Norman spends $100. He spends $35 on a video game. What percentage of his original $100 does Norman have left after buying the game?

Answer: D is the right answer. The solution set of the given equation={-2,10}.

Explanation:

Given equation: [tex]x^2-8x=20[/tex]

The standard perfect square trinomial equation is [tex]x^2+2ax+a^2=(x+a)^2[/tex]

On comparing this with the left side of the given equation ,we get 2a=-8

⇒a= -4 and [tex]a^2=16[/tex]

Now to make given equation perfect square add 16 on the both sides, we get [tex]x^2-8x+16=20+16\\\Rightarrow(x-4)^2=36[/tex]

Taking square root on both the sides we get,

[tex]x-4=-6\ or\ x-4=6[/tex]

add 4 on both sides, we get

⇒x= -6+4 or x=6+4

⇒x=-2 or x=10

Therefore, the solution set of the given equation={-2,10}.

Thus D is the right answer.

Answer:

The fraction of students in Zoe's class who have rodents is [tex]\frac{1}{10}[/tex].

Step-by-step explanation:

In Zoe's class, 4 /5 of the students have pets.

Of the students who have pets, 1/8 have rodents.

This means [tex]\frac{1}{8} of \frac{4}{5}[/tex] have rodents.

So,fraction of students who have rodents = [tex]\frac{1}{8}\times\frac{4}{5}[/tex]

= [tex]\frac{1}{10}[/tex]

The fraction of students in Zoe's class who have rodents is [tex]\frac{1}{10}[/tex].

Final answer:

The local hospital can treat a maximum of 480 patients if they follow the 1:4 nurse-to-patient ratio and have 120 nurses.

Explanation:

The local hospital can treat a maximum of 480 patients if they follow the 1:4 nurse-to-patient ratio and have 120 nurses.

To calculate the maximum number of patients the hospital can treat, we divide the number of nurses by the nurse-to-patient ratio. In this case, the ratio is 1:4, so for every 1 nurse, there are 4 patients. Therefore, each nurse can handle 4 patients.

To find the maximum number of patients, we multiply the number of nurses by the number of patients each nurse can handle. In this case, 120 nurses multiplied by 4 patients per nurse equals 480 patients.

[tex]\left(\dfrac{g}{f}\right)(x)=\dfrac{g(x)}{f(x)}\\\\\text{We have}\ f(x)=x\ \text{and}\ g(x)=1.\ \text{Substitute}\\\\\left(\dfrac{g}{f}\right)(x)=\dfrac{1}{x}\\\\\text{The domain}:\ x\neq0\\\\Answer:\ \boxed{\text{All real numbers except 0}\to x\in\mathbb{R}-\{0\}}[/tex]

The domain of the function is a real number except 0 because the function is not defined at x = 0.

The domain means all the possible values of x and the range means all the possible values of y.

The functions are given below.

f(x) = x

g(x) = 1

Then the domain of the function (g/f)(x) will be

(g/f)(x) = 1 / x

Then the graph of the function is given below.

The domain of the function is a real number except 0 because the function is not defined at x = 0.

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Final answer:

To find the length of the rectangle, set up a proportion using the given information. Solve the equation to find the length of the rectangle is 10 feet.

Explanation:

To find the length of the rectangle, we can set up a proportion using the given information. Let the length of the rectangle be L and the width be W. From the problem, we know that the width is 2 feet shorter than the length, so we can write the equation W = L - 2. We also know that the area of the rectangle is 80 square feet, so we can write the equation L * W = 80.

Substituting W = L - 2 into the equation L * W = 80, we get L * (L - 2) = 80. Expanding and rearranging the equation gives us L2 - 2L - 80 = 0. Factoring the quadratic equation, we find (L - 10)(L + 8) = 0.

Since we are looking for the length of the rectangle, we discard the negative solution and find that L = 10. Therefore, the length of the rectangle is 10 feet.

Answer:

Option C. $125.25

Step-by-step explanation:

Jeremy is shopping online for skating equipment.

The price of  long board with trucks and wheels = $146.25

Jeremy gets a discount on his purchase = $21.00

the final amount that Jeremy would be billed.

We subtract the discount from the price of item.

= $146.25 - $21.00 = $125.25

The final amount that Jeremy would be billed is $125.25.

Answer:

16%; 2.5%; 34%; 81.5%

Step-by-step explanation:

Using the empirical rule, we know that 68% of data falls within one standard deviation of the mean; 95% of data falls within two standard deviations of the mean; and 99.7% of data falls within 3 standard deviations of the mean.

This means from the mean to 1 standard deviation (σ) above is 34% of data; from the mean to 1 σ below is 34% of data; from 1 σ to 2σ above is 13.5% of data; from 1σ to 2σ below is 13.5% of data; from 2σ to 3σ above is 2.35% of data; from 2σ to 3σ below is 2.35% of data; more than 3σ above is 0.15% of data; and more than 3σ below is 0.15% of data.

647 is 1 σ above the mean.  This means that we go from here above;

13.5+2.35+0.15 = 16%

747 is 2σ above the mean.  This means that we go from here above:

2.35+0.15 = 2.5%

447 is 1σ below the mean and 547 is the mean.  This means that we have 34%.

347 is 2σ below the mean and 647 is 1 above the mean.  This means we go from:

13.5+34+34 = 81.5%

To find the percentage of GMAT scores between 347 and 647, find the z-scores and use a z-table to calculate the cumulative area.

To find the percentage of GMAT scores between 347 and 647, we need to find the area under the bell curve between these two scores. First, we need to find the z-scores for both scores using the formula z = (x - μ) / σ. For 347, the z-score is (-200) / 100 = -2, and for 647, the z-score is 100 / 100 = 1.

Next, we need to find the percentage of data between these z-scores. We can use a z-table to find the cumulative area. The cumulative area for -2 is 0.0228 and for 1 is 0.8413.

To find the percentage between these two z-scores, we subtract the cumulative area for -2 from the cumulative area for 1: 0.8413 - 0.0228 = 0.8185.

Therefore, the percentage of GMAT scores between 347 and 647 is 81.85%.

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Final answer:

The effective rate on a $10,000 treasury bill with a nominal rate of 4% for 13 weeks is 4.06%.

Explanation:

The effective rate on a treasury bill is the annualized interest rate that takes into account the compounding of interest over the term of the bill. To calculate the effective rate, you can use the formula:

[tex]Effective Rate = (1 + (Nominal Rate / M))^M - 1[/tex]

Where:

Plugging in the values:

Effective Rate =  [tex](1 + (0.04 / 4))^4[/tex]- 1

= [tex](1 + 0.01)^4 - 1[/tex]

= [tex]1.01^4 - 1[/tex]

= 1.04060401 - 1

= 0.04060401 (or 4.06% rounded to two decimal places)

Therefore, the effective rate on a $10,000 treasury bill with a nominal rate of 4% for 13 weeks is 4.06%.

x = (1 ±√41)/6 is the correct answer.

To solve the equation 10 - 6x - 9x^2 = -9x, we'll use the quadratic formula. The solutions for x are (3 + √369)/18 and (3 - √369)/18.

To solve the equation 10 - 6x - 9x2 = -9x, we'll start by bringing all the terms to one side of the equation to set it equal to zero. Rearranging the equation, we get 9x2 - 3x - 10 = 0. We can then use factoring, the quadratic formula, or completing the square to solve for x. In this case, let's use the quadratic formula.

The quadratic formula states:

x = (-b ± √(b2 - 4ac))/(2a)

Using the values from our equation, we have:

x = (-(-3) ± √((-3)2 - 4(9)(-10)))/(2(9))

Simplifying further, we have:

x = (3 ± √(9 + 360))/18

x = (3 ± √369)/18

Therefore, the solutions for x are:

x = (3 + √369)/18

x = (3 - √369)/18

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Answer:

Isosceles triangle.

Step-by-step explanation:

A triangle has been given in this question with the sides 5 cm, 5 cm, 7 cm.

As per definition of the triangle if two sides are equal then opposite angles of these corresponding sides will be equal.

More than this if two sides of a triangle are equal then the triangle is called as isosceles triangle.

Therefore the given triangle with the equal sides 5 cm, 5 cm will be the isosceles triangle.

Numbers that are used to represent the rank or position of an object or a person are known as ordinal numbers.

The ordinary number for 3.25 x [tex]10^{4}[/tex] is 32500.

Numbers that are used to represent the rank or position of an object or a person are known as ordinal numbers.

We have,
3.25 x [tex]10^{4}[/tex]

We need to remove the decimal point and the exponents 4.

Let us find in two parts:

3.25 can be written as 325/100 ______(1)

[tex]10^{4}[/tex] can be written as 10 x 10 x 10 x 10 = 10000 ______(2)

Now,

From (1) and (2)
= 3.25 x [tex]10^{4}[/tex]

= (325 / 100) x 10000

= (325/100) x 100 x 100

100 can be canceled.

= 325 x 100

= 32500

Thus the ordinary number for 3.25 x [tex]10^{4}[/tex] is 32500.

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To find the cost per can when buying 3 packages of cans, multiply the cost of a single package by 3 to get the total cost, then divide the total cost by the total number of cans to find the cost per can.

To find the cost per can when buying 3 packages of 10 cans each:

The loan amount is calculated by amortization and Brand K will be $340.32 cheaper than Brand J

Loan amortisation is the practise of making recurrent payments over time to completely pay off the principal and interest on a loan.

Mortgage amortisation is a word used in finance to describe the process of paying down your mortgage. The mortgage lender establishes a payment plan for you when you take out a mortgage. This uncomplicated plan, which includes equal payments over the course of your loan if you have a fixed-rate mortgage, is easy to understand.

The amount is calculated using the amortization formula:

P = a ÷ {{[(1 + r/n)^nt] - 1} ÷ [r/n(1 + r/n)^nt]}

where:

P is monthly payment

a is credit amount

r is the interest rate

t is the time in years

n is number of times the interest is compounded

Given data ,

Let the total loan amount for the brand J be represented as J

a = $975

r = 14.55% = 0.1455

t = 8 years

n = 12

Now , the amortization formula is

P = a ÷ {{[(1 + r/n)^nt] - 1} ÷ [r/n(1 + r/n)^nt]}

P = 975 ÷ {{[(1 + 0.1455/12)^12×8] - 1} ÷ [0.1455/12(1 + 0.1455/12)^12×8]}

P = $17.24

Total amount paid J = $17.24 × 96 = $1655.04

Let the total loan amount for the brand K be represented as K

a = $265

r = 14.55% = 0.1455

t = 3 years

n = 12

Now , the amortization formula is

P = a ÷ {{[(1 + r/n)^nt] - 1} ÷ [r/n(1 + r/n)^nt]}

P = 265 ÷ {{[(1 + 0.1455/12)^12×3] - 1} ÷ [0.1455/12(1 + 0.1455/12)^12×3]}

P = $9.13

Total amount paid K = $9.13 × 12 × 3 × 4 = $1314.72

The difference of amount of sofa j and sofa k = D

D = J - K

D = $1 655.04 - $ 1314.72 = $ 340.32

Hence , Brand K will be cheaper than Brand J by $340.32

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Logan's treasure is represented as 25 cm away on his map; using the scale of 1 cm to 5 meters, it can be calculated that he is 125 meters away from the treasure by multiplying the map distance by the scale factor.

Logan has created a treasure hunt map where the scale indicates that 1 cm on the map corresponds to an actual distance of 5 meters. To determine the actual distance Logan is from the treasure, we first note that the treasure is shown as 25 cm away from his location on the map. Since the scale factor is 1 cm to 5 meters, we can set up a simple multiplication to find the actual distance.

The calculation would be as follows:

Scale factor: 1 cm = 5 meters

Map distance: 25 cm

Actual distance: 25 cm x 5 meters/cm

By multiplying the map distance by the scale factor, we get:

Actual distance = 25 x 5 = 125 meters

Therefore, Logan is 125 meters away from the treasure.

Answer:14/5 is the correct answer, just took test

Step-by-step explanation: