In a​ volcano, erupting lava flows continuously through a tube system about 15 kilometers to the sea. Assume a lava flow speed of 0.5 kilometer per hour and calculate how long it takes to reach the sea.

Answer:

Sample space = 36

P(sum of 6) = 5/36

Step-by-step explanation:

Number of faces on a dice = 6

The sample space, for a toss of 2 dice ; (Number of faces)^number of dice

Sample space = 6^2 = 6*6 = 36

Sum of numbers appearing on the dice = 6

The sum of 6 from the roll of two dice has 5 different outcomes ; Hence, required outcome = 5

Total possible outcomes = sample space = 36

Probability, P = required outcome / Total possible outcomes

P = 5 / 36

Probabilities are used to determine the chances of events

The given parameters are:

[tex]n=6[/tex] --- the faces of a six-sided die

[tex]r = 2[/tex] -- the number of dice

(a) The number of sample points

This is calculated as:

[tex]Sample = n^r[/tex]

So, we have:

[tex]Sample = 6^2[/tex]

Evaluate the exponent

[tex]Sample = 36[/tex]

Hence, the number of sample points is 36

(b) The probability that the sum of 6

See attachment for the sample space of the sum of two dice.

From the sample space, there are 5 outcomes where the sum is 6.

So, the probability is:

[tex]Pr = \frac{5}{36}[/tex] --- where 36 represents the number of sample points

Divide 5 by 36

[tex]Pr = 0.1389[/tex]

Hence, the probability that the sum of the numbers appearing on the dice is equal to 6 is 0.1389

Read more about probabilities at:

https://brainly.com/question/10707698

Answer:

x=7

y=11

z=7

Step-by-step explanation:

x + y + z = 25

y+z= 18

Z= 7

Substitute the third equation into the second

y+z=18

y+7 = 18

y = 18-7

y = 11

Now substitute y=11 and z=7 into the first

x +y+z = 25

x+11+7 = 25

x+18 = 25

x = 25-18

x=7

Answer:

Step-by-step explanation:

You have three data points. Equation of the line passing through (30,2), (45,2.75), and (60,3.50):

y = 0.5x + 0.5

It takes 0.5 hour to clean up.

Answer:[tex]2\sqrt[4]{4}[/tex]

Step-by-step explanation:

[tex]64^{\frac{1}{4} }= \sqrt[4]{64}=\sqrt[4]{(2)(2)(2)(2)(4)}=2\sqrt[4]{4}[/tex]

Answer:

AC = 377.19

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

tan theta = opp /adj

tan 5 = 33/AC

AC tan 5 = 33

AC = 33/ tan 5

AC = 377.19

Answer:

H0 : μ ≥ 98.6

H1 : μ < 98.6

Step-by-step explanation:

The population mean temperature, μ = 98.6

The null hypothesis takes up the value of the population mean temperature as the initial truth ;

The alternative hypothesis on the other hand is aimed at using a sample size of 109 to establish if the mean temperature is less than the population mean temperature.

The hypothesis ;

Null hypothesis, H0 : μ ≥ 98.6

Alternative hypothesis ; H1 : μ < 98.6

...

Calculate Energy Cost by Appliance

Answer:

4

Step-by-step explanation:

We want the cubed root of 64  

(64)^(1/3)  

(4*4*4) ^ (1/3)  

4  

Unless this is 3 * sqrt(64)  

then it would be  

3 sqrt(8*8)  

3 (8)  

24

Answer:

441

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

i simply used the unit circle

Answer:

6 11/12

Step-by-step explanation:

4 1/6 + 2 3/4

Get a common denominator of 12

4 1/6 *2/2  + 2 3/4 *3/3

4 2/12 + 2 9/12

6 11/12

Answer:

He detailed 16 cars.

912/57=16

Step-by-step explanation:

Answer:

According to the proposed interrogate, as well as the graph provided, the correct answers to such are identified as B. Y = -2x + 5 and C. 2x + y = 4.

Step-by-step explanation:

To evaluate such, a comprehension of linear Cartesian data is required:

Slope = rise/run. If there is a negative rise, the direction of the line is proportional to the left-hand side as it exponentially grows or augments in units.

Y-intercept: The peculiar point in which the linear data observed intersects the y-axis.

X-intercept: The peculiar point in which the linear data observed intersects the x-axis.

Since this is a negative linear, all negative slopes apply.

The interrogate states, “Check all that apply.” Thus, there may be more than one correct answer, shall such be disseminated.

A. Cannot be the answer as the line should have been a horizontal line contained within quadrants I and II on the Cartesian Plane.

B. Contains a negative slope, thus is disclosed as a correct answer.

C. This configuration is denoted in “Standard Form” or “General Form”. To convert this to “Slope-Intercept Form” the following must be executed mathematically:

2x + y = 4

Y = -2x + 4 <== Slope-Intercept Form (Contains a negative slope, thus considered a correct answer.

