3.   Solve z2 – 15z + 56 = 0 using the zero product property.      A. z = 8, 7 B. z = –5, –2 C. z = 8, –4 D. z = –4, 7

Answer:

96

36

60

6.51

Step-by-step explanation:

The area of a shape is the amount of space it occupies.

The dimension of the paper is given as: 12-inch by 8-inch

So, its area is:

[tex]\mathbf{A_1 =12 \times 8}[/tex]

[tex]\mathbf{A_1 =96}[/tex]

The dimensions of the 4 right triangles are: Two 2 inches by 9 inches, and two 3 inches by 6 inches

So, the combined area is:

[tex]\mathbf{A_2 = 2 \times \frac 12 \times 2 \times 9 + 2 \times \frac 12 \times 3 \times 6}[/tex]

[tex]\mathbf{A_2 = 36}[/tex]

The area of the parallelogram is the difference between the areas of the paper and the four right triangles.

So, we have:

[tex]\mathbf{A_3 = A_1 - A_2}[/tex]

[tex]\mathbf{A_3 = 96 - 36}[/tex]

[tex]\mathbf{A_3 = 60}[/tex]

The area of a parallelogram is:

[tex]\mathbf{Area = Base \times Altitude}[/tex]

The base is given as 9.22

So, we have:

[tex]\mathbf{60 = 9.22\times Altitude}[/tex]

Divide both sides by 9.22

[tex]\mathbf{6.51 = Altitude}[/tex]

Rewrite as:

[tex]\mathbf{Altitude = 6.51}[/tex]

Hence, the altitude of the parallelogram is 6.51 inches

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The correct numbers to use in solving problems about spans of time like B.C. and A.D. should be “integers”.

Integers are whole numbers (not a fractional number or not a decimal number) which can take a value of negative, zero, or positive number. Example of integers would be -1, 0 and 1.

In calculations, the time period would be on the x-axis. Since B.C. and A.D. are two different spans of time, therefore in the calculations, the date of BC should be negative (negative x-axis) while the date of AD should be positive (positive x-axis). This would place the origin as the common reference.

To solve problems about spans of time that include B.C. and A.D. dates, Integers will be used .

The terms A.C. and B.C. stands for anno Domini and before Christ

These are used to label  years in the Gregorian calendars.

For solving a Problem that involve B.C and A.D. , Integers will be used

As the time span are neither in fraction or decimal

It can be negative , 0 and positive

B.C will be on the negative side of the x axis and A.D. will be equal to the positive side of the x axis.

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Answer: 400/400 which reduces to 1/1

Step-by-step explanation:

Answer:

i personally think it's 4

Step-by-step explanation:

even tho this was 4 years ago ehhhhhhh

Answer:

The 3 in the hundreds place has 10 times the value of the 3 in the tens place.

Step-by-step explanation:

In a base-10 place-value number system such as the one we customarily use, the value of a given digit is multiplied by 10 when it is placed one position farther to the left of the decimal point.

The threes in this number are in adjacent positions—one is in the tens place, and the one to its left is in the hundreds place. The digit in the hundreds place has a value of 300, which is 10 times the value of 30 that the digit in the tens place has.

In 2006, 112.8 million households owned at least one TV set. About 5.8 million households owned 3 or more TV sets in 2006. What percentage of those owning atleast one TV set was this? Round to the nearest integer

5.8 / 112.8 = 0.051418 which is 5.1418 percent, rounds down to 5%.

Answer:

  7.85 pounds (or 7 17/20 pounds)

Step-by-step explanation:

In decimal, the total is ...

   4.25 + 3.60 = 7.85 . . . pounds

As mixed numbers, the total is ...

  (4 +1/4) + (3 +3/5) = (4 +3) + (1/4 +3/5) = 7 +(5/20 +12/20) = 7 17/20 . . . pounds

Lowell bought 7 17/20 pounds of fruit.

_____

Comment on the math

Any calculator can add these numbers for you. You may have to enter them as (4+1/4) and (3+3/5) if your calculator does not support mixed number entry. Depending on the calculator, you may be able to get it to show you the mixed number result. If you want a mixed number and you get a decimal number, you may have to reduce the fraction yourself:

  7 85/100 = 7 17/20 . . . . . . a factor of 5/5 can be removed from the fraction

___

Any two fractions can always be added using the formula ...

  a/b + c/d = (ad +bc)/(bd)

Here, that means the sum of 1/4 and 3/5 is ...

