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Please show workings and diagrams.​

Question:

(a) How many bacteria would be found in 24 hours

(b) How many bacteria would be found in 2 days

(c) How long for 1000 bacteria to be found

Answer:

(a) 282429536481 bacteria

(b) [tex]7.97*10^{22[/tex] bacteria

(c) 6 days

Step-by-step explanation:

The question illustrates an exponential function

[tex]y = ab^x[/tex]

Where

[tex]a = Initial\ Value = 1[/tex]

[tex]b=Rate = 3[/tex] --- i.e. triples

[tex]x = number\ of\ hours[/tex]

Solving (a): Bacteria in 24 hours

In this case:

[tex]x = 24[/tex]

Substitute [tex]x = 24[/tex], [tex]b = 3[/tex] and [tex]a = 1[/tex]

So:

[tex]y = ab^x[/tex]

[tex]y = 1 * 3^{24[/tex]

[tex]y = 1 * 282429536481[/tex]

[tex]y = 282429536481[/tex] bacteria

Solving (b): Bacteria in 2 days

[tex]2\ days =48\ hours[/tex]

So:

[tex]x = 48[/tex]

Substitute [tex]x = 48[/tex], [tex]b = 3[/tex] and [tex]a = 1[/tex]

So:

[tex]y = ab^x[/tex]

[tex]y = 1 * 3^{48[/tex]

[tex]y =7.97*10^{22[/tex] bacteria

Solving (c): How long for 1000 bacteria

In this case:

[tex]y = 1000[/tex]

Substitute [tex]y = 1000[/tex], [tex]b = 3[/tex] and [tex]a = 1[/tex]

So:

[tex]y = ab^x[/tex]

[tex]1000 = 1 *3^x[/tex]

[tex]1000 = 3^x[/tex]

Take Log of both sides

[tex]Log1000 = Log3^x[/tex]

This gives:

[tex]Log1000 = xLog3[/tex]

Make x the subject

[tex]x = \frac{Log1000}{Log3}[/tex]

[tex]x \approx 6[/tex]

Hence: It takes 6 days

Answer:

192

Step-by-step explanation:

8 x 24 = 192

[tex]4(t+\frac{1}{4})=3[/tex]   distribute by multiplying 4 into the parenthesis.

[tex]4t+1 = 3[/tex]

    [tex]-1[/tex]   [tex]-1[/tex]     subtract 1 on both sides, solve for 3 - 1, which is 2.

__________

[tex]\frac{4t}{4} =\frac{2}{4}[/tex]     divide 4 on both sides.

[tex]t = \frac{2}{4}[/tex]       simplify 2/4.

[tex]t = \frac{1}{2}[/tex]       final answer

hope this helps :)

Answer:

C = $2.40

n = 6

Step-by-step explanation:

For Noelle,

Equation that represents the monthly cost 'C',

C = 0.2n + 1.20

Here, n = number of checks written in a month

For Micah,

Monthly cost for writing checks 'C' = $1.20

Number of checks 'n' = 3

Since, Cost of writing checks ∝ Number of checks written

C' ∝ n

C' = kn

k = [tex]\frac{C'}{n}[/tex]

Here, k = proportionality constant

For C' = 1.2 and n = 3

k = [tex]\frac{1.2}{3}[/tex]

k = 0.4

Equation will be,

C' = 0.4n

For any month C = C'

Therefore, 0.2n + 1.20 = 0.4n

0.4n - 0.2n = 1.20

0.2n = 1.20

n = 6

Number of checks written by Noelle and Micah = 6

For n = 6,

C = 0.2(6) + 1.20

C = $2.40

Cost of writing checks = $2.40

Answer:

85%

40% × ? = 34

? =

34 ÷ 40% =

34 ÷ (40 ÷ 100) =

(100 × 34) ÷ 40 =

3,400 ÷ 40 =

85

Step-by-step explanation:

x^2-25=

[tex] {x}^{2} - 25 = (x - 5)(x + 5) [/tex]

Answer:

4.222222 or jus 4.2 with - over the 2 to indicate multiple 2's

Answer:

4.875

Step-by-step explanation:

Pretty simple, just divide the numerator by the denominator.

Answer:

If the attached graph is the one you mean, the answer is g(x) = (x-4)^2 + 1

The equation of the blue graph is,

⇒ g (x) = (x - 4)² + 1

Given that;

The given function is,

⇒ f (x) = x²

Since, It is given that both graph has same shape it means the equation of blue graph is in the form of;

⇒ g (x) = (x - h)² + k

Where, (h,k) is the vertex of the parabola.

Hence, From the given graph it is noticed that vertex of blue parabola is (4,1),

Therefore, the equation of parabola is,

⇒  g (x) = (x - 4)² + 1

Thus, The equation of the blue graph is,

⇒ g (x) = (x - 4)² + 1

Learn more about the function visit:

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Answer:

A. A reflection over the x-axis and a vertical stretch.

Step-by-step explanation:

Let [tex]h(x) = x^{2}[/tex], to obtain [tex]k(x) = -4\cdot x^{2}[/tex], we need to use the following two operations:

(i) Vertical stretch

[tex]g(x) = k\cdot f(x)[/tex], [tex]k\in \mathbb{R}^{+}[/tex]

(ii) Reflection over the x-axis

[tex]g(x) = -f(x)[/tex]

Let prove both transformations in [tex]h(x)[/tex]:

Step 1 - Vertical stretch ([tex]k = 4[/tex])

[tex]h'(x) = 4\cdot x^{2}[/tex]

Step 2 - Reflection over the x-axis

[tex]k(x) = -4\cdot x^{2}[/tex]

Hence, correct answer is A.

