There is a 20% chance that a particular volcano will erupt during any given decade. A random number generator generated 10 sets of random numbers from 1 to 5 as shown. The number 1 represents the volcano erupting. Find the experimental probability that the volcano will erupt in 1 or 2 of the next 5 decades

By solving a system of equations, we will see that the parking lot is 210ft by 200ft.

For a rectangle of length L and width W, the perimeter is:

P = 2*(L + W)

And the area is:

A = L*W

Here we know that the perimeter is 820 ft and the area is 42,000 ft²

Then we can write the two equations (ignoring units).

820 = 2*(L + W)

42,000 = L*W

We can isolate L in the first equation to get:

820/2 = L + W

410 - W = L

Now we can replace that in the other equation:

42,000 = (410 - W)*W = 410*W - W^2

Now we want to solve the quadratic equation:

-W^2 + 410*W - 42,000 = 0

The solutions are given by:

\(W = \frac{-410 \pm \sqrt{410^2 - 4*(-1)*(-42000)} }{-2} \\\\W = \frac{-410 \pm 10 }{-2}\)

Then the solutions are:

W = (-410 + 10)/(-2) = 200

W = (-410 - 10)/2 = 210

If we take W = 200, then:

L = 410 - W  = 410 - 200 = 210

So we can conclude that the parking lot is 200ft by 210ft.

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Answer: C, 210 ft

Step-by-step explanation: edge :)

Step-by-step explanation:

-4|8-5n|=19

-4/-4|8-5n|=19/-4

|8-5n|=4.75

5n=4.75-8

5n=-3.25

5n/5=-3.25/5

n=-0.65

if it is wrong sory

The answer is in the image!

Answer: any negative value

Step-by-step explanation:

g(x)= ax², inc on x<0 & dec on x>0

Firstly we need to get the derivative of g(x)

g'(x)=2ax

for inc interval g'(x) should be +ve

x<0 (i.e. x= -ve), then a must be -ve

for dec interval g'(x) should be +ve

x>0 (i.e. x= +ve), then a must be -ve

so in both cases a must be a negative constant

The ordered triple representing \(3u - 2v\) is \((13, -8, 5)\).

To find an ordered triple representing \(3u - 2v\),

where \(u = (5, -2, 3)\) and \(v = (1, 1, 2)\),

we can perform the following operations:

\(3u = 3(5, -2, 3)\)

\(3u = (15, -6, 9)\)

\(2v = 2(1, 1, 2)\)

\(2v = (2, 2, 4)\)

Now, subtracting 2v from 3u gives:

\(3u - 2v = (15, -6, 9) - (2, 2, 4)\)

\(3u - 2v = (15-2, -6-2, 9-4)\)

\(3u - 2v = (13, -8, 5)\)

Therefore, the ordered triple representing 3u - 2v is (13, -8, 5).

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Answer:

(3, 0)

Step-by-step explanation:

x-intercept is where the line touches the x-axis

It is the point on the line where y=0

Answer:

3,0

Step-by-step explanation:

the point where the line cuts the x axis is the x-intecept

Answer:

a. 15L will last the cafe 3 days if they're using 4L every day

b. 15L will last them 7 days if they're using 2L every day

Step-by-step explanation:

division.

Answer:

The probability that one marble drawn at random is not blue is 70%

The solution of the expression \(\sqrt{z^4\times z^{\frac{-3}{2}}\) will be z⁵.

Expression in maths is defined as the relation of numbers variables and functions by using mathematical signs like addition, subtraction, multiplication and division.

In mathematics, expression is defined as the relationship of numbers, variables, and functions using mathematical signs such as addition, subtraction, multiplication, and division.

The expression will be solved as:-

\(E = \sqrt{z^4\times z^{\frac{-3}{2}}\)

\(E = \sqrt{(z)^{4- {\frac{3}{2}\)

E = z⁵

Therefore, the solution of the expression is z⁵.

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The perimeter of the figure is 58 m.

To find the perimeter of the given figure we can divide the figure in three rectangles.

Rectangle 1:

Perimeter= 2 (l + w)

= 2(5 + 2)

= 2 x 7

= 14 m

Rectangle 2:

Perimeter= 2 (l + w)

= 2(5 + 1)

= 2 x 6

= 12 m

Rectangle 3:

Perimeter= 2 (l + w)

= 2(14 + 2)

= 2 x 16

= 32 m

So, the perimeter of the figure is

= 14 + 12 + 32

= 58 m

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The sample size needed to be 99​% confident that the sample proportion will not differ from the true proportion by more than ​4% is given as follows:

n = 1037.

A confidence interval of proportions has the bounds given by the rule presented as follows:

\(\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}\)

In which the variables used to calculated these bounds are listed as follows:

The margin of error is given as follows:

\(M = z\sqrt{\frac{\pi(1-\pi)}{n}}\)

The confidence level is of 99%, hence the critical value z is the value of Z that has a p-value of \(\frac{1+0.99}{2} = 0.995\), so the critical value is z = 2.575.

