a Fair coin is tossed 3 times. What is the probability of getting at least one heads and at least one tails?​

Answer:

1/2

Step-by-step explanation:

The results of the roll can be

1,2,3,4,5,6

The rolls that are less than 4 are 1,2,3

P( less than 4) = number of rolls less than 4 / total

                        = 3/6

                         =1/2

Answer:

1). a = 10, b = 6

2). a = 5, b = 3, c = 8

Step-by-step explanation:

Given expression is,

1). [tex]\frac{7^{6}\times 7^8}{7^4}[/tex] = [tex]\frac{7^a}{7^4}=7^4[/tex]

= [tex]\frac{7^{2+8}}{7^4}[/tex] [Since [tex]x^{m}\times x^n=x^{(m+n)}[/tex]]

= [tex]\frac{7^{10}}{7^4}[/tex]

= [tex]7^{{10-4}}[/tex]

= [tex]7^{6}[/tex]

Therefore, a = 10 and b = 6

2). [tex]\frac{2^5}{4}=\frac{2^5}{2^a}=2^b=c[/tex]

= [tex]\frac{2^5}{2^2}[/tex]

= [tex]2^{{5-2}}[/tex]

= [tex]2^{3}[/tex]

= 8

Therefore, a = 5, b = 3 and c = 8

Answer:

2.5 sec

Step-by-step explanation:

Height of wall = 2.5 m

initial speed of ball = 14 m/s

height from which ball is kicked = 0.4 m

we calculate the speed of the ball at the height that matches the wall first

height that matches wall = 2.5 - 0.4 = 2.1 m

using [tex]V^{2}[/tex] = [tex]U^{2}[/tex] + 2as

where a = acceleration due to gravity = -9.81 m/s^2 (negative in upwards movement)

[tex]V^{2}[/tex] = [tex]14^{2}[/tex] + 2(-9.81 x 2.1)

[tex]V^{2}[/tex] = 196 - 41.202

[tex]V^{2}[/tex] = 154.8

v = [tex]\sqrt{154.8}[/tex] = 12.44 m/s

this is the velocity of the ball at exactly the point where the wall ends.

At the maximum height, the speed of the ball becomes zero

therefore,

u = 12.44 m/s

v = 0 m/s

a = -9.81 m/s^2

t = ?

using V = U + at

0 = 12.44 - 9.81t

-12.44 = -9.81

t = -12.44/-9.81

t = 1.27 s

the maximum height the ball reaches will be gotten with

[tex]V^{2}[/tex] = [tex]U^{2}[/tex] + 2as

a = -9.81 m/s^2

0 = [tex]14^{2}[/tex] + 2(-9.81s)

0 = 196 - 19.62s

s = -196/-19.62 = 9.99 m. This the maximum height reached by the ball.

height from maximum height to height of ball = 9.99 - 2.5 = 7.49 m

we calculate for the time taken for the ball to travel down this height

a = 9.81 m/s^2 (positive in downwards movement)

u = 0

s = 7.49 m

using s = ut + [tex]\frac{1}{2}[/tex]a[tex]t^{2}[/tex]

7.49 = (0 x t) +  [tex]\frac{1}{2}[/tex](9.81 x [tex]t^{2}[/tex] )

7.49 = 0 + 4.9[tex]t^{2}[/tex]

[tex]t^{2}[/tex]  = 7.49/4.9 = 1.53

t = [tex]\sqrt{1.53}[/tex] = 1.23 sec

Total time spent above wall = 1.27 s + 1.23 s = 2.5 sec

Answer: A (4, -7) B (9, -7)

Step-by-step explanation:

When it’s reflected over the x-axis, the y coordinates become negative but the x coordinates don’t change

x coordinates: 4, 9

y coordinates: 7, 7

Reflected over x-axis: (4, -7), (9, -7)

Answer:

the length of ab is 8

x=3

Step-by-step explanation:

Answer:

y = x + 15

Step-by-step explanation:

You swim 15 minutes more than a friend.The friend swims x minutes.

The amount of time you swim is 15 more than x.

Your time is y

Therefore y = x + 15 would be the equation.

Answer:

[tex]\fbox{\begin{minipage}{14em}Lorrie's inequality is incorrect\end{minipage}}[/tex]

[tex]\fbox{\begin{minipage}{16em}The solution is: d is greater than 16\end{minipage}}[/tex]

Step-by-step explanation:

Step 1: Define the problem

Given:

Lorrie biked [tex]d[/tex] miles in time [tex]t = 2[/tex] hours.

Lorrie traveled at speed [tex]s[/tex] which is greater than [tex]8[/tex] (mile/hour).

Task:

Lorrie wants to determine the distance she may have traveled.

Key point:

The relation among the distance biked [tex]d[/tex], time [tex]t[/tex], and the speed [tex]s[/tex] is represented:

[tex]d = s[/tex] x [tex]t[/tex]

Step 2: Substitute given data into the main relation

with: [tex]s > 8[/tex] and [tex]t = 2[/tex]

=>     [tex]d = s[/tex] x [tex]t[/tex]

=>     [tex]d[/tex] > [tex]8[/tex] x [tex]2[/tex]

Simplify:

        [tex]d > 16[/tex]

Step 3: Verify Lorrie's inequality

Lorrie uses the inequality [tex]2d > 8[/tex] to conclude that she traveled a distance [tex]d[/tex] at most [tex]4[/tex] miles, or [tex]d < 4[/tex].

Considering the correct answer is at step 2, in which, [tex]d > 16[/tex].

=> Lorrie's conclusion is incorrect.

Hope this helps!

:)

Answer:

Lorrie should have used division in the inequality instead of multiplication. She would have determined that she biked more than 16 miles instead of at most 4 miles.

Step-by-step explanation:

took the test

[tex]\text{Simplify:}\\\\(3x^2-4x+2)-(2x^2-4x-5)\\\\3x^2-4x+2-2x^2+4x+5\\\\x^2-4x+2+4x+5\\\\x^2+2+5\\\\x^2+7\\\\\boxed{\text{Two terms}}[/tex]

Answer:

(Satellite images of both the buildings on a single coordinate grid are shown in the ATTACHMENT)

MARCI SHOULD WIN

AREA OF MUSEUM > AREA OF SCHOOL

Step-by-step explanation:

Find the area of School in Grid squares:

Area of School = 20 Grid squares*10*10

Area of School = 2000 m²

Find the area of Museum in Grid squares:

[tex]A=\pi{r^2}\\A=\pi(3^2)\\A=9\pi[/tex]

Area of Museum = 9п grid squares

Area of Museum = 2826 m²

AREA OF MUSEUM > AREA OF SCHOOL

Answer:

D

Step-by-step explanation:

A. The domain of this function is infinite, since x can be any number.

B. To find the y intercept, you need to set x to 0. 7^x will become 1, and 6*1=6, so the y intercept is (0,6).

C. This function is not always decreasing. For instance, when x is positive, it exponenentially increases.

D. As I said before, the y intercept of the function is (0,6), meaning that this statement is correct.

Hope this helps!

Answer:

option c is correct

Step-by-step explanation:

please mark me brainlest

please thanks

Answer:

Step-by-step explanation:

Answer is C.  0.132

Answer:

√24

Step-by-step explanation:

4.89897948 will be the answer. Which is a number in between 4 and 5. Hope this helps :)

Answer:

12 units³

Step-by-step explanation:

The required formula is V = (1/3)πr²h, where r is the radius and h is the height.  Here we get:

V = (1/3)π(2)²(9) = (1/3)π(9)(4) = 12 units³

Answer:

a = 0

Step-by-step explanation:

=> 3(a+4)-5(a-2) = 22

Opening Brackets

=> 3a+12-5a+10 = 22

=> 3a-5a+12+10 = 22

=> -2a+22 = 22

Subtracting 22 to both sides

=> -2a = 0

Dividing both sides by -2

We get,

=> a = 0

Answer:

a = 0

Step-by-step explanation:

3(a+4)-5(a-2)=22

3a+12-5a+10=22

-2a+22=22

Subtract 22 from both sides

-2a=0

Multiply both sides by -1

2a= -0

2a=0

Divide both sides by 2

a=0

Hey I just realized my answer is really similar to Ujalakhan01's so sorry if it seems like I copied them.

Answer:

First one

Step-by-step explanation:

Step-by-step explanation:

first minute = 24 wildebeest

by 20 min = (20 × 3) + 24 = 84 wildebeest

Answer:

see below

Step-by-step explanation:

g(x) = (x² - 2 * 1/2 x) - 6

      = (x - 0.5)² - 0.25 - 6

      = 1(x - 0.5)² - 6.25

Answer:

-2/3

Step-by-step explanation:

Perpendicular slopes have lines that multiply to -1

m* 3/2 = -1

Multiply each side by 2/3

m* 3/2 * 2/3 = -1 * 2/3

m = -2/3

The slope of the perpendicular line is -2/3

Answer:

The answer is B

I use an online graphing calculator called Desmos. You should check it out some time :)

Answer:

the third option

Step-by-step explanation:

the inverse of a statement is just the opposite. So the opposite of your statement would be "if a quadrilateral is NOT a rectangle, then it is NOT a parallelogram."

hope this helps!

