A scientist inoculates mice, one at a time, with a disease germ until he finds 2 that have contracted the disease. if the probability of contracting the disease is 1/6, what is the probability that 8 mice are required?

The requried, Devon needs to score between 46% and 95% on the fifth test to receive a final grade of a B in the course.

To find the range of grades Devon needs on the fifth test to receive a final grade of a B (between 80% and 90% inclusive), we need to consider the average of all five tests.

Let's denote the grade on the fifth test as "x" (in percentage).

The average of the five tests will be:

Average = (92% + 82% + 88% + 92% + x) / 5

To achieve a final grade of a B, the average must be greater than or equal to 80% but less than 90%:

80% ≤ Average < 90%

Now, substitute the given grades and the variable "x" into the average equation:

(92% + 82% + 88% + 92% + x) / 5 ≥ 80%

(92 + 82 + 88 + 92 + x) / 5 ≥ 80

(354 + x) / 5 ≥ 80

354 + x ≥ 400

x ≥ 400 - 354

x ≥ 46

Now, for the upper limit:

(92 + 82 + 88 + 92 + x) / 5 < 90

(354 + x) / 5 < 90

354 + x < 450

x < 450 - 354

x < 96

So, Devon needs to score between 46% and 95% on the fifth test to receive a final grade of a B in the course.

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Devon must score between 46% and 91% on his fifth test to achieve a B average in the course.

To determine the range of grades on the fifth test that would give Devon a final grade of B, we need to calculate the average of the five test scores. For an average to fall between 80% and 90%, the total sum of the five test grades must be between 400% and 449%, since 5 tests × 80% = 400% and 5 tests × 89% (just below 90%) = 445%. Devon's current grades add up to 92% + 82% + 88% + 92% = 354%. Therefore, to achieve a B, his fifth test score needs to be between 400% - 354% = 46% and 445% - 354% = 91%.

Answer:

5x30 + 5x7

Step-by-step explanation:

hope this helps :)

the answer is commutative. hope this helps!

Shilo is using commutative and associative

"For any numbers 'a' and 'b', a + b = b + a"

"For any real numbers 'a', 'b' and 'c',

a × (b + c) = a × b + a × c"

For any numbers 'a', 'b' and 'c',

(a + b) + c = a + (b + c)

For any real number a,

the additive identity is a + 0 = 0 + a = a

For given question,

Shilo is trying to compute the value of 27 + 55 + 13.

She adds 27 + 13 to get 40, and then adds on 55.

⇒ 27 + 55 + 13

= 27 + 13 + 55                  ...........(commutative property, 55 + 13 = 13 + 55)

= (27 + 13) + 55                ...........(associative property)

= 40 + 55

= 95

Therefore, Shilo is using commutative and associative property.

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Answer:

Step-by-step explanation:

Given that there is a circle of .... inches with central angle 0.25 inches

by formula we have arc = radius *central angle in radians

The radii are given three options as 10,20,4 and corresponding arcs as

25,5, 16 inches.

By matching we find that 10(0.25) not equals 25

But 20(0.25) = 5 inches

Also 4(0.25) not equals 16 inches

Hence correct answer is radius = 20 and central arc = 5 inches

Answer:

The correct option is D.

Step-by-step explanation:

The given expression is

[tex](\frac{4}{7})^3[/tex]

According to the property of exponent.

[tex](\frac{a}{b})^n=\frac{a^n}{b^n}[/tex]

Using this property the given expression can be written as

[tex](\frac{4}{7})^3=\frac{4^3}{7^3}[/tex]

[tex](\frac{4}{7})^3=\frac{64}{343}[/tex]

The simplified form of the given expression is [tex]\frac{64}{343}[/tex].

Therefore the correct option is D.

The perimeter of the triangle will be 31.18 inches.

The perimeter of a shape is defined as the total distance around the shape. It is the length of the outline or boundary of any two-dimensional geometric shape.

If we  draw a perpendicular line from one of the vertices of the triangle we get  2 right angled triangles  each with  altitude 9 ins  and vertex angle = 30 degrees.   So:-

[tex]Cos 30 =\dfrac{ 9} {h}[/tex]    

where h = one of the sides of the equilateral triangle

[tex]h = \dfrac{9 }{ cos 30} = 10.392 \ inches[/tex]

Therefore the perimeter of the triangle =

[tex]3 \times 10.392 = 31.1769 \ inches[/tex]

Answer is 31.18 inches to the nearest hundredth.

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3/5 is the number which  can be distributed across two terms inside parentheses

Two or more expressions with an Equal sign is called as Equation.

The given equation is 3/5 (x-10) = 18-4x-1

According to the distributive property, multiplying the sum of two or more addends by a number produces the same result as when each addend is multiplied individually by the number and the products are added together.

To solve the above equation we have to distribute 3/5 on LHS

3/5x-30/5 = 18-4x-1

3/5x-6 = 17-4x

Hence, 3/5 is the number which  can be distributed across two terms inside parentheses

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Answer:

Step-by-step explanation:

What you have todo is to multiply the length by the width

Which is 20×12 = 240

Then multiply 240 by 8.91

This should give you $2,138.4

Length of each side of a triangle with equal measurements is equals to [tex]12in[/tex].

" Perimeter is defined as the total length around the boundary of any two dimensional geomertic shape."

Formula used

Perimeter of a rectangle [tex]= 2 ( L + W)[/tex]

[tex]L =[/tex] length of the rectangle

[tex]W =[/tex] Width of the rectangle

Perimeter of a triangle with equal length [tex]= 3s[/tex]

[tex]s =[/tex] side length of a triangle

According to the question,

Given,

Length of a rectangle [tex]'L'= 13 in[/tex]

Width of a rectangle [tex]'W' = 5 in[/tex]

Substitute the value in the formula we get,

Perimeter of a rectangle [tex]= 2( 13 + 5)[/tex]

                                          [tex]= 36 in[/tex]

Substitute the value in the perimeter of a triangle with equal side length,

[tex]3s = 36 in\\\\\implies s = \frac{36}{3} \\\\\implies s = 12in[/tex]

Hence, Length of each side of a triangle with equal measurements is equals to [tex]12in[/tex].

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subtracting the smaller number from the larger number

ex. 1+ -5 becomes 5-1 = 4, since the larger number is the negative, the answer is negatives oit is -4

ex2. -5+7 = 7-5 = 2, since the larger number is positive, the answer is positive 2

a) domain are the x's

 so 0.5, 2, 2,2.5, 3

b) range is the y's so:

3, 6, 9, 12,15

c) it is not a function, since there are 2 x's that equal 2 but the 2 y's that go with them are different numbers (2,6) & (2,9)

3/4 = 9/12

9/12 + 7/12 = 16/12 = 1 4/12 = 1 1/3 hours

The simplest form is 3/40

A fraction is a part of a whole. In arithmetic, the number is expressed as a quotient, in which the numerator is divided by the denominator.

Given:

30 * 1/4%

= 30* 1/400

= 30/400

=3/40

=0.075

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Answer:  The required example is x = 5.

Step-by-step explanation:  Given that if x is a prime nu mber, then x+1 is not a prime number.

We are to give a counterexample for this.

Let us consider that

[tex]x=5.[/tex]

Then, we know that x is a prime number.

But, we get

[tex]x+1=5+1=6,[/tex] which is not a prime number.

Thus, the required example is x = 5.