Call an integer $n$ oddly powerful if there exist positive integers $a$ and $b$, where $b>1$, $b$ is odd, and $a^b = n$. How many oddly powerful integers are less than $2010$?

Answers

Answer 1

Answer:

There are 16 oddly powerful integers less than 2010

Step-by-step explanation:

∵ b is an odd integer

∵ b > 1

∴ The first value of b is 3

∵ a is an integer

- We can use a = 1, 2, 3, ..........

∵ [tex]a^{b}=n[/tex]

∵ n < 2010

- Let a = 1, 2, ............... 12 because 12³ is greatest integer  < 2010

∵ 1³ = 1, 2³ = 8, 3³ = 27, 4³ = 64, 5³ = 125, 6³ = 216, 7³ = 343,

   8³ = 512, 9³ = 729, 10³ = 1000, 11³ = 1331, 12³ = 1728

∴ There are 12 oddly powerful integers with b = 3

Now the second value of b is 5

[tex]1^{5}=1[/tex] but we took 1 before so we will start with 2

∵ [tex]2^{5}=32[/tex], [tex]3^{5}=243[/tex], [tex]4^{5}=1024[/tex]

- [tex]4^{5}[/tex] is the greatest integer < 2010

∴ There are 3 oddly powerful integers with b = 5

Now the third value of b is 7

∵ [tex]2^{7}=128[/tex]

- [tex]2^{7}[/tex] is the greatest integer < 2010

∴ There is 1 oddly powerful integers with b = 7

Now the fourth value of b is 9

∵ [tex]2^{9}=512[/tex]

- [tex]2^{9}[/tex] is the greatest integer < 2010

- But we used 512 before

∴ There is no oddly powerful integers with b = 9

- 9 is the greatest value of b which makes [tex]a^{b}<2010[/tex]

∵ 12 + 3 + 1 = 16

There are 16 oddly powerful integers less than 2010


Related Questions

Which statement is correct?

A kilometer is 100 times the length of a meter.

A kilometer is 1,000 times the length of a meter.

A centimeter is 100 times the length of a meter.

A meter is 10 times the length of a centimeter.

Answers

Answer:

A centimeter is 100 times the length of a meter.

A kilometer is 1,000 times the length of a meter.

The statement that asserts a true claim would be:

B). A kilometer is [tex]1,000[/tex] times the length of a meter.

Metric System

The metric system is a measurement system that employs the meter, liter, and gram as base units of length (distance), capacity (volume), and weight (mass).Kilometers are [tex]1,000[/tex] meters. In the metric system, the meter is the basic unit for measuring length or distance.[tex]1[/tex] kilometer [tex]=1000[/tex] metersSo, a kilometer is [tex]\boldsymbol{1,000}[/tex] times the length of a meter.

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The sum of three consecutive even numbers is 522.find the number

Answers

Answer: 172, 174 and 176

Step-by-step explanation:

Since they are even numbers,

Let x be the number, x + 2 be the second number and x +4 the third number

can think of this as x+(x+2)+(x+4)=522

so you get 3x=522-6

3x= 516

so x=172

If x is 172, second number is 174 and third number is 176

Brandy drove three times as far as Trisha. Together, they drove 48 miles. Which equation below can be used to find the number of miles Trisha drove?

Answers

48=4x can be used to determine the miles covered by Trisha that is 12 miles.

Total distance covered comprises the sum of distances covered by individual entities. Sum means adding like terms in mathematics.

Given, the total number of miles covered by both of them, t= 48 miles

If miles covered by Trisha = x

Then, miles covered by Brandy = 3x (as Brandy drove three times as far as Trisha ).

The total distance covered comprises miles covered by Trisha as well as Brandy.

t=x+3x

On adding the like terms.

t=4x

Substituting t=48,

48=4x

Dividing 4 both sides of the equation,

48/4=4x/4

12=x

x=12 miles

So, the Number of miles Trisha drove is 12.

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How many interior angles does a star have

Answers

five acute angles: the rest of this text does not matter.

How do you multiply 342 and 13.5

Answers

Answer:

Step-by-step explanation: first multiply 342 and 135

then put the decimal just before the ones digit.

answer is

4617.0

please mark  as brainliest

the point A ( 5,3) translate 3 to the right and 1 down. what is the new point? (x,y)----> (x+3,4-1)

Answers

Answer:

(8, 2) OR (x + 3, y - 1)

Step-by-step explanation:

Step 1:  Add 3 to 5 and subtract 1 from 3

(5 + 3, 3 - 1)

(8, 2) OR (x + 3, y - 1)

Answer:  (8, 2) OR (x + 3, y - 1)

Determine whether the two expressions are equivalent. If so, tell what property is applied.
(20 – 4) – 2 and 20 – (4 – 2)

Answers

These two expressions are not equivalent

Both expressions (20 – 4) – 2 and 20 – (4 – 2) are equivalent, simplifying to 14. The equivalence exemplifies the Associative Property of Addition.

The question asks to determine whether the two expressions (20 – 4) – 2 and 20 – (4 – 2) are equivalent, and if so, to identify the property applied. To determine equivalence, we need to simplify both expressions. The first expression, (20 – 4) – 2, simplifies to 16 – 2 which equals 14. The second expression, 20 – (4 – 2), simplifies to 20 – 2 which also equals 14. Therefore, both expressions are equivalent, and the property applied here is the Associative Property of Addition, which allows us to change the grouping of the numbers we're adding (or subtracting, in this case) without changing the result.

Solve proportion S/84=3/21

Answers

Answer:

S=21

Step-by-step explanation:

First cross multiply, next divide. I hope this helped!

Answer: S = 12

Step-by-step explanation:

S/84 =3/21

Cross multiply to find the value of S

21 x S= 84 x 3

21S= 252

S= 252/21

S= 12

If i have 6 bottles of water and each weigh 3/5 pounds how much do i have

Answers

You have 3 and 3/5 pounds of water.

To find this, simply multiply 3/5 by 6/1 (multiplying straight across). 6 times 3 is 18 and 5 times 1 is 5. Thus meaning you have 18/5 pounds, which simplified is 3 and 3/5 pounds.

I hope this helps!

Answer:

if you multiply 3/5 ×6 that would be 3.6 or in mix number that would be 3⅗

What is 926 divided by 38? and also what is its remainder ​

Answers

Hello!

The answer to your problem is 24 R 14 (R for remainder)

Here is my work show.

Answer: 24.37

Step-by-step explanation:

926/36 = 24.3684

Rounded = 24.37

22.4 divide by 134.4

Answers

Hello 0.166666... is the answer
the answer is: 0.166666666666667

PLEASE ANSWER

For Saturday’s debate tournament, Sarah ordered 3 cookies for each student participant and a tray of 30 cookies for the sponsors’ hospitality room. This relationship can be expressed by the function C = 3s + 30, where s is the number of student participants and C is the number of cookies ordered. Which is the dependent quantity in this functional relationship?

A. The number of cookies ordered
B. The number of trays ordered
C. The number of student participants
D. The number of sponsors

Answers

Answer:

A

Step-by-step explanation:

The cookies ordered is the dependent quantity/variable because the other variables don't depend on anything that is quantifiable.

The dependent quantity in this functional relationship is A. The number of cookies ordered.

A dependent quantity simply refers to the quantity that depends on another quantity or is determined by another quantity.

Based on the information given, the dependent quantity in this functional relationship is the number of cookies ordered since it depends on other factors such as the number of trays and students.

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Tony has $10 to buy apples and bananas for a fruit salad. Apples cost $2 per pound and bananas cost $1 per pound. Write and graph an inequality to describe the situation. Then give two possible combinations of pounds of apples and bananas that Tony can buy. HELP

Answers

The equation of inequality would be = 2 x + y ≤ 10 for the process of purchase.

Explanation:

Total amount of money tony have , T = $10

Thus the cost of apple, (We can represent as Ca) = $2

Also the cost of banana,(We can represent as  Cb) = $1

Let x be the number of apples bought

Let y be the number of bananas bought

Total expenditure to buy fruits, E = $2 x + $1 y

So,The equation of inequality would be = 2 x + y ≤ 10 for the process of purchase.

A wise man once said, “400 reduced by 4 times my age is 168.” What is his age?

Answers

Answer: the man is 58!

Step-by-step explanation: please mark brainliest

we could use this equation

168=400-4a         an a= uknown age

-400     -400

-232=-4a

divide by -4 on both sides to get the variable by itself

58=a

a=58

and to double check we can do this

168=400-4(58)     by susbtuting the variable

168=400-232

168=168     correct

2x + y = 3
4x + 3y = 1

Answers

Answer:

x = 4, y = -5 OR (4, -5)

Step-by-step explanation:

Step 1:  Solve for y in the first equation

2x + y - 2x = 3 - 2x

y = 3 - 2x

Step 2:  Plug in that into the second equation to get x

4x + 3(3 - 2x) = 1

4x + 9 - 6x = 1

-2x + 9 - 9 = 1 - 9

-2x / -2 = -8 / -2

x = 4

Step 3:  Use x to find y

y = 3 - 2(4)

y = 3 - 8

y = -5

Answer:  x = 4, y = -5 OR (4, -5)

Y=3-2x for the first one

Y=1/3-4x/3 for the second one

The measure of Mis 57°. What is the measure of its complementary angle?
A 33
B90°
C123
D180°

Answers

Answer:

A 33°

Step-by-step explanation:

Complementary angle of 57° = 90° - 57° = 33°

2x+15=145
Solve for x

Answers

Answer:

Step-by-step explanation:2x=145-15

2x=130

X=130/2

X=65

Triangle A B C has centroid G. Lines are drawn from each point through the centroid to the midpoint of the opposite side to form line segments A E, B F, and C D. The length of line segment A G is 2 x + 10, the length of line segment F G is 2 x minus 1, and the length of line segment G B is 3 x + 6.

G is the centroid of triangle ABC.

What is the length of AE?

units

Answers

Answer:

The length of AE is 39 units.

Step-by-step explanation:

Given:

G is the centroid of a triangle ABC.

Lines are drawn from each point through the centroid to the midpoint of the opposite side to form line segments AE, BF, and CD.

The length of line segment A G is 2 x + 10, the length of line segment F G is 2 x minus 1, and the length of line segment G B is 3 x + 6

To Find: Length of the AE.

The centroid of the triangle is always cut the line in the ratio of 2:1. For clarification, the image is provided.

Hence,

G divides the line BF into a 2:1 ratio.

Thus,

[tex]\begin{aligned}&2FG=BG\\&2(2x-1)=3x+6\\&4x-2=3x+6\\&x=8 \end{aligned}[/tex]

Also,

G divides the line AE into a 2:1 ratio.

Therefore,

[tex]AG=2GE\\GE=AG/2[/tex]

Line segment AE is the sum of AG and GE.

Thus,

[tex]AE=AG+GE\\AE=AG+AG/2\\AE=3AG/2\\AE=3(2x+10)/2\\AE=39[/tex]

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The length of AE is 9 units.

Given that G is the centroid, it divides each median into two segments with the ratio of 2:1, where the longer segment is toward the vertex and the shorter segment is toward the midpoint of the opposite side.

Let's denote the length of AG as a, the length of BG as b, and the length of FG as c. According to the given information:

1. AG = 2x + 10

2. FG = 2x - 1

3. BG = 3x + 6

We know that AG = 2GE and BG = 2GE. Thus:

[tex]\[ AG = 2GE \implies GE = \frac{AG}{2} = \frac{2x + 10}{2} = x + 5 \]\[ BG = 2GE \implies GE = \frac{BG}{2} = \frac{3x + 6}{2} = \frac{3}{2}x + 3 \][/tex]

Since GE is common, we can equate the expressions:

[tex]\[ x + 5 = \frac{3}{2}x + 3 \][/tex]

Solving for x:

[tex]\[ \frac{1}{2}x = 2 \][/tex]

x = 4

Now that we've found the value of x, we can substitute it back into the expressions for AG and FG to find their lengths:

AG = 2x + 10 = 2(4) + 10 = 18

FG = 2x - 1 = 2(4) - 1 = 7

Now, we know that AE = AG - GE:

AE = AG - GE = 18 - (x + 5) = 18 - (4 + 5) = 18 - 9 = 9

So, the length of AE is 9 units.

The length of a rectangle is 4 more than 3 times the width. If the perimeter of the rectangle is 18.4 cm, what is the area of the rectangle?

Answers

Area of the rectangle is 10.27 cm²

Step-by-step explanation:

Step 1: Let the width of the rectangle be x, then length = 4 + 3x. Find the dimensions if perimeter = 18.4 cm

Perimeter = 2(length + width)

⇒ 18.4 = 2 (x + 4 + 3x)

⇒ 18.4 = 2(4x + 4)

⇒ 18.4 = 8x + 8

⇒ 8x = 10.4

⇒ x = 10.4/8 = 1.3

∴ 4 + 3x = 4 + 3×1.3 = 7.9

Step 2: Find area of the rectangle.

Length = 7.9 cm and width = 1.3 cm

⇒ Area = length × width

             = 7.9 × 1.3 = 10.27 cm²

What is the change that occurs to the parent function f(x) = x^2 given the function f(x) = (x + 1)^2 - 5.

Answers

The translation is down 5 because if you simplify or solve the second f(x), it would be x^2 - 5. I hope this helps :)

what equation is equivalent to 3(2x-5)=4(x+3)

Answers

Answer:

6x-15 = 4x+12

Step-by-step explanation:

3*2x = 6x

3*-5 = -15

4*x=4x

4*3=12

6x-15 = 4x+12

Answer:

6x - 15 = 4x + 12

Explanation:

Simplify 3 * 2x = 6x. 3 * -5 =  -15. 4 * x = 4x. And 4 * 3 = 12. Then just put 'em together! :D

What is the value of x ?
A : 15
B : 30
C: 45
D : 60

Answers

Answer:

A

Step-by-step explanation:

So that is a 90 degree angle and there is an angle of 30. 30-90 is 60. 60 divided by 4 is 15. So thus the answer is A,15.

Answer:

15

Step-by-step explanation:

90 is right angle

90 - 30 = 60

60 / 4 = 15 <---- theres the answer

hope i helped

What must be the length of ZY in order for ZY to be tangent
to circle X at point Y?
14 units
15 units
16 units
17 units

Answers

Answer:

15 units

Step-by-step explanation:

The picture of the question in the attached figure

we know that

Triangle XYZ is a right triangle, because segment ZY is tangent to circle X at point Y

so

Applying the Pythagorean Theorem

[tex]XZ^2=XY^2+ZY^2[/tex]

we have

[tex]XZ=8+9=17\ units\\XY=8\ units[/tex]

substitute the given values

[tex]17^2=8^2+ZY^2[/tex]

[tex]ZY^2=289-64\\ZY^2=225\\ZY=15\ units[/tex]

Answer:

15

Step-by-step explanation:

A movie theater sells small and large boxes of popcorn.
• A small box of popcorn costs $1.50.
• A large box of popcorn costs $4.00.
• A total of 25 boxes of popcorn were sold totaling $75.00.
How many large boxes of popcorn were sold?
A 6
B. 10
C.
12
D.
15

Answers

The answer would be ten

There 15 large boxes of popcorn were sold. The option D is correct.

We need to determine the number of large boxes of popcorn sold. Let's denote the number of small boxes as s and the number of large boxes as l. We are given the following information:

The cost of a small box of popcorn is $1.50.

The cost of a large box of popcorn is $4.00.

A total of 25 boxes of popcorn were sold.

The total revenue from popcorn sales was $75.00.

We can set up two equations based on this information:

s + l = 25 (the total number of boxes sold)

1.50s + 4.00l = 75.00 (total revenue from sales)

Let's solve for l using these equations. Multiplying the first equation by 1.50 gives us:

1.50s + 1.50l = 37.50

Subtracting this from the second equation:

(1.50s + 4.00l) - (1.50s + 1.50l) = 75.00 - 37.50

2.50l = 37.50

l = 37.50 / 2.50

l = 15

A 12inch diameter pizza has 22 calories per square inch. About how many calories are in the entire pizza? Use 3.14 for pi. Select from the drop-down menu to correctly complete the statement

Answers

Step-by-step explanation:

Diameter of pizza = 12 inch

Therefore, radius r = 6 inch

[tex]Area \: of \: entire \: pizza \\ = \pi {r}^{2} \\ = 3.14 \times {6}^{2} \\ = 3.14 \times 36 \\ = 113.04 \: {inch}^{2} \\ \\ amount \: of \: calories \: in \: entire \: pizza \\ = area \: of \: pizza \\ \times calories \: per \: square \: inch \\ = 113.04 \times 22 \\ = 2,486.88 \\ [/tex]

An electronics store reduced the price of a TV from $1000 to $880. What was the percent of decrease?

Answers

Answer:

12% decrease

Step-by-step explanation:

think of 1000 as 100% and thin 880 as 88% subtract those 12%

Final answer:

The price decrease from $1000 to $880 represents a 12% decrease. This is figured out by taking the difference in price, dividing it by the original price, and then multiplying by 100%.

Explanation:

The percentage decrease is calculated by taking the difference in price divided by the original price, and then multiplying by 100 to get a percentage. In this case, the difference in price is the original price minus the sale price. This would be $1000 - $880 = $120. So, the formula would be ($120/$1000)*100. The calculated percentage decrease is 12%, meaning the price of the TV has been reduced by 12%.

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How should I prove this???​

Answers

Since UVX is 90 degrees Angle 6 and Angle 5 are complementary. Then, Angle 5 and Angle 4 are the same since they were bisected by WVY. This makes Angle 4 and Angle 5 the same, so you can say that Angle 6 + Angle 5 are complementary and Angle 6 and Angle 4 are complementary.

How do u graph y=15x+35?

Answers

Hey there!

This is slope intercept form, where y=mx+b, where b is the y-intercept (where the line hits the y-axis) and the slope (rate of change).

If you wanted to graph this line, we can see that the y intercept in 35. Therefore, our line is going have one point on (0,35). Our slope is 15, which is positive, showing that our line will go up. Because the slope is fifteen, for every single increase of 1 there is in x, there will be an increase of 15 in y. This will give us points like (1,15) (2,30) (3,45). Therefore, this will be a very steep line.

You can use this info to graph your line.

Answer:

PLS PASS BRAINLIEST

Step-by-step explanation:

put the first point on 35 on y axis

now count 15 from 35 which is 50 and move one to the right

which is (50,1)

and keep on reapeting that

Find the composite area of the shaded region

Answers

Answer:

what region

Step-by-step explanation:

A 20 packet box of detergent sells for $5.49. What is the unit rate


Answers

Answer:$0.27

Step-by-step explanation:

20=$5.49

1=20/5.49

1=$0.2745

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