As we have no estimate, the parameter is given as follows:

\(\pi = 0.5\)

Then the sample size for M = 0.04 is obtained as follows:

\(M = z\sqrt{\frac{\pi(1-\pi)}{n}}\)

\(0.04 = 2.575\sqrt{\frac{0.5(0.5)}{n}}\)

\(0.04\sqrt{n} = 2.575 \times 0.5\)

\(\sqrt{n} = \frac{2.575 \times 0.5}{0.04}\)

\((\sqrt{n})^2 = \left(\frac{2.575 \times 0.5}{0.04}\right)^2\)

n = 1037.

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Answer:

-5, -4 1/4, -4.1, -3 3/5, -1, -0.6, 0, 1, 2, 2.1, 4.5

Step-by-step explanation:

Answer:

4 lollipops and 3 penicls in each bag, so 50 bags

Step-by-step explanation:

I've had to do this one before

Answer:

k = -3

k =5

Step-by-step explanation:

\(d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\d = 5\\(-1,1) =(x_1,y_1)\\(2,k)=(x_2,y_2)\\\)

\(5=\sqrt{\left(2-\left(-1\right)\right)^2+\left(k-1\right)^2}\\\\\mathrm{Square\:both\:sides}:\quad 25=k^2-2k+10\\25=k^2-2k+10\\\\\mathrm{Solve\:}\:25=k^2-2k+10:\\k^2-2k+10=25\\\\\mathrm{Subtract\:}25\mathrm{\:from\:both\:sides}\\k^2-2k+10-25=25-25\\k^2-2k-15=0\\\\\mathrm{Solve\:by\:factoring}\\\\\mathrm{Factor\:}k^2-2k-15:\quad \left(k+3\right)\left(k-5\right)\\\mathrm{Solve\:}\:k+3=0:\quad k=-3\\\)

\(\mathrm{Solve\:}\:k-5=0:\quad k=5\\\\k =5 , k=-3\)

A = (-1, 1) and B = (2, k) so:

\(d(A,B)=\sqrt{(x_B-x_A)^2+(y_B-y_A)^2}=\sqrt{(2-(-1))^2+(k-1)^2}=\\\\=\sqrt{3^2+(k-1)^2}=\sqrt{9+k^2-2k+1}=\sqrt{k^2-2k+10}\\\\\\d(A,B)=5\\\\\sqrt{k^2-2k+10}=5\quad|(\ldots)^2\\\\\big|k^2-2k+10\big|=25\\\\k^2-2k+10=25\qquad\vee\qquad k^2-2k+10=-25\\\\k^2-2k-15=0\qquad\vee\qquad k^2-2k+35=0\\\\\\\Delta_1=(-2)^2-4\cdot1\cdot(-15)=64>0\qquad\text{two solutions}\\\\\Delta_2=(-2)^2-4\cdot1\cdot35=-136<0\qquad\text{no solutions}\\\\\\k_1=\dfrac{2-\sqrt{64}}{2}=\dfrac{2-8}{2}=\dfrac{-6}{2}=\boxed{-3}\)

\(k_2=\dfrac{2+\sqrt{64}}{2}=\dfrac{2+8}{2}=\dfrac{10}{2}=\boxed{5}\)

Answer:

16

Step-by-step explanation:

140 divided by 9 = 15.5

you need 16 vans to hold 140 tourists

Answer:

your answer is D

Step-by-step explanation:

hope this helps

The value of w for the expression of angle 6w + 13 will be 13. The correct option is A.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that a quadrilateral has 4 sides. One angle of regular quadrilateral measures (6w+13).

The value of 'w' will be calculated as,

6w + 13 = 90

6w = 90 - 13

6w = 77

w = 12.83 or 13

Therefore, the value of w for the expression of angle 6w + 13 will be 13. The correct option is A.

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Answer:

$14

Step-by-step explanation:

80% of 70= 56

70-56=14

9514 1404 393

Answer:

  12 units

Step-by-step explanation:

Reflection over two lines x units apart is equivalent to a translation of 2x units. Since the given lines are 6 units apart, ...

  the equivalent translation is of 12 units.

___

Example:

Lines at x=0 and x=6. Point (x, 0). After reflection over x=0, the point is located at (2·0 -(x), 0) = (-x, 0). After reflection of that over x=6, the point is located at (2·6 -(-x), 0) = (12 +x, 0). That is, 12 has been added to the x-coordinate, meaning the point was translated 12 units. (The translation is in the direction the second line is from the first.)

\(\large{\boxed{\sf y = \dfrac{2}{3} | x -6|- 7}}\)

Absolute value of a graph formula:

Identify the vertex : (h, k) = (6, -7)

Take two points: (6, -7), (9, -5)

 \(\sf Find \ slope \ (a) : \sf \ \dfrac{y_2 - y_1}{x_2- x_1} \ = \ \ \dfrac{-5-(-7)}{9-6} \ = \ \ \dfrac{2}{3}\)

Join them to build the equation:   \(\bf{y = \dfrac{2}{3} |x - 6| - 7}\)

Answer:

\(g(x)=\dfrac{2}{3}|x-6|-7\)

Step-by-step explanation:

Translations

For \(a > 0\)

\(f(x-a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units right}\)

\(f(x)-a \implies f(x) \: \textsf{translated}\:a\:\textsf{units down}\)

\(y=a\:f(x) \implies f(x) \: \textsf{stretched parallel to the y-axis by a factor of}\:a\)

-----------------------------------------------------------------------------------------

Parent function:  \(f(x)=|x|\)

\(f(0)=|0|=0 \implies \textsf{The vertex of the parent function is at (0, 0)}\)  

From inspection of the graph, the vertex of the transformed function is at (6, -7).  Therefore, there has been a translation of:

\(\textsf{6 units right}\implies f(x-6) =|x-6|\)

\(\textsf{and 7 units down}\implies f(x-6)-7=|x-6|-7\)

From inspection of the graph, we can see that it has been stretched parallel to the y-axis:

\(\implies a\:f(x-6)-7=a|x-6|-7\)

The line goes through point (0, -3)

Substituting this point into the above equation to find \(a\):

\(\implies a|0-6|-7=-3\)

\(\implies 6a=4\)

\(\implies a=\dfrac{2}{3}\)

Therefore,

\(\implies g(x)=\dfrac{2}{3}|x-6|-7\)

The conditional probability for this problem is given as follows:

C. P(A|B) = 2/5 = 0.4 = 40%.

The parameters that are needed to calculate a probability are listed as follows:

Then the probability is calculated as the division of the number of desired outcomes by the number of total outcomes.

For this problem, we have that 5 students play soccer, and of those, 2 play basketball, hence the conditional probability is given as follows:

C. P(A|B) = 2/5 = 0.4 = 40%.

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the value οf f(h(-1)) will be ∛2.

A unique kind οf relatiοn called a functiοn is οne in which each input has precisely οne οutput. In οther wοrds, the functiοn prοduces exactly οne value fοr each input value. The graphic abοve shοws a relatiοn rather than a functiοn because οne is mapped tο twο different values. The relatiοn abοve wοuld turn intο a functiοn, thοugh, if οne were instead mapped tο a single value. Additiοnally, οutput values can be equal tο input values.

The x-values are input intο the functiοn machine. The functiοn machine then perfοrms its οperatiοns and οutputs the y-values. The functiοn within can be any functiοn.

f(x) = ∛x+3

g(x)= 8x³-3

h(x)= 2x+1

f((h(-1))= f(-1) = ∛2

Hence the value οf f(h(-1)) will be ∛2.

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Answer:

  (d)  (1, 2)

Step-by-step explanation:

You want to know which of the given points satisfies the inequality.

We find it easiest to plot the given points on a graph of the solution. This shows us that (1, 2) is a solution to the inequality. (It lies in the solution area.)

__

Additional comment

Another way to choose the answer is to try each of the points in the inequality.

If you can visualize the boundary line (without plotting it) as a line with positive slope and a y-intercept of 2, you can more readily reject the first choice and accept the last choice. (0, 3) is above the y-intercept, and (1, 2) is to the right of it (in the solution space).

You may also recognize the x-intercept will be -3, so the second choice lies above the boundary line.

Answer:

3:7

Step-by-step explanation:

Let x = pounds of the $10 rice in the mixture

Let y = pounds of the $30 rice in the mixture

Total cost of the $10 rice = 10x

Total cost of the $30 rice = 30y

(10x + 30y) / (x + y) = 24

Solve this equation for y/x:

10x + 30y = 24(x + y)

10x + 30y = 24x + 24y

30y - 24y = 24x - 10x

6y = 14x

y/x = 6/14  simplify the fraction

y/x = 3/7

So, the ratio of the two different types of rice (y:x) is 3:7, meaning a pound of the rice mixture has 3 parts of the $30 rice to 7 parts of the $10 rice.

Answer:

b

Step-by-step explanation:

trust me

On solving the provided question we can say that, Number of students jumped greater than 8.5 but less than 11.5 is 7 students.

the frequency or reality that something occurs frequently or a great number of times within a specific time frame. The frequency of buses, for instance, has been the subject of more complaints in recent months.

Number of students jumped greater than 8.5 but less than 11.5= frequency of length of jump greater than 8.5 but less than 11.5

AND,

frequency of length of jump greater than 8.5 but less than 11.5 is -

Number of students jumped greater than  8.5 and less than  9.5 + Number of students jumped greater than 9.5 but less than 10.5 + Number of students jumped greater than 10.5 but less than 11.5=

3+3+1=7 ( since, sum of respective frequencies of the three class)

so, Number of students jumped greater than 8.5 but less than 11.5 is 7 students.

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Answer: x=35

Step-by-step explanation:

Reason: The two line segments CF and AH point in the same direction, and they never intersect. Therefore, we consider them parallel.

Skew lines are ones that point in different directions. An example of a pair of skew lines would be AB and DE. Skew lines never intersect, but we don't consider them parallel.

Answer:

Domain = (-∞, ∞) Range = (-∞, ∞)

End Behavior: As X -> -∞, Y -> -∞ | As X -> ∞, Y -> ∞

Inflection Point: (2,0)

Step-by-step explanation: