 6 number in the list [ 6 = (11+1)/2 ]

Which is 66.

The 25th percentile (the median) of the set 27, 34, 35, 48, 48

is the 3rd number [ 3 = (5+1/)2 ]

Which is 35.

The 75th percentile (the median) of the set 75, 85, 85, 96, 99

is the 3rd number [ 3 = (5+1/)2 ]

Which is 85.

The statement that correctly describes the horizontal asymptote of g(x) is:

Limit of g (x) as x approaches plus-or-minus infinity = 6, so g(x) has an asymptote at y = 6.

In this problem, the function is:

[tex]g(x) = \frac{42x^3 - 15}{7x^3 - 4x^2 - 3}[/tex]

The horizontal asymptote is given as follows:

[tex]y = \lim_{x \rightarrow \infty} g(x) = \lim_{x \rightarrow \infty} \frac{42x^3 - 15}{7x^3 - 4x^2 - 3} = \lim_{x \rightarrow \infty} \frac{42x^3}{7x^3} = \lim_{x \rightarrow \infty} 6 = 6[/tex]

Hence the correct statement is:

Limit of g (x) as x approaches plus-or-minus infinity = 6, so g(x) has an asymptote at y = 6.

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Answer:

y=6.72x^0.996x

Step-by-step explanation:

The possible values of the number of dollars in the original pile of money is on the interval (200, 440)

We are told that Jeri finds a pile of money with at least $200.

Now, let x be  the additional amount over the  original amount of $200.

The greater side of the  inequality will be expressed as;

Original  pile  =  (200 + x)

After  she gives away $80 and as such she has;  (120 + x)

And  she gives (1/3)  of  this away  which means she will have;

=  (1/3) (120 + x)

Thus, she  must  have  (2/3)  of this left

=  (2/3)(120 + x) = amount in her right pocket

The lesser  side of the inequality is expressed as;

(x + 200)  -  200   =   x

Thus, we now have  that;

2[120 + x ]/3  >  x

240 + 2x  >  3x

240 > 3x - 2x

240 > x

x < 240

Thus, we can conclude that the original  amount could be on the interval   (200, 440)

The possible values of the number of dollars in the original pile of money is on the interval (200, 440)

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Answer:

3rd option

Step-by-step explanation:

y is negative below the x- axis , that is for values of x in the interval

x > - 6 and x < 6

The amount of the galleys or the number of galleys.

If given the amount of galleons, you can find the amount of galleys by dividing the number of given galleons by 5.

If given the amount of galleys, you can find the amount of galleons by multiplying the number of given galleys by 5.

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The length of the diagonal and the shorter base are 17. 24 feet and 18. 7 feet long respectively.

The cosine rule is given as;

[tex]c = \sqrt{a^2 + b^2 - 2ab cos \alpha }[/tex]

c = length of the diagonal

a = base length = 22 feet

b = 7 feet

[tex]c = \sqrt{7^2 + 22^2 - 2 * 7 * 22 cos 40}[/tex]

[tex]c = \sqrt{533 - 308 * 0. 7660}[/tex]

[tex]c = \sqrt{533 - 235. 93}[/tex]

[tex]c = \sqrt{297. 072}[/tex]

[tex]c = 17. 24[/tex] feet

Using sine rule

[tex]\frac{a}{sin A } = \frac{c}{sin C}[/tex]

[tex]\frac{a}{sin 70} = \frac{17. 24}{sin 40}[/tex]

Cross multiply

[tex]a[/tex] × [tex]sin 60[/tex] = [tex]c[/tex] × [tex]sin 70[/tex]

[tex]a[/tex] × [tex]0. 8660[/tex] = [tex]17. 24[/tex] × [tex]0. 9397[/tex]

[tex]a = \frac{16. 20}{0. 8660}[/tex]

a = 18. 7 feet long

Thus, the length of the diagonal and the shorter base are 17. 24 feet and 18. 7 feet long respectively.

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The linear equation for the cost that the household spend in water is given by:

C(d) = 237d + 1200.

A linear function is modeled by:

y = mx + b

In which:

For this problem, the free usage of 1200 liters is the y-intercept, while the daily usage of 237 liters is slope. Hence the function for the amount the household spends in water in d days is given as follows:

C(d) = 237d + 1200.

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Answer:

0,5*0,5=0,25

Step-by-step explanation:

assuming a die of 6 faces

25

0,5 for < 4; 0,5 for < 3

Answer:

10 unit^2.

Step-by-step explanation:

The base of the triangle (CE)

= 6 - 2 = 4 units

The height = 5

Area = 1/2 * 4 * 5

= 10 unit^2.

Answer:

10

Step-by-step explanation:

area = hight ×base÷2

hight = 5-0

= 5

base = 6-2

= 4

area = 4×5÷2

=10

The expected value of the proposition which is the net expected outcome is; $20.89.

We are given that;

There is a deck of cards.

There are 3 kinds of cards that have value under 4 (or equal). These 3 cards are 2, 3, 4 and they are in total 4 * 3 = 12 cards.

The probability that we draw such a card = 12/52 = 0.23.

Thus, the probability that we do not draw such a card = 1 - 0.23 = 0.77.

Now, If we play the game once, we will get 0.23 of the times $208 and 0.77 of the times $35.

Thus, the net total expected outcome is: (0.23*208) - (0.77*35)

= $20.89.

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