how many integers from 1 to 700 are divisible by 2, 5 and 7

Answers

Answer 1

Final answer:

There are 10 integers from 1 to 700 that are divisible by 2, 5, and 7. This is calculated by finding the least common multiple (LCM) of the numbers, which is 70, and then determining how many multiples of 70 are within the given range.

Explanation:

The question asks to find out how many integers from 1 to 700 are divisible by 2, 5, and 7. An integer divisible by 2, 5, and 7 is also divisible by their least common multiple (LCM). The LCM of 2, 5, and 7 is 70 since 2 x 5 x 7 = 70. So, the task is to find the number of multiples of 70 between 1 and 700.

To find the number of multiples of 70 in that range, you can use the following steps:

Divide the largest number in the range (700) by 70 to find the highest multiple within the range. ∑(700 ÷ 70 = 10).Since we started from 1 and 70 is the first multiple, the total count is the result of the division.

Therefore, there are 10 integers from 1 to 700 that are divisible by 2, 5, and 7.

Related Questions

Noel Devine bought a new dishwasher for $320. He paid 20 down and made 10 monthly payments of $34 what actual yearly interest rate did Noel pay?

Answers

IN finding the interest we need to use the following formula:
Interest= Principal x Rate x Time or I= PRT
Substitute values: I= [$20 + ($10 x $34)] -320 =$40
P= $320
R=?
T=10 months/year
I=PRT
Since R is a missing term, we will solve for R using this formula: R=I/PT
R= [$20 + ($10 x $34)-320] / ($320 x 10 months)
T=10 months÷12 months=0.83
R= ($40)/ $320 X 0.83
R= 40/ 265.6
R=15.06024096

First we need to find the amount financed, total payments and total interest

Amount financed
320-20=300

Total payments
34×10=340

Total interest=total payments-amount financed
Total interest=340-300=40

Now to find the yearly interest rate use the formula of
I=(2yc)÷(m×(n+1))
I ?
Y number of months in a year 12
C total interest 40
M amount financed 300
N number of payments 10
I=(2×12×40)÷(300×(10+1))
I=0.2909×100=29.09%

Hope it helps!

What is 60000 x 1000?

Answers

the answer is 60000000

The solution is, the value is 60000 x 1000 =60000000.

What is multiplication?

In mathematics, multiplication is a method of finding the product of two or more numbers. It is one of the basic arithmetic operations, that we use in everyday life.

here, we have,

given that,

60000 x 1000

i.e. we have to multiply 60000 with 1000

so, we get,

60000 x 1000

=60000000

Hence, The solution is, the value is 60000 x 1000 =60000000.

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Which percent is represented by the diagram below?

1.25%
12.5%
125%
1250%

Answers

Your answer will be B 12.5% because there's one whole that equals 10 and the second box that has 2 and a half that's equals 2.5 and then you add them together...

10+2.5=12.5

So your answer is B 12.5.

1 whole section is shaded...so thats 100%
25 out of 100 in the other box.....thats 25%

so u have 125% that is shaded

Find an expression in simplest form for the verbal description.

The sum of the cost of dinner d and a $12 tip divided equally between 4 people

Answers

D+$3 that’s all you need

60,488 rounded to the nearest 10,000

Answers

It would be 60,000 because

With the 488 it would be rounded for the nearest hundredth to 500 then if you had to round it to the nearest 1,000 from 60,500 it would be 61,000

So even with 61,000 rounded to the nearest 10,000 it would still be 60,000 in order to get 70,000 it would need to be 65,000 and anything above to be rounded to the 70,000 mark.

a certain brand of vitamin C contains 300 mg per tablet. A bottle contains 150 vitamins. How many total grams of vitamin C are in the bottle?

Answers

300 mg/tablet

150 tabletsx(300mg/1 tablet)=150x300=45000 mg=45 grams

45 grams is the anwer hope it helped

Expand and simplify:
(x+2)(x+3)

Answers

The answer is x² + 5x + 6. All you have to do is distribute. I hope this helps love! :)

By what percent will a fraction change if its numerator is decreased by 50% and its denominator is decreased by 25%?

Answers

(N/2)/(3D/4) = 2N/3D
So it is decreased by 1/3.

(N/2)÷(3D/4) = 2N/3D

So the answer is 33.33333% or 33 1/3%

Which of these indicates that a bank is likely to be answerable to the Office of the Comptroller of the Currency?
a.
The bank lists the initials “NA” after its name.
b.
The bank has the word “Federal” in its name.
c.
The bank is qualified to give loans.
d.
The bank is owned by the government.

Answers

Which of these indicates that a bank is likely to be answerable to the Office of the Comptroller of the Currency?

a. The bank lists the initials “NA” after its name.

The full form of N.A is N stands for national and A stands for Association. This inclusion of initials helps the banks to be distinguished as national and legal.

The bank is qualified to give loans indicates that a bank is likely to be answerable to the Office of the Comptroller of the Currency.Option a is correct.

What is the role of the Currency Comptroller?

All federal savings organizations, national banks, and federal branches and agencies of foreign banks are chartered, governed, and overseen by the Office of the Comptroller of the Currency (OCC).

The OCC is a stand-alone division of the U.S. Department of the Treasury, and the Comptroller of the Currency is in charge of it.

The OCC makes ensuring that national banks and federal savings organizations run securely, fairly access financial services, treat customers fairly, and adhere to all relevant laws and regulations.

Thus, the bank is qualified to give loans indicates that a bank is likely to be answerable to the Office of the Comptroller of the Currency.Option a is correct.

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Explain why the point (-3,2) is diffrent from the point (2,-3)?

Answers

(-3,2) would result in the point moving over to the left and up 2. (2,-3) would be represented by going to the right 2 units, and down 3.

Write the ratio 28 inches to 9 feet as a fraction in simplest form

Answers

28/108

In simplest form it would be: 7/27

What power can you write to represent the volume of a cube shown? write the power as an expression with a base and an exponent and ,then find the volume of the cube.

Answers

a volume can be a great thing to use and a volume cube

the perimeter of a school crossing sign is 102 inches what is the length of each side

Answers

Add up all sides lengths:

s+6 + s+6 + s + s + 2s = 102

solve for s:

6s + 12 = 102
6s = 90
s= 15

The lengths of sides are as follows:

15, 21, 21, 15, 30 inches

I hope that helps!

Answer:

The length of each side is 21 inches, 21 inches, 15 inches, 30 inches and 15 inches.

Step-by-step explanation:

Consider the provided figure.

It is given that the perimeter of a school crossing sign is 102 inches.

The figure have 5 sides having the length s+6, s+6, s, 2s and s.

Now the perimeter is the sum of all sides,

s+6+s+6+s+2s+s=102

6s+12=102

6s=102-12

6s=90

s=15 inches

The length of each side is:

s+6=15+6=21 inches

s=15 inches

2s=2×15=30 inches

s=15 inches

Hence, the length of each side is 21 inches, 21 inches, 15 inches, 30 inches and 15 inches.

If a computer cost$600.00 and the sales tax rate is 7.5 percent, what is the total cost

Answers

7.5% of 600 = 45, total cost = 600+45 = $645

Solve the equation:

(x^4 - x + y)dx - xdy=0

Answers

keeping in mind that "dx" is the delta x, or differential over the x-axis, whilst "dy" is the delta y or differential over the y-axis,

[tex]\bf (x^4-x+y)dx-xdy=0\implies \stackrel{\textit{distributing dx}}{x^4dx-xdx+ydx}-xdy=0 \\\\\\ ydx=xdy-x^4dx+xdx\implies y=\cfrac{xdy-x^4dx+xdx}{dx} \\\\\\ y=\stackrel{\textit{distributing the denominator}}{x\cfrac{dy}{dx}-x^4+x}[/tex]

What is the angle above the x axis (i.e., "north of east") for a vector with components (15 m, 8 m)?

Answers

If you draw out the two components in a head-to-nose fashion, you will create a right angle triangle something like the picture, that is if I interpreted the information right (the way I interpreted it is 15m east and 8m north);
The dotted line represents the x-axis;
Θ represents the desired angle;
Using trigonometry, we can create and solve an equation to get the angle (Θ);
In this case, you can use use sin or cos, I'll go with sin:
SinΘ = opp/hyp
SinΘ = 8/15
Θ = Sin⁻¹(8/15)
= 32.23.... ⇒ 32.2°

Answer:28.071

Step-by-step explanation:

Given

vector component is (15,8)

i.e. its x component is 15 from origin and y component is 8 m

So angle made by vector with x axis is

[tex]tan\theta =\frac{8}{15}[/tex]

[tex] \theta =tan^{-1}\frac{8}{15} [/tex]

Draw or write to show that the number 18 is an even number

Answers

If you divide it in half, and the two halves are whole numbers, then you know it is an even number.

Final answer:

The number 18 is considered an even number because it can be divided by 2 to result in another integer. This is confirmed by writing 18 as 2 times 9, which results in an even product.

Explanation:

In mathematics, an even number is any integer that can be exactly divided by 2 without leaving a remainder. For example, the numbers 2, 4, 6, 8, and 10 are even because each can be divided by 2 to result in another integer. If you divide an even number by 2, the result is always a whole number, and that's not the case with odd numbers. Let us examine the number 18.

If we write 18 as 2 times 9, we see that it has been turned into a product of 2 and another integer (9, in this case). This indicates that 18 is indeed an even number. Therefore, we can be sure of the fact that the number 18 is an even number, because it can be divided by 2 without leaving a remainder.

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Write the equation of the sphere in standard form. 2x2 + 2y2 + 2z2 = 12x − 24z + 1

Answers

The standard equation of a sphere with center C(a, b, c) and radius r is:

[tex](x-a)^2 + (x-b)^2 + (x-c)^2 = r^2[/tex]
Now, the given equation is :

[tex]2x^2 + 2y^2 + 2z^2 = 12x - 24z + 1 \\ 2x^2 + 2y^2 + 2z^2 - 12x + 24z - 1 = 0 \\[/tex]

combine the x, y and z terms and complete the square for each variable
[tex](2x^2 - 12x) + 2y^2 + (2z^2 + 16z) = 1 \\ (x^2 - 6x) + y^2 + (z^2 + 8z) = 1/2 [/tex]

complete square for x by adding 9 to both sides

we do not complete square for y because there is not a translation on that axis

complete square for z by add 16 to both sides
[tex] (x^2 - 6x + 9) + y^2 + (z^2 - 8x + 16) = 1/2 + 9 + 16 \\ (x - 3)^2 + y^2 + (z - 4)^2 = 25 1/2[/tex]

The standard equation of a sphere with center C(a, b, c) and radius r is:

[tex] (x-a)^{2}+ (y-b)^{2}+ (z-c)^{2}=r^{2}[/tex]

We have the equation:

[tex]2x^2+2y^2+2z^2=12x-24z+1[/tex]

which can be regrouped to fit the standard form, using completing the square as follows:

first divide both sides by 2

[tex]x^2+y^2+z^2=6x-12z+ \frac{1}{2} \\\\(x^2-6x)+y^2+(z^2+12z)= \frac{1}{2}\\\\(x^2-2\cdot3\cdot x)+y^2+(z^2+2 \cdot6 \cdot z)= \frac{1}{2}\\\\(x^2-2\cdot3\cdot x+3^2)-3^2+y^2+(z^2+2 \cdot6 \cdot z+6^2)-6^2= \frac{1}{2}\\\\(x-3)^2+y^2+(x+6)^2=9+36+0.5\\\\(x-3)^2+y^2+(x+6)^2=45.5\\\\\(x-3)^2+y^2+(x+6)^2=( \sqrt{45.5} )^2[/tex]

Answer: [tex](x-3)^2+y^2+(x+6)^2=( \sqrt{45.5} )^2[/tex]

Last week, Donnell practiced the piano 3 hours longer than Marcus. Together, Marcus and Donnelly practiced the piano for 11 hours. For how many hours did each young man practice the piano?

Answers

Marcus practiced for 4 hours and Donnelley played 7 hours

Find all the square number that are greater then 20 but less then 50

Answers

5^2 = 25
6^2 = 36
7^2 = 49
8^2 = 64

So the answer is 5,6,7

Hope this helped!

Joelle is working on a school report in a word processor. She wants to place a figure which is 13.09 cm wide so that it appears centered on the page. The width of the page is 21.59 cm.

How much margin should she leave on the left so that the figure is centered?

Do I divide the width by 13.09 to get the answer? Not very sure

Answers

Alright, so for it to be centered, it needs to be x cm away from the left side and therefore x away from the right side (due to that if it's centered, it needs to be the same distance away from both), making the total width x+13.09+x=21.59=13.09+2x. Subtracting 13.09 from both sides, we get 8.5=2x and by dividing both sides by 2 we get x=3.25

Answer:

The answer is 4.25 cm.

Step-by-step explanation:

Given is - Joelle wants to place a figure which is 13.09 cm wide so that it appears centered on the page. The width of the page is 21.59 cm.

To solve, this first we will 13.09 from the 21.59, and then divide that number in half to find the left and right margin.

[tex]21.59-13.09=8.5[/tex]

[tex]\frac{8.5}{2}= 4.25[/tex]

Therefore, the answer is 4.25 cm.

maggie’s brother is 6 years younger than four times her acne. the sum of their ages is 34. how old is maggie

Answers

m + b = 34
b = 4m - 6

m + 4m - 6 = 34
5m - 6 = 34
5m = 34 + 6
5m = 40
m = 40/5
m = 8 <=== Maggie's age

b = 4m - 6
b = 4(8) - 6
b = 32 - 6
b = 26 .....brothers age

Maggie is 13 because if you

how do you write 12.325 in expanded form

Answers

10 + 2 + 0.3 + 0.02 + 0.005

hope this helps

10.000+2.000+300+20+5

Are you shipping box has a height equal to its with which is equal to its length of the box can hold 1525 cm³ what is the length of one of its sides

Answers

check the picture below.

A recipe calls for 400 grams of flour. if leena makes one quarter of the recipe, how many kilograms of flour will she need?

Answers

300 more grams of flour

You have $27 to spend at the mall and a coupon for $6 off at your favourite store. A t-shirt costs $11 how many tshirts can you buy using your coupon and money

Answers

3 shirts is the most you can buy excluding tax. if im not right tell me plz ?

First we need to found out how much you could buy WITHOUT coupon,
which is 2 shirts that cost $ 22.
You will have $5 Leftover.

Since you have a $6 dollar off coupon, you could buy one more t-shirt with
$ 5 (11 - 6 = 5)

So, the amount of t-shirt you could buy WITH coupon is 3 T-shirts.

In the number 555.55 each digit is a 5 but the value of each 5 is different based on its place in the number. How does the value of the 5 in the tenths place compare to the value of the underlined digit 5

Answers

Final answer:

The value of each 5 in the number 555.55 depends on its place value. A 5 in the tenths place (representing 1/10 or 0.1) would have a much smaller value compared to a 5 in the hundreds place in the same number, due to the multiplying factor of ten for each place value.

Explanation:

In the number 555.55, each digit is indeed a 5. However, the value of each 5 changes depending on its place value. The tenths place, to the right of the decimal point, represents tenths or 1/10 (0.1).

If the underlined digit 5 is in the hundreds place, for example, it will have a value of 500. To compare, the value of the 5 in the tenths place (which is 0.5) is much smaller than the value of the 5 in the hundreds place. In fact, it's 1,000 times smaller because each move to the left in place value multiplies the digit by 10.

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A school PTA wants to rent a dunking tank for its annual fundraising carnival. The cost is $80 for the first three hours and then $19.75 for each additional hour or part thereof. How long can the tank be rented if up to $200 is budgeted for this expense?

Answers

The tank can be rented up to about 9 hours

The tank can be rented for maximum of 6 hours.

We have school PTA wants to rent a dunking tank for its annual fundraising carnival. The cost is $80 for the first three hours and then $19.75 for each additional hour or part thereof.

We have to determine how long can the tank be rented if up to $200 is budgeted for this expense.

The critical level for the number of bacteria spread is 1000. Starting from 500, if the bacteria count rises by 5 every second, then determine whether after 30 seconds the critical level is passed or not?

Initial count = 500

Count increasing per second = 5

Critical level = 1000

Assume that the bacteria count after t seconds is y. Then -

y = 500 + 5t

for t = 30 ↔ y = 150 + 500 = 650 < 1000 → Critical level not passed.

According to question, we have -

Cost for first three hours = $80

Cost for additional hour = $19.75

Total Budget = $200

Assume that the tank can be bought for 'n' hours. Then -

80 + 19.75n ≤ 200

Solving the inequality -

19.75n + 80 - 80 ≤ 200 - 80

19.75n ≤ 120

n ≤ 6.07

n ≤ 6

Hence, the tank can be rented for maximum of 6 hours.

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3 4/5 as a improper fraction may u pls explain how u get the answer

Answers

[tex]\bf \stackrel{\textit{mixed fraction}}{a\frac{b}{c}}\qquad \stackrel{\textit{improper fraction}}{\cfrac{a\cdot c+b}{c}} \\\\\\ thus\implies \stackrel{mixed}{3\frac{4}{5}}\implies \cfrac{3\cdot 5+4}{5}\implies \stackrel{improper}{\cfrac{19}{5}}[/tex]

Should the quotient of an integer divided by a nonzero integer always be a rational number? Why or Why not?

Answers

Yes, it will always be a rational number. I'll expound on this by defining what a rational number is. It is any number that can be expressed as a fraction. Otherwise, it is called an irrational number with a non-terminating decimal expansion. So, although 1/3 has a non-terminating decimal expansion because it is equal to 0.33333333...., it is still a rational number because it can be expressed into a fraction.

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