You are an assistant director of the alumni association at a local university. You attend a presentation given by the university’s research director and one of the topics discussed is what undergraduates do after they matriculate. More specifically, you learn that in the year 2018, a random sample of 216 undergraduates was surveyed and 54 of them (25%) decided to continue school to pursue another degree, and that was up two percentage points from the prior year. The Dean of the College of Business asks the research director if that is a statistically significant increase. The research director says she isn’t sure, but she will have her analyst follow up. You notice in the footnotes of the presentation the sample size in the year of 2017 was 200 undergraduates, and that 46 of them continued their education to pursue another degree.

There is a short break in the meeting. Take this opportunity to answer the dean’s question using a confidence interval for the difference between the proportions of students who continued their education in 2018 and 2017. (Use 95% confidence level and note that the university has about 10,000 undergraduate students).

Answer:

8

Step-by-step explanation:

Math Word Problem: Twice one number added to another number is 18. Four times the first number minus the other number is 12. Find the number.?

Let the two numbers be x and y

As per statement twice one number added to another number is 18.

2x + y = 18

y = 18 - 2x…Eq..1

Four times the first number minus the other number is 12.

4x - y = 12…Eq..2

Now substituting the value of y from Eq..1 to Eq..2

4x - y = 12

4x - (18 - 2x) = 12

4x - 18 + 2x = 12

4x + 2x = 12 + 18

6x = 30

x = 30 / 6

x = 5

Thus one number is 5. Now calculating the other number by putting the value of x in Eq. 1

y = 18 - 2x

y = 18 - 2×5

y = 18 - 10

y = 8

Other number is 8

Answer the two numbers are 5 and 8

Let us check the correctness of answer by putting the value of x and y in Eq. 1

y = 18 - 2x

8 = 18 - 2 × 5

8 = 18 - 10

8 = 8

Means answer is correct

Answer:

P [ X < 67 ] =  0,66,81      or    66,81 %

Step-by-step explanation:

We assume Normal Distribution  N ( μ ; σ )    N ( 76 ; 6 )

z score for 67 is :

z(s) =  (  X - μ  ) /σ

z(s) =  (  67 - 76 ) / 6

z(s) =  - 9 / 6

z(s) = - 1,5

with 1,5 we fnd n z-table area undr the curve  α = 0,6681

Then  P [ X < 67 ] =  0,66,81      or    66,81 %

Answer:

correct option is C)  2.8

Step-by-step explanation:

given data

string vibrates form =  8 loops

in water loop formed =  10 loops

solution

we consider  mass of stone = m

string length = l

frequency of tuning = f

volume = v

density of stone = [tex]\rho[/tex]

case (1)  

when 8 loop form with 2 adjacent node is [tex]\frac{\lambda }{2}[/tex]

so here

[tex]l = \frac{8 \lambda _1}{2}[/tex]      ..............1

[tex]l = 4 \lambda_1\\\\\lambda_1 = \frac{l}{4}[/tex]

and we know velocity is express as

velocity = frequency × wavelength   .....................2

[tex]\sqrt{\frac{Tension}{mass\ per\ unit \length }}[/tex]   =   f × [tex]\lambda_1[/tex]

here tension = mg

so

[tex]\sqrt{\frac{mg}{\mu}}[/tex]   =   f × [tex]\lambda_1[/tex]     ..........................3

and

case (2)  

when 8 loop form with 2 adjacent node is [tex]\frac{\lambda }{2}[/tex]

[tex]l = \frac{10 \lambda _1}{2}[/tex]      ..............4

[tex]l = 5 \lambda_1\\\\\lambda_1 = \frac{l}{5}[/tex]

when block is immersed

equilibrium  eq will be

Tenion + force of buoyancy = mg

T + v × [tex]\rho[/tex] × g = mg

and

T = v × [tex]\rho[/tex] - v × [tex]\rho[/tex] × g    

from equation 2

f × [tex]\lambda_2[/tex] = f  × [tex]\frac{1}{5}[/tex]  

[tex]\sqrt{\frac{v\rho _{stone} g - v\rho _{water} g}{\mu}} = f \times \frac{1}{5}[/tex]     .......................5

now we divide eq 5 by the eq 3

[tex]\sqrt{\frac{vg (\rho _{stone} - \rho _{water})}{\mu vg \times \rho _{stone}}} = \frac{fl}{5} \times \frac{4}{fl}[/tex]

solve irt we get

[tex]1 - \frac{\rho _{stone}}{\rho _{water}} = \frac{16}{25}[/tex]

so

relative density [tex]\frac{\rho _{stone}}{\rho _{water}} = \frac{25}{9}[/tex]

relative density = 2.78 ≈ 2.8

so correct option is C)  2.8

4) 2x-2y+3 > 0

although it is spelt "26" on the choices

Answer:

Find a common denominator on the right side of the equation

Step-by-step explanation:

The equation before the problem is

X² + b/a(x) + (b/2a)²= -c/a + b²/4a²

The next step in solving the above equation is to fibd tge common denominator on the right side of the equation.

