At a large Midwestern university, a simple random sample of 100 entering freshmen in 1993 found that 20 of the sampled freshmen finished in the bottom third of their high school class. Admission standards at the university were tightened in 1995. In 1997, a simple random sample of 100 entering freshmen found that only 10 finished in the bottom third of their high school class. Let p 1 and p 2 be the proportions of all entering freshmen in 1993 and 1997, respectively, who graduated in the bottom third of their high school class. What is a 90% plus four confidence interval for p 1 – p 2?

Answer:

[tex]\frac{4}{52} \times \frac{4}{51} = \frac{16}{2652} = 0.00603 = 0.603\%[/tex]

Step-by-step explanation:

There are 52 cards in a standard deck, and there are 4 suits for each card. Therefore there are 4 twos and 4 tens.

At first we have 52 cards to choose from, and we need to get 1 of the 4 twos, therefore the probability is just

[tex]\frac{4}{52}[/tex]

After we've chosen a two, we need to choose one of the 4 tens. But remember that we're now choosing out of a deck of just 51 cards, since one card was removed. Therefore the probability is

[tex]\frac{4}{51}[/tex]

Now to get the total probability we need to multiply the two probabilities together

[tex]\frac{4}{52} \times \frac{4}{51} = \frac{16}{2652} = 0.00603 = 0.603\%[/tex]

Answer: 18π

okokok gg

Step-by-step explanation:

Here angle is given in degree.We have convert it into radian.

[tex] {1}^{\circ} =( { \frac{\pi}{180} } )^{c} \\ \therefore \: {80}^{\circ} = ( \frac{80\pi}{180} ) ^{c} = {( \frac{4\pi}{9} })^{c} \: = \theta ^{c} [/tex]

Area of green shaded regions = A

[tex] \sf \: A = \frac{1}{2} { {r}^{2} }{ { \theta}^{ c} } \\ = \frac{1}{2} \times {9}^{2} \times \frac{4\pi}{9} \\ = 18\pi \: {cm}^{2} [/tex]

Answer:

rectangle

Step-by-step explanation:

Perimeter of 20 feet

rectangle (square is technically a rectangle):

sides 5 and 5

5*5 = 25ft²

Circle:

20/(2π) = 3.18309...

3.1809...²π = 31.831ft²

Max area of rectangle (i.e. square) has a smaller area than a circle.

Step-by-step explanation:

before Tax

Coast = 888

in 2ND Item = $21

• 888/21

= $42.28

9514 1404 393

Answer:

Step-by-step explanation:

For continuous compounding the "rule of 69" applies. That is the doubling time can be found from ...

  t = 69.3147/r . . . . where r is the interest rate in percent.

Here, r=2, so ...

  t = 69.3147/2 = 34.6574 . . . years

That's 34 years and 240 days.

Here we want to solve a question involving fractions, we will find that:

3/4 gallon fils the complete bin.

Ok, so we know that 1/2 gallon of water, fills 2/3 of the bin.

We want to find the total amount of water that would fill the entire bin.

So we could write an equation like:

amount of water =  amount of the bin that it fills.

Then, using the above information, we have:

1/2 gal  = 2/3 of a bin

Now we want to get at 1 on the right side, this would mean "1 bin"

Then we multiply both sides by (3/2)

(3/2)*(1/2) gal = (3/2)*(2/3) of a bin

3/4 gal = 1 bin

From this, we can conclude that (3/4) gallons of water would fill the complete bin.

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

https://brainly.com/question/4837080

x = 0,75 gallons      or       x  = 3/4   gallons      The volume of the bin

The volume of the bin is: In terms of a fraction

1  =  3/3      or any unitary fraction   5/5    7/7    9/9

We will take 3/3 since we have the information that 2/3 of the volume of the bin was filled with 2/3 of a gallon

If  2/3 of the volume of the bin was filled with 1/2 gallon then we make a rule of three according to:

If     0,5  gal.         fill    2/3 of the volume of the bin   then

          x   gal         fill     3/3  ( the volume of the bin)

solving

0,5 (gal) * 3/3    =   (2/3)*x       ( The equation)

0,5*3 = 2*x

x  =  (0,5*3)/2

x = 0,75 gallons      or       x  = 3/4   gallons

Answer:

Step-by-step explanation:

Let length = y    width = x

y = 3x + 2

Perimeter = Sum of all sides (or sum of both lengths and both widths)

2y + 2x

2(3x + 2) + 2x

6x + 4 + 2x

8x + 4

Answer:  [tex]9\sqrt{3}[/tex]

==========================================================

Explanation:

For any 30-60-90 triangle, the short leg is always half the hypotenuse.

This makes the short leg to be 18/2 = 9 units long.

We then multiply this by [tex]\sqrt{3}[/tex] to get the length of the long leg.

[tex]\text{long leg} = (\text{short leg})*\sqrt{3}\\\text{long leg} =9\sqrt{3}[/tex]

Or you could use the pythagorean theorem to solve [tex]x^2+9^2 = 18^2[/tex] and you should get [tex]x = \sqrt{243} = 9\sqrt{3}[/tex]

Answer:

Write an algorithm to add two numbers entered by user. Step 2: Declare variables num1, num2 and sum. Step 3: Read values num1 and num2. Step 4: Add num1 and num2 and assign the result to sum.

Answer:

Step-by-step explanation:

4x*sqrt(2x-x²)=2x-1

sqrt(2x-x²)=(2x-1)/4x

2x-x² = 4x^2 -4x + 1 /(16x^2)

32x^3 - 16x^4 =  4x^2 -4x + 1

[tex]-16x^4+32x^3-4x^2+4x-1=0\\[/tex]

[tex]x = 1.92887[/tex]

Answer:

Kindly check explanation

Step-by-step explanation:

H0 : μ = 15.7

H1 : μ < 15.7

This is a one sample t test :

Test statistic = (xbar - μ) ÷ (s/√(n))

n = sample size = 33

Using calculator :

The sample mean, xbar = 15.41

The sample standard deviation, s = 0.419

Test statistic = (15.41 - 15.70) ÷ (0.419/√(33))

Test statistic = - 3.976

Using the Pvalue calculator :

Degree of freedom, df = n - 1 ; 33 - 1 = 32

Pvalue(-3.976, 32) = 0.000187

Decison region :

Reject H0 if Pvalue < α

Since Pvalue < α ; we reject H0

There is significant evidence to conclude that the true average height of the seedlings treated with an extract from Vinca minor roots is less than 15.7 cm.

Answer:

To maximize the monthly rental profit, 90 units should be rented out.

The maximum monthly profit realizable is $38,200.

Step-by-step explanation:

Vertex of a quadratic function:

Suppose we have a quadratic function in the following format:

[tex]f(x) = ax^{2} + bx + c[/tex]

It's vertex is the point [tex](x_{v}, y_{v})[/tex]

In which

[tex]x_{v} = -\frac{b}{2a}[/tex]

[tex]y_{v} = -\frac{\Delta}{4a}[/tex]

Where

[tex]\Delta = b^2-4ac[/tex]

If a<0, the vertex is a maximum point, that is, the maximum value happens at [tex]x_{v}[/tex], and it's value is [tex]y_{v}[/tex].

In this question:

Quadratic equation with [tex]a = -12, b = 2160, c = -59000[/tex]

To maximize the monthly rental profit, how many units should be rented out?

This is the x-value of the vertex, so:

[tex]x_{v} = -\frac{b}{2a} = -\frac{2160}{2(-12)} = \frac{2160}{24} = 90[/tex]

To maximize the monthly rental profit, 90 units should be rented out.

What is the maximum monthly profit realizable?

This is p(90). So

[tex]p(90) = -12(90)^2 + 2160(90) - 59000 = 38200[/tex]

The maximum monthly profit realizable is $38,200.

Answer:

it is

[(2+3+4+6)-2*4]:4=1.75

I THINK

Step-by-step explanation:

Answer:

Should be (C). Can't verify.

545

ED2021

Answer:

The third choice down

Step-by-step explanation:

|-2x| = 4

There are two solutions, one positive and one negative

-2x = 4  and -2x = -4

Divide by -2

-2x/-2 = 4/-2    -2x/-2 = -4/-2

x = -2   and x = 2

Answer:

"A"

Step-by-step explanation:

