What is the value of n?

Answer:

see explanation

Step-by-step explanation:

The n th term of an AP is

[tex]a_{n}[/tex] = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

(1)

Given a₁ = 5 and a₄ = [tex]\frac{9}{2}[/tex] , then

5 + 3d = [tex]\frac{9}{2}[/tex] ( subtract 5 from both sides )

3d = - [tex]\frac{1}{2}[/tex] ( divide both sides by 3 )

d = - [tex]\frac{1}{6}[/tex]

add - [tex]\frac{1}{6}[/tex] to each term

5,  [tex]\frac{29}{6}[/tex],  [tex]\frac{14}{3}[/tex],  [tex]\frac{9}{2}[/tex]

(2)

Given a₁ = - 4 and a₆ = 6, then

- 4 + 5d = 6 ( add 4 to both sides )

5d = 10 ( divide both sides by 5 )

d = 2

Add 2 to each term

- 4,  -2,  0,  2,  4,  6

(3)

Given a₂ = 38 and a₆ = - 22, then

a₁ + d = 38 → (1)

a₁ + 5d = - 22 → (2)

Subtract (1) from (2) term by term

4d = - 60 ( divide both sides by 4 )

d = - 15

Substitute d = - 15 into (1)

a₁ - 15  = 38 ( add 15 to both sides )

a₁ = 53

Thus

53,  38,  8,  - 7,  - 22

Answer: 6,247,000,000,000

Step-by-step explanation:

Here we have the number:

6.247x10^12 and we want to write this in standard form.

You can see that we have a 10^12, this means that we need to move the decimal dot 12 places to the right, if there is not a decimal to the right, we add a zero.

6.247x10^12 = 62.47x10^11 = 624.7x10^10 = 6,247x10^9 = 62,470x10^8 and so on.

eventually, the standard form is:

6.247x10^12 = 6,247,000,000,000

So we end with 12 digits after the six.

Answer:

Step-by-step explanation:

x + x + 2x = 80

4x =80

X = 20

Nick = 20

Paul = 20

Krutika = 40

Answer:

AB= 5 units

Image of coordinates is shown in the attachment.

Answer:

The 95% confidence interval (6.9, 8.2) they obtained means that "We are 95% confident that the population mean duration is between 6.9 and 8.2 days".

Option B from the complete Question.

Step-by-step explanation:

Confidence Interval for the population mean is basically an interval of range of values where the true population mean can be found with a certain level of confidence.

Mathematically,

Confidence Interval = (Sample mean) ± (Margin of error)

Margin of Error is the width of the confidence interval about the mean.

It is given mathematically as,

Margin of Error = (Critical value) × (standard Error of the mean)

Critical value will be obtained using the t-distribution if there is no information provided for the population standard deviation and it is obtained from the z-tables if the population standard deviation is known or the sample size is large enough that the sample properties can be approximated to be the same as the population properties.

Standard error of the mean = σₓ = (σ/√n)

σ = standard deviation of the sample

n = sample size

Confidence Interval = (Sample mean) ± [(Critical value) × (standard Error of the mean)]

So, the confidence interval (6.9, 8.2) obtained in the question means that "We are 95% confident that the population mean duration is between 6.9 and 8.2 days".

Hope this Helps!!!

Answer:

150 cans were thrown away

Step-by-step explanation:

If the weight of 10 aluminum cans=0.16 kilogram

Each can weighs=0.16 kilograms/10

=0.016kg per can

If the family threw away 2.4 kilogram of aluminum in a month,

How many cans did they throw away?

Total cans thrown away= Total kilogram of cans/each kilogram of cans

=2.4kg/0.016kg

=150 cans

150 cans were thrown away

Answer:

3

[tex]d\in R,\hspace{5}d\neq 0[/tex]

Step-by-step explanation:

You can solve for any variable. From the first equation, let's solve for c :

[tex]\frac{c+1}{d} =5\\\\c+1=5d\\\\c=5d-1[/tex]

Now, replace the value of c into the other equation:

[tex]\frac{30d}{2c+2} \\\\\frac{30d}{2(5d-1)+2} \\[/tex]

Using distributive property

[tex]\frac{30d}{10d-2+2} =\frac{30d}{10d} =3[/tex]

However, keep in mind that this is true for:

[tex]d\in R,\hspace{5}d\neq 0[/tex]

Answer:

3 3/5 or 18/5

Step-by-step explanation:

When we divide by fractions, we multiply by the reciprocal of the fraction.

So, 3 ÷ 5/6 is

3*6/5

=18/5

=3 3/5

Have a great day!

Answer:

18/5

3 3/5

3.6

Step-by-step explanation:

3 ÷ 5/÷6

3 × 6/5 → 18/5 (can be 18/5, 3 3/5 or 3.6)

Hope this helps! :)

Answer:

6 and 102 = 62

119 and 23 = 38

96 and 51 = 33

28 and 87 = 65

Step-by-step explanation:

just did mine :D

Answer:

  a(b+c-d)

Step-by-step explanation:

Each term has a factor of "a", so that can be factored out. The remaining factor cannot be factored any further.

  ab +ac -ad = a(b +c -d)

Answer:

a(b + c - d)

Step-by-step explanation:

'a' is common to all three terms of the given expression.  Thus, the expression in factored form is a(b + c - d).

Answer:

Step-by-step explanation:

#2:  Amber is correct.  The distribution is skewed to the left.

Answer:

Coordinate of A: -9

Coordinate of Q: 9

Step-by-step explanation:

1 - 10 = -9

1 + 8 = 9

Answer:

1/6

Step-by-step explanation:

sequence should be 1/6,1/3,1/2,2/3

common difference=1/3-1/6=2/6-1/6=1/6

or 1/2-1/3=(3-2)/6=1/6

or c.d.=2/3-1/2=(4-3)/6=1/6

Answer:

The answer is 1/6.

Step-by-step explanation:

I got it right when I did it.

Answer:

Step-by-step explanation:

To find c we use cosine

cos ∅ = adjacent / hypotenuse

c is the hypotenuse

BC is the adjacent

cos 35° = 5 / c

Hope this helps you

Answer:

the answer is B. C= 5 / cos(35)

Step-by-step explanation:

i took the test

Answer:

The coordinates of the x-intercepts are;

(-1, 0) and (-11, 0)

The coordinate of the y-intercept is;

(0, 11)

Step-by-step explanation:

The given function is f(x) = x² + 12·x + 11

The x-intercept is at f(x) = 0 which gives;

0 = x² + 12·x + 11 which has been factored as (x + 1)(x+11) such that we have;

(x + 1)(x+11) = 0

x  = -1, or x = -11

The y-intercept occurs at x = 0, we therefore have;

f(0) = (0)² + 12·(0) + 11 = 11

Therefore, we have f(0) = 11 = Y

Given that at the x-intercept, y = 0, then the coordinates of the x-intercepts are;

(-1, 0) and (-11, 0)

Given that at the y-intercept, x = 0, then the coordinate of the y-intercept is;

(0, 11).

Answer:

man up there is right

Step-by-step explanation:

Answer:

3x + 4y = - 14

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Given

3x + 4y = 12 ( subtract 3x from both sides )

4y = - 3x + 12 ( divide all terms by 4 )

y = - [tex]\frac{3}{4}[/tex] x + 3 ← in slope- intercept form

with slope m = - [tex]\frac{3}{4}[/tex]

Parallel lines have equal slopes, thus

y = - [tex]\frac{3}{4}[/tex] x + c ← is the partial equation

To find c substitute (- 2, - 2) into the partial equation

- 2 = [tex]\frac{3}{2}[/tex] + c ⇒ c = - [tex]\frac{7}{2}[/tex]

y = - [tex]\frac{3}{4}[/tex] x - [tex]\frac{7}{2}[/tex] ← in slope- intercept form

Multiply through by 4 to clear the fractions

4y = - 3x - 14 ( add 3x to both sides )

3x + 4y = - 14 ← in standard form

Answer:

The length of the hypotenuse is 8 inches; the length of the longer leg is 4√3 inches.

Step-by-step explanation:

Note that tan 60 degrees = (length of longer leg) / (length of shorter leg), or

                tan 60 degrees = (length of longer leg) / 4 in.

Thus, (length of longer leg) = (4 in)(tan 60 degrees)

                                              = (4 in) [√3/1] = 4√3 in

Also, cos 60 degrees = (adjacent side) / (hypotenuse.  We want to find the hypotenuse and thus solve this equation for it:

(hypotenuse) = (adjacent side) / (cos 60) = (4 in)( 2/1 ) = 8 in

The length of the hypotenuse is 8 inches; the length of the longer leg is 4√3 inches.

Answer:

No, it is not possible to construct a triangle with lengths of its sides as 4 cm, 3 cm and 7 cm because here we see that sum of the lengths of two sides is equal to third side i.e., 4+3 = 7. As we know that, the sum of any two sides of a triangle is greater than its third side, so given statement is not correct.

Step-by-step explanation:

Answer:

-11x+8 or 8-11x

Step-by-step explanation:

Answer:

(6, -4)

Step-by-step explanation:

If ABCD is dilated by a factor of 2, you multiply the coordinates by 2. For the coordinate D', you would multiply 3 by 2 to get 6 and you would multiply -2 by 2 to get -4. Answer: (6, -4)

[tex]P_(_A_o_r_B_)[/tex] = 1

This means that the probability of event A or event B of happening is 1 or certainly would happen.

Answer:

C. 61

Step-by-step explanation:

Two sides are equal, so the triangle is an isosceles triangle.

Both base angles are equal.

Angles in a triangle add up to 180 degrees.

58 + x + x = 180

58 + 2x = 180

2x  = 122

x = 61

Answer:

Step-by-step explanation:

Given: 4X-3Y=17

so, 4x-17 = 3Y

=> Y = (4X-17)/3

Substituting the value in second equation, we get,

=> -78 + m(4x-17)/3 = 2

=>2+78 = m(4x-17)/3

=> 80*3 = m(4x-17)

=>m= 240/(4x-17)

Hope It Helps!!

Answer:

so confusing.. but I think I have an idea.. p and q are integers equal to 0

Step-by-step explanation:

Answer:

Step-by-step explanation:

8 faces and 12 vertices means hexagon as its base

That means 6+6 edges of its bases and 6 side edges.

6+6+6=18  

Answer:

The absolute value function that models the path of the ball is

[tex]f(x) = \left | -\frac{3}{4}\cdot x + 15 \right |[/tex]

The coordinates when the ball passes within 3 meters of the wall is [tex]\left (3, 12\tfrac{3}{4} \right )[/tex]

Step-by-step explanation:

Given that the ball rolls without other external influences, we have;

(y - 0) = (x - 15)

The slope, m is give by the relation;

m = (y₂ - y₁)/(x₂ - x₁)

m = (15 - 0)/(0-20) = -3/4

The equation of the path of the ball in slope and intercept form is presented as follows;

y = m·x + c

15 = -3/4 ×0 + c = 15

c = 15

The absolute value function that models the path of the ball is then;

[tex]f(x) = \left | -\frac{3}{4}\cdot x + 15 \right |[/tex]

The vale of the function when x = 3 is given by the relation

[tex]f(x) = \left | -\dfrac{3}{4}\times 3 + 15 \right | = \dfrac{51}{4}[/tex]

Therefore, we have the coordinates as  [tex]\left (3, 12\tfrac{3}{4} \right )[/tex].

Answer:

A

achievements

Step-by-step explanation:

Answer:A is the ans

Step-by-step explanation:

Feel pleasure to help u