The winner of a 200 mile race drove his car to victory at a rate of 108.4493 mph. What was his time to the nearest thousandth of an hour)?

Answer:

The volume  [tex]V = \frac{75}{2}[/tex] units

Step-by-step explanation:

From the question we are told that

 The equation of the plane is  [tex]z = 2x + 5y + 1[/tex]

The range of the rectangle on the x and y axis is  [tex]\{ (x, y) | -1 \le x \le 0 , 1 \le y \le 4 \}[/tex]

Generally the volume is mathematically represented as

        [tex]V = \int\limits^{4}_{1} \int\limits^0_{-1} {z} \, da[/tex]

Here stands for the area of the solid

So    

           [tex]V = \int\limits^{4}_{1} \int\limits^0_{-1} {(2x + 5y + 1 )} \, dxdy[/tex]

           [tex]V = \int\limits^{4}_{1} [{(\frac{2x^2}{2} + 5xy + x )} ] | \left \ 0} \atop {-1}} \right. \, dy[/tex]

            [tex]V = \int\limits^{4}_{1} [{(x^2 + 5xy + x )} ] | \left \ 0} \atop {-1}} \right. \, dy[/tex]

          [tex]V = \int\limits^{4}_{1} [{((0)^2 + 5(0)y + (0) )} ] -[{((-1)^2 + 5(-1)y + (-1) )} ] \, dy[/tex]

        [tex]V = \int\limits^{4}_{1} 5y \, dy[/tex]

        [tex]V = 5 [ \frac{y^2}{2} ]|\left \ 4 } \atop { 1 }} \right. \, dy[/tex]

       [tex]V = 5( [ \frac{4^2}{2} ] - [ \frac{1^2}{2} ] )[/tex]

        [tex]V = \frac{75}{2}[/tex]

Answer:

Vectors [tex]p_{1} = 2+5\cdot x + 3\cdot x^{2}[/tex], [tex]p_{2} = 4+11\cdot x +6\cdot x^{2}[/tex] and [tex]p_{3} = 1+2\cdot x +x^{2}[/tex] are linearly independent.

Step-by-step explanation:

From Linear Algebra, we must remember that a set of vectors is linearly independent if and only if coefficients of its linear combinations are all zeroes. That is:

[tex]\Sigma\limits_{i=1}^{n} \alpha_{i}\cdot p_{i}= 0[/tex], where [tex]\alpha_{i} = 0[/tex]. (Eq. 1)

Where:

[tex]p_{i}[/tex] - i-th Polynomial of the set of vectors, dimensionless.

[tex]\alpha_{i}[/tex] - i-th coefficient associated with the i-ith polynomial of the set of vectors, dimensionless.

Let [tex]p_{1} = 2+5\cdot x + 3\cdot x^{2}[/tex], [tex]p_{2} = 4+11\cdot x +6\cdot x^{2}[/tex] and [tex]p_{3} = 1+2\cdot x +x^{2}[/tex] elements of the set of vectors, whose linear combination is:

[tex]\alpha_{1}\cdot p_{1}+\alpha_{2}\cdot p_{2}+\alpha_{3}\cdot p_{3}= 0[/tex]

[tex]\alpha_{1}\cdot (2+5\cdot x+3\cdot x^{2})+\alpha_{2}\cdot (4+11\cdot x +6\cdot x^{2})+\alpha_{3}\cdot (1+2\cdot x+x^{2}) = 0[/tex]

[tex](2\cdot \alpha_{1}+4\cdot \alpha_{2}+\alpha_{3})+(5\cdot \alpha_{1}+11\cdot \alpha_{2}+2\cdot \alpha_{3})\cdot x+(3\cdot \alpha_{1}+6\cdot \alpha_{2}+\alpha_{3})\cdot x^{2} = 0[/tex]

Values of coefficient are contained in the following homogeneous system of linear equations:

[tex]2\cdot \alpha_{1}+4\cdot \alpha_{2}+\alpha_{3} = 0[/tex] (Eq. 2)

[tex]5\cdot \alpha_{1}+11\cdot \alpha_{2}+2\cdot \alpha_{3} = 0[/tex] (Eq. 3)

[tex]3\cdot \alpha_{1}+6\cdot \alpha_{2}+\alpha_{3} = 0[/tex] (Eq. 4)

The solution of this system is:

[tex]\alpha_{1} = 0[/tex], [tex]\alpha_{2} = 0[/tex], [tex]\alpha_{3} = 0[/tex]

Which means that given set of vectors are linearly independent.

Answer:

18 students for each teacher and 10 for each tutor, and if the academy had 80 students it would have 8 tutors

Step-by-step explanation:

Answer:

All real numbers are solutions.

0=0

Step-by-step explanation:

Let's solve your equation step-by-step.

x+2x−1=−8+3x+7

Step 1: Simplify both sides of the equation.

x+2x−1=−8+3x+7

x+2x+−1=−8+3x+7

(x+2x)+(−1)=(3x)+(−8+7)(Combine Like Terms)

3x+−1=3x+−1

3x−1=3x−1

Step 2: Subtract 3x from both sides.

3x−1−3x=3x−1−3x

−1=−1

Step 3: Add 1 to both sides.

−1+1=−1+1

0=0

Answer:

All real numbers are solutions.

Answer:

(5, -3)

Step-by-step explanation:

translation rule: (x+5, y+2)

(0+5, -5+2)

(5, -3)

Answer:

The first picture is a function. The second picture is not a function.

Step-by-step explanation:

The first one is a function because no x-values repeat. Different x-values can be paired with the same y-function.

The second one is not a function because it fails the horizontal line test. The line would touch in two spots, therefore failing the line test.

Answer:

31x+21

Step-by-step explanation:

7x+3(8x+7)

7x+24x+21

31x+21

Answer 31x + 21

Step-by-step explanation: can’t

Answer:

The first one

Step-by-step explanation:

Answer:

t = 3.74165738677 or 3.74

Step-by-step explanation:

Step 1:

( t - 3 )² = 6      Equation

Step 2:

t² - 3² = 6       Open Parentheses

Step 3:

t² - 9 = 6          Exponents

Step 4:

t² = 14         Add 9 on both sides

Step 5:

t = [tex]\sqrt{14}[/tex]       Find the square root of 14

Answer:

t = 3.74165738677 or 3.74        Round

Hope This Helps :)

Answer:

The arrow is at a height of 48 ft after approximately 0.55s and after 5.45s.

Step-by-step explanation:

took the assignment

Answer:

The beam of the light is moving along the shoreline at the rate of [tex]\mathbf{ 160 \ \pi \ mi/min}[/tex]

Step-by-step explanation:

From the given information: Let say x is the distance between the lighthouse and the shoreline. Then, the  tangent of  trigonometry can be written as:

[tex]tan (\theta )=\dfrac{x}{4}[/tex]

In respect to time, the expression can be derived as:

[tex]sec^2 (\theta) \dfrac{d \theta}{dt} = \dfrac{1 }{4}\dfrac{dx}{dt}[/tex]

[tex]\dfrac{dx}{dt}=\dfrac{4}{cos ^2 (\theta) }\dfrac{d \theta}{dt}[/tex]

To estimate the value of [tex]\dfrac{dx}{dt}[/tex], we need to know cos²(θ) and D

where;

D = [tex]\sqrt{4^2+4^2}= \sqrt{32}\ mi[/tex]

[tex]cos (\theta) = \dfrac{4}{D}[/tex]

[tex]cos (\theta) = \dfrac{4}{\sqrt{32}}[/tex]

[tex]cos (\theta) = \dfrac{4}{\sqrt{16 \times 2}}[/tex]

[tex]cos (\theta) = \dfrac{4}{4 \sqrt{\ 2}}[/tex]

[tex]cos (\theta) = \dfrac{1}{ \sqrt{\ 2}}[/tex]

[tex]cos ^2 (\theta)= \dfrac{1}{2}[/tex]

Finally, we substitute the value of [tex]cos^2(\theta)[/tex] and [tex]\dfrac{d \theta}{dt}[/tex] in the expression derived earlier.

i.e.

[tex]\dfrac{dx}{dt} = \dfrac{4}{\dfrac{1}{2}}\times 10 \ rev/min[/tex]

where;

10 rev/min = (10 × 2π) rad/min = 20π rad/min

Then:

[tex]\dfrac{dx}{dt} = \dfrac{4}{\dfrac{1}{2}}\times 20 \ \pi[/tex]

[tex]\mathbf{\dfrac{dx}{dt} = 160 \ \pi \ mi/min}[/tex]

Answer:

288

Step-by-step explanation:

The ratio of gas to miles is 3:72. That is a proportion. 3:72 is the same as 12:288. (multiply both by 4)

(1.) 20.4

(2.) 150

(3) 8

(4.) 15

Answer:

add them all up and subtract 420 from 15+20+12!

Step-by-step explanation:

hope this helps

Complete question :

An electronics store receives a shipment of 35 graphing calculators, including 7 that are defective. 8 of these calculators are selected for a local high school. (A) How many selections can be made? (B) How many of these selections will contain no defective calculators?

Answer:

23535820 ways

3108105 ways

Step-by-step explanation:

A.) How many selections can be made:

Number of ways of selecting 8 calculators from 35

35C8 :

Combination formula :

nCr = n! /(n-r)! r!

35C8 = 35! / (35-8)!8!

35C8 = 35! / 27! 8!

35C8 = (35*34*33*32*31*30*29*28) / (8*7*6*5*4*3*2*1)

35C8 = 948964262400 / 40320

= 23535820 ways

B.) number of non-defective calculators :

35 - 7 = 28

28C8 = n! /(n-r)! r!

28C8 = 28! / (28-8)!8!

28C8 = 28! / 20! 8!

28C8 = (28*27*26*25*24*23*22*21) / (8*7*6*5*4*3*2*1)

28C8 = 2506375872000 / 40320

= 3108105 ways

Answer:

x = 8

Step-by-step explanation:

Step 1:

17x + 14 + 4x - 2 = 180          Sum of a line

Step 2:

21x + 12 = 180        Combine Like Terms

Step 3:

21x = 168       Subtract 12 on both sides

Step 4:

x = 168 ÷ 21      Divide

Answer:

x = 8

Hope This Helps :)

Step-by-step explanation:

4x - 2 + 17x + 14 = 180

21x + 12 = 180

Subtract 12 from both sides and you get :

21x = 168

Devide

[tex] \frac{21x}{21} = \frac{168}{21} \\ x = 8[/tex]

Answer:

Option (b)

Step-by-step explanation:

From the graph attached in the figure,

Graph (a) is a scatter plot of a data set.

Data in this graph is not connected. In other words, a scatter plot represents a discrete function.

Similarly, in the graph (b) there is a straight line.

All points lying on this straight line are connected and follow the same rule.

Therefore, graph (b) represents a continuous function.

Therefore, Option (b) is the correct option.

Answer:

C. 125%

Step-by-step explanation:

Because an entire box of 100 is colored, we automatically know it is at least 100%. Which means both A and B are incorrect. There are two tens filled, so we have 120%. There is another 5 boxes are filled, so we have 125%, which is C.

I hope that this helps! :)

Answer:

k = 3.5

Step-by-step explanation:

From the graph in the picture attached,

Relation between balloons height (y) is directly proportional to the time (x)

y ∝ x

y = kx

Where 'k' is a proportionality constant.

Now we substitute the point (8, 28) in the equation,

28 = k(8)

k = [tex]\frac{28}{8}[/tex]

k = 3.5

k ≈ 3.5

Therefore, value of constant 'k' is 3.5

Answer:

205.74 cm

Step-by-step explanation:

Answer:

t=3

Step-by-step explanation:

5t-4=|11

+4 |+4

5t= | 15

÷5 | ÷5

t = 3

Answer and Step-by-step explanation:

Solution:

The equation is given by:

z – z0 = a(x – x0) + b(y – y0).

The point (1, 2, 3) is given , substitute them for x0, y0 and z0:

Z – 3 = a (x – 1) + b(y-2)

Both a and b should be negative, because normal vector to point in the negative x and y direction so that plane will enclose a tetrahedron with finite area in the first octant.

This will only happen if z becomes smaller as we move towards the positive x and y directions.

To find expressions for V, firstly find expression for x, y and z intercepts.

X – Intercepts (y and z = 0) : 2b +a -3 / a

y- Intercepts (x, z = 0): 2b + a- 3 / b

z – Intercepts( x, y = 0): 3 – a – 2b

The base is = (2b+a-3)2/ 2ab

Volume is 1/3 base x height, so

V (a, b) = - (2b+a-3)3 / 6ab

The gradient vector:

ΔV (a, b) = |- (3(2b+a-3)2 ab-b (2b+a-3)3)/6a2b2, (6(2b+a-3)2 ab-a(2b+a-3)3)/6a2b2| = 0

b (2b+a-3)2 [ (2b+a-3) -3a] = 0

a (ab + a-3)2 [(2b +a -3) – 6b] = 0

Where a, b not equal to 0.

We cannot solve for 2b +a-3 = 0 because, that will lead to V = 0, which is impossible.

Therefore, we only solve for second halves equations, which are system of linear equations:

-2a + 2b = 3 and a – 4b = 3

Which gives a = -3 and b = -3/2

Put in equation:

Z – 3 = -3 (x-1) – 3/2 (y-2)

3x +3/2 y +z = 9

Multiplying by 2:

6x + 3y + 2z = 18.

Answer:

The range of the following set of points is {4, -2, -8}

Step-by-step explanation:

∵ The set of points is {(3, 4), (7, -2), (11, -8)}

∵ The range is the y-coordinates of these points

∵ The y-coordinates of the points are 4, -2, -8

∴ The range is {4, -2, -8}

∴ The range of the following set of points is {4, -2, -8}

Complete Question

Problem 9-8 (modified). The height of adult males in a particular city is normally distributed, with mean 69.5 in. and standard deviation 2.65 in.

When a random sample is taken of size  20, find (1) the standard error of Xbar

(2) the probability that Xbar falls within .5 in. of the true mean

Probability=

Answer:

1

[tex]\sigma_{\= x} = 0.5926[/tex]

2

[tex]P( 69 < \= X < 70) = 0.60134[/tex]

Step-by-step explanation:

From the question we are told that

  The true  mean is  [tex]\mu = 69.5 \ in[/tex]

  The standard deviation is  [tex]\sigma = 2.65 \ in[/tex]

    The sample size is n =  20

Generally the standard error of Xbar[tex](\= x)[/tex] is mathematically represented as

     [tex]\sigma_{\= x} = \frac{\sigma }{\sqrt{n} }[/tex]

=>  [tex]\sigma_{\= x} = \frac{ 2.65 }{\sqrt{ 20 } }[/tex]

=>  [tex]\sigma_{\= x} = 0.5926[/tex]

Generally for  [tex]\= x[/tex] to fall within 0.5 of the true mean the [tex]\= x[/tex] must be within

     [tex]a = \mu + 0.5[/tex]

=>   [tex]a = 69.5 + 0.5[/tex]

=>   [tex]a = 70[/tex]

or  [tex]b = \mu -0.5[/tex]

=>    [tex]b = 69.5 -0.5[/tex]

=>    [tex]b = 69[/tex]

Generally the probability that  [tex]\= x[/tex] fall with 0.5  of the true mean is mathematically represented as

     [tex]P( 69 < \= X < 70) = P(\frac{69 - 69.5 }{ 0.5926} < \frac{\= X - \mu }{ \sigma_{\= x} } <\frac{70- 69.5 }{ 0.5926})[/tex]

=>  [tex]P( 69 < \= X < 70) = P(-0.844 < Z < 0.844)[/tex]

=>  [tex]P( 69 < \= X < 70) = P( Z < 0.844) - P( < -0.844)[/tex]

From the z table the probability of  (  Z    < 0.844)  and   (  Z    < -0.844)  is  

     [tex]P( Z < 0.844) = 0.80067[/tex]

and

    [tex]P( Z < - 0.844) = 0.19933[/tex]

So

   [tex]P( 69 < \= X < 70) = 0.80067 - 0.19933[/tex]

=>  [tex]P( 69 < \= X < 70) = 0.60134[/tex]

The standard error of the given data comes to be 0.593.

It is given that

mean [tex]\mu[/tex] = 69.5 inch

Standard deviation [tex]\sigma[/tex] = 2.65 inch

Sample size n =20

The standard error is a statistical term that measures the accuracy with which a sample distribution represents a population by using standard deviation.

The standard error is given by:

[tex]SE =\frac{\sigma}{\sqrt{n} }[/tex]

[tex]SE =\frac{2.65}{\sqrt{20} }[/tex]

[tex]SE=0.593[/tex]

Hence, the standard error of the given data comes to be 0.593.

To get more about standard errors visit:

https://brainly.com/question/1191244

Answer:

the correct answer is 180.8. i saw that other ppl had this answer on brianly but had 0 star ratings even though they were correct.

Step-by-step explanation: i just took this test and trusted the person who ansered and got it wrong.

Answer:

y =-3/2x+4

Step-by-step explanation:

simple

Answer:

14.98

Step-by-step explanation:

I used a calculater