Rationalize the denominator of square root of negative 9 over open parentheses 4 minus 7 i close parentheses minus open parentheses 6 minus 6 i close parentheses.

Answer:

Option A is correct.

Step-by-step explanation:

Given: A 6-sided cube is rolled.

To find: Probability of getting a number greater than 3.

Total number of outcome when a 6-sided cube is rolled = 6

Favorable outcome = { 4 , 5  6 }

Number of favorable outcome = 3

Theoretical Probability is a probability based on reasoning written as a ratio of the number of favorable outcomes to the number of possible outcomes.

[tex]Probability=\frac{Number\:of\:favorable\:outcome}{Number\:of\:Total\:outcome}[/tex]

[tex]Probability=\frac{3}{6}=\frac{1}{2}[/tex]

Therefore, Option A is correct.

Answer:

The correct option is B) $680.

Step-by-step explanation:

Consider the provided information.

Her total amount invested was $1,500. At the end of the year, she had earned $106.40 in interest.

Let she invested x amount with 8% interest rate.

Total amount she invested was $1,500, thus the amount she invested with 6% interest rate was 1500-x.

Total interest she earn was $106.40

Write this information into mathematical form.

[tex]x\times \frac{8}{100}+\frac{6}{100}(1500-x)=106.40[/tex]

[tex]x\times 0.08+0.06(1500-x)=106.40[/tex]

[tex]0.08x+90-0.06x=106.40[/tex]

[tex]0.08x-0.06x=106.40-90[/tex]

[tex]0.02x=16.4[/tex]

[tex]x=820[/tex]

Hence, she invested $820 with 8% interest rate.

The amount she invested with 6% interest rate was 1500-x.

Substitute the value of x in above.

1500-820=680

Hence, she invested $680 with 6% interest rate.

The correct option is B) $680.

12) 10.77 + 2.09 + 0.75 = 13.61

13.61 x 1.07 = $14.56

 total amount = $14.56

14) C shows the possible combinations

Answer:

c 4.47

Step-by-step explanation:

got it right on my test

The distance from (−3, 1) to (−1, 5) is 4.47

Slope of line is defined as the angle of line.  

The distance between two points is found by

[tex]d = \sqrt{( (x_2-x_1)^2 + (y_2-y_1)^2)}[/tex]

[tex]d = \sqrt{ ( (-1--3)^2 + (5-1)^2)}[/tex]

[tex]d=\sqrt{( (2)^2 + (4)^2)}[/tex]

[tex]d=\sqrt{(4+16)}[/tex]

[tex]d=\sqrt{(20)}[/tex]

d = 4.472135955

Rounding to the nearest hundredth

d = 4.47

Hence,  the distance from (−3, 1) to (−1, 5) is 4.47

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The number of cubes should be 1.440.

Calculate the volume of each shape is as follows:

Volume of rectangle = [tex]6 \times 5\div 6 \times 1\ 2\div 6 = 6\ 2\div 3[/tex] cubic inches.

And,

Volume of cube =[tex] 1\div6 \times 1\div6 \times 1\div6 = 1\div216[/tex] cubic inch.

Now

divide the volume of the rectangle by the volume of the cube:

So,

[tex]= (6\ 2\div 3) \div (1\div 216)[/tex]

= 1.440

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Value of x is 1 + 5√2

Given that;

(x - 1)² = 50

Find:

Value of x

Computation:

(x - 1)² = 50

By taking square root both side

x - 1 = √50

x - 1 = 5√2

x = 5√2 + 1

x = 1 + 5√2

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The answer would be B

Using the formula for compound interest, if you deposit $2,000 at 10% each year, the future balance in your account after 10 years would be approximately $5,187.12. This is due to the effect of compounding where the interest is calculated on both the principal and the accumulated interest.

The subject of this question is compound interest which is a Mathematics topic typically covered in High School. The formula A=p(1+r)^t is used to calculate the future balance in your savings account considering compound interest. Here, 'A' represents the future balance, 'p' is the current principle or balance, 'r' is the rate of interest, and 't' is time in years.

To answer your specific question: If you deposit $2,000 at a 10% rate each year, how much money will be in your account in 10 years? Let's plug the numbers into the formula. In this case, p=$2000, r=0.10 (as 10% equals 0.10 in decimal), and t=10 years.

So, A = 2000*(1 + 0.10)^10. Solving this, the future balance in your account after 10 years would be approximately $5,187.12. This is significantly more than simple interest ($100 × 0.05 × 3 = $15 in your example) due to the effect of compounding, as the interest is calculated on the principal plus the accumulated interest.

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The weight of each tire in pounds is approximately:

Full steel bead tire: 1.76 pounds.

Lighter wheel: 1.54 pounds.

Given that the weight of a full steel bead tire is approximately 800 grams, while a lighter wheel weighs only 700 grams.

We need to convert the weights into pound.

To convert the weight of each tire from grams to pounds, we'll use the conversion factor that there are 453.592 grams in one pound.

Weight of a full steel bead tire in pounds:

800 grams x (1 pound / 453.592 grams) ≈ 1.76 pounds

Weight of a lighter wheel in pounds:

700 grams x (1 pound / 453.592 grams) ≈ 1.54 pounds

Rounded to 2 decimal places:

Weight of a full steel bead tire = 1.76 pounds

Weight of a lighter wheel = 1.54 pounds

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Final answer:

The company must sell either 2,000 or 5,000 items to break even, as determined by setting the profit function to zero and factoring the resulting quadratic equation.

Explanation:

To determine how many items must be sold for the company to break even, we need to set the profit function p(x) equal to zero and solve for x. In this case, the profit function is given by p(x) = -4x^2 + 28x - 40. Setting this to zero, we have:

-4x^2 + 28x - 40 = 0

Now, we need to solve this quadratic equation for x. To do this, we can factor the equation, use the quadratic formula, or complete the square. Since the coefficients are manageable, we'll try to factor first:

-4(x^2 - 7x + 10) = 0

Let's look for two numbers that multiply to 10 and add up to 7, which are 5 and 2. We can now factor further:

-4(x - 5)(x - 2) = 0

From the factored form, we get two potential solutions for x when the profit is zero:

x = 5

x = 2

Since x represents the number of items sold in thousands, the company must sell either 2,000 or 5,000 items to break even.

Answer: Simplifying the square roots and adding the similar square roots the answer is option c. 6 square root of 5 end root minus 4 square root of 7

Solution:

3√5-2√7+√45-√28

45=9*5 and 28=4*7. Replacing in the equation above:

3√5-2√7+√(9*5)-√(4*7)

Using √(a*b)=√a√b

3√5-2√7+√9√5-√4√7

√9=3 and √4=2. Replacing in the equation above:

3√5-2√7+3√5-2√7

Adding similar square roots:

(3+3)√5+(-2-2)√7=

(6)√5+(-4)√7=

6√5-4√7

The correct conversion from scientific notation to standard notation are:

            b)   [tex]8.05\times 10^5[/tex]

            e)   [tex]7.09\times 10^{-6}[/tex]

We know that when we have  a power of 10 as positive then the decimal is shifted to the right and if the power of 10 is negative then we shift the decimal to the left.

a)

         [tex]1.71\times 10^3[/tex]

As the power of 10 is positive hence we shift the decimal to the right 3 places.

Hence, the conversion is:

         [tex]1.71\times 10^3=1710[/tex]

b)

           [tex]8.05\times 10^5[/tex]

Again the power of 10 is positive and hence we will shift the decimal 5 places to the right and the conversion is done as follows:

        [tex]8.05\times 10^5=805000[/tex]

c)

       [tex]2.4\times 10^4[/tex]

Since, the power of 10 is positive and hence we will shift the decimal 4 places to the right and we convert the number to standard notation as:

      [tex]2.4\times 10^4=24000[/tex]

d)

           [tex]8.25\times 10^{-3}[/tex]

Since, the power of 10 is negative and hence we will shift the decimal 3 places to the left and we convert the number to standard notation as:

        [tex]8.25\times 10^{-3}=0.00825[/tex]

e)

             [tex]7.09\times 10^{-6}[/tex]

Since, the power of 10 is negative and hence we will shift the decimal 8 places to the left.

Hence, we convert our number to standard notation:

[tex]7.09\times 10^{-8}=0.00000709[/tex]

It is accurate to convert scientific notation to standard notation in the following ways:

B [tex]8.05x10^5=805,000[/tex]

C [tex]2.4x10^4= -24,000[/tex]

E [tex]7.09x10^-^6=0.0000070[/tex]

Firstly, Let's evaluate each conversion one by one:

[tex]1.71x 10^3=0.00171[/tex]

This conversion is not true. The correct value of[tex]1.71x 10^3[/tex] is 1710.

[tex]8.05x10^5=805,000[/tex]

This conversion is true.

[tex]2.4x10^4= -24,000[/tex]

This conversion is true.

[tex]8.25x10^-^3=-8,250[/tex]

This conversion is not true. The correct value of [tex]8.25x 10^-^3[/tex] is 0.00825.

[tex]7.09x10^-^6=0.0000070[/tex]

This conversion is true.

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