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iVinArrow [24]
2 years ago
6

What is the next number in the sequence? 55, 34, 21, 13, 8…?

Mathematics
1 answer:
Svetllana [295]2 years ago
4 0
The next number is 5.

Each number in the sequence is the (positive) difference of the previous two numbers.
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Consider a paint-drying situation in which drying time for a test specimen is normally distributed with σ = 7. The hypotheses H0
pshichka [43]

Answer:

(a) The value \bar x = 72.3 is 1.21 standard deviations below the null value of <em>μ</em>.

(b) The mean drying time of paint is not less than 74.

Step-by-step explanation:

The hypothesis for the single mean test is:

<em>H₀</em>: <em>μ</em> = 74 vs. <em>Hₐ</em>: μ < 74.

The information provided is:

<em>σ</em> = 7

<em>n</em> = 25

As the population standard deviation is known, we will use a <em>z</em>-test for single mean.

(a)

The <em>z</em>-score is a Normal distribution with mean 0 and variance 1. It is also defined as the number of standard deviations a raw score is from the mean.

The <em>z</em>-score for sample mean is given by:

z=\frac{\bar x-\mu}{\sigma/\sqrt{n}}

If \bar x = 72.3 compute the corresponding <em>z</em>-score as follows:

z=\frac{\bar x-\mu}{\sigma/\sqrt{n}}

  =\frac{72.3-74}{7/\sqrt{25}}\\=-1.21

Thus, the value \bar x = 72.3 is 1.21 standard deviations below the null value of <em>μ</em>.

(b)

So the test statistic is, <em>z</em> = -1.21.

Compute the <em>p</em>-value of the test as follows:

p-value=P(Z

*Use a <em>z</em>-table.

The decision rule says to, reject the null hypothesis if the <em>p</em>-value is less than the significance level <em>α</em> = 0.01 and vice-versa.

<em>p</em>-value = 0.1131 < <em>α</em> = 0.01

The null hypothesis was failed to be rejected.

Thus, the mean drying time of paint is not less than 74.

6 0
2 years ago
Which is the better buy on potatoes?<br> 3 lbs. for $.90<br> 5 lbs. for $1.60
myrzilka [38]

Answer:

3 pounds for 90 cents.

Step-by-step explanation:

The 5 pound bag costs 32 cents a pound

The 3 pound bag is 30 cents a pound

7 0
2 years ago
Q2.What is the ratio of volumes of the two cylinders formed by rolling a sheet of dimensions lxb in two different ways? Q3.What
Kobotan [32]

Answer:

2. b : l

3. 20cm

4. 49 cm^{2}

5. (2\pi+1):2\pi

Step-by-step explanation:

<u>Solution 2:</u>

Let cylinder is rolled along 'l':

Height of cylinder , h = length of rectangle = l

Perimeter of base = b

Let 'r' be the radius of cylinder's base:

2\pi r = b\\\Rightarrow r = \dfrac{b}{2\pi}

Volume of a cylinder is given as:

V = \pi r^{2} h

Putting the values:

V_1 = \pi (\dfrac{b}{2\pi})^2 l\\\Rightarrow V_1 =  (\dfrac{b^2}{4\pi}) l

Let cylinder is rolled along 'b':

Height of cylinder , h = length of rectangle = b

Perimeter of base = l

Let 'r' be the radius of cylinder's base:

2\pi r = l\\\Rightarrow r = \dfrac{l}{2\pi}

Volume of a cylinder is given as:

V = \pi r^{2} h

Putting the values:

V_2 = \pi (\dfrac{l}{2\pi})^2 b\\\Rightarrow V_2 =  (\dfrac{l^2}{4\pi}) b

Taking ratio:

V_1:V_2 = \dfrac{(\dfrac{b^2}{4\pi}) l}{(\dfrac{l^2}{4\pi}) b} = b:l

Solution 3:

Rectangle is rolled along its length to make a cylinder, so height will be equal to its length.

\therefore height of cylinder = 20 cm

Solution 4:

Side of square = 7 cm

Height of cylinder =Side of square = 7 cm

7 cm will be the circumference of the circle.

i.e. 2\pi r = 7 cm

Curved surface area of a cylinder:

CSA = 2\pi rh

Putting the above values:

CSA = 7 \times 7 = 49 cm^{2}

Solution 5:

As calculated in above step:

CSA = 2\pi rh = 7 \times 7 = 49 cm^{2}

Total surface area = 2\pi r^{2} + 2\pi r h

Calculating value of r:

2\pi r = 7 cm

\Rightarrow 2  \pi r = 7\\\Rightarrow r = \dfrac{7}{2\pi}

Total surface area =

2\pi (\dfrac{7}{2\pi})^{2} + 49\\\Rightarrow \dfrac{49}{2\pi}+49\\\Rightarrow 49(\dfrac{1}{2\pi}+1) cm^2

Ratio of TSA: CSA is

49(\dfrac{1}{2\pi}+1) cm^2 : 49 cm^2\\\Rightarrow (\dfrac{1}{2\pi}+1):1\\\Rightarrow (2\pi+1): 2\pi

5 0
2 years ago
When multiplying two negative integers, what is the sign of the product?
geniusboy [140]
When mutiplying two negatives you will get a positive so answer A
6 0
3 years ago
Read 2 more answers
What is 4.66666666667 as a fraction
ss7ja [257]

Step-by-step explanation:

466666666667/100000000000

7 0
3 years ago
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