Suppose that x is normally distributed with a mean of 10 and a standard deviation of 3. find p(x ≤ 6). note: round your answer, if necessary, to two places after the decimal. please express your answer with two places after the decimal.

You can use the fact that when staying in the same column and walking from row to row, there is addition of 10.

First choose a row. Since there are 10 columns per row, thus changing the row by choosing same column will give difference of 10.

Go down in rows on same column and you'll see increment of 10, and go up in rows with same column and you'll see decrement of 10.

]This is the key reason behind that straight columns of multiples of 10s.

Let the number be x

Then moving from row to row on the same column, we will get:

x, x + 10, x + 20, x + 30, ...

If x = 10, we get 10, 20, 30, 40 which are multiples of 10 since

[tex]10 + 10 = 10 \times 2\\10 + 20 = 10 \times 3\\...\\ 10 + 10y = 10 \times (y+1)[/tex]

See the given table below:

[tex]\begin{array}{cccc}\cdots&x&\cdots & 10\\\cdots & x + 10 & \cdots & 10 + 10 = 10 \times 2 = 20\\\cdots & x+ 10 + 10 = x + 20 & \cdots & 20 + 10 = 10 \times 2 + 10 = 10 \times 3 = 30\\\cdots & \cdots & \cdots & \cdots\end{array}[/tex]

The last column, therefore, has multiples of 10 since adding 10 for multiple of 10 is like multiplying 10 by one bigger number which is same as increasing multiples of 10.

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Let x specify the number of 16 ounce serving

If you buy the mug you acquire the first serving including the mug.

So the price of x is:

295 + 50(x - 1)

the x - 1 here shows that the first serving with the mug.

And then count the whole thing in cents.

The fee of throwaway cups is 85x

So breakeven is computed by:

295 + 50(x - 1) = 85x

295 + 50x - 50 = 85x

245 = 35x

x = 245/35 = 7

Checking this will give us:

mug 2.95 + 50*6 = 5.95

disposable

8.5*7 = 5.95

So the answer is D.

The break-even point occurs after nine soft drink purchases(8,0.5). Hence, the correct option is b.

First, let's consider the cost of the mug with a soft drink:

Mug + Soft drink = $2.95

Next, the cost of each refill:

Refill = $0.50

Then, the cost of a soft drink in a disposable cup:

Disposable cup soft drink = $0.85

To find the break-even point, let's set up the equation. Let x be the number of refills (including the initial drink from the mug):

Cost of mug with initial drink + (Cost per refill × number of refills) = Cost of disposable cup × number of drinks

2.95 + 0.50x = 0.85x

Now we solve for x:

2.95 = 0.85x - 0.50x

2.95 = 0.35x

x = 2.95 / 0.35

x = 8.43

Since we cannot have a fraction of a refill, we will round up to the nearest whole number. Therefore, the break-even point is after 9 refills (including the initial drink from the mug).

The approximate break-even point is after purchasing nine 16-ounce drinks. Therefore, the correct answer is (8, 0.5).

Expression that has all the four basic mathematical operators can be written as [tex](\dfrac{a+b}{2}) \times [c-(a+b)][/tex].

In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.

Let's take three numbers, a, b, and c.

Now, the expression in the word can be written as, The product of the addition of the first two numbers (a and b), divided by 2 and the sum subtracted from c.

If we try to write the above statement as an expression then we can write it as,

[tex](\dfrac{a+b}{2}) \times [c-(a+b)][/tex]

Hence, An expression that has all the four basic mathematical operators can be written as [tex](\dfrac{a+b}{2}) \times [c-(a+b)][/tex].

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Final answer:

The computation described involves multiplying six by three, adding eight, subtracting two, and then dividing the result by four. This results in the expression ((6 * 3) + 8 - 2) / 4, incorporating all four basic mathematical operations.

Explanation:

Writing the computation in words for an expression that uses all four operations - addition, subtraction, multiplication, and division - helps in understanding the application of these operations in a complex expression. Here's an example:

First, multiply six by three, then add eight to the product. From this sum, subtract two. Finally, divide the result by four. This sequence of operations involves all four basic mathematical operations.

The corresponding expression for the described computation is: ((6 * 3) + 8 - 2) / 4.

Breaking down the expression:

Final answer:

The solution set to the given inequality '-3x < 5.92 - 15.4' is {5, 10}.

Explanation:

The student's question seems to be about solving an inequality to find which values from a given set satisfy it. While the inequality itself appears to be incorrectly written or has a typo, I'll assume it's meant to be '-3x < 5.92 - 15.4'.

We can begin by simplifying the right side of the inequality:

5.92 - 15.4 = -9.48

So the inequality becomes:

-3x < -9.48

To solve for x, we divide both sides by -3, remembering to reverse the inequality sign because we are dividing by a negative number:

x > 9.48 / 3

x > 3.16

Now we can compare this result to the set of numbers given: (-10, -5, 0, 5, 10).

The only numbers greater than 3.16 are 5 and 10.

Therefore, the solution set to the inequality is {5, 10}.

Final answer:

Nathan rides a total distance of 2 1/4 miles when he rides 9/12 of a mile each day for 3 days. To calculate this, multiply the daily distance by the number of days and simplify the result.

Explanation:

To calculate the distance Nathan rides his bike if he rides 9/12 of a mile each day for 3 days, you need to multiply the distance he rides in a day by the number of days he rides.

So, the total distance Nathan rides is:

9/12 mile/day × 3 days = 27/12 miles

To simplify the fraction:

Therefore, Nathan rides a total distance of 2 1/4 miles over the three days.

Holly used a total of 53/72 cup of chicken for her stir fry, by adding 5/8 cup and 1/9 cup together after converting them to have a common denominator.

Holly is making a stir fry and needs to calculate the total amount of chicken she has used.

Initially, she measures 5/8 cup of chicken and then adds 1/9 cup of chicken.

To find the total amount of chicken used, we need to add these two fractions together.

This is a simple arithmetic operation called fraction addition.

First, we find a common denominator for the two fractions, which in this case is 72 (the least common multiple of 8 and 9).

Next, we convert each fraction to an equivalent fraction with the common denominator.

The fraction 5/8 converts to (5×72)/(8×72) = 45/72, and 1/9 converts to (1×72)/(9×72) = 8/72.

Now that the fractions share a common denominator, we can add them:

45/72 + 8/72 = 53/72

The sum of the two fractions gives us the total amount of chicken used by Holly, which is 53/72 cup.

To find out how much chicken Holly used altogether, we need to add the two fractions together. First, we find a common denominator, then convert the fractions to have that denominator. Finally, we add the numerators and keep the denominator the same. Holly used a total of 53/72 cup of chicken for her stir fry.

To find out how much chicken Holly used altogether, we need to add the two fractions together.

First, we need to find a common denominator for these fractions. The smallest number that both 8 and 9 can divide into is 72.

Next, we need to convert both fractions to have a denominator of 72. To do this, we multiply the numerator and denominator of each fraction by the same number.

For the first fraction, we multiply both the numerator and denominator by 9, obtaining 45/72. For the second fraction, we multiply both the numerator and denominator by 8, obtaining 8/72.

Now that we have both fractions with a denominator of 72, we can add them together. 45/72 + 8/72 = 53/72.

Therefore, Holly used a total of 53/72 cup of chicken for her stir fry.

The polynomial in standard form after subtraction will be 12a² - 9a + 5.

A polynomial expression is an algebraic expression with variables and coefficients. Unknown variables are what they're termed. We can use addition, subtraction, and other mathematical operations. However, a variable is not divisible.

It simply implies subtracting something from an entity, group, location, etc. Subtracting from a collection or a list of ways is known as subtraction.

The polynomial is given below.

-7a² + 3a - 9 and 5a² - 6a - 4

Subtract -7a² + 3a - 9 from 5a² - 6a - 4, then we have

(5a² - 6a - 4) - (-7a² + 3a - 9)

Simplify the equation, then we have

(5a² - 6a - 4) - (-7a² + 3a - 9)

5a² - 6a - 4 +  7a² - 3a + 9

12a² - 9a + 5

The polynomial in standard form after subtraction will be 12a² - 9a + 5.

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Answer:

B. Taxable income

Step-by-step explanation:

Taxable income is the amount of money that a person earns in a period of time that can be taxated by the government, you could earn money that is not taxated, for example life insurances from deceased family members is not taxable, also upto a certain amount of money as a gift is not taxable. So the tax bracket a person falls into depends solely on the taxable income that they make in a year.

Final answer:

B: Taxable income

A person's tax bracket is determined by their taxable income, which is their adjusted gross income minus any deductions and exemptions.

Explanation:

The tax bracket into which a person falls is determined by his or her taxable income.

Taxable income is the amount of income that is subject to the official tax rates for each bracket.

This figure is the result of subtracting deductions and exemptions from your adjusted gross income (AGI). It's important to note that taxable income and AGI are not the same, as the latter is your income from various sources minus specific adjustments but before deductions and exemptions.

To calculate taxable income, the equation used is: taxable income = adjusted gross income - (deductions + exemptions).

Income Tax Brackets are the thresholds of income that are taxed at varying rates. As an individual’s taxable income increases, not only does the amount of tax paid increase, but typically so does the percentage of tax on additional income, as the tax rates in higher brackets are usually higher.

We can prove that ΔDEF = ΔHGF as follows; A: Yes, the triangles are congruent by SAS.

How to prove the congruence

Side DE is congruent to GH as seen in the fact that both have two line marks. These are opposite angles (EFD and HFG) and these angles are congruent.

Note that the opposite sides of a triangle are congruent and corresponding angles are also congruent. This is true of angles DEF and HGF. So, we can conclude that the triangles are congruent by SAS.

Complete Question:

Can you prove that ADEF = AHGF? Justify your answer:

A: Yes, the triangles are congruent by SAS. B: Yes, the triangles are congruent by SSS. C: Yes, the triangles are congruent by SSA. D: No, not enough information is given

The product 4^3×4^(-3) is equal to 1.

Take care of the exponents.

4^3= 4*4*4

4^3= 64

=4^-3

The product meaning in maths is a number that you get to by multiplying two or more other numbers together.

Make it a fraction to make the power positive.

[tex]=\frac{1}{4^3}[/tex]

Now, simplify.

[tex]=\frac{1}{64}[/tex]

=64* 1/64= 1

Therefore, The product 4^3×4^(-3) is equal to 1.

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9.5000032 i think i'm not sure

Answer:

B

Step-by-step explanation:

picture:)

To find h(x) = f(x) - g(x), we substitute and simplify the given functions. The result is h(x) = 2 × 3ˣ - 3²ˣ. This solution involves basic algebraic manipulation and exponent rules.

Let's start by defining the given functions:

We need to find h(x) = f(x) - g(x). Substitute the expressions for f(x) and g(x):

Now simplify the expression inside the parentheses:

Combine like terms:

Thus, the function h(x) = 2 × 3ˣ - 3²ˣ is found by subtracting g(x) from f(x).

The probability that the second card is yellow after one green card is drawn and not replaced from a deck of 8 (3 yellow, 5 green) cards is 3/7. The correct answer is option b) 3/7.

To find the probability that the second card is yellow after drawing one green card (and not replacing it), we can follow these steps:

Thus, the probability that the second card is yellow is 3/7, which is corresponding to (b).