what are the roots of x in -10x^2 + 12x - 9=0

The suitable way to use the numbers 8, 6, and 2 to create an expression with an exponent that results in the value of 8 is by utilizing the equation 2^3. This equation means 'two raised to the power of three', meaning 2 multiplied by itself thrice, giving us the desired result, 8.

To solve this question, we need to consider the mathematical operation of exponentiation, which involves a base number and an exponent. The exponent represents the number of times the base number is to be multiplied by itself.

Given the numbers 8, 6, and 2, we aim to use each number only once to create an expression that includes an exponent and yields a value of 8. The suitable way to do this is by following the equation 2^3 (where 2 is the base number and 3 is the exponent).

To explain further, an exponent is the number of times a number, known as the base, is multiplied by itself. For instance, 2^3 should be read as 'two raised to the power of three', essentially depicting 2 * 2 * 2, resulting in 8. This follows the standard rules of Exponential Arithmetic.

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Final answer:

The wallet contains a total of $55, given that there are 8 $5 bills and 15 $1 bills.

Explanation:

The student's question involves determining the total amount of money in a wallet given a specific mix of $1 bills and $5 bills. According to the information provided, there are 23 bills in total, with 7 more $1 bills than $5 bills.

Let's denote the number of $5 bills as x. Therefore, there are x + 7 $1 bills. The total number of bills is the sum of the number of $1 bills and the number of $5 bills, which gives us the equation:

x + (x + 7) = 23

Solving the equation for x will give us the number of $5 bills:

2x + 7 = 23

2x = 23 - 7

2x = 16

x = 8

Now, since there are 8 $5 bills, and 7 more $1 bills than $5 bills, we have:

Number of $1 bills = 8 + 7 = 15

Thus, the total amount of money in the wallet is:

($5 × 8) + ($1 × 15) = $40 + $15 = $55

Therefore, the wallet contains $55.

The problem is about converting between two units of currency from kursh to riyals. The two unit multipliers from this scenario are: 1 riyal equals 20 kursh and 1 kursh equals 1/20 riyal. The conversion from 16,000 kursh to riyals would be 800 riyals.

The question is about converting between two units of currency, specifically from kursh to riyals based on the exchange rate provided. It's a classic problem in unit conversion.

a. The two unit multipliers implied by this relationship are:

b. To convert 16,000 kursh to riyals, you would use the first unit multiplier. Given that 1 riyal equals 20 kursh, you simply divide the amount in kursh by 20 to get the equivalent amount in riyals. So, 16000 kursh ÷ 20 = 800 riyals.

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The value of x would be equal to (180-y)/2

An equation represents equality of two or more mathematical expression.

To solve an equation, then they usually mean to find the values of the unknowns for which that equation would be true (the equality between expressions should hold true for those values).

Solutions to an equation are those values of the variables involved in that equation for which the equation is true.

We are given the equation as- 180=2x+y

Now solving;

180=2x+y

180=2x+y

180-y=2x

(180-y)/2=x

x = (180-y)/2

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Answer:

I think it is 9 because I know u multiply at the start plus I used a calculator and got 9 so if it is not my calculator it broke

Answer:

The correct option is b.

Step-by-step explanation:

The given expression is

[tex]x^3-4x^2+2x+10=x^2-5x-3[/tex]

Simplify the equation.

[tex]x^3-4x^2+2x+10-x^2+5x+3=0[/tex]

[tex]x^3-5x^2+7x+13=0[/tex]

It is given that 3+2i is a root of the equation and (x-3-2i) is a factor.

By complex conjugate root theorem if a+ib is a root of an equation then a-ib must be the root of the equation.

It means 3-2i is a root of the equation and (x-3+2i) is a factor.

[tex](x-3-2i)(x-3+2i)=(x-3)^2-(2i)^2=x^2-6x+9+4=x^2-6x+13[/tex]

Divide [tex]x^3-5x^2+7x+13=0[/tex] by [tex]x^2-6x+13[/tex], to find the remaining factor.

By the long division method, the quotient is (x+1) and remainder is 0. It means (x+1) is a remaining factor of the given equation. Equate each factor equal to 0, to find the remaining roots.

[tex]x+1=0[/tex]

[tex]x=-1[/tex]

Therefore the correct option is b.

Answer:

David earns $1,020 a week, and his weekly profit is $670.

Step-by-step explanation:

Since David walks six dogs per day, and each dog is $20, he earns a total of $120 per day from those six dogs. Also, knowing that he walks the six dogs five days a week, he earns $600 from walking the six dogs for five days per week alone. Using this same logic for the three dogs he walks seven days a week, we can conclude that he gets $60 from walking those three dogs. Knowing he walks those three dogs seven days a week, he gets $420 from walking those three dogs. Combining the totals gives us $1,020, the amount of money he earns per week. Since his weekly expenses are $350, we subtract that from $1,020 to get his weekly profit: $670.

The value corresponding to the 90th percentile (p90) is 94.84. Option  A is correct.

To find the value corresponding to the 90th percentile (p90), we first need to find the standard deviation of the scores.

We know that the third quartile (Q3) is 83, which corresponds to the 75th percentile (p75). Since the distribution is approximately normal, we can use the properties of the normal distribution to find the standard deviation.

In a standard normal distribution, the value corresponding to the p75 is approximately 0.6745 standard deviations above the mean. So, we can set up the following equation:

70 + 0.6745 * standard deviation = 83

Now, solve for the standard deviation:

standard deviation = (83 - 70) / 0.6745 ≈ 19.3047

Next, to find the value corresponding to the p90, we use the properties of the normal distribution again. The value corresponding to the p90 is approximately 1.2816 standard deviations above the mean.

Now, calculate p90:

p90 = 70 + 1.2816 * standard deviation
       ≈ 70 + 1.2816 * 19.3047
       ≈ 94.84

Rounding to two decimal places, we get p90 ≈ 94.84. So, the answer is (a) 94.84.

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To find p90 in a normally distributed set of scores, we need to find the standard deviation. Using the mean and q3, we can find the IQR and estimate the standard deviation. Finally, we can use the standard deviation to find the value corresponding to the 90th percentile.

To find the value of p90 in a normally distributed set of scores, we need to first find the standard deviation of the scores. We know that the mean is 70 and q3 (the third quartile) is 83. Using the formula for the interquartile range (IQR = q3 - q1), we can calculate the value of q1. Subtracting q1 from q3 gives us the IQR. Since the distribution is approximately normal, we can assume that the IQR is approximately 1.35 times the standard deviation. Dividing the IQR by 1.35 gives us the standard deviation. Finally, we can use the standard deviation to find the z-score corresponding to the 90th percentile and then find the corresponding value in the original distribution using the mean and standard deviation. The correct answer is option (a) 94.84.

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x = 3

y = 15

Let's establish the proportion below to find the value of x and y

XP / DN = XS / DF = PS / NF

Since only 2 sides of XPS is given, then

Therefore,

4y = 60

y = 60 / 4

y = 15

17x = 57

x = 57 / 17

x = 3

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To determine what percent 2/3 is of 1/4, convert both fractions to percent form, where 1/4 is 25%. Converting 2/3 to a percent gives approximately 66.67%, and dividing this by 25% gives 266.68%. Thus, 2/3 is 266.68% of 1/4.

To find out what percent 2/3 is of 1/4, you first need to express the fractions in a way that allows comparison. A standard way of expressing a fraction as a percent involves having a denominator of 100. Since you know 1/4 equals 25 percent, you can use this as a basis for comparison with 2/3.

To convert 2/3 to a decimal, divide the numerator by the denominator: 2 divided by 3 equals approximately 0.6667. To then convert that decimal to a percent, multiply by 100, getting approximately 66.67 percent. To find what percent 2/3 is of 1/4, divide 66.67 by the percent value of 1/4, which is 25, and then multiply by 100 to get the percentage. This gives you (66.67 / 25) x 100 = 266.68 percent. So, 2/3 is 266.68 percent of 1/4.

Answer: a0 =$97.5  ; a1 =$87.96 ; a2=$282.48; a3=$1,722.5 ; a4=$1,553.96 ; a5=$4,990.48

Step-by-step explanation:

Hi, to solve this problem we have to multiply each total by the commission in decimal form (6 / 100= 0.06).

So:

$1625 x 0.06 = $97.5

$1,466 x 0.06 =$87.96

$4,708 x 0.06 =$282.48

And finally, to obtain the total costs we have to add to each total the commission of the total.

$1625 + $97.5 = $1,722.5

$1,466 +$87.96 = $1,553.96

$4,708 +$282.48 = $4,990.48

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Final answer:

To find the original price of a pair of shoes after a 60% discount, divide the sale price by (1 minus the discount percentage). The original price of the pair of shoes is $110.

Explanation:

To find the original price of a pair of shoes after a 60% discount, we can use the formula:

Original price = Sale price / (1 - Discount percentage)

Substituting the given values:

Original price = $44 / (1 - 0.60)

Original price = $44 / 0.40

Original price = $110

Therefore, the original price of the pair of shoes was $110.

Final answer:

To determine the original price before a discount, subtract the discount percentage from 1, convert it to a decimal, and divide the sale price by this number. In this case, the original price for the shoes before a 60% discount, resulting in a $44 sale price, is $110.

Explanation:

To find the original price of an item before a discount, you can use the following steps:

Therefore, the original price of the shoes was $110 before the 60% discount was applied.

Answer:

75% of the original volume is left.

Step-by-step explanation:

Deniz had a full gallon of milk, or 16 cups of milk, and then she poured out 4 cups of milk. That is:

Then,

The total left is:

[tex]\\ Total_{left} = \frac{16}{16} - \frac{4}{16} = \frac{12}{16} = \frac{3}{4}[/tex], since we are dealing here with fractions with the same denominator.

In other words, [tex]\\ \frac{3}{4} = 0.75[/tex] is the amount of milk left in the container.

In terms of percentage, [tex]\\ \frac{3}{4} = 0.75[/tex] is equivalent to [tex]\\ 0.75*100\% = 75\%[/tex] of the original volume, because Deniz poured out [tex]\\ \frac{4}{16} = \frac{1}{4} = 0.25[/tex] or [tex]\\ 0.25*100\% = 25\%[/tex] from the original volume.

So, Deniz left 75% of the original volume of milk after pouring out 25% of it.        

This can be represented in the graph below.

Answer:

75%

Step-by-step explanation:

Answer:

Step-by-step explanation:

The area of a circle is given by A = π*r²

If diameter is 10 units, the radius is 5, so:

A = π * 5² = 78,54units²