Find the sum of A.5 B.3 C.4 D.1

Using arithmetic sequences, it is found that there are:

a) 257 numbers that are are divisible by 5 and by 7.

b) 1543 numbers that are divisible by 5 but not by 7.

c) 1800 numbers that are divisible by 5.

d) 1286 numbers that are divisible by 7.

In an arithmetic sequence, the difference between consecutive terms is always the same, called common difference d.

The nth term of an arithmetic sequence is given by:

[tex]a_n = a_1 + (n-1)d[/tex]

In which [tex]a_1[/tex] is the first term.

Item a:

We apply the general formula and solve for n, thus:

[tex]a_n = a_1 + (n-1)d[/tex]

[tex]9975 = 1015 + 35(n-1)[/tex]

[tex]35n - 35 = 8960[/tex]

[tex]35n = 8995[/tex]

[tex]n = \frac{8995}{35}[/tex]

[tex]n = 257[/tex]

There are 257 numbers that are are divisible by 5 and by 7.

Item b:

First, we find the number of multiples of 5, with [tex]a_1 = 1000, a_n = 9995, d = 5[/tex]. Thus:

[tex]a_n = a_1 + (n-1)d[/tex]

[tex]9995 = 1000 + 5(n-1)[/tex]

[tex]5n - 5 = 8995[/tex]

[tex]5n = 9000[/tex]

[tex]n = \frac{9000}{5}[/tex]

[tex]n = 1800[/tex]

Of those numbers, 257 are multiples of 35, which means that they also are multiplies of 7, thus they are removed.

1800 - 257 = 1543.

There are 1543 numbers that are divisible by 5 but not by 7.

Item c:

From the previous item, there are 1800 numbers that are divisible by 5.

Item d:

We find the number of multiples of 7, with [tex]a_1 = 1001, a_n = 9996, d = 7[/tex]. Thus:

[tex]a_n = a_1 + (n-1)d[/tex]

[tex]9996 = 1001 + 7(n-1)[/tex]

[tex]7n - 7 = 8995[/tex]

[tex]7n = 9002[/tex]

[tex]n = \frac{9002}{7}[/tex]

[tex]n = 1286[/tex]

There are 1286 numbers that are divisible by 7.

A similar problem is given at https://brainly.com/question/23901992

Answer:

17+21+14+17+12+15+16 / 7 and the answer is 16

Step-by-step explanation:

STEP N0#1 add all the data/ numbers together

STEP NO#2 divide the sum you got by the number of data points/ number

the number you get after dividing is the mean

Answer: 1.50x-75=10

Step-by-step explanation: they have $60 dollars because 10 times 1.50 is $15 so they have $60 to spend on blankets

Answer:

x = 110°

Step-by-step explanation:

The sum of the interior angles in a quadrilateral is 360°. This means:

x + x + x - 30 + 1/2x + 5 = 360° - we can simplify this

3 1/2x - 25 = 360° - now add 25 to both sides

3 1/2x = 385 - finally divide both sides by 3 1/2

x = 385 ÷ 3.5 = 110

x = 110°

Hope this helps!

Answer:

the answer is 7.2 cm

Step-by-step explanation:

14^2 is 196

12^2 is 144

196 - 144 = 52

square root of 52 = 7.2

also i did FLVS & got it right lol

Answer: The rate of change of momentum of a body over time is directly proportional to the force applied and occurs in the same direction as the applied force.

We can write the law as:

Where F is a force, and P is the momentum.

Remember that the momentum is defined as the quantity of motion, such that:

P = M*V

Where M is the mass of the moving object and V is the velocity of the moving object.

Or we can write the second law as:

F = M*a

M = mass

a = acceleration

Happy To Help ;)

Step-by-step explanation:

Using the binomial distribution, it is found that there is a 0.4295 = 42.95% probability that at least 4 of them say job applicants should follow up within two weeks.

For each manager, there are only two possible outcomes. Either they say job applicants should follow up within two weeks, or they do not say it. The opinion of a manager is independent of any other manager, which means that the binomial distribution is used to solve this question.

Binomial probability distribution  

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

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

The parameters are:

In this problem:

The probability that at least 4 of them say job applicants should follow up within two weeks is [tex]P(X \geq 4)[/tex], which is given by:

[tex]P(X \geq 4) = 1 - P(X < 4)[/tex]

In which:

[tex]P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)[/tex]

Then:

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

[tex]P(X = 0) = C_{8,0}.(0.41)^{0}.(0.59)^{8} = 0.0147[/tex]

[tex]P(X = 1) = C_{8,1}.(0.41)^{1}.(0.59)^{7} = 0.0816[/tex]

[tex]P(X = 2) = C_{8,2}.(0.41)^{2}.(0.59)^{6} = 0.1985[/tex]

[tex]P(X = 3) = C_{8,3}.(0.41)^{3}.(0.59)^{5} = 0.2759[/tex]

[tex]P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) = 0.0147 + 0.0816 + 0.1985 + 0.2759 = 0.5707[/tex]

[tex]P(X \geq 4) = 1 - P(X < 4) = 1 - 0.5705 = 0.4295[/tex]

0.4295 = 42.95% probability that at least 4 of them say job applicants should follow up within two weeks.

