A magician asks an audience member to pick any number from 6 to 15.
What is the theoretical probability that an individual chooses the number the magician has in mind?

Answer:

The length of each side is 10.5

Step-by-step explanation:

If you mean h as in the hypotenuse:

perimeter= 45    side h= 24    find x

45 - 24 = 2x

21 = 2x

/2     /2

10.5 = x

Answer:

325/3

Step-by-step explanation:

[tex]48+4^2+\frac{3}{5}\\\\\mathrm{Convert\:element\:to\:fraction}:\quad \:48=\frac{48\cdot \:5}{5}\\\\=\frac{48\cdot \:5}{5}+\frac{3}{5}\\\\\mathrm{Since\:the\:denominators\:are\:equal,\\\\\:combine\:the\:fractions}:\\\\\quad \frac{a}{c}\pm \frac{b}{c}=\frac{a\pm \:b}{c}\\\\=\frac{48\cdot \:5+3}{5}\\\\48\cdot \:5+3=243\\\\=4^2+\frac{243}{5}\\\\=16+\frac{243}{5}\\\\=\frac{16\cdot \:5}{5}+\frac{243}{5}\\\\=\frac{16\cdot \:5+243}{5}\\\\16\cdot \:5+243=323\\\\=\frac{323}{5}[/tex]

Answer:

5/6

Step-by-step explanation:

you must flip 3 over 5 and multiply

Answer:

75°

Step-by-step explanation:

In a parallelogram, any two adjacent angles are supplementary. In other words, they total 180.

Angle D and Angle E are adjacent. Thus, they are supplementary. In other words:

[tex]\angle D +\angle E =180[/tex]

Substitute them for the equations:

[tex]7x+21+15+5x=180[/tex]

Combine like terms and add on the left:

[tex]12x+36=180[/tex]

Subtract 36 from both sides:

[tex]12x=144[/tex]

Divide both sides by 12:

[tex]x=12[/tex]

Thus, the value of x is 12.

Note that Angle D and Angle C are also adjacent. Thus, their angles also equal 180.

So:

[tex]\angle D+\angle C =180[/tex]

Substitute the equation for D:

[tex]7x+21+\angle C=180[/tex]

Plug in 12 for x:

[tex]7(12)+21+\angle C =180[/tex]

Simplify:

[tex]84+21+\angle C =180\\105+\angle C =180[/tex]

Subtract 105 from both sides:

[tex]\angle C =75\textdegree[/tex]

Thus, Angle C is 75 degrees.

Answer:

63/10 : 9/2

Step-by-step explanation:

6.3 is 6 and 3/10

we can turn that into an improper fraction so its 63/10

4.5 is 4 and 1/2

we can turn this into an improper fraction with is 9/2

so now its 63/10 : 9/2 as a ratio

Hope this helps. Good luck.

[tex] \frac{ \frac{19}{3}kg }{ \frac{9}{2}kg } [/tex]

Answer:

6/36 (16.667%)

Step-by-step explanation:

Answer:

5/36

Step-by-step explanation:

Answer:

Step-by-step explanation:

Given the domain and target set of functions f and g expressed as;

f(x) = 2x+3 an g(x) = 5x+7 we are to find the following;

a) f◦g

f◦g = f[g(x)]

f[g(x)] = f[5x+7]

To get f(5x+7), we will replace the variable x in f(x) with 5x+7 as shown;

f(x) = 2x+3

f(5x+7) = 2(5x+7)+3

f(5x+7) = 10x+14+3

f(5x+7) = 10x+17

Hence f◦g = 10x+17

b) g◦f

g◦f = g[f(x)]

g[f(x)] = g[2x+3]

To get g(2x+3), we will replace the variable x in g(x) with 2x+3 as shown;

g(x) = 5x+7

g(2x+3) = 5(2x+3)+7

g(2x+3) = 10x+15+7

g(2x+3) = 10x+22

Hence g◦f = 10x+22

c) For (f◦g)−1 (inverse of (f◦g))

Given (f◦g) = 10x+17

To find the inverse, first we will replace (f◦g) with variable y to have;

y = 10x+17

Then we will interchange variable y for x:

x = 10y+17

We will then make y the subject of the formula;

10y = x-17

y = x-17/10

Hence the inverse of the function

(f◦g)−1 = (x-17)/10

d) For the function f−1◦g−1

We need to get the inverse of function f(x) and g(x) first.

For f-1(x):

Given f(x)= 2x+3

To find the inverse, first we will replace f(x) with variable y to have;

y = 2x+3

Then we will interchange variable y for x:

x = 2y+3

We will then make y the subject of the formula;

2y = x-3

y = x-3/2

Hence the inverse of the function

f-1(x) = (x-3)/2

For g-1(x):

Given g(x)= 5x+7

To find the inverse, first we will replace g(x) with variable y to have;

y = 5x+7

Then we will interchange variable y for x:

x = 5y+7

We will then make y the subject of the formula;

5y = x-7

y = x-7/5

Hence the inverse of the function

g-1(x) = (x-7)/5

Now to get )f−1◦g−1

f−1◦g−1 = f-1[g-1(x)]

f-1[g-1(x)] = f-1(x-7/5)

Since f-1(x) = x-3/2

f-1(x-7/5) = [(x-7/5)-3]/2

= [(x-7)-15/5]/2

= [(x-7-15)/5]/2

= [x-22/5]/2

= (x-22)/10

Hence f−1◦g−1 = (x-22)/10

e) For the composite function g−1◦f−1

g−1◦f−1 = g-1[f-1(x)]

g-1[f-1(x)] = g-1(x-3/2)

Since g-1(x) = x-7/5

g-1(x-3/2) = [(x-3/2)-7]/5

= [(x-3)-14)/2]/5

= [(x-17)/2]/5

= x-17/10

Hence g-1◦f-1 = (x-17)/10

Answer:

The answer is

Step-by-step explanation:

To find the equation of a line given a point and slope we use the formula

where

m is the slope

( x1 , y1) is the point

From the question

Slope / m = - 2

The point is ( 10, - 9)

Substitute the values into the above formula

That's the final answer is

Hope this helps you

Answer:

The point estimate = 0.507

Margin error of  a given confidence interval = 0.032

Step-by-step explanation:

The point estimate is calculated by using the sample statistics of a population.

Thus; point estimate can be expressed with the formula:

[tex]\overline x = \dfrac{\sum \limits ^n _{i=1} \ x _i}{n}[/tex]

Given that : 0.475 < p < 0.539

[tex]\overline x = \dfrac{0.475+0.539}{2}[/tex]

[tex]\overline x = \dfrac{1.014}{2}[/tex]

[tex]\overline x = 0.507[/tex]

The point estimate = 0.507

The margin of error  which shows  the percentage of points that the derived results would differ from that of the given population value can be calculated with the formula:

Margin error of  a given confidence interval = [tex]\mathtt{\dfrac{upper \ confidence \ limit - lower \ confidence \ limit }{2}}[/tex]

Margin error of  a given confidence interval =  [tex]\dfrac{0.539-0.475}{2}[/tex]

Margin error of  a given confidence interval = [tex]\dfrac{0.064}{2}[/tex]

Margin error of  a given confidence interval = [tex]0.032[/tex]

Answer:

x  = - 2 is confirmed to be the real solution of the equation.

Step-by-step explanation:

We are tasked with the following activities

Conjecture: How many solutions do [tex]x^3 - 5x^2 + 28 = 0[/tex]  have?

Find the real solution(s) of the equation.

Then use polynomial long division to find the other solution(s).

To start with the how many solutions that  [tex]x^3 - 5x^2 + 28 = 0[/tex]  have

suppose that -2 happens to be a root of the equation, we can easily replace x = - 2 in the given equation. Then , we will have :

[tex](-2)^3 - 5(-2)^2 + 28 = 0[/tex]

[tex]-8 - 5\times 4 + 28 = 0[/tex]

-8 - 20  + 28 = 0

-28 - 28 = 0

0 = 0

The equation resulted to 0 = 0 when x = -2 , as such -2 happens to be one root of the equation

So , as x = - 2

x + 2 = 0  

x  = - 2 is confirmed to be the real solution of the equation.

A picture showing the polynomial long division method used for solving the polynomial equation and other solution(s) can be found in the attached file below.

Complete Question

A biologist reports a confidence interval of (3.5,4.9) when estimating the mean height (in centimeters) of a sample of seedlings. What is the estimated margin of error and the sample mean?

Answer:

The  margin of error is  [tex]E = 0.7[/tex]

The  sample mean is  [tex]\= x = 4.2[/tex]

Step-by-step explanation:

from the question we are told that

   The  upper limit is  [tex]k = 4.9[/tex]

    The  lower limit is  [tex]r = 3.5[/tex]

Generally the margin of error is mathematically represented as

      [tex]E = \frac{k - r}{ 2}[/tex]

      [tex]E = \frac{ 4.9 - 3.5 }{2}[/tex]

     [tex]E = 0.7[/tex]

Generally the sample mean is mathematically evaluated as

        [tex]\= x = k - E[/tex]

=>    [tex]\= x = 4.9 - 0.7[/tex]

=>    [tex]\= x = 4.2[/tex]

Answer:

8.9 is the answer i just took the test

Answer:

Distance covered by Sean

= 540-x-y inches

Distance covered by Hannah =x

Step-by-step explanation:

Sean and Hannah are 540 inches apart and begin walking towards each other. Sean walks 2.6 times as fast as Hannah

Distance covered by Hannah =x

Distance between sean and Hannah= y

Distance covered by Sean= 540-x-y

Sean speed= (540-x-y)/t

Hannah speed= x/t

(540-x-y)/t /(x/t )= 2.6

(540-x-y)/x = 2.6

(540-x-y)= 2.6x

540 = 3.6x +y ...

Answer:

Test is Left tailed test

Parameter tested is standard deviation

Step-by-step explanation:

We are given the hypothesis as;

Null hypothesis; H0: σ = 8.6

Alternative hypothesis; H1: σ < 8.6

Where;σ is a constant generally known in statistics as the standard deviation.

Now, it's the alternative hypothesis that will let us know whether this is left tailed, right tailed or two tailed.

Alternative hypothesis says σ < 8.6.

This means that the values of σ that satisfy this hypothesis are less than 8.6 and thus are on the left hand side of 8.6 on a number line. Thus, the shaded region in a normal distribution curve will be on the left.

Thus, it's a left tailed test

Answer:

C' ( -10 , 4)

D' (-10 , 6)

E' (-8 , 6)

F' (-8 , 4)

Answer:

7.8

Step-by-step explanation:

Answer:

The answer is 3.6

Step-by-step explanation:

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

d=[tex]\sqrt{(2)^{2}+(3)^{2} }[/tex]

d=[tex]\sqrt{4+9}[/tex]

d=[tex]\sqrt{13}[/tex]

d=3.6

Answer:

C: infinitely many solutions

Step-by-step explanation:

Answer:

The  value is  [tex]Z = 6.299*10^{16} \ ways[/tex]

Step-by-step explanation:

From the question we are told that  

      The  number of countries is  n  =  12

Generally the number of way of selecting 3 from a block of 45  

        [tex]\left 45} \atop {}} \right.C _3 = \frac{ 45! }{ (45-3) ! 3!}[/tex]

       [tex]\left 45} \atop {}} \right.C _3 = 14190[/tex]

Generally the number of way of selecting 4 from a block of 57  

        [tex]\left 57} \atop {}} \right.C _3 = \frac{ 57! }{ (57-4) ! 4!}[/tex]

         [tex]\left 57} \atop {}} \right.C _3 = 395010[/tex]

Generally the number of way of selecting (12 - (4 + 3) = 5) from a block of 69

         [tex]\left 69} \atop {}} \right.C _5 = \frac{ 69! }{ (69-5) ! 5!}[/tex]

         [tex]\left 69} \atop {}} \right.C _3 = 11238513[/tex]

The ways of  selecting 12 countries in the United Nations  serve on a council is mathematically represented as

               [tex]Z = 14190 * 395010* 11238513[/tex]

               [tex]Z = 6.299*10^{16} \ ways[/tex]

Answer:

yes

Step-by-step explanation:

Answer:

C. [tex] z = 82 [/tex]

Step-by-step explanation:

To find z, find x first:

[tex] 105 = \frac{1}{2}(x + 120) [/tex] (angle of intersecting chord theorem)

Solve for x

[tex] 105*2 = \frac{1}{2}(x + 120)*2 [/tex]

[tex] 210 = x + 120 [/tex]

[tex] 210 - 120 = x + 120 - 120 [/tex]

[tex] 90 = x [/tex]

[tex] x = 90 [/tex]

Find z:

Full circle = 360°

Therefore,

[tex] x + z + 68 + 120 = 360 [/tex]

[tex] 90 + z + 68 + 120 = 360 [/tex]

[tex] z + 278 = 360 [/tex]

[tex] z + 278 - 278 = 360 - 278 [/tex]

[tex] z = 82 [/tex]

Answer:

A -3 − 4i C 13 + i

Step-by-step explanation:

We add the real part and the imaginary part separately.

Adding A and C will give us 10 - 3i:

-3 - 4i + 13 + i

= -3 + 13 - 4i + i

= 10 - 3i.

Answer:

  see below

Step-by-step explanation:

The cube of something to the 1/3 power is the original something. The cube of a cube root of something is the original something. Since the cube of a cube root is the same as the cube of a 1/3 power, the 1/3 power is equivalent to the cube root.

The applicable rules of exponents are ...

  (a^b)^c = a^(bc)

=====================================================

Explanation:

The domain is the set of all real numbers. This is because the graph goes on forever to the left and right. We can use any x value we want as an input. There are no restrictions to worry about such as to prevent dividing by zero errors.

To say "all real numbers" in interval notation, we write [tex](-\infty, \infty)[/tex] which is another way of saying [tex]-\infty < x < \infty[/tex]

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

The range in interval notation is [tex][3, \infty)[/tex] since y = 3 is the smallest y output possible, and we could have larger y values as well. So basically [tex]y \ge 3[/tex] can be used to describe the range without saying much else.

Note the use of a square bracket to include 3 as part of the interval.

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

There are no x intercepts because this graph does not cross the x axis. The lowest point is at (-2,3) so there's no way we could reach y = 0. Put another way, y = 0 is not part of the range so we cannot have any x intercepts.

There is one y intercept and it is at (0,7) where the graph crosses the y axis. For any function, the max number of y intercepts is 1.

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

When it says "interval positive", its asking "which part(s) of the graph are above the x axis?". That would be the entire graph meaning we have the interval [tex](-\infty, \infty)[/tex]. Every point on this V shaped curve is of the form (x,y) where y is positive.

So this means that we do not have any points with a negative y value, and therefore the answer to "interval negative" is none.

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

Now onto the "interval increasing". This is similar to the previous section, but now we're looking when the graph is going uphill as we read from left to right. This happens on the interval [tex](-2, \infty)[/tex] or put another way when x > -2.

The graph goes downhill whenever x < -2. So that's why the answer for the "interval decreasing" is [tex](-\infty, -2)[/tex]

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

Note the points (-2,3) and (0,7) are on the V shaped graph. These points have x coordinates of x = -2 and x = 0, which are the endpoints of the interval we're focusing on.

Compute the slope of the line through those two points

m = (y2-y1)/(x2-x1)

m = (7-3)/(0-(-2))

m = (7-3)/(0+2)

m = 4/2

m = 2

The positive slope means the line goes uphill as we read from left to right

The average rate of change on the interval [-2, 0] is the value 2

In other words, we go up 2 units each time we move to the right 1 unit.

Answer:

the answer is c: 44

hope it helps

:)

The value of m in the equation one-half m minus three-fourths n equals 16, when n equals 8 is 44.

A linear equation is an equation that has the variable of the highest power of 1. The standard form of a linear equation is of the form Ax + B = 0.

The equation form;

1/2m - 3/ 4n = 16

Substituting the value of n in the equation, we have;

½m - ¾n = 16

½m - (¾×8) = 16

½m - 6 = 16

½m = 16 + 6

½m = 22

m = 44

Hence, The value of m in the equation one-half m minus three-fourths n equals 16, when n equals 8 is 44.

Learn more about linear equations;

https://brainly.com/question/10413253

#SPJ5

Answer:

options a is correct

4/7 likely

Probability = Favourable outcomes/ Total outcomes

All outcomes that we have are = 1,2,3,4,5,6,7,8

→ Total outcomes are 8 .

Favourable outcomes are = 1,3,5,7

→ Favourable outcomes are 4.

P(odd) = 4 divided by 8

→ P( odd) is 1/2 , 50% , equally likely.

So option 2nd is correct .

Answer:

500 pa

Step-by-step explanation:

[tex]Force = 25N\\Area = 0.05m^2\\\\Pressure = \frac{Force}{Area}\\ \\Pressure = \frac{25}{0.05}\\\\ Pressure = 500 Pascals[/tex]

Answer:

8x+5

Step-by-step explanation:

8-6=2

2× 4x= 8x

8x+5

Answer:

Step-by-step explanation:

Use PEMDAS rule :

P = Parentheses

E = Exponents

M = Multiplication

D = Division

A = Addition

S = Subtraction

Let's solve :

[tex] \sf{5 + 4 \times {(8 - 6)}^{2} }[/tex]

⇒[tex] \sf{5 + 4 \times {2}^{2} }[/tex]

⇒[tex] \sf{5 + 4 \times 4}[/tex]

⇒[tex] \sf{5 + 16}[/tex]

⇒[tex] \sf{21}[/tex]

Hope I helped!

Best regards!

Answer:

it is this graph

Step-by-step explanation:

it is this graph

Answer:

B

Step-by-step explanation:

Answer:

[tex]m = 0.2[/tex]

Step-by-step explanation:

To solve this equation we're basically trying to isolate m on one side.

The equation is [tex]m^2=0.04[/tex].

If we want to make it [tex]m=x[/tex], we have to find the square root of both sides, as the square root of something squared is just that something.

[tex]\sqrt{m^2} = \sqrt{0.04}[/tex]

To find the square root of 0.04, we need to think "what number multiplied by itself get us 0.04?"

This number is 0.2.

So:

[tex]m = 0.2[/tex]

Hope this helped!