Suppose Diana, an educational researcher at a local university, wants to test the impact of a new Spanish course that integrates cultural-immersion teaching techniques with standard teaching practices. She selects a simple random sample of 64 freshmen and divides them into 32 pairs, matched on IQ and high school GPA. She randomly selects one member of each pair to take the new course, while the other member in the pair takes the traditional course.

Next, Diana records the course grade, tallied on a scale from 0 to 4, for all sample members at the end of the semester, and she computes the difference in grades between the members in each matched pair by subtracting the traditional course grade from the new course grade. She wants to determine if the new Spanish course improves or weakens student performance. She runs a matched-pairs t-test to test the null hypothesis, H0:μ=0, against the alternative hypothesis, H1:μ≠0, where μ is the mean course grade difference for the student population.

The sample statistics for Diana's test are summarized in the table.

Variable description Sample mean Sample standard deviation Standard error estimate

traditional course grade x⎯⎯trad= 3.33496 strad=2.02198 SEtrad=0.33700
new course grade x⎯⎯new=3.45287 snew=2.11043 SEnew=0.35174
difference (new − traditional) x⎯⎯=0.11791 s=0.31452 SE=0.05242


Although Diana does not know the standard deviation of the underlying population of course grade differences, she assumes that the population is normally distributed because the sample data are symmetric, single-peaked, and contain no outliers.

Required:
Compute the t-statistic for Diana's matched-pairs t-test.

Answer:

72 in²

Step-by-step explanation:

We obtain the value of EC:

From Pythagoras :

EC = √CD² - DE²

EC = √10² - 6²

EC = √100 - 36

EC = √64

EC = 8

To obtain AE:

AE = √AB² - BE²

AE = √(√52)² - 6²

AE = √52 - 36

AE = √16

AE = 4

Hence, we can obtain the areas of each triangle :

△ABE = △ADE

△BCE = △CDE

AREA OF △ABE = 1/2 * base * height

= 1/2 * 4 * 6 = 12 in²

AREA OF △BCE = 1/2 * base * height

= 1/2 * 6 * 8 = 24 in²

HENCE, total area of fabric :

(2 * 12) + (2 * 24)

24 in² + 48 in²

= 72 in²

Answer:

C = StartFraction pi times 4 over 2 EndFraction.

Step-by-step explanation:

the circumference of a circle=

C= 2 times PI times radius

Radius= d/2

sooo it is

C = StartFraction pi times 4 over 2 EndFraction.

Answer:

C = StartFraction pi times 4 over 2 EndFraction.

Step-by-step explanation:

the circumference of a circle=

C= 2 times PI times radius

Radius= d/2

sooo it is

C = StartFraction pi times 4 over 2 EndFraction.

Answer:

P'(C) = 0.98

Step-by-step explanation:

Given that,

P(C) = 0.02 (The probability of getting C)

We need to find the complement of P(C) i.e. P'(C).

We know that,

P(C)+P'(C)=1

P'(C) = 1-P(C)

= 1-0.02

= 0.98

So, the complement of P(C) is equal to 0.98.

Given:

The table of point scored in 5 games.

After game 6, the mean number of points scored per game is 9.

To find:

The points scored by Maya in game 6.

Solution:

Let x be the points scored by Maya in game 6. Then sum of scores in all 6 games is:

[tex]Sum=8+12+10+6+14+x[/tex]

[tex]Sum=50+x[/tex]

We know that, the formula for mean is:

[tex]\text{Mean}=\dfrac{\text{Sum of all observations}}{\text{Total number of observations}}[/tex]

So, the mean number of points scored per game is:

[tex]\text{Mean}=\dfrac{50+x}{6}[/tex]

It is given that the mean number of points scored per game is 9.

[tex]\dfrac{50+x}{6}=9[/tex]

[tex]50+x=9\times 6[/tex]

[tex]x=54-50[/tex]

[tex]x=4[/tex]

Therefore, the correct option is A.

Answer:

6

Step-by-step explanation:

Answer:

8π/5

Step-by-step explanation:

Length of an arc, L

L = θ / 360° * (2πr)

r = Radius = 4 ; θ = 72

Hence,

L = 72/360 * (2π4)

L = 1/5 * 8π

L = 8π/5

Answer:

15

Step-by-step explanation:

Answer:

15

Step-by-step explanation:

Answer:

58.1

Step-by-step explanation:

Answer:

4.16%/ year

Step-by-step explanation:

[tex]\boxed{e\:=\:-2.}[/tex] ✅

[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\orange{:}}}}}[/tex]

[tex]2e - 3(2e + 3) = 3e + 5 \\ ⇢2e - 6e - 9 = 3e + 5 \\ ⇢ - 4e - 3e \: = 5 + 9 \\ ⇢ - 7e = 14 \\ ⇢e = \frac{14}{ - 7} \\ ⇢e = - 2[/tex]

[tex]{ \bf{ \underbrace{To\:verify :}}}[/tex]

[tex]2e - 6e - 9 = 3e + 5 \\⇢2 \times - 2 - 6 \times - 2 - 9 = 3 \times - 2 + 5 \\ ⇢ - 4 + 12 - 9 = - 6 + 5 \\ ⇢12 - 13 = - 1 \\ ⇢ - 1 = - 1 \\ ⇢L.H.S.=R. H. S  [/tex]

Hence verified.

[tex]\large\mathfrak{{\pmb{\underline{\orange{Happy\:learning }}{\orange{.}}}}}[/tex]

Answer:

The green triangle is the rotation.  It is rotated 90 degrees about the origin (0,0).  P is at (-1.1).  Q is at(-2,3).  R is at (-5,2).

The red triangle is the reflection.  It has been reflected over the x=axis.  X is at (1,-1).  Y is at (3,-2).  Z is at (2,-5).

Step-by-step explanation:

The green triangle is the rotation.  It is rotated 90 degrees about the origin (0,0).  P is at (-1.1).  Q is at(-2,3).  R is at (-5,2).

The red triangle is the reflection.  It has been reflected over the x=axis.  X is at (1,-1).  Y is at (3,-2).  Z is at (2,-5).

Answer:

=−9

=9

Step-by-step explanation:

4

2

=

3

2

4

4x^{2}=324

4x2=324

4

2

−

3

2

4

=

04

2

−

3

2

4

=

0

4x^{2}-324=0

4x2−324=0

4

(

2

−

8

1

)

=

04

(

2

−

8

1

)

=

0

4(x^{2}{\color{#c92786}{-81}})=0

4(x2−81)=0

4

(

2

+

9

−

9

−

8

1

)

=

0

Answer:

Step-by-step explanation:

2a+b^3

2*5.6+(2)^3

11.2+8

19.2

Answer:

19.2

Step-by-step explanation:

2(5.6)+2^3

11.2+8

19.2

Answer:

a) Mode number = 2

b) Median  = 64.5  = 4 people in car as 0.5 in 64.5 is close to 76

              = 4 people

c) Mean number is  505/6 =   84.1666666667 then we see where 84.16 lies and see this lies with =  3 people

Step-by-step explanation:

45  is 1

198 is 2

121 is 3

76 is 4

52 is 5

13 is 6

Mode we look for the highest frequency and see 198 is the amount and 2 people in car is the subject, we give the subject and that is 2 people in car is the highest frequency and would be the mode.

Median is shown in the answer as we add up.

Mean we add up all frequency and divide by the amount of subjects = 6.

a) Mode number = 2

b) Median = 13, 45, 52, here 76, 121, 198    mid number between

             = (76-52 )/ 2  + (52)= 24 /2 + (52) = 12 + 52 + 0.5 if even number    

median  = 64.5  in a cumulative graph though which is not asked here it would be exactly half of 505 = 257.5 and interquartile we half again and add on 257.5 and show the range values interquartile as 1/2(252.5) and 1/2(252.5+ 505) = 126.25 as one value and 757.5 as the other by drawing a horizontal line from y axis to the points so vertical lines can represnt the cars median and interquartile.

c. Mean number is  505/6 =   84.1666666667 then we see where 84.16 lies and see this lies with 3 seats

For cumulative frequency we can relist numbers like this

45

45 +198 = 243

243 +  121 = 364

364+76 = 440

440 + 52 = 492

492+13 = 505 to plot graph.

But if there was group of measures or time etc then we would always plot the highest of each set for cumulative x axis and use the 2 values to see the ratio for histograms ie) 198/2 = 99 so that all values are read in equal proportions and 2 is a data below the graph not on the graph as 2 does not show as a box count just a name below on x axis. So we have to use the ratio as explained for histograms.

Answer: Simple regression

Step-by-step explanation:

A regression analysis that involves one independent variable and one dependent variable is called the simple regression.

The Simple Regression Analysis shows the relationship that exist between the dependent variable which is the value that's to be predicted and the independent variable. The dependent variable depends on the independent variable

Answer:

x = 3.6

Step-by-step explanation:

Since ABCD ~ EFGH, therefore:

AB/EF = AD/EH

AB = 3

EF = 2

AD = x

EH = 2.4

Plug in the values into the equation:

3/2 = x/2.4

Cross multiply

3*2.4 = 2x

7.2 = 2x

Divide both sides by 2

7.2/2 = x

3.6 = x

x = 3.6

Answer:

A

Step-by-step explanation:

Answer:

78 inches

Step-by-step explanation:

5 hours = 390 inches

1 hour = 390 / 5

1 hour = 78 inches

Therefore the snail travels 78 inches in 1 hour.

Hope this helps!

Answer:

c and e is your answers

Step-by-step explanation:

Hope it helps :3

Answer:

solution below

Step-by-step explanation:

quadratic formula (note the + before the radical is ±)

[tex]\frac{-b+\sqrt{b^2-4*a*c}}{2a}}[/tex]

Let's plug in the numbers and simply for the first one

[tex]\frac{-(-8)+\sqrt{-8^2-4*2*5}}{2*2}}=\frac{8+\sqrt{24}}{4}}[/tex]

this simplies to

[tex]\frac{8+2\sqrt{6}}{4}=\frac{4+\sqrt{6}}{2}[/tex]

Do this same process with all the other ones

Answer:

[tex]x = 3[/tex]

Step-by-step explanation:

[tex]6x + 1 - 2x = 13[/tex]

[tex]4x+1 = 13[/tex]

[tex]4x+1-1 = 13-1[/tex]

[tex]4x = 12[/tex]

[tex]\frac{4x}{4} = \frac{12}{4}[/tex]

[tex]x = 3[/tex]

Answer:

x = 3

Step-by-step explanation:

6x-4-2x+5=13 (simplify)

4x+1=13 (4x+1 - 1 ; 13-1)

4x=12 (4x/4 ; 12/4)

x=3

Step-by-step explanation:

done hope this helped you

Answer:

1. [tex]a = 8[/tex]

2. [tex]b = \frac{1}{8}[/tex]

3. [tex]c = 2 \frac{3}{5}[/tex]

4. [tex]d = \frac{13}{50}[/tex]

Step-by-step explanation:

Answer:

x = 30, y = 15

Step-by-step explanation:

x = 2*15 = 30

(Central angle is twice the inscribed angle standing on the same arc.)

Similarly,

y = 15

(Base angles of isosceles triangle are equal)

Answer:

4 to the 2nd power is the equivalent to 2 to the 4th power

Step-by-step explanation:

2⁴ = 16 = 4²

Answer:

16

Step-by-step explanation:

2*2*2*2= 16

Answer:

65 degrees

Step-by-step explanation:

Angles in a triangle add to 180°.

Answer:

Your answer is 2.

Answer:

Slope intercept form with m= -7

Step-by-step explanation:

Slope intercept form is y=mx+b

where m=slope and b=y-intercept

so

y=-7x+2

Slope (m)= -7

y-intercept = 2

Answer:

8.4%

Step-by-step explanation:

let x = interest rate

55,000(1 + x)^16 = 200,000

divide both sides by 55,000

(1 + x)^16 = 3.636

find the invese of 16

1 + x = 1.084

x = 0.084

x = 8.4

Answer:

Commutative property of multiplication

Step-by-step explanation:

Properties of Multiplication:

Commutative:

Multiplying two or more factors in a different order.

ex: 2 x 4 x 5 = 2 x 5 x 4

Associative:

Multiplying factors in parenthesis with different grouping. usually to make the problem simpler.

ex: (13 x 4) x 25 = 13 x (4 x 25)

Distributive:

Distributing a multiplicand to factors in parenthesis.

ex: 2(4 - 1) = 2(4) - 2(1)

ex: 2(8+7) = 2(8) + 2(7)

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-Chetan K