Determine by inspection whether the vectors are linearly independent. Justify your answer.
[4 1], [3 9], [1 5], [-1 7]
Choose the correct answer below.
A.The set is linearly dependent because at least one of the vectors is a multiple of another vector.
B. The set is linearly independent because at least one of the vectors is a multiple of another vector.
C. The set is linearly dependent because there are four vectors but only two entries in each vector.
D. The set is linearly independent because there are four vectors in the set but only two entries in each vector.

Answer:   [tex]\dfrac{7}{1,337,220}=5.2\times 10^{-6}[/tex]

Step-by-step explanation:

Order does not matter so it is a Combination.

There are 14 men and we are going to choose 12 --> ₁₄C₁₂

There are 27 people and we are going to choose 12  --> ₂₇C₁₂

[tex]\dfrac{_{14}C_{12}}{_{27}C_{12}}\rightarrow\dfrac{14!}{(14-12)!}\div \dfrac{27!}{(27-12)!}=\large\boxed{\dfrac{7}{1,337,220}}[/tex]

Probabilities are used to determine the chances of an event

The probability of selecting 12 males is: [tex]\frac{7}{1337220}[/tex]

The parameters are given as:

[tex]n = 24[/tex] --- sample size

[tex]Male = 14[/tex]

[tex]Female = 13[/tex]

[tex]r = 12[/tex] ---- number of jury pool

The number of ways of selecting 12 members of the jury, from a total of 27 is:

[tex]^nC_r = \frac{n!}{(n - r)!r!}[/tex]

So, we have:

[tex]^{27}C_{12} = \frac{27!}{(27 - 12)!12!}[/tex]

[tex]^{27}C_{12} = \frac{27!}{15! \times 12!}[/tex]

[tex]^{27}C_{12} = 17383860[/tex]

The number of ways of selecting 12 members of the jury, from a total of 14 male is:

[tex]^nC_r = \frac{n!}{(n - r)!r!}[/tex]

So, we have:

[tex]^{14}C_{12} = \frac{14!}{(14 - 12)!12!}[/tex]

[tex]^{14}C_{12} = \frac{14!}{2! \times 12!}[/tex]

[tex]^{14}C_{12} = 91[/tex]

So, the probability of selecting 12 males is:

[tex]Pr = \frac{^{14}C_{12}}{^{27}C_{12}}[/tex]

[tex]Pr = \frac{91}{17383860}[/tex]

Simplify

[tex]Pr = \frac{91/13}{17383860/13}[/tex]

[tex]Pr = \frac{7}{1337220}[/tex]

Hence, the required probability is: [tex]\frac{7}{1337220}[/tex]

Read more about probabilities at:

https://brainly.com/question/11234923

Answer:

100

Step-by-step explanation:

height = constant/ width

Taking the point (5,20)

where 5 is the width and 20 is the height

20 = constant/ 5

Multiply each side by 5

5*20 = constant

100 = constant

Answer:

h(x) = -x^2 - 1

Step-by-step explanation:

well y, h(x), f(x), n(x), or any other something of x is all the same thing y.

So if f(x) is -x^2 - 1,

Then h(x) is also -x^2 - 1

Answer:

288 possible seating arrangements.

Step-by-step explanation:

There are 4 possible choices for the first seat.

There are 3 possible choice for the sixth seat.

There are 4 possible choices for the second seat.

There are 3 possible choices for the third seat.

There are 2 possible choices for the fourth seat

There is only 1 possible choices for the fifth seat.

4×3×4×3×2×1=

12×4×3×2×1=

48×3×2×1=

144×2×1=

288×1=

288 possible seating arrangements.

Answer:

the amount of space occupied by a three-dimensional solid object

Step-by-step explanation:

Volume is a measure of the space in a 3D solid object enclosed by the closed surfaces of the solid object.

By using the definition of volume, we can see that the correct option is the last one:

"The amount of space occupied by a three-dimensional solid object"

Volume is defined as a 3-dimensional metric derived from longitude, that measures a region in the space. So, each region that "takes space" has a volume.

With that in mind, the option that correctly describes volume is the last option:

"The amount of space occupied by a three-dimensional solid object"

If you want to learn more about volume, you can read:

https://brainly.com/question/1972490

Answer:

29 ft x 58 ft

Step-by-step explanation:

Let x be the length of each side perpendicular to the wall, and y be the length of the side parallel to the wall.