Answer:

x = -2/3  x=1

Step-by-step explanation:

We cant solve by substitution with just one equation

-3x^2 + x +2=0

Factor out a negative

-(3x^2 -x-2) = 0

Divide by negative 1

(3x^2 -x-2) = 0

Factor

(3x +2) (x-1)=0

Using the zero product property

3x+2 =0   x-1 =0

3x= -2   x=1

x = -2/3  x=1

Answer:

[tex]x = \frac{2}{3} \\ x = - 1[/tex]

Step-by-step explanation:

[tex]x - 3 {x}^{2} + 2 = 0 \\ - 3 {x}^{2} + x + 2 = 0 \\ - 3 {x}^{2} - 3x + 2x + 2 = 0 \\ - 3x(x + 1) + 2(x + 1) = 0 \\ ( - 3x + 2)(x + 1) = 0[/tex]

[tex] - 3x + 2 = 0 \\ - 3x = - 2 \\ \frac{ - 3x}{ - 3} = \frac{ - 2}{ - 3} \\ x = \frac{2}{3} [/tex]

[tex]x + 1 = 0 \\ x = - 1[/tex]

hope this helps

brainliest appreciated

good luck! have a nice day!

Answer:

B

Step-by-step explanation:

When you finish solving an equation and find the answer to be that two numbers are equal to each other when they are in fact, this means that the equation has no solutions because not values could make it true. Hpope this helps!

Answer:

I think it is B

Step-by-step explanation:

Answer:

[tex]|p-q|-(|p|-|q|) = 20[/tex]

Step-by-step explanation:

First let's find the value of 'p-q':

[tex]p - q = 9i + 12j - (-6i - 8j)\\p - q = 9i + 12j + 6i + 8j\\p - q = 15i + 20j\\[/tex]

To find |p-q| (module of 'p-q'), we can use the formula:

[tex]|ai + bj| = \sqrt{a^{2}+b^{2}}[/tex]

Where 'a' is the coefficient of 'i' and 'b' is the coefficient of 'j'

So we have:

[tex]|p - q| = |15i + 20j| = \sqrt{15^{2}+20^{2}} = 25[/tex]

Now, we need to find the module of p and the module of q:[tex]|p| = |9i + 12j| = \sqrt{9^{2}+12^{2}} = 15[/tex]

[tex]|q| = |-6i - 8j| = \sqrt{(-6)^{2}+(-8)^{2}} = 10[/tex]

Then, evaluating |p-q|-{|p|-|q|}, we have:

[tex]|p-q|-(|p|-|q|) = 25 - (15 - 10) = 25 - 5 = 20[/tex]

Answer:

45.45 batteries

Step-by-step explanation:

The probability of any random battery being defective is 1 in 11, the number of expected defects in a population of 500 batteries is given by:

[tex]E= \frac{1}{11}*500\\E=45.45\ batteries[/tex]

45.45 batteries are expected to be defective.

Answer:

45

Step-by-step explanation:

Answer:

The answer is 2 different angles, 53° and 127°.

Explanation:

As you subtract 180° from the given angle to find the other angle, you will get only 2 angles either 53° or 127°.

Answer:

see below

Step-by-step explanation:

Because ∠ABE and ∠CBD are vertical angles, ∠ABE = ∠CBD = 40°.

Answer:

The angle of ∠ABE is 40°.

Step-by-step explanation:

Given that ∠ABE and ∠CBD are opposite vertical angles so they have the same measure of angles.

Answer:

We need to subtract both equations. 2x3+30x-130-2x3+3x+520

that gives

30x-130+3x + 520

33x+390

D is answer

Answer:

D. 33x + 390

Step-by-step explanation:

Profit is the difference between revenue and cost so subtract the given polynomials:

2x³ + 30x – 130 - (2x³ – 3x – 520) = 2x³ + 30x – 130 -2x³+3x+520

combine like terms: 33x +390

Answer:

No, Electric Pole is 40 ft

Step-by-step explanation:

tan 66.8° = [tex]\frac{x}{15}[/tex]

x = 35

but that is from the top of Danny, so you need to add 5 (his height)

Electric Pole is 40 ft

Answer:

Step-by-step explanation:

Take you ruler and draw a horizontal line from point (0,-2)

When you do, the point where y = -2 is when x = - 3

Answer:

x = -3

Step-by-step explanation:

the question asks for what x the function = -2

if you imagine horizontal line passing through -2 then you cann see that it crosses graph when x = -3 and 0

Answer:

Options A, E

Step-by-step explanation:

If the angle doesn't lie inside this triangle, we can assume it is an exterior angle, provided it is between a side of this triangle and an adjacent side extended outward;

[tex]< 4 - Doesn't Lie In Triangle, - Exterior Angle,\\< 3 - Lies In Triangle, - Interior Angle,\\\\< 6 - Doesn't Lie In Triangle, Execption, - Neither Interior Nor Exterior,\\\\< 1 - Lies In Triangle - Interior Angle,\\< 5 - Doesn't Lie In Triangle - Exterior Angle\\\\< 2 - Lies in Triangle - Interior Angle[/tex]

Refer to Solution below;

A. Check!

E. Check!