X² + b/a(x) + (b/2a)²= -c/a + b²/4a²

X² + b/a(x) + (b/2a)²= -4ac/4a² + b²/4a²

X² + b/a(x) + (b/2a)²=( b²-4ac)/4a²

The right side of the equation now has a common denominator

The next step is to factorize the left side of the equation.

(X+b/2a)²= ( b²-4ac)/4a²

Squaring both sides

X+b/2a= √(b²-4ac)/√4a²

Final equation

X=( -b+√(b²-4ac))/2a

Or

X=( -b-√(b²-4ac))/2a

Answer:

Paula will travel 234 miles in 4.5 hours

Step-by-step explanation:

Step 1: We first find the speed Paula is going in hours, we divide 130 mile by 2.5 hours to get 52 miles per hour

Step 2: We multiple 52 miles per hour with 4.5 hours to get 234 miles

Therefore Paula will travel 234 miles in 4.5 hours

Step-by-step explanation:

or,[(√-x-1)+(√x+9)]^2=4^2

or,(√-x-1)^2+2√(-x-1)(x+9)+(√x+9)^2=16

or,-x-1+2√-x^2-10x-9 +x+9=16

or,2√-x^2-10x-9=8

or,√-x^2-10x-9=4

squaring on both sides

or,-x^2-10x-9=16

or,-x^2-10x=25

or,-x(x+10)=25

Either,

x=-25 or, x=15.

Answer:

a)  z (score) 1,53

b)  z ( score) - 1,96

c) 200 students

Step-by-step explanation:

Normal Distribution N ( 74;10)

a) From z-table, and for 6,3 %  ( 0,063 ) we find the z (score) 1,53

Note : 6,3 % or 0,063 is the area under the curve, the minimum score neded to get A

b) To fail   2,5 %  ( 0,025 ) from z-table  get - 1,96

c) If the group of  student who did not pass the course (5) correspond to 2,5 % then by simple rule of three

5                 2,5

x ?               100

x = 500/2,5

x = 200

Answer:

35 or 25

Step-by-step explanation:

Answer:

[tex]V(m) = (2 + 5m)^3[/tex]

Step-by-step explanation:

Given

Solid Shape = Cube

Edge = 2 feet

Increment = 5 feet per minute

Required

Determine volume as a function of minute

From the question, we have that the edge of the cube increases in a minute by 5 feet

This implies that,the edge will increase by 5m feet in m minutes;

Hence,

[tex]New\ Edge = 2 + 5m[/tex]

Volume of a cube is calculated as thus;

[tex]Volume = Edge^3[/tex]

Substitute 2 + 5m for Edge

[tex]Volume = (2 + 5m)^3[/tex]

Represent Volume as a function of m

[tex]V(m) = (2 + 5m)^3[/tex]

Answer:

Step-by-step explanation:

vector OA=a

vector OB=b

vector OX= λ vector OA=λa

vector OY=μ vector OB=μb

a.

1.vector BX=(vector OX-vector OB)=λa-b

ii. vector AY=(vector OY-vector OA)=μb-a

b.

5 vector BP=2 vector BX

5(vector OP-vector OB)=2 (vector OX-vector OB)

5(vector OP-b)=2(λa-b)

5 vector OP-5b=2λa-2b

5 vector OP=2λa-2b+5b

vector OP=1/5(2λa+3b)

ii

complete it.

Answer:

6.28 m

Step-by-step explanation:

If a wheel travels with one full revolution, it would have travelled the circumference's distance from it's starting point.

The circumference of a circle is [tex]2\pi r[/tex]

Let's assume [tex]\pi[/tex] is 3.14 and solve for the equation.

[tex]2\cdot3.14\cdot1\\6.28[/tex]

Hope this helped!

Answer:

Mean = 1.6

Variance = 0.84

Standard deviation = 0.916

Step-by-step explanation:

We are given the following probability distribution below;

            X                         P(X)              [tex]X \times P(X)[/tex]         [tex]X^{2} \times P(X)[/tex]

            0                          0.1                     0                        0

            1                           0.4                   0.4                     0.4

            2                          0.3                   0.6                     1.2

            3                          0.2                  0.6                    1.8      

         Total                                               1.6                    3.4    

Now, the mean of the probability distribution is given by;

         Mean, E(X) =  [tex]\sum X \times P(X)[/tex]  = 1.6

Also, the variance of the probability distribution is given by;

        Variance, V(X) =  [tex]\sum X^{2} \times P(X) - (\sum X \times P(X))^{2}[/tex]

                                 =  [tex]3.4 - (1.6)^{2}[/tex]

                                 =  3.4 - 2.56 = 0.84

And the standard deviation of the probability distribution is given by;

          Standard deviation, S.D. (X) =  [tex]\sqrt{Variance}[/tex]

                                                         =  [tex]\sqrt{0.84}[/tex]  = 0.916.

Answer: The percentage change is 56.67%.

Step-by-step explanation:

From 120 meals to 52 meals, change in meals = ( 120- 52) meals

= 68 meals

The percentage change = [tex]\dfrac{\text{change in meals}}{\text{Original quantity of meals}}\times100[/tex]

[tex]=\dfrac{68}{120}\times100\\\\=56.67\%[/tex]

Hence, the percentage change is 56.67%.

[tex]|\Omega|=_{12}C_3=\dfrac{12!}{3!9!}=\dfrac{10\cdot11\cdot12}{2\cdot3}=220\\|A|=4\cdot3\cdot5=60\\\\P(A)=\dfrac{60}{220}=\dfrac{3}{11}\approx0,273[/tex]

Answer:

0.273

Step-by-step explanation:

Total number of balls is 4+3+5 = 12

There are 6 ways to draw 3 different colors (WBR, WRB, BWR, BRW, RWB, RBW) each with a chance of 4/12 · 3/11 · 5/10 = 1/22

So the total chance is 6 · 1/22 = 6/22 = 3/11 ≈ 0.273

Answer:

the other person is right

you should try putting the WHOLE question

Step-by-step explanation:

Answer:

third option is the first step

Answer:

C

Step-by-step explanation:

It is c bro

Answer:

-7/1, -2.1, square root of 5, square root of 9, and last 3.5

Step-by-step explanation:

Square root of 9 is 3.

Square root of 5 is 2.24

-7/2 as a decimal is -3.5

So, from least to greatest order is:

-7/2 > -2.1 > Square root of 5 > Square root of 9 > 3.5

Answer:

(2) If 300 lunches were sold, then 120 chose tacos.

Step-by-step explanation:

We can evaluate each option and see if it makes it true.

For 1: If 200 lunches were served, 10 more students chose pizza over hotdogs.

We can find how many pizzas/hotdogs were given if 200 lunches were served by relating it to 100.

20% chose hotdog, which is [tex]\frac{20}{100}[/tex]. Multiply both the numerator and denominator by two: [tex]\frac{40}{200}[/tex] - so 40 students chose hotdogs.

Same logic for pizza: 30% chose pizza - [tex]\frac{30}{100} = \frac{60}{200}[/tex] so 60.

60 - 40 = 20, not 10, so 1 doesn't work.

2: If 300 lunches were sold, then 120 chose tacos.

Let's set up a proportion again. 40% of 100 is 40.

[tex]\frac{40}{100} = \frac{40\cdot3}{300} = \frac{120}{300}[/tex]

So 120 tacos were chosen - yes this works!

Hope this helped!

Answer:

(DNE,DNE)

Step-by-step explanation:

-24x-12y = -16. Equation one

6x +3y = 4. Equation two

Multiplying equation two with +4 gives

4(6x +3y = 4)

24x +12y = 16...result of equation two

-24x -12y= -16...

A careful observation to the following equation will help us notice that the both equation are same thing.

Multiplying minus to equation one gives

-(-24x-12y=-16)

24x+12y = 16.

Since the both equation are same, there is no solution to it.

Answer:

c. 72

Step-by-step explanation:

you just have to see what is the lowest number the three denominators: 8, 9, 12, all go into

8 times 9=72 and 12 times 6=72, which makes answer choice C. &2 the least common denominator for the fractions 1/8, 2/9, and 3/12.

Answer:

c.72 he's right love you guys byeee you all welcome

Step-by-step explanation:

Answer:

No, it's not enough

Step-by-step explanation:

Given

Tilling Dimension = 4m by 2m

Tile Dimension = 400mm by 400mm

Required

Determine the 45 tiles is enough

First;

The area of the tiling has to be calculated

[tex]Area = Length * Breadth[/tex]

[tex]Area = 4m * 2m[/tex]

[tex]Area = 8m^2[/tex]

Next, determine the area of the tile

[tex]Area = Length * Breadth[/tex]

[tex]Area = 400mm * 400mm[/tex]

Convert measurements to metres

[tex]Area = 0.4m* 04m[/tex]

[tex]Area = 0.16\ m^2[/tex]

Next, multiply the above area result by the number of files

[tex]Total = 0.16m^2 * 45[/tex]

[tex]Total = 7.2m^2[/tex]

Compare 7.2 to 8

Hence, we conclude that the 45 tiles of 400mm by 400 mm dimension is not enough to floor his bathroom

Answer: n is a positive odd number.

Step-by-step explanation:

Ok, we know that the function is something like:

f(x)=a(x+k)^1/n + c

In the graph we can see two thigns:

All the values of the graph are positive values (even for the negative values of x), but in the left side we can see that the function decreases and is different than the right side.

So this is not an even function, then n must be an odd number (n odd allows us to have negative values for y = f(x) that happen when x + k is negative).

Also, we can see that the function increases, if n was a negative number, like: n = -N

we would have:

[tex]f(x) = \frac{a}{(x+k)^{1/N}} + c[/tex]

So in this case x is in the denominator, so as x increases, we would see that the value of y decreases, but that does not happen, so we can conclude that the value of n must be positive.

Then n is a positive odd number.

Answer:

D) Positive Even Integer

Step-by-step explanation:

just did it

Answer:

217.0588235294118

Step-by-step explanation:

Convert all height to inches.

5' 8" = 68 inches

6' = 72

205/68 = 3.014705882352941

Height/Weight Ratio * Evan's Height = 217.0588235294118

Answer:

B. ⅕

Step-by-step explanation:

Fraction of families having more than 2 pets = families with pets of 3 and above ÷ total number of families in the apartment

From the dot plot above, 3 families have 3 pets, and 1 family has 4 pets.

Number of families with more than 2 pets = 3 + 1 = 4

Fraction of families with more than 3 pets = [tex] \frac{4}{20} = \frac{1}{5} [/tex]

The fraction of families that have more than two pets is B. [tex]\frac{1}{5}[/tex]

Given that:

Fraction of families having more than 2 pets = families with pets of 3 and above/total number of families in the apartment

From the dot plot above:

Number of families with more than 2 pets

= 3 + 1

= 4

Fraction of families with more than 3 pets = [tex]\frac{4}{20} = \frac{1}{5}[/tex]

Read more about dot plots here:

https://brainly.com/question/25957672

#SPJ5

Answer:

2√2

Step-by-step explanation:

hope you understand.

Answer:

x(x + 11)

Step-by-step explanation:

x^2 + 11x when factored gives a result of x(x + 11)

Answer:

x(x+11)

Step-by-step explanation:

We are given the expression:

[tex]x^2+11x[/tex]

This can be factored using the Greatest Common Factor (GCF).

The GCF of x^2 and 11x is x.

Factor out an x.

[tex]x(x+11)[/tex]

x^2+11x factored is: x(x+11).

Answer:

B

Step-by-step explanation:

we take the only point we know

(0,20)

in A when x =0

[tex]f(x)=e^{20x} =e^{20*0}=1[/tex]

in B when x=0

[tex]f(x)=20e^x=20e^0=20*1=20[/tex]

fits

in C

[tex]f(x)=20^x=20^0=1[/tex]

in D

[tex]f(x)=20^{20x}=20^{20*0}=20^0=1[/tex]

so the only choice is B

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

Explanation:

The original line has a given slope of -6/13. The opposite reciprocal is 13/6. We flip the fraction and the sign from negative to positive.

With any two perpendicular slopes, they always multiply to -1

(-6/13)*(13/6) = (-6*13)/(13*6) = -78/78 = -1

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

Since the perpendicular slope is 13/6, we need to see which of the four answer choices produces a slope of 13/6. Use the slope formula.

This is something you do through trial and error. You could start with A and work your way to D, or just pick at random. I'll go through each one by one starting at choice A.

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

Let's try choice A

m = (y2 - y1)/(x2 - x1)

m = (2 - (-4))/(-7 - 13)

m = (2 + 4)/(-7 - 13)

m = 6/(-20)

m = -3/10, we can see that choice A is not the answer, since we want m = 13/6 instead.

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

Let's try choice B

m = (y2 - y1)/(x2 - x1)

m = (2 - (-4))/(-7 - 6)

m = (2 + 4)/(-7 - 6)

m = 6/(-13)

m = -6/13, that doesn't work either

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

Let's try choice C

m = (y2 - y1)/(x2 - x1)

m = (-7 - 6)/(-4 - 2)

m = -13/(-6)

m = 13/6, we found the answer

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

For the sake of completeness, here is what choice D would look like

m = (y2 - y1)/(x2 - x1)

m = (-4 - 9)/(-4 - 6)

m = -13/(-10)

m = 13/10, which isn't the slope we want