The length of Amy's rectangular kitchen is 12 feet.  If the area of the room is at least 96       square feet, what is the smallest width the room could have? Show your work

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:

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:

205.74 cm

Step-by-step explanation:

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 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 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:

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:

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:

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}

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:

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:2.00

Step-by-step explanation:

Answer:20

Step-by-step explanation:

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:

14.98

Step-by-step explanation:

I used a calculater

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:

t=3

Step-by-step explanation:

5t-4=|11

+4 |+4

5t= | 15

÷5 | ÷5

t = 3

(1.) 20.4

(2.) 150

(3) 8

(4.) 15

Answer:

y =-3/2x+4

Step-by-step explanation:

simple

Answer:

(5, -3)

Step-by-step explanation:

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

(0+5, -5+2)

(5, -3)

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: 7.1% and 6%.

Step-by-step explanation:

Given data:

Sample size (n) = 11

Standard deviation = 2.2

Margin of error confidence level 95% = 1.96

Margin of error confidence level of 90% = 1.65

Solution:

P = 2.2/11

= 0.2.

ME = z √p (1-p)/n

at 95% interval

ME = 1.96 * √ 0.2 ( 1 – 0.2 ) / 11

= 1.96 * 0.03636

= 0.071.

= 7.1%

At 90% interval

ME = 1.65 * √ 0.2 ( 1 – 0.2 ) / 11

= 1.65 * 0.03636

= 0.06.

= 6%

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

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:

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

Step-by-step explanation:

hope this helps