A birthday cake is in the shape of 2 cylinders, one smaller one on top of another larger one. The radius of the bottom layer of cake is (3x  2) and the radius of the top layer of cake is (x  4) . The height for each layer is 6 cm. Determine a simplified expression for the difference in volume between the cake layers.

Answer:

0.3. and 2

Step-by-step explanation:

For this equation: a=1, b=0.3333333333333333, c=0.8333333333333334

1x2+0.333333x+0.833333=0

Step 1: Use quadratic formula with a=1, b=0.3333333333333333, c=0.8333333333333334.

x=

−b±√b2−4ac

2a

x=

−(0.333333)±√(0.333333)2−4(1)(0.833333)

2(1)

x=

−0.3333333333333333±√−3.222222

2

i think this is right :)

Answer:

4/5

Step-by-step explanation:

cos B = 3/5

cos Ф = adjacent/hypothesis

hypothesis ² = adjacent² + opposite²

5²= 3²+ o²

25 = 9+o²

25-9=o²

16 = o²

√16 = o = 4

Sin B = opposite/hypothesis = 4/5

Answer:

<1 and <2 are alternate exterior angles

<3 and <4 are consecutive interior angles

Step-by-step explanation:

<1 and <2 are alternate exterior angles

Alternate exterior angles are on opposite outside of the lines

<3 and <4 are consecutive interior angles

Consecutive interior angles are on the same side on the inside of the line

Answer:

Wavelength

Step-by-step explanation:

The picture below is an example of a wavelength which is very similar.

Step-by-step explanation:

[tex]PQR=( {x}^{2} - yz)( {y}^{2} - {x}^{2} )( {z}^{2} - xy) = \\ = {x}^{2} {y}^{2} {z}^{2} - {x}^{3} {y}^{3} - {x}^{4} {z}^{2} + {x}^{5} y - {y}^{3} {z}^{3} + \\ + x {y}^{4} z + xy {z}^{3} - {x}^{2} {y}^{2} z[/tex]

I don't know if it was necessary to open the brackets, but I think you can write it like this:

[tex]PQR=( {x}^{2} - yz)( {y}^{2} - {x}^{2} )( {z}^{2} - xy) \\ [/tex]

Answer:

22?

Step-by-step explanation:

Just take 40 and subtract the 7 to get 33 and then 2 to get 31 and 9 to get 22.

Answer:

22 more rolls

Step-by-step explanation:

if she needs to sell 40 and she has sold 9+7+2=18 than you subtract 18 from 40 getting 22 more rolls

Answer:

it is a 7 step process explained in explanation section

Step-by-step explanation:

Step one

fill 7 litre bucket then pour it in 4 liter bucket

output: 7 litre bucket has 3 litres and 4 litres bucket has 4 liter in it

Step two

drain four liter bucket and pour 3 liter from 7 litre bucket in it

output: 7 litre bucket has 0 litres and 4 litres bucket has 3 liter in it

step 3

fill 7 litre bucket and transfer water from it in 4 liter bucket which has already 3 liter in it

output: 7 litre bucket has 6 litres and 4 litres bucket has 4 liter in it

step 4

drain four liter bucket and pour 4 liter from 7 litre bucket which has 6 litre in it

output: 7 litre bucket has 2 litres and 4 litres bucket has 4 liter in it

step 5

drain 4 litre bucket and pour 2 litre from 7 litre bucket

output: 7 litre bucket has 0 litres and 4 litres bucket has 2 liter in it.

step 6

fill 7 liter bucket fully

output: 7 litre bucket has 7 litres and 4 litres bucket has 2 liter in it.

step 7

pour water from 7 liter bucket in 4 litre bucket which has already 2 litre in it

output: 7 litre bucket has 5 litres and 4 litres bucket has 4 liter in it.

