A group of 59 randomly selected students have a mean score of 29.5 with a standard deviation of 5.2 on a placement test. What is the 95% confidence interval for the mean score, , of all students taking the test

Greetings from Brasil...

X = 2 liter container

Y = 3 liter container

the total of containers are:

X + Y = 400

the capacity of the containers is

2X + 3Y = 1100

Assembling the equation system

2X + 3Y = 1100

X + Y = 400       x(-2)

2X + 3Y = 1100

-2X  -2Y = - 800    

X + Y = 400    so

X + 300 = 400

X = 400 - 300

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BR:

Observe que:

1 vasilha de 2L = 1 × 2 = 2L

2 vasilhas de 2L = 2 × 2 = 4L

3 vasilhas de 2L = 3 × 2 = 6L

X vasilhas de 2L = X × 2 = 2X litros

.....

1 vasilha de 3L = 1 × 3 = 2L

2 vasilhas de 3L = 2 × 3 = 4L

3 vasilhas de 3L = 3 × 3 = 6L

X vasilhas de 3L = X × 3 = 3X litros

Logo 2X + 3Y = 1100

Existem X e Y vasilhas que num total sao 400, logo

X + Y = 400

Answer:

one solution

Step-by-step explanation:

The given system of equations has one solution.

Hence option A is correct.

The given system is

4x-2y=8

2x+y=2

Since we know that,

For system

a₁x + b₁ y = c₁

a₂x + b₂y = c₂

If

a₁/a₂ = b₁/b₂ = c₁/c₂   then it has an infinite solution

a₁/a₂ ≠ b₁/b₂              then unique solution

a₁/a₂ = b₁/b₂ ≠ c₁/c₂   then no solution

Here we have

a₁ =  4, b₁ = -2 and c₁ = 8

a₂ = 2, b₂ = 1  and  c₂ = 2

Now since

a₁/a₂ ≠ b₁/b₂   ⇒ 4/2  ≠ -2/1

                      ⇒ 2 ≠ -2

Hence, the given system has a unique solution.

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Answer:

$125,800

Step-by-step explanation:

Amount (A) = ?

Principal (P) = $85,000

Rate (r) = 6%

Time (t) = 8 years

Simple interest formula;

A = P(1 + rt)

A = $85,000(1 + 0.48)

A = $125,800

Answer:

The answer is A.

Step-by-step explanation:

In a linear equation, y = mx + b, m is represented as gradient (slope) and b is the y-intercept.

So for this question, m is 2/3 and b is 1.

Step-by-step explanation:

Hey, there !!!

According to your question,

total c.p = 532.50

tax rate =6%

let original price be x.

now,

total c.p = x + tax rate of x.

or, 532.50= x+ (6/100) × x

or, 532.50 = 106x/100

or, 53200 = 106x

or, x= 53200/106

Therefore, the original price was 501.88.

Hope it helps...

Answer:

The answer is option C.

3a - b = 10

Hope this helps you

Answer:

[tex]12 {y}^{9} - 6 {y}^{5} + 4 {y}^{2} + 21[/tex]

Step-by-step explanation:

divide each term by 2y^3

Multiply through by the least common denominator.

Answer:

13

Step-by-step explanation:

f(x) = 3x + 7

f(2) = 3(2) + 7

f(2) = 6 + 7

f(2) = 13

Answer:

7

Step-by-step explanation:

Take the amount of money and divide by the cost per fish

46/6 =7 with 4 dollars remaining

She can buy 7 goldfish

Answer:

7

Step-by-step explanation:

7 x 6 = 42

I believe the value is negative 4. If not, well, try any negative below that, such as -5,6,7,8, etc.

Answer:

y is less than -3

Step-by-step explanation:

To do this you would just subtract 9 from both sides so you get -y is greater than 3. Since you cannot have y as a negative number you will divide -1 from both sides but when you do that you will have to flip the sign so you get y is less than -3.

Answer:

1/6

Step-by-step explanation:

As we already know that selected bulb is defective the required probability doesn't depend on functional bulbs at all.

The probability, that selected defective bulb is from Box2 is number of defective bulbs in Box 2  divided by total number of defective bulbs.

P(defective in box 2)= N(defective in box 2)/N(defective total)

As we know there is only 1 defective lamp in box 2.

So N(defective in box 2)=1

Total number of defective bulbs is Box1- 2 defective  bulbs,  box2- 1 defective bulbs, box3 - 3 defective bulbs. Total are 6 defective bulbs.

So N(defective total)=6

So P(defective in box 2)=1/6

Answer:  103 adult tickets

Step-by-step explanation:

Adult tickets (a) = a

Student tickets (s) = 2a

Total = 309

a + 2a = 309

     3a = 309

      a = 103

Answer:

Step-by-step explanation:

Total tickets sold = 309

Let the number of adult tickets sold be x

Let the number of student tickets sold be 2x

Adult tickets + student tickets = 309

[tex]x + 2x = 309[/tex]

Collect like terms

[tex] 3x = 309[/tex]

Divide both sides of the equation by 3

[tex] \frac{3x}{3} = \frac{309}{3} [/tex]

Calculate

[tex]x = 103[/tex]

Hence, 103 adult tickets were sold.

Hope this helps..

Good luck on your assignment...

Answer:

Step-by-step explanation:

Using chain rule to find the partial deriviative of z with respect to s and t i.e ∂z/∂s and ∂z/∂t, we will use the following formula since it is composite in nature;

∂z/∂s = ∂z/∂x*∂x/∂s +  ∂z/∂y*∂y/∂s

Given the following relationships z = x⁸y⁹, x = s cos(t), y = s sin(t)

∂z/∂x = 8x⁷y⁹, ∂x/∂s = cos(t), ∂z/∂y = 9x⁸y⁸ and ∂y/∂s = sin(t)

On substitution;

∂z/∂s = 8x⁷y⁹(cos(t)) + 9x⁸y⁸ sin(t)

∂z/∂s = 8(scost)⁷(s sint)⁹(cos(t)) + 9(s cost)⁸(s sint)⁸ sin(t)

∂z/∂s = (8s⁷cos⁸t)s⁹sin⁹t + (9s⁸cos⁸t)s⁸sin⁹t

∂z/∂s = 8s¹⁶cos⁸tsin⁹t + 9s¹⁶cos⁸tsin⁹t

∂z/∂s = 17s¹⁶cos⁸tsin⁹t

∂z/∂t =  ∂z/∂x*∂x/∂t +  ∂z/∂y*∂y/∂t

∂x/∂t = -s sin(t) and ∂y/∂t = s cos(t)

∂z/∂t  = 8x⁷y⁹*(-s sint) + 9x⁸y⁸* (s cos(t))

∂z/∂t = 8(scost)⁷(s sint)⁹(-s sint) + 9(s cost)⁸(s sint)⁸(s cos(t))

∂z/∂t = -8s¹⁷cos⁷tsin¹⁰t + 9s¹⁷cos⁹tsin⁸t

∂z/∂t = -s¹⁷cos⁷tsin⁸t(8sin²t-9cos²t)

Answer:

f(x) = -(x + 1)² - 2

Step-by-step explanation:

f(x) = a(x - h)² + k

-6 = a(1 - -1)² + -2

-6 = a(4) -2

-4 = 4a

a = -1

f(x) = -(x + 1)² - 2

Answer: It is a scalene triangle.

Step-by-step explanation:

It is scalene because the length between T and V are not equal,the length between T and S is not equal and the length between V and S is also not equal. All the side lengths of the triangle have different measures.

Answer:

(-1,-2)

Step-by-step explanation:

[tex]6x-y=-4\\y=6x+4\\y=6(-2)+4=-8\\y=6(-1)+4=-2\\y=6(0)+4=4[/tex]

so the only one is (-1,-2)

Answer:

10

Step-by-step ex1planation:

Answer:

Graph is attached below

Step-by-step explanation:

You first need to plot any two points on the coordinate plane(you can also do more than two points to make it more accurate). Then, using a ruler connect the points and extend the line outwards.

The plotted straight line is as shown in below graph.

Given straight line equation is y = x + 2

To plot a straight line, take two different values of x which output different values of y. Then plot those points in the graph.

After plotting those two points, you connect both dots with straight line and extend that line infinitely from both endpoints.

Example, take x = 1 and x = 2 for straight line y = x + 2

Then we get:

For x = 1, y = 1 + 2 = 3

For x = 2, y = 2 + 2 = 4

The plot of points (1,3) and (2,4) and the straight line y = x + 2 is shown below.

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Answer:

3x

Step-by-step explanation:

39*x / 13

39/13 * x

3*x

3x

Answer:

3x

Step-by-step explanation:

We are given the expression:

39*x /13

We want to simplify this expression. It can be simplified because both the numerator (top number) and denominator (bottom number) can be evenly divided by 13.

(39*x /13) / (13/13)

(39x/13) / 1

3x / 1

When the denominator is 1, we can simply eliminate the denominator and leave the numerator as our answer.

3x

The expression 39*x/13 can be simplified to 3x

Answer:

a. k = 3

b. N = 27

c. n = 9

Step-by-step explanation:

Given that,

Source :          sS                 dF            mS                F

Between:                            k -1        sSB/k-1             mSB

within                                  N-K        sSw/N-K           mSw

total                                     N-1

Therefore F ( 2, 24 ) = F ( K - 1, N - K )

so K - 1 = 2

K = 2 + 1

K = 3

N - K = 24

N - 3 = 24

N = 24 + 3

N = 27

married, single and divorced are equal sizes

so n = N/3

n = 27 / 3

n = 9

a. k = 3

b. N = 27

c. n = 9

Answer:

1/6

Step-by-step explanation:

The probability of even number is 1/2. The probability of number greater than 4 is 1/3, because only 5 and 6 are greater than 4.

Multiply these two values

1/2*1/3= 1/6

Answer:

the first blank is 2, the second one is 1

Answer:

Yellow box #1=2

Yellow box #2=1

Step-by-step explanation:

#1) 8-6=2

#2)8-7=1

Answer:

x=7

Step-by-step explanation:

Answer:

[tex]w=\frac{t+8}{3}[/tex]

Step-by-step explanation:

[tex]3w - 8 = t[/tex]

Add 8 on both sides.

[tex]3w - 8 + 8 = t + 8[/tex]

[tex]3w = t + 8[/tex]

Divide both sides by 3.

[tex]\frac{3w}{3} =\frac{t+8}{3}[/tex]

[tex]w=\frac{t+8}{3}[/tex]

The value of w is w = (t + 8)/3 in terms of t after solving and making the subject w the answer is w = (t + 8)/3.

It is defined as the combination of constants and variables with mathematical operators.

We have an equation:

3w - 8 = t

To solve for w in terms of t

Make the subject as w

In the equation:

3w - 8 = t

Add 8 on both sides:

3w - 8 + 8 = t + 8

3w = t + 8

Divide by 3 on both sides:

3w/3 = (t + 8)/3

w = (t + 8)/3

The equation represents a function of w in terms of t

As we know, the function can be defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

Thus, the value of w is w = (t + 8)/3 in terms of t after solving and making the subject w the answer is w = (t + 8)/3.

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Answer:

Thickness of rectangle prism is 20 inches.

Step-by-step explanation:

Given:

Surface area of rectangular prism, A =  992 sq inches.

Height, h = 12 inches

Width, w = 8 inches

To find:

Thickness / length of prism, [tex]l[/tex] = ?

Solution:

First of all, let us learn the formula for surface area of a rectangular prism.

Formula for surface area of a prism is given as:

[tex]A=2(wl+hl+hw)[/tex]

As there are 6 faces, each face is a rectangle and area of all the faces is considered in the formula. It is just like a cuboid like structure.

Putting all the given values in the formula to find the value of [tex]l[/tex]:

[tex]992=2(8l+12l+8 \times 12)\\\Rightarrow 496 = 20l + 96\\\Rightarrow 20 l =496-96\\\Rightarrow 20 l =400\\\Rightarrow l = \dfrac{400}{20}\\\Rightarrow l = 20\ inches[/tex]

So, the answer is Thickness of rectangle prism is 20 inches.

Answer:

(a) C = 80 a = 5.938cm c = 9.097cm

(b) unsure

(c) b= 22.147cm

A = 48.16 degrees

C = 22.82 degrees

Note angle sum higher than 180 due to rounding inaccuracies

Step-by-step explanation:

(a) <C == 180 - (40 + 60) == 80 (Interior angles on triangle have sum of 180 degrees)

side a = (8*sin(40))/sin(60) == 5.938cm by law of sines

side c = (8*sin(80))/sin(

60) == 9.097cm by law of sines

(b) unsure

(c) b^2 = 17^2 + 11^2 - 2(17)(11)cos(104) --> Law of cosines

b^2 = 289 + 121 - 2(187)cos(104)

b^2 = 400 - -90.479

b^2 = 490.479

b = 22.147 cm

sin(A)/17cm = sin(104)/22.147cm

A = arcsin((17/22.147)*sin(104))

A = 48.16 degrees

sin(C)/11cm = sin(104)/22.147cm

C = arcsin((11/22.147)*sin(104))

C = 28.82 degrees

Answer:

The confidence interval is  [tex]25.16 < \mu < 26.85[/tex]

Step-by-step explanation:

From  the question we are given a data set

     25.5, 26.1, 26.8, 23.2, 24.2, 28.4, 25.0, 27.8, 27.3, and 25.7.

The mean of the this sample data is  

       [tex]\= x = \frac{\sum x_i}{n}[/tex]

where is the sample size with values  n =  10

         [tex]\= x = \frac{25.5+ 26.1+ 26.8+23.2+ 24.2+ 28.4+ 25.0+ 27.8+ 27.3+ 25.7}{10}[/tex]

          [tex]\= x = 26[/tex]

The standard deviation is evaluated as

             [tex]\sigma = \sqrt{\frac{\sum (x-\= x)}{n} }[/tex]

substituting values

     [tex]= \sqrt{\frac{ ( 25.5-26)^2, (26.1-26)^2, (26.8-26)^2, (23.2-26)^2}{10} }[/tex]

