If the diagonal path is 750 feet long and the width of the park is 450 feet, what is the length, in the feet, of the park?

Answer:

The two inequalities are;

P ≤ 90e^(0.047t)

P ≤ 270 + 100·t

Step-by-step explanation:

The parameters given for the testing of the new growth inhibitor are;

The growth rate of the bacteria = 4.7% exponentially

The growth inhibitor lowers the growth rate

The population of bacteria after time, t = P

The increase in the number of bacteria per unit time in the 100

The maximum number of bacteria in the standard tube = 270

Therefore, the number of bacteria after the first filling of the tube is P ≤ 270 + 100·t

The equation for exponential growth is [tex]A_0 e^{kt}[/tex]

Where:

A₀ = Initial population = 90

k = Percentage growth rate as percentage

t = Time

The equation for the population of bacteria under the influence of the inhibitor is therefore;

P ≤ [tex]90 \times e^{0.047 \cdot t}[/tex] which is P ≤ 90e^(0.047t).

Answer:

P≤270+100t

P≤90e^(0.047t)

Answer:

Step-by-step explanation:

Let x be the random variable representing the time (in minutes) taken for a dose of a certain drug to be effective as a sedative on lab animals. Since it is normally distributed and the population mean and population standard deviation are known, we would apply the formula,

z = (x - µ)/σ

Where

x = sample mean

µ = population mean

σ = standard deviation

From the information given,

µ = 1

σ = √variance = √0.01 = 0.1

the probability that the time taken for a randomly selected animal is between 1 and 1.1 minutes is expressed as

P(1 ≤ x ≤ 1.1)

For x = 1,

z = (1 - 1)/0.1 = 0

Looking at the normal distribution table, the probability corresponding to the z score is 0.5

For x = 1.1

z = (1.1 - 1)/0.1 = 1

Looking at the normal distribution table, the probability corresponding to the z score is 0.84

Therefore,

P(1 ≤ x ≤ 1.1) = 0.84 - 0.5 = 0.34

The the proportion of animals for which the time taken is between 1 and 1.1 minutes is 0.34

Answer:

David is 12 years old.

Step-by-step explanation:

Let r = Rebecca's age

Let d = David's age

let p = Dad's age

David is 3 times as younger than his dad:

d = [tex]\frac{p}{3}[/tex]

David is 2 times older than Rebecca:

d = 2r

Rebecca is 30 years younger than the dad:

r = p-30

All three equations can be solved by a system

2r = [tex]\frac{p}{3}[/tex]

r = p-30

multiplying r = p-30 by negative 2 and adding it to 2r = [tex]\frac{p}{3}[/tex]

0 = (-2p + p/3) + 60

multiplying new equation by 3

0 = (-6p + p) + 180

5p = 180

p = 36

d = 36/3 = 12

Answer:

1:00 PM

Step-by-step explanation:

According to the conditions given in the question, i confirm that the time time asked here is 1:00 PM.

at 1:00 PM, its 5 minutes (odd),  clearly, more than half an hour away from the next o clock. It is closer to 5 PM than 5 AM.

Answer:

m=3, n=5

Step-by-step explanation:

(3+√5)² = (3+√5)(3+√5) =

3² + 3√5 + 3√5 + √5·√5 = 9 + 6√5 + 5 = 14+6√5

Answer:

Solution,

Area of rectangle= 524.4 m^2

Length(L)= 6.9 m

Breadth(B)=?

Now,

[tex]area = length \times breadth \\ or \: 524.4 = 6.9 \times b \\ or \: 524.4 = 6.9b \\ or \: b = \frac{524.4}{6.9} \\ b = 76 \: m[/tex]

Again,

Perimeter of rectangle:

[tex]2(l + b) \\ = 2(6.9 + 76) \\ = 2 \times 82.9 \\ = 165.8 \: m[/tex]

Hope this helps...

Good luck on your assignment.....

Answer:

The perimeter of the rectangle is 165.8cm

Step-by-step explanation:

Area of a rectangle = length × width

Area = 524.4m²

length = 6.9m

524.4 = 6.9 × width

width = 524.4 / 6.9

width = 76m

Perimeter of a rectangle =

2(length ) + 2(width)

length = 6.9m

width = 76m

Perimeter = 2( 6.9) + 2(76)

= 13.8 + 152

The final answer is

= 165.8cm

Hope this helps you

Answer:

i dont get it, can you please rephrase it?

Answer

A or B

Step-by-step explanation:

the lowest is 1/7 = 5/35 = 10/70

the highest is 1/5 = 7/35 = 14/70

so answer A and B are OK

C and D are out of range

Answer:

A

Step-by-step explanation:

When multiplying numbers with exponents, the exponents add together.  This means that the correct answer is letter A.

Answer:

Both/Neither.

Step-by-step explanation:

For the circle, the area is π(6)^2= 36π. 3/4 of that is 27π. Now, for the ring, area of outer circle is 36π. The area of inner circle is 9π. So, area of ring is 27π. That means, both will take the same amount of paint.

Answer:

144

Step-by-step explanation:

We will use permutations to solve this problem

There are 4 pairs each having a male and a female.

The total number of sample points is 4! = 4*3*2*1= 24

He chooses the male first  then the number of sample space he is left with are 3! = 3*2*1=6

The total number of ways he can select is 4! 3! = 24 * 6= 144

Another way of finding it out is

he has 4 pairs  each having a male and a female so he chooses 1st male then he would choose from this

4 female choices*3 male choices * 3 female choices *2 male choices *2 female choices *1 male choices *1 female choices *= 4*3*3*2*2*1*1= 144

The zookeeper can feed all the animals in 144 ways

The number of different animals is given as:

[tex]n = 4[/tex]

The number of ways to feed any of the 4 male animals is:

[tex]Ways = 4![/tex]

Expand

[tex]Ways = 4 \times 3 \times 2 \times 1[/tex]

[tex]Ways = 24[/tex]

From the question, we understand that the female of the particular animal cannot be selected (yet).

So, there are 3 female animals left.

The number of ways to feed any of the 3 female animals is:

[tex]Ways = 3![/tex]

Expand

[tex]Ways = 3 \times 2 \times 1[/tex]

[tex]Ways = 6[/tex]

So, the number (n) of ways to feed all the animals is:

[tex]n = 24 \times 6[/tex]

[tex]n = 144[/tex]

Hence, he can feed all the animals in 144 ways

Read more about permutation at:

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Answer:

No solution

Step-by-step explanation:

If you graph this system of equations, they do not intersect in any way and therefore there is no solution.

Answer:

sss

Step-by-step explanation:

as you seen your puestion it says they are similar by side if you ask me by what because your given is side

Answer:

Step-by-step explanation:

If she can husk 8 in 24mins

⟩ 8 = 24

Let x = ears of corn in 33mins

⟩ 8 = 24

x = 33

If less more divide

⟩ 24x = 8×33

⟩ x = 264÷24

⟩ x = 11 mins

Answer:

a) x = 5

b) x = 4

Step-by-step explanation:

a) x:2 = 10:4

Product of extremes = Product of means

=> x*4 = 10*2

=> 4x = 20

Dividing both sides by 4

=> x = 5

b) 3:x = 6:8

Product of extremes = Product of Means

=> 3*8 = 6*x

=> 24 = 6x

Dividing both sides by 6

=> x = 4

Answer:

Solution,

[tex]a. \: \: \frac{x}{2} = \frac{10}{4} \\ \: \: or \: x \times 4 = 10 \times 2 \: ( \: cross \: multiplication) \\ \: \: or \: 4x = 20 \\ or \:x = \frac{20}{4} \\ \: \: \: x = 5[/tex]

[tex]b. \: \frac{3}{x} = \frac{6}{8} \\ or \: 6 \times x = 3 \times 8 \: ( \: cross \: multiplication) \\ or \: 6x = 24 \\ \: or \: x = \frac{24}{6} \\ x = 4[/tex]

Hope this helps...

Good luck on your assignment

Answer:

a) About 2261.95

b) $11.94

Step-by-step explanation:

a) The lateral area of a cone can be calculated via A=πrl

b) Simple do 2261.95/400 and round to the nearest 1 to get 6.  Then multiply 6 by 1.99 to get 11.94

Hope it helps <3

Answer:

20:27

Step-by-step explanation:

Answer:

x can take any value and are viable in this situation if and only if it is a positive number

Step-by-step explanation:

We know that the area of a rectangle is given by:

A = x * y

So if we replace we have:

12 ≤ x * y ≤ 36

We divide by y, and we have:

12 / y ≤ x ≤ 36 / y

Which means that the value of x depends on y, that is to say if y is worth 1, the inequality would be:

 12 ≤ x ≤ 36

In the event that y is equal to 2:

 12/2 ≤ x ≤ 36/2

 6 ≤ x ≤ 18

Which means, that depending on y, x can take any value and are viable in this situation if and only if it is a positive number.

The image of the function is missing, you can see it at the end of the answer.

For a rectangle of length L and width W, the area is given by:

A = L*W

We will find that the solution is: 3/2 ≤ x ≤ 11/2

Here we have:

L = 3

W = 2x + 1

Then the area equation is:

A = 3*(2x + 1) = 6x + 3

And we also have the inequality:

12 ≤ A ≤ 36

Replacing A with the equation we get:

12 ≤ 6x + 3 ≤ 36

Now we solve this for x:

12 - 3 ≤ 6x ≤ 36 - 3

9  ≤ 6x  ≤ 33

Now we divide both sides by 6.

9/6 ≤ x ≤ 33/6

3/2 ≤ x ≤ 11/2

If you want to learn more, you can read:

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Answer:

61

Step-by-step explanation:

Definition of conguency

*figure on the right is rotated a bit

Answer:

4^2

Step-by-step explanation:

4^4 times 4^3 is equal to 4^7 since you just add the exponents. Then, when dividing, you subtract the exponents, so 4^7/4^5 is 4^2. I hope this is helpful!

Answer:

the answer is

Step-by-step explanation:

4 to the power of 2

you add 4 and 3 which is 7

and 7 subtract 5 which is

4 to the power of 2

Answer:

The values of x are:

x : -3, -2, -1, 0, 1, 2, 3

Let's solve each by putting each value of x into each equation:

a [tex]y = 2^x[/tex]

> x = -3

=> y = 2^(-3) = 1/8

> x = -2

=> y = 2^(-2) = 1/4

> x = -1

=> y = 2^(-1) = 1/2

> x = 0

=> y = 2^0 = 1

> x = 1

=> y = 2^1 = 2

> x = 2

=> y = 2^2 = 4

> x = 3

=> y = 2^3 = 8

b. [tex]y = -2^x[/tex]

> x = -3

=> y = -2^(-3) = -1/8

> x = -2

=> y = -2^(-2) = -1/4

> x = -1

=> y = -2^(-1) = -1/2

> x = 0

=> y = -2^0 = -1

> x = 1

=> y = -2^1 = -2

> x = 2

=> y = -2^2 = -4

> x = 3

=> y = -2^3 = -8

c. [tex]y = (3)(2^x)[/tex]

> x = -3

=> y = 3 * 2^(-3) = 3 * 1/8 = 3/8

> x = -2

=> y = 3 * 2^(-2) = 3 * 1/4 = 3/4

> x = -1

=> y = 3 * 2^(-1) = 3 * 1/2 = 3/2

> x = 0

=> y = 3 * 2^0 = 3 * 1 = 3

> x = 1

=> y = 3 * 2^1 = 3 * 2 = 6

> x = 2

=> y = 3 * 2^2 = 3 * 4 = 12

> x = 3

=> y = 3 * 2^3 = 3 * 8 = 24

Input these values into the table.

Answer:

a y = 2^x

> x = -3

=> y = 2^(-3) = 1/8

> x = -2

=> y = 2^(-2) = 1/4

> x = -1

=> y = 2^(-1) = 1/2

> x = 0

=> y = 2^0 = 1

> x = 1

=> y = 2^1 = 2

> x = 2

=> y = 2^2 = 4

> x = 3

=> y = 2^3 = 8

b. y = -2^x

> x = -3

=> y = -2^(-3) = -1/8

> x = -2

=> y = -2^(-2) = -1/4

> x = -1

=> y = -2^(-1) = -1/2

> x = 0

=> y = -2^0 = -1

> x = 1

=> y = -2^1 = -2

> x = 2

=> y = -2^2 = -4

> x = 3

=> y = -2^3 = -8

c. y = (3)(2^x)

> x = -3

=> y = 3 * 2^(-3) = 3 * 1/8 = 3/8

> x = -2

=> y = 3 * 2^(-2) = 3 * 1/4 = 3/4

> x = -1

=> y = 3 * 2^(-1) = 3 * 1/2 = 3/2

> x = 0

=> y = 3 * 2^0 = 3 * 1 = 3

> x = 1

=> y = 3 * 2^1 = 3 * 2 = 6

> x = 2

=> y = 3 * 2^2 = 3 * 4 = 12

> x = 3

=> y = 3 * 2^3 = 3 * 8 = 24

Step-by-step explanation:

Answer:

Step-by-step explanation:

2/3(6y + 9)

2/3(6y) = 4y

2/3(9) = 6

=4y + 6 (A)

Answer:

The area of the square adjacent to the third side of the triangle is 11 units²

Step-by-step explanation:

We are given the area of two squares, one being 33 units² the other 44 units². A square is present with all sides being equal, and hence the length of the square present with an area of 33 units² say, should be x² = 33 - if x = the length of one side. Let's make it so that this side belongs to the side of the triangle, to our convenience,

x² = 33,

x = [tex]\sqrt{33}[/tex] .... this is the length of the square, but also a leg of the triangle. Let's calculate the length of the square present with an area of 44 units². This would also be the hypotenuse of the triangle.

x² = 44,

x = [tex]\sqrt{44}[/tex] .... applying pythagorean theorem we should receive the length of a side of the unknown square area. By taking this length to the power of two, we can calculate the square's area, and hence get our solution.

Let x = the length of the side of the unknown square's area -

[tex]\sqrt{(44)}^2[/tex] = [tex]x^2[/tex] + [tex]\sqrt{33}^2[/tex],

x = [tex]\sqrt{11}[/tex] ... And [tex]\sqrt{11}[/tex] squared is 11, making the area of this square 11 units².

Answer:

Step-by-step explanation:

If the triangle is right then area of square adjacent to the longest side is equal to sum of areas of squares adjacent to its other sides. (As in Pythagorean theorem)

So:

    33 units² + ? =  44 units²

     ? =  44 units² - 33 units²

     ? = 11 units²

Answer:

Step-by-step explanation:

given,

initial count of bacteria(P)=4,80,000 ,

increasing rate of bacteria(R)=2.5%,

time(T)= 2 hours

amount(A)=p(1+R/100)^T

A=480000(1+2.5/100)^2

A=480000*(1681/1600)

A=504300

therefore, the bacteria at the end of 2 hours is 504300(approx)

Answer:

itchkirdcbn

Step-by-step explanation:

86rfbbcgui6g....

Answer:

6+3x

Step-by-step explanation:

Have a good day and stay safe!

Answer:

Let the number be x

The above statement is written as

Hope this helps you

Answer:

38

Step-by-step explanation:

Using the five number summary it is 38 since it is 75 percent of the sample

You have the correct answer. Nice work

==========================================================

Explanation:

If the values aren't sorted, then list them from smallest to largest. The values are already sorted for us, so we move onto the next step.

That next step is to find the median. The median is 29 because four values are smaller than it, and four values are larger than it. The value 29 is right in the middle. This value is in slot 5.

Next, split the data into two halves where L = {21,24,25,28} is the lower half and U = {35,37,39,42} is the upper half. As you can see, any value in set L is smaller than the median. While any value in set U is larger than the median.

The third quartile is the median of set U. We have four values in this set, so the median will be between slots 3 and 4 (between 37 and 39)

Average 37 and 39 to get (37+39)/2 = 38. We see that 38 is the midpoint of 37 and 39.

Therefore, the third quartile is 38.

Answer:

1) Formula for experimental probability:

Experimental Probability = [tex]\frac{No.OfFavourableOutcomes}{No.OfPossibleOutcomes}[/tex]

2) Any performance or a random experiment is called a trial.

Answer:

162°

Step-by-step explanation:

This is a hexagon, so the sum of the angle measures will be 720°

Add up the measures

40x=720

Divide

X=18

Multiply by 9 to find angle of D

9*18=162

The measure of the interior angle at vertex D is 162°. Hence, option B. is the right choice.

Polygons are closed plane figures formed by the intersection of 3 or more non-collinear line segments.

The sum of interior angles of an n side polygon = (n-2)180°.

We are given a 6 side polygon ABCDEF.

∴ n = 2.

The sum of interior angles of polygon ABCDEF = (6-2)180° = 4*180° = 720°.

The angles are 2x, 9x, 2x, 9x, 9x, and 9x.

Their sum = 2x + 9x + 2x + 9x + 9x + 9x = 40x.

This sum = The obtained sum

or, 40x = 720°

or, x = 720°/40 = 18°.

∴ Interior angle at vertex D = 9x = 9*18° = 162°. Hence, option B. is the right choice.

Learn more about Polygons at

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