Answer:

option a all real values of x where x < −1

Step-by-step explanation:

Answer: 0.25

Step-by-step explanation:

0.75-0.5= 0.25

Answer:

d= 0.75-0.5

d= 0.25

Step-by-step explanation:

so firstly you subtract 0.5 from both sides

d= 0.75-0.5

d=0.25

the answers are c and d

Answer:

8/5

Step-by-step explanation:

I'd write the following:

2       1

---- ÷ ----

 5      4

To divide by a fraction (such as 1/4), invert the divisor fraction and multiply instead:

2       4

---- · ---- = 8/5

 5      1

Answer:

x=2 or 5/3

Step-by-step explanation:

the explanation is in the picture

please like and Mark as brainliest

Answer:

x = 5/3

x = -2

Step-by-step explanation:

6x² + 2x - 20 = 0

(6x - 10)(x + 2)

= 6x² + 12x - 10x - 20

= 6x² + 2x - 20

6x - 10 = 0

6x = 10

x = 10/6

x = 5/3

x + 2 = 0

x = -2

Answer: 10.3 pounds of CO2 is produced

Step-by-step explanation:

Assuming there are 30 days in a month, if the microwave is run for 10 minutes per day, then the number of minutes for which the microwave is run in a month is

30 × 10 = 300 minutes

We would convert from minutes to hours

60 minutes = 1 hour

Therefore,

300 minutes = 300/60 = 5 hours

Also,

1000 watts = 1 kW

Therefore,

1500 watts = 1500/100 = 1.5kw

Therefore, the number of kWh is

1.5 × 5 = 7.5 kWh

If 1.37 pounds CO2 per kWh, then

If 1kWh = 1.37 pounds CO2, then

7.5 kWh = 7.5 × 1.37 = 10.3 pounds rounded to the nearest tenth

Final answer:

A 1500-watt microwave running for 10 minutes per day for one month emits approximately 10.3 pounds of CO2 when rounding to the tenths place.

Explanation:

The question is how much carbon dioxide is produced from running a 1500-watt microwave for 10 minutes a day for a month. To solve this, we first need to calculate the total energy used by the microwave in kWh. Since the microwave uses 1500 watts and is used for 10 minutes daily, we convert this to hours:

10 minutes = 10/60 hours = 1/6 hour

Power in kWh = Power in watts / 1000

Energy used per day in kWh = (1500 watts / 1000) x (1/6 hour) = 0.25 kWh

Next, we need to calculate the monthly energy use:

Energy used per month in kWh = 0.25 kWh/day x 30 days = 7.5 kWh

Using the given conversion factor of 1.37 pounds of CO2 per kWh, the total CO2 emissions can be calculated:

CO2 emissions = 7.5 kWh x 1.37 pounds CO2/kWh = 10.275 pounds of CO2

Finally, rounding to the tenths place:

CO2 emissions for the month = 10.3 pounds (rounded)

Answer:

− 21 x + 28 ,  7 ,  3 x − 4 ,  − 7 ( 3 x − 4 ) ,  − 7 , 3 x + 4 ,  − ( 21 x − 4 )

Step-by-step explanation:

too much to explain sorry

Hope this helped!

The factor of the expression -21x + 28 is equal to  -7(3x – 4). The correct option is B.

The numerical variables and operations denoted by the addition, subtraction, multiplication, and division signs are combined in the mathematical expression.

Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols. They can also denote the operation order and other properties of the logical syntax.

Given expression is -21x + 28, The value of the expression will be calculated as,

E = -21x + 28

Take -7 common from the whole expression,

E = -21x + 28

E = -7 ( 3x - 4 )

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Answer: The required confidence interval is (56.1,66.9).

Step-by-step explanation:

Since we have given that

53.1, 60.2, 60.6, 62.1, 64.4, 68.6

[tex]\bar{x}=\dfrac{53.1+60.2+60.6+62.1+64.4+68.6}{6}=\dfrac{369}{6}=61.5[/tex]

n = 6

Margin of error = 5.4

At 95% level of confidence, z = 1.96

So, the confidence interval would be

[tex]\bar{x}\pm \text{Margin of error}\\\\=61.5\pm 5.4\\\\=(61.5-5.4,61.5+5.4)\\\\=(56.1,66.9)[/tex]

Hence, the required confidence interval is (56.1,66.9).

