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3 years ago

10

A food product in your kitchen has been contaminated with one bacteria cell. Assume conditions are ideal and bacteria are dividi

ng every 20 minutes. At this rate, how many bacteria cells will there be after 1 hour and 40 minutes

1 answer:

tamaranim1 [39]3 years ago

5 0

70 cells?
140 divided by 20 = 70

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Hi can someone help me ty happy holiday days

earnstyle [38]

Answer:

128 , 512, 2048

Step-by-step explanation:

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2 years ago

Help me please !!!!!!

PilotLPTM [1.2K]

The correct answer is B. x is greater than -2.

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3 years ago

1. Drag and drop an answer to each box to correctly complete the derivation of a formula for the area of a sector of a circle.

N76 [4]

Answer:-

Central angle , Ф/2π , A = Ф/2 r²

The ratio is 1/3 , V = 1/3 Bh

The equation of the circle in standard form is (x - 4)² + (k - 1)² = 25

Step-by-step explanation:

* Lets revise the rules of the area of the sector of a circle

- The area of the sector which has a central angle Ф° is

(Ф°/360°) × πr², where 360° is the measure of the circle and r is

the radius of the circle

- The area of the sector which has a central angle Ф radians is

(1/2) r²Ф

* Lets complete the missing in the 1st picture

- The ratio of the sector's area A to the circle's area is equal to the

ratio of the <u>central angle</u> to the measure of a full rotation of the circle

- A full rotation of a circle is 2π. This proportion can written as

A/πr² = <u>Ф/2π</u>

<em>- </em>Multiply both sides by πr² to get <u>A = Ф/2 r²</u> where Ф is the measure

of the central angle and r is the radius of the circle

* Lets revise the rules of the volume of the prism and the volume

of the pyramid, where they have the same base and height

- The volume of the prism = area of the base × its height

- The volume of the pyramid = 1/3 × area of the base × its height

- From them the ratio of the volume of the pyramid to the volume

of the prism is <u>1/3</u>

- The formula of the volume of the prism is V = Bh, where B is the

area of the base and h is the height, the formula of the volume

of the pyramid is <u>V = 1/3 Bh</u>

<u></u>

* Lets revise the standard form of the equation of a circle with

center (h , k) and radius r

- The equation is: (x - h)² + (y - k)² = r²

∴ x² - 2hx + h² + y² - 2ky + k² - r² = 0

∵ x² - 8x + y² - 2y - 8 = 0

- Lets equate the two equation

∴ x² - 2hx + h² + y² - 2ky + k² - r² = x² - 8x + y² - 2y - 8 = 0

∵ -2h = -8 ⇒ ÷ -2

∴ h = 4

∵ -2k = -2 ⇒ ÷ -2

∴ k = 1

∵ h² + k² - r² = -8

∴ (4)² + (1)² - r² = -8

∴ 16 + 1 - r² = -8

∴ 17 - r² = -8 ⇒ subtract 17 from both sides

∴ -r² = -15 × -1

∴ r² = 25

* Substitute the values of h , k , r in the equation of the standard

form of the circle

∴ (x - 4)² + (k - 1)² = 25

* The equation of the circle in standard form is <u>(x - 4)² + (k - 1)² = 25</u>

<u></u>

8 0

3 years ago

For the summer camp, Josie orders 45 sets of markers. One -fifth of the sets need to go to the office 2/3 of the sets go to the

Degger [83]

Answer:

6 sets

Step-by-step explanation:

(“of”=multiply)

Step 1.

1/5 of 45 sets = 45 x 1/5 = 9 sets.

Step2.

2/3 of 9 sets = 9 x 2/3 = 6 sets

Final Answer:

6 sets

7 0

3 years ago

In a random sample of 600 cars making a right turn at a certain intersection, 157 pulled into the wrong lane. Test the hypothesi

nevsk [136]

Answer:

a)

<em>The statistic value |Z| = 2.053 > 1.96 at 0.05 Level of significance</em>

<em>Null hypothesis is rejected</em>

<em>Alternative hypothesis is Accepted</em>

<em> Actually 30% of all drivers make not this mistake at the given intersection</em>

<em>b)</em>

<em>The test statistic value |Z| = 2.053 >2.576 at 0.01 Level of significance</em>

<em>Null hypothesis is Accepted</em>

<em> Actually 30% of all drivers make this mistake at the given intersection</em>

Step-by-step explanation:

<u><em>Step(i):</em></u>-

Given Population proportion = 30% or 0.30

Given data In a random sample of 600 cars making a right turn at a certain intersection, 157 pulled into the wrong lane

sample proportion

$p^{-} = \frac{x}{n} = \frac{157}{600} = 0.2616$

<em>Null hypothesis:- H₀: p = 0.30</em>

<em>Alternative hypothesis : H₁:p≠0.30</em>

<u><em>Step(ii):-</em></u>

a)

<em>Test statistic </em>

$Z = \frac{p^{-}-P }{\sqrt{\frac{p(1-p)}{n} } }$

$Z = \frac{0.2616-0.30 }{\sqrt{\frac{0.30(1-0.30)}{600} } }$

Z = -2.053

<em> |Z| = |-2.053| = 2.053</em>

<em>Level of significance = 0.05</em>

<em>Z₀.₀₅ = 1.96</em>

<em>The calculated value |Z| = 2.053 > 1.96 at 0.05 Level of significance</em>

<em>Null hypothesis is rejected</em>

<em>Alternative hypothesis is Accepted</em>

<u><em>Conclusion:</em></u><em>-</em>

<em> Actually 30% of all drivers make not this mistake at the given intersection</em>

<em>b)</em>

<em>Given level of significance = 0.01</em>

<em>Z₀.₀₁ = 2.576</em>

<em>The calculated value |Z| = 2.053 >2.576 at 0.01 Level of significance</em>

<em>Null hypothesis is Accepted</em>

<em> Actually 30% of all drivers make this mistake at the given intersection</em>

7 0

2 years ago