The amount of wire available is:

[tex]116 = 2x+y\\y=116-2x[/tex]

The area of the region is:

[tex]A=xy=x(116-2x)\\A(x)=116x-2x^2[/tex]

The value of 'x' for which the derivate of the area function is zero will yield the maximum area:

[tex]A(x)=116x-2x^2\\A'(x) = 116-4x=0\\x=29\ ft[/tex]

The value of y is:

[tex]y=116-2*29\\y=58\ ft[/tex]

The dimensions of the region with the largest area are 29 ft x 58 ft.

Answer:

8 colors

Step-by-step explanation:

There should be at least 8 different colors available for coloring the sections. The one color is used to color all the small triangles on the upper most and lower most lines, then there will be required another color so that the edges does not matches with the previous color. For the bigger hexagon shapes in the center we will require different colors for all of them because all of the hexagon shapes touches a line and an edge with each other.

Answer:

its 2 trust me

Step-by-step explanation:

its two cause if you think about it and color in the hexagons and triangles two different colors it works

Answer:

200.52 in^2

Step-by-step explanation:

to find the area of a circle, you square 6 and multiply it by pi in this case 3.14.

that gives you 113.04 but because this is only a half circle, it is 56.52 in^2.

Next, you need to find the rectangle. multiply 12(length) by 12(Width) to get 144 add 144 to 56.52 to get 200.52.

Hope this helped if it did please give me brainliest it helps me a lot. :)

Have a good day!

Answer:

C = 150S + 3,500.

$6,050.

Step-by-step explanation:

It costs $3,500 to rent the trucks, so your constant/y-intercept will be $3,500.

It will cost $150 for every ton of sugar, so your slope will be $150.

You then have your equation:

C = 150S + 3,500.

If you were to transport 17 tons of sugar...

C = 150 * 17 + 3,500

C = 2,550 + 3,500

C = $6,050.

Hope this helps!

Answer:

C = $6050

Equation:

To write the equation, we have to remember that C is the total cost, so that means the equation should end in "= C". S is the amount of sugar, so the equation would look something like this:

[tex]3500+150(S)=C[/tex]

3500 is at the beginning since that is the cost for the trucks, and each ton of sugar costs $150, and that would get multiplied by S amount of sugar, to get the total cost, C.

Solving the equation

To solve the equation when S = 17, we simply have to plug in S as 17 into our equation we wrote above.

[tex]3500+150(17)=C[/tex]

150 * 17 is 2550, and 3500 + 2550 is 6050, which is C.

C = $6050

Answer:

6

Step-by-step explanation:

We can establish 6 as an upper bound, since 1*2*3 = 6, and 6 is clearly the greatest number that is a divisor of itself.

We can show that the product of any three consecutive numbers is divisible by 6, because out of any three consecutive integers, at least one must be divisible by 3, and at least one must be divisible by 2. Since the product must have factors of 2 and 3, it must also have 6 as a factor.

Answer:

Side length: 3 cm.

Surface area: 54 cm squared.

Step-by-step explanation:

The formula for a cube is the side length cubed, since the formula for a rectangular prism is length times width times height. Those three measurements are the same for a cube.

So, since the volume is 27 cm cubed, we can say that the side length of the cube is the cube root of 27 cm cubed, or 3 cm.

There are 6 sides on a cube, and every cube has the same area. Since the side length of the cube is 3 cm, the area of one side of the cube is 3 * 3 = 9 cm squared. 9 * 6 = 54 cm squared.

Hope this helps!

Answer:

120 cm

Step-by-step explanation:

If you rearrange the lines you will get a rectangle whose sides are 25 cm and 35 cm.

To get a triangle, move the lines inside the rectangle keeping them parallel to the lines in front of them.

Let P the perimeter of the rectangle:

P = 25*2 + 35*2 = 50+70 = 120 cm

Answer: A) 15

Step-by-step explanation:

Because of Pythagorean Theorem, 9^2+12^2=BC^2.  Thus, 81+144=BC^2.  Thus, 225=BC^2.  Thus, 15=BC.

Hope it helps, and ask if you want further clarification <3

Answer:

The 95%   confidence interval is   [tex]768.44 < \mu <777.55[/tex]

Step-by-step explanation:

From the question we are told that  

    The  sample size is n = 48

    The sample mean is  [tex]\= x = 773 \ lb[/tex]

     The standard deviation is  [tex]\sigma = 16.1 \ lb[/tex]

Now given that the confidence level is  95% , then the level of significance is mathematically represented as

          [tex]\alpha = 100 - 95[/tex]

          [tex]\alpha = 5 \%[/tex]

          [tex]\alpha = 0.05[/tex]

Next we obtain the  critical value of  [tex]\frac{\alpha }{2}[/tex] from the normal distribution table , the value is

              [tex]Z_{\frac{\alpha }{2} } = 1.96[/tex]

The reason we are obtaining critical values of   [tex]\frac{\alpha }{2}[/tex] instead of    [tex]\alpha[/tex] is because  

[tex]\alpha[/tex] represents the area under the normal curve where the confidence level interval (   [tex]1-\alpha[/tex] ) did not cover which include both the left and right tail while

[tex]\frac{\alpha }{2}[/tex]is just the area of one tail which what we required to calculate the margin of error

 The  margin of error is mathematically represented as

      [tex]MOE = Z_{\frac{\alpha }{2} } * \frac{\sigma }{ \sqrt{n} }[/tex]

substituting values

     [tex]MOE = 1.96 * \frac{ 16.1 }{ \sqrt{48} }[/tex]

     [tex]MOE = 4.555[/tex]

The 95% confidence interval to estimate the mean breaking weight for this type cable is mathematically evaluated as

      [tex]\= x - MOE < \mu < \= x - MOE[/tex]

substituting values

    [tex]773 - 4.555 < \mu < 773 + 4.555[/tex]

     [tex]768.44 < \mu <777.55[/tex]

Answer:

√3/2

Explanation:

The directional derivative at the given point is gotten using the formula;

∇f(x,y)•u where u is the unit vector in that direction.

∇f(x,y) = f/x i + f/y j

Given the function f(x, y) = y cos(xy),

f/x = -y²sin(xy) and

f/y = -xysin(xy)+cos(xy)

∇f(x,y) = -y²sin(xy) i + (cos(xy)-xysin(xy)) j

∇f(x,y) at (0,1) will give;

∇f(0,1) = -0sin0 i + cos0j

∇f(0,1) = 0i+j

The unit vector in the direction of angle θ is given as u = cosθ i + sinθ j

u = cos(π/3)i+ sin(π/3)j

u = 1/2 i + √3/2 j

Taking the dot product of both vectors;

∇f(x,y)•u = (0i+j)•(1/2 i + √3/2 j)

Note that i.i = j.j = 1 and i.j = 0

∇f(x,y)•u = 0 + √3/2

∇f(x,y)•u = √3/2

The directional derivative of [tex]f[/tex] at the given point in the direction indicated is [tex]\frac{\sqrt{3}}{2}[/tex].

The directional derivative is represented by the following formula:

[tex]\nabla_{\vec v} f = \nabla f(x_{o},y_{o}) \cdot \vec v[/tex]    (1)

Where:

The gradient of [tex]f[/tex] is calculated below:

[tex]\nabla f (x_{o},y_{o}) = \left[\begin{array}{cc}\frac{\partial f}{\partial x} (x_{o}, y_{o}) \\\frac{\partial f}{\partial y} (x_{o}, y_{o})\end{array}\right][/tex] (2)

Where [tex]\frac{\partial f}{\partial x}[/tex] and [tex]\frac{\partial f}{\partial y}[/tex] are the partial derivatives with respect to [tex]x[/tex] and [tex]y[/tex], respectively.

If we know that [tex](x_{o}, y_{o}) = (0, 1)[/tex], then the gradient is:

[tex]\nabla f(x_{o}, y_{o}) = \left[\begin{array}{cc}-y^{2}\cdot \sin xy\\\cos xy -x\cdot y\cdot \sin xy\end{array}\right][/tex]

[tex]\nabla f (x_{o}, y_{o}) = \left[\begin{array}{cc}-1^{2}\cdot \sin 0\\\cos 0-0\cdot 1\cdot \sin 0\end{array}\right][/tex]

[tex]\nabla f (x_{o}, y_{o}) = \left[\begin{array}{cc}0\\1\end{array}\right][/tex]

If we know that [tex]\vec v = \cos \frac{\pi}{3}\,\hat{i} + \sin \frac{\pi}{3} \,\hat{j}[/tex], then the directional derivative is:

[tex]\Delta_{\vec v} f = \left[\begin{array}{cc}0\\1\end{array}\right]\cdot \left[\begin{array}{cc}\cos \frac{\pi}{3} \\\sin \frac{\pi}{3} \end{array}\right][/tex]

[tex]\nabla_{\vec v} f = (0)\cdot \cos \frac{\pi}{3} + (1)\cdot \sin \frac{\pi}{3}[/tex]

[tex]\nabla_{\vec v} f = \frac{\sqrt{3}}{2}[/tex]

The directional derivative of [tex]f[/tex] at the given point in the direction indicated is [tex]\frac{\sqrt{3}}{2}[/tex]. [tex]\blacksquare[/tex]

To learn more on directional derivatives, we kindly invite to check this verified question: https://brainly.com/question/9964491

Answer:

C. in five hours Caroline wraps an odd number of packages

Step-by-step explanation:

for A until hours you would multiply 2 by 9 and 2 by 9 is 18 and that's an even number so it's not A.

A eliminated.

for B in 3 hours 3 by 9 is 27 and that's an odd number so B is automatically eliminated.

for C in 5 hours all you would do is multiply the 9 by 5 and 9 by 5 is 45 and 45 is indeed an odd number so C is your answer.

for D 7 by 9 is 63 and 63 is an odd number so we already know that C is the answer but still we got to check and D is wrong because 63 is not an even number.

Answer:

Perpendicular Slope: 8/5

Parallel Slope: -5/8

Step-by-step explanation:

First, let's rewrite the line into slope intercept form.

-5x - 8y = 3

-8y = 5x + 3

y = -5x/8 + -3/8

Okay, so now we know the slope, -5/8, and the y-intercept, -3/8.

For a line to be perpendicular, the slope needs to be opposite of the given line's slope.  This will cause the two lines to cross at a 90-degree angle, and therefore be perpendicular.

So a perpendicular line could be as follows:

y = 8x/5 + -3/8

So the perpendicular slope would be 8/5.

For a line to be parallel, the slope needs to be the same so that the two lines will never cross.

So a parallel line could be as follows:

y = -5x/8 + 1

So the parallel slope would be -5/8.

Cheers.

Answer:

Perpendicular Slope: [tex]\boxed{\frac{8}{5}}[/tex]

Parallel Slope: [tex]\boxed{-\frac{5}{8}}[/tex]

Step-by-step explanation:

Part 1: Rewrite into slope-intercept form

Firstly, the equations are written in standard form and not slope-intercept form, so to change that, follow the steps below.

Note: Remember the slope-intercept form equation - [tex]\boxed{y=mx+b}[/tex]

[tex]-5x-8y=3\\\\5x + (-5x-8y)=3+5x\\\\-8y=5x+3\\\\\frac{-8y}{-8} =\frac{5x+3}{-8} \\[/tex]

[tex]y=-\frac{5}{8}x-\frac{3}{8}[/tex]

Add [tex]5x[/tex] to both sides of the equation to isolate the y-variable. Then, divide by the coefficient of y to isolate it entirely. The equation is now in slope-intercept form.

Part 2: Determine the perpendicular slope

Perpendicular slopes are reciprocals of the given slopes. To turn the original slope into its reciprocal counterpart, follow these steps:

To follow this for the slope of the given equation:

Part 3: Determine the parallel slope

Parallel slopes are equal - otherwise, the lines would eventually intersect. Therefore, the given slope is also the parallel slope.

The parallel slope is [tex]\boxed{-\frac{5}{8}}[/tex].

Answer:

In 10 years she'll have approximately $21865.4 in her account.

Step-by-step explanation:

When an amount is compounded continuously its value over time is given by the following expression:

[tex]v(t) = v(0)*e^{rt}[/tex]

Applying data from the problem gives us:

[tex]v(10) = 12000*e^{(0.06*10)}\\v(10) = 12000*e^{0.6}\\v(10) = 21865.4[/tex]

In 10 years she'll have approximately $21865.4 in her account.

Answer:

21,865.43

previous answer left out the last digit

Step-by-step explanation:

x^3 - 3x^2 - 18x

Using the FOIL method, I arrived at my solution!

Answer:

Decay rate K = -2.44%

Step-by-step explanation:

From the question, we want to know the decay rate of strontium 90

Mathematically, this is accessible from its decay equation

From the decay equation, we can see that that ;

At = Ao e^-0.0244t

Generally, the decay equation of a radioactive sample can be written as

At = Ao e^-kt

where K represents the decay constant

From the equation, we can see that;

k = 0.0244 which when represented as a percentage is 2.44%

Since it’s a decay we can say that the decay rate is -2.44%

The answer is : -2.44%

Answer:

7.8 =x

Step-by-step explanation:

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

tan theta = opp / adj

tan 48 = x/7

7 tan 48 = x

7.774287604 = x

To the nearest tenth

7.8 =x

Answer:

[tex] \sqrt{392 {x}^{7} } [/tex]

Simplify

that's

[tex] \sqrt{392} \times \sqrt{ {x}^{7} } \\ \\ = \sqrt{196 \times 2} \: \times \sqrt{ {x}^{7} } \\ \\ = 14 \sqrt{2} \times \sqrt{ {x}^{7} } \\ \\ = 14 \sqrt{2x ^{7} } [/tex]

Hope this helps you

Answer:

4h - 6 = 70.

Step-by-step explanation:

Jahill's height is 70 inches. That is 6 inches shorter than 4 times his sister's height, h. That is the same thing as 4 times h minus 6.

70 = 4 * h - 6

4 * h - 6 = 70

4h - 6 = 70

4h = 76

h = 19.

His sister is 19 inches tall.

Hope this helps!

Answer:

Hello! The answer will be below! :3

Step-by-step explanation:

Question: Jahlil is 6 inches shorter than 4 times his sister’s height. Jahlil’s height is 70 inches. Which equation represents h, his sister’s height in inches?

Answer:The answer is 4h - 6 =70

(His sister is 19 inches tall)

Steps:

4 * h - 6 = 70

So, 4h - 6 = 70......

And 4h will be 76 which means h will equal to 19

His sisters hight is about 19in. tall.....

Hope this helps! :)

⭐️Have a wonderful day!⭐️

Answer:

A:-4

Step-by-step explanation:

If you simplify 9(2x+1)<9x-18 you will get 9x<-27. That will mean x<-3 and the only answer for something less than -3 is -4.

If the answer was right, please put 5 stars.

Answer:

The answer would be-4

Step-by-step explanation:

Here,

9(2x+1) < 9x-18

or, 18x+9 < 9x-18

or, 18x-9x<-18-9

or, 9x<-27

or, x= -27/9

Therefore, the value of x is -4.

Hope it helps...

Shortest is Vindale to Wildgrove to Clarksville

18.9 + 13.2 = 32.1 km.

Answer:

X+3=-5

Step-by-step explanation:

Once you solve the initial equation for x, you will find that the value for x is -8. You can confirm this by doing 2^-5, which will in turn give you 1/32.

Once you know the value of x, you can plug it into the equation and see which one is true, which in this case is the first one, because -8+3 gives you -5

Answer: C. p = p

Step-by-step explanation:

A tautology is a statement that is always true.

A. p = q

This is not always true. Counterexample: p = 1 & q = 2

B. p = q

This is the same as A (above)

C. p = p

This is ALWAYS true!

D. q = p

This is the same as A but in reverse order.

Answer:

Maximum value of r = 7

Step-by-step explanation:

We have this function:

[tex]r=7\cos(4\theta)[/tex]

and we want to calculate the maximum values for r.

This can be done by deriving, but there is a simpler way.

If we look at the function, the maximum values of r will be found when the cosine function is maximum.

The maximum values for the cosine function is 1, so the maximum values for r are:

[tex]r_{max}=7\cdot 1=7[/tex]

This maximum values happen when the cosine function has a value of 1.

We know that this happens for every natural number n that satisfies:

[tex]\cos(\dfrac{n\pi}{2})=1[/tex]

Then, we can calculate the values of theta that satisfy this condition:

[tex]4\theta=\dfrac{n\pi}{2}\\\\\\\theta=\dfrac{n\pi}{8}[/tex]

For every natural n, when theta has a value of (nπ/8), the values of r are maximum.

Answer:

C.  y = 1

Step-by-step explanation:

For two line to be parallel, they have to have the same slope.  The slope for the equation y = 4 is 0.  This cancels out answer choices A, B, and D.  

A and B have an undefined slope since they are vertical lines.

D has a slope of 4.

Also, the line has to go through the point (-3, 1).  Since the line has a slope of 0, the equation will include the y-value.  The y-value for this point is 1.  This gives you an answer of y = 1.

Answer:

y = 1

Step-by-step explanation:

Just took the practice test and got it right