If I like geometry, then I like math.
Choose the equivalent statement

Answer:

2. 3 to the power of -5

4. 2 to the 5th power times 6 to the -5 power

Step-by-step explanation:

(2⁵)/(6⁵)

(2/6)⁵

(1/3)⁵

(3^-1)⁵

3^(-5)

(2/6)⁵

2⁵ × (6^-1)⁵

2⁵ × (6^-5)

Steps to solve:

2^5/6^5

~Apply exponent rules

(1/3)^5

1^5/3^5

~Simplify

1/243

Now, we can solve for each option.

Option 1:

1/3 ≠ 1/243

This is incorrect.

Option 2:

3^-5 = 1/243

This is correct.

Option 3:

-4^-5

-1/4^5

-1/1024 ≠ 1/243

This is incorrect.

Option 4:

2^5 * 6^-5

2^5 * 1/6^5

2^5/6^5

1^5/3^5

1/243 = 1/243

This is correct.

Therefore, the correct answers are options 2 and 4.

Best of Luck!

Answer:

A. 314

Step-by-step explanation:

Volume of a cone= π*radius^2*height/3

Pi*radius^2=3.14*25=78.5

78.5 * height/3=78.5*12/3=78.5 x 4= 314

Step-by-step explanation:

3x + 9 - 3 = 46 - 2x

3x + 6 = 46 - 2x

3x + 2x = 46 - 6

5x = 40

x = 40 / 5 = 8

x = 8

Given:

a) 3 × 3 × 3 × 3 × 3

b) 4 × 4 × 4 × 5 × 5

c) 9 × 7 × 9 × 9 × 7 × 9

To find:

The index notation.

Solution:

a) Using multiplication rule of indices:

[tex]a^{n} \times a^{m}=a^{n+m}[/tex]

[tex]3\times3\times3\times3\times3=3^{1+1+1+1+1}[/tex]

                           [tex]=3^5[/tex]

Therefore, [tex]3\times3\times3\times3\times3=3^{5}[/tex]

b) Using multiplication rule of indices:

[tex]4\times4\times4\times5\times5=4^{1+1+1}5^{1+1}[/tex]

                          [tex]=4^35^2[/tex]

Therefore, [tex]4\times4\times4\times5\times5=4^{3}5^{2}[/tex]

c) Using multiplication rule of indices:

[tex]9\times7\times9\times 9\times7\times9=9^{1+1+1+1}7^{1+1}[/tex]

                                 [tex]=9^47^2[/tex]

Therefore, [tex]9\times7\times9\times 9\times7\times9=9^{4}7^{2}[/tex]

Answer:

[tex]v = 183 {cm}^{3} to \: the \: nearest \: whole \: number[/tex]

Step-by-step explanation:

Volume of a cone is given as:

[tex]v = \frac{1}{3} \times\pi \times \ {r}^{2} \times h[/tex]

where,

pi = 3.14

r = radius = half of diameter; 10cm/2 = 5cm

h = height = 3cm + 4cm = 7cm

Thus,

[tex]v = \frac{1}{3} \times 3.14cm \times {5}^{2} cm \times 7cm[/tex]

[tex]v = \frac{1}{3} \times 3.14cm \times 25cm \times 7cm[/tex]

[tex]v = \frac{1}{3} \times 549.50 {cm}^{3} [/tex]

[tex]v = \frac{549.50 {cm}^{3} }{3} [/tex]

[tex]v = 183.17 {cm}^{3} [/tex]

[tex]v = 183 {cm}^{3} to \: nearest \: whole \: number[/tex]

Number of 25 cents coins is  80 and number of 50 cents coins is 20.

Step-by-step explanation:

Given,

A bag contains of total value $ 30.

Number of 25 cent coins is four times that of 50 cent coins.

To find number of 25 cents coin is x

Number of 50 cents coin is y

According to the problem,

[tex]\frac{x}{4} +\frac{y}{2} = 30[/tex] ----- eq 1

x = 4y------ eq 2

Now, we will solve these two equation.

Putting the values of x = 4y in eq 1 we get,

[tex]\frac{4y}{4} +\frac{y}{2} = 30[/tex]

or,  [tex]y +\frac{y}{2} = 30[/tex]

or, [tex]\frac{3y}{2}[/tex] = 30

or, y = 20

So, x = 4×20 = 80

Hence,

Number of 25 cents coins = 80 and number of 50 cents coins = 20

Answer:

Step-by-step explanation:

Let 25 cent coin be A and 50 cent coin be B

Given

Total value of 25 cents coin and 50cents coin is $30

That’s

25A + 50B = 30

Also, 25 cents coin is equal to four times that of 50

So,

A = 4B

We now have

25A + 50B = 30

A = 4B

Substitute 4B for A into the first equation

25(4B) + 50B = 30

25 x 4B + 50B = 30

100B + 50B = 30

150B = 30

Divide both sides by 150 to isolate B

150B/150 = 30/150

B = 1/5

Recall

A = 4B

Therefore

A = 4 x 1/5

= 4/5

Number of 25 cents coin is 4/5 and that of 50 cents coin is 1/5

Answer:

3927 litres of oil to the nearest litre.

Step-by-step explanation:

The volume of the cylinder = π r^2 h

= π * 100^2 * 250.

When half full the volume is  

1/2 * π  * 100^2 * 250

=  3926991 cm^3     Dividing this by 1000:

= 3927 litres.

A cylindrical tank is half-full of oil.

There are 3928 liters of oil in the tank

Volume of cylinder is teh amount of material the cylinder holds.  Volume is the density of the cylinder.

Volume Formula :

[tex]volume = \pi r^2h[/tex]

Given the radius of the cylinder is 100cm

Height of the cylinder is 250 cm

Substitute all the values inside the formula

[tex]V=\pi (100)^2(250)\\V=2500000\pi[/tex]

Cylinder tank is half full of oil . To find half of the volume , we divide the volume by 2

[tex]V=2500000\pi\\Half - full = \frac{2500000}{2}\pi \\Half-full =3926990.817 cm^3[/tex]

Given that 1 litre= 1000cm^3

convert cubic centimeter to litres

[tex]1000cm^3= 1litre \\3926990.817 cm^3=\frac{3926990.817 }{1000} \\1250000 cm^3=3927.99 liters[/tex]

There are 3928 liters of oil in the tank

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Median: 31

( Q1 ) Lower Quartile: 26

( Q2 ) Upper Quartile: 38

Interquartile Range: 38 - 26 = 12

answer : Median: 31; Q1 (or Lower Quartile ) = 26

Answer:

first one

Step-by-step explanation:

31 is the median and the Q1 is the left side of the box

Answer

Logarithm base 9 of 729 is 3.

Step-by-step explanation:

Answer:

The width is 2 cm and the length is 7 cm.

Step-by-step explanation:

Hope this helps!

The least common denominator of 1/3 5/8 and 1/2 will be 24.

What is Least common multiple?

The Least common multiple of two or more numbers are the smallest number that is multiple of two or more numbers.

Given that;

The numbers are,

⇒ 1/3, 5/8 and 1/2

Now,

To find the least common denominator of 1/3 5/8 and 1/2,

We need to find the least common multiple of 3, 8 and 2 as

The LCM of {3, 8, 2} = 24

Thus, The least common denominator of 1/3 5/8 and 1/2 will be 24.

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The least common denominator of 1/3, 5/8, and 1/2 is 24. It's the smallest number that all the denominators (3, 8, and 2) can divide into evenly, and it helps in adding or comparing fractions with different denominators.

The least common denominator (LCD) of the fractions 1/3, 5/8, and 1/2 is the smallest number that all of the denominators can divide into evenly. When looking for the least common denominator, we can use the method of listing multiples or the method of prime factorization.

For the fractions given, we list the multiples of each denominator:

The smallest multiple that they all have in common is 24, which is the least common denominator. It's important to note that by finding the LCD, we can easily add or compare fractions with different denominators.

Answer:

18

Step-by-step explanation:

tell if it helped

Answer:

18 feet

Step-by-step explanation:

We are 15 above ground and 3 feet below ground

Add the lengths together

15+3 = 18 feet for the pole length

Step-by-step explanation:

We know that we have the formula that F = ma

Given

Force (F) = 7.5 N

Acceleration (a) = 15 m/s²

Mass (m) = ?

Now

F = ma

7.5 = m * 15

m = 7.5/ 15

Mass = 0.5 kg

The mass of the football is 500 g.

Step-by-step explanation:

Given,

F = 7.5 N

Acceleration (f) = 15 m/s²

To find the mass (m) of the ball.

Formula

F = mf

According to the problem,

m×15 = 7.5

or, m = [tex]\frac{7.5}{15}[/tex] = 0.5 kg = 500 g

Hence,

The mass of the football is 500 g.

Answer:

exponential

Step-by-step explanation:

Answer:

the pythagorean theorem is an equation to figure out the side of a triangle. theformula is a squared plus b squared equals c squared.

Step-by-step explanation:

Answer:

The pythagorean theorem is an equation to figure out the side of a triangle. And the formula is A squared plus B squared equal C squared and it better to always know the missing triangle

Step-by-step explanation:

Answer:

A strong correlation

Step-by-step explanation:

The closer the correlation coefficient is to the number 1 the stronger the correlation is.

The correlation coefficient r = 0.875 indicates a strong correlation coefficient.

A statistical metric known as correlation shows how much two or more variables change in relation to one another.

The given correlation coefficient is r = 0.875.

Since the value of r is greater than 0.7, the correlation is strong.

Hence, the correlation coefficient r = 0.875 indicates a strong correlation coefficient.

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Answer:

2401

hope i helped

Answer:

Volume: 5200 cubic centimeters

Surface area: 1520 square centimeters

Step-by-step explanation:

Volume = [1/2 x 5 x side x apothem] x height

(The apothem is that little 8 cm mark, the height is 26, the side is 10.)

Plug those values in:

V = 1/2 * 5 * s * a * h

  =  1/2 * 5 * 10 * 8 * 26 = 5200 cubic centimeters

Surface area = 2(base area) + 5(lateral area)

SA = 2(200) + 5(260) = 1520 square centimeters

Answer:

The answer is 116 degrees.

Step-by-step explanation:

The value of CT is 13x - 1.

A line segment is defined as a measured path between two places. Line segments can make up any polygon's sides because they have a set length.

The figure given below shows a line segment CT, where the length of line segment CT refers to the distance between its endpoints, C and T.

Given that J is the midpoint of CT

CJ = 8x-5 and JT = 5x+4

C______________J______________T

⇒ CT = CJ + JT

Since J is the midpoint of CT, So CJ = JT

⇒ CT = CJ + JT

Substitute the values of CJ = 8x-5 and JT = 5x+4 in the above equation,

⇒ CT= (8x-5)+(5x+4)

⇒ CT= 8x-5+5x+4

Rearrange the likewise terms, and apply the arithmetics operation,

⇒ CT = 8x + 5x - 5 + 4

⇒ CT = 13x - 1

Hence, the value of CT is 13x - 1.

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Final answer:

To find the length of CT, solve the equation 8x-5 = 5x+4 to find x, then substitute the value of x into either CJ or JT to find the segment's length and double it.

Explanation:

The student is asking a geometry problem where they need to find the length of the segment CT given that J is the midpoint of CT with CJ being 8x-5 and JT being 5x+4. Since J is the midpoint, these two segments are equal in length, thus the equation to solve is 8x-5 = 5x+4.

To find the value of x, follow these steps:

Once x is found, substitute it back into either CJ or JT expression to find the length of one segment. Then, double that length to find CT, as CT is equal to 2 times CJ or 2 times JT.

Answer:

x=12

Step-by-step explanation:

Answer:

x=10

Step-by-step explanation:

15/9=x/6

15/9   simplified by 3  equal 5/3

5/3=10/6 (multiplied by2 )

10/6=x/6

so x=10

Answer:

you could just add a negative if that makes since to you

Step-by-step explanation:

Adjust the sign on the integer to be subtracted to subtract integers. When all signs are positive, then the answer is positive. If both signs are negative, then the answer is negative. When the signs vary, deduct the lesser absolute value from the greater absolute value.

Answer:

There is no graph

Step-by-step explanation:

Answer: ben

Step-by-step explanation:b

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n

ben

Answer:

k = 4

Step-by-step explanation:

f(x)=5x+k

Let x =2

f(2) = 5*2 +k

f(2) = 10+k

We know f(2) = 14

14 = 10+k

Subtract 10 from each side

14-10 = 10+k-10

4 =k

We are given the function f(x) = 5x + k when k is a constant, x equals 2, and f(x) equals 14

Steps to solve:

14 = 5x + k; x = 2

~Substitute

14 = 5(2) + k

~Simplify

14 = 10 + k

~Subtract 10 to both sides

14 - 10 = 10 - 10 + k

~Simplfy

4 = k

Best of Luck!

Answer:

organisms are interconnected through their feeding patterns:

they process the route flow transmit through the intercellar silicosis.

Step-by-step explanation:

Answer:

Food Chain

Step-by-step explanation:

Answer:

Explanation:

Since the results are not shown properly, I attach the picture with full question inlcuding the diagram that shows the results correctly.

You need to determine P(burger|fries)

That is the ratio of people that ordered burgers from the set of people that ordered fries (the intersection of the two circles) to the total people who ordered fries (the blue circle, including the intersection of the two circles).

The venn diagram shows that the set of people who ordered fries was 10% + 40% = 50% (the percentage inside the blue circle, including the intersection with the purple circle)

And from that set, the subset of people who also ordered burgers is 40% (the intersection of the two circles).

Thus, the probability that a randomly chosen customer ordered a burger given that they ordered fries is:

       [tex]P(burger\mid fries)=\dfrac{P(burger\cap fries)}{P(fries)}[/tex]

        [tex]{P (burger\mid fries)=\dfrac{40\% }{50\% }=0.80=80\%[/tex]

The probability that a randomly chosen customer ordered a burger given that he ordered fries is 80%.

To determine the probability that a randomly chosen customer ordered a burger given that he ordered fries, the following calculation must be performed:

Therefore, the probability that a randomly chosen customer ordered a burger given that he ordered fries is 80%.

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Answer: 41 out of 1

Step-by-step explanation: