When an antibiotic is introduced into a culture of 70,000 bacteria, the number of bacteria decreases at a continuous rate. After 5 hours, there are only 40,000 bacteria. Determine the the continuous rate. Round your answer to the nearest tenth of a percent. Use a positive sign if it is a continuous growth rate or negative sign if it is a continuous decay rate. Do not write the percent sign in your response.

Answer:

a y a r d = a 2 y r d a y a r d = a 2 y r d

Step-by-step explanation:

Answer:

Number is two

Step-by-step explanation:

First of all we find the closest factors of 864 which are 32 x 27

Simply them we have

32 x 27 = 2^5 x 3³

So

Next we know that to be aperfect cube, each exponent needs to be equally divided by divisible by 3.

So If we multiply 864 x 2 we get

Then

1728 = 2^6 x 3³

So if we finally

Take the cube root of that is 2²* 3^1 = 4 x 3= 12

So 2² x 3^1

So if we equate the powers we have the answer as 2.

Answer: C. and F.

Step-by-step explanation:

Answer:

1594

Step-by-step explanation:

Answer:

b=sqrt7

Step-by-step explanation:

16=9+b^2

Answer:

The length of the hypotenuse is 13 cm, so the area of the missing square is 13^2 = 169 cm.

Answer:

Step-by-step explanation:

The first questions are answered on the attachment.

Answer:

C

Step-by-step explanation:

the area (A) of the parallelogram is calculated as

A = bh ( b is the base and h the perpendicular height )

here b = 9 \(\frac{1}{2}\) and h = 5 , then

A = 9 \(\frac{1}{2}\) × 5 = 47 \(\frac{1}{2}\) ft²

4320 the number of permutations of the letters abcdefg that contain the string bcd.

The number of permutations that contain the string BCD is obtained by multiplying the number of arrangements from Step 1 and the fixed arrangement of BCD from Step 2.

Total permutations = 24 x 1 = 24 We can do this by using the concept of permutations with restrictions.

Let's consider the string bcd as a single letter. Then, we need to arrange the remaining letters along with this 'new' letter.

This can be done in 6! ways (since there are 6 letters left to be arranged).

However, in each of these arrangements, the string bcd can be arranged in 3! ways among themselves.

Therefore, the required number of permutations will be: 6! x 3! = 4320

So, there are 4320 permutations of the letters abcdefg that contain the string bcd.

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Answer: 1 1/4

Step-by-step explanation:

Using trigonometry, the Law of Sines States establishes a relationship between a triangle's side-to-angle ratios. When you know the measurements of a few angles and sides, you can utilize this law to answer a number of triangle-related issues.

In non-right triangles, you can use the Law of Sines to determine any missing angles or side lengths.

The Law of Sines can be used to determine the triangle's missing angle, mB, as it says:

If sin(A)/a = sin(B)/b, then sin(C)/c

Given: c = 67, a = 64, mA = 72.

Let's figure out mB:

sin(A)/a equals sin(B)/b

The values are as follows: sin(72) / 64 = sin(B) / 67

Now let's figure out sin(B):

sin(B) is equal to (sin(72) / 64)*67.

Calculator result: sin(B) = 0.8938

We can use the inverse sine (sin(-1)) of the value: to determine the angle mB.

Sin(-1)(0.8938) mB 63.03 degrees mB

Thus, the triangle's missing angle mB is roughly 63.03 degrees.

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9514 1404 393

Answer:

  1/4^2

Step-by-step explanation:

The applicable rule of exponents is ...

  a^-b = 1/a^b

__

Then ...

  4^-2 = 1/4^2

Answer:

A triangle measures 180° , so you do 50°+40° =90° then you do 180°- 90° = 90° , Therefore your answer is A. Hope this helps bye:)

Answer:

90

180-40-50=90

the triangle have 180 angle so 180 minus with 40 and 50 and you will get the m<B angle

Answer:

I think the answer is (smallest to largest): 2 ⁹/10 , 3³/6 , 3⅝

Step-by-step explanation:

I turned them into top heavy fractions e.g. 3³/6 =⁴²⁰/120 , 3⅝ = ⁴³⁵/120 , 2⁹/10 =

³⁴⁸/120 And then I compared these. I hope this is correct and that this helped x (also I'm from the UK so sorry if my explanation is different from how your taught wherever live

Answer:

k

Step-by-step explanation:

After 8 seconds the ball height was 42 units.

It is given that on a game show, contestants shoot a foam ball toward a target. The table includes points along one path the ball can take to hit the target where x is the time that has passed since the ball was launched and y is the height at this time.

It is required to find how high was the ball after 8 seconds.

It is defined as the graph of a quadratic function that has something bowl-shaped.

The orbit of the ball will be a parabola.

We know the standard form of a quadratic function:

\(\rm y=ax^2+bx+c\)      where \(\rm \\a\neq 0\)

At x = 0 and y = 10, we get:

\(\rm 10 =a(0)^2+b(0)+c\\\rm 10= c\\\rm c=10\)

At x = 2 and y=24, we get:

\(\rm 24= a(2)^2+b(2)+c\\\rm 24=4a+2b+10\\\rm 4a+2b=14\)....(1)

At x = 16 and y = 10, we get:

\(\rm 10= a(16)^2+b(16)+c\\\rm 10=256a+16b+10\\\rm 256a+16b=0 \\\)....(2)

By solving equations (1) and (2), we get;

a = - 1/2, b = 8 and c = 10

Putting these values in the standard form of a quadratic function, we get:

\(\rm y = - \frac{1}{2} x^2+8x+10\\\)

Now, after 8 seconds means when x = 8, we get:

\(\rm y=-\frac{1}{2}\times 8^2 +8\times8+10\\\rm y = -32+64+10\\\rm y= 42\)

Thus, after 8 seconds the ball height was 42 units.

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Answer:

b

Step-by-step explanation:

A and B have the same elements, the measure of AUB will be equal to the measure of B.

To show that if m*(A) = 0, then m*(AUB) = m*(B), we need to prove the following:
1. If m*(A) = 0, then A is a null set.
2. If A is a null set, then AUB = B.
3. If AUB = B, then m*(AUB) = m*(B).
Let's break down each step:
1. If m*(A) = 0, then A is a null set:
  - By definition, a null set has a measure of 0.
  - Since m*(A) = 0, it implies that A has no elements or its measure is 0.
  - Therefore, A is a null set.
2. If A is a null set, then AUB = B:
  - Since A is a null set, it means that it has no elements or its measure is 0.
  - In set theory, the union of a null set (A) with any set (B) results in B.
  - Therefore, AUB = B.
3. If AUB = B, then m*(AUB) = m*(B):
  - Since AUB = B, it implies that both sets have the same elements.
  - The measure of a set is defined as the sum of the measures of its individual elements.
  - Since A and B have the same elements, the measure of AUB will be equal to the measure of B.
  - Therefore, m*(AUB) = m*(B).
By proving these three steps, we have shown that if m*(A) = 0, then m*(AUB) = m*(B).

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Answer:  £ 3675.79

Step-by-step explanation:

A = P(1 + r)^t

A = final amount = x

P = initial principal balance = 3200

r = interest rate = 0.02

t = number of years elapsed = 7

x = 3200(1.02)^7

x = 3200 * 1.14868567

x = 3675.79414

x = 3675.79

Answer:y=415 x = 21.5

Step-by-step explanation:

We can see 4x-37 = 49

4x = 86

x = 21.5

4(21.5) -3 = 83

Then we can see what the other side is because they are equal

y/5 = 83

83 x 5 = 415

y=415

Step-by-step explanation:

Quadrant I: Both values are positive.

Quadrant II: x-value is -ve, y-value is +ve.

On the x-axis: y-value is 0.

On the y-axis: x-value is 0.

The point (9, 0) has a y-value of 0.

=> It lies on the x-axis.

Answer:

this is incorrect. 42% of 78 is actually 32.76

Answer:

Step-by-step explanation:

Opppppssssssss

The histogram representing the data is attcwhwd in the picture below.

Answer:

C On exactly 25% of these days, Shane drank 3 to 4 glasses of water.

Step-by-step explanation:

The number of 8 - ounce glasses is represented on the x - axis and the number of days on the y - axis.

From the histogram ;

Shane drank 1 - 2 glasses on exactly 1 day

Shane drank 3 - 4 glasses on exactly 3 days

Shane drank 5 - 6 glasses on exactly 6 day

Total number of days = 12

60% of 12 = 7.2

On exactly 60% of the days, which is 7.2 days, number of glasses drunk isn't covered by the histogram

25% of 12 ; 0.25 * 12 = 3 days

From the histogram, number of glasses consumed is 3 - 4 glasses ; which is the only true statement about the histogram in the options given.

Answer:X is equal to -4 twice

Step-by-step explanation:

The solution to the equation 2x² + 8x = x² - 16 is x = -4.

Option A is the correct answer.

Solutions are the values of an equation where the values are substituted in the variables of the equation and make the equality in the equation true.

We also find the solution in a system of equations using the substitution or elimination method.

Example:

2x + 4 = 8

The solution is x = 2.

We have,

To solve the equation 2x² + 8x = x² - 16, we first simplify it by moving all the terms to one side:

2x² + 8x - x² + 16 = 0

Simplifying further, we get:

x² + 8x + 16 = 0

This is a quadratic equation of the form ax² + bx + c = 0, where a = 1, b = 8, and c = 16.

We can solve this equation by factoring it:

(x + 4)(x + 4) = 0

This gives us two solutions:

x + 4 = 0 or x + 4 = 0

x = -4 or x = -4

Therefore,

The solution to the equation 2x² + 8x = x² - 16 is x = -4.

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Answer:

B.

Step-by-step explanation:

One of the lines is going to have the y-intercept of -3

Answer:

There are infinitely many solutions

Step-by-step explanation:

The right side is the exact same as the left side, except the two numbers are flipped.

Answer:

(-∞, ∞)

Step-by-step explanation:

For the new coordinates of point A, that is A' = (x', y'), we have:

x' = 2 . cos (180º) = 2 . (-1) = -2

y' = 10 . cos (180º) = -10

The same happens to the other points. So, for B we have :

x' = 3 . (-1) = -3

y' = -4 . (-1) = 4

And for C:

x' = -3 . (-1) = 3

y' = 1 . (-1) = -1

Therefore, the new coordinates will be:

A'(-2, -10)

B'(-3, 4)

C'(3, -1)

Answer:

0.04233 ounces of medicine in a day

Step-by-step explanation:

Answer:

(x/4)+10

Step-by-step explanation:

Quotient=division, so x/4

Increased by 10, so (x/4)+10

Answer:

8 Days with 6 ounces of Dog Food left Over

Step-by-step explanation:

12 Cans per Case x 12.5 ounces per can = 150 Ounces Total

150 Ounces/18 ounces per day= 8.3333333333333 Days

.3333333333333 Days x 18 ounces = 6 remaining ounces.