Find the limit (if it exists). (If an answer does not exist, enter DNE.) lim_(x->7)f(x) text(, where ) f(x)={(x**2-8 x+7 text(if ) x < 7,-x**2 + 8 x - 7 text(if ) x >= 7)

Answer: 0.42

Step-by-step explanation:

Given: Mean : [tex]\mu=954\text{ dollars}[/tex]

Standard deviation : [tex]234\text{ dollars}[/tex]

Sample size : [tex]n=61[/tex]

The formula to calculate z score is given by :-

[tex]z=\dfrac{X-\mu}{\dfrac{\sigma}{\sqrt{n}}}[/tex]

For X=960

[tex]z=\dfrac{960 -954}{\dfrac{234}{\sqrt{61}}}=0.200262812203\approx0.2[/tex]

The p-value =[tex]P(X\geq960)=1-P(X<960)=1-P(z<0.2)=1-0.5792597=0.4207403\approx0.42[/tex]

Hence,  the probability that a single randomly selected value is at least 960 dollars = 0.42

let's recall that on the IV Quadrant the sine/y is negative and the cosine/x is positive, whilst the hypotenuse is never negative since it's just a distance unit.

[tex]\bf \stackrel{\textit{on the IV Quadrant}}{cot(\theta )=\cfrac{\stackrel{adjacent}{6}}{\stackrel{opposite}{-7}}}\qquad \impliedby \textit{let's find the \underline{hypotenuse}} \\\\\\ \textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies c=\sqrt{a^2+b^2} \qquad \begin{cases} c=hypotenuse\\ a=adjacent\\ b=opposite\\ \end{cases} \\\\\\ c=\sqrt{6^2+(-7)^2}\implies c=\sqrt{36+49}\implies c=\sqrt{85} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\bf tan(\theta )=\cfrac{\stackrel{opposite}{-7}}{\stackrel{adjacent}{6}}\qquad \qquad sec(\theta )=\cfrac{\stackrel{hypotenuse}{\sqrt{85}}}{\stackrel{adjacent}{6}}\qquad \qquad csc(\theta )=\cfrac{\stackrel{hypotenuse}{\sqrt{85}}}{\stackrel{opposite}{-7}}[/tex]

[tex]\bf sin(\theta )=\cfrac{\stackrel{opposite}{-7}}{\stackrel{hypotenuse}{\sqrt{85}}}\implies \stackrel{\textit{and rationalizing the denominator}}{\cfrac{-7}{\sqrt{85}}\cdot \cfrac{\sqrt{85}}{\sqrt{85}}\implies -\cfrac{7\sqrt{85}}{85}} \\\\\\ cos(\theta )=\cfrac{\stackrel{adjacent}{6}}{\stackrel{hypotenuse}{\sqrt{85}}}\implies \stackrel{\textit{and rationalizing the denominator}}{\cfrac{6}{\sqrt{85}}\cdot \cfrac{\sqrt{85}}{\sqrt{85}}\implies \cfrac{6\sqrt{85}}{85}}[/tex]

Answer:

These are the five remaining trigonometric functions:

Explanation:

Quadrant IV corresponds to angle interval 270° < θ < 360.

In this quadrant the signs of the six trigonometric functions are:

The expected values of the five remaining trigonometric functions of θ are:

1) Tangent:

2) Secant

       sec θ = ± (√85)/ 6

       Choose positive, because secant is positive in Quadrant IV.

       sec θ = (√85) / 6

3) Cosine

4) Sine

       sin²θ = 1 - 36×85/(85)² = 1- 36/85 = 49/85

       sinθ = ± 7 / (√85) = ± 7(√85)/85

       Choose negative sign, because it is Quadrant IV.

       sinθ = - 7 (√85) / 85

5) Cosecant

Answer with explanation:

1.

Let a, and b be two numbers between 20 and 5 , which is in geometric progression.

