For three consecutive years, Sam invested some money at the start of the year. The first year, he invested x dollars. The second year, he invested $2,000 less than 5/2 times the amount he invested the first year. The third year, he invested $1,000 more than 1/5 of the amount he invested the first year.

During the same three years, Sally also invested some money at the start of every year. The first year, she invested $1,000 less than 3/2 times the amount Sam invested the first year. The second year, she invested $1,500 less than 2 times the amount Sam invested the first year. The third year, she invested $1,400 more than 1/4 of the amount Sam invested the first year.

If Sam and Sally invested the same total amount at the end of three years, the amount Sam invested the first year is $ and the amount Sally invested the last year is $ .

Answer:

Option C -This could easily happen with a fair coin after only 4 flips.

Step-by-step explanation:

Given : A fellow classmate tosses 4 coins and finds that 3 of them come up tails.

To find : Which of the following is the best conclusion for her to come to?        

Solution :

According to statement,

A fellow classmate tosses 4 coins and finds that 3 of them come up tails.

This could be happen when coin is tossed or flip 4 times and the coin must be fair.

As when we flip 4 coins the possible outcomes were

HHHH     THHH      HTHH      TTHH

HHHT      THHT      HTHT      TTHT

HHTH      THTH      HTTH      TTTH

HHTT      THTT       HTTT       TTTT

So, The best conclusion for her is Option C

This could easily happen with a fair coin after only 4 flips.

The combined age of  Lily and Ezekiel is 42.

Lily is 14 older than her little brother Ezekiel. In 8 years, Lily will be twice as old as Ezekiel will be then. What is Lily and Ezekiel's combined To be determined.

In mathematics it deals with numbers of operations according to the statements.

Let the age of lily be L and the gare of her brother Ezekiel is E.
Lily is 14 older than her little brother Ezekiel.

L = 14 + E  - - - - - -(1)

In 8 years, Lily will be twice as old as Ezekiel will be then.

L = 2(E)

put L in equation 1.

2E = 14 + E
2E - E = 14
E = 14

Now put E in equation 1

L = 14 + 14
L = 28

Combined age of  Lily and Ezekiel's = 28 + 14
                                                       = 42

Thus, the combined age of  Lily and Ezekiel's is 42.

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If three lines meet at a single point, we say that the lines are concurrent.

Note that median is a line joining one vertex of a triangle with the midpoint of its opposite side.

Draw two medians for the given isosceles triangle.

Now, join the point of intersection of these medians and the third vertex.

If we prove the midpoint of the opposite side lies on this line, then it will be proved that the medians of the given isosceles triangle meet at a point.

Hence, here is the correct statement with blanks filled.

The midpoint of a side lies on the line containing the opposite vertex and the point where the other two medians intersect.

2 2/3 = 8/3

8/3= 40/15

13/15 - 40/15 = -27/15 =  -1 12/15

right triangle us pythagorean theorem

a^2 + b^2 = c^2

75^2 + 100^2 = C^2

5625 +10000 = c^2

15625 =c^2

c=Sqrt(15625) = 125

hypotenuse = 125

 answer is C

Answer:

63.4 pounds of tomatoes were used in each batch

Step-by-step explanation:

A factory used 396.25 pounds of tomatoes to make 6.25 batches of salsa.

Or, In 6.25 batches of salsa 396.25 pounds of tomatoes were used.

In 1 batch of salsa , [tex]\dfrac{396.25}{6.25}[/tex] pounds of tomatoes will be used.

i.e. In 1 batch of salsa , 63.4 pounds of tomatoes will be used.

Hence, 63.4 pounds of tomatoes were used in each batch

Answer:

positive linear association

hope this helps

Answer:

(1,-3)

Step-by-step explanation:

A figure has a vertex at (-1, -3). If the figure has line symmetry about the y-axis, find the coordinates

When a vertex is reflected over y axis then the value of y remains the same , the x value becomes -x

for (x,y) reflected over line symmetry y axis

(x,y) becomes (-x,y)

So the vertex (-1,-3) becomes (1,-3)

Hermina can calculate the length of the diagonal on her 10" by 15" rectangle of cardboard by using the Pythagorean theorem. The formula states that the square of the hypotenuse (diagonal) is equal to the sum of the squares of the other two sides, the length and the width. Thus, by inputting the values into the formula, we get a diagonal length of about 18.03".

The question involves calculating the length of the diagonal on a rectangular piece of cardboard. In mathematics, the Pythagorean theorem is used to calculate the length of a diagonal. In this case, the length and width of the rectangle are given as 10" and 15" respectively. We can apply the theorem, which states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. The diagonal here acts as the hypotenuse, with the other two sides being the length and width of the rectangle. Therefore, the length of the diagonal is the square root of the sum of squares of these sides, which would be sqrt(10^2 + 15^2), resulting in approximately 18.03".

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In a place value relationships. The relationship between 2 the same digit place next to each other is the value of the number to left is 10 times bigger than to the value to the left and from the decimal point to the right is 10 times smaller of value than the digit in their right.

Let say for example:
1111
1 thousands, 1 hundreds, 1 tens, and 1 