D. Likewise, this configuration is denoted in “Standard Form” or “General Form”. To convert this to “Slope-Intercept Form” the following must be executed mathematically:

X - y = 9

-y = -x + 9

Y = x - 9 <== Slope-Intercept Form (Cannot be considered as the correct answer, given the positive slope configuration, thus is marked out).

Thus far, as evaluated, the correct answers to the proposed interrogate, as according to the linear data provided in the Cartesian Plane is acknowledged, and henceforth disseminated, as B. Y = -2x + 5 and C. 2x + y = 4.

*I hope this helps.

Answer:

(2, -3) and r = 3.

Step-by-step explanation:

you can also plug this equation in desmos but I guess it's good to know how to do it also:

The equation of a circle is (x-h)^2 + (y-k)^2 = r^2

Now in order to make a perfect square on both sides, we need to do this:

First add 9 to both sides:

x^2 + 6x + 9 + y^2 -4y +4 = 9.

I purposely shifted it to show the perfect square created when you add 9 to both sides. Factor:

(x+3)^2 + y^2 - 4y + 4 = 9.

now the second bolded part is allso a perfect square. Factor:

(x+3)^2 + (y-2)^2 = 9

Based on the equation of a circle, the center must be at (2, -3) and the radius is the square root of 9 which is 3.

:)

9514 1404 393

Answer:

  2, 1, -1/2, -1/4, 1/8

Step-by-step explanation:

Use n = 1 through 4:

  [tex]a_{1+1}=\dfrac{(-1)^{1+1}\cdot a_1}{2}\ \Rightarrow\ a_2=\dfrac{1\cdot2}{2}=1\\\\a_3=\dfrac{(-1)^3\cdot 1}{2}=-\dfrac{1}{2}\\\\a_4=\dfrac{(-1)^4\cdot(-\dfrac{1}{2})}{2}=-\dfrac{1}{4}\\\\a_5=\dfrac{(-1)^5\cdot(-\dfrac{1}{4})}{2}=\dfrac{1}{8}[/tex]

The first 5 terms are ...

  2, 1, -1/2, -1/4, 1/8

Answer:

The right answer is:

(a) -10.67

(b) 0.7986

Step-by-step explanation:

(a)

According to the question,

X                          P(X)                  X.P(X)                 X2.P(X)

12130                  0.002               24.26                 294274

-35                      0.998               -34.93                1222.55      

Now,

[tex]\Sigma x.P(x) = -10.67[/tex]

or,

[tex]\Sigma x^2.P(x) = 295496.35[/tex]

hence,

The mean will be:

[tex]\Sigma x.P(x) = -10.67[/tex]

(b)

According to the question,

n = 12

p = 0.125

q = 1 - p

  = 0.875

Now,

⇒ [tex]P(X=x) = \binom{n}{x} p^x q^{n-x}[/tex]

By substituting the values, we get

⇒ [tex]P(X \geq 1)=1-(\binom{12}{0} 0.125^0. 0.875^{12-0})[/tex]

⇒                  [tex]=1-(1 (0.125^0) (0.875^{12}))[/tex]

⇒                  [tex]=1-(1(1.0)(0.2014))[/tex]

⇒                  [tex]=1-(0.2014)[/tex]

⇒                  [tex]=0.7986[/tex]    

Applying log rules leaves us with the following equation:

x^2 + 8 = 6x

Change to standard form and solve using factoring.

x^2 - 6x + 8 = 0

(x - 4)(x - 2) = 0

x = 4

x = 2

Hope this helps!

Answer:

Lift

Step-by-step explanation:

Finding patterned and relationship between large sets of data can be obtained using the association rule as it finds insights, relationships and trends within sets of data variables. Lift is a parmater of interest whichbus used when performing analysis on association between variables in datasets. The Lift is literally the ratio of confidence to expected confidence. Where, the confidence of association is divided by the expected confidence (benchmark confidence).

9514 1404 393

Answer:

  23°

Step-by-step explanation:

The angle a vector makes relative to the +x axis is found as ...

  α = arctan(y/x) = arctan(4.30/10.3) ≈ 22.66°

The angle is about 23°.

__

Additional comment

This vector resides in the first quadrant, so no adjustment of the angle is needed. In other quadrants, 180° may need to be added or subtracted from the angle given by the arctan function to arrive at the correct value. (Some calculators and spreadsheets have an ATAN2(x, y) function that takes signs into account.)

Answer:

2.5 km left

The midpoint is half of 5, which is 2.5, so he'll still have 2.5 km left to complete

Answer:

The answer is "0.624"

Step-by-step explanation:

[tex]b = 5x\\\\h = x\\\\ l = 10 \\[/tex]

Using formula:

[tex]V = (\frac{1}{2})(b)(h)(l) \\\\[/tex]

   [tex]= \frac{1}{2} \times (5x)\times (x) \times (10)\\\\= 5x\times x \times 5\\\\= 25x^2[/tex]

[tex]\frac{dV}{dt} = 50x \ \frac{dx}{dt} \\\\\text{(where x represents the height in feet and}\ \frac{dv}{dt} = 13\ \frac{ft^3}{min})\\\\\frac{dx}{dt} = (\frac{1}{50})(\frac{1}{x}) \ \frac{dV}{dt}\\\\[/tex]

When the water is 5 inches deep then:

[tex]x = (\frac{5}{12})\ ft\\\\13 =50(\frac{5}{12}) \ \frac{dx}{dt}\\\\13 \times 12 =50(5) \ \frac{dx}{dt}\\\\\frac{13 \times 12}{50 \times 5} = \frac{dx}{dt}\\\\\frac{156}{250} = \frac{dx}{dt}\\\\ \frac{dx}{dt}= 0.624[/tex]

Answer:

4.67 mph

Step-by-step explanation:

Speed with no wind = 14 mph

Let wind speed = w mph

Thus;

Speed with wind = 14 + w

Speed against the wind = 14 - w

Now, we are told that against the wind he bikes 10 miles.

Thus, from; time = distance/speed, we have;

Time = 10/(14 - w)

Also, we are told he biked 20 miles with the wind. Thus;

Time = 20/(14 + w)

We are told the times he used in both cases are the same.

Thus;

10/(14 - w) = 20/(14 + w)

Divide both sides by 10 to get;

1/(14 - w) = 2/(14 + w)

Cross multiply to get:

1(14 + w) = 2(14 - w)

14 + w = 28 - 2w

w + 2w = 28 - 14

3w = 14

w = 14/3

w = 4.67 mph

Answer:

The profit is maximum when x = 40.

Step-by-step explanation:

Cost function, C = 40 x + 300

Revenue function, R = 80 x - 0.5 x^2

The profit function is

[tex]P = R - C\\\\P = 80 x - 0.5 x^2 - 40 x - 300\\\\P = - 0.5 x^2 + 40 x - 300\\\\\frac{dP}{dx} = - x + 40\\\\So, \frac{dP}{dx} = 0\\\\-x + 40 = 0 \\\\x = 40[/tex]

So, the profit is maximum when x = 40 .

Answer:

C

Step-by-step explanation:

In the graph given, we can expect the x axis to be horizontal and the y axis to be vertical. This means that the arm span represents y and the height represents x.

Therefore, if a girl on her team is 63 inches tall, we can say that y=x+2, and since height is x, y = 63 + 2 = 65

Answer:

His least score for him in the fourth paper has to be 76.

Step-by-step explanation:

Given that Michael has an average of 68% in his 3 papers but that is below the pass mark of 70%, to determine what must be his least score in the fouth paper to enable him pass the following calculation must be performed:

(70 x 4) - (68 x 3) = X

280 - 204 = X

76 = X

Therefore, his least score for him in the fourth paper has to be 76.

Given:

A clients rash measures 5 cm × 4 cm.

To find:

The measure in inches.

Solution:

We know that,

2.54 cm = 1 inch

1 cm [tex]=\dfrac{1}{2.54}[/tex] inch

1 cm [tex]\approx 0.3937[/tex] inch

Using this conversion, we get

5 cm [tex]=5\times 0.3937[/tex] inches

5 cm [tex]=1.9685[/tex] inches

4 cm [tex]=4\times 0.3937[/tex] inches

4 cm [tex]=1.5748[/tex] inches

Therefore, the measure in inches is 1.9685 inches × 1.5748 inches.

Answer:

x+5

Step-by-step explanation:

Answer:

2x-8+6-3x +2x +7

= 2x -3x +2x -8+6+7

=4x-3x-8+13

= 1x+5

Answer:

The 99% confidence interval for the true mean checking account balance for local customers is ($439.29, $888.99).

Step-by-step explanation:

We have the standard deviation for the sample, which means that the t-distribution is used to solve this question.

The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So

df = 14 - 1 = 13

99% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 13 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.99}{2} = 0.995[/tex]. So we have T = 3.0123

The margin of error is:

[tex]M = T\frac{s}{\sqrt{n}} = 3.0123\frac{279.29}{\sqrt{14}} = 224.85[/tex]

In which s is the standard deviation of the sample and n is the size of the sample.

The lower end of the interval is the sample mean subtracted by M. So it is 664.14 - 224.85 = $439.29

The upper end of the interval is the sample mean added to M. So it is 664.14 + 224.85 = $888.99.

The 99% confidence interval for the true mean checking account balance for local customers is ($439.29, $888.99).

Answer:

If you want the area of something with the sides 14cm and 7cm then it would be 98 cm.

Step-by-step explanation:

Area = length * width

Area = 14 cm * 7 cm

Area = 98 cm