Answer: Sofia used the length of one of the legs as c when she should have used the length of the longest side as c.

Step-by-step explanation: The leg is the smallest number and the hypothenuse is the biggest nunber.

Answer:

Sofia used the length of one of the legs as c when she should have used the length of the longest side as c.

Step-by-step explanation:

Answer:

9 months

Step-by-step explanation:

Answer:

it will be 9 months like the first person said

Answer:

(-3,1.5) (0,3) (3'3)

Step-by-step explanation:

multiply all the coordinates by 1/2

Answer:

y = 11

x = 11 root 3

[tex]x = 11\sqrt{3} [/tex]

[tex]y = 11[/tex]

Step-by-step explanation:

Cos 60 =

[tex] \frac{y}{22} \\ 0.5 = \frac{y}{22} \\ 0.5 \times 22 = y \\ 11 = y[/tex]

[tex]for x \\ \sin(60) = \frac{x}{22} \\ \frac{ \sqrt{3} }{2} = \frac{x}{22} \\ \frac{ \sqrt{3} }{2} \times 22 = x \\ 11 \sqrt{3 } = x[/tex]

Answer:

y = 11

x = 11 root \3

Step-by-step explanation:

Answer:

4.5 x 14 = 63

Explanation:

The area of a parallelogram is the product of any base and the altitude to that base: A = bh.

Answer:

[tex]a_{n}[/tex] = 3n + 32

Step-by-step explanation:

There is a common difference d between consecutive terms, that is

d = 38 - 35 = 41 - 38 = 3

This indicates the sequence is arithmetic with n th term ( explicit formula )

[tex]a_{n}[/tex] = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Here a₁ = 35 and d = 3 , then

[tex]a_{n}[/tex] = 35 + 3(n - 1) = 35 + 3n - 3 = 3n + 32

Answer:

3

Step-by-step explanation:

us the formula

y1 - y2 divided by x1 - x2

=gradient

6 - 3 divided by 5 - 4 = gradient

3 = gradient

hope this helps

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Answer:

X [tex]\leq[/tex] -5

Step-by-step explanation:

Answer:

x ≥ -6

Step-by-step explanation:

Here you go, this might help you

https://courses.lumenlearning.com/collegealgebracoreq/chapter/temp-4-review/

Answer:

x = 14

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Equality Properties

Algebra I

Geometry

Step-by-step explanation:

Step 1: Define

We can see from the diagram that the 2 angles are supplementary

(6x - 10)° + (7x + 8)° = 180°

Step 2: Solve for x

Answer: 9.24

Step-by-step explanation:

12*77 = 924

= 9.24

The answer to the given question is estimating 12% (percent) of 77, we get the answer 9.24.

To calculate 12% of 77 precisely, we can use the following formula: percent / 100 × given number

= 12% of 77

= (12/100) × 77

= 9.24

Therefore, 12% of 77 is 9.24.A percentage is a way of expressing a number as a fraction of 100. The symbol "%" is used to is used to indicate a percentage. For example, if we say that something is 25%, we mean that it is 25 out of 100 or 0.25 as a decimal. Percentages are used in many different areas, such as finance, statistics, and science. They can be used to represent proportions, rates of change, or as a way to compare different quantities. One common use of percentages is to calculate percentage change or increase. This is done by finding the difference between two values and expressing it as a percentage of the original value.

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Answer:

4 ft by 7 ft.

Step-by-step explanation:

Answer:

Step-by-step explanation:

See attached diagram (not to scale).

All given details reflected.

a) Find the measure of XZ using the law of cosines:

b) Now using the law of sines find the measure of angle X:

The bearing of Z from X is:

Answer:

The answer is 125. If you were to pair 250 people in 2, that would be 250 divided by 2.  And 250 divided by 2 is 125.

Step-by-step explanation:

Step-by-step explanation:

1. Use the Pythagorean theorem to solve for side KM:

2. Cosine is adjacent over hypotenuse, so cosine of M would be KM/34, or 30/34

3. Tangent is opposite over adjacent, so tangent of L will be KM/16, or 30/16

4. Sine is opposite over hypotenuse, so sine of M will be 16/34

5. KM=30, solved for in step 1.

hope this helps!!

A rational number is a number that can be expressed as a fraction of integers.

The conclusion the student can make about product xy is that:

D- the product ry is rational because it can be written as the quotient of an Integer and a nonzero Integer.​

Given that:

[tex]x = \frac ab[/tex]

[tex]y = \frac cd[/tex]

The product xy is:

[tex]x \times y = \frac ab \times \frac cd[/tex]

So, we have:

[tex]x \times y = \frac{ac}{bd}[/tex]

From the question, we understand that:

[tex]Integers \to a, c[/tex]

This means that, ac would be an integer (by closure property)

Also:

[tex]Non\ zero \to b,d[/tex]

This means that, bd would be non-zero i.e. [tex]bd \ne 0[/tex]

So, we have:

[tex]x \times y = \frac{ac}{bd}[/tex]

[tex]x \times y = \frac{Integer}{Non\ zero}[/tex]

The quotient of an integer and a non-zero integer is always be rational.

Hence, option (d) is correct.

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Answer:

$200.00/$25.50 = g

Step-by-step explanation:

200.00 / 25.50 = 7 games

Answer:

y+4=-2(x+1)

Step-by-step explanation:

y-y1=m(x-x1)

y-(-4)=-2(x-(-1))

y+4=-2(x+1)

4. Overall, there are 45 students.

13 students achieved a mark over 65

[tex]\frac{13}{45} *100[/tex] = 29%

Therefore the answer is b. 29%

5. b is incorrect.

This is because retrievers account for 10% of the dogs, not 15%.

100%-(35% + 45% + 10%) = 10%