So,the series is as Follows =20 , a, b, 5

Common ratio

          [tex]=\frac{\text{Second term}}{\text{First term}}[/tex]

[tex]\frac{20}{a}=\frac{a}{b}=\frac{b}{5}\\\\b^2=5 a---(1)\\\\a^2=20 b\\\\\frac{b^4}{25}=20 b-----\text{Using 1}\\\\b^3=500\\\\b=(500)^{\frac{1}{3}}\\\\b=5\times (4)^{\frac{1}{3}}\\\\5a=25\times (4)^{\frac{2}{3}}\\\\a=5\times (4)^{\frac{2}{3}}[/tex]

2.

44 -32-3

=12-3

=9

3.

⇒Sin (2.4)=Sin(2+0.4)

⇒Sin 2 ×Cos (0.4)+Cos 2 × Sin (0.4)

⇒Sin (A+B)=Sin A×Cos B+Cos A×Sin B

Answer:

1) C. 2

2) A. 2

Step-by-step explanation:

1. We need to descompose 256 into its prime factors:

[tex]256=2*2*2*2*2*2*2*2=2^8[/tex]

We must rewrite the expression [tex]\sqrt[8]{256}[/tex]:

[tex]=\sqrt[8]{2^8}[/tex]

We need to remember that:

[tex]\sqrt[n]{a^n}=a[/tex]

Then:

[tex]=2[/tex]

2. Let's descompose 16 into its prime factors:

[tex]16=2*2*2*2=2^4[/tex]

We must rewrite the expression [tex]\sqrt[4]{16}[/tex]:

[tex]=\sqrt[4]{2^4}[/tex]

Then we get:

[tex]=2[/tex]

For [tex]\(\sqrt[8]{256}\)[/tex] , the answer is 2 (C), and for [tex]\(\sqrt[4]{16}\)[/tex], the answer is also 2(A), obtained through prime factorization and simplifying using the property [tex]\(\sqrt[n]{a^n} = a\)[/tex].

Let's go into more detail for both questions:

1. [tex]\(\sqrt[8]{256}\)[/tex]:

  - First, find the prime factorization of 256: [tex]\(256 = 2^8\)[/tex]

  - Rewrite the expression as [tex]\(\sqrt[8]{2^8}\)[/tex].

  - Using the property [tex]\(\sqrt[n]{a^n} = a\)[/tex], simplify to 2.

  - Therefore, [tex]\(\sqrt[8]{256} = 2\)[/tex]

  - Correct answer: C. 2

2. [tex]\(\sqrt[4]{16}\)[/tex]:

  - Start with the prime factorization of 16: [tex]\(16 = 2^4\)[/tex]

  - Express the expression as [tex]\(\sqrt[4]{2^4}\)[/tex]

  - Apply the property  [tex]\(\sqrt[n]{a^n} = a\) to get \(2\).[/tex]

  - Thus,  [tex]\(\sqrt[4]{16} = 2\)[/tex]

  - Correct answer: A. 2

In both cases, understanding the prime factorization and utilizing the property of radicals [tex](\(\sqrt[n]{a^n} = a\))[/tex] helps simplify the expressions and find the correct values.

For this case we have the following expression:

[tex](\frac {-27x ^ 0 * y ^ {- 2}} {54x ^ {- 5} * y ^ {- 4}}) ^ {- 2} =[/tex]

By definition we have to:

[tex]a^0= 1[/tex]

So:

[tex](\frac {-27y ^ {- 2}} {54x ^ {- 5} * y ^ {- 4}}) ^ {- 2} =[/tex]

Simplifying:

[tex](\frac {-y ^ {- 2}} {2x ^ {- 5} * y ^ {- 4}}) ^ {- 2} =[/tex]

By definition of power properties we have to:

[tex](a ^ n) ^ m = a ^ {n * m}[/tex]

So, rewriting the expression we have:

[tex]\frac {-y ^ {- 2 * -2}} {4x ^ {- 5 * -2} * y ^ {- 4 * -2}} =\\\frac {-y ^ {4}} {4x ^ {10} * y ^ {8}} =[/tex]

SImplifying:

[tex]\frac {-y ^ {4-8}} {4x ^ {10}} =\\\frac {-y ^ {- 4}} {4x ^ {10}} =\\- \frac {1} {4x ^ {10} y^ {4}}[/tex]

Answer:

[tex]- \frac {1} {4x ^ {10} y ^ {4}}[/tex]

Answer: [tex]H_0:\mu=40[/tex]

[tex]H_0:\neq40[/tex]

Step-by-step explanation:

Claim 1. : Mean age of online dating service users is 40 years.

i.e. [tex]\mu=40[/tex], since it has equals sign so we take this as null hypothesis.