An exponential function is a mathematical concept characterized by a constant base elevated by a variable exponent. The rate of growth or decay of the function is proportional to its current value, leading to exponential growth or decay.

An exponential function is a mathematical concept where a constant base is elevated by a variable exponent. The base could be any positive value different from one. A simple example of this type of function is f(x) = 2^x, where 2 is the constant base and x is the variable exponent.

The unique property of an exponential function is that the rate of growth or decay is proportionate to its current value. This means, as the variable x increases, the function value increases exponentially when the base is greater than one - thus showing exponential growth. Conversely, if the base is less than one but greater than zero, the function value decreases as x increases - thus representing exponential decay.

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Answer:

The width is 4 feet

Step-by-step explanation:

Yes, I might be able to answer it! Hello there!

In this question, we are asked to calculate the height of a pool which has a shape of right rectangular prism.

The key to solving this problem is simply by knowing the formula for the volume of a right rectangular prism.

Mathematically the volume V is w * h * l where w , h and l are the width, height and length respectively.

Now let’s input these values and get what the height of the pool is.

It would be easier if you had the measurements are in decimals;

137 1/2 becomes 137.5

6 1/4 becomes 6.25

5 1/2 becomes 5.5

kindly note the fraction 1/2 is 0.5 in decimals while the fraction 1/4 is 0.25 in decimals

So now let’s compute the height;

137.5 = w * 6.25 * 5.5

w = 137.5/(6.25 * 5.5)

w = 137.5/(34.375)

w = 4 feet

Answer:

3:4

Step-by-step explanation:

Before we start to deal with the ratio, we need all lengths in the same units.

The width is 18 inches.

The height is 2 feet.

Let's convert the height to inches. Then we will have both dimensions in the same units, inches.

2 ft * (12 in.)/ft = 24 in.

Now we have:

width = 18 in.

height = 24 in.

ratio of width to height = 18 in. to 24 in. = 18/24 = 3/4 = 3:4

The ratio of the width to the height of the bonsai tree is 3:4 after converting the height into inches and simplifying the ratio.

The question asks to find the ratio of the width of a bonsai tree to its height. Since the width is given in inches and the height in feet, we first need to convert the height into inches to have a consistent unit of measure. There are 12 inches in 1 foot, so the bonsai tree's height is 2 feet times 12 inches/foot, which equals 24 inches.

Now, we can write the ratio of the width to height as 18 inches (width) to 24 inches (height). This simplifies to 3:4 after dividing both terms by the greatest common factor, which is 6.

Step-by-step explanation:

I just finished the assignment and got everything right ;)

Hope i helped!

Answer:

c

Step-by-step explanation:

Answer:

1 out of 6 for green die and 1 out of 6 for red die

Step-by-step explanation:

As we know there are six numbers on both of the dices

so if we toss a die there is a 1 out of 6 outcomes that a 4 comes out for the green die and 1 out of 6 outcomes again for the red die

The probability that a 4 shows on the green die and a 5 shows on the red die is given by P ( C ) = 1/36

The probability that an event will occur is measured by the ratio of favorable examples to the total number of situations possible

Probability = number of desirable outcomes / total number of possible outcomes

The value of probability lies between 0 and 1

Given data ,

Let the probability that a 4 shows on the green die and a 5 shows on the red die be represented as P ( C )

Now , the number of outcomes in a roll of die = { 1 , 2 , 3 , 4 , 5 , 6 } = 6 outcomes

And , probability that a 4 shows on the green die P ( A ) = 1/6

The probability that a 5 shows on a red die P ( B ) = 1/6

Now , it is an independent experiment

So , the compound probability is P ( C ) = P ( A ) . P ( B )

And , the probability that a 4 shows on the green die and a 5 shows on the red die P ( C ) = ( 1/6 ) ( 1/6 )

The probability that a 4 shows on the green die and a 5 shows on the red die P ( C ) = 1/36

Hence , the probability is P ( C ) = 1/36

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Answer:

θ = 170°

Step-by-step explanation:

Given angle is in radian as,

[tex]\theta^{c} = \dfrac{17 \pi}{18}[/tex]

Here, [tex]\theta^{c}[/tex] symbol represents the angle is in radian.

To convert given angle into degree, multiply the given angle with conversion factor as follows,

[tex]\theta^{\circ} = \theta^{c} \times \left(\frac{180}{\pi }\right)^{\circ}[/tex]

Substituting the values,

[tex]\theta^{\circ} =  \dfrac{17 \pi}{18} \times \left(\dfrac{180}{\pi }\right)[/tex]

Cancelling out the common terms,

[tex]\theta^{\circ} =17\times \left(10\right)[/tex]

Therefore,

[tex]\theta^{\circ} =170^{\circ}[/tex]

Therefore the value of given angle in degree is 170°

To convert radians to degrees, utilize the conversion factor 180/π. In this instance, we have the angle (17π / 18) radians, which simplifies to 170 degrees when converted to the degree format.

The subject topic of this conversation is about converting radians to degrees. Specifically, we're looking at how to convert the radian measurement = 17 / 18 into degrees.

One radian is equivalent to 180/ degrees. As such, to convert radians to degrees, you multiply the radian measurement by this conversion factor (180/).

Have a look at the calculation: = (17 / 18) * (180/).

The cancels out leaving us with / * . This calculation gives us = 170 degrees.

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Answer:

The second, third and fifth are true.

Step-by-step explanation:

1) False, the radius is d÷2=8÷2=4 cm

2) True, C = 2×π×r = π×d = 8π

3) True, C = 8π = 8 × 22/7 = 176÷6 ≈ 25,14

4) False, C = 25,14 ≈ 25

5) True, C = 8π = 8×3,14 = 25,12

Answer: B,C,E

Step-by-step explanation:

Answer:

Therefore a= 90°,b=54°, x=54°, y= 162°

Step-by-step explanation:

a=90°

a:b=5:3

5+3= 8

5/8 x A = 90

A is the sum of the angles of a and b divided in the ratio 5:3

5A/8 = 90

cross multiply

5A= 90 X8 = 720

5A=720

A= 720/5= 144°

b= 3/8 x 144 = 3x144/8 = 432/8 = 54

a= 90

b= 54

x:y is in the ratio of 1:3

the Sum of angles in a Quadrilateral is 360°

if the sum of a and b is 144°

then the reamining angles is 360-144= 216°

then x:y=1:3

1+3=4

x= 1/4 x 216= 54°

y= 3/4 x 216= 162°

Therefore a= 90°,b=54°, x=54°, y= 162°

we can see that b = x = 54°

Answer:

The top angle is 60 degrees

Step-by-step explanation:

Triangle angle sum equals to 180. 90 plus 30 is 120 and when you subtract that from 180 tada! 60

Answer:

A) (2+x)/(4+x) × 100 = 75

B) 4

Step-by-step explanation:

2 out of 4

(2+x) out of (4+x)

(2+x)/(4+x) × 100 = 75

(2+x)/(4+x) = 3/4

8 + 4x = 12 + 3x

x = 4

Answer:

No

Step-by-step explanation:

If the ratios of the corresponding sides are equal then they would be the sides of 2 similar triangles.

Calculate the ratio of corresponding sides.

[tex]\frac{6}{1.5}[/tex] = 4

[tex]\frac{10}{2.5}[/tex] = 4

[tex]\frac{12}{3.5}[/tex] ≠ 4

Thus the sides are not the corresponding sides of similar triangles.

Answer:

(6x² + 4x +1) - (4x + 20) = 6x² + 21

Step-by-step explanation:

(6x² + 4x +1) - (4x + 20)

= 6x² + 4x -4x + 1 + 20

= 6x² + 21

Answer:

Step-by-step explanation:

Use the point-slope formula.

y - y_1 = m(x - x_1)  when :     x_1 = -5  and    y_1 =3 and   m= -6/5

the equation :   y - 3 = -6/5(x +5)

Answer:

y=-6/5x-3

Step-by-step explanation: