Q. An arithmetic series has first term a and common difference d, where d is a prime number. The sum of the first n terms of the series is S, and Sm=39 S2m = 320 Find the value of d and the value of m Show clear algebraic working. (Total for question = 5 marks)​

Answer:

0.7880

Step-by-step explanation:

0.7883

Hope it helps!

Answer:A

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

8/50 = 4/25

give the sinplest fraction answer

Answer:

6) 9 3/5

7) 1/50

8) 28/45

Step-by-step explanation:

6) 8÷5/6=8x6/5=48/5=9 3/5

7) 1/5÷10=1/50

8) 7/5÷9/4=7/5x4/9=28/45

Answer:

a) 0.0287 = 2.87% probability that three non-defective components in a batch of seven components.

b) 0.0336 = 3.36% probability that 8 non-defective components are drawn before the first defective component is chosen.

Step-by-step explanation:

A sequence of Bernoulli trials composes the binomial distribution.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

And p is the probability of X happening.

The probability that a selected component is non-defective is 0.8

This means that [tex]p = 0.8[/tex]

a) Three non-defective components in a batch of seven components.

This is P(X = 3) when n = 7. So

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 3) = C_{7,3}.(0.8)^{3}.(0.2)^{4} = 0.0287[/tex]

0.0287 = 2.87% probability that three non-defective components in a batch of seven components.

b) 8 non-defective components are drawn before the first defective component is chosen.

Now the order is important, so the we just multiply the probabilities.

8 non-defective, each with probability 0.8, and then a defective, with probability 0.2. So

[tex]p = (0.8)^8*0.2 = 0.0336[/tex]

0.0336 = 3.36% probability that 8 non-defective components are drawn before the first defective component is chosen.

Answer:

3/12

Step-by-step explanation:

Answer:

2/6

Step-by-step explanation:

it is equal to 1/3. The others are equal to 1/4 and 1/24 so 1/3 is the largest

Answer:

The point estimate for the true difference between the population means is of -2.62 years.

The 95% confidence interval for the difference between the true mean ages for cars owned by students and faculty is between -3.4 years and -1.84 years.

Step-by-step explanation:

Before building the confidence interval, we need to understand the central limit theorem, and subtraction between normal variables.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]

Subtraction of normal variables:

When we subtract normal variables, the mean is the subtraction of the mean, while the standard deviation is the square root of the sum of variances.

A sample of 138 cars owned by students had an average age of 5.13 years. The population standard deviation for cars owned by students is 3.45 years.

This means that:

[tex]\mu_{s} = 5.13, \sigma_{s} = 3.45, n = 138, s_s = \frac{3.45}{\sqrt{138}} = 0.2937[/tex]

A sample of 111 cars owned by faculty had an average age of 7.75 years.  The population standard deviation for cars owned by faculty is 2.08 years.

This means that [tex]\mu_{f} = 7.75, \sigma_{f} = 2.08, n = 111, s_f = \frac{2.08}{\sqrt{111}} = 0.2658[/tex]

Difference between the true mean ages for cars owned by students and faculty.

s - f

Mean:

[tex]\mu = \mu_s - \mu_f = 5.13 - 7.75 = -2.62[/tex]

This is the point estimate for the true difference between the population means.

Standard deviation:

[tex]s = \sqrt{s_s^2+s_f^2} = \sqrt{0.2937^2+0.2658^2} = 0.3961[/tex]

Confidence interval:

We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:

[tex]\alpha = \frac{1 - 0.95}{2} = 0.025[/tex]

Now, we have to find z in the Ztable as such z has a pvalue of [tex]1 - \alpha[/tex].

That is z with a pvalue of [tex]1 - 0.025 = 0.975[/tex], so Z = 1.96.

Now, find the margin of error M as such

[tex]M = zs = 1.96*0.3961 = 0.78[/tex]

The lower end of the interval is the sample mean subtracted by M. So it is -2.62 - 0.78 = -3.4

The upper end of the interval is the sample mean added to M. So it is -2.62 + 0.78 = -1.84

The 95% confidence interval for the difference between the true mean ages for cars owned by students and faculty is between -3.4 years and -1.84 years.

Answer:

[tex]3(x - 6) - 8x = - 2 + 5(2x + 1) \\ 3x - 18 - 8x + 2 - 10x - 5 = 0 \\ = > - 15x - 21 = 0 = > - 15x = 21 = > x = - \frac{7}{5} [/tex]

Answer:

7161 km³

Step-by-step explanation:

28²+b²=32.5²

784+b²=1056.25

b²=1056.25-784

b²=272.25

b=√272.25

b=16.5

1/2x28x16.5x31=7161

Answer:

I got you rn

Step-by-step explanation:

its 42 because opposite angles are congruent

Answer:

Step-by-step explanation:

z = 53 + 39     {Exterior angle property of triangle}

z = 92°

Answer: 3/4 + 7/12 - (-4) = 3/4 + 7/12 + 4 (two minuses make a plus)

3/4 + 7/12 + 4/1 = 9/12 + 7/12 + 48/12           (4 = 4/1 or 4 divided by 1)  

(to add the fractions the denominators need to be the same. Multiply both the denominator and numerator by the same number)

(9+7+48)/12 = 64/12 = 5 and 1/3 or 16/3

We can also get this answer by leaving the 4 as a whole number:

9/12 + 7/12 +4 = 16/12 + 4 = 1 and 1/3 + 4 = 5 and 1/3

If you put the sum in a calclator you also get 5 and 1/3.

Hope this helps :)

Answer:

1. x = 14

2. c = 12

3. d = 4

4. w = 8

5. z = 54

6. d = 20

7. n = 26.4

8. k = 15

Step-by-step explanation:

Answer:

The angles are adjacent and x=100

The area of a circle is pi times the radius squared (A = π r²).

Bing + us = Bingus. That's all

Answer:

it's very hard lol

Bing+us

=Bingus

Step-by-step explanation:

oh my gawd... hope it's ryt

thanks lol

Answer:

x + y = 7 an equation to represe.

Answer:

x = 24

Step-by-step explanation:

3X +5 +2x-4 +2x +11 = 180

7x +12 = 180

7x = 180 - 12

7x = 168

7x/7 = 168/7

x =24

Answer:

I don't know if your ask which nomial it is but its a trinomial if that's what your asking

Answer:

80°C

Step-by-step explanation:

you will say :

(176-33) x 5/9 = 70

Answer:

-16/3 = -5.3333333333

Step-by-step explanation:

Answer:

Well 1 centimeter is 10 millimeters.

260000 mm divided by 10 is 26000

so 26000 centimeters

Answer:

by now you should have the answer right?

Step-by-step explanation:

Answer:

$9.24

Step-by-step explanation:

1.68÷2=0.84

1.68×5+0.84=9.24

Answer:

length = 8 ft

width = 5 ft

Step-by-step explanation:

width = w

length = w + 3

Area of rectangular garden = 40 square feet

length  *width = 40

(w + 3) *w = 40

w*w + 3*w = 40

w² + 3w = 40

w² + 3w - 40 = 0

w² + 8w - 5w - 8*5 = 0

w(w + 8) - 5 (w +8) =0

(w + 8) (w - 5) = 0

w - 5 = 0       {Ignore w + 8 =0, as measurement will not be in -ve}

w = 5 ft

l = 5 + 3

l = 8 ft

Answer: I'm assuming that there were multiple choices provided for this question.. but just to help you, when a number is within the absolute value, it changes any number to a positive:

|-2.6| = 2.6

So any number higher than that work for this question :-)

Answer:

Box-4 → (+)

Step-by-step explanation:

To find the value in the 4th box, we will expand the given logarithmic expression.

log₄x⁵y³ = log₄x⁵ + log₄y³

             = 5log₄x + 3log₄y

Therefore, each box will have the values as,

Box-1 → 5

Box-2 → log₄

Box-3 → x

Box-4 → (+)

Box-5 → 3

Box-6 → log₄

Box-7 → y

There is the (+) sign in Box-4.

Answer:

I don't know thats hard um well yeah