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:
Numbers that are divisible by 5 and 7 are multiples of 35, as the least common multiple of 5 and 7 are 35, thus we have an arithmetic sequence with [tex]d = 35[/tex].The first multiple of 35 in this interval is 1015, so [tex]a_1 = 1015[/tex].The last multiple of 35 in this interval is 9975, so [tex]a_n = 9975[/tex].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
Khả năng gặp rủi ro khi đầu tư vào các dự án I, II tương ứng là 9%, 7% và gặp rủi ro đồng thời khi đầu tư cả hai dự án là 4%. Nếu đầu tư cả hai dự án, tính xác suất để: a) Ít nhất một dự án gặp rủi ro. b) Chỉ dự án I gặp rủi ro
Answer:
pogi mooooo loooodsssssssss
Factor use please help I need this and quick
[tex]8a^{3} +\sqrt{3^{2}*3 } b^{3}[/tex]
[tex]8a^{3} +(\sqrt{3^{2} } *\sqrt{3})b^{3} \\\\[/tex]
[tex]8a^{3} +(3^{\frac{2}{2} } *\sqrt{3} )b^{3}[/tex]
[tex]8a^{3} +(3*\sqrt{3} )b^{3}[/tex]
[tex]8a^{3} +3*\sqrt3} *b^{3}[/tex]
State if the triangle are congruent by sss sas asa aas or not congruent
Answer:
(a) SSS
.........................
73,498 to the nearest thousand
Answer:
73,000
Step-by-step explanation:
if the hundred is smaller than 500, you round down, if it's larger then round up :)
Given f(x)=3x(to the scnd power)−5x−2. What is the value of f(−2/3)? 1 8/3 3 10/3
Given:
[tex]f(x)=3x^2-5x-2[/tex]; find f(-2/3)
Answer:
[tex]f(-\frac{2}{3} )=\frac{8}{3}[/tex]
Step-by-step explanation:
1. Insert [tex]-\frac{2}{3} \\[/tex] as X; [tex]f(-\frac{2}{3}) = 3 (-\frac{2}{3} )^2 - 5 (-\frac{2}{3}) - 2[/tex]
2. Solve equation; [tex]f(-\frac{2}{3} )=\frac{8}{3}[/tex]
1.) if a person weighs 160 pounds, what is his mass in kilograms
Answer:
72.56
Step-by-step explanation:
Divide the number of pounds by 2.205
160/2.205 = 72.56
Mae receives $79.00 for working one 10-hour day. One day she had to stop after working 7 hours because of a doctor’s appointment. How much did she make that day? I need help
2x - 6 >8
What is the Second Step?
Answer:
8
Step-by-step explanation:
i used the calculator
1.Add 66 to both sides.
[tex]2x=8+6[/tex]
2. Simplify 8+6 to 14
[tex]2x=14[/tex]
3. Divide both sides by 22.
[tex]x=14/2[/tex]
4. Simplify [tex]14/2[/tex] to [tex]7[/tex]
Then your answer should be [tex]x=7[/tex]
Correct answer will get brainiest
Answer:
x=75
Step-by-step explanation:
(2x-67)+(x-23)+3x=360
6x-67-23=360
6x=450
x=75
I need help, please.
[tex]p = 2(l + w) = 2.(15 + 12) = 54 cm[/tex]
Can someone help me please
Answer:
181.25 square feet
1/6 quart water
1/18 cup milk
1/3 beef bouillon cube, and 2/3 a large carrot
Step-by-step explanation:
Divide 2/5 divided by 4 in simplest terms
Answer:
1/10
Step-by-step explanation:
Eloise rides her bike1 7/10 miles on Wednesday and 1 5/10 miles on Thursday. How many miles does Eloise ride her bike altogether? Enter your answer as a mixed number in the simplest form
Answer:
3 2/10
Step-by-step explanation:
start with an equation:
1 7/10+1 5/10 = ?
convert mixed fractions into improper fractions:
17/10+15/10 = ?
add:
32/10
simplift:
3 2/10
I need help with this question. Thank you!
Answer:
gradient is the same as slope The gradient or slope of line A = 3/1 or 3
The gradient of line B is -4/1 or -4
gradient or slope = rise over run = y/x.
if the line goes up from the left to the right, The slope is positive.
if the line goes down from the left to the right, The slope is negative
In a normal distribution the mean is 30.What will be the value of median of this distribution?
Answer:
30
Step-by-step explanation:
because in normal distribution
mean=median=mode
Second angle of a triangle is 10 degree larger than first angle. Third angle is 10
larger than second angle. Find the smallest angle of the triangle.
Alec is 3 years older than 11 times the age of his nephew Luke. If A represents Alec's age and L represents Luke's age, which equation is true?
