In a petri dish, a certain type of bacterium doubles in number every 20
minutes
There were originally 8, or 23 bacteria in the dish. After 140 minutes, the
number of bacteria has doubled 7 times, multiplying by 27.
Now the population of bacteria is 23.27. Expressed as a power, how many
bacteria are in the petri dish after 140 minutes?
O A. 210
B. 410
C. 27
D. 221
SUBMIT

Answer:

Step-by-step explanation:

<2 is congruent to <5; Segment AB is congruent to Segment DE

Given

<3≅<4

Vertical angle theorem

ΔCDB≅ΔCAE

AAS

Segment BC is congruent to Segment EC

CPCTC

also  have no idea what I am doing half/half

The value of the probability of the different events are,

The value of the probability P (3) is,

⇒ 1 / 5

And, The value of the probability P (blue & green) is,

⇒ 8/45

We have to given that;

A box contains 2 red marbles, 5 green marbles and 8 blue marbles.

Hence, Total marbles = 2 + 5 + 8 = 15

So, The value of the probability P (3) is,

⇒ 3 / 15

⇒ 1 / 5

And, The value of the probability P (blue & green) is,

⇒ 8/15 x 5/15

⇒ 8/15 x 1/3

⇒ 8 / 45

Thus, The value of the probability P (3) is,

⇒ 1 / 5

And, The value of the probability P (blue & green) is,

⇒ 8/45

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The bakery should use the range to determine whether or not the equipment changes have worked. The correct answer is C.

To determine whether the equipment changes made by the bakery have resulted in more uniform-sized muffins, they should use the measure of variability. The most suitable measure, in this case, would be the range.

The range is calculated by finding the difference between the maximum and minimum values in a data set. In this scenario, the bakery made 25 muffins and measured each one. By finding the range of the measurements, they can assess the spread of sizes among the muffins.

Here's how they can use the range to evaluate the effectiveness of the equipment changes:

Collect the measurements of all 25 muffins.

Determine the maximum and minimum measurements.

Calculate the range by subtracting the minimum measurement from the maximum measurement.

If the range of the muffin sizes is smaller compared to the range before the equipment changes, it suggests that the modifications have resulted in more uniform-sized muffins. Conversely, if the range remains similar or larger, it indicates that the changes might not have effectively improved the uniformity of muffin sizes.

Therefore, the bakery should use the range to determine whether or not the equipment changes have worked. The correct answer is C.

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Answer:

B

Step-by-step explanation:

since domain should be in positive i thinks this should be answer B

Answer:

1350

Step-by-step explanation:

A:B = 13:5 = 975:x

x=975/13*5 =375

total =975+375 = 1350

We use the proportional method

Let A = water used in household A.

Let B = water used in household B.

A to B = 13 to 5

A = 260 gal

260 to B = 13 to 5

260/B = 13/5

13B = 5 * 260

B = 100

A + B = 260 + 100 = 360

The total is 360 gallons.

Answer:

25 cups of apple juice and 10 cups of sparking water.

Step-by-step explanation:

After 4 half-lives, only 1/16th (or 0.0625) of the initial amount of the radioactive isotope will remain.

The amount of a radioactive isotope remaining after a certain number of half-lives can be calculated using the formula:

Amount remaining = Initial amount × (1/2)^(number of half-lives)

In this case, we are given the initial amount as "grams" and we want to find out the amount remaining after 4 half-lives.

So, the equation becomes:

Amount remaining = Initial amount × (1/2)^4

Since each half-life reduces the quantity to half, (1/2)^4 represents the fraction of the initial amount that will remain after 4 half-lives.

Simplifying the equation:

Amount remaining = Initial amount × (1/16)

Therefore, after 4 half-lives, only 1/16th (or 0.0625) of the initial amount of the radioactive isotope will remain.

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Answer:

12.57in^2

Step-by-step explanation:

A = 2x2xπ = 12.57

Since ΔABC and ΔACD are similar triangles, therefore the length of AC is 18 m.

Similar triangles are triangles with corresponding sides that have the same ratio.

Thus:

AD is parallel to BC (bases of a trapezoid are parallel)

Therefore:

∠ACB = ∠CAD (alternate interior angles)

This implies that, ΔABC ~ ΔACD by AA similarity theorem.

Thus:

AC/DA = CB/AC

Substitute

AC² = 12 × 27

AC = √324

AC = 18 m

Therefore, since ΔABC and ΔACD are similar triangles, therefore the length of AC is 18 m.

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Answer:

B.) 51/64

Step-by-step explanation:

Answer:

Positive Slope

Step-by-step explanation:

The slope is going up Right

Step-by-step explanation:

let Sean weight be x

then kerry's weight is twice as Sean that means 2x

and Bob weighs 15kg

three of them altogether weigh 125

that means 15 +2x + x = 125

15+ 3x= 125

we collect like terms

3x= 125-15

3x= 110

therefore x= 36.67kg

Answer:

to solve a system of linear equations graphically we graph both equations in the same coordinate system, the solution to the system will be in the point where the 2 lines intersect.

In order to calculate continuous interest, we can use the formula below:

Where A is the amount after t years, P is the principal (initial value) and r is the interest rate.

So, using A = 2P and r = 0.0475, we have:

Therefore it will take 14.59 years to double the investment.

The total surface area of solid is,

S = 220 m²

And,  The volume of the prism is, 200 m³

We have to given that;

A solid prism is shown in figure.

Since, The surface area of a prism is,

S = (2 × Base Area) + (Base perimeter × height)

Where, "S" is the surface area of the prism.

Hence, We get;

base area = 5 x 10 = 50 m²

height = 4 m

Base Perimeter = 2 (5 + 10) = 30

Hence, We get;

S = (2 x 50) + (30 x 4)

S = 100 + 120

S = 220 m²

Since, A prism is a solid shape that is bound on all its sides by plane faces. The volume of a prism is expressed as;

V = base area × height.

Now, For given figure,

Volume of the prism = base area × height

base area = 5 x 10 = 50 m²

height = 4 m

Hence, Volume = 50 × 4 m³

= 200 m³

Thus, The volume of the prism is, 200 m³

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Answer:

1.(-4,2)

2.(2,4)

3.(-2,8)

Answer:

(1,2) (0,4) (-4,2)

Step-by-step explanation:

took the quiz and got it right.

Answer: letra “q” no es un número

Step-by-step explanation:

84.13% of the printing jobs will be acceptable.

The new standard deviation required to achieve a minimum of 95% of jobs acceptable is 0.121.

The darkness of the print is measured quantitatively using an index. If the index is greater than or equal to 2.0 then the darkness is acceptable. Anything less than 2.0 means the print is too light and not acceptable. The machines print at an average darkness of 2.2 with a standard deviation of 0.20.

The mean of the darkness of the print is µ = 2.2 and the standard deviation is σ = 0.20.Therefore, the z-score can be calculated as; `z = (x - µ) / σ`.The index required for acceptable prints is 2.0. Thus, the percentage of prints that are acceptable can be calculated as follows;P(X ≥ 2.0) = P((X - µ)/σ ≥ (2.0 - 2.2) / 0.20)P(Z ≥ -1) = 1 - P(Z < -1)Using the standard normal table, P(Z < -1) = 0.1587P(Z ≥ -1) = 1 - 0.1587= 0.8413.

To find the new standard deviation, we can use the z-score formula.z = (x - µ) / σz = (2.0 - 2.2) / σz = -1Therefore, P(X ≥ 2.0) = 0.95P(Z ≥ -1) = 0.95P(Z < -1) = 0.05Using the standard normal table, the z-score value of -1.645 corresponds to a cumulative probability of 0.05. Hence,z = (2.0 - 2.2) / σ = -1.645σ = (2.0 - 2.2) / -1.645= 0.121.

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We need to find the coordinate of piston C.

The coordinate of c is, (6, 4).

Hence, the correct option is c.

Answer:

I just want point

Step-by-step explanation:

The expression "F = {(x, y) : φ(x, y, p)}" represents a set of ordered pairs (x, y) that satisfy a condition defined by the function φ. The interpretation and nature of the set F depend on the specific function φ and the parameter p, which determine the relationship between the variables x, y, and p.

The expression "F = {(x, y) :  φ(x, y, p)}" represents a set F consisting of ordered pairs (x, y) that satisfy a particular condition defined by the function  φ, which takes the variables x, y, and p as inputs.

To fully understand the meaning of F, we need to delve into the function  φ and its relationship with the variables x, y, and p. The function φ could represent a wide range of mathematical relationships or conditions that determine the inclusion of certain pairs (x, y) in the set F.

For instance, let's consider a specific example where vraphi(x, y, p) is defined  φ(x, y, p) = \(x^2 + y^2 - p^2.\)In this case, F = {(x, y) : \(x^2 + y^2 - p^2\)= 0} represents a set of ordered pairs (x, y) that satisfy the equation \(x^2 + y^2 - p^2 = 0.\) This equation represents a circle with radius p centered at the origin (0, 0). Consequently, F corresponds to all the points lying on the circumference of this circle.

It is important to note that the specific meaning and implications of F heavily rely on the nature of the function  φ and the parameter p. Different functions and parameters will yield distinct sets F with their own unique characteristics and interpretations.

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Step-by-step explanation:

Slope 1/2    point    5,1  

  in point slope form would be

    (y-1) = 1/2 (x-5)

Answer:

3.2 The Factor Theorem and The Remainder Theorem 257

3.2 The Factor Theorem and The Remainder Theorem

Suppose we wish to find the zeros of f(x) = x

3 + 4x

2 − 5x − 14. Setting f(x) = 0 results in the

polynomial equation x

3 + 4x

2 − 5x − 14 = 0. Despite all of the factoring techniques we learned1

in Intermediate Algebra, this equation foils2 us at every turn. If we graph f using the graphing

calculator, we get

The graph suggests that the function has three zeros, one of which is x = 2. It’s easy to show

that f(2) = 0, but the other two zeros seem to be less friendly. Even though we could use the

‘Zero’ command to find decimal approximations for these, we seek a method to find the remaining

zeros exactly. Based on our experience, if x = 2 is a zero, it seems that there should be a factor

of (x − 2) lurking around in the factorization of f(x). In other words, we should expect that

x

3 + 4x

2 − 5x − 14 = (x − 2) q(x), where q(x) is some other polynomial. How could we find such

a q(x), if it even exists? The answer comes from our old friend, polynomial division. Dividing

x

3 + 4x

2 − 5x − 14 by x − 2 gives

x

2 + 6x + 7

x−2 x

3 + 4x

2 − 5x − 14

−

x

3 −2x

2

6x

2 − 5x

−

6x

2 −12x)

7x − 14

− (7x −14)

0

As you may recall, this means x

3 + 4x

2 − 5x − 14 = (x − 2)

x

2 + 6x + 7

, so to find the zeros of f,

we now solve (x − 2)

x

2 + 6x + 7

= 0. We get x − 2 = 0 (which gives us our known zero, x = 2)

as well as x

2 + 6x + 7 = 0. The latter doesn’t factor nicely, so we apply the Quadratic Formula to

get x = −3 ±

√

2. The point of this section is to generalize the technique applied here. First up is

a friendly reminder of what we can expect when we divide polynomi

Step-by-step explanation:

Answer:

Speed= Dist/time= p/x miles per minute

Time to run q miles=q divided by p/x= qx/p minutes

Step-by-step explanation:

Answer:

50

Step-by-step explanation:

Equation: 2+4+6+8+30

Sum: 50

8+2=10

4+6=10

10+10=20+30=50.

Final answer: 50

By the Mean Value Theorem, there exists a number c in (1, 7) such that ƒ'(c) = 2/c and 2/c = ln7 / 6, and c ≈ 0.909.

The Mean Value Theorem (MVT) states that if a function ƒ(x) is continuous on the closed interval [a, b] and differentiable on the open interval (a, b), then there exists a number c in (a, b) such that:

ƒ'(c) = [ ƒ(b) - ƒ(a) ] / (b - a)

ƒ(x) = 2lnx - 8 is continuous on the closed interval [1, 7], since it is the sum and composition of continuous functions.

ƒ(x) = 2lnx - 8 is differentiable on the open interval (1, 7), since its derivative ƒ'(x) = 2/x is defined and continuous on (1, 7).

Therefore, the Mean Value Theorem can be applied to ƒ(x) on [1, 7]. To find the value of c, we need to solve the equation:

ƒ'(c) = [ ƒ(b) - ƒ(a) ] / (b - a)

Substituting the given values, we get:

2/c = [ 2ln7 - 2ln1 ] / (7 - 1)

2/c = ln7

c = 2 / ln7

c ≈ 0.909

Therefore, by the Mean Value Theorem, there exists a number c in (1, 7) such that ƒ'(c) = 2/c and 2/c = ln7 / 6, and c ≈ 0.909.

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Answer:

A 573308928

B. 124176266400000000000000000

Answer:

Length = 14, Width = 7

Step-by-step explanation:

Step 1:

Length + Length + Width + Width = Perimeter

Step 2:

2w + 2w + w + w = 42

Step 3:

6w = 42

Step 4:

w = 7

Step 5:

7 × 2 = 14

i hope this helps you.     :)

Answer:

Length = 14, Width = 7

Step-by-step explanation:

It would take 90 hours on the first machine, 20 hours on the second machine, and 0 hours on the third machine to produce 100 units of Product A and 50 units of Product B.

What is matrix ?

A matrix is a rectangular array of numbers, symbols, or expressions arranged in rows and columns.

Here is an example of a 2x3 matrix that represents a problem in industrial engineering:

Suppose a company produces two types of products, Product A and Product B, and they use three different machines to manufacture these products. The number of hours required to produce each unit of each product using each machine is given by the following matrix:

| 2  3  4 |

| 4  2  3 |

This matrix represents a system of linear equations that can be solved using matrix inversion to find the number of hours required to produce a given number of units of each product. For example, suppose the company needs to produce 100 units of Product A and 50 units of Product B. To find the number of hours required for each machine, we can set up the following system of equations:

2x + 3y + 4z = 100

4x + 2y + 3z = 50

where x, y, and z represent the number of hours required for each machine.

To solve this system of equations using matrix inversion, we can first write the system in matrix form:

| 2  3  4 |   | x |   | 100 |

| 4  2  3 | * | y | = | 50  |

| 0  0  0 |   | z |   | 0   |

Next, we need to find the inverse of the coefficient matrix:

| 2  3  4 |^-1 = 1/10 | -6  12 -3 |

| 4  2  3 |          |  9 -6  4 |

| 0  0  0 |          |  0  0  0 |

Finally, we can solve for x, y, and z by multiplying both sides of the equation by the inverse of the coefficient matrix:

| x |   | -6  12 -3 |   | 100 |   | 90 |

| y | = |  9 -6  4  | * | 50  | = | 20 |

| z |   |  0  0  0  |   | 0   |   | 0  |

Therefore, it would take 90 hours on the first machine, 20 hours on the second machine, and 0 hours on the third machine to produce 100 units of Product A and 50 units of Product B.

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