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lakkis [162]
3 years ago
5

A standard number cube is rolled once. What is the probabilty that a number less than 3 is rolled? *

Mathematics
2 answers:
vodka [1.7K]3 years ago
6 0
There are three numbers that are 3 or less out of the 6 possible numbers so the probability is 3/6=1/2
Artemon [7]3 years ago
3 0

The probability that a number less than 3 is rolled is 2/3 or 66%

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Solve each equation (Polynomial equations)
lesya [120]

{ {e}^{x} }^{2}  =  \frac{1}{ {e}^{2} } \times  {e}^{3x}  \\ \Leftrightarrow  { {e}^{x} }^{2}  =  {e}^{ 3x}  \times  {e}^{ - 2}  \\ \Leftrightarrow  { {e}^{x} }^{2}  =  {e}^{3x - 2}  \\ \Leftrightarrow  {x}^{2}  = 3x - 2 \\ \Leftrightarrow  {x}^{2}  - 3x + 2 = 0 \\ \Leftrightarrow (x - 1)(x - 2) = 0 \\ x = 1 \: \vee \: x = 2 \\  \\ {32}^{ {x}^{2} - 2x }  =  \frac{1}{ {4}^{x} } \\  \Leftrightarrow  {( {2}^{5} )}^{ {x}^{2} - 2x }  = {2}^{ - 2x}  \\ \Leftrightarrow  {2}^{5 {x}^{2} - 10x }  =  {2}^{ - 2x}  \\ \Leftrightarrow 5 {x}^{2}  - 10x =  - 2x \\ \Leftrightarrow 5 {x}^{2}    - 8x = 0 \\ \Leftrightarrow x(5x - 8) = 0 \\ \Leftrightarrow x = 0 \: \vee \: x =  \frac{8}{5}  \\  \\  { {e}^{x} }^{3}  =  {2}^{2x} \\ \Leftrightarrow  {x}^{3}  =  ln( {2}^{2x} )  \\ \Leftrightarrow  {x}^{3}  - 2x ln(2)  = 0 \\ \Leftrightarrow x( {x}^{2}  - 2 ln(2) ) = 0 \\ \Leftrightarrow x = 0 \:\vee \:  {x}^{2}  = 2 ln(2)  \\ \Leftrightarrow x = 0 \:\vee \: x =  \sqrt{2 ln(2) }  \:\vee \: x =  -  \sqrt{2 ln(2) }

8 0
4 years ago
0.40 ___0.04 Please answer only if you are 100 percent sure a c =
natulia [17]

Step-by-step explanation:

0.40 ___0.04

We are given with two decimal numbers. Compare the numbers and complete the blank by < or > or =

To compare the decimals , compare each digit from left to right

0 is equal to 0

4 is greater than 0

so we can say 0.40 is greater than 0.04

0.40 > 0.04

Both decimal numbers are not equal

Answer:

0.40 > 0.04

8 0
3 years ago
Which formula should be used?
klio [65]
V=(pi)(r^2)h-(2/3)(pi)(r^3)
7 0
3 years ago
Verify the trigonometric identity. convert the left side of the relationship to look like the right side.
Tomtit [17]

Answer:

Verified

Step-by-step explanation:

Use \tan{x}=\frac{\sin{x}}{\cos{x}}  , \sin^2{x}+\cos^2{x}=1 and \sec{x}=\frac{1}{\cos{x}}

LHS=\tan^2{x}+1=\frac{\sin^2{x}}{\cos^2{x}} + 1=\frac{\sin^2{x}+\cos^2{x}}{\cos^2{x}}=\frac{1}{\cos^2{x}}=\sec^2{x}=RHS

5 0
3 years ago
Use the scale of 1cm=45 km
alex41 [277]

Answer:

d = 7.4 cm is the distance between the two cities on the map.

Step-by-step explanation:

Let d = the distance measured on the map in centimeters (cm) between any two locations and let D be the actual distance in kilometers (km) between these same two locations.

Since the scale on the map is 1 cm = 45 km, then the ratio of the distance on the map to the actual distance is equal to 1cm/45 km; therefore the quotient of any measured distance d on the map divided by the corresponding much longer actual distance D would have to maintain (equal) this same ratio; In other words, we can set up the following proportion to solve for d given the actual distance D = 333 km as follows:

1 cm/45 km = d/D

Substituting, we get:

1 cm/45 km = d/333 km

d/333 km = 1 cm/45 km

(d/333 km)(333 km) = (1 cm/45 km)(333 km)

d = (333 km/45 km)(1 cm)

d = 7.4 cm is the distance between the two cities on the map.

Check:

1 cm/45 cm = d/333 km

1 cm/45 cm = 7.4 cm/333 km

1 cm/45 cm = 1 cm/45 km (Therefore, the distance ratio of the map has been maintained

3 0
2 years ago
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