                  [tex]\cdot \ \cdot \ \cdot \sqrt{\frac{ ( 24.2-26)^2, (28.4-26)^2+( 25.0-26)^2+ (27.8-26)^2+( 27.3-26)^2+( 25.7-26)^2}{10} }[/tex]

     [tex]\sigma = 1.625[/tex]

The  confidence level is given as 90% hence the level of significance is calculated as

    [tex]\alpha = 100 -90[/tex]

    [tex]\alpha =10[/tex]%

   [tex]\alpha = 0.10[/tex]

Now the critical values of [tex]\frac{\alpha }{2}[/tex] is obtained from the normal distribution table as

      [tex]Z_{\frac{\alpha }{2} } = 1.645[/tex]

The reason  we are obtaining  the critical values of [tex]\frac{\alpha }{2}[/tex] instead of  [tex]\alpha[/tex] is because  we are considering two tails of the area under the normal curve

  The margin of error is evaluated as

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

substituting values

           [tex]MOE = 1.645 * \frac{1.625 }{\sqrt{10} }[/tex]

           [tex]MOE = 0.845[/tex]

The  90%, two sided confidence interval is mathematically evaluated as

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

           [tex]26 - 0.845 < \mu < 26 + 0.845[/tex]

           [tex]25.16 < \mu < 26.85[/tex]

Given that the lower and the upper limit is greater than  25 then we can assure the manufactures  that the battery life exceeds 25 hours

Answer: Franklin could end at 4 different points.

Step-by-step explanation:

Given: Franklin the fly starts at the point (0,0) in the coordinate plane.

At each point, Franklin takes a step to the right, left, up, or down.

i.e. there are 4 choices of directions [A coordinate plan has 4 quadrants]

If he moves 10 steps, then the number of different points Franklin could end up at =  choices of directions

= 4

Hence, Franklin could end at 4 different points.

Answer: Option D, composition.

Step-by-step explanation:

In a function f(x) = y

x is the input, and the set of the possible values of x is called the domain.

y is the output, and the possible values of y is called the range.

Now, if we have two functions:

f(x) = y

g(x) = y.

we can define the composition of functions as: using the output of one function as the input of the other function, we can write this as:

f( g(x)) or fog(x)

In words, first we evaluate the function g in the point x, and the output of that is used as the input for the function f.

Then, the correct option here is D, composition.

Answer:

(a) n(t) = P(0)*e^(0.010939940t)

(b) 12,674,681 (nearest unit)

(c) 14 years (nearest year)

Step-by-step explanation:

rate = 1.1% / year = 1.011

(a)

P(0) = 12,000,000  = population in 2010

In compound interest format, after t years

P(t) = P(0)* (1.011)^t

Given format = P(0)* e^(rt)

therefore

e^(rt) = 1.011^t       use law of exponents

(e^r)^t = 1.011^t

e^r = 1.011

r = log_e(1.011) = 0.010939940   (to 9 decimal places)

required formula is

n(t) = P(0)*e^(0.010939940t)

(b)

in 2015,

P(0)=12000000, n = 5 (years after 2010)

n(5) = 12000000*e^( 0.010939940 * 5 ) = 12,674,680.6 = 12,674,681 (nearest unit)

(c)

to reach 14 million, we equate

n(t) = 14,000,000

12,000,000 *e^(0.010939940*t) = 14,000,000

e^(0.010939940*t) = 14000000/12000000 = 7/6

take log on both sides

0.010939940*t = log(7/6)

t = log(7/6) / 0.010939940 = 14.091 years = 14 years to the nearest year.

See graph attached.  Y-axis is in millions, x-axis is in years.

a) [tex]n(t) = 12e^{0.011t}[/tex]

b) The estimate for the population in 2015 is of 12.7 million.

c) The fish population will reach 14 million after 14 years.

d) The sketch is given at the end of this answer.

------------------------------------

Item a:

The exponential model is:

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

In which:

Thus, the model is:

[tex]n(t) = 12e^{0.011t}[/tex]

Item b:

2015 is 2015 - 2010 = 5 years after 2010, thus this is n(5).

[tex]n(5) = 12e^{0.011(5)} = 12.7[/tex]

The estimate for the population in 2015 is of 12.7 million.

Item c:

This is t for which n(t) = 14, thus:

[tex]n(t) = 12e^{0.011t}[/tex]

[tex]14 = 12e^{0.011t}[/tex]

[tex]e^{0.011t} = \frac{14}{12}[/tex]

[tex]\ln{e^{0.011t}} = \ln{\frac{14}{12}}[/tex]

[tex]0.011t = \ln{\frac{14}{12}}[/tex]

[tex]t = \frac{\ln{\frac{14}{12}}}{0.011}[/tex]

[tex]t = 14[/tex]

The fish population will reach 14 million after 14 years.

Item d:

At the end of this answer, the sketch is given.

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