A box contains seven green marbles, six blue marbles and eight orange marbles. Without looking, you choose two marbles out of the bag. What is the probability that the first two picked will both be green if you don’t replace the marble after the first pick?

In scientific notation, 0.00001 is equal to 1 × 10⁻⁵.

Scientific notation is a way of expressing very big or very small numbers conveniently and with the appropriate number of significant figures.  The general expression for the scientific notation is shown below:

M × 10ⁿ

M is a number that is greater than or equal to 1 but less than 10 and n is the number of times you have to multiply M by 10 to get the number.

The value of n can be easily determined by looking at the decimal point and counting the number of times it is moved to the left or to the right until a proper value of M is obtained.

The steps are as follows:

        NOTE: If the decimal point was moved to the left, then the

                    exponent n  will be written as positive (+x).

                    If the decimal point was moved to the right, then the

                   exponent  n will be written as negative (-x).

Applying the steps to the problem:

STEP 1: 0.00001

The decimal point is four places away from the digit 1.

STEP 2:  To get a number M that is greater than or equal to 1 but less than 10, the decimal point must be moved five places to the right and placed after the digit 1. (000001 or 1)

STEP 3: Since the decimal point was moved five places to the right, the exponent should have a magnitude of 5 and a negative sign. (1 × 10⁻⁵)

Keywords: scientific notation, exponential notation

Scientific notation is a form that can be used to represent very large or very small numbers

The option that gives the correct representation of 0.00001 is scientific notation (standard form) is the option;

Reason:

Required: To convert 0.00001 to a power of 10

Solution:

The method to convert a decimal to a scientific notation is given by moving the decimal point to the right of the first significant digit then multiply the result by 10 raised to the negative of the number of places the decimal point is moved

Where;

a = The number having only one digit to the left of the decimal point

b = The number of places the decimal point is moved (b is positive moving left and negative for moving right)

The given decimal number is 0.00001

Therefore, the decimal can be moved 5 places to the right to give;

0.00001 = 1.0 × 10⁻⁵ = 10⁻⁵

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D is the correct answer.

Step-by-step explanation:

D. Glenda chooses to check 300 monitors.

A binomial experiment is defined as a statistical experiment which consists of n repeated trials. Only two possible outcomes are possible in each trial- either its a success or a failure. Here the probability of success remains the same on every trial.

Now, to know about the defects through binomial experiment Glenda must choose a number of computers or trials. So, option D is correct.

The statement that will make this process into a binomial experiment is that,

⇒ Glenda checks the monitors until she has 300 non-defective monitors."

Hence, Option C is correct.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

We have to given that;

Glenda checks the computer monitors made at her company for defects. It has been shown that 0.5% of the monitors are defective.

Since, A binomial experiment is defined as a statistical experiment which consists of n repeated trials.

Only two possible outcomes are possible in each trial- either its a success or a failure. Here the probability of success remains the same on every trial.

Hence, For check several monitors and record if they are defective,

Glenda checks the monitors until she has 300 non-defective monitors."

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Final answer:

To sketch the polynomial graph without plotting points beyond intercepts, identify the x-intercepts from the factors, note the behavior at these points due to the powers, and connect them considering the end behavior akin to y = x^13.

Explanation:

To sketch a possible graph of the given polynomial f(x) = (x + 8)^3(x + 6)^2(x + 2)(x - 1)^3(x - 3)^4(x - 6), we can use its intercepts and the behavior near these intercepts. The intercepts are the x-values for which f(x) = 0. These are at x = -8, x = -6, x = -2, x = 1, x = 3, and x = 6.

Since these factors are raised to different powers, the graph will behave differently at each intercept. Also, since the highest power in the polynomial is 13 (3+2+1+3+4+1), the end behavior of f(x) as x approaches positive or negative infinity will resemble that of y = x^13.

Here's a step-by-step guide for sketching the graph:

Plot the x-intercepts on the x-axis: (-8, 0), (-6, 0), (-2, 0), (1, 0), (3, 0), (6, 0).

For each intercept, note that if the factor has an odd power, the graph crosses the x-axis, and if it has an even power, the graph touches the x-axis and turns back.

At x = -8, since the power is 3 (odd), the graph crosses the axis and behaves similarly to y = x^3, starting from the bottom.

At x = -6 and x = -2, the powers are 2 (even), so the graph will just touch the axis and turn back.

At x = 1, the power is 3 (odd), so the graph will cross the axis with the behavior of y = x^3.

At x = 3, the power is 4 (even), hence the graph touches the axis and turns back.

At x = 6, as the factor is raised to the first power (odd), the graph crosses the x-axis.

Finally, connect these points with smooth curves, keeping in mind the end behavior of the graph will rise on both ends because the degree is 13, an odd number.

Remember that the final graph should show the pattern of rising and falling appropriately between these intercepts based on the powers of each factor.

Answer:

Step-by-step explanation:

n=sample size =200

Mean = x bar = 55 hours

Std deviation (Population) = 7 hours

For 99% confidence level

Z critical value = 2.58

Margin of error = ±2.58(std error)

Std error = [tex]\frac{7}{\sqrt{n} } =0.495[/tex]

Hence margin of error = ±0.495(258)=1.28

Confidence interval = (55-1.28, 55+1.28) = (53.72, 56.28)

~(53.73, 56.27)

Hence option A

52 weeks per year

 biweekly means she gets paid every 2 weeks

 so 52/2 = 27

22500/27 = 833.33 each paycheck

[tex]\frac{x^{-3}y^{12}}{x^{15}y^{-15}}[/tex]  shows the correct step that is from the simplification from the given expression [tex][\frac{xy^4}{x^{-5}y^5}]^3[/tex]. Option d is correct.

Simplification is defined as the solution making tendency to expressions.

Here,  expression [tex][\frac{xy^4}{x^{-5}y^5}]^3[/tex]

Multiply the whole power 3 in the square bracket.
Gives,
⇒[tex]\frac{x^{-3}y^{12}}{x^{15}y^{-15}}[/tex]  

Thus, [tex]\frac{x^{-3}y^{12}}{x^{15}y^{-15}}[/tex]  shows the correct step that is from the simplification from the given expression [tex][\frac{xy^4}{x^{-5}y^5}]^3[/tex].

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Answer: So, The circumference of Meg's picture frame is smaller than the perimeter of Pam's picture frame by 0.64 feet.

Step-by-step explanation:

Since we have given that

Area of Pam 's picture frame which is square in shape = 3 sq. ft.

As we know the formula for "Area of square ":

[tex]Area=Side^2\\\\3=Side^2\\\\\sqrt{3}\ ft=Side[/tex]

So, Perimeter of square frame would be

[tex]Perimeter=4\times side\\\\Perimeter=4\times \sqrt{3}\\\\Perimeter=6.93\ ft[/tex]

Radius of Meg's circular frame = 1 foot

So, Circumference of circular frame would be

[tex]2\pi r\\\\=2\times \dfrac{22}{7}\times 1\\\\=\dfrac{44}{7}\\\\=6.29\ ft[/tex]

So, The circumference of Meg's picture frame is smaller than the perimeter of Pam's picture frame by 6.93-6.29=0.64 feet.

Answer:

Important information like the common difference, 1st term, the # of terms; the last term must be included to find the sum of a series.

Answer:

Refer graph attached below

Step-by-step explanation:

Given equation  [tex]x^2-4=5[/tex]

We have to  Solve the given equation  [tex]x^2-4=5[/tex] graphically.

We first solve the given equation [tex]x^2-4=5[/tex]

Consider the given equation [tex]x^2-4=5[/tex]

Adding 4 both sides, we have

[tex]\Rightarrow x^2-4+4=5+4[/tex]

Simplify, we get,

[tex]\Rightarrow x^2=9[/tex]

[tex]\Rightarrow x^2-9=0[/tex]

To plot the graph let [tex]x^2-9=y[/tex] be the equation

It will be a parabola with vertex (0,9).

Refer graph attached below

Answer:

Option A is correct.

Step-by-step explanation:

We are given that, the model for the depreciating value of a semi-truck is,

[tex]y = A_{O}(0.83)^x[/tex]

1. It is required to find the value of the truck initially i.e. when x= 0.

So, substituting x= 0, we have,

[tex]y = A_{O}(0.83)^0[/tex]

i.e. [tex]y = A_{O}\times 1[/tex]

i.e. [tex]y = A_{O}[/tex]

Since, the graph passes through the point (0,70,000).

Thus, we get, [tex]A_{O}=70,000[/tex]

Hence, the initial value is 70,000.

2. It is required to find the value of the truck initially i.e. when x= 50,000

That is, when x= 0, the value of y= 50,000.

Graphically, it means that the graph would cut y-axis at the point (0,50,000).

Thus, the y-intercept would be at 50,000.

Change in the initial value will not have any affect on the rate of the graph.

So, from the above, we get,

Option A is correct.

If Marisol has a gross annual pay of $50,000 and receives total employee benefits of 14.5% of her gross annual pay, then you can find how many benefits she receives, using proportion:

[tex] \$50,000 - 100\%,\\ \$x - 14,5\% [/tex].

Then

[tex] \dfrac{50000}{x} =\dfrac{100}{14.5} ,\\\\ x=\dfrac{50000\cdot 14.5}{100}=500\cdot 14.5=7250 [/tex].

In total she will receive $50,000+$7250=$57250.

Answer: $57250.

Answer:

(the square root of 2 minus the square root of 6) / 4

It’s a little surprising that this question didn’t come up earlier.  Unfortunately, there’s no intuitive way to understand why “the energy of the rest mass of an object is equal to the rest mass times the speed of light squared” (E=MC2).  A complete derivation/proof includes a fair chunk of math (in the second half of this post), a decent understanding of relativity, and (most important) experimental verification.

Answer:

The value of x is 1.6

Step-by-step explanation:

We have been given that triangle CDF ∼ triangle MKP.

Therefore, the ratio of the corresponding sides are equal.

Hence, we have

[tex]\frac{DC}{MK}=\frac{CF}{MP}[/tex]

Plugging the known values, we get

[tex]\frac{9}{1.8}=\frac{8}{0.x}[/tex]

Cross multiplying, we get

[tex]9x=8\times1.8[/tex]

Divide both sides by 9

[tex]x=\frac{8\times1.8}{9}[/tex]

Simplifying, we get

[tex]x=8\times10.2\\\\x=1.6[/tex]

The value of x is 1.6