Please solve and explain the two problems.

Answer:

Step-by-step explanation:

The null and the alternative hypothesis are:

[tex]\mathbf{ H_o: \rho = 0} \\ \\ \mathbf{H_1: \rho \ne 0}[/tex]

The test statistics is as follows:

[tex]t = \dfrac{r\sqrt{n-2} }{\sqrt{1-r^2}}[/tex]

[tex]t = \dfrac{0.4 \sqrt{30-2} }{\sqrt{1-0.4^2}}[/tex]

[tex]t = \dfrac{0.4 \sqrt{28} }{\sqrt{0.84}}[/tex]

t = 2.3094

The critical value

[tex]t_{\alpha/df} = t_\ \{0.05/2 \ , \ 30-2 \} } \\ \\ = t_{0.025,28} = \pm 2.048 ( from \ the \ t-tables)[/tex]

Decision rule:

To reject [tex]H_o[/tex] if t > [tex]t_{\alpha/df}[/tex].

So since t > [tex]t_{\alpha/df}[/tex]. we reject [tex]H_o[/tex] at ∝ = 0.05

Conclusion: There is sufficient evidence to conclude that blood pressure and patient calcium are linearly related.

Answer:

Va entre-3y-4

Step-by-step explanation:

Step-by-step explanation:

split the area between -1 and 0 into four parts

it'll be the part closest to -1

Answer:

The 95%  confidence interval is

           [tex] 5.92  <   \mu  <  7.284 [/tex]

Step-by-step explanation:

From the question we are told that

  The data is  6.5   6.7    7.2    6.4    7.3

Generally the sample  mean is mathematically represented as

         [tex]\= x = \frac{\sum x }{n}[/tex]

=>      [tex]\= x = \frac{ 5.5 + 6.5 + \cdot 7.3 }{ 6}[/tex]

=>      [tex]\= x = 6.6[/tex]

Generally the standard deviation is mathematically represented as

         [tex]\sigma = \sqrt{ \frac{ \sum (x_i - \= x )^2 }{ n-1} }[/tex]

=>      [tex]\sigma = \sqrt{ \frac{ (5.5 - 6.6 )^2 +(6.5 - 6.6 )^2 + \cdot + (7.3 - 6.6 )^2 }{ 6-1} }[/tex]

=>      [tex]\sigma = 0.6512[/tex]

Gnerally the degree of freedom is mathematically represented as

         [tex]df = n- 1[/tex]

=>       [tex]df = 6 -1[/tex]

=>       [tex]df = 5[/tex]

From the question we are told the confidence level is  95% , hence the level of significance is    

      [tex]\alpha = (100 - 95 ) \%[/tex]

=>   [tex]\alpha = 0.05[/tex]

Generally from the t distribution table the critical value  of  [tex]\frac{\alpha }{2}[/tex] is  

   [tex]t_{\frac{\alpha }{2} , 5 } = 2.571 [/tex]

Generally the margin of error is mathematically represented as  

      [tex]E = t_{\frac{\alpha }{2}, 5  } *  \frac{\sigma }{\sqrt{n} }[/tex]

=>    [tex]E =  2.571  *  \frac{0.6512}{\sqrt{6} }[/tex]

=>    [tex]E = 0.6835 [/tex]

Generally 95% confidence interval is mathematically represented as  

      [tex]\= x  -E <   \mu  <  \= x  +E[/tex]

=>     [tex]6.6  - 0.6835 <   \mu  <  6.6  +  0.6835[/tex]

=>     [tex] 5.92  <   \mu  <  7.284 [/tex]

Answer:

[tex] x = 4 [/tex]

Step-by-step explanation:

Since the diagonals of a parallelogram bisects each other, therefore:

[tex] x + 1 = 2x - 3 [/tex]

Collect like terms

[tex] x - 2x = -1 - 3 [/tex]

[tex] -x = -4 [/tex]

Divide both sides by -1

[tex] x = 4 [/tex]

Answer:

#6-

1. 9x30=(9x10)+(9x10)+(9x10)

2. 9x30=9(10+10+10)

3. 9x30=270

#7-

1. 7x50=7x(10+10+10+10+10)

2. 7x50=7x(25+25)

3. 7x50=350

#8-

1. 2x90=(2x45)+(2x45)

2. 2x90=90+90

3. 2x90=180

Step-by-step explanation:

Hope this helps!

Answer:

sorryyyyyuuuuuuuuuuuuuuuuuuu

Answer:

-3n = 27

Step-by-step explanation:

Answer:

Step-by-step explanation:

Sally owes 7 dollars to Matthew. She opens her piggy bank and takes out 7 dollars. Now, how much money does she owe to Matthew?

-7 + 7 = 0

-7 + 7 is the same as  7 - 7

You can clearly see that 7-7 is 0.

Answer:

You are in debt of $7. You pay the bank $7. How many money do you owe now?

Answer:

y=1.5

Step-by-step explanation:

if (y = 3) is  (x = 10) and (y = ?) is (x = 5) we see that x is half of the first equation in the second. This means we divide both variables in the first equation by half to get the second. [(x = 10) / 2 = (x = 5)] therefor, [(y = 3) / 2 = (y = 1.5)]. Making your answer 1.5.

Hope this helps :)

Answer:

P(X is greater than 30) = 0.06

Step-by-step explanation:

Given that:

Sample proportion (p) = 0.5

Sample size = 30

The Binomial can be approximated to normal with:

[tex]\mu = np = 50 \times 0.5 \\ \\ \mu= 25[/tex]

[tex]\sigma = \sqrt{np(1-p) } \\ \\ \sigma = \sqrt{50 \times (0.5)(1-0.5) } \\ \\ \sigma = 3.536[/tex]

To find:

P(X> 30)

So far we are approximating a discrete Binomial distribution using the continuous normal distribution. 30 lies between 29.5 and 30.5

Normal distribution:

x = 30.5, [tex]\mu[/tex] = 25, [tex]\sigma[/tex] = 3.536

Using the z test statistics;

[tex]z = \dfrac{x - \mu}{\sigma}[/tex]

[tex]z = \dfrac{30.5 - 25}{3.536}[/tex]

[tex]z = \dfrac{5.5}{3.536}[/tex]

z = 1.555

The p-value for P(X>30) = P(Z > 1.555)

The p-value for P(X>30) = 1 - P (Z< 1.555)

From the z tables;

P(X> 30) = 1 - 0.9400

Thus;

P(X is greater than 30) = 0.06

Answer:

1806 seats.

Step-by-step explanation:

From the question given above, the following data were obtained:

Row 1 = 24 seats

Row 2 = 27 seats

Row 3 = 30 seats

Total roll = 28

Total number of seat =?

From the above data, we can liken the roll to be in arithmetic progress.

Also, we are asked to determine the total number of seats in the theater.

Thus the sum of the sequence can be written as:

Roll 1 + Roll 2 + Roll 3 +... + Roll 28 i.e

24 + 27 + 30 +...

Thus, we can obtain obtained the total number of seats in the theater by applying the sum of arithmetic progress formula. This can be obtained as follow:

First term (a) = 24

Common difference (d) = 2nd term – 1st term

Common difference (d) = 27 – 24 = 3

Number of term (n) = 28

Sum of the 28th term (S₂₈) =?

Sₙ = n/2 [2a + (n –1)d]

S₂₈ = 28/2 [2×24 + (28 –1)3]

S₂₈ = 14 [48 + 27×3]

S₂₈ = 14 [48 + 81]

S₂₈ = 14 [129]

S₂₈ = 1806

Thus, the number of seats in the theater is 1806.

Answer: POQ = 125

Step-by-step explanation: If you don’t want to read my long explanation, I drew a diagram of my work. :>

First we need to establish that POQ is a vertical angle to SOT, this makes the angles equal. We also need to establish that because the definition of an altitude, that T And S both form right angles. (An altitude is a perpendicular segment from a vertex of a triangle to the opposite side.) Now let’s take a look at the quadrilateral that is formed inside the triangle, the quadrilateral being RSOT. Luckily we know the measure of three of the angles, R=55, T=90, and S=90. If you didn’t know beforehand all angles of a quadrilateral add up to 360, so we can add up the angles we’ve already found to find the missing angle O/ SOT. When we add the angles, and then subtract that from 360 we get 125, so SOT=125. Remember that we established that SOT and POQ are vertical angles, so if SOT=125 then POQ=125.

I really hoped my explanation was good, this was my first time giving an answer. Also I’m sorry if my method of finding the answer wasn’t helpful, but this was the only way I could think of.

I accidentally gave myself a one star rating, that sucks.

9514 1404 393

Answer:

  41

Step-by-step explanation:

The product of segment lengths from the point of intersection to the circle is the same for both chords.

  QC·QE = QD·QF

  2x(21) = (x+4)(30)

  14x = 10(x +4) . . . . . divide by 3

  4x = 40 . . . . . . . . . . subtract 10x

  x = 10 . . . . . . . . . . . .divide by 4

  2x +21 = EC = 2(10) +21 . . . . . find EC

  EC = 41

Answer:

A. [tex]t = \frac{d}{r}[/tex]

Step-by-step explanation:

Given

[tex]d = rt[/tex]

Required

Determine the time

From the question, we understand that:

[tex]d = distance[/tex]

[tex]r = rate[/tex]

[tex]t = time[/tex]

This question implies that we make t the subject of formula.

[tex]d = rt[/tex]

Divide both sides by r

[tex]\frac{d}{r} = \frac{rt}{r}[/tex]

The equation becomes:

[tex]\frac{d}{r} = t[/tex]

Reorder the equation.

[tex]t = \frac{d}{r}[/tex]

The correct option is (a) [tex]t = \frac{d}{r}[/tex]

Answer: [tex]d = 103.23 miles[/tex] apart.

Step-by-step explanation:

given data:

ship a = 20miles. = 60miles

ship b = 28miles. = 84miles

time interval = 3hrs.

θ = 90

[tex]d = \sqrt{a^{2}+b^{2}-2ab (cos90) }[/tex]

[tex]d = \sqrt{60^{2}+84^{2}-2(60)(84) *(cos90) }[/tex]

[tex]d = \sqrt{3600+7056-10080*(cos90) }[/tex]

[tex]d = \sqrt{10656-10080*(cos90) }[/tex]

[tex]d = \sqrt{10656-0[/tex]

[tex]d = \sqrt{10656[/tex]

[tex]d = 103.23 miles[/tex]

Answer:

t = 3/16

Step-by-step explanation:

Solve the proportion fraction numerator 15 t over denominator 5 end fraction equals fraction numerator 2 t plus 3 over denominator 6 end fraction

From the above question, we are to solve for t

The above expression is written Mathematically as:

15t/5 = 2t + 3/6

We cross Multiply

15t(6) = 5(2t + 3)

90t = 10t + 15

Collect like terms

90t - 10t = 15

80t = 15

t = 15/80

t = 3/16

Answer is 7.b  because of the angles

Answer:

m∠A = 25° and m∠C = 25°

Step-by-step explanation:

The sum of all three angles in a triangle must add up to 180°.  Since the measure of angle B is 130°, the sum of the other two angles have to be 50°.  

Also, the triangle is isosceles, meaning two of the sides are equal in length.  For those sides, their corresponding angles must also be equivalent.  In this case, it's the two smaller angles.  Since we have 50° between the two angles, A and C, divide 50 by 2 to get 25° for both angle measurements.  

The statement that must be true is m ∠A = 25° and m ∠C = 25°. The correct option is the second option m ∠A = 25° and m ∠C = 25°

From the question, we are to determine which of the statements must be true

From the given information,

m ∠B = 130°

Since the triangle is an isosceles triangle, the base angles must be equal

That is,

m ∠A = m ∠C

But, angles in a triangle sum up to 180°

Then,

∠A + ∠B + ∠C = 180°

This becomes

2 × ∠A + 130° = 180°

2 × ∠A = 180° - 130°

2 × ∠A = 50°

∠A = 50° ÷ 2

∠A = 25°

Since ∠A = ∠C

Therefore,

∠C = 25°

Hence, the statement that must be true is m ∠A = 25° and m ∠C = 25°. The correct option is the second option m ∠A = 25° and m ∠C = 25°

Learn more on Geometry here: https://brainly.com/question/14440001

Answer:

well there are eight total red cookies and there been two that had been bitten out of already that makes the ration 2:8

Answer:

5 bags

Step-by-step explanation:

Answer:

The answer to your question is given below

Step-by-step explanation:

From the question given above, the mean score is 23.

Thus, we can obtain the distance from the mean (absolute deviation) by using the following formula:

Mean deviation = | mean – Score |

Mean = 23

For Score 21:

Mean deviation = | mean – Score |

Mean deviation = | 23 – 21 | = 2

For Score 22:

Mean deviation = | mean – Score |

Mean deviation = | 23 – 22 | = 1

For Score 28:

Mean deviation = | mean – Score |

Mean deviation = | 23 – 28 | = 5

For Score 29:

Mean deviation = | mean – Score |

Mean deviation = | 23 – 29 | = 6

SUMMARY:

Score >> Mean >> Absolute deviation

21 >>>>> 23 >>>>> 2

21 >>>>> 23 >>>>> 2

21 >>>>> 23 >>>>> 2

22 >>>>> 23 >>>>> 1

22 >>>>> 23 >>>>> 1

22 >>>>> 23 >>>>> 1

22 >>>>> 23 >>>>> 1

22 >>>>> 23 >>>>> 1

28 >>>>> 23 >>>>> 5

29 >>>>> 23 >>>>> 6

Given that,

The area of a rectangular dining table = 9000 sq ft

Solution,

Let the width is b ft. Length is 20 less then four time the width.

Length = (4b-20) ft

The formula for the area of a rectangle is given by :

A = lb

Substitute all the values,

[tex]9000=b(4b-20)\\\\4b^2-20b-9000=0\\\\\text{It is a quadratic equation, when we solve it we get :}\\\\b=50,-45\ feet[/tex]

Neglecting negative value, b = 50 ft

Length, l = (4(50)-20)

l = 180 ft

So, the length is 180 ft and width is 50 ft.

Answer:

52/20

Step-by-step explanation:

Common sense and simple math

Answer:

ok

Step-by-step explanation:

Answer:

$25 a lamp

Step-by-step explanation:

First divide $10,000  by 500 lamps to find how much one of them cost

That is $20 a lamp so then multiply .25 *20 or 1/4 *20

you get 5 than add 20 +5=25

Answer:

ramrari focus and concentration garnu. Ani lightly linu SABAI problems haru .

Answer:

the best way to learn maths is by regular hard work and by practicing of maths daily