Answer:
A = 11L + 3
Hope this Help
If y varies directly with x and y = 6 when x = 2, what is the constant of variation, k? a. 12 c. 3 b. 2 d. 4 Please select the best answer from the choices provided A B C D
Which equation, when solved, results in a different value of x than the other three? O -7-9-20 0 + 5 3 7 X=-20 4 O 3 4. - (b)*--20 +7(49-2-06-4) 8 O
Answer:
1
Step-by-step explanation:
(e+1)x3=6 what will be the amount of e
Answer:
e=1
Step-by-step explanation:
(e+1)×3=6
3e+3=6
3e=6-3
3e=3
e=3/3
e=1
:)
In the 2004 Summer Olympics, Adam van Koeverden of Oakville, Ontario, won two medals. He won the gold medal in the men’s 500 m kayak race, with a time of 1 min 37.9 s. He also won the bronze medal in the 1000 m race, with a time of 3 min 28.2 s. In which race did he row with greater speed?
Answer:
Adam van Koeverden at the 2004 Olympic at Athens. Van Koeverden paddled to victory in the Men's K1 500 m kayaking event, adding a gold medal to the bronze he won days earlier in the 1000 m to become Canada's first double medallist in the summer Olympics since Donovan Bailey and Clara Hughes at Atlanta in 1996.
Step-by-step explanation:
Pls mark me as brainliest
What is the unit cost per bottle if a pack of 12 bottles of juice sells for $6? (1 point)
$0.50 per bottle
$0.72 per bottle
$5.00 per bottle
$7.20 per bottle
Step-by-step explanation:
12 bottles = $6
1 bottle = 6/12
= $0.50 per bottle.
Hope it helps :)
HELPPPPPPPpppppppppppppppppp
Answer:
B
Step-by-step explanation:
even if the variables confuse you just look at the inequalitiy symbols; all of them, except for B, are not correct
you wouldn't use < because this implies you can't spend $150
you wouldn't use > or ≥ because these imply you can afford to spend more than $150
HELP!!! Type the correct answer in the box.
The formula for the volume, V, of a cone having the radius, r, and the height, h, is shown below.
[tex]V=\frac{1}{3} \pi r^{2} h[/tex]
Write the formula to calculate the height, h.
Answer:
cone height formulas are, h = 3V/πr 2 and h = √l2 - r2, where V = Volume of the cone, r = Radius of the cone, and l = Slant height of the cone.
Enter an inequality that represents the phrase "the sum of 4 and y is less than 6." Draw a graph that represents the inequality.
Please help AND give a good explanation. Like I am finding this super hard and well I can NOT get this question wrong unless I want a C on this. Help :(
9514 1404 393
Answer:
4 + y < 6
see attached for a graph
Step-by-step explanation:
The English description "the sum of A and B" is written symbolically as ...
A + B
The symbol for "is less than" is <.
Then "the sum of 4 and y is less than 6" will be written ...
4 + y < 6
__
The solution to this is found by subtracting 4 from both sides of the inequality:
4 +y -4 < 6 -4
y < 2 . . . . . . . . . simplified solution
The graph of this is a number line with an open circle at y=2, and shading to the left of that point, where values on the number line are less than 2.
9.35 x 9 = 3.15 is this an overestimate or underestimate?
Answer:
7/187
Step-by-step explanation:
thats it simplified if this helps
the general solution of sinx + cosx =√2 is..??
The answer is A. x= [tex]\pi[/tex]/4 +2[tex]\pi[/tex]n
Answer:
the general solution has answer
2nπ+π/4
4 1/6 - 3 3/5
Show your work pls
Answer:
-78/30 or -2 3/5
Step-by-step explanation:
4 1/6 - 3 3/5
25/6 - 18/5
30-108\30
= -78/30 or -2 3/5
Answer:
4 1
6
–
3 3
5
=
17
30
Step-by-step explanation:
4 1
6
–
3 3
5
= (4 – 3) + (
1
6
–
3
5
)
= 1 +
1 × 5
6 × 5
–
3 × 6
5 × 6
= 1 +
5
30
–
18
30
= 1 +
5 – 18
30
= 1 +
-13
30
=
17
30
Suppose that you and a friend are playing cards and decide to make a bet. If you draw three face cards, where a face card is a Jack, a Queen, or a King, in succession from a standard deck of 52 cards without replacement, you win $40. Otherwise, you pay your friend $10. What is the expected value of your bet? Round your answer to the nearest cent, if necessary.
Answer:
Step-by-step explanation:
Expected value of the bet =
P(you make the correct draw) * 40 + P(you do not make the correct draw) * (-10) =(4/52)(4/51)(4/50) * 40 + (1 - (4/52)(4/51)(4/50)) * (-10) =
(64/132600) * 40 + (1 - 64/132600) *(-10) =
64/3315 + (132536/132600) * (-10) =
64/3315 - (132536/13260) =
64/3315 - 33134/3315 =
-33070/3315 =
-9.97586726998 =
-$9.98, rounded to the nearest cent
(i.e., the expected value of the bet is a loss of $9.98)
HI i need help wit this work
Answer:
1/6 in 1/2 = B
1/6 in 2/3 = C
1/4 in 1/2 = D
1/9 in 1/3 = A
Step-by-step explanation: