The weight of a cat is normally distributed with a mean of 9 pounds and a standard deviation of 2 pounds. Using the empirical rule, what is the probability that a cat will weigh less than 11 pounds?

I assume you meant to type f(x)=2^x.

Using the normal distribution, the probabilities are given as follows:

a. 0.4602 = 46.02%.

b. 0.281 = 28.1%.

The z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The parameters are given as follows:

[tex]\mu = 959, \sigma = 263, n = 37, s = \frac{263}{\sqrt{37}} = 43.24[/tex]

Item a:

The probability is one subtracted by the p-value of Z when X = 984, hence:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{984 - 959}{263}[/tex]

Z = 0.1

Z = 0.1 has a p-value of 0.5398.

1 - 0.5398 = 0.4602.

Item b:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem:

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{984 - 959}{43.24}[/tex]

Z = 0.58

Z = 0.58 has a p-value of 0.7190.

1 - 0.719 = 0.281.

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Answer:

length = 4 cm

Width = 5 cm

Step-by-step explanation:

      Area of rectangle = length * width

length = (x - 3) meters

Width = (x - 2) meter

Area = 20 square meters

  (x - 3)*(x - 2) = 20

Use FOIL method.

   x*x + (x)(-2) + (-3)*x + (-3)*(-2) = 20

                         x² -2x  - 3x + 6 =20

         Combine like terms

                        x² - 5x + 6  = 20

Now subtract 20 from both side

                     x² - 5x + 6 - 20 = 0

                           x² - 5x - 14  = 0

Factorize the equation and find the roots

         Sum = -5

   Product = -14

    Factors =  (-7) , 2

When we add (-7) + 2 = -5 and when we multiply (-7)*2 = -14

x² + 2x - 7x - 14 = 0

 x(x + 2) -7(x + 2) = 0

 (x + 2)(x - 7)  = 0

  x - 7 = 0    {Ignore (x + 2 = 0) as measurements wont't be in negative}

x = 7

length = x - 3

          = 7 - 3

   [tex]\sf \boxed{\bf length = 4 \ cm}[/tex]

width = x - 2

         = 7 - 2

    [tex]\sf \boxed{\bf width = 5 \ cm }[/tex]

Answer:

33

Step-by-step explanation:

Apply BODMAS(Brackets Of Division Multiplication Addition Subtraction)

Answer:

+33

Step-by-step explanation:

first (24÷8), 8x(3), 14-8+3+24 =33

Answer:

dSutlrysl07tris5eiruwf3rtst47er747y3utgxgudjdudufnlgjfngvi

The profits at x = $185 is 0 and the graph is attached below:

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

Function is to model the profits of a new pet-monitoring system, so, if the profits are y and x then y = f(x)

The curve shows that y is negative at values of x< $95, then the profits increase when x varies between $95 and $140.

The profits reach a maximum at $140 and then the profits start to reduce as x increases again.

So, the profits at x = $185 is 0.

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Answer:

a on edge

Step-by-step explanation:

I js did it

The loss on the sale of equipment of $25 will appear in cash flow for operating activities section.

The cash flow statement is a financial statement that gives aggregate data regarding the cash inflows that a company receives.

The loss on sales of equipment will be:

Cost of equipment = $500

Less accumulated depreciation = $375

Less sale of equipment = $25

Here, the loss on the sale of equipment of $25 will appear in cash flow for operating activities section.

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The number of ways different the sequences of adenine, thymine, cytosine and guanine can be arranged along a short strand of DNA with 5 base units is 120

Permutation is the number of ways of arrangement for a given set.

The formula for a permutation is given as P(n, r) = n! / (n-r)!

Where n = items chosen from = 5

r is the number of items = 4

Substitute values into the formula

P(5, 4) = [tex]\frac{5!}{5-4!}[/tex]

P(5,4) = [tex]\frac{5 * 4* 3*2*1}{1}[/tex]

P(5,4) = [tex]\frac{120}{1}[/tex]

P(5,4) = 120

Therefore, the number of ways different the sequences of adenine, thymine, cytosine and guanine can be arranged along a short strand of DNA with 5 base units is 120

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Answer:

The answer is actually 120.

Step-by-step explanation:

I have the keysheet to the questions.

Answer:

A) 2

Step-by-step explanation:

Because the slope is negative of line 2 the distance is getting smaller

The volume of the copper wire is 226.080 cm³ and the mass of the wire is 2,012.112 g/cm³.

Given that, the length of copper wire=200 m=200000 mm and the diameter of the copper wire=1.2 mm.

We need to find the volume of the copper wire.

The formula to find the volume of a cylinder is πr²h.

Now, the volume of the copper wire=πr²h=[tex]\frac{22}{7} \times (0.6)^{2} \times 200000=2,26,080[/tex] mm³=226.080 cm³

If the density of copper is 8.9 g/cm³, find the mass of the wire.

We know that [tex]Density=\frac{Mass}{Volume} }[/tex].

⇒8.9 g/cm³=[tex]\frac{Mass}{226.080}[/tex]

⇒Mass=2,012.112 g/cm³

Therefore, the volume of the copper wire is 226.080 cm³ and the mass of the wire is 2,012.112 g/cm³.

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Answer:

18.75 inches

Step-by-step explanation:

Inches:feet

3. : 8

X. : 50

(Cross multiply)

8x=150

X=150÷8=18.75

Answer:

y+3=10

solution,

y+3=10

y+3-3=10-3

y=7

thus,

y=7ans

Answer:

v ≥ 5

Step-by-step explanation:

v ≥ 5

The function which is used to represent the graphed geometric sequence is

[tex]f(x) = 80{( \frac{1}{4}) }^{x - 1} [/tex]

Let a be first term and r common ratio of the Geometric progression.

The Geometric sequence is of the form a,ar,ar^2, ...

The common ratio will be ar/a.

From the graph, we can find out the sequence as 80,20,5, ...

Here we can see that the sequence is in Geometric Progression.

First term a=80

Common ratio r= ar/a

= 20/80

=1/4

General term of Geometric sequence is

[tex]f(x) = a {r}^{x - 1} [/tex]

Substituting the value a = 80 and r = 1/4,

we get,

[tex]f(x) =80 { (\frac{1}{4} )}^{x - 1} [/tex]

Hence, the correct answer is

[tex]f(x) =80 { (\frac{1}{4} )}^{x - 1} [/tex]

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Answer:

5

Step-by-step explanation:

As seen in the figure, we know that because ΔABC is isosceles, ∠B = ∠C, so we know that 75 = 3x, x = 15. Next, following the rule that all angles in a triangle sum to 180°, we can set up this equation and solve it:

  4y + 10 + 75 + 75 = 180

                          4y = 180 - 160

                            y = 20

                         ∴ y = 5

Answer:

- 439

Step-by-step explanation:

evaluate f(- 7) and substitute the value obtained into s(x)

f(- 7) = 3(- 7) = - 21 , then

s(- 21) = 2 - (- 21)² = 2 - 441 = - 439

Answer:

A. (s*t)(-7)=-439

Step-by-step explanation:

(s*t)(-7) is the same as s(t(-7)). First find t(-7)

t(-7)=3(-7)=-21

t(-7)=-21

Plug -21 into s(t(-7)) for t(-7).

Find s(-21).

s(-21)=2-(-21)^2=-441+2=-439

Hope this helps!

If not, I am sorry.

Answer:

x = -2, y = 3

Step-by-step explanation:

2x + 3y = 5

5x - 2y = -16

In order to find the value of a variable, we must eliminate the other variable by multiplying the equations to get the same coefficient.

We can multiply the first equation by 5 and the second one by 2 to get the same coefficient for x, the equations then become:

10x + 15y = 25

10x - 4y = -32

Now we can subtract:

19y = 57

y = 3

Since we know the value of y, we can substitute it into one of the original equations:

2x + 3(3) = 5

2x + 9 = 5

2x = -4

x = -2

The equation will be given as y = 6x for the given information in the question.

The complete question is as below:-

Mr Hann is trying to decide how many new copies of a book to order for his students. Each book weighs 6 ounces Which ordered pair is a viable solution if x represents the number of books he orders and y represents the total weight of the books, in ounces?

Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication and division.

Here we are given that the weight of each book is 6 ounces. If there are x number of books, the weight of x books will be 6 times x.

And if y represents the total weight, we can form an equation describing the relation between a number of books and their net weight. The equation can be

y = 6x

Hence all the ordered pairs satisfying the above equation will represent the number of books and the total weight.

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All the solution of the equation x³ + 8x² + 100x + 800 = 0 will be 10i, -10i, and -8. Then the correct option is D.

It is a method for dividing a polynomial into pieces that will be multiplied together. At this moment, the polynomial's value will be zero.

The equation is given below.

          x³ + 8x² + 100x = -800

x³ + 8x² + 100x + 800 = 0

Then the factor of the equation will be

x³ + 8x² + 100x + 800 = 0

x² (x + 8) + 100(x + 8) = 0

        (x² + 100)(x + 8) = 0

Then all the solution of the equation will be

x = 10i, -10i, and -8.

Then the correct option is D.

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Answer:

d

Step-by-step explanation:

The attached graph represents the solution set of [tex]3e^x > \frac 12^x[/tex]

The complete options are not given.

So, I would plot the graph that represents the solution set

The inequality is given as:

[tex]3e^x > \frac 12^x[/tex]

Start by splitting the inequalities as follows:

[tex]f(x) > 3e^x[/tex]

[tex]g(x) > \frac 12^x[/tex]

The above means that we plot the graphs of f(x) and g(x) to represent the solution set

See attachment

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Answer:

80 m is distance traveled

Step-by-step explanation:

if object moves at 20m/s, then in 4 seconds the expression 20 x 4 is used to get 80. 80 m traveled

The surface area is multiplied by a factor of 16

The dimensions are given as:

The factor of the surface area is calculated as:

Surface area = Factor^2

So, we have:

Surface area = 4^2

Evaluate

Surface area = 16

Hence, the surface area is multiplied by a factor of 16

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16

Step-by-step explanation:

Answer:

Step-by-step explanation:

A function can only have one output for an input.  That is, for any value of x, there must be a unique value of y.

{(-6,-1), (13,8), (1,6), (1,-10)}   Not a  Function:  (1,6) and (1,-10)

{(10,5), (10,-5), (5,10), (5,-10)}  Not a  Function:  (10,5) and (10,-5)

{(3,5), (-17,-5), (3,-5), (-17,5)}   Not a Function:  (3,5) and (3,-5)

{(10,5), (-10,-5), (5,10), (-5,-10)}  Function:  No duplicate values of y for a value of x.

The polynomial 7x² + 6x + 7 is equal to the sum of polynomials 1 and 2.

Polynomials are mathematical expressions involving variables raised with non-negative integers and coefficients and constants with only operations of addition, subtraction, multiplication and non-negative exponentiation of variables involved. Example, x² + 3x + 5.

As per the given informations, the first polynomial is 2x² + 2x + 1.

The second polynomial equal is 5x² + 4x + 6.

Now, the sum of the two polynomial can be written as,

Sum = 5x² + 4x + 6 + 2x² + 2x + 1 = 7x² + 6x + 7

Therefore, the polynomial 7x² + 6x + 7 is equal to the sum of polynomials 1 and 2.

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Answer:       B.     [–4, 0)  ∪  [2, ∞)

To find the range, find out what y-values are possible for the function in the graph.

We need to pay attention to what symbols to use.

Solid circle

Empty circle

Arrow

Square brackets: [ and ]

Curved brackets: ( and )

Union of sets: ∪

Let's start by looking for the lowest possible y-value at the bottom of the diagram. On the graph, the point (4, –4) marked with a solid circle.

The function touches the point and stops. Since the y-value is –4, the lowest possible y-value is:     [tex]-4[/tex]

If we follow the blue line upwards, we find an empty circle at (0, 0). The y-value in (0, 0) is 0. This means that the function gets close, but does not include:     [tex]0[/tex]

So, the first part of our range is:

The blue line on the top starts where y = 2 at a solid circle. So, the function includes the y-value:    [tex]2[/tex]

If we follow this blue line upwards, it ends with an arrow. This means it will keep going to infinity, which is the symbol:    [tex]\infty[/tex]

So, the second part of our range is:

Put the lower and upper blue lines together with the union of sets symbol. The range is expressed as:    [–4, 0)  ∪  [2, ∞)

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Answer:

p =43

Step-by-step explanation:

Finding the angle in a triangle

The angle next to 133, angle a,  is 180-133 = 47 because the angles form a straight line

The angle next to 90, angle b, is 180-90 = 90,  because the angles form a straight line

We have a triangle.  The angles in a triangle equal 180 degrees

a+b+ p =180

47+90+p = 180

137 + p = 180

p = 180-137

p =43

The simplified product of [tex]2\sqrt{5x^{3} }[/tex] and -3[tex]\sqrt{10x^{2} }[/tex] is -30[tex]x^{5/2} \sqrt{2}[/tex].

Given Two expressions: -3[tex]\sqrt{10x^{2} }[/tex] and 2[tex]\sqrt{5x^{3} }[/tex].

We have to multiply both the expressions and it can be done as under:

-3[tex]\sqrt{10x^{2} }[/tex] *2[tex]\sqrt{5x^{3} }[/tex]

Firstly we have to multiply -3 with 2 to get

=-6[tex]\sqrt{10x^{2} }\sqrt{5x^{3} }[/tex]

Then we have to find square root of x cube and x square which is x to the power 3/2 and x to the power 1.

=[tex]-6x^{3/2} x\sqrt{10}\sqrt{5}[/tex]

Now we have to multiply both the numbers in the root to get the answer;

=-6[tex]x^{5/2} \sqrt{50}[/tex]

Square root of 50 is 5 root 2.

=-6*5[tex]\sqrt{2}[/tex][tex]x^{5/2}[/tex]

=-30[tex]\sqrt{2}[/tex][tex]x^{5/2}[/tex]

Hence the simplified product is -30[tex]\sqrt{2}[/tex][tex]x^{5/2}[/tex].

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The trigonometric relation is solved and the length of side DE is given by the relation DE = 3.8 ( tan 40° )

Trigonometry is the study of the relationships between the angles and the lengths of the sides of triangles

The six trigonometric functions are sin , cos , tan , cosec , sec and cot

Let the angle be θ , such that

sin θ = opposite / hypotenuse

cos θ = adjacent / hypotenuse

tan θ = opposite / adjacent

tan θ = sin θ / cos θ

cosec θ = 1/sin θ

sec θ = 1/cos θ

cot θ = 1/tan θ

Given data ,

Let the triangle be represented as ΔEFD

Now , the measure of side EF = 5 units

The measure of side DF = 3.8 units

And , from the trigonometric relations , we get

tan θ = opposite / adjacent

On simplifying , we get

tan 40° = DE / DF

Multiply by DF on both sides , we get

DE = 3.8 ( tan 40° )

Hence , the trigonometric relation is solved

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