The
Olympic time for men's 400-m hurdles
has been decreasing by about 0.09 seconds per
year since 1930, when the record was 52 seconds.
Predict what the time will be in 2010

Answer:

-3

Step-by-step explanation:

As included in the image you put, slope is rise over run or y2-y1/x2-x1.

y2-y1/x2-x1

we'll replace x and y with the coordinate points given

-3 - 3/2-0

-6/2             simplify

-3/1

slope is -3/1 or -3.

The incorrect statement is:

B. The three-part inequality - 5x < 15x^2 < 3 is equivalent to - 6 ≤ 5 - x < 6.

In the given statement, there is an error in the inequality. The correct statement should be:

The three-part inequality - 5x < 15x^2 < 3 is equivalent to - 6 ≤ 5 - x and 5 - x < 6.

When solving the three-part inequality - 5x < 15x^2 < 3, we need to split it into two separate inequalities. The correct splitting should be:

- 5x < 15x^2 and 15x^2 < 3

Simplifying the first inequality:

- 5x < 15x^2

Dividing by x (assuming x ≠ 0), we need to reverse the inequality sign:

- 5 < 15x

Simplifying the second inequality:

15x^2 < 3

Dividing by 15, we get:

x^2 < 1/5

Taking the square root (assuming x ≥ 0), we have two cases:

x < 1/√5 and -x < 1/√5

Combining these inequalities, we get:

- 5 < 15x and x < 1/√5 and -x < 1/√5

Therefore, the correct statement is that the three-part inequality - 5x < 15x^2 < 3 is equivalent to - 6 ≤ 5 - x and 5 - x < 6, not - 6 ≤ 5 - x < 6 as stated in option B.

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Answer:

quadrant 1

Step-by-step explanation:

quadrant 1 is (-,+)

Answer:

83 kids total

Step-by-step explanation:

There are 54 girls on the playground. There are 25 fewer boys than girls on the playground. How many kids are on the playground?

girls = 54

boys = 54 - 25 = 29

54 + 29 = 83 kids total

kids that are on the playground are 83.

Merging objects and identifying them since one big bunch is done through addition. In arithmetic, addition is the technique of adding two or more integers together. The product can meet are the quantities that are included, and the outcome of the operation, or the final response, is referred to as the sum.

The total number of girls that are present is 54

The data given is that there are

25 fewer boys taht are4 present

The total number of boys will be

boys = 54 - 25 = 29

The number of kids that are present will be the total of boys and girls that are present.

Kids = boys + girls

54 + 29 = 83 kids total

The quantity of kids that are present in the playground is 83.

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Answer:

19

Step-by-step explanation:

1st day: x

2nd day: x+3

3rd day: x+4

Equation: x+(x+3)+(x+4)=64

                 3x+7=64

                   3x=57

                      x=19

I hope you found this answer helpful!!!!!!(sorry if instructions aren't clear)

The bank reconciliation reveals various errors and discrepancies between ABC Company's records and the bank statement, including missing deposits, incorrect check charges, outstanding checks, unrecorded interest proceeds, fees, NSF charges, and recording errors.

Upon analyzing the bank reconciliation for ABC Company, several discrepancies between the company's records and the bank statement are identified:

A deposit of Br. 410.90 made after banking hours does not appear on the bank statement. This indicates that the deposit was not processed by the bank before the statement was generated.

A check drawn for Br. 79 was charged by the bank as Br. 973. This suggests an error by the bank in processing the check, resulting in an incorrect charge to ABC Company.

Outstanding checks are checks issued in July but have not yet been paid by the bank. The checks include check numbers 801, 888, 890, and 891, with respective amounts of Br. 100.00, Br. 10.25, Br. 294.50, and Br. 205.00.

A check written for Br. 210 was charged by the bank as Br. 120, indicating an error in the bank's recording.

The proceeds from the collection of an interest-bearing note receivable from David, with a face amount of Br. 500, are not reflected in the bank statement.

A Br. 24.75 interest earned on the average account balance during July is included in the bank statement.

A check for Br. 10, which was recorded in the check register as Br. 100, was returned with the statement. This discrepancy could be due to an error in recording the check amount.

A Br. 5.00 fee was charged by the bank for handling the collection of a note receivable.

A Br. 50.25 check from customer John, deposited by ABC Company, was charged by the bank as Non-Sufficient Funds (NSF), indicating that the customer's check bounced.

A Br. 12.70 service charge was imposed by the bank for the month of July.

Check number 875 was issued on July 20 for Br. 85 but was erroneously recorded in the cash payment journal as Br. 58 for the payment of telephone expenses.

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SOLUTION

Given the question in the image, the following are the solution steps to answer the question.

STEP 1: Write the given equation

Hence, the reason for 2 is "Division Property of Equality"

Answer:

-3c

hope it helps

Step-by-step explanation:

Based on the Law of Cosines; it was proven that:

Please note that the given equation on number 3 is wrong. The correct equation should be: a² + b² + 2bx = c². The explanation why the given equation is incorrect will be explained later.

Based on the unshaded triangle, we can find that:

cos Θ = x/a

Next, we will prove that: cos (180 - C) = x/a

Remember that:

cos (A + B) = cos A cos B - sin A sin B

Law of Cosines: c² = a² + b² - 2ab. cos C

cos C = - [c² - (a² + b²)] /2ab ... (i)

Then:

cos Θ = cos (180 - C)

cos (180 - C) = cos 180 . cos C - sin 180 . sin  C

We subtitute equation (i):

cos (180 - C) = (-1) (- [c² - ((a² + b²)] / 2ab) - 0 sin C

cos (180 - C) = [c² - (a² + b²)]/ 2ab ... (ii)

If we focus on the unshaded triangle, we can find an equation of a, where:

a² = h² + x² ... (iii)

And if we combine both triangle into a giant triangle, we can make another equation of c. where:

c² = (x + b)² + h² ... (iv)

We will subtitute equation (iv) into equation (ii):

cos (180 - C) =  [c² - (a² + b²)]/ 2ab

cos (180 - C) = [(x + b)² + h² - (a² + b²)] / 2ab

cos (180 - C) = [x² + b² + 2bx + h² - a² - b²] / 2ab

cos (180 - C) = [x² + 2bx + h² - a²] / 2ab ... (v)

We subtitute equation (iii) into equation (v):

cos (180 - C) = [x² + 2bx + h² - a²] / 2ab

cos (180 - C) = [a² + 2bx - a²] / 2ab

cos (180 - C) = 2bx / 2ab

cos (180 - C) = x/a --> PROVEN!

Next, we will try to show why the given equation of a² + b² - 2bx = c² is incorrect.

We know that:

a² + b² - 2ab cos C = c²

c² = (x + b)² + h²

We will try to find the value of cos C:

a² + b² - 2ab cos C = (x + b)² + h²

a² + b² - 2ab cos C = x² + b² + 2bx + h²

a² - 2ab cos C = a² + 2bx

- 2 ab cos C = 2bx

cos C = - x/a

We will subtitute the value of cos C under the Law of Cosines:

c² = a² + b² - 2ab cos C

c² = a² + b² - 2ab (- x/a)

c² = a² + b² + 2bx --> PROVEN!

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The value of e can be calculated by  e = A - f/2.

Usually, simplification involves proceeding with the pending operations in the expression.

For example, 5 + 2 is an expression whose simplified form can be obtained by doing the pending addition, which results in 7 as its simplified form.

Simplification usually involves making the expression simple and easy to use later.

We have been given an expression as;

A =e+f/2

We need to find the solution for 'e'.

So,

A = e+f/2

Subtract from f/2 on each side, we get;

A - f/2 = e

Thus, e = A - f/2

Therefore, the value of e can be calculated by  e = A - f/2.

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Answer:

plug in whatever you found for x and see if its equal on both sides.

Step-by-step explanation:

Answer:

To check an answer for an equation, you can substitute the answer you've found in place of the variable you solved it for.

The value of the unknown, x, can be plugged into the equation. You can then compare both sides to see if they are equal.

For your given equation, let's substitute 1 for x in the equation you've given.

3x + 5 = x + 7

3(1) + 5 = 1 +7

Simplify this.

3 + 5 = 8

8 = 8

You know that 8 does equal 8, so your value for x is correct.

I hope this helps you ^^

Good luck :)

Option A is the answer of this question.

The ratio of the strawberries to the blueberries is 32 strawberries: 30 blueberries (option d).

Ratio expresses the relationship between two or more numbers. It shows the frequency of the number of times that one value is contained within other value(s). The sign that is used to represent ratio is :.

The ratio of strawberries to blueberries - total number of strawberries : total number of blueberries.

(8 x 4) : 30

32 : 30

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Answer: A. 8 strawberries: 30 blueberries

Step-by-step explanation:

Answer:

y = 8

x = 11.3

option 2

Step-by-step explanation:

We can recognize this right triangle as a special triangle, a 45° - 45° - 90° triangle more specifically. This triangle would be isosceles because the two base angles are both 45°. Since the triangle is isosceles, we can say that the legs are congruent, so y = 8. In a 45° - 45° - 90° triangle, the hypotenuse is √2 times the legs. To find x, we can set up the equation:

8 * √2 =x

x = 8√2 or about 11.3

The range is the best measure of variability for this data, and its value is 4.

The line plot displays the number of roses purchased per day at a grocery store, with the data values ranging from 0 to 4 (since there are no dots above 4).

The best measure of variability for this data is the range, which is the difference between the maximum and minimum values in the data set. In this case, the minimum value is 0 and the maximum value is 4, so the range is:

Range = Maximum value - Minimum value = 4 - 0 = 4

Therefore, the range is the best measure of variability for this data, and its value is 4.

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The maximum number of performers in each row so that all the rows are equal in length is 8.

From the information, the marching band needs to create rows for its performance. there are 24 instruments and 16 flag bearers.

Therefore, we will find the highest common factor for both numbers. This will be:

24 = 1 2 3 4 ,6 8 12 24

16 = 1 2 4 16

Therefore the highest factor is 8

The maximum number of performers in each row so that all the rows are equal in length is 8.

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Answer:

The value of limit = \(\frac{13}{8}\)

Step-by-step explanation:

Explanation:-

Given  \(\lim_{x \to 4} \frac{x^{2}+5 x-36 }{x^{2}-16 }\)

      =  \(\lim_{x \to 4} \frac{x^{2}+9 x-4 x-36 }{(x-4)(x+4) }\)

     = \(\lim_{x \to 4} \frac{(x(x-4)+9(x-4) }{(x-4)(x+4) }\)

     =\(\lim_{x \to 4} \frac{((x-4)(x+9)}{(x-4)(x+4) }\)

   = \(\frac{4+9}{4+4}\)

  = \(\frac{13}{8}\)

Hence the limit exists and The value of limit = \(\frac{13}{8}\)

Answer:

157908.83

Step-by-step explanation:

RD formula is :

\(P(1+\frac{r}{m} ) [(1+\frac{r}{m} )^{N} -1 }]{\frac{m}{r}\)

where P: Principal / rd amount = $2000

r : interest = 8% = 0.08

m : no. of times compounded in a year = 1 (compounded annually)

N : time = 25 years

Amt =

\(2000(1+\frac{0.08}{1} ) [(1+\frac{0.08}{1} )^{25} -1 }]{\frac{1}{0.08}\)

\(= 2000(1.08) [1.08^{25} -1 }]{\frac{1}{0.08}\)

= 157908.83

Answer:

Step-by-step explanation:

calculate the difference height (P) is -6 and (t) is 2.85

Δy divided by Δx = rate of change

3-9 = -6

6.23-3.41 = 2.85

then divide

2.85 / -6 = .475

Your answer will be - .475

\(\huge \bf༆ Answer ༄\)

The value of x, for given problem is ~

\({ \qquad{ \sf{ \dashrightarrow}}}  \:  \: \sf \: |x| = 10\)

\({ \qquad{ \sf{ \dashrightarrow}}}  \:  \: \sf \:x = \pm10\)

The required answers are + 10 and -10 because we can get | x | = 10 for both the values of x.

that is ;

\({ \qquad{ \sf{ \dashrightarrow}}}  \:  \: \sf \: |10| = 10\)

and

\({ \qquad{ \sf{ \dashrightarrow}}}  \:  \: \sf \: | - 10| = 10\)

I hope you understood ~

Answer:

C. Robbie's glider

Step-by-step explanation:

P.S -The exact question is -

Given - Melissa and Robbie are flying remote control gliders.

The altitude of Melissa's glider, h(s), in feet, is modeled by this function, where sis time, in seconds, after launch.

m(s) = 0.4(s³ - 11s² + 31s – 1)

The altitude of Robbie's glider is modeled by function r, where sis time, in seconds, after launch.

To find - Which glider reaches the greater maximum altitude in the first 6 seconds after launch?

A. Neither glider reaches a maximum altitude on the given interval.

В. Melissa's glider

C. Robbie's glider

D. Both gliders reach the same altitude on the given interval.

Proof -

At t = 6 sec,

Melisa glider is

h(6) = 0.4((0.6)³ - 11(0.6)² + 31(0.6) – 1)

      = 0.4( 0.216 - 3.96 + 18.6 - 1 )

      = 0.4(13.856) = 5.5424

⇒h(6) = 5.5424

∴ we get

At t = 6 seconds, Melissa glider is at the altitude of 5.54 feet

Now,

From the figure, we can see that,

At t = 6 seconds, Robbie's glider is approximately at an altitude of 13 feet

Now,

As 13 > 5.5

So,

Robbie's glider is at maximum height in 6 seconds after the launch.

So,

The correct option is - C. Robbie's glider

Answer:

50

Step-by-step explanation:

18+(16×2)

18+32

=50

Answer:

Fraction: 1/3 Decimal: 0.333333333

Step-by-step explanation:

Answer:

One example of a fraction that can be represented as a repeating decimal is 1/3. If you divide 1 by 3 using a calculator or long division, you will see that the decimal representation of 1/3 is 0.3333..., where the 3's repeat indefinitely. This can also be represented as 0. (3)

Another example of a fraction that can be represented as a repeating decimal is 2/7. If you divide 2 by 7 using a calculator or long division, you will see that the decimal representation of 2/7 is 0.2857142857142857..., where the digits 142857 repeat indefinitely. This can also be represented as 0. (142857)

It is worth noting that not all fractions can be represented as repeating decimals, for example 1/4 = 0.25 and 1/2 = 0.5 are not repeating decimals.

Step-by-step explanation:

The freighter is approximately 164.33 miles from the city.

We can use the Law of Cosines to solve this problem. Let's label the distances as follows:

d: distance between the city and the freighter

x: distance between the city and the island

y: distance between the island and the freighter

First, we need to find x using the given coordinates:

N23°38'W is equivalent to S23°38'E, so we have:

cos(23°38') = x/48

x = 48cos(23°38') ≈ 42.67 miles

Next, we can use the coordinates of the freighter to find y:

N11°26'E is equivalent to E11°26'N, and N12°16'W is equivalent to S12°16'E. This means that the angle between the island and the freighter is:

23°38' + 11°26' + 12°16' = 47°20'

cos(47°20') = y/d

We can rearrange this equation to solve for y:

y = dcos(47°20')

Now we can use the Law of Cosines to solve for d:

d² = x² + y² - 2xy cos(90° - 47°20')

d² = 42.67² + (d cos(47°20'))² - 2(42.67)(d cos(47°20')) sin(47°20')

d² = 1822.44 + d² cos²(47°20') - 2(42.67)(d cos(47°20')) sin(47°20')

d² - d² cos²(47°20') = 1822.44 - 2(42.67)(d cos(47°20')) sin(47°20')

d² (1 - cos²(47°20')) = 1822.44 - 2(42.67)(d cos(47°20')) sin(47°20')

d² sin²(47°20') = 1822.44 - 2(42.67)(d cos(47°20')) sin(47°20')

d² = (1822.44 - 2(42.67)(d cos(47°20')) sin(47°20')) / sin²(47°20')

d ≈ 164.33 miles

Therefore, the freighter is approximately 164.33 miles from the city.

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The volume of the rectangular pyramid is 64 cubic feet.

A pyramid with a rectangular base is known as a rectangle pyramid. When viewed from the bottom, this pyramid seems to be a rectangle. As a result, the base has two equal parallel sides.

The apex, which is located at the summit of the pyramid's base, serves as its crown. Right or oblique pyramids can be seen in rectangular shapes. If it is a right rectangular pyramid, the peak will be directly over the base's center; if it is an oblique rectangular pyramid, the apex will be angled away from the base's center.

The volume of a rectangular pyramid is given as:

V = (l)(b)(h) / 3

V = (6)(8)(4) / 3

V = 192 / 3

V = 64 cubic feet.

Hence, the volume of the rectangular pyramid is 64 cubic feet.

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The correct question is:

The area of the shaded region in terms of π is equal to 25π/3 cm².

In Mathematics and Geometry, the area of a sector can be calculated by using the following formula:

Area of sector = θπr²/360

Where:

By substituting the given parameters into the area of a sector formula, we have the following;

Area of sector = θπr²/360

Area of sector = 120(π/360) × 5²

Area of sector = (π/3) × 25

Area of sector = 25π/3 cm²

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.