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Answer:

The  test is a two -tailed test

Step-by-step explanation:

From the question we are told that

    The  sample size is n  =  31

     The  sample mean is  [tex]\= x =11[/tex]

      The sample standard deviation is  [tex]\sigma = 3[/tex]

       The null hypothesis is  [tex]H_o: \mu \le 10[/tex]

         The  alternative hypothesis is  [tex]H_1 : \mu > 10[/tex]  

         The level of significance is [tex]\alpha = 0.05[/tex]

The test  statistics is mathematically represented as

       [tex]t = \frac{ \= x - \mu }{ \frac{\sigma }{\sqrt{n} } }[/tex]

substituting values

      [tex]t = \frac{ 11 - 10 }{ \frac{3}{\sqrt{ 31} } }[/tex]

     [tex]t = 1.85[/tex]

The  p- value is mathematically represented as

       [tex]p-value = p( t > 1.856) = 0.0317[/tex]

Looking at the value of  [tex]p-value \ and \ \alpha[/tex] we see that [tex]p-value < \alpha[/tex] hence we reject the null hypothesis

Given the that the p value is less than 0.05 it mean the this is a two-tailed test

Answer:

1:3

2:4

3:6

Step-by-step explanation:

we can divide both sides by 6 and get 1:2

we can divide both sides by 3 and get 2:4

we can divide both sides by 2 and get 3:6

Answer:

12:24, 3:6, 2:4

Step-by-step explanation:

What we are looking for here is a ratio that, when you divide/multiply the same constant on both parts of the ratio, you get 6:12.

6:12 is the same thing as 1:2, so we can find ratios equivalent to 1:2 (the first value will be half the second).

Hope this helped!

(2x+1)(x-3)

y(x-3) .... let y = 2x+1

y*x+y(-3) .... distribute

xy - 3y

x( y ) - 3( y )

x( 2x+1 ) - 3( 2x+1) ... replace y with 2x+1

2x^2 + x - 6x - 3 ..... distribute

2x^2 - 5x - 3

Answer is choice A

Answer:

24 = x+6

x = 18

Step-by-step explanation:

N = 24

T = x

N = x+6  

24 = x+6

Subtract 6 from each side

24-6 = x+6-6

18 = x

Time has 6 marbles

Nirja has 6 more than Tim,

So you can subtract 6 from 24 to find x:

24-6 = x

Or you can add 6 to x to equal 24:

x + 6 = 24

You don't list the choices but it should be one of these.

Solve:

24 - 6 = x

x = 18

Answer:

[tex]\boxed{\frac{3}{5}}[/tex]

Step-by-step explanation:

The trigonometric functions are described as follows:

[tex]sin = \frac{opposite}{hypotenuse}\\\\cos = \frac{adjacent}{hypotenuse}\\\\tan = \frac{opposite}{adjacent}[/tex]

Using reference angle ∠A, use the sin trigonometric function. This will be the side opposite (cannot be the hypotenuse) of ∠A over the side adjacent (cannot be the hypotenuse).

The side opposite of ∠A is 3. The hypotenuse of the triangle is 5.

[tex]\boxed{\frac{3}{5}}[/tex]  is the final answer!

Answer:

Rewrite  

( 4 − 3 i ) 2  as  ( 4 − 3 i )( 4 − 3 i ) . ( 4 − 3 i) ( 4 − 3 i ) Expand  ( 4 − 3 i ) ( 4 − 3 i )

using the FOIL Method.

4 ⋅ 4 + 4 ( -3 i ) − 3 i ⋅ 4 − 3 i ( − 3 i )

Simplify and combine like terms.

7 − 24 i

Step-by-step explanation:

Answer:

7 -24i

Step-by-step explanation:

(4 - 3i) ^2

(4-3i) * (4-3i)

FOIL

first 4*4 = 16

outer 4 * -3i = -12i

inner -3i *4 = -12i

last -3i*-3i = 9i^2 = 9 (-1) = -9

Add together

16 -12i-12i -9

Combine like terms

7 -24i

We know that this is a right triangle, so one of the sides has to be 90 (indicated by the square on the corner)  The angles of all triangles must add to exactly 180.  Subtract 90 and 35 from 180

If we do that, we get 55.  We know that the unknown angle is 55 now.  Now, it asks us for b.  We can pythagoras theorem which states that (a^2 + b^2 = c^2)  We already know c (c is 20)  It does not tell us 2 of the sides but we do know that the answer is either B or D.  

The side opposite of 90* should be the largest.  The size opposite of 55 would be the second largest one.  The side opposite of 35 would be the smallest one.  Using pythagoras theorem again, I can try plugging in both 11.47 and 16.38 with c^2 - b^2 = a^2  

11.47:

400 - 132 =268  (sq root now = 16.37) this would mean that A is larger than B.  B should be larger than A.  Try the other one

16.37:

400 -268 = 132 (sq root = 16.37) this would mean that B is larger than A which is what we want.

Thus, 16.37  = B and the last option would be correct (D)

Hope this helps, give an honest rating for me please

Answer:

"Teens and Distracted Driving: Texting, Talking and Other Uses of the Cell Phone Behind the Wheel"

a. The inference made involves estimation.  The question provided that the statements were made on the basis of the resulting data and not on the basis of some hypothesis testing.

This implies that some statistics were calculated from sample data to approximate the population parameter, as shown in the statements.  The statements were not an attempt to establish the statistical significance of some claims.

b. The population of interest is American teenagers between 12-17.

Step-by-step explanation:

An inference from data is a statistical estimation by which some statistics are calculated based on the sample data of 800 teens between the ages of 12 and 17.  The statistics serve as an approximation to the population parameter.

Inference based on hypothesis testing establishes if a claim has statistical significance by providing  statistical evidence in favor of the claim or against it.

Answer:

0.204

Step-by-step explanation:

The formula to use to solve this is the combination formula.

Combination formula =

C(n, r) = nCr = n!/r! (n - r)!

Total number of kittens = 8 boy kittens + 9 girl kittens

= 17 kittens

Step 1

We find the probability of choosing 4 boy kittens out of 8 boy kittens

= 8C4 = 8!/4! × (8 - 4)!

= 8C4 = 8! / 4! × 4!

= 8C4 = 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1/ (4 × 3 × 2 × 1) × (4 × 3 × 2 × 1)

8C4 = 70

Step 2

We find the probability of choosing 7 girl kittens out of 9 girl kittens

9C7 = 9!/7! × (9 - 7)!

= 9C7 = 9! / 7! × 2!

= 9C7 = 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1/ (7 × 6 × 5 × 4 × 3 × 2 × 1) × (2 × 1)

9C7 = 36

Step 3

Find the probability of Picking 11 kittens out of 17 kittens

17C11 = 17!/11! × (17 - 11)!

= 17C11 = 17! / 11! × 6!

= 17C11 = 17 × 16 × 15 × 14 × 13 × 12 × 11 × 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1/ (11 × 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1) × (6 × 5 × 4 × 3 × 2 × 1)

17C11 = 12,376

Step 4

The final step

The probability that the director chooses 4 boy kittens and 7 girl kittens

= 8C4 × 9C7/ 17C11

= 70 × 36/12376

= 2520/12376

= 0.2036199095

Approximately to 3 decimal places = 0.204

Therefore, the probability that the director chooses 4 boy kittens and 7 girl kittens is 0.204

Answer:

We have the magnitude, M, and the angle A.

(The angle is always measured from the +x-axis)

Then we have that:

x = M*cos(A)

y = M*sin(A)

in this case:

M = 9m

A = -80°

x = 9m*cos(-80°) = 1.562

y = 9m*sin(-80) = -8.86m

Now, the component parallel to the x axis is:

x = 9m*cos(-80°) = 1.562 m

And the slope of something parallel to the x-axis is always zero, as this is a constant line.

Answer:

ok as we know 15 is a whole number by itself and 3/8 is the decimal part

so we know it is 15. something

that something is 3/8 to find decimal you do 3/8

3/8 is = .375

so 15.375 is the answer

hope it helps

brainliest give me pls

Answer:

Mean: 169.4

Median: 171

Mode: 181

Step-by-step explanation:

I first sorted the numbers by value, least to greatest.

145 147 153 153 167 170 170 172 181 181 181 182 185 185

We can see that 181 occurs the most, 3 times, so it's the mode.

The median of this set will be the middle number(s).

When we take away 6 numbers from both sides we are left with 170 and 172, and the mean of these two numbers is 171. So the median is 171.

We can add all the numbers and divide by 14 to get the mean.

[tex]147+153+170+172+185+181+182+185+181+170+181+167+153+145=2372\\\\2372\div14\approx169.4[/tex]

Hope this helped!

Answer:

2(8-d)

2(8-5)   (substituting d=5)

2(3)

=6

Step-by-step explanation:

The required expression is f = 6 for d =5 in the for the expression f = 2 (8 -d).

An algebraic expression is consists of variables, numbers with various mathematical operations,

The expression,

f = 2 (8 - d)              (1)

To evaluate the expression for d = 5

Substitute the value of d = 5 in equation (1),

f = 2 (8 - 5)

f = 2 x 3

f = 6

The required expression is f=6.

To know more about Algebraic expression on:

https://brainly.com/question/19245500

#SPJ2

Answer:

Kindly check explanation

Step-by-step explanation:

Given the data:

Age(x)

7

8

5

8

8

7

7

7

9

8

5

8

6

5

8

Height (Y)

47.3

48.8

41.3

50.4

51

47.1

46.9

48

51.2

51.2

40.3

48.9

45.2

41.9

49.6

The estimated regression equation:

ŷ = 2.73953X + 27.91395

Where ;

X = independent variable

ŷ = predicted or dependent variable

27.91395 = intercept

C.) To obtain the variation in sample values of height estimated by the model, we obtain the Coefficient of correlation:

Using the online pearson correlation Coefficient calculator :

The correlation Coefficient is 0.9696.

which means that the regression model estimated in part (b) explains approximately (0.9696 * 100) = 96.96% = 97% of the variation in the height in the sample.

In part (D), we found

[tex]2\sin(4\pi t)+5\cos(4\pi t)=\sqrt{29}\sin\left(4\pi t+\tan^{-1}\left(\dfrac52\right)\right)[/tex]

so the phase [tex]\phi[/tex] is [tex]\tan^{-1}\left(\frac52\right)\approx1.19\,\rm rad[/tex], which falls between 0 and [tex]\frac\pi2[/tex]. This means the weight is somewhere between the maximum positive position (where [tex]\phi[/tex] would be 0) and the equilibrium position (where [tex]\phi[/tex] would be [tex]\frac\pi2[/tex]), and would be traveling in the negative direction.

Answer:

quadrant 2

Step-by-step explanation:

Answer:

the number is 80

Step-by-step explanation:

let x be an unknown number so from the above question we deduce that

(70/100)*x=56

70x/100=56

70x=56*100

70x=5600

70x/70=5600/70

x=80

Answer: 0.05412

Step-by-step explanation:

Formula : Odds of having an event is given by  [tex]o=\dfrac{p}{1-p}[/tex], where p = probability that event happens.

In terms to find p , we use [tex]p=\dfrac{o}{1+o}[/tex]

Given, he back of the ticket lists the odds of winning each dollar value: 0.05 for $10, 0.04 for $25, 0.01 for $50, and 0.003 for $100.

Let X be the worth of ticket.

Then, the probability that the ticket is worth at least $25 =

[tex]P(X\geq 25)=P(X=25)+P(X=50)+P(X=100)[/tex]

[tex]=\dfrac{0.04}{1+0.04}+\dfrac{0.01}{1+0.01}+\dfrac{0.003}{1+0.003}\\\\=0.05135[/tex]

The odds that the ticket is worth at least $25 = [tex]\dfrac{0.05135}{1-0.05135}[/tex]

=0.05412

hence, the odds that the ticket is worth at least $25 is 0.05412 .

[tex]A \cap B=\{10,30\}[/tex]

Answer:

Option A is the correct option

Step-by-step explanation:

[tex] \mathrm{Given}[/tex]

A = { 10 , 30 }

B = { 10 , 20 , 30 , 40 , 50 , 60 , 70 , 80 , 90 }

Now, let's find A ∩ B

A ∩ B = { 10 , 30 } ∩ { 10 , 20 , 30 , 40 , 50 , 60 , 70 , 80 , 90 }

The intersection of sets A and B is the set of all elements which belong to both A and B

A ∩ B = { 10 , 30 }

The intersection of sets A and B is denoted by ( A ∩ B ) and read as A intersection B.

Hope I helped!

Best regards!

━━━━━━━☆☆━━━━━━━

▹ Answer

(-39/35, 9/7)

▹ Step-by-Step Explanation

5y + 2y = 9

-5x - 2y = 3

Solve the equation:

y = 9/7

-5x - 2y = 3

Substitute the value of y:

-5x - 2 * 9/7 = 3

x = -39/35

(x, y) = (-39/35, 9/7)

Hope this helps!

CloutAnswers ❁

━━━━━━━☆☆━━━━━━━

To solve this system by addition, we start by adding both of our equations together but notice that the x terms and the y terms cancel out.

This leaves us with 0 on the left side and on the right side,

9 + 13 = 12 so we are left with the equation 0 = 12.

Since 0 = 12 is a false statement, this means that

there is no solution to our system of equations.

Answer:

45.35

Step-by-step explanation:

From the above question, we are told that the annual effective rate = 10% = 0.10

Note also that payment is been made every 2 years

Hence , we apply the formula of effective interest rate for a period of 2 years.

Effective Interest rate(j) = (1 + r)² - 1

= (1 + 0.10)² - 1

= 1.10² - 1

= 1.21

= 0.21

Present value of perpetuality = t/[j × j/(1 + r)²]

Where t = time in years = 2

r = 0.10

= 2/ [0.21 × 0.21/(1 + 0.10)²

= 54.87528

Present value at time t = 0

= 54.87528(1 + r)^-2

= 54.87528(1 + 0.10) ^-2

= 54.87528(1.10)^-2

= 45.35

Therefore, the present value at time (t) is 0 = 45.35

Answer:

  42

Step-by-step explanation:

A graphing tool is useful for finding the points of intersection of these lines. If the equations are numbered 1, 2, 3 in the order given, we can find the points of intersection to be ...

  equations 1, 2: A(5, -2)

  equations 2, 3: B(10, 0)

  equations (3, 1): C(-2, 12)

Then the area can be found from the coordinates using the formula ...

  A = (1/2)|x1(y2-y3) +x2(y3-y1) +x3(y1-y2)|

  = (1/2)|5(0-12) +10(12-(-2)) -2(-2-0))| = (1/2)|-60 +140 +4|

  A = 42

The area of the triangular region is 42 square units.

Answer:

Step-by-step explanation:

[tex]\log _9\left(5\right)=y\\y=\log _9\left(5\right)[/tex]

Answer:

Step-by-step explanation:

[tex]a \: apples = 1 \: hours\\x \: apples = 5 \: hours\\x = 5a\\Total \:no \:of \:apples \:picked\\\:by \:david \:= 5a\\\\\\b \:apples = 1 \:hour\\x \:apples = 8 hours\\x = 8b\\Total \:no \:of \:apples \:picked\\ \:by \:elanor = 8b\\\\Total \:no \:of \:Apples =5a+8b[/tex]

Answer:

15x+6u−3

Step-by-step explanation:

This means -3 times -5x, -3 times -2u, and -3 times 1.

Do this and you have, 15x+6u-3.

Answer:

14 °F

Step-by-step explanation:

To answer this problem, we will use the known celsius to fahrenheit conversion formula.

[Celsius * (9/5)] + 32 = Fahrenheit

Now we just plug in the value of celsius:

[-10 * (9/5)] + 32 = Fahrenheit

[ -2 * 9 ] + 32 = Fahrenheit

[ -18 ] + 32 = Fahrenheit

14 = Fahrenheit

So you should right 14(°F) on the label.

Cheers.

Answer:

A, E

Step-by-step explanation:

There should be 2^8-1 proper subsets of A. Its every one besides { }

Answer:

15.7 in  

Step-by-step explanation:

A slice of a round pie is a sector of a circle.

The perimeter of a slice is the arc length s plus twice the radius r.

P = s + 2r

s = rθ = r(16/360) = r/22.5. So,

16 = (r/22.5) + 2r = (r + 45r)/22.5 = 46r/22.5

16 × 22.5 = 46r

360 = 46r

r = 7.826  

D = 2r = 2 × 7.826 = 15.7 in

The diameter of the cake should be 15.7 in.

Check:

[tex]\begin{array}{rcl}P & = & s + 2r\\& = & \dfrac{r}{22.5} + 2r\\\\16 & = & \dfrac{7.826}{22.5} + 2 \times 7.826\\\\16 & = & 0.35 + 15.65\\16 & = & 16.00\\\end{array}[/tex]

It checks.

Answer:

Option (3)

Step-by-step explanation:

From the picture attached,

Bar graph sketched shows the grades earned by the students in an exam.

Number of students who achieved the grade A = 17

Number of students who achieved grade B = 14

Number of students with grade C = 5

Number of students with grade D = 9

Total students who took the exam = 17 + 14 + 5 + 9 = 45

Option (1)

"[tex]\frac{1}{5}[/tex] of the students earned a C"

Fraction of students who earned C = [tex]\frac{\text{Students who earned C}}{\text{Total students}}[/tex]

                                                          = [tex]\frac{5}{45}[/tex]

                                                          = [tex]\frac{1}{9}[/tex]

Therefore, this option is incorrect.

Option (2)

"3% more students earned an A then B"

Percentage of students who earned A = [tex]\frac{\text{Students got A}}{\text{Total students who took the exam}}\times 100[/tex]

                                                                = [tex]\frac{17}{45}\times 100[/tex]

                                                                = 37.78%

Percentage of students who earned B = [tex]\frac{\text{Students got B}}{\text{Total students who took the exam}}\times 100[/tex]

                                                                = [tex]\frac{14}{45}\times 100[/tex]

                                                                = 31.11%

Difference in percentage = 37.78 - 31.11

                                          = 6.67%

Therefore, this option is not correct.

Option (3)

"20% of the students earned a D"

Percentage of students who earned D = [tex]\frac{\text{Students got D}}{\text{Total students who took the exam}}\times 100[/tex]

                                                                 = [tex]\frac{9}{45}\times 100[/tex]

                                                                 = 20%

Option (3) is the correct option.

Option (4)

" [tex]\frac{1}{4}[/tex] of the class earned a B"

Fraction of class who earned B = [tex]\frac{\text{Students got B}}{\text{Total students who took the exam}}[/tex]

                                                    = [tex]\frac{14}{45}[/tex]

Therefore, Option (4) is not correct.                                        

Answer:

  45, 180, 145

Step-by-step explanation:

Let n represent the first number. Then "one number" is 4n, and the third number is n+100. The sum of the three numbers is ...

  n + 4n + (n+100) = 370

  6n = 270

  n = 45

  4n = 180

  n+100 = 145

The three numbers are 45, 180, 145.