The first and last term of an AP are 1 and 121 respectively. If the sum of the series is 671,find a) the number of terms (n) in the AP b) the common
difference between them​

Answer:

The  probability is  [tex]P(X < 900 ) = 0.0918[/tex]

Step-by-step explanation:

From the question we are told that

   The sample mean is  [tex]\= x = 1100[/tex]

    The  standard deviation is  [tex]\sigma = 150[/tex]

     The random number value is  x =900

The probability that a trainee earn less than 900 a month is mathematically represented as

       [tex]P(X < x) = P(\frac{X -\= x}{\sigma} < \frac{x -\= x}{\sigma} )[/tex]

Generally the z-value for the normal distribution is mathematically represented as

       [tex]z = \frac{x -\mu }{\sigma }[/tex]

So From above we have

      [tex]P(X < 900 ) = P(Z < \frac{900 -1100}{150} )[/tex]

      [tex]P(X < 900 ) = P( Z <-1.33)[/tex]

Now from the z-table

    [tex]P(X < 900 ) = 0.0918[/tex]

Answer:

(H1, T1)

Step-by-step explanation:

Since we know that the only number option is 1, we can cancel out the first 3 options. and obviously, there are only heads, and tails. So, using only the # 1 and heads and tails, we can conclude that the answer is (H1, T1).

Answer:

D. (H1, T1)

Step-by-step explanation:

Since all outcomes require card #1 is chosen, so any answer with 2 or 3 can be rejected, therefore the answer is

D. (H1, T1)

Answer:

outside the circle i think

Step-by-step explanation:

Answer:

inside the circle

Step-by-step explanation:

Answer:

Perimeter= 40 units

Step-by-step explanation:

Ok

We are asked to look for the perimeter.

We have some clue given.

All at right angle and some sides are given it's full length.

We have the bae to be 11 unit

The height to be 7 unit.

What this mean is that taking either the base or the height should sum up to either 11 or 7 respectively.

Let's go for the other side of the height.

Let's take all the vertical height and sum it up to 7 because the right side is equal to 7.

So we have 7+7+11

But it's not complete yet.

We are given a dimension 2.

And the 2 is in two places so it's total 2*2= 4

The two is for a small base .

The base is actually an extra to the 11 of the other base.

So summing up

We have 2*11 + 2*7 + 2*2

Perimeter= 22+14+4

Perimeter= 40 units

Answer:

cars are dum

Step-by-step explanation:

Answer:

The answer is 15.6/31 or 1/2

Step-by-step explanation:

The data in the question is sufficient to find an answer for it.

1. I look at the temperature and rainfall chart for Brighton, United Kingdom.

2. Check for rainy season and dry season.

3. The rainy season lasts approximately 5 months while the dry season (which still has some rainfall) lasts approximately 7 months. All together, 12 months of the calendar year.

4. July happens to fall within the dry season. The temperature and rainfall statistics are observed.

The number of rainfall days is 15.6 and we know there are 31 days in July.

If the approximate number of days it rains in Brighton, in July, is 15.6 then the probability of rainfall in the month is 15.6/31 which is = 0.503 or 0.5

Therefore, there's a 50% chance of having rainfall in Brighton, on any day in the month of July.

In fraction, 0.5 = 1/2

Answer:

15.9degrees

Step-by-step explanation:

in photo above

Answer:

[tex]\boxed{15.95\°}[/tex]

Step-by-step explanation:

The angle can be found by using trigonometric functions.

tan (θ) = [tex]\frac{opposite}{adjacent}[/tex]

tan (θ) = [tex]\frac{4}{14}[/tex]

θ = [tex]tan^{-1} \frac{4}{14}[/tex]

θ = 15.9453959

θ ≈ 15.95

Answer: [tex]\dfrac{1}{12}[/tex]

Step-by-step explanation:

Given: Emily has a box with 4 different colored tiles: one red, one green, one blue and one yellow.

We assume that repetition is not allowed

Total number of ways to draw two tiles = [tex]^4P_2=\dfrac{4!}{(4-2)!}[/tex]  [By permuattaions]

[tex]=\dfrac{4\times3\times2}{2}=12[/tex]

Favourable outcome = First green then red  (only one way)

So, the probability of drawing the green before the red [tex]=\dfrac{\text{favorable outcomes}}{\text{Total outcomes}}[/tex]

[tex]=\dfrac{1}{12}[/tex]

hence, the required probability =[tex]\dfrac{1}{12}[/tex]

Answer:

a)the proportion of student is 0.1082

b)

H1: p = .08

H2: p not equal to 0.08

H1: p =0 .08

H2: p < .08

H1: p =0 .08

H2: p >0 .08

c)z=1.45

d) the p value is 0.1470

e)null hypothesis cannot be accepted,There is no enough evidence to reject the  null hypothesis.

Step-by-step explanation:

CHECK THE ATTACHMENT FOR DETAILED EXPLANATION

Add the top and bottom numbers together, divide that by 2 then multiply by the height.

15.3 + 19.5 = 34.8

34.8/2 = 17.4

17.4 x 11.1 = 193.14

Answer is 193.1 m^2

Answer:

Barts total cost is (c)213.36

Step-by-step explanation:

First, you subtract 6% from $219

=204.92

add shipping,

+7.50

=213.36

Hope this helps <3

Answer:

C. $213.36

Step-by-step explanation:

The original price is $219 and the discount is 6% which is equal to $13.14

$219 - $13.14 + $7.50 (shipping cost) = $213.36

Answer:

Step-by-step explanation:

Hello!

Miguel has four chips, two have the number "1", one has the number "3" and the other has the number "5"

If the experiment is "choosing two chips and looking at their numbers" there are the following possible outcomes:

S= {(1,1)(1,3)(1,5)(3,1)(5,1)(3,5)(5,3)}

The sample space for the experiment has 7 possible combinations.

a)

Be X: the amount of money Miguel will receive or owe.

If two chips with the same number are chosen he will receive $2

If the chips have different number he will owe $1

Looking at the possible outcomes listed above, out of the 7, in only one he will select the same number (1,1)

So the probability of him receiving $2 will be 1/7

Now out of the 7 possible outcomes, 6 will make Miguel owe $1, so you can calculate its probability as: 6/7

  xi  | $2 | -$1

P(xi) | 1/7 | 6/7

b)

To calculate the expected value or mean you have to use the following formula:

[tex]\frac{}{X}[/tex]= ∑[xi*P(xi)]= (2*1/7)(-1*6/7)= -4/7= $-0.57

c)

The expected value is $-0.57, meaning that Miguel can expect to owe $0.57 at the end of the game.

d)

To make the game fair you have to increase the probability of obtaining two chips with the same number. Any probability close to 50% will make the game easier. For example if you change the experiment so that for earning $2 the probability is 4/7 and for owing $1 the probability is 3/7, the expected earnings will be:

(2*4/7)+(-1*3/7)= $0.71

I hope this helps!

Answer:

9 in.

Step-by-step explanation:

Given that the line 10 in. and line 4 in. are parallel, then the two triangles are similar.

As such, the ratio of the sides would give the same results.

Hence,

4/6 = 10/(6 + x)

cross multiplying

4(6 + x) = 60

Dividing both sides by 4

6 + x = 15

collecting like terms

x = 15 - 6

= 9

Answer:

A. 0.89.

Step-by-step explanation:

The value of correlation coefficient ranges from -1 to 1. Any value outside this range cannot possibly be correlation coefficient of a scatter plot representing relationship between two variables.

The scatter plot given shows a positive correlation between average daily temperatures and number of visitors, as the trend shows the two variables are moving in the same direction. As daily temperature increases, visitors also increases.

From the options given, the only plausible correlation that can represent this positive relationship is A. 0.89.

Answer:

lmkjhvjgcfnhjkhbmgnc gfghh

Step-by-step explanation:

Answer:

the solutions to the inequality ys-x+1 are shaded on the graph. which point is B. (3 ,-2)

Answer:

b

Step-by-step explanation:

Answer:

I think that is the C

Step-by-step explanation:

Answer:

Option B is the correct answer.

Step-by-step explanation:

here, arc RT =162°

as in question given that the value of arc RT is 162° the value of angle RST is 1/2 of 162°.

so, its value must be 81°only.

hope it helps..

Answer:

Dian has $250 originally.

Step-by-step explanation:

Let the total money Dian has originally = $S

Dian gave [tex]\frac{2}{5}[/tex] of her total money to Justin,

Money given to Justin = [tex]\frac{2}{5}(\text{S})[/tex]

Money left with Dian = S - [tex]\frac{2}{5}(\text{S})[/tex]

                                   = [tex]\frac{\text{5S-2S}}{5}[/tex]

                                   = [tex]\frac{3S}{5}[/tex]

Since Dian has $150 left then the equation will be,

[tex]\frac{3S}{5}=150[/tex]

S = [tex]\frac{150\times 5}{3}[/tex]

S = $250

Therefore, Dian has $250 originally.

Answer:

x = 3 ± sqrt(11)

Step-by-step explanation:

x^2 - 6x + 9 = 11

Recognizing  that this is a perfect square trinomial

(x-3) ^2 =11

Taking the square root of each side

sqrt((x-3) ^2) = ± sqrt(11)

x-3 =± sqrt(11)

Add 3 to each side

x = 3 ± sqrt(11)

Answer:

[tex]\large\boxed{\sf \ \ x = 3+\sqrt{11} \ \ or \ \ x = 3-\sqrt{11} \ \ }[/tex]

Step-by-step explanation:

Hello,

   [tex]x^2-6x+9=11\\<=> x^2-2*3*x+3^2=11\\<=>(x-3)^2=11\\<=> x-3=\sqrt{11} \ or \ x-3=-\sqrt{11}\\<=> x = 3+\sqrt{11} \ or \ x = 3-\sqrt{11}[/tex]

Do not hesitate if you have any question

Hope this helps

Answer:16.1%

Step-by-step explanation:

Answer:

The investment needs the rate of growth to be approximately 16.1%.

Step-by-step explanation:

Answer: 0.476

Step-by-step explanation:

Let A = Event of choosing an even number ball.

B = Event of choosing an 8 .

Given, A lottery game has balls numbered 1 through 21.

Sample space: S= {1,2,3,4,5,6,7,8,...., 21}

n(S) = 21

Then, A= {2,4,6,8, 10,...(20)}

i.e. n(A)= 10

B= {8}

n(B) = 1

A∪B = {2,4,6,8, 10,...(20)} = A

n(A∪B)=10

Now, the probability of selecting an even numbered ball or an 8 is

[tex]P(A\cup B)=\dfrac{n(A\cup B)}{n(S)}[/tex]

[tex]=\dfrac{10}{21}\approx0.476[/tex]

Hence, the required probability =0.476

Answer:

A

Step-by-step explanation:

[tex]g(x) = \frac{3}{{x}^{2} + 2x} \\ {x}^{2} + 2x - \frac{3}{g(x)} = 0 \\ x = \frac{1}{2} \Big( - 2 + \sqrt{12 + \frac{12}{g(x)} }\Big) \\ x = - 1 + \sqrt{1 \pm \frac{3}{g(x)} } [/tex]

Now replace $x$ by $g^{-1}(x)$ and $g(x)$ by $x$ and you have your answer.

Answer:

Step-by-step explanation:

The formula of a slope:

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

We have

[tex](-3;\ -8)\to x_1=-3;\ y_1=-8\\(4;\ 6)\to x_2=4;\ y_2=6[/tex]

Substitute:

[tex]m=\dfrac{6-(-8)}{4-(-3)}=\dfrac{6+8}{4+3}=\dfrac{14}{7}=2[/tex]

The formula for the slope m of the line that passes through two points [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] is the following:

[tex]m=\dfrac{y_1-y_2}{x_1-x_2}[/tex]

We have points (4,6) and (-3,-8). Let's plug these values into the formula for slope:

[tex]m=\dfrac{6-(-8)}{4-(-3)}[/tex]

[tex]=\dfrac{14}{7}=2[/tex]

The slope of the line passing through the two points is 2. Let me know if you need any clarifications, thanks!

Answer:

Probability of obtaining no more than two defective tubes = 0.816

Step-by-step explanation:

The Probability of obtaining no more than two defective tubes in a randomly selected sample of 15 tubes is obtained using the binomial distribution formula: nCr × p^r × q^(n -r).

Where n is number of samples;

r is maximum number of defective tubes, r ≤ 2;

p is probability of defective tubes = 10% or 0.1

q is probability of non-defective tubes, q = 1 - p

Further explanations and calculations are given in the attachment below:

Answer:

D. 4 real roots and 0 complex roots

Step-by-step explanation:

If I assume that the function you are saying is

[tex]F(x)=x^4+x^3-5x^2+x-6[/tex]

There should be up to "4 roots," there can't be more or less than 4 total solutions. First, we need to check how many sign changes are there in this function. There are 3 positive real roots. Now lets check for negative roots.

[tex]F(-x)=x^4-x^3-5x^2-x-6[/tex]

There are is only 1 negative real root. Since we basically have 4 real roots, and the max is 4. There should be 4 real roots and 0 complex roots.

Answer:

3 is not a solution

Step-by-step explanation:

6x – 7 = 12?

Substitute 3 in for x and see if the equation is true

6*3 - 7 = 12

18-7 = 12

11 =12

This is false so 3 is not a solution

Answer:C

Step-by-step explanation:

Pemdas

3+5(10)

5*10=50

3+50=53

Answer:

[tex] S.A = 246.6 in^2 [/tex]

Step-by-step explanation:

The figure given above is a square pyramid, having a square base and 4 triangular faces on the sides that are of the same dimensions.

Surface area of the square pyramid is given as: [tex] B.A + \frac{1}{2}*P*L [/tex]

Where,

B.A = Base Area of the pyramid = 9*9 = 81 in²

P = perimeter of the base = 4(9) = 36 in

L = slant height of pyramid = 9.2 in

Plug in the values into the given formula to find the surface area

[tex] S.A = 81 + \frac{1}{2}*36*9.2 [/tex]

[tex] = 81 + 18*9.2 [/tex]

[tex] = 81 + 165.6 [/tex]

[tex] S.A = 246.6 in^2 [/tex]

Answer:

Option b.

Step-by-step explanation:

Note: The given expression is not in correct form. Consider the given expression is [tex]i^0\times i^1\times i^2\times i^3\times i^4[/tex].

Let as consider the given expression is  

[tex]i^0\times i^1\times i^2\times i^3\times i^4[/tex]

We know that,

[tex]i^0=1,i^2=-1,i^3=-i,i^4=1[/tex]

Using these values, we get

[tex]i^0\times i^1\times i^2\times i^3\times i^4=1\times i\times (-1)\times (-i)\times 1[/tex]

[tex]=i^2[/tex]

[tex]=-1[/tex]

The value of given expression is -1.

Therefore, the correct option is b.