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4 years ago

A coin is tossed and a number cube is rolled. What is P(heads, a number, a number less than 5)

Mathematics

2 answers:

KonstantinChe [14]4 years ago

7 0

That would be 1/2 * 4/6

= 1/2 * 2/3 = 1/3 (answer)

stepladder [879]4 years ago

5 0

In a coin, there are 2 sides - heads and tails. The probability of getting a head is $\frac{1}{2}$

In a number cube, there are 6 numbers. The probability of being a number is 1.

The 6 numbers in a number cube are: 1, 2, 3, 4, 5, 6. There are 4 numbers less than 5. The probability of being less than 5 is $\frac{4}{6}$ .

Now multiply the 3 probabilities together:

$\frac{1}{2} \times \frac{1}{1} \times \frac{4}{6} = \frac{4}{12} \rightarrow \frac{1}{3}$

Your answer is A.

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NASA launches a rocket at t = 0 seconds. Its height, in meters above sea-level, as a function of time is given by h ( t ) = − 4.

Oliga [24]

Answer:

$\displaystyle 1)48.2 \: \: \text{sec}$

$\rm \displaystyle 2)3021.6 \: m$

Step-by-step explanation:

<h3>Question-1:</h3>

so when flash down occurs the rocket will be in the ground in other words the elevation(height) from ground level will be 0 therefore,

to figure out the time of flash down we can set h(t) to 0 by doing so we obtain:

$\displaystyle - 4.9 {t}^{2} + 229t + 346 = 0$

to solve the equation can consider the quadratic formula given by

$\displaystyle x = \frac{ - b \pm \sqrt{ {b}^{2} - 4 ac} }{2a}$

so let our a,b and c be -4.9,229 and 346 Thus substitute:

$\rm\displaystyle t = \frac{ - (229) \pm \sqrt{ {229}^{2} - 4.( - 4.9)(346)} }{2.( - 4.9)}$

remove parentheses:

$\rm\displaystyle t = \frac{ - 229 \pm \sqrt{ {229}^{2} - 4.( - 4.9)(346)} }{2.( - 4.9)}$

simplify square:

$\rm\displaystyle t = \frac{ - 229 \pm \sqrt{ 52441- 4( - 4.9)(346)} }{2.( - 4.9)}$

simplify multiplication:

$\rm\displaystyle t = \frac{ - 229 \pm \sqrt{ 52441- 6781.6} }{ - 9.8}$

simplify Substraction:

$\rm\displaystyle t = \frac{ - 229 \pm \sqrt{ 45659.4} }{ - 9.8}$

by simplifying we acquire:

$\displaystyle t = 48.2 \: \: \: \text{and} \quad - 1.5$

since time can't be negative

$\displaystyle t = 48.2$

hence,

at 48.2 seconds splashdown occurs

<h3>Question-2:</h3>

to figure out the maximum height we have to figure out the maximum Time first in that case the following formula can be considered

$\displaystyle x _{ \text{max}} = \frac{ - b}{2a}$

let a and b be -4.9 and 229 respectively thus substitute:

$\displaystyle t _{ \text{max}} = \frac{ - 229}{2( - 4.9)}$

simplify which yields:

$\displaystyle t _{ \text{max}} = 23.4$

now plug in the maximum t to the function:

$\rm \displaystyle h(23.4)- 4.9 {(23.4)}^{2} + 229(23.4)+ 346$

simplify:

$\rm \displaystyle h(23.4) = 3021.6$

hence,

about 3021.6 meters high above sea-level the rocket gets at its peak?

5 0

3 years ago

The base of a trinagle is increased by 20% and it’s height is increased by 30%. By what percent is the area of the triangle incr

Molodets [167]

Lets say the base is x and the height is y. The new base would be 1.2x and the new height would be 1.3y

Area of a triangle is base times height divided by 2:

1.2x*1.3y/2 = (1.2*1.3 + x*y)/2 = 1.56xy/2 = 0.78xy = 78% of xy

But a normal area would be 50% of xy

78% - 50% = 38%

ANSWER: 38% increase

4 0

3 years ago

Use elimination to solve each system of equations 2x-y=-1 3x-2y=1

mixer [17]

$2x-y=-1 \ \ \ |\times (-2) \\
3x-2y=1 \\ \\
-4x+2y=2 \\
\underline{3x-2y=1 \ \ \ \ } \\
-4x+3x=2+1 \\
-x=3 \ \ \ |\times (-1) \\
x=-3 \\ \\
2x-y=-1 \\
2 \times (-3)-y=-1 \\
-6-y=-1 \ \ \ |+6 \\
-y=5 \ \ \ |\times (-1) \\
y=-5 \\ \\
\boxed{(x,y)=(-3,-5)}$

8 0

4 years ago

Read 2 more answers

Please help with this question i will mark you brainliest!

adell [148]

9514 1404 393

Answer:

equation: y = 4x

graph is attached

Step-by-step explanation:

Let y represent the cost of the peaches in dollars. Let x represent their weight in pounds. Then the relation between the two variables is ...

cost = (cost per pound) × (pounds)

y = 4x

This graphs as a line through the origin with a slope of 4. In the attached, the x- and y-axes have different scales so more of the graph can be seen.

8 0

3 years ago

What set of three numbers could represent the lengths of the side of a right triangle?

klemol [59]

Answer:

C.) 5, 12, 13

Step-by-step explanation:

In a right triangle, the sum of the squares of the two shorter sides must equal the square of the longest side (Pythagoras).

a² + b² = c²

We can test each set of numbers to see which one fits.

A.) 8² + 12² = 16²

64 + 144 = 256

208 ≠ 256

B.) 6² + 7² = 8²

36 + 49 = 64

85 ≠ 64

C.) 5² + 12² = 13²

25 + 144 = 169

169 = 169

The numbers 5, 12, and 13 could represent the lengths of the sides of a right triangle.

D.) 16² + 32² = 36²

256 + 1024 = 1296

1280 ≠ 1296

7 0

3 years ago