2. An economist reports that 576 out of a sample of 1,200 middle-income American households participate in the stock market. A confidence interval of [0.468, 0.492] was calculated. What confidence level was used in this calculation

Answer:

Hello,

19

Step-by-step explanation:

2 methodes:

1)

[tex]y=-4x^2+20x-6\\\\=-4(x^2-5x)-6\\\\=-4(x^2-2*\dfrac{5}{2}*x+\dfrac{25}{4} ) +25-6\\\\=-4(x-\frac{5}{2} )^2+19\\\\Maximum\ =19 \ if\ x=\dfrac{5}{2} \\[/tex]

2)

y'=-8x+20=0 ==> x=20/8=5/2

and y=-4*(5/2)²+20*5/2-6=-25+50-6=19

finding maximums/minimums in quadratic equations:

The maximum value is 19

We want to find the maximum value of:

y = -4z^2+20z-6

Here, you can see that we have a quadratic equation with a negative leading coefficient.

This means that the arms of the graph will go downwards. From this, we can conclude that the maximum will the at the vertex (the highest point).

Remember that for a general equation like:

y = a*x^2 + b*x + c

The x-value of the vertex is:

x = -b/(2a)

(you can see that the variable is a different letter, that does not matter, is just notation)

Then for our equation:

y = -4z^2+20z-6

The z-value of the vertex is:

z = -20/(2*-4) = -20/-8 = 5/2

Then the maximum of the equation:

y = -4z^2+20z-6

is that equation evaluated in z = 5/2

So we get:

y = -4*(5/2)^2 + 20*(5/2) - 6  = 19

The maximum value is 19

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Answer:

Quartic cause highest degree is 4

Answer:

Prove:

Using 1

n³+2n = (1)³+2(1) = 1+2= 3 ---> 3/3= 1 ✔

Using 2

n³+2n = (2)³+2(2)= 8+4=12 --> 12/3=4✔

Using 3

n³+2n= (3)³+2(3)= 27+6= 33 --> 33/3=11✔

So it is proven that n³+2n is divisible by 3 for every positive integer.

I hope this helps

if u have question let me know in comments

Answer:

Solution : ( - 5, 5π / 4 )

Step-by-step explanation:

There are four cases to consider here, the first two with respect to r > 0, the second two with respect to r < 0. r is the directed distance from the pole, and theta is the directed angle from the positive x - axis. Let's start by listing coordinates when r is positive. r here is 5 units from the positive x - axis.

( 5, θ ) theta here is between 30 and 60 degrees, so we can say it's about 45 degrees.

( 5, θ ) theta here is the remaining negative side of 360 - 45 = 315. That would make it - 315.

And when r is negative ( r < 0 ),

( - 5, θ ) now the point is going to lie on the ray pointing in the opposite direction of the terminal side of theta. This will be 45 degrees more than 180, or 180 + 45 = 225 degrees.

Right away we know that ( - 5, 225° ) is our solution, we don't have to consider the second case. Converting 225 to radians in terms of π will be 5π / 4 radians, giving us a solution of ( - 5, 5π / 4 ) or option b.

Answer:

The total number of branches = total possibilities = the denominator of a probability.

So the second choice is correct.

Let me know if this helps!

Answer:

Step-by-step explanation: answer B (the denominator of a probability)

Answer:

Step-by-step explanation:

Hey there!

The range is the possible y values, so the range of this graph would be all real numbers less than or equal to -5.

Let me know if this helps :)

Answer:

24

Step-by-step explanation:

For ABCD the three longest are:

60,40,30

60 to 40 is 20

40 to 30 is 10

so each time it's decreasing by 1/2

For EFGH the two shortest are:

6 and 12

12 to 6 is 1/2

Assuming there is a pattern

it logically would be 24

as 12(2)=24

Answer:

Algebra deals with knowing the value of unknown variables and functional relationships, while trigonometry touches on triangles, sides and angles and the relationship between them.

Algebra is more on polynomial equations, x and y while trigonometry more on sine, cosine, tangent, and degrees.

Trigonometry is much more complicated than algebra but algebra has its uses in our daily lives, be it calculating distance from point to another or determining the volume of milk in a milk container.

Step-by-step explanation:

Answer:

Although both Algebra II and Trigonometry involve solving mathematical problems, Algebra II focuses on solving equations and inequalities while Trigonometry is the study of triangles and how sides are connected to angles.

hope this answer helps u

pls mark as brainliest .-.

