Find how many six-digit numbers can be formed from the digits 2, 3, 4, 5, 6 and 7 (with repetitions), if:

the numbers formed must be divisible by 25

or

the odd digits must occupy even positions (i.e. 2nd, 4th, and 6th) and the even digits must occupy odd positions (i.e. 1st, 3rd and 5th)

Answers

Answer 1

Answer:

case 1 = 2592

case 2 =  729

case 1 + case 2 =  2916

(this is not a direct adition, because case 1 and case 2 have some shared elements)

Step-by-step explanation:

Case 1)

6 digits numbers that can be divided by 25.

For the first four positions, we can use any of the 6 given numbers.

For the last two positions, we have that the only numbers that can be divided by 25 are numbers that end in 25, 50, 75 or 100.

The only two that we can create with the numbers given are 25 and 75.

So for the fifth position we have 2 options, 2 or 7,

and for the last position we have only one option, 5.

Then the total number of combinations is:

C = 6*6*6*6*2*1 = 2592

case 2)

The even numbers are 2,4 and 6

the odd numbers are 3, 5 and 7.

For the even positions we can only use odd numbers, we have 3 even positions and 3 odd numbers, so the combinations are:

3*3*3

For the odd positions we can only use even numbers, we have 3 even numbers, so the number of combinations is:

3*3*3

we can put those two togheter and get that the total number of combinations is:

C = 3*3*3*3*3*3 = 3^6 = 729

If we want to calculate the combinations togheter, we need to discard the cases where we use 2 in the fourth position and 5 in the sixt position (because those numbers are already counted in case 1) so we have 2 numbers for the fifth position and 2 numbers for the sixt position

Then the number of combinations is

C = 3*3*3*3*2*2 = 324

Case 1 + case 2 = 324 + 2592 = 2916


Related Questions

Howard wants to use multiplication to solve w=5 divided by 1/5 Which multiplication equation can Howard use?

A:5*1/5=w

B:1/5*5=w

C:5=1/5*w

Answers

Answer:

C.5=1/5*w

Step-by-step explanation:

W=5÷1/5

Multiply both sides by 1/5

(1/5)w=5÷1/5(1/5)

(1/5)w=5×5/1(1/5)

1/5*w=25/1 * 1/5

1/5*w=25/5

1/5*w=5

It can also be written as

5=1/5*w

Answer:

5 1/5 * w

Step-by-step explanation:

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Mandy paints four square walls that are ten feet on each side. Which expression represents the total square footage that Mandy painted?

4 × 10 squared
4 squared × 10
4 × 10 × 2
10 squared + 4

Answers

Answer:

i think its c

Step-by-step explanation:

Final answer:

The correct expression for the total square footage that Mandy painted is 4 × 10 squared, which totals 400 square feet when calculated.

Explanation:

The expression that represents the total square footage that Mandy painted when she paints four square walls that are ten feet on each side is 4 × 10 squared. To understand why, let us analyze a related problem where Marta has one square with a side length of 4 inches and another larger square with dimensions that are twice the first square, which means the side length of the larger square is 8 inches (4 inches × 2).

The area of a square is calculated by squaring its side length, so the smaller square has an area of 16 square inches (4 inches squared), and the larger square will have an area of 64 square inches (8 inches squared). This demonstrates that the area of the larger square is four times larger than the area of the smaller square, as the scale factor of the side lengths is squared to obtain the ratio of the areas.

Similarly, for Mandy's wall painting, each wall is 10 feet by 10 feet, so the area of one wall is 10 feet squared, which equals 100 square feet. Since there are four walls, the total area is 4 × 100 square feet, or 400 square feet in total. The correct expression for the total square footage Mandy painted is 4 × 10 squared.

If sound travels 2 miles and 10 seconds how far does sound travel in 2 minutes

Answers

Answer:

24 miles

Step-by-step explanation:

2 miles:10 seconds

? miles: 120 seconds

120 divided by 10 =12

12 x 2 =24

Final answer:

Sound travels 2 miles in 10 seconds, giving it a speed of 0.2 miles per second. In 2 minutes, which equals 120 seconds, sound will travel 24 miles.

Explanation:

If sound travels 2 miles in 10 seconds, we can calculate the speed of sound by dividing the distance traveled by the time it took. To find out how far sound would travel in 2 minutes, we must first calculate its speed:

Speed = Distance / Time

Speed = 2 miles / 10 seconds

Speed = 0.2 miles/second

Now, let's convert 2 minutes to seconds since the speed is in miles per second:

2 minutes = 2 x 60 seconds = 120 seconds

Finally, we calculate how far sound travels in 2 minutes:

Distance in 2 minutes = Speed x Time

Distance in 2 minutes = 0.2 miles/second x 120 seconds

Distance in 2 minutes = 24 miles

Therefore, sound travels 24 miles in 2 minutes.

Can someone please find C for me

Answers

45 degrees? I may be wrong. 360/8=45


Using the greatest common factor for the terms, how can you write 56 + 32 as a product?

A) 4(14 + 8)
B) 7(4 + 8)
C) 8(7 + 4)
D) 14(4 + 2)

PLZ HELP

Answers

Answer:

8(7+4) (C.)

Step-by-step explanation:

First find the biggest number thta can go into 56 and 32:

8!

Since C. is the only one that has an 8 out in the front, let's try that one:

[tex]8*7=56[/tex]

[tex]8*4=32[/tex]

So C. Is correct!

Convert each measurement into another measurement unit. How many inches are in 5 ft?

Answers

Answer:

60 inches

Step-by-step explanation:

Multiply the length value by 12

A compressed air tank carried by scuba divers has a volume of 8.00 L and a pressure of 141 atm at 22.0°C. What is the volume (in liters) of air in the tank at STP?

A) 993 L
B) 1,044 L
C) 1,224 L
D) 1,280 L

Answers

Answer:

Volume of air in the tank =1,044 Liter

Step-by-step explanation:

Given:

Tank volume = 8 Liter

Pressure = 141 atm

Temperature = 22°C = 273° + 20° = 295° K

Find:

Volume of air in the tank = ?

Computation:

[tex]\frac{Pressure\times Tank\ volume}{Tempreture} =\frac{Pressure\times Air\ volume}{Tempreture}\\\\\frac{141\times 8}{295} =\frac{1\times Air\ volume}{273.15}\\\\\frac{1,128}{295} =\frac{Air\ volume}{273.15}\\\\Air\ volume=1,044.45[/tex]

Volume of air in the tank =1,044 Liter

Answer:

1,044 Liter

Step-by-step explanation:

What is the "unknown" in this problem that we need to find?

Answers

Answer:sorry i cant help but i dont see an unknown in this question please edit your answer so we can see something.Thank you.

Step-by-step explanation:

If two triangles are congruent, which of the following statements must be
true? Check all that apply.
A. The triangles have the same shape, but not the same size.
B. The corresponding angles of the triangles are congruent.
C. The triangles have the same shape and size.
D. The corresponding sides of the triangles are congruent.
SUBM

Answers

Answer:

C. The triangles have the same shape and size.

B with C together also is accepted.

Two triangles are congruent if their corresponding sides are equal in length, and their corresponding angles are equal in measure.

Step-by-step explanation:

All the rest are wrong.

The correct answer(s) is B and c

25% of what number is 30?

Answers

to find the 25% of 30  

first 25/100=0.25

then we write 0.25 x 30=7.5

so the answer is 7.5 or 120

Answer:

The answer is 120

On a coordinate plane, a parabola opens up. It goes through (negative 6, 0), has a vertex at (negative 4, negative 4), and goes through (negative 2, 0). The graph of the function f(x) = (x + 6)(x + 2) is shown. Which statements describe the graph? Check all that apply. The vertex is the maximum value. The axis of symmetry is x = –4. The domain is all real numbers. The function is increasing over (–∞, –4). The function is negative over (–6, –2).

Answers

Answer:The axis of symmetry is x=-4

The domain is all real numbers

The function is negative over (-6,-2)

Step-by-step explanation:

Its right

The statement that described the graph should be

The axis of symmetry is x=-4

The domain is all real numbers

The function is negative over (-6,-2)

What is a parabola in the graph?

A parabola refers to the U-shaped curve that should be drawn for a quadratic function. The graph of the parabola should be considered downward at the time when the value of a should be less than 0, a < 0.

So based on this, we can conlcude that the above 3 statements should be considered and the other statements should be incorrect.

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What is the value of a+b?

Answers

the answer is c

Step-by-step explanation:

because I was working on it

Emilio has worn a gray shirt on 7 of the last 14 days. What is the experimental probability that Emilio will wear a gray shirt tomorrow?

Answers

Answer:

Step-by-step explanation:

7/14

Step-by-step explanation:

When Rachel puts gas in her car, she records the distance that she has driven since her last
fill-up and the number of gallons of gas that her car has used. She uses this information to
predict the amount of gas that her car will use to travel different distances,

Answers

g=0.04 times d

Step-by-step explanation:

if you multiply 0.04 with every number under the d column then you’ll get the outcome of each number under g

The relationship between the number of gallons of gas that the car uses g, and the number of miles the car has driven d, is given by the equation g=0.04d. Since the values of g and d are linearly connected.

Which is said to be a Linear equation?A linear equation is an algebraic equation that has the highest degree as 1.The general form of the linear equation is [tex]y=ax+c[/tex]. Where y is the dependent variable and x is the independent variable.So, as the value of x increases the value of y also increases linearly and forms a straight line.

Given data:

It is given that,

A table of content about the distance traveled by Rachel and the gas used for that distance.

The distance is given in miles as d and the gas is given in gallons as g

The values of d given in the table are 14, 70, 109, and 140. Here the order is increasing.

The values of g given in the table are 0.56, 2.8, 4.36, and 17.6. Here also the order is increasing.

Finding the relationship between g and d:

Since the values of g and d are increasing linearly and g is depending on d, consider a linear equation as follows:

[tex]g=ad+c[/tex]

Finding a and c from the obtained equation:

From the table, when d=14, g=0.56 and d=70, g=2.8

On substituting these values in the equation we get

0.56=14a+c

2.8=70a+c

Subtracting 1st equation from the 2nd equation,

2.8-0.56=(70a+c)-(14a+c)

⇒ 2.24=56a

⇒ a=0.04

On substituting a value in any of the equations we get

0.56=(0.04)(14)+c

⇒ c=0

Thus, the required equation becomes g=0.04d. This says that the g and d values are linearly related to each other.

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What is the length of line segment CD with endpoints (Negative 3 2) and (2, 2) as shown on the coordinate plane? On a coordinate plane, line C D goes from (negative 3, 2) to (2, 2). 2 units 3 units 4 units 5 units

Answers

Answer:

5 units

Step-by-step explanation:

im taking the test rn

What type of transformation is shown?
A) Dilation
Eliminate
B) Reflection
C) Rotation
D) Translation

Answers

Answer:

A Dilation

Step-by-step explanation:

your dilating the original shape to a new size

Answer:

A) Dilation

Step-by-step explanation:

I did this last year and when the original shape stays the same and another shape either grows or shrinks it's dilation.

f(x)=x^2. What is g(x)

Answers

Answer:

D

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

Having the line moving to the right we know that it has to be in parentheses.  And

Determine the equation for the line of best fit to represent the data.

scatter plot with points going up from about zero comma negative 3 to the right to about 7 comma zero

y equals three sevenths times x minus 3
y equals negative three sevenths times x minus 3
y equals seven thirds times x minus 3
y equals three sevenths times x plus 3

Answers

Answer:

A) y equals three sevenths times x minus 3

God has a plan for everyone!!

Hi xevysxvuiwhcusvidbufbicdbidvudbusviw

Answers

Answer:

29

Step-by-step explanation:

i know my math


Bob Jones bought a new log cabin for $63,000 at 10% interest for 30 years. Prepare an amortization schedule for the first three periods.

Answers

6300 is the correct answer

the perimeter of an equilateral triangle is 150cm. If the length of the altitude of the triangle is x√3cm, what is the value of x?​

Answers

Answer:

X = 25

Step-by-step explanation:

To solve this question, we'll first of all find determine the side length of the triangle from the perimeter.

Perimeter of an equilaterial triangle = 3 * s

S = side length

Perimeter = 150cm

150 = 3s

S = 150 / 3

S = 50cm

The side lengths are 50cm each since they are all equal.

To find x,

We have to divide the triangle equally into two different part.

Check the first attachment for better illustration on how the equilaterial triangle is.

Check the second attachment for better illustration on the triangle when its divided into a right angle triangle.

From the right angle triangle, we can use pythagorean theorem to solve for x

a² = b² + c²

a = 50cm

b = 25cm

c = x√(3)

50² = [x√(3)]² + 25²

2500 = x² * 3 + 625

2500 - 625 = 3x²

1875 = 3x²

X² = 1875 / 3

X² = 625

X = √(625)

X = 25

Factor the polynomial using the pattern.
x2 - 9x + 20

Answers

Answer: To factorize the quadratic expression

x2−9x+20, one must find the two numbers that add together to give 9, and multiply together to give 20. Those two numbers are 4 and 5, which factor into the expression

(x−4)(x−5). The signs are due to the fact that the first sign in the expression is a positive, which tells us that both signs must be the same, and the first sign is a negative, which means that, due to the positive sign in the expression, both signs are negative. To do the opposite, expanding, one must multiply

x by x, to get x2, add together 4 and 5 to get 9, and multiply them to get 20.

Answer:

Answer: To factorize the quadratic expression

x2−9x+20, one must find the two numbers that add together to give 9, and multiply together to give 20. Those two numbers are 4 and 5, which factor into the expression

(x−4)(x−5). The signs are due to the fact that the first sign in the expression is a positive, which tells us that both signs must be the same, and the first sign is a negative, which means that, due to the positive sign in the expression, both signs are negative. To do the opposite, expanding, one must multiply

x by x, to get x2, add together 4 and 5 to get 9, and multiply them to get 20.

Step-by-step explanation:

Which is the best estimate for the average rate of change for the quadratic function graph on the interval 4 ≤ x ≤ 12? A) 1 B) 2 C) 3 D) 4

Answers

The average rate of change will be given by 16a + b

What is average rate?

Average Rate: A single rate that applies to real estate at many locations and is calculated as the weighted average of the various rates that are appropriate at each site.

It is the average amount by which the function changed per unit throughout that time period. It is calculated using the slope of the line linking the interval's ends on the graph of the function.

Given:

A general quadratic function of x is given by f(x) = ax² +bx +c

Now, the rate of change of the function f(x) is given by df(x)/ dx.

Therefore, df(x)/ dx = 2ax+ b

Now, the value of x ranges between 4 ≤ x ≤ 12.

So, at x= 4

df(x)/ dx = 2a(4) + b= 8a+ b

and, x= 12

df(x)/ dx = 2a(12) + b= 24a+ b

Thus, the average rate of change will be given by

(8a+ b) + (24a+ b) / 2

= 32a+ 2b/ 2

= 16a + b

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Paul rolled a number cube. What is the probability he will roll a 5 or 6

Answers

Answer:

2/6, 33.33, or 33.33%

Step-by-step explanation:

6 total possible outcomes, and 2 in this scenario.

That's 2 over 6.

Hope this helps!

Answer:

2 chances divide by 6 sides = 0.333333 or 1/3 or 33% like the other person said.

Step-by-step explanation:

Coach Chapman has 54 students signed up for a jump rope competition. He only has 18 jump ropes. What is the ratio of jump ropes to students?

brainliest

Answers

Answer:

1:3

Step-by-step explanation:

The question is asking what the ratio of jump ropes to students is.

The order of the question matters.

Since they ask for the jump ropes first and then the students, we

get a ratio of 18:54.

Find the GCF (Greatest Common Factor)

The GCF is 18.

Divide 18:54 by 18.

18/18=1

54/18=3

The answer is 1:3.

Sanjay has 59 toy cars. 12 of the cars are blue and 23 of the cars are red. The rest of the cars are white.
How many more toy cars are white than blue? Enter the answer in the box.
toy cars

Answers

Answer: 12

Step-by-step explanation: 12+23 = 35

59-23 is 24

24 is the number of white cars so if 12 of the cars are blue, you just subtract 12 from 24 giving you 12 as the difference between white and blue cars

Final answer:

Sanjay has 12 more white toy cars than blue. There are 24 white cars in total after subtracting the number of blue and red cars from the total.

Explanation:

Sanjay has a total of 59 toy cars, of which 12 are blue and 23 are red. To find out how many toy cars are white, we need to subtract the number of blue and red cars from the total number of cars.

Total number of cars = 59

Number of blue cars = 12

Number of red cars = 23

Subtract the number of blue and red cars from the total:
59 - 12 - 23 = 59 - 35 = 24

So, there are 24 white cars.

To find out how many more white cars there are than blue cars, subtract the number of blue cars from the number of white cars:

24 (white cars) - 12 (blue cars) = 12

Therefore, there are 12 more white toy cars than blue toy cars.

Which is the parametric form of the polar equation r=-3theta

A.x=3thats cos theta

Y=3theta sin theta

B.x=-3theta cos theta

Y=-3theta sin theta

C.x=-3cos theta

Y=-3 sin theta

D.x=-theta cos theta

Y=-theta sin theta

Answers

Answer:B

Step-by-step explanation:

Given

[tex]r=-3\theta [/tex]

so [tex]x=-3\theta \cos \theta \quad \ldots(i)[/tex]

and

[tex]y=-3\theta \sin \theta \quad \ldots(ii)[/tex]

squaring and adding [tex](i)[/tex] and [tex](ii)[/tex] we get

[tex]x^2+y^2=(-3\theta \cos \theta)^2+(-3\theta \sin \theta)^2[/tex]

[tex]x^2+y^2=r^2=9\theta ^2\cos ^2 \theta +9\theta ^2\sin ^2 \theta [/tex]

[tex]r^2=9\theta ^2[/tex]

[tex]r=-3\theta [/tex]

for [tex]r[/tex] to be negative both [tex]x[/tex] and [tex]y[/tex] must be negative

kenneth drove 177.55 miles in 3 7/20 hours. what was his average speed

Answers

Kenneth's average speed, we divide the total distance by the total time traveled. In this case, Keneth's average speed was approximately 52.91 miles per hour.

Kenneth's average speed, you can use the formula:

Average Speed = Total Distance/Total Time.

In this case, Kenneth drove 177.55 miles in 3 7/20 hours.

First, convert the mixed number time to an improper fraction:

3 7/20 = 67/20.

Now, substitute the values into the formula:

Average Speed = 177.55 / (67/20).

To divide by a fraction, multiply by its reciprocal:

Average Speed = 177.55 * (20/67).

Average Speed ≈ 52.91 miles per hour.

Therefore, Keneth's average speed was approximately 52.91 miles per hour.

Suppose that the amount of algae in a pond doubles every 3 hours. If the pond initially contains 50 pounds of algae, how much algae will be in the pond after 8 hours.In this exponential situation, what would the y-intercept be? CHOICES:
(0,3)
(0,2)
(0,50)
(0,8)

Answers

Answer:

After 8 hour there will be 317.64 pounds of algae.

y-intercept: (0, 50)

Step-by-step explanation:

At time = 0 hours, there are 50 pounds of algae, after 3 hour there will be 100 pounds of algae, after 6 hour there will be 200 pounds of algae, and so on.

Exponential growth is modeled by the following equation:

y = x0*(1 + r)^t

where x0 is the amount of algae at the beginning, r is the rate of change, and y is the amount of algae after t hours. Replacing with data:

100 = 50*(1 + r)^3

2 = (1 + r)^3

ln(2) = 3*ln(1 + r)

r = exp(ln(2)/3) - 1

r = 0.26

This result can be checked as follows

y = 50*(1 + 0.26)^6 = 200

After 8 hours:

y = 50*(1 + 0.26)^8 = 317.64

The y-intercept corresponds to t = 0

y = 50*(1 + 0.26)^0 = 50

True or false: the Pythagorean theorem can be applied to every triangle

Answers

False because it must have a right angle.
Final answer:

The Pythagorean theorem can only be applied to right triangles.

Explanation:

The Pythagorean theorem can be applied to right triangles only.

It states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

So, while the Pythagorean theorem cannot be applied to every triangle, it can be used to find the length of one side of a right triangle given the lengths of the other two sides.

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