A mountain is in the shape of a cone whose height is about 4.2 kilometers and whose base radius is about 6 kilometers. Approximate the volume of the mountain in

cubic kilometers.

Answer: 35

Step-by-step explanation: It's an arith metic sequence that can be represented throigh the equation y= 65-5x where 5 is the amount of hous since 4pm and if you insert 6 for x you get 35

The mathematics problem involves subtraction, where the temperature drops 5 degrees per hour from 4pm to 10pm. The equation to represent this would be 65 - 5*6 = T. After performing the calculation, we find the temperature at 10pm is 35 degrees Fahrenheit.

In this problem, you are dealing with a decline in temperature over time, which is considered as a subtraction problem. Since the temperature drops by 5 degrees every hour from 4pm to 10pm, that's a total of six hours (10pm - 4pm = 6 hours), so you'll subtract 5 degrees 6 times from the initial temperature of 65 degrees.

The equation to represent this problem is:

65 - 5*6 = T

This means you are subtracting 5 degrees six times from the initial temperature of 65 Fahrenheit to get the temperature (T) at 10pm. So, the calculation would be:

65 - (5*6) = 65 - 30 = 35

So, the temperature at 10pm is 35 degrees Fahrenheit.

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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:

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:

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:

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]

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:

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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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:

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:

-(-7)=7

Step-by-step explanation:

the opposite of the Justine score (-7) = Meghan  score  (7)

-(-7)=7

Final answer:

The correct representation of Meagan's score as the opposite of Justine's is -(-7) = 7, which is option D, where the double negative results in a positive score.

Explanation:

The trivia game scenario presents a situation where Justine and Meagan end up with opposite scores, with Justine losing 7 points and Meagan gaining the opposite. To express this numerically, if Justine's score change is represented as -7, then Meagan's score, being the opposite, is the negation of Justine's score, which is -(-7). This negation flips the sign of Justine's score change, resulting in a positive 7 for Meagan. Therefore, the correct way to represent that “the opposite of Justine’s score was equal to Meagan’s score” is -(-7) = 7.

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

Answer:

answer is b (max y + min y)/2

Step-by-step explanation:

Answer:

(max y + min y)/2

Step-by-step explanation:

k=4

Answer:

28.46

Step-by-step explanation:

Use a^2+b^2=c^2 to find height

Then use the area formula bh/2 to find area :))

Answer: 44.1

Step-by-step explanation:

Answer:

exponential

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:

0.4

Step-by-step explanation:

10 divided by 25

Answer:

[tex]3 {x}^{2} (2 {x}^{5} ) = 6 {x}^{7} [/tex]

Answer:

27 gallons, 2 quarts

Step-by-step explanation:

The measurements are given in gallons and quarts. Lets convert everything to quarts.

We know:

4 quarts = 1 gallons

So,

Rain Barrel Capacity = 47*4  + 1 = 189 quarts

Jiko uses 12 gallon  2 quart to water flower garden = 12*4  + 2 = 50 quarts

Jiko uses 7 gallons 1 quarts to water trees = 7*4  + 1 = 29 quarts

He used up = 50 + 29 = 79 quarts

Remaining Water in Rain Barrel = 189 - 79 = 110 quarts

In gallons and quarts:

27 * 4 = 108 quarts

So, water left = 27 gallons, 2 quarts

Answer:

There is no graph

Step-by-step explanation:

Answer: ben

Step-by-step explanation:b

e

n

ben

Answer:

both rates of change equal the slope of the line (3/4)

Step-by-step explanation:

Part a)

We calculate the rate of change using the formula:

[tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

for the first interval [0,6], we calculate the y-values at x=0 and x=6;

at x=0 : [tex]y=\frac{3}{2} (0)+2=2[/tex]

at x=6 : [tex]y=\frac{3}{2} (6)+2=11[/tex]

therefore, the rate of change in this interval is: [tex]\frac{y_2-y_1}{x_2-x_1}=\frac{11-2}{6-0}=\frac{9}{6} =\frac{3}{2}[/tex]

For the second interval [-4,4], we calculate the y-values at x=-4 and x=4;

at x=-4 : [tex]y=\frac{3}{2} (-4)+2=-4[/tex]

at x=4 : [tex]y=\frac{3}{2} (4)+2=8[/tex]

therefore, the rate of change in this interval is: [tex]\frac{y_2-y_1}{x_2-x_1}=\frac{8-(-4)}{4-(-4)}=\frac{12}{8} =\frac{3}{2}[/tex]

Part b):

Notice that both rates of change equal the value of the slope of the linear function (3/2)

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:

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:

30 times one for every 5 hours she baby sits

Answer:

B. [tex]y = 6x[/tex]

Step-by-step explanation:

Step 1: Divide 30 by 5

[tex]\frac{30}{5}\\\\=30 \div 5\\\\= 6[/tex]

Therefore, the answer closest to that is B. y = 6x.

Answer:

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

Step-by-step explanation:

Hope this helps!

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]

Step-by-step explanation:

The radius of the circle = 10

The central angle of the arc = 3[tex]\frac{\pi }{2}[/tex]

By formula, S = rΘ

where S is the lenth of the arc

r is the radius of the circle

Θ is the central angle of the arc

substituting the values in the formula, we get

S = rΘ = 10 (3[tex]\frac{\pi }{2}[/tex]) = 15[tex]\pi[/tex] = 47.1