Claim 2. : Mean age of online dating service users is not 40 years.

[tex]\mu\neq40[/tex]

⇒ Null Hypothesis : [tex]H_0:\mu=40[/tex]

Alternative hypothesis : [tex]H_0:\neq40[/tex]

Answer:

Height of cables = 23.75 meters

Step-by-step explanation:

We are given that the road is suspended from twin towers whose cables are parabolic in shape.

For this situation, imagine a graph where the x-axis represent the road surface and the point (0,0) represents the point that is on the road surface midway between the two towers.

Then draw a parabola having vertex at (0,0) and curving upwards on either side of the vertex at a distance of [tex]x = 600[/tex] or [tex]x = -600[/tex], and y at 95.

We know that the equation of a parabola is in the form [tex]y=ax^2[/tex] and here it passes through the point [tex](600, 95)[/tex].

[tex]y=ax^2[/tex]

[tex]95=a \times 600^2[/tex]

[tex]a=\frac{95}{360000}[/tex]

[tex]a=\frac{19}{72000}[/tex]

So new equation for parabola would be [tex]y=\frac{19x^2}{72000}[/tex].

Now we have to find the height [tex](y)[/tex]of the cable when [tex]x= 300[/tex].

[tex]y=\frac{19 (300)^2}{72000}[/tex]

y = 23.75 meters

Answer: 23.75 meters

Step-by-step explanation:

If we assume that the origin of the coordinate axis is in the vertex of the parabola. Then the function will have the following form:

[tex]y = a (x-0) ^ 2 + 0\\\\y = ax ^ 2[/tex]

We know that when the height of the cables is equal to 95 then the horizontal distance is 600 or -600.

Thus:

[tex]95 = a (600) ^ 2[/tex]

[tex]a = \frac{95} {600 ^ 2}\\\\a = \frac {19} {72000}[/tex]

Then the equation is:

[tex]y = \frac{19}{72000} x ^ 2[/tex]

Finally the height of the cables at a point 300 meters from the center is:

[tex]y = \frac{19}{72000}(300) ^ 2[/tex]

[tex]y =23.75\ meters[/tex]

Answer: a.- discrete   b.- continous

Step-by-step explanation: Discrete Variable. Variables that can only take on a finite number of values are called "discrete variables." All qualitative variables are discrete. Some quantitative variables are discrete, such as performance rated as 1,2,3,4, or 5, or temperature rounded to the nearest degree.

Continuous Variable. If a variable can take on any value between its minimum value and its maximum value, it is called a continuous variable; otherwise, it is called a discrete variable.

The number of fish caught during a fishing tournament is a discrete variable, and the time it takes for a light bulb to burn out is a continuous variable

Let's define what variables are. Variables are any representation of a phenomenon or property that changes over time. In simple terms, variables are "things" that change, meaning they don't have a constant value. Variables can be either discrete or continuous.

To understand these concepts it's better to understand first what continuous means, continuous variables are those which can take any value whatsoever over time. This last statement is the main idea but it's not self-explanatory, a test to check whether a variable is continuous or not is to take any 2 possible outcomes of that variable, and check if that variable can take any value between those 2 possible outcomes. If the test gives positive then our variable is continuous, if not then it's discrete.

Let's test the first question. During a fishing tournament, each person can fish only one fish at a time, therefor possible outcomes are 1 fish, or 2 fish, or 3, or 4, and so on. This means that we will never be able to get, for example, 1.5 fish (which is a value between 2 possible outcomes, 1 fish and 2 fish), therefor our variable is discrete.

Let's test the second question. The time it takes for a light bulb to burn out has many possible outcomes, examples are 1 second, 2.5 seconds, 10 minutes, etc. If we check between any of those possible outcomes, we will always be able to find a time, doesn't matter how precise, in which the light bulb could burn. This means that the time for a light bulb to burn is continuous.

Variable, Continuous, Discrete, Interval

Answer:

(-1, 11) is a max value; parabola is upside down

Step-by-step explanation:

We can answer this question backwards, just from what we know about parabolas.  This is a negative x^2 parabola, so that means it opens upside down.  Because of this, that means that there is a max value.  

The vertex of a parabola reflects either the max or the min value.  In order to find the vertex, we put the equation into vertex form, which has the standard form:

[tex]y=a(x-h)^2+k[/tex]

where h and k are the coordinates of the vertex.

To put a quadratic into vertex form, you need to complete the square.  That process is as follows. First, set the quadratic equal to 0.  Then make sure that the leading coefficient is a positive 1.  Ours is a -5 so we will have to factor it out.  Then, move the constant to the other side of the equals sign.  Finally, take half the linear term, square it, and add it to both sides.  We will get that far, and then pick up with the rest of the process as we come to it.

[tex]-5x^2-10x+6=y[/tex]

Set it to equal zero:

[tex]-5x^2-10x+6=0[/tex]

Now move the 6 to the other side:

[tex]-5x^2-10x=-6[/tex]

Factor out the -5:

[tex]-5(x^2+2x)=-6[/tex]

Take half the linear term, square it, and add it to both sides.  Our linear term is 2x.  Half of 2 is 1, and 1 squared is 1, so add it to both sides.  Keep it mind that we have the =5 out front of those parenthesis that will not be forgotten.  So we are not adding in a +1, we are adding in a (+1)(-5) which is -5:

[tex]-5(x^2+2x+1)=-6-5[/tex]

In completing the square, we have created a perfect square binomial on the left.  Stating that binomial along with simplifying on the right gives us:

[tex]-5(x+1)^2=-11[/tex]

Now, bring the -11 over to the other side and set it back to equal y and you're ready to state the vertex:

[tex]-5(x+1)^2+11=y[/tex]

The vertex is at (-1, 11)

Answer:

89

Step-by-step explanation:

So the line segment CD is 12.7 and half that is 6.35.  I wanted this 6.35 so I can look at the right triangle there and find the angle there near the center.  This will only be half the answer.  So I will need to double that to find the measure of arc CD.  

Anyways looking at angle near center in the right triangle we have the opposite measurement, 6.35, given and the hypotenuse measurement, 9.06, given. So we will use sine.

sin(u)=6.35/9.06

u=arcsin(6.35/9.06)

u=44.5 degrees

u represented the angle inside that right triangle near the center.  

So to get angle COD we have to double that which is 89 degrees.  

So the arc measure of CD is 89.  

Answer: 0.9826

Step-by-step explanation:

Given : Mean : [tex]\lambda =3\text{ calls per minute}[/tex]

For two minutes period the new mean would be :

[tex]\lambda_1=2\times3=6\text{ calls per two minutes}[/tex]

The formula to calculate the Poisson distribution is given by :_

[tex]P(X=x)=\dfrac{e^{-\lambda_1}\lambda_1^x}{x!}[/tex]

Then ,the required probability is given by :-

[tex]P(X\geq2)=1-(P(X\leq1))\\\\=1-(P(0)+P(1))\\\\=1-(\dfrac{e^{-6}6^0}{0!}+\dfrac{e^{-6}6^1}{1!})\\\\=1-0.0173512652367\\\\=0.982648734763\approx0.9826[/tex]

Hence, the probability that at least two calls are received in a given two-minute period is 0.9826.

Answer:

c

Step-by-step explanation:

i think not 100 percent sure

The simplification method would be the best to solve the given equation.

simplify means making it in a simple form by reducing variables in an equation.  we can achieve simplification easily by using PEMDAS.

Given equation 2x² - 7 = 9;

By simplify

2x² = 16

x² = 8

x = √8, -√8

Hence, for given equation simplification using PEMDAS is the best way of solving because it can be easily broken into parts to find the value of x.

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Answer:

Part 1) Option A. h(2) = 86.00 means that after 2 seconds, the height of the ball is 86.00 ft.

Part 2) Option  A. 16 cm; 21 cm; 32 cm

Step-by-step explanation:

Part 1)

we have

[tex]h(t)=-16t^{2}+150[/tex]

where

t ----> is the time in seconds after the ball is dropped

h(t) ----> he height in feet of a ball dropped from a 150 ft

Find h(2)

That means ----> Is the height of the ball  2 seconds after the ball is dropped

Substitute the value of t=2 sec in the equation

[tex]h(2)=-16(2)^{2}+150=86\ ft[/tex]

therefore

After 2 seconds, the height of the ball is 86.00 ft.

Part 2) The perimeter of a triangle is 69 cm. The measure of the shortest side is 5 cm less than the middle side. The measure of the longest side is 5 cm less than the sum of the other two sides. Find the lengths of the sides

Let

x----> the measure of the shortest side

y ----> the measure of the  middle side

z-----> the measure of the longest side

we know that

The perimeter of the triangle is equal to

P=x+y+z

P=69 cm

so

69=x+y+z -----> equation A

x=y-5 ----> equation B

z=(x+y)-5 ----> equation C

substitute equation B in equation C

z=(y-5+y)-5

z=2y-10 -----> equation D

substitute equation B and equation D in equation A and solve for y

69=(y-5)+y+2y-10

69=4y-15

4y=69+15

4y=84

y=21 cm

Find the value of x

x=21-5=16 cm

Find the value of z

z=2(21)-10=32 cm

The lengths of the sides are 16 cm, 21 cm and 32 cm

Answer:

[tex]k(x)=2^{x}[/tex] ⇒ 1st answer

Step-by-step explanation:

* Lets explain how to solve the problem

∵ [tex]g(x)=3(2^{x})[/tex]

∵ [tex]h(x)=2^{x+1}[/tex]

- Lets revise this rule to use it

# If [tex]a^{n}*a^{m}=a^{n+m}====then==== a^{n+m}=a^{n}*a^{m}[/tex]

- We will use this rule in h(x)

∵ [tex]h(x)=2^{x+1}[/tex]

- Let a = 2 , n = x , m = 1

∴ [tex]h(x)=2^{x}*2^{1}[/tex]

- Now lets find k(x)

∵ k(x) = (g - h)(x)

∵ [tex]g(x)=3(2^{x})[/tex]

∵ [tex]h(x)=2^{x}*2^{1}[/tex]

∴ [tex]k(x)=3(2^{x})-(2^{x}*2^{1})[/tex]

- We have two terms with a common factor [tex]2^{x}[/tex]

∵ [tex]2^{x}[/tex] is a common factor

∵ [tex]\frac{3(2^{x})}{2^{x}}=3[/tex]

∵ [tex]\frac{2^{x}*2^{1}}{2^{x}}=2^{1}=2[/tex]

∴ [tex]k(x) = 2^{x}[3 - 2]=2^{x}(1)=2^{x}[/tex]

* [tex]k(x)=2^{x}[/tex]

Answer:

CDI: 1.43/1.24x100= 115 What does this index mean? Good market potential.

Step-by-step explanation:

Answer: CDI: 1.43/1.24x100= 115 What does this index mean? Good market potential.

Step-by-step explanation:

Answer: The answer should be D on edg

Please see the attachment for graph.

For x=1, Put x=1 into equation:

[tex]y = -4\sqrt{1} = - 4[/tex]

For x=4, Put x=4 into equation:

[tex]y = -4\sqrt{4} = - 8[/tex]

For x=9, Put x=9 into equation:

[tex]y = -4\sqrt{9} = - 12[/tex]

     1          -4

     4          -8

     9         -12

Now we plot the points on graph and join the points.

Please see the attachment for graph.

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Answer:

A)0.5

Step-by-step explanation:

We can see in the graph , that it is bell-shaped along x =2. A bell-shaped graph along one value is called symmetric graph and it represents a normal distribution.

Since, the give graph is symmetric around x=2, so the mean of the data is 2.

The point immediate left to the mean represents x-σ

so,

2 - σ = 1.5

So,

σ = 0.5

The sigma represents standard deviation.

Hence, Option A is correct ..

Answer:

its A

Step-by-step explanation:

Answer:9

Step-by-step explanation:

1st triangle is similar to the second one as the angles of both of the triangles are the same..

So we know the ratio of the similar lines will be constant.it means,

XY/PQ=XZ/PR=YZ/QR

So,Xy/PQ=XZ/PR

21/7=27/x

X=(27×7)/21

X=9

Thats the value of pr..

Answer:

13.4%

Step-by-step explanation:

Use binomial probability:

P = nCr p^r q^(n-r)

where n is the number of trials,

r is the number of successes,

p is the probability of success,

and q is the probability of failure (1-p).

Here, n = 16, r = 2, p = 0.25, and q = 0.75.

P = ₁₆C₂ (0.25)² (0.75)¹⁶⁻²

P = 120 (0.25)² (0.75)¹⁴

P = 0.134

There is a 13.4% probability that exactly 2 students will withdraw.

The probability that exactly 2 out of 16 students will withdraw from an introductory statistics class, given a historical withdrawal rate of 25%, can be calculated using the binomial probability formula.

This problem falls into the category of binomial probability. We define 'success' as a student withdrawing from the course. The number of experiments is 16 (as there are 16 students), the number of successful experiments we are interested in is 2 (we want to know the probability of exactly 2 student withdrawing), and the probability of success on a single experiment is 0.25 (as per the given 25% withdrawal rate).

To calculate binomial probability, we can use the binomial formula P(X=k) = C(n, k)*(p^k)*((1-p)^(n-k)), where:
P(X=k) = probability of k successes
C(n, k) = combination of n elements taken k at a time
p = probability of success
n, k = number of experiments, desired number of successes respectively.

Substituting our values into this formula, we get:
P(X=2) = C(16, 2) * (0.25^2) * ((1-0.25)^(16-2)).

You will have to calculate the combination and simplify the expression to get your final probability.

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Answer: Hence, the probability of having no girls is 0.0313.

Step-by-step explanation:

Since we have given that

Number of children a family has = 5

Number of outcomes would be [tex]2^5=32[/tex]

Probability of having a girl = [tex]\dfrac{1}{2}=0.5[/tex]

We need to find the probability of having no girls.

P(no girls ) = P( all boys )

So, it becomes,

[tex]P(all\ boys)=(0.5)^5=0.03125\approx 0.0313[/tex]

Hence, the probability of having no girls is 0.0313.

Answer:

The last choice is the one you want

Step-by-step explanation:

If you plug in the values of x to our rational function, the y values you get back match those in the last choice.  The limit is -4; we see that as our x value approach 0 (but cannot equal 0!!), the y values get closer and closer to -4.  So that's the limit!

Answer:

  9t^3 +t^2

Step-by-step explanation:

The perimeter of the figure is the sum of the lengths of the sides. The side lengths are represented by the polynomials shown, so the perimeter (P) is their sum:

  P = (4t^3 -5) + (4t^3 -5) + (t^2 +9) + (t^3 -t^2 -11) + (t^2 +12)

Rearranging to group like terms:

  P = (4t^3 +4t^3 +t^3) + (t^2 -t^2 +t^2) + (-5 -5 +9 -11 +12)

  P = 9t^3 +t^2

The perimeter of the figure is represented by the polynomial 9t^3 +t^2.

Answer:

[tex]9t^3+t^2[/tex]

Step-by-step explanation:

We are given a figure of a polygon with mentioned side lengths and we are to find the perimeter of it.

For that, we will simply add the given side lengths and simplify them.

Perimeter of polygon = [tex] ( 4 t ^ 3 - 5 ) + ( 4 t ^ 3 - 5 ) + ( t ^ 2 + 9 ) + ( t ^ 2 + 1 2 ) + ( t ^ 3 - t ^ 2 - 1 1 ) [/tex]

= [tex] 4 t ^ 3 + 4 t ^ 3 + t ^ 3 + t ^ 2 - t ^ 2 + t ^ 2 - 5 - 5 + 9 - 1 1 + 1 2 [/tex]

Perimeter of polygon = [tex]9t^3+t^2[/tex]

Answer with explanation:

Let, A=[1,1,2]

B=[1,2,1]

C=[2,1,5]

⇒Now, Writing vector , A in terms of Linear combination of C and B

A=x B +y C

⇒[1,1,2]=x× [1,2,1] + y×[2,1,5]

1.→1 = x +2 y

2.→ 1=2 x +y

3.→ 2= x+ 5 y

Equation 3 - Equation 1

→3 y=1

[tex]y=\frac{1}{3}[/tex]

[tex]1=x+\frac{2}{3}\\\\x=1 -\frac{2}{3}\\\\x=\frac{1}{3}[/tex]

So, Vector A , can be written as Linear Combination of B and C.

⇒Now, Writing vector , B in terms of Linear combination of A and C

Now, let, B = p A+q C

→[1,2,1]=p× [1,1,2] +q ×[2,1,5]

4.→1= p +2 q

5.→2=p +q

6.→1=2 p +5 q

Equation 5 - Equation 4

-q =1

q= -1

→2= p -1

→p=2+1

→p=3

So, Vector B , can be written as Linear Combination of A and C.

⇒Now, Writing vector , C in terms of Linear combination of A and B

C=m A + n B

[2,1,5] = m×[1,1,2] + n× [1,2,1]

7.→2= m+n

8.→1=m +2 n

9.→5=2 m +  n

Equation 8 - Equation 7

n= -1

→m+ (-1)=2

→m=2+1

→m=3

So, Vector C , can be written as Linear Combination of A and B.

So, All the three vectors , A=[1,1,2],B=[1,2,1],C=[2,1,5] can be written as Linear combination of each other.

⇒≡But , the two vectors, (0.4,3.7,-1.5) (0.2,0),can't be written as Linear combination of each other as first vector is of order, 1×3, and second is of order, 1×2.

None of the selections is correct.

In this case, we must check the existence of a set of real coefficients such that the following two linear combinations exist:

[tex]\alpha_{1}\cdot (1, 1, 2)+\alpha_{2}\cdot (1, 2,1)+\alpha_{3}\cdot (2, 1, 5) = (0.4, 3.7, -1.5)[/tex]   (1)

[tex]\alpha_{4}\cdot (1,1,2)+\alpha_{5}\cdot (1,2,1) + \alpha_{6}\cdot (2,1,5) = (0, 2, 0)[/tex]   (2)

Now we proceed to solve each linear combination:

[tex]\alpha_{1}+\alpha_{2}+2\cdot \alpha_{3} = 0.4[/tex]

[tex]\alpha_{1}+2\cdot \alpha_{2}+\alpha_{3} = 3.7[/tex]

[tex]2\cdot \alpha_{1}+\alpha_{2}+5\cdot \alpha_{3} = -1.5[/tex]

The system has no solution, since the third equation is a linear combination of the first and second ones.

[tex]\alpha_{4}+\alpha_{5}+2\cdot \alpha_{6} = 0[/tex]

[tex]\alpha_{4}+2\cdot \alpha_{5}+\alpha_{6} = 2[/tex]

[tex]2\cdot \alpha_{4}+\alpha_{5}+5\cdot \alpha_{6} = 0[/tex]

The system has no solution, since the third equation is a linear combination of the first and second ones.

None of the selections is correct. [tex]\blacksquare[/tex]

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Answer:

true

Step-by-step explanation:

Answer:

True

Step-by-step explanation:

If 2 events are independent, then one event will not affect the other

Answer:

After how many years is the fish population 60?

x=2.71 years

Step-by-step explanation:

The fish population increases by a factor of 1.5 each year. We have the equation that represents this situation

[tex]f (x) = 20 (1.5) ^ x[/tex]

Where x represents the number of years elapsed f(x) represents the amount of fish.

Given this situation, the following question could be posed

After how many years is the fish population 60?

So we do [tex]f (x) = 60[/tex] and solve for the variable x

[tex]60 = 20 (1.5) ^ x\\\\\frac{60}{20} = (1.5)^x\\\\3 = (1.5)^x\\\\log_{1.5}(3) = log_{1.5}(1.5)^x\\\\log_{1.5}(3) = x\\\\x =log_{1.5}(3)\\\\x=2.71\ years[/tex]

Observe the solution in the attached graph

Answer:

  1287

Step-by-step explanation:

The number of combinations of 13 diamonds taken 5 at a time is ...

  13C5 = 13·12·11·10·9/(5·4·3·2·1) = 13·11·9 = 1287

Answer:

The equal balances will be $114 after 8 weeks

Step-by-step explanation:

* Lets study the information in the problem

- Manuel and Ruben both have bank accounts

- The system of equations models their balances y after x weeks

- Manuel balance is y = 11.5x + 22

- Ruben balance is y = -13x + 218

- After x weeks they will have same balances, means the values of y

 will be equal at the same values of x

- The solve the problem we will equate the two equations to find x

  and then substitute this x in on of the equation s to find the

  balance y

- Lets do that

∵ Manuel balance is y = 11.5x + 22

∵ Ruben balance is y = -13x + 218

∵ After x weeks their balances will be equal

- Equate the equations

∴ 11.5x + 22 = -13x + 218

- add 13 x for both sides

∴ 11.5x + 13x + 22 = 218

∴ 24.5x + 22 = 218

- subtract 22 from both sides

∴ 24.5x = 218 - 22

∴ 24.5x = 196

- Divide both sides by 24.5

∴ x = 8

- Their balances will be equals after 8 weeks

- To find the balance substitute x by 8 in any equation

∵ y = 11.5x + 22

∵ x = 8

∴ y = 11.5(8) + 22

∴ y = 92 + 22 = 114

∴ The equal balances will be $114

* The equal balances will be $114 after 8 weeks

Answer:

The equal balances will be $114 after 8 weeks

Step-by-step explanation:

Answer:

The product is:

[tex]-28x^4y^6[/tex]

Step-by-step explanation:

We need to find product of the terms:

-4x3y2(7xy4)

For multiplication we multiply constants with constants and power of same variables are added

[tex]-4x^3y^2(7xy^4)\\=(-4*7)(x^3*x)(y^2*y^4)\\=(-28)(x^{3+1})(y^{2+4})\\=(-28)(x^4)(y^6)\\=-28x^4y^6[/tex]

So, the product is:

[tex]-28x^4y^6[/tex]

Answer:

  p(on schedule) ≈ 0.7755

Step-by-step explanation:

A suitable probability calculator can show you this answer.

_____

The z-values corresponding to the build time limits are ...

  z = (37.5 -45)/6.75 ≈ -1.1111

  z = (54 -45)/6.75 ≈ 1.3333

You can look these up in a suitable CDF table and find the difference between the values you find. That will be about ...

  0.90879 -0.13326 = 0.77553

The probability assembly will stay on schedule is about 78%.

Using the normal distribution, it is found that there is a 0.7747 = 77.47% probability that the build time will be such that assembly will stay on schedule.

Normal Probability Distribution

In a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

In this problem:

X = 54

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{54 - 45}{6.75}[/tex]

[tex]Z = 1.33[/tex]

[tex]Z = 1.33[/tex] has a p-value of 0.9082.

X = 37.5

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{37.5 - 45}{6.75}[/tex]

[tex]Z = -1.11[/tex]

[tex]Z = -1.11[/tex] has a p-value of 0.1335.

0.9082 - 0.1335 = 0.7747.

0.7747 = 77.47% probability that the build time will be such that assembly will stay on schedule.

A similar problem is given at https://brainly.com/question/24663213