Answer:

Step-by-step explanation:

[tex]\left[\begin{array}{ccc}x_{1} &x_{2} &x_{3} \\y_{1} &y_{2} &y_{3} \end{array}\right][/tex]  ---------> [tex]\left[\begin{array}{ccc}-x_{1} &-x_{2} &-x_{3} \\y_{1} &y_{2} &y_{3} \end{array}\right][/tex]

[tex]\left[\begin{array}{ccc}-3&-6&-3\\-3&3&3\end{array}\right][/tex]

9514 1404 393

Answer:

  3/11 were left

Step-by-step explanation:

A packet of oranges is 11/11. Subtracting 4/11 +4/11 = 8/11 from that leaves ...

  11/11 -8/11 = (11 -8)/11 = 3/11

3 elevenths were left.

Answer:

Answer is 5√6 ( none of the objectives )

Step-by-step explanation:

[tex] \sqrt{10} \times \sqrt{15} \\ = \sqrt{150} \\ = \sqrt{25 \times 6} \\ = \sqrt{25} \times \sqrt{6} \\ = 5 \times \sqrt{6} \\ = 5 \sqrt{6} [/tex]

Answer:

The coefficient is 6

Step-by-step explanation:

The coefficient is the number in front of the variable

The variable is x

The coefficient is 6

Answer:

6

Step-by-step explanation: The coefficient of this would be the real number that is in front of a variable that is not a variable like x, and that number is 6. So, the coefficient of 6x is 6.

The first answer of the missing blank is 4/5.

The second answer of the missing blank is 2.

The third answer of the missing blank is 25.

*For all of these solutions, I will be using the common rules for logarithms.*

Solution for the first question:

Log9^4/5 must equal log9^4-log9^5, or it could also equal the more proper version, which is simplified: 2log9^2-log9^5.

Solution for the second question:

Log3^22 must equal log3^11+log3^2, if you break it down.

Solution for the third question:

Log9^25 must equal 2log9^5 because it will be like this when simplifying it:

log9^25=2log9^5

log9^5²=2log9^5

2log9^5=2log9^5

These are all of the step-by-step procedures for all three of these given questions. Anyways, I hope that this helped you!

Answer: [tex]n(t) = 110000(0.35)^t[/tex]

Step-by-step explanation:

Given: Rate of of all aluminum cans distributed will be recycled each year. = 35%

= 0.35

Total cans distributed =  110,000

Now , the number of cans recycled in 1 year = 110,000 ×0.35

The number of cans recycled in 2 years   = 110,000 ×0.35 ×0.35  = 110,000 ×(0.35)²

..so on

The number of cans recycled in t years   = [tex]110000(0.35)^t[/tex]

Let n(t) be the number still in use after time t, in years:

Then, [tex]n(t) = 110000(0.35)^t[/tex]

Answer:

C

Step-by-step explanation:

Answer:

C: 512 = 2w2

Step-by-step explanation:

on edge

Answer:

256 outcomes.

Step-by-step explanation:

Each time you flip the coin you have two possible outcomes, it can either come up with heads or tails.

You're going to flip the coin eight times so the first time you can have 2 possible outcomes, the second time you have 2 possible outcomes, the third time you have 2 possible outcomes, etc.

Since you are going to do this eight times you are going to multiply each of the outcomes, so you will have:

Possible outcomes = 2×2×2×2×2×2×2×2= 256

Thus, there are 256 different outcomes in total.

Answer:

5/36 ; 1/12 ; 2/9 ; yes

Step-by-step explanation:

Given the following :

Roll of two fair dice : green and red

Probability = (number of required outcomes / number of total possible outcomes)

(a) What is the probability of getting a sum of 6?

Number of required outcomes = 5

P(sum of 6) = 5/36

b.) What is the probability of getting a sum of 10?

Number of required outcomes = 3

P(sum of 10) = 3 / 36 = 1/12

c.) What is the probability of getting a sum of 6 or 10?

P(getting a sum of 6) + P(getting a sum of 10)

(5/36) + (1/12) = (5 + 3) / 36

= 8/36 = 2/9

The events are mutually exclusive because each event cannot occur at the same time.

Jane is given a $100 gift to start and saves $35 a month from her allowance.

   After 1 month, Jane has saved

   After 2 months, Jane has saved

   After three months, Jane has saved

   and so on

In general, after x months Jane has saved

This means that it makes sense to represent the relationship between the amount saved and the number of months with one constant rate (in this case the constant rate is 35). It makes sense because the amount of money increases by $35 each month. Since the amount of increase is constant, we get constant rate. Also the initial amount is known ($100), so there is a possibility to write the equation of linear function representing this situation.

Step-by-step explanation:

Answer:

k(x) = 6x

Step-by-step explanation:

A function shows the relationship between two or more variables. It shows the relationship between an independent and a dependent variable.

Given that the amount of water being poured into the tube is given by f(x) = 12x, where x is in minutes and the amount of water draining out of the tub is given by the function g( x )=6x. The amount of water remaining in the tube after x minutes is gotten by finding the difference between the amount of water entering the tube and the amount leaving the tube after x minutes. If k is the function representing the amount of water in the tube after x minutes, it is given by:

k(x) = f(x) - g(x)

k(x) = 12x - 6x

k(x) = 6x

Answer:

Calculated value of F = 0.0535

The critical region is F >F ₀.₀₅ (6,21) = 2.575

Reject H0

Step-by-step explanation:

1. Null hypothesis

H0: µ Nitrogen = µ Phosphorus = µ Both = µ Neither

2. Alternative hypothesis

H1: Not all means are equal.

3. The degrees of freedom for the numerator of the F-ratio = k- 1= 7-1=6

4.The degrees of freedom for the denominator of the F-ratio = n-k= 28-7

= 21

5. The significance level is set at α-0.05

The critical region is F >F ₀.₀₅ (6,21) = 2.575

The test statistic to use is

F = sb²/ sw²

Which if H0 is true has an F distribution with v₁=k-1 and v₂= n-k degrees of freedom

Correction Factor = CF = Tj²/n = (410)²/28= 6003.57

Total SS ∑∑X²- C. F = 6108- 6003.57= 104.43

Between SS ∑T²j/r - C.F = 42036/ 7 - 6003.57 =  1.57286

Within SS = Total SS - Between SS= 104.43- 1.573= 102.86

The Analysis of Variance Table is

Source Of                 Sum of          Mean              Computed

Variation          d.f     Squares       Squares               F

Between

Samples          6         1.57286       0.2621               0.0535

Within

Samples         21       102.86           4.898

Calculated value of F = 0.0535

Pvalue = 2.575

Since it is smaller than 5 % reject H0.

Answer:

It is not symmetric, but skewed left. Data appears more to be on the left side.

Step-by-step explanation:

The smallest value is 24 and the largest is 43 . The difference between these two values is 19 which can be divided into into intervals of 4.

19/4= 4.75 It will be rounded to 5.

The class interval can of 5. Starting from 20 we get class intervals and frequency distribution as

Class Intervals          Data                                        Frequency      

20-24                           24                                              1

25- 29                           28,                                            1

30-34                            34,30,34,30,33,31,                   6

35-39                         35,36,39,37,35,36,39,37,           14

                                         38,39,35,35,36,36

40-44                                43,40,41                                3

The class intervals are inclusive of both upper and lower limits. The difference between the lower limits of two consecutive classes or upper limits of two consecutive classes must be the same.

As we see the difference here is that of 5 between the two upper or lower limits of consecutive classes.

The histogram is attached which shows the class intervals along x- axis and data frequency along y- axis.

Answer:

192 [tex]ft^2[/tex]

Step-by-step explanation:

Given that

Volume of spherical sculpture = 256 ft³

[tex]\pi[/tex] is used as 3.

To find:

Surface area of sculpture = ?

Solution:

First of all, let us learn about the formula for Volume and Surface Area of Sphere:

1. [tex]Volume =\frac{4}{3}\pi r^3[/tex]

2. [tex]Surface\ Area = 4\pi r^2[/tex]

Given volume is 256 ft³.

[tex]256 = \dfrac{4}{3}\pi r^3\\\Rightarrow 256 = \dfrac{4}{3}\times 3 r^3\\\Rightarrow 256 = 4 r^3\\\Rightarrow r^3=64\\\Rightarrow \bold{r = 4\ ft}[/tex]

Now, let us put r = 4 in the formula of Surface Area to find the value of Surface Area:

[tex]Surface\ Area = 4\pi 4^2 = 4 \times 3 \times 16 = \bold{192\ ft^2}[/tex]

So, approximate surface area of sculpture is 192 [tex]ft^2[/tex].

Answer:

192

Step-by-step explanation:

Answer:

Step-by-step explanation:

The gross profit rate of the company is expressed as [tex]P = \dfrac{S - C}{S}[/tex] where C is the cost of goods sold and S is the net sales. If the net sales S = $1,200,000, and gross profit ratio is 0.20, the cost of goods sold will be expressed as shown;

Making C the subject of the formula from the expression given.

[tex]P = \dfrac{S - C}{S}\\\\cross \ multiply\\\\SP = S-C\\\-C = SP-S\\\\C = S -SP\\[/tex]

Substituting P = 0.20 and S = $1,200,000 into the resulting equation, we will have;

[tex]C = $1,2000,000 - 0.2($1,2000,000)\\C = $1,2000,000- 240,000\\ C = 960,000[/tex]

Hence the cost of goods sold is $960,000

Answer:

Ben and Susan will be 340 miles apart

Step by Step Solution

Step 1: We plot the problem on a graph to visualize the problem

Step 2: We notice that the problem creates a right triangle with the distance Ben and Susan travel as the legs of the right triangle

Step 3: We can use the Pythagorean Theorem: a²+b²=c² to solve the distance between Ben and Susan

Step 4: We enter the numbers into the formula

a² + b² = c²

300² + 160² = c²

90000 + 25600 = c²

115600 = c² *square root both sides

c = 340

Therefore Ben and Susan are 340 miles apart

Ben and Susan  are apart by 340 miles.

After drawing diagram according to question, it is observed that a right angle triangle is formed.

The distance between Ben and Susan is represented by Hypotenuse of right angle triangle shown in attached diagram.

Applying Pythagoras theorem in right triangle shown in attached diagram.

  Distance between Ben and Susan =  

                   [tex]\sqrt{(300)^{2}+(160)^{2} } =\sqrt{90000+25600}=\sqrt{115600} =340 miles.[/tex]

Therefore, Ben and Susan  are apart by 340 miles.

Learn more:

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Answer:

425 or 937

Step-by-step explanation:

First, I listed out all the possible numbers for the first digits, namely, the squares under 10.

1*1=1

2*2=4

3*3=9

Since all the digits have to be different, the first digit cannot be 1 because 1 squared is 1. So that leaves us 4 and 9 to work with, which I tried out one at a time.

Starting with 4:

2 squared is 4.

42

2 times 2 plus 1 equals 5.

425

Starting with 9:

3 squared is 9.

93

2 times 3 plus 1 equals 7.

937

So here we have two numbers that both work and meet the requirements (unless I understood the problem wrong at the part where it says "...the second digit in the 3rd digit on one more than twice the second digit")!

I hope this helped! :D

no bc it is not no no no no no no no

Answer:

13

5 - -8

When you subtract a negative number it changes to an addition so 5- -8 becomes 5 + 8 which equals 13.

Answer:

8

Step-by-step explanation:

f(x)=x²+4 ( find quadratic equation: given vertex)

g(x)=x+2  ( find linear equation : given 2 points)

(f-g)(-2)

(x²+4-x-2)of (-2)

x²-x+2  now find (f-g)(-2)

-2²-(-2)+2=4+2+2=8

Answer:

Step-by-step explanation:

For b

To find side b we use the sine rule

a = 7

A = 23°

B = 32°

b = ?

Substitute the values into the above formula

That's

Divide both sides by sin 23°

b = 9.493573

To find side c we use sine rule

C = 125°

So we have

Divide both sides by sin 23°

c = 14.67521

Hope this helps you

Answer:

Part a ) The degrees of freedom for the given two sample non-pooled t test is 24

Part b ) The degrees of freedom for the given two sample non-pooled t test is 30

Part c ) The degrees of freedom for the given two sample non-pooled t test is 30

Part d ) The degrees of freedom for the given two sample non-pooled t test is 25

Step-by-step explanation:

Degrees of freedom for a non-pooled two sample t-test is given by;

Δf = {[ s₁²/m + s₂²/n ]²} / {[( s₁²/m)²/m-1] + [(s₂²/n)²/n-1]}

Now given the information;

a) :- m = 12, n = 15, s₁ = 4.0, s₂ = 6.0

we substitute

Δf =  {[ 4²/12 + 6²/15 ]²} / {[( 4²/12)²/12-1] + [(6²/15)²/15-1]}

Δf  = 30184 / 1241

Δf  = 24.3223 ≈ 24 (down to the nearest whole number)

b) :- m = 12, n = 21, s₁ = 4.0, s₂ = 6.0

we substitute using same formula

Δf = {[ s₁²/m + s₂²/n ]²} / {[( s₁²/m)²/m-1] + [(s₂²/n)²/n-1]}

Δf = {[ 4²/12 + 6²/21 ]²} / {[( 4²/12)²/12-1] + [(6²/21)²/21-1]}

Δf = 56320 / 1871

Δf = 30.1015 ≈ 30 (down to the nearest whole number)

c) :- m = 12, n = 21, s₁ = 3.0, s₂ = 6.0

we substitute using same formula

Δf = {[ s₁²/m + s₂²/n ]²} / {[( s₁²/m)²/m-1] + [(s₂²/n)²/n-1]}

Δf = {[ 3²/12 + 6²/21 ]²} / {[( 3²/12)²/12-1] + [(6²/21)²/21-1]}

Δf = 29095 / 949

Δf = 30.6585 ≈ 30 (down to the nearest whole number)

d) :- m = 10, n = 24, s₁ = 4.0, s₂ = 6.0

we substitute using same formula

Δf = {[ s₁²/m + s₂²/n ]²} / {[( s₁²/m)²/m-1] + [(s₂²/n)²/n-1]}

Δf = {[ 4²/10 + 6²/24 ]²} / {[( 4²/10)²/10-1] + [(6²/24)²/24-1]}

Δf = 1044 / 41  

Δf = 25.4634 ≈ 25 (down to the nearest whole number).