A variable is normally distributed with mean 6 and standard 2 deviation .
a. Find the percentage of all possible values of the variable that lie between 5 and 9.
b. Find the percentage of all possible values of the variable that exceed 1.
c. Find the percentage of all possible values of the variable that are less than 4.

There are 10,080 different ways in which the friends can seat on the circular table.

There are 9 friends, such that two of them need to be separated by exactly two people.

Because the table is circular, we can consider the first position as the position where Bob is.

Now let's count the number of options for each of the other 8 positions. (counting to the left).

The next two positions have 7 and 6 options respectively (as these can be taken by any of the other 7 friends)

For the next seat, we could seat Anna or one of the remaining 5 friends.

Let's assume we seat Anna there, then for each of the next positions, we will have, respectively, 5, 4, 3, 2, 1 options.

The total number of combinations is given by the product between the numbers of options, so we have:

C = 7*6*5*4*3*2*1

But we also need to consider the case where Anna is on the first position (and Bob on the third), so we just need to add a factor equal to 2.

C = 2*(7*6*5*4*3*2*1) = 10,080

There are 10,080 different ways in which the friends can seat on the circular table.

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The range, standard deviation, and variance of the numbers of medals won by these countries are 28, 8.845, and 78.2353, respectively.

A range is given to a parameter to allow maximum leverage to the parameter. for example, if a vendor wants a rod of diameter 20 cm, then he may give a range of ±1 cm., which means he will accept the rod of 19(20-1) cm to 21(20+1) cm.

The range  of the numbers of medals won by these countries is,

Range =  Max - Min = 29 - 1 = 28

To find the standard deviation we need to know the following details,

Now, the standard deviation of medals won by these countries is,

[tex]\sigma = \sqrt{\dfrac{\sum x^2 - \frac1n (\sum x)^2}{n-1}}\\\\\sigma = \sqrt{\dfrac{\4372 - \frac{234^2}{18}}{18-1}}\\\\\sigma = 8.845[/tex]

The variance of the numbers of medals won by these countries is,

v = σ²

v = 78.2353

Hence, the range, standard deviation, and variance of the numbers of medals won by these countries are 28, 8.845, and 78.2353, respectively.

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The sign of the leading coefficient can be found using the graph of a polynomial function.

Polynomial is the combination of variables and constants systematically with "n" number of power in ascending or descending order.

[tex]\rm a_1x+a_2x^2+a_3x^3+a_4x^4..........a_nx^n[/tex]

We have given the graph of polynomial functions:

In the first graph:

The leading coefficient is positive.

x → ∞, f(x) → ∞

x → -∞, f(x) → -∞

Degree of a function = 3

In the second graph:

The leading coefficient is negative.

x → ∞, f(x) → -∞

x → -∞, f(x) → -∞

Degree of a function = 4

In the third graph:

The leading coefficient is positive.

x → ∞, f(x) → ∞

x → -∞, f(x) → ∞

Degree of a function = 4

In the fourth graph:

The leading coefficient is negative.

x → ∞, f(x) → -∞

x → -∞, f(x) → ∞

Degree of a function = 3

Thus, the sign of the leading coefficient can be found using the graph of a polynomial function.

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The different councils consisting of 5 freshmen and 7 sophomores are possible 9216.

We have given that,

A pool of possible candidates for a student council consists of 14 freshmen and 8 software.

We have to determine the how many different councils consisting of 5 freshmen and 7 sophomores are possible

[tex]_n C_r=\frac{n !}{r ! (n-r) !}_n C_r = number of combinations\\\n = total number of objects in the set\\\r = number of choosing objects from the set[/tex]

The total number of the council is

[tex]_{10} C_5\times _9 C_7[/tex]

=252(36)

=9216

The different councils consisting of 5 freshmen and 7 sophomores are possible 9216.

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Answer:

the type of growth defined by the equation is Exponential growth.

Step-by-step explanation:

Exponential growth :-Exponential growth is a pattern of data that shows greater increases with passing time, creating the curve of an exponential function. It occurs when the instantaneous rate of change of a quantity with respect to time is proportional to the quantity itself

expression for exponential growth -

f(x) = k(1+t)^x

f(x) = exponential growth

k = initial amount

t = rate of growth

x = no  of time interval

therefor,

the equation shown in the question represents exponential growth with increasing time.

hence, Exponential growth is the correct answer.

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Rate of change (ROC) refers to how quickly something changes over time.

Given data :

The rate of change will be the same for all years. The rate of change is 7%. The . basic formula for this equation is: I(1+R)^T, where I = Initial amount, R = Rate of growth, and T = Time. So the R here is 0.07, or 7%. The growth RATE is constant, the growth AMOUNT will increase each year.

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Answer:

f(5) = -1

Step-by-step explanation:

The points on the graph are (0,4), (1,3),(2,2), (3,1), (4,0), (5,-1).

The answers are in the form:

f(x) = y

That is, the number in the parenthesis is the x and the number by itself on the right is the y. The only one that is a point on the line is f(5) = -1, which is the point (5,-1)

1

Step-by-step explanation:

when we put 1 in the equation the nominator becomes zero and it becomes undefined

Hii!

___________________________________________________________

[tex]\stackrel\star\rightsquigarrow\circ\boldsymbol{\underbrace{Answer:}}}\circ\leftharpoonup[/tex]

The value of x should be 5! ^^

[tex]\stackrel\star{\rightsquigarrow\circ\boldsymbol{\underbrace{Explanation:}}}\circ\leftharpoonup[/tex]

[tex]\boxed{\\\begin{minipage}{7cm} For\,an\,expression \\ \boldsymbol{to\,be\,und efined,} \\ \,its\,denominator\,should\,be\,zero \end{minipage}}}[/tex]

Remember this! ^^

Now let's consider this:

Which value of x will make the denominator equal to 0?

Is it 1? If we stick 1 in, we will not obtain 0.

[tex]\twoheadrightarrow\sf y=\cfrac{3\cdot1-3}{1-5}[/tex]

[tex]\bullet[/tex] Simplify this

[tex]\twoheadrightarrow\sf y=\cfrac{3-3}{-4}[/tex]

---

We will obtain 0 in the numerator, but not in the denominator; if the numerator is 0, then the fraction, or fractional expression, is 0.

Let's try 5. 5-5 is equal to 0, so this sounds promising! ^^

[tex]\twoheadrightarrow\sf y=\cfrac{3\cdot5-3}{5-5}[/tex]

[tex]\bullet[/tex] Look what we obtain when we simplify

Don't we obtain 15-3/0?

Like I said above, if an expression has 0 as its denominator, it's undefined.

--

Hope that this helped! Best wishes.

[tex]\textsl{Reach far. Aim high. Dream big.}[/tex]

--

Answer:

  D.  330.6

Step-by-step explanation:

To evaluate the function for a specific value of x, put that value where x is in the function definition, and do the arithmetic.

__

T(x) = x +0.14x . . . . . given function definition

T(290) = 290 +0.14×290 = 290 +40.6 . . . . substitute 290 for x

T(290) = 330.6

The value of T(290) will be 330.6.The relation between them is shown as T(x)  is dependent and x is the independent variable. Option D s correct.

A connection between independent variables and the dependent variable is defined by the function.

Functions help to represent graphs and equations. A function is represented by the two variables one is dependent and another one is an independent function.

Given relation;

T(x) = x +0.14x

Substitute the value of x we get;

T(290) = 290 +0.14×290

T(290) = 330.6

Hence, option D s correct.

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Answer:

c. $29,000

Step-by-step explanation:

since 20% of 145,000 = 29,000

to calculate use

(20/100) * 145,000

or

(y/100) * x

y = the precentage

x = the price of the house

therefore your answer is c. $29,000

hope this helps:)

Answer:

Step-by-step explanation:

You are given a system of equations and asked to solve it by the method of addition. That method requires you add a multiple of one equation to the other so that one of the variables is eliminated. In some cases, this is easier if multiples of both equations are added together. The resulting single-variable equation is then solved in the usual way.

__

The given system of equations is ...

We notice the first equation has the variables on opposite sides of the equal sign, and both their coefficients are 1. The second equation has the variables on the same side of the equal sign, and their coefficients are 0.08 and 0.02.

To eliminate a variable by the "addition method," we need to have the variable on the same side of the equal sign with opposite coefficients. Or, we need to have the variable on opposite sides of the equal sign with the same coefficient.

Both of the x-variables are on the left side, so we need opposite coefficients. We can get that by multiplying the first equation by -0.08, or by multiplying the second equation by -12.5. We judge the first of these choices to be easier.

The y-variables are on opposite sides of the equal sign, so we need equal coefficients. We can get that by multiplying the first equation by 0.02, or the second equation by 50.

We choose to multiply the first equation by 0.02, so we can eliminate the y-variable. Here is the result of doing that, then adding the results

  (0.02)(x) +(0.08x +0.02y) = (0.02)(y +1300) +(350)

  0.10x +0.02y = 0.02y +376 . . . . . eliminate parentheses

  0.10x = 376 . . . . . . . . . subtract 0.02y from both sides. y is eliminated

  x = 3760 . . . . . . . . . divide by 0.10

  y = x -1300 = 2460

__

The amount invested at 8% was $3760; the amount invested at 2% was $2460.

_____

Additional comment

We chose to eliminate y for a couple of reasons. x is the amount at the higher rate. We have found that solving for the higher-rate amount usually works best for preventing errors. The other reason is that multiplying by 0.02 results in smaller numbers, which we consider easier to deal with.

Had we multiplied by -0.08 to eliminate x, we would have ...

  -0.08(x) +(0.08x +0.02y) = -0.08(y +1300) +(350)

  0.02y = -0.08y +246

We judge -0.08(1300) +350 harder to calculate mentally, than 0.02(1300) +350.

  0.10y = 246

  y = 2460; x = 2460+1300 = 3760

Answer:

Step-by-step explanation:

Answer:

Statement 1 is correct

Angles UST and QSR are complementary.

Step-by-step explanation:

Complementary angles are those angles whose addition gives result of 90°

Congruent angles are those angles which are equal to each other. We can say that there values are same.

Here angle RSU is complementary to angle UST.

Therefore there addition is equal to 90°

∠RSU + ∠UST =  90° - (i)

Here angle QSR is congruent to angle RSU.

Therefore their values are equal.

It means ∠QSR =∠RSU -(ii)

From equation (i) and (ii) we get

∠QSR + ∠UST =  90°

So angles UST and QSR are complimentary angles.

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Answer:

Step-by-step explanation:

A

Notice that the difference in the absolute values of consecutive coefficients is constant:

|-7| - 1 = 6

13 - |-7| = 6

|-19| - 13 = 6

and so on. This means the coefficients in the given series

[tex]\displaystyle \sum_{i=1}^\infty c_i a^{i-1} = \sum_{i=1}^\infty |c_i| (-a)^{i-1} = 1 - 7a + 13a^2 - 19a^3 + \cdots[/tex]

occur in arithmetic progression; in particular, we have first value [tex]c_1 = 1[/tex] and for [tex]n>1[/tex], [tex]|c_i|=|c_{i-1}|+6[/tex]. Solving this recurrence, we end up with

[tex]|c_i| = |c_1| + 6(i-1) \implies |c_i| = 6i - 5[/tex]

So, the sum to [tex]n[/tex] terms of this series is

[tex]\displaystyle \sum_{i=1}^n (6i-5) (-a)^{i-1} = 6 \underbrace{\sum_{i=1}^n i (-a)^{i-1}}_{S'} - 5 \underbrace{\sum_{i=1}^n (-a)^{i-1}}_S[/tex]

The second sum [tex]S[/tex] is a standard geometric series, which is easy to compute:

[tex]S = 1 - a + a^2 - a^3 + \cdots + (-a)^{n-1}[/tex]

Multiply both sides by [tex]-a[/tex] :

[tex]-aS = -a + a^2 - a^3 + a^4 - \cdots + (-a)^n[/tex]

Subtract this from [tex]S[/tex] to eliminate the intermediate terms to end up with

[tex]S - (-aS) = 1 - (-a)^n \implies (1-(-a)) S = 1 - (-a)^n \implies S = \dfrac{1 - (-a)^n}{1 + a}[/tex]

The first sum [tex]S'[/tex] can be handled with simple algebraic manipulation.

[tex]S' = \displaystyle \sum_{i=1}^n i (-a)^{i-1}[/tex]

[tex]\displaystyle S' = \sum_{i=0}^{n-1} (i+1) (-a)^i[/tex]

[tex]\displaystyle S' = \sum_{i=0}^{n-1} i (-a)^i + \sum_{i=0}^{n-1} (-a)^i[/tex]

[tex]\displaystyle S' = \sum_{i=1}^{n-1} i (-a)^i + \sum_{i=1}^n (-a)^{i-1}[/tex]

[tex]\displaystyle S' = \sum_{i=1}^n i (-a)^i - n (-a)^n + S[/tex]

[tex]\displaystyle S' = -a \sum_{i=1}^n i (-a)^{i-1} - n (-a)^n + S[/tex]

[tex]\displaystyle S' = -a S' - n (-a)^n + \dfrac{1 - (-a)^n}{1 + a}[/tex]

[tex]\displaystyle (1 + a) S' = \dfrac{1 - (-a)^n - n (1 + a) (-a)^n}{1 + a}[/tex]

[tex]\displaystyle S' = \dfrac{1 - (n+1)(-a)^n + n (-a)^{n+1}}{(1+a)^2}[/tex]

Putting everything together, we have

[tex]\displaystyle \sum_{i=1}^n (6i-5) (-a)^{i-1} = 6 S' - 5 S[/tex]

[tex]\displaystyle \sum_{i=1}^n (6i-5) (-a)^{i-1} = 6 \dfrac{1 - (n+1)(-a)^n + n (-a)^{n+1}}{(1+a)^2} - 5 \dfrac{1 - (-a)^n}{1 + a}[/tex]

[tex]\displaystyle \sum_{i=1}^n (6i-5) (-a)^{i-1} =\boxed{\dfrac{1 - 5a - (6n+1) (-a)^n + (6n-5) (-a)^{n+1}}{(1+a)^2}}[/tex]

Answer:

The rate at which the temperature drops.

Step-by-step explanation:

In science, the dependent variable is what you are measuring.
In math, the dependent variable is what you are evaluating.

Same idea, different topic.

Answer:

d=temp drop

t=hours

dependent variable is the temperature drops because the number of hours will tell you how much the temprature drops

this is the equation

total temp drops=t x 5

hope this helps!?

The point is (6, 5).

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

Given :

y - 2 = 3(x - 5)

Those point will satisfy after putting the value of x and y we get LHS= RHS.

take (4, 5)

5-2 = 3(4-5)

3= -3

Hence, not satisfied.

take, (6, 5)

5-2 = 3(6-5)

3= 3

Hence, satisfied.

take, (5, 5)

5-2 = 3(5-5)

3= 0

Hence, not satisfied.

take, (1, 4)

4-2 = 3(1-5)

2= -12

Hence, not satisfied.

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

Work Shown:

x = exterior angle

9x = interior angle

interior + exterior = 180

9x+x = 180

10x = 180

x = 180/10

x = 18

n = number of sides

n = 360/x

n = 360/18

n = 20

There are 20 sides to the regular polygon.

Side notes:

Answer:

20

Step-by-step explanation:

Plug in -4 for n:

(-4)^2 - (-4) = 16 + 4 = 20

The width of a cell with the length (l) of the cell is [tex]\frac{2}{3}[/tex] mm and area (A) of the cell is [tex]\frac{1}{12}[/tex] mm² is [tex]\frac{1}{8}[/tex].

Given that, the length (l) of the cell is [tex]\frac{2}{3}[/tex] mm and area (A) of the cell is [tex]\frac{1}{12}[/tex] mm².

We need to find the width of the cell.

The area of a rectangle is the product of its length and width. So, the area of the rectangle = Length×Width square units.

Now, the area of a cell = [tex]\frac{2}{3}[/tex] ×Width=  [tex]\frac{1}{2}[/tex] mm².

⇒Width=[tex]\frac{\frac{1}{12} }{\frac{2}{3} } ={\frac{1}{12} \times {\frac{3}{2}=\frac{1}{8}[/tex]

Therefore, the width of a cell with the length (l) of the cell is [tex]\frac{2}{3}[/tex] mm and area (A) of the cell is [tex]\frac{1}{12}[/tex] mm² is  [tex]\frac{1}{8}[/tex].

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Answer:

78

Step-by-step explanation:

plug in -3 as x

6(2(-3)^2-5)

6(2(9)-5)

6(18-5)

6(13)

78

Answer:

  A. single triangle. C = 8.74°, A = 1.26°, a = 1.01

Step-by-step explanation:

When two sides and an angle are given, the possibility of two (or zero) triangles exists only when the given angle is opposite the shorter of the two given sides. That is not the case here, so the given measures define one unique triangle.

The law of sines tells us the sides and angles have the relation ...

  sin(A)/a = sin(B)/b = sin(C)/c

We can use this first to find angle C:

  sin(C) = c/b·sin(B)

  C = arcsin(c/b·sin(B)) = arcsin(7/8·sin(170°)) ≈ 8.7394°

  ∠C ≈ 8.74°

Now that we know two angles, we can find the third:

  A = 180° -B -C = 180° -170° -8.74° = 1.26°

  ∠A = 1.26°

Using the law of sines again, we can find the measure of side 'a'.

  a = b·sin(A)/sin(B) = 8·sin(1.26°)/sin(170°) ≈ 1.01346

The measure of segment 'a' is about 1.01 units.

__

Additional comment

If 'a', 'b', and angle A are given, there will be zero triangles if b/a·sin(A) > 1. If b/a·sin(A) < 1 and b > a, there will be two (2) triangles. Otherwise, as here, there will be one unique triangle.

Answer:

[tex] \dfrac{149}{40} [/tex]

[tex] \dfrac{38}{15} [/tex]

Step-by-step explanation:

[tex] (\dfrac{7}{8} + \dfrac{4}{5}) - (\dfrac{9}{20} + \dfrac{-5}{2}) =  [/tex]

[tex] = (\dfrac{7}{8} \times \dfrac{5}{5} + \dfrac{4}{5} \times \dfrac{8}{8}) - (\dfrac{9}{20} + \dfrac{-5}{2} \times \dfrac{10}{10}) [/tex]

[tex] = (\dfrac{35}{40} + \dfrac{32}{40}) - (\dfrac{9}{20} + \dfrac{-50}{20}) [/tex]

[tex] = \dfrac{67}{40} - (-\dfrac{41}{20}) [/tex]

[tex] = \dfrac{67}{40} + \dfrac{41}{20} \times \dfrac{2}{2} [/tex]

[tex] = \dfrac{67}{40} + \dfrac{82}{40} [/tex]

[tex] = \dfrac{149}{40} [/tex]

[tex] (-\dfrac{6}{4} + \dfrac{3}{2}) + (\dfrac{6}{5} + \dfrac{4}{3}) = [/tex]

[tex] = (-\dfrac{3}{2} + \dfrac{3}{2})+ (\dfrac{6}{5} \times \dfrac{3}{3} + \dfrac{4}{3} \times \dfrac{5}{5}) [/tex]

[tex] = 0 + \dfrac{18}{15} + \dfrac{20}{15} [/tex]

[tex] = \dfrac{38}{15} [/tex]

Answer:

4

Step-by-step explanation:

Area of a triangle = bh/2

B = 2h

16 = 2h × 2/2

h×2 = 16

2h = 16

* put a square root on both sides then u will get the answer which is

Height of the triangle = 4

An expression is defined as a set of numbers, variables, and mathematical operations. The value of (16/81)^(1/2) is 4/9.

In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.

The value of the given expression (16/81)^(1/2) can be calculated as shown below,

[tex](\dfrac{16}{81})^{\frac12}\\\\=\sqrt{\dfrac{16}{81}}\\\\= \dfrac49[/tex]

Hence, the value of (16/81)^(1/2) is 4/9.

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Answer:

★The square root of 16/81 = 4/9.

Answer:

7.07106781187

Answer:

75%

Step-by-step explanation:

48x=36

x=36/48

x=3/4

x=0.75=75%

To solve this problem, you will use the distributive property to create an equation that can be rearranged and solved using the quadratic formula.

Use the distributive property to distribute 3x into the term (x + 6):

[tex]3x(x+6)=-10[/tex]

[tex]3x^2+18x=-10[/tex]

To create a quadratic equation, add 10 to both sides of the equation:

[tex]3x^2+18x+10=-10+10[/tex]

[tex]3x^2+18x+10=0[/tex]

The quadratic formula is defined as:

[tex]\displaystyle x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}[/tex]

The model of a quadratic equation is defined as ax² + bx + c = 0. This can be related to our equation.

Therefore:

Set up the quadratic formula:

[tex]\displaystyle x=\frac{-18 \pm \sqrt{(18)^2 - 4(3)(10)}}{2(3)}[/tex]

Simplify by using BPEMDAS, which is an acronym for the order of operations:

Brackets

Parentheses

Exponents

Multiplication

Division

Addition

Subtraction

Use BPEMDAS:

[tex]\displaystyle x=\frac{-18 \pm \sqrt{324 - 120}}{6}[/tex]

Simplify the radicand:

[tex]\displaystyle x=\frac{-18 \pm \sqrt{204}}{6}[/tex]

Create a factor tree for 204:

204 - 1, 2, 3, 4, 6, 12, 17, 34, 51, 68, 102 and 204.

The largest factor group that creates a perfect square is 4 × 51. Therefore, turn 204 into 4 × 51:

[tex]\sqrt{4\times51}[/tex]

Then, using the Product Property of Square Roots, break this into two radicands:

[tex]\sqrt{4} \times \sqrt{51}[/tex]

Since 4 is a perfect square, it can be evaluated:

[tex]2 \times \sqrt{51}[/tex]

To simplify further for easier reading, remove the multiplication symbol:

[tex]2\sqrt{51}[/tex]

Then, substitute for the quadratic formula:

[tex]\displaystyle x=\frac{-18 \pm 2\sqrt{51}}{6}[/tex]

This gives us a combined root, which we should separate to make things easier on ourselves.

Separate the roots at the plus-minus symbol:

[tex]\displaystyle x=\frac{-18 + 2\sqrt{51}}{6}[/tex]

[tex]\displaystyle x=\frac{-18 - 2\sqrt{51}}{6}[/tex]

Then, simplify the numerator of the roots by factoring 2 out:

[tex]\displaystyle x=\frac{2(-9 + \sqrt{51})}{6}[/tex]

[tex]\displaystyle x=\frac{2(-9 - \sqrt{51})}{6}[/tex]

Then, simplify the fraction by reducing 2/6 to 1/3:

[tex]\boxed{\displaystyle x=\frac{-9 + \sqrt{51}}{3}}[/tex]

[tex]\boxed{\displaystyle x=\frac{-9 - \sqrt{51}}{3}}[/tex]

The final answer to this problem is:

[tex]\displaystyle x=\frac{-9 + \sqrt{51}}{3}[/tex]

[tex]\displaystyle x=\frac{-9 - \sqrt{51}}{3}[/tex]

The area of the sector, to 4 decimal places, is 78.6794 cm².

We have given that,

Sector Area= ( angle of sector/360). R2

We have to determine the Sector Area

Area of sector = ∅/360 × πr².

We have given the following:

∅ = 46°

Radius (r) = 14 cm

Area of sector = 46/360 × π(14²)

Area of sector ≈ 78.6794 cm²

The area of the sector is approximately 78.6794 cm².

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The length of the infinite zigzag path is 1

Note that the infinite zigzag path is embedded in an isosceles triangle

Using angle π/4, we have that

Tan π/4 = opposite/ adjacent

[tex]tan \frac{3. 412}{4} = \frac{x}{1}[/tex]

[tex]tan 0. 7855 = x[/tex]

[tex]x = 0. 014[/tex]

To find the longer part 'y',  use the Pythagorean theorem

[tex]y^{2} = (0.014)^2 + (1)^2[/tex]

[tex]y^2 = 1.879 * 10^-4 + 1[/tex]
[tex]y^2 = 1. 00[/tex]

[tex]y = \sqrt{1. 000}[/tex]

[tex]y = 1. 000[/tex]

The length of the infinite zigzag path is the same as the length of the longer part of the triangle which equals 1.

Thus, the length of the infinite zigzag path is 1

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