a+b >c

a+c>b

b+c>a

~~~~~~~~~~~~

A. T,T,T

B. T,T,F

C. T,F,T

Answer:

The answer is "36.14%"

Step-by-step explanation:

The complete question is given in the attached file please find it.

[tex]\mu =41\\\\\sigma= 4\\\\P(42<\bar{x}<48)= p(\bar{x}<48)-p(\bar{x}<42)\\\\Z =\frac{(42-41)}{4} = \frac{1}{4} =0.25\\\\Z =\frac{(48-41)}{4} = \frac{7}{4} = 1.75\\\\[/tex]

Using z-table to find the value.

[tex]\to P(41<\bar{x}<48) = 0.9599- 0.5987 = 0.3614\times 100= 36.14\%[/tex]

This means that between 42 and 48 months, 36.14 % of scanners could be predicted will break down.

Answer:

can you say again please

Answer:

The 95% confidence interval for the true difference between the mean times on this course for teams of Siberian Huskies and teams of other breeds of sled dogs is (-0.8276, 0.2276).

Step-by-step explanation:

Before building the confidence interval, we need to understand the central limit theorem and subtraction of normal variables.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.  

Subtraction between normal variables:

When two normal variables are subtracted, the mean is the difference of the means, while the standard deviation is the square root of the sum of the variances.

Siberian Huskies:

Sample of 47, mean of 5.2 minutes, standard deviation of 1.4. So

[tex]\mu_1 = 5.2[/tex]

[tex]s_1 = \frac{1.4}{\sqrt{47}} = 0.2042[/tex]

Others:

Sample of 39, mean of 5.5 minutes, standard deviation of 1.1. So

[tex]\mu_2 = 5.5[/tex]

[tex]s_2 = \frac{1.1}{\sqrt{39}} = 0.1761[/tex]

Distribution of the difference:

[tex]\mu = \mu_1 - \mu_2 = 5.2 - 5.5 = -0.3[/tex]

[tex]s = \sqrt{s_1^2+s_2^2} = \sqrt{0.2042^2+0.1761^2} = 0.2692[/tex]

Confidence interval:

We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:

[tex]\alpha = \frac{1 - 0.95}{2} = 0.025[/tex]

Now, we have to find z in the Z-table as such z has a p-value of [tex]1 - \alpha[/tex].

That is z with a pvalue of [tex]1 - 0.025 = 0.975[/tex], so Z = 1.96.

Now, find the margin of error M as such

[tex]M = zs[/tex]

In which s is the standard error. So

[tex]M = 1.96(0.2692) = 0.5276[/tex]

The lower end of the interval is the sample mean subtracted by M. So it is -0.3 - 0.5276 = -0.8276.

The upper end of the interval is the sample mean added to M. So it is -0.3 + 0.5276 = 0.2276

The 95% confidence interval for the true difference between the mean times on this course for teams of Siberian Huskies and teams of other breeds of sled dogs is (-0.8276, 0.2276).

First check the characteristic solution: the characteristic equation for this DE is

r ² - 3r + 2 = (r - 2) (r - 1) = 0

with roots r = 2 and r = 1, so the characteristic solution is

y (char.) = C₁ exp(2x) + C₂ exp(x)

For the ansatz particular solution, we might first try

y (part.) = (ax + b) + (cx + d) exp(x) + e exp(3x)

where ax + b corresponds to the 2x term on the right side, (cx + d) exp(x) corresponds to (1 + 2x) exp(x), and e exp(3x) corresponds to 4 exp(3x).

However, exp(x) is already accounted for in the characteristic solution, we multiply the second group by x :

y (part.) = (ax + b) + (cx ² + dx) exp(x) + e exp(3x)

Now take the derivatives of y (part.), substitute them into the DE, and solve for the coefficients.

y' (part.) = a + (2cx + d) exp(x) + (cx ² + dx) exp(x) + 3e exp(3x)

… = a + (cx ² + (2c + d)x + d) exp(x) + 3e exp(3x)

y'' (part.) = (2cx + 2c + d) exp(x) + (cx ² + (2c + d)x + d) exp(x) + 9e exp(3x)

… = (cx ² + (4c + d)x + 2c + 2d) exp(x) + 9e exp(3x)

Substituting every relevant expression and simplifying reduces the equation to

(cx ² + (4c + d)x + 2c + 2d) exp(x) + 9e exp(3x)

… - 3 [a + (cx ² + (2c + d)x + d) exp(x) + 3e exp(3x)]

… +2 [(ax + b) + (cx ² + dx) exp(x) + e exp(3x)]

= 2x + (1 + 2x) exp(x) + 4 exp(3x)

… … …

2ax - 3a + 2b + (-2cx + 2c - d) exp(x) + 2e exp(3x)

= 2x + (1 + 2x) exp(x) + 4 exp(3x)

Then, equating coefficients of corresponding terms on both sides, we have the system of equations,

x : 2a = 2

1 : -3a + 2b = 0

exp(x) : 2c - d = 1

x exp(x) : -2c = 2

exp(3x) : 2e = 4

Solving the system gives

a = 1, b = 3/2, c = -1, d = -3, e = 2

Then the general solution to the DE is

y(x) = C₁ exp(2x) + C₂ exp(x) + x + 3/2 - (x ² + 3x) exp(x) + 2 exp(3x)

Answer:

a) Yes , Cause The Expected Returns of stock A is Higher than that of B

b) No,  Cause The Expected Returns of stock B is Lower than that of A

Step-by-step explanation:

From the question we are told that:

Beta A \beta A=1.4

Beta B \beta B=0.8

Stock 1 Growth rates of earnings and dividends G_1=10\%

Stock 2 Growth rates of earnings and dividends  G_2=5\%

Stock 1  Dividend yields D_1=5\%

Stock 2 Dividend yields  D_2=7\%

Generally the equation for Expected Returns is mathematically given by

Expected Returns =Growth rates+Dividend yields

For Stock 1

Expected\ Returns =G_1+D_1

Expected\ Returns =5%+10%

Expected\ Returns =15%

For Stock 2

Expected\ Returns =G_2+D_2

Expected\ Returns =7%+5%

Expected\ Returns =12%

Therefore

a) Yes , Cause The Expected Returns of stock A is Higher than that of B

b) No,  Cause The Expected Returns of stock B is Lower than that of A

Answer:

It's impossible because the figure is greater than 10

Step-by-step explanation:

[tex]{ \boxed{ \bf{antilog \: of \: x = \frac{x}{ log} = {10}^{x} }}}[/tex]

Therefore:

[tex]{ \sf{anti(547.840) = {10}^{547.840} }} \\ { \tt{ \red{math \: error \: !}}}[/tex]

Answer:

8.7 feet

Step-by-step explanation:

Use the square area formula, a = s², where s is the side length of the square.

Plug in the area and solve for s:

a = s²

75 = s²

√75 = s

8.7 = s

So, to the nearest tenth of a foot, the height is 8.7 feet

Answer:

C.    AA

Step-by-step explanation:

Since m<Y = 27°, then m<W = 27°.

We have two angles of one triangle (A and B) congruent to two angles of the other triangle (W and X).

Answer: C.   AA

Answer:

10d

Step-by-step explanation:

5d on 1 side, double it to get 10d cuz from Point O to Point D, y increases from 0 to 5d and since the triangles are congruent, we can add another 5d (or in total 10d).

Answer:

chocolate chips are $2.00 per pound.

nd walnuts must be $3.50 per pound.

Step-by-step explanation:

Let x be the price of walnuts and y the price of chocolate chips.

2x + 5y = 17 (i)

8x + 3y = 34 (ii)

Multiply (i) by 4 to get

8x + 20y = 68

Subtract (ii) to get

 17y = 34

Dividing by 17, we see that chocolate chips are $2.00 per pound.

Substituting y=2 in (i) or (ii), walnuts must be $3.50 per pound.

Answer:

Step-by-step explanation:

In order to find out how long it takes for the rocket to hit the ground, we only need set that position equation equal to 0 (that's how high something is off the ground when it is sitting ON the ground) and factor to solve for t:

[tex]0=-4.9t^2+112t+395[/tex]

Factor that however you are factoring in class to get

t = -3.1 seconds and t = 25.9 seconds.

Since time can NEVER be negative, it takes the rocket approximately 26 seconds to hit the ground.

Answer:  [tex]8\sqrt{2}[/tex]

==========================================================

Work Shown:

Focus entirely on triangle ABD (or on triangle BCD; both are identical)

The two legs of this triangle are AB = 8 and AD = 8. The hypotenuse is unknown, so we'll say BD = x.

Apply the pythagorean theorem.

[tex]a^2 + b^2 = c^2\\\\c = \sqrt{a^2 + b^2}\\\\x = \sqrt{8^2 + 8^2}\\\\x = \sqrt{2*8^2}\\\\x = \sqrt{8^2*2}\\\\x = \sqrt{8^2}*\sqrt{2}\\\\x = 8\sqrt{2}\\\\[/tex]

So that's why the diagonal BD is exactly [tex]8\sqrt{2}\\\\[/tex] units long

Side note: [tex]8\sqrt{2} \approx 11.3137[/tex]

Answer:

Confidence Interval

Lower Limit = $4,233.3

Upper Limit = $4,766.7

With 95% confidence, the mean profit per customer that SoftBus can expect to obtain is between $4,233.30 and $4,766.7 based on the given sample data.

Step-by-step explanation:

The z-score of 95% = 1.96

             Profit         Mean      Square Root

                          Difference    of MD

P1        $5,000       $500        $250,000

P2         4,500          0              0

P3         4,000       -500         $250,000

Total $13,500                        $500,000

Mean $4,500 ($13,500/3)    $166,667 ($500,000/3)

Standard Deviation = Square root of $166,667 = 408.2

Margin of error = (z-score * standard deviation)/n

= (1.96 * 408.2)/3

= 266.7

= $266.7

Confidence Interval = Sample mean +/- Margin of error

= $4,500 +/- 266.7

Lower Limit = $4,233.3 ($4,500 - $266.7)

Upper Limit = $4,766.7 ($4,500 + $266.7)