  1/4 + 3/5 = (1·5 +4·3)/(4·5) = (5+12)/20 = 17/20 . . . . . the result above

In some cases, you may have to reduce the resulting fraction.

Lowell bought [tex]4 \frac{1}{4}[/tex] pounds of fruit.

To find the total weight of fruit Lowell bought, we need to add the weights of the apples and oranges together.

Lowell bought [tex]4 \frac{1}{4}[/tex] pounds of apples and [tex]3 \frac{3}{}[/tex] pounds of oranges. To add these fractions, we need to find a common denominator, which in this case is 20.

Converting both fractions to twentieths, we have [tex]\frac{17}{20}[/tex] pounds of apples and [tex]\frac{68}{20}[/tex] pounds of oranges. Adding these together, we get a total of [tex]\frac{85}{20}[/tex] pounds. Simplifying the fraction, we find that Lowell bought [tex]4 \frac{1}{4}[/tex] pounds of fruit.

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Answer:

See below.

Step-by-step explanation:

We are going to take the quadratic formula ax²+bx+c=0

a.Divide all terms in the equation by a.

[tex]\frac{ax^{2} }{a} +\frac{b}{a}x+\frac{c}{a}=0\\\\x^{2} +\frac{b}{a}x+\frac{c}{a}  =0[/tex]

b.Subtract the constant (the term without an x) from both sides.

[tex]x^{2} +\frac{b}{a}x+\frac{c}{a} -\frac{c}{a}  =\frac{-c}{a} \\\\x^{2} +\frac{b}{a}x=-\frac{c}{a}[/tex]

c.Add a constant (in terms of a and b) that will complete the square.

[tex]x^{2} +\frac{b}{a}x=-\frac{c}{a}\\\\[tex]x^{2} +\frac{b}{a}x+\frac{b^{2} }{4a^{2} }  =-\frac{c}{a} +\frac{b^{2} }{4a^{2}}\\\\(x+\frac{b}{2a}) ^{2}  =\frac{-4ac+b^{2} }{4a^{2} }[/tex]

d.Take the square root of both sides of the equation.

[tex]x+\frac{b}{2a}  =[tex]\\x+\frac{b}{2a} =\frac{\sqrt{-4ac+b^{2} } }{2a}\\x=\frac{\sqrt{-4ac+b^{2} } }{2a}-\frac{b}{2a} [/tex]

e.Solve for x.

[tex]x=-b+\frac{\sqrt{b^{2}-4ac } }{2a}[/tex]

The probability of randomly selecting a heart or a spade is 1/2. The probability of randomly selecting a heart or a spade or a club is 3/4. The probability of randomly selecting a two or a diamond is 17/52.

(a) There are 13 hearts and 13 spades in a standard deck of cards. The probability of randomly selecting a heart or a spade can be calculated as:

P(Heart or Spade) = P(Heart) + P(Spade) = 13/52 + 13/52 = 26/52 = 1/2

(b) To find the probability of randomly selecting a heart or a spade or a club, we add the probability of selecting a club to the previous result:

P(Heart or Spade or Club) = P(Heart or Spade) + P(Club) = 1/2 + 13/52 = 39/52 = 3/4

(c) There are 4 twos and 13 diamonds in a standard deck of cards. The probability of randomly selecting a two or a diamond can be calculated as:

P(Two or Diamond) = P(Two) + P(Diamond) = 4/52 + 13/52 = 17/52

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Answer:

a=1 b=5 c=-5

We solve by using the quadratic formula.

x = -5 +- sq root (5² - 4*1*-5) / (2 * 1)

x = [-5 +- sq root (25 + 20)]/ 2

Step-by-step explanation:

Answer:

29.68%

Step-by-step explanation:

Allen's monthly take-home pay is $3000

His monthly rent is $750

Now both his monthly take-home pay and his rent increase by $200

So, After increase Allen's monthly take-home pay =$3000+$200= $3200

After increase His monthly rent = $750+200=$950

Now we are supposed to find what percentage of Allen's take-home pay will be used to pay rent

So, percentage = [tex]\frac{\text{Rent after increase}}{\text {Take- home pay after increase}} \times 100[/tex]

                          = [tex]\frac{950}{3200}\times 100[/tex]  

                          = [tex]\frac{950}{32}[/tex]  

                          = [tex]29.68\%[/tex]  

Hence 29.68% of Allen's take-home pay will be used to pay rent.                          

To calculate the new area of Hans's expanded garden, multiply the new length by the new width. The new garden will have an area of 3600 ft^2.

The original garden area is 400 ft2, with a length of 40 ft and a width of 10 ft.

To find the new garden's area after expansion:

100/5 =20

16 + 18 +20 +22 +24 = 100

middle number is 20

The speed of the boat in still water is 4mph and the speed of the current is 2mph.

Using the distance formula expressed as:

Distance = speed * time

d = st

Let x be the ​crew's rowing rate in still water and;

let y be the rate of the current

If a crew rows with the​ current and it travels 18 miles in 3 hours, the

3(x+y)=18

If they row against the​ current, the crew rows 6 miles in 3 hours then;

3(x-y)=6  

The equations becomes

x + y = 6

x - y = 2

Add both equations

2x = 6 + 2

2x = 8

x = 4

Recall that x + y = 6

4 + y = 6

y = 2

Hence the speed of the boat in still water is 4mph and the speed of the current is 2mph.

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Final answer:

The standard deviation of the average amount of caffeine in a carton containing 30 bottles of an energy drink is approximately 4.564 mg.

Explanation:

To calculate the standard deviation of the average amount of caffeine in a carton containing 30 bottles of an energy drink, we can use the concept of the sampling distribution of the sample mean.

When independent random samples of a fixed size are taken from a population, the standard deviation of the sample means (σx-bar) is equal to the population standard deviation (σ) divided by the square root of the sample size (n), which is also known as the standard error of the mean.

The formula to find the standard deviation of the sample means is:

σx-bar = σ / √n

In this case, the population standard deviation is given as 25 mg of caffeine, and the sample size is 30 bottles.

So, we calculate the standard deviation of the average amount of caffeine as follows:

σx-bar = 25 mg / √30

σx-bar ≈ 25 mg / 5.477

σx-bar ≈ 4.564 mg (rounded to three decimal places)

Thus, the standard deviation of the average amount of caffeine in a carton containing 30 bottles is approximately 4.564 mg.

The discount offered on the jeans is 25 percent. The sales tax charged on the jeans is 6.5 percent. Markup on the jeans after allowing discount is 60 percent.

a. To find the percent of discount, we need to calculate the actual discount and divide it by the original price, then multiply by 100. From the given information, the original price of the jeans is $39.99 and the discount is $10.00. Therefore, the actual discount is $10.00 and the original price is $39.99. The percent of discount to the nearest percent is:

Percent of discount = (actual discount / original price) x 100

Percent of discount = (10.00 / 39.99) x 100

Percent of discount = 25%

Therefore, the percent of discount to the nearest percent is 25%.

b. To find the percent of sales tax, we need to divide the sales tax by the subtotal, then multiply by 100. From the given information, the subtotal is $29.99 and the sales tax is $1.95. Therefore, the percent of sales tax to the nearest tenth of a percent is:

Percent of sales tax = (sales tax / subtotal) x 100

Percent of sales tax = (1.95 / 29.99) x 100

Percent of sales tax = 6.5%

Therefore, the percent of sales tax to the nearest tenth of a percent is 6.5%.

c. The price of the jeans includes a 60% markup, which means that the selling price is 160% of the cost price. Let x be the cost price of the jeans. Then, the selling price of the jeans is 1.6x. After the discount of $10.00, the selling price becomes 1.6x - 10.00. The percent of markup after the discount to the nearest percent is:

Percent of markup = ((selling price - cost price) / cost price) x 100

Percent of markup = (((1.6x - 10.00) - x) / x) x 100

Percent of markup = (0.6x - 10.00) / x x 100

Percent of markup = 60 - (1000 / x)

Percent of markup = 60%.

So, the percent of markup after the discount is approximately 60%.

Answer:

The square is inscribed in a circle that means the square is drawn inside a circle such that it's vertices lie on the circle.

You need to remember that the vertices of the square lie on the circumference of circle and the center of circle is also the midpoint of diagonals of the square i.e. Diagonal of the square is equal to diameter of the circle.

We could also see the image of such figure.

To locate the vertices of a square inscribed in a circle, follow these steps: draw the circle, choose a point on the circumference, create a radius, find the midpoint, and connect the points to form a square.

To locate the vertices of a square inscribed in a circle, you can follow these steps:

Now you have located the vertices of a square inscribed in circle C.