A retired couple invested $6000 in bonds at a simple interest rate of 5.1%. At the end of one year, how much interest did they receive on their investment? Please show your work.

0.806 miles per minute

There are 60 minutes in an hour, so replace the unit "hour" by 60 minutes and recompute.

... 48.36 mi/h = 48.36 mi/(60 min) = (48.36/60) mi/min = 0.806 mi/min

The car's average speed was calculated by dividing the total distance of 48.36 miles by the total time of 60 minutes, resulting in an average speed of 0.806 miles per minute.

To compute the car's average speed per minute, we need to divide the total distance covered by the total time in minutes. This is because speed is defined as the rate at which an object covers distance. The distance travelled by the car is 48.36 miles (the total distance), and the time is 1 hour. To transform this hour into minutes, we multiply by 60, as there are 60 minutes in an hour. So,

1 hour = 60 minutes

Therefore, to find the average speed, we take the total distance and divide by the total time in minutes. Using this, we find:

Average speed = Total distance / Total time

Average speed = 48.36 miles / 60 minutes = 0.806 miles per minute.

Therefore, the car's average speed was approximately 0.806 miles per minute.

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b.)x³-7x²+3x+36

(x-4)(x²-3x-9)

Distribute x and -4 to x²-3x-9

=x²(x)-3x(x)-9(x)+x²(-4)-3x(-4)-9(-4)

=x³-3x²-9x-4x²+12x+36

Combine all liked terms

=x³-7x²+3x+36

Answer:

d. -8

Step-by-step explanation:

Remember that you cannot possibly divide anything by 0, so if the denominator gives as a result 0, you are dealing with an impossibility, in order for a franction to give as a result 0, the numerator has to be 0, so we just need to equalize the numerator to 0 and solve for x to know how can we make the rational expression 0:

2x+16=0

2x=-16

x=-16/2

x=-8

So in order to make the expression equal to 0 x needs to be equal to -8,

The solution is, the graph of f(x) is vertically stretched by a factor of 3 and shifted 7 units down, as f(x) = x changes to h(x) = 3x² - 7.

Graph transformation is the process by which an existing graph, or graphed equation, is modified to produce a variation of the proceeding graph.

here, we have,

Given that,

here is a graph of f(x) = x which is transformed into h(x) = 3x² - 7.

The graph of a the equation -

f(x) = x

is a straight line.

now, we get, When it is squared and multiplied by 3, we get -

h(x) = 3x²

which is a parabola stretched by a factor of 3 in vertical direction along    

+ y axis.

When 7 is subtracted, it will shift the graph down by 7 units.

h(x) = 3x² - 7

Therefore, the graph of f(x) is vertically stretched by a factor of 3 and shifted 7 units down, as f(x) = x changes to h(x) = 3x² - 7.

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Complete question:

What is the effect on the graph of f(x) = x when it is transformed to

h(x) = 3x2 - 7?

A. The graph of f(x) is vertically stretched by a factor of 3 and shifted

7 units down.

B. The graph of f(x) is horizontally compressed by a factor of 3 and

shifted 7 units to the right.

C. The graph of f(x) is horizontally stretched by a factor of 3 and

shifted 7 units down.

D. The graph of f(x) is vertically stretched by a factor of 3 and shifted

7 units to the right

The probability that the money will be in next pocket is 0.25.

We have a pair of cargo pants with six pockets and $10 in one of the pockets.

We have to find out the probability that the money will be in the next pocket you check after checking two pockets without success.

The formula to calculate the probability of an event is -

In the question it is given -

Total  money = $10

Total no. of pockets = 6 = n(S)

After two unsuccessful check in two pockets, new sample space =

n(S') = n(S) - 2 = 4

Hence, the probability that the money will be in the next pocket you check is -

P(A) = [tex]\frac{1}{4} = 0.25[/tex]

Hence, the probability that the money will be in next pocket will be  0.25.

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Answer:

x=28

Step-by-step explanation:

We can use similar triangles and proportions to solve this problem.  Put the side of the small triangle over the same side of the larger triangle.

x               42

---------- = ----------

x+10           42+15

Simplify

x               42

---------- = ----------

x+10           57

Using cross products

57x = 42 (x+10)

Distribute

57x = 42x+420

Subtract 42x from each side

57x-42x = 42x-42x +420

15x = 420

Divide each side by 15

15x/15 = 420/15

x=28

Answer: The value of x is 28 units.

Step-by-step explanation:

Since we have given that

DC ║ PA

So, By Basic Proportionate theorem, if a line drawn parallel to the third side and intersect the other two sides, then the other two sides are divided into same ratio.

So, it becomes,

[tex]\frac{RC}{CA}=\frac{RD}{DP}\\\\\frac{x}{10}=\frac{42}{15}\\\\15\times x=10\times 42\\\\x=\frac{420}{15}=28\\\\x=28[/tex]

Hence, the value of x is 28 units.

The ratio of rolls greater than three to rolls less than or equal to three is 36:21, which simplifies to 12:7 after dividing both terms by the greatest common divisor of 3.

Since Craig rolled the die 57 times, and it landed on a number greater than three 36 times, then it landed on a number less than or equal to three the remaining number of times. Subtracting the number of greater rolls from the total rolls:

Total rolls: 57

Rolls greater than three: 36

Rolls less than or equal to three = 57 - 36 = 21

Now, we can establish the ratio of rolls greater than three to rolls less or equal to three:

Ratio = Rolls greater than three : Rolls less than or equal to three = 36 : 21

And if needed, we can simplify this ratio by dividing both sides by their greatest common divisor, which is 3:

Simplified Ratio = 12 : 7

Answer: old selling priceof businesss math text rose = $138.89

Explanation:

In year 2015, Price of business math text rose = $150

Suppose privious price (year 2014)= x dollars

Previous price is 8% less than the price in 2015 because given that $150 is 8% more than previous year price.

Now write the linear equation for the given information:

x + 8% of x = 150

Solve for x

x + [tex] \frac{8}{100} [/tex]x = 150

x + 0.08x = 150

1.08x = 150

divide 1.08 both the side

x = [tex] \frac{150}{1.08} [/tex]

x = $138.89

Old selling price = $138.89

Final answer:

The sum of 6 and 3 is 9, and one-third of this sum is 3 when you divide 9 by 3.

Explanation:

In mathematics, a sum is the result of adding two or more numbers or quantities together. It represents the total or aggregate of those quantities. The process of finding this total is called addition.

Thus,

To calculate one-third the sum of the numerals 6 and 3, we first find the sum of 6 and 3, which is 9.

Then, we need to take one-third of 9.

To find one-third of a number, you divide the number by 3.

So one-third of 9 is 9 divided by 3, which equals 3.

Therefore, one-third the sum of 6 and 3 is 3.

Answer:

Step-by-step explanation:

As in any "solve for ..." problem, you reverse (undo) the operations done to the variable of interest. Generally, you do that in reverse order.

1. y is divided by z then the quotient added to x. To solve for y, we subtract x, then multiply by z.

... w - x = y/z . . . . . . . subtract x from the given equation

... z(w -x) = y . . . . . . . multiply by z

___

2. To solve for z, it is more convenient to start with the equation for y that is the result of the first question. We divide that by the coefficient of z.

... z = y/(w -x)

From w=x+y/z, the value of y = z(w - x)

w=x+y/z

This is changing the subject formula. The first thing to do is to subtract x from both sides. This will be:

w - x = x + y/z - x

w - x = y/z

Then, we cross multiply

z(w - x) = y

Therefore, y = z(w - x)

Since y = z(w - x)

Then, to get the value of z goes thus:

z = y/(w - x)

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The value of the sample median is 172.

The value of the sample mean is 169.4.

The value of the sample variance is 52.3

It is the middle value of the given set of numbers after arranging the given set of numbers in order.

We have,

The heights in centimeters of 5 students are: 165, 175, 176, 159, 172

Now,

Arrange the heights in order.

159, 165, 172, 175, 176

Median = 172

Mean = (159 + 165 + 172 + 175 + 176) / 5 = 847 / 5 = 169.4

Sample variance.

= ∑ (x - Mean)² / (n - 1)

= 209.2 / 4

= 52.3

∑ (x - Mean)²

= (159 - 169.4)² + (165 - 169.4)² + (172 - 169.4)² + (175 - 169.4)² + (176 - 169.4)²

= 108.16 + 19.36 + 6.76 + 31.36 + 43.56

= 209.2

Thus,

The sample mean = 169.4

The sample median = 172

The sample variance = 52.3  

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Using the binomial probability formula, sum up the probabilities for 0, 1, and 2 smartphone users using their phones in meetings, which will give you the total probability for fewer than 3.

The subject of this question appears to be probability theory, a branch of mathematics that studies the likelihood of different outcomes. The problem presented involves calculating the probability of a certain number of smartphone users behaving in a specified way. In this case, it's about finding the likelihood that fewer than 3 out of 12 selected individuals use their smartphones in meetings or classes.

To solve this, we'll use a binomial probability formula: P(X=r) = (nCr) * p^r * (1-p)^(n-r), where:

You will need to sum up the probabilities for 0, 1, and 2 smartphone users using their phones in meetings or classes to get the total probability for fewer than 3.

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To write a percent as a fraction in lowest terms, first remember that a percent is a ratio that compares a number to 100. 43% can be written as the ratio 43 to 100 or 43/100.

Therefore, 43% can be written as the fraction 43/100.