Find the indicated binomial probability. A multiple choice test has 30 questions, and each has four possible answers, of which one is correct. If a student guesses on every question, find the probability of getting exactly 12 correct.

Answer:

the car overtake the truck at time 11:40 am.

Step-by-step explanation:

We have both vehicules going at constant speed from city a to city b. The distance is unknown, but can be written as d.

We will express the time in hours (and decimals of hours).

The truck speed can be calculated estimating the time between arrival and start:

- The arrival time is 1.15 pm. This is t2=13.25.

- The starting time is 9:15 am. This is t1=9.25.

The truck took t2-t1=13.25-9.25=4 to go from city a to b.

The average speed is then:

[tex]v_t=\dfrac{\Delta x}{\Delta t}=\dfrac{d}{4}[/tex]

We can write the equation for the position x(t) for the truck as:

[tex]x(t)=x_0+v_t\cdot t=x_0+\dfrac{d}{4}t\\\\\\x(13.25)=x_0+\dfrac{d}{4}(13.25)=d\\\\x_0=d-3.3125d=-2.3125d\\\\\\x(t)=-2.3125d+0.25d\cdot t[/tex]

For the car we have:

- The arrival time is 12:45 am. This is t2=12.75.

- The starting time is 10 am. This is t1=10.

The car took t2-t1=12.75-10=2.75.

The average speed is then:

[tex]v_c=\dfrac{\Delta x}{\Delta t}=\dfrac{d}{2.75}[/tex]

We can write the equation for the position x(t) for the car as:

[tex]x(t)=x_0+v_c\cdot t=x_0+\dfrac{d}{2.75}t\\\\\\x(12.75)=x_0+\dfrac{d}{2.75}(12.75)=d\\\\x_0=d-4.6363d=-3.6363d\\\\\\x(t)=-3.6363d+0.3636d\cdot t[/tex]

The time at which the car overtake the car is the time when both vehicles have the same position:

[tex]x(t)/d=-2.3125+0.25\cdot t = -3.6363+0.3636\cdot t\\\\-2.3125+3.6363=(0.3636-0.25)t\\\\1.3238=0.1136t\\\\t=1.3238/0.1136\approx11.65[/tex]

The car overtakes the truck at t=11.65 hours or 11:39 am.

Working backwards, on Wednesday morning we have 60 / (1/2) = 120 pounds of ice.

2/3 melts on Tuesday so 120 pounds must be 1/3 of the ice.

120 / (1/3) = 360

Answer: D. 360

Answer:

the null hypothesis would be: p = 70%/0.7

The alternative hypothesis would be: p < 0.7

Step-by-step explanation:

The null hypothesis is most of the time always the default statement while the alternative hypothesis is tested against the null and is its opposite.

In this case study the null hypothesis would be: the proportion of men who own cats is 70%: p = 0.7

The alternative hypothesis would be: the proportion of men who own cats is smaller than 70% : p < 0.7

Answer:

x=8/3 OR 2.7

Step-by-step explanation:

-1.3+4.6x=0.3+4x

4.6x-4x=0.3+1.3

0.6x=1.6

x=1.6/0.6=8/3

x=8/3 OR 2.7

Hope this helps!

Answer:

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

Step-by-step explanation:

[tex]-1.3+4.6x = 0.3 +4x[/tex]

Collecting like terms

[tex]4.6 x -4x = 0.3+1.3[/tex]

[tex]0.6x = 1.6[/tex]

Dividing both sides by 0.6

x = 1.6 / 0.6

x = 2 2/3

Answer:

x≤9  

Step-by-step explanation:

x−15≤−6

Add 15 to each side

x−15+15≤−6+15

x≤9  

Answer:

[tex]\boxed{x\leq 9}[/tex]

Step-by-step explanation:

[tex]x-15 \leq -6[/tex]

[tex]\sf Add \ 15 \ to \ both \ parts.[/tex]

[tex]x-15 +15 \leq -6+15[/tex]

[tex]x\leq 9[/tex]

Answer:

Point of faulty equipment car = 0.2614 (Approx)

Step-by-step explanation:

Given:

Total number of car = 700

Faulty equipment car = 183

Find:

Point of faulty equipment car

Computation:

Point of faulty equipment car = Faulty equipment car / Total number of car

Point of faulty equipment car = 183 / 700

Point of faulty equipment car = 0.261428571

Point of faulty equipment car = 0.2614 (Approx)

Answer:

59 accidents were investigated.

Step-by-step explanation:

The question above is a probability question that involves 2 elements: causes of accidents.

Let

A = Alcohol

E = Excessive speed

In the question, we are given the following information:

18 accidents involved Alcohol and Excessive speed =P(A ∩ E)

26 involved Alcohol = P(A)

12 accidents involved excessive speed but not alcohol = P( E ) Only

21 accidents involved neither alcohol nor excessive speed = neither A U B

We were given P(A) in the question. P(A Only) = P(A) - P(A ∩ E)

P(A Only) = 26 - 18

= 8

So, only 8 accident involved Alcohol but not excessive speed.

The Total number of Accidents investigated = P(A Only) + P( E only) + P(A ∩ E) + P( neither A U B)

= 8 + 12 + 18 + 21

= 59

Therefore, 59 accidents were investigated.

Answer:

3 pairs

Step-by-step explanation:

Top and Bottom

Front and Back

Side and Side.

Cereal Boxes have 6 sides

Answer:

41.1 miles

Step-by-step explanation:

84 - 42.9 = 41.1

Answer:

interior angle (2)= 70

interior angle (3)= 60

Step-by-step explanation:

Given:

exterior angle=120°

interior angle (1)=50°

Required:

interior angle (2)=?

interior angle (3)=?

Formula:

exterior angle=interior angle (1) + interior angle (2)

Solution:

exterior angle=interior angle (1)+ interior angle (2)

120°=50°+interior angle (2)

120°+50°=interior angle (2)

70°=interior angle (2)

interior angle (3)= 180°-interior angle (1)- interior angle (2)

interior angle (3)=180°-50°+70°

interior angle (3)=180°-120°

interior angle (3)= 60°

Theorem:

Theorem 1.16

The measure of an exterior angle of a triangle is greater than either of the measures of the remote interior angles.

Hope this helps ;) ❤❤❤

Answer:

D

Step-by-step explanation:

100/5=20

20*7=140

Answer:

100yd²

Step-by-step explanation:

length=4x

width=x

perimeter=2(l+w)

50=2(4x+x)

50=2(5x)=10x

50=10x

x=5yd

width=5yd

length=20yd

area=length×width

=20×5

=100yd²

Answer:

[tex]\boxed{\red{100 \: \: {yd} ^{2}}} [/tex]

Step-by-step explanation:

width = x

length = 4x

so,

perimeter of a rectangle

[tex] p= 2(l + w) \\ 50yd = 2(4x + x) \\ 50yd= 2(5x) \\ 50yd= 10x \\ \frac{50yd}{10} = \frac{10x}{10} \\ x = 5 \: \: yd[/tex]

So, in this rectangle,

width = 5 yd

length = 4x

= 4*5

= 20yd

Now, let's find the area of this rectangle

[tex]area = l \times w \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 20 \times 5 \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 100 {yd}^{2} [/tex]

Answer:

y = 6x - 26

Step-by-step explanation:

1. find slope: (y₂ - y₁) / (x₂ - x₁)

(-2 - 10) / (4 - 6) = -12 / -2 = 6

basic equation: y = 6x + b

2. plug in (x,y) value using one set of coordinates.

10 = 6(6) + b

10 = 36 + b

b = 10 - 36

b = -26

3. plug b in to find full equation.

y = 6x -26

Answer:

y = -1/6 x + 11

Step-by-step explanation:

In order to write an equation of a line you need slope (m) and y-intercept (b) or where the graph grosses the y- axis. since you are given two points (6, 10) and (4, -2). Slope when given two points is (y - y) / (x - x)

                                                                  so (-2 - 10) / (6 - 4) = 6 / - 1 =- 6

use the equation y = mx + b and substitute either point (6, 10) or (4, -2) as a replacement for x and y respectively. (I chose (6, 10) because they are positive numbers. Substituting x = 6 and y = 10 and m = -6  into y = mx + b

10 = -6(6) + b

10 = -36 + b

b = 46 (add -36 to both sides)

so our equation: y = -6x + 46 :-)

Answer:

Step-by-step explanation:

1. Preferred Share dividends.

There are 300,000 preference shares and each of them got $2.85. Total dividends are;

= 300,000 * 2.85

= $855,000‬

2. Total dividends = $3,500,000

Dividends left for Common Shareholders (preference gets paid first)

= 3,500,000 - 855,000

= $2,645,000

Common shares number 2,500,000

Dividend per share of common stock = [tex]\frac{2,645,000}{2,500,000}[/tex]

= $1.06

Answer:

0

Step-by-step explanation:

Hope this helps

Answer:

Third option

Step-by-step explanation:

We can't factor this so we need to use the quadratic formula which states that when ax² + bx + c = 0, x = (-b ± √(b² - 4ac)) / 2a. However, we notice that b (which is 6) is even, so we can use the special quadratic formula which states that when ax² + bx + c = 0 and b is even, x = (-b' ± √(b'² - ac)) / a where b' = b / 2. In this case, a = 1, b' = 3 and c = 7 so:

x = (-3 ± √(3² - 1 * 7)) / 1 = -3 ± √2

Answer:

A. a straight line passing

Step-by-step explanation:

Answer:

a straight line passing

Step-by-step explanation:

Answer:

Hence, none of the options presented are valid. The plane is represented by [tex]3 \cdot x + 3\cdot y + 2\cdot z = 6[/tex].

Step-by-step explanation:

The general equation in rectangular form for a 3-dimension plane is represented by:

[tex]a\cdot x + b\cdot y + c\cdot z = d[/tex]

Where:

[tex]x[/tex], [tex]y[/tex], [tex]z[/tex] - Orthogonal inputs.

[tex]a[/tex], [tex]b[/tex], [tex]c[/tex], [tex]d[/tex] - Plane constants.

The plane presented in the figure contains the following three points: (2, 0, 0),  (0, 2, 0), (0, 0, 3)

For the determination of the resultant equation, three equations of line in three distinct planes orthogonal to each other. That is, expressions for the xy, yz and xz-planes with the resource of the general equation of the line:

xy-plane (2, 0, 0) and (0, 2, 0)

[tex]y = m\cdot x + b[/tex]

[tex]m = \frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

Where:

[tex]m[/tex] - Slope, dimensionless.

[tex]x_{1}[/tex], [tex]x_{2}[/tex] - Initial and final values for the independent variable, dimensionless.

[tex]y_{1}[/tex], [tex]y_{2}[/tex] - Initial and final values for the dependent variable, dimensionless.

[tex]b[/tex] - x-Intercept, dimensionless.

If [tex]x_{1} = 2[/tex], [tex]y_{1} = 0[/tex], [tex]x_{2} = 0[/tex] and [tex]y_{2} = 2[/tex], then:

Slope

[tex]m = \frac{2-0}{0-2}[/tex]

[tex]m = -1[/tex]

x-Intercept

[tex]b = y_{1} - m\cdot x_{1}[/tex]

[tex]b = 0 -(-1)\cdot (2)[/tex]

[tex]b = 2[/tex]

The equation of the line in the xy-plane is [tex]y = -x+2[/tex] or [tex]x + y = 2[/tex], which is equivalent to [tex]3\cdot x + 3\cdot y = 6[/tex].

yz-plane (0, 2, 0) and (0, 0, 3)

[tex]z = m\cdot y + b[/tex]

[tex]m = \frac{z_{2}-z_{1}}{y_{2}-y_{1}}[/tex]

Where:

[tex]m[/tex] - Slope, dimensionless.

[tex]y_{1}[/tex], [tex]y_{2}[/tex] - Initial and final values for the independent variable, dimensionless.

[tex]z_{1}[/tex], [tex]z_{2}[/tex] - Initial and final values for the dependent variable, dimensionless.

[tex]b[/tex] - y-Intercept, dimensionless.

If [tex]y_{1} = 2[/tex], [tex]z_{1} = 0[/tex], [tex]y_{2} = 0[/tex] and [tex]z_{2} = 3[/tex], then:

Slope

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

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

y-Intercept

[tex]b = z_{1} - m\cdot y_{1}[/tex]

[tex]b = 0 -\left(-\frac{3}{2} \right)\cdot (2)[/tex]

[tex]b = 3[/tex]

The equation of the line in the yz-plane is [tex]z = -\frac{3}{2}\cdot y+3[/tex] or [tex]3\cdot y + 2\cdot z = 6[/tex].

xz-plane (2, 0, 0) and (0, 0, 3)

[tex]z = m\cdot x + b[/tex]

[tex]m = \frac{z_{2}-z_{1}}{x_{2}-x_{1}}[/tex]

Where:

[tex]m[/tex] - Slope, dimensionless.

[tex]x_{1}[/tex], [tex]x_{2}[/tex] - Initial and final values for the independent variable, dimensionless.

[tex]z_{1}[/tex], [tex]z_{2}[/tex] - Initial and final values for the dependent variable, dimensionless.

[tex]b[/tex] - z-Intercept, dimensionless.

If [tex]x_{1} = 2[/tex], [tex]z_{1} = 0[/tex], [tex]x_{2} = 0[/tex] and [tex]z_{2} = 3[/tex], then:

Slope

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

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

x-Intercept

[tex]b = z_{1} - m\cdot x_{1}[/tex]

[tex]b = 0 -\left(-\frac{3}{2} \right)\cdot (2)[/tex]

[tex]b = 3[/tex]

The equation of the line in the xz-plane is [tex]z = -\frac{3}{2}\cdot x+3[/tex] or [tex]3\cdot x + 2\cdot z = 6[/tex]

After comparing each equation of the line to the definition of the equation of the plane, the following coefficients are obtained:

[tex]a = 3[/tex], [tex]b = 3[/tex], [tex]c = 2[/tex], [tex]d = 6[/tex]

Hence, none of the options presented are valid. The plane is represented by [tex]3 \cdot x + 3\cdot y + 2\cdot z = 6[/tex].

Answer:

It is A    3x+3y+2z=6

Step-by-step explanation:

Answer: 3 hours

Step-by-step explanation:

Here is the correct question:

Betty and karen have been hired to paint the houses in a new development. Working together the women can paint a house in two thirds the time that it takes karen working alone. Betty takes 6 hours to paint a house alone. How long does it take karen to paint a house working alone?

Since Betty takes 6 hours to paint a house alone, that means she can paint 1/6 of the house in 1 hour.

Karen can also paint 1/x in 1 hour

Both of them will paint the house in 3/2 hours.

We then add them together which gives:

1/6 + 1/x = 3/2x

The lowest common multiple is 6x

1x/6x + 6/6x = 9/6x

We then leave out the denominators

1x + 6 = 9

x = 9 - 6

x = 3

Karen working alone will paint a house in 3 hours.

Answer:

The answer is (1,-5). (i.e x=1 and y=-5).

Hope it helps..

Answer:

(1,-5)

Step-by-step explanation:

Answer:

The beryllium atom; 1.99 times larger.

Step-by-step explanation:

The beryllium atom is 0.000000000112 meters, while the nitrogen atom is 0.000000000056 meters. So, the beryllium atom is larger than the other.

(1.12 * 10^-10) / (5.6 * 10^-11)

= (1.112 / 5.6) * (10^-10 + 11)

= 0.1985714286 * 10

= 1.985714286 * 10^0

So, the beryllium atom is about 1.99 times larger than the other.

Hope this helps!

Answer:

decreases.

Step-by-step explanation:

Type II error is one in which we fail to reject the null hypothesis that is actually false. Null hypothesis is a statement that is to be tested against the alternative hypothesis and then decision is taken whether to accept or reject the null hypothesis. The power of Type II error is 1 - [tex]\beta[/tex]. As the power increases the probability of Type II error decreases.

Answer:

AB = 20 tan55°

Step-by-step explanation:

Using the tangent ratio in the right triangle

tan55° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{AB}{BC}[/tex] = [tex]\frac{AB}{20}[/tex] ( multiply both sides by 20 )

20 tan55° = AB

Answer:

D (13,5)

Step-by-step explanation:

X 2 3 4 5

Y 2 5 9 13

So the ordered pairs are (2,2),(3,5), (4,9), (5,13)

and the ordered pairs for the inverse are

(2,2),(5,3), (9,4), (13,5)

from which D (13,5) is found among the options.

Answer:

b

Step-by-step explanation:

In general, if we have [tex]x^a=x^b,[/tex] then [tex]a=b.[/tex] Thus, the first answer choice is correct.

Answer:

[tex]\boxed{\red{2x - 1 = 5x - 14}}[/tex]

First answer is correct.

Step-by-step explanation:

we know that,

[tex] {x}^{a} = {x}^{b} [/tex]

[tex]a = b[/tex]

So, according to that,

[tex] {5}^{(2x - 1)} = {5}^{(5x - 14)} [/tex]

Therefore,

[tex]2x - 1 = 5x - 14[/tex]

Answer:

Step-by-step explanation:

cos^-1(6/13)=62.5136°

sin(2*62.5136°)=0.8189

cos(2*62.5136°)=-0.5740

Answer:

Perimeter of the picture and frame = 38.4inches

Area of the picture and frame = 92.16inches²

Step-by-step explanation:

A square frame is made up of 4 different pieces. The shape of each piece = Rectangle

The perimeter of the rectangle = 24

Perimeter of the rectangle = 24 inches

The perimeter of a rectangle = 2L + 2W

The Width of a Rectangle is always on her than the length hence.

24 = 2L + 2W

24 = 2( L + W)

24/2 = L + W

12 = L + W

Because the width is always longer than the length

W > L

Width of wooden frame = 4 × Length

Therefore;

4 × L = W

Which gives

L + W = 12 inches

4 × L + L = 12 inches

L×(4 + 1)

= 5L = 12 inches

L = 12/5 = 2.4 inches

W = 4 × L = 4 × 12/5

W = 48/5 = 9.6 inches

Side length of wooden frame, L =9.6

The perimeter of the picture frame = 4 × L= 4 × 9.6= 38.4 inches

The area of the picture frame = L²

= L × L

= 9.6 × 9.6 = 92.16inches².

Answer:

x= 45

Step-by-step explanation:

In this diagram, there is an angle that is split into 2 angles.

The angle is a 90 degree angle. We know this because of the little square in the corner that denotes a right angle.

Therefore, the 2 angles inside of the right angle must add to 90 degrees. The 2 angles that make up the right angle are x and 45.

x+45=90

We want to find x. We need to get x by itself. 45 is being added on to x. The inverse of addition is subtraction. Subtract 45 from both sides.

x+45-45=90-45

x= 90-45

x=45

The measure of angle x is 45 degrees.

Answer:

Random variable

Step-by-step explanation:

The reason it is a random variable is because a, the definition fits, and b you can use context clues as well, such as 'determined by chance' which is another example of random! So, the answer is random, because random variables are determined by chance. Hope this helped.

Answer:

"A random variable is a variable that has a single numerical value, determined by chance, for each outcome of a procedure."

A random variable is distinct on the off chance that it takes on a countable number of quantities.