A similar problem is given at https://brainly.com/question/25166697

Answer:

31

Step-by-step explanation:

sum of the bordering angles is 180° so

(5x-16) + (x+10) = 180

5x - 16 + x + 10 = 180

6x - 6 = 180

6x = 186

x = 186 ÷ 6

x = 31

Answer:

The answer is x=31.

5x-16+x+10=180

6x-6=180

6x=186

x=31

Then, 5(31)-16=

155-16= 139

Also, x+10=

31+10=41

Solution check:

139+41=180, so x=31 is correct.

Answer:

1 pint(of blood) for every 14 lbs of weight

Step-by-step explanation:

Answer:

One pint.

Step-by-step explanation:

A person has approximately one pint of blood for every 14 pounds of body weight.

Hope this helps! :D

Answer:

Step-by-step explanation:

9th square number = 81

5th square number=25

81-25=56

56 is a multiple of 8 as 8 x 7=56

Answer:

12

Step-by-step explanation:

Waterfalls to Canoes = 6 units

Canoes to Fishing Area = 6 units

Total = 6+6 = 12

Answer:

D. X=-2

Step-by-step explanation:

Answer:

$2.80

Step-by-step explanation:

24.40-13.20=11.20

11.20/4=2.8

Answer:

Thanks man

Step-by-step explanation:

Answer:

thx

Step-by-step explanation:

Answer:

20 million

Step-by-step explanation:

5 million SUVs are 25% of the total number of vehicles.

0.25x = 5,000,000

x = 20,000,000

Answer: 20 million

The question is an illustration of proportions.

A total of 20 million vehicles were looked into

The proportions are given as:

[tex]SUV = 25\%[/tex]

[tex]Trucks= 10\%[/tex]

Let the total number of vehicles be v.

The number of SUVs is given as 5 million.

So, we have:

[tex]SUV = 25\% \times v[/tex]

Substitute 5 million for SUV

[tex]5\ million= 25\% \times v[/tex]

Express the percentage as decimal

[tex]5\ million= 0.25 \times v[/tex]

Divide both sides of the equation by 0.25

[tex]20\ million = v[/tex]

Rewrite the equation as

[tex]v =20\ million[/tex]

Hence, 20 million vehicles were looked into

Read more about proportions at:

https://brainly.com/question/16981404

Answer:

$200,000

Step-by-step explanation:

They all won $10,000,000 and

each person got a 0.02 share of the $10,000,000

Each person received

10,000,000*0.02 = $200,000

Answer:

Carl shades the 4s row in the multiplication table.

Step-by-step explanation:

4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48. This is the pattern 4, 8, 2, 6, 0, 4, 8, 2, 6, etc.

Answer:

75 marks

Step-by-step explanation:

one question worth 3 marks

so 25×3=75

Answer:

Answer A

Step-by-step explanation:

Alt Interior angles make two angles parallel

f(x) = 4 means "y=4".

If you draw in y=4 as a line on the graph, you're looking for points where the f(x) graph hits y=4.  (see picture below)

This happens at one point and the x-value of that point is -2.

-2 is the only x-value where this happens.

Answer:

11

Step-by-step explanation:

I subtracted 126 from 410 and got 284 then I divided 16 from 284 and got 11

Modeling the box representation Mathematically can be done using the multiplication sentence 0.06 × 4 = 0.24

The entire box has 100 holes ;

Each shading takes up 6 boxes which is 6/100 of the entire box ; Area per shading :

The number 6 set shading represented on the box = 4

The multiplication model :

0.06 × 4 = 0.24

Therefore, the multiplication sentence which represents the model is 0.06 × 4 = 0.24

Learn more : https://brainly.com/question/25310757

Answer:

the equation for y=20=1/2

Step-by-step explanation:

y=1/4

y=0.25

Answer:

Jina has $10,

Tony has $40,

and Henry has $20

Step-by-step explanation:

So if we use a little bit of algebra, let's say

Jina's amount = a.

Henry has $10 more than Jina, so that would make Henry's amount: a + 10. Tony has two times more dollars than Henry, so multiply Henry's amount

(a + 10) by 2, and you get: 2(a + 10).

Here's to make things easier on the eye for you:

Jina's amount = a

Henry's amount = (a + 10)

Tony's amount : 2(a + 10)

Next, form an equation by adding each of the three's amounts together:

Jina's amount + Henry's amount + Tony's amount

= a + (a + 10) + 2(a + 10)

= a + a + 10 + 2a + 20

(add the a's together and the numbers together. Then, put the total amount, $70, on the other side of the equation)

4a + 30 = 70

(subtract 30 from both sides of the equation: 4a + 30 - 30 = 70 - 30)

= 4a = 40

(and now, simplify by dividing by 4)

a = 10

Substitute 10 for a:

Jina: a = $10

Henry = (a + 10) = (10 + 10) = $20

Tony = 2(a + 10) = 2(10 + 10) = 2(20) = $40

Add them all up if you want to check if its correct:

$10 + $20 + $40 = 70$ ✔

Sorry if this explanation was a bit long, I hope you understand ^^.

Answer:

5 9/10

Step-by-step

Have the fraction with common denominators: 5/10 and 4/10

Answer:

d=140

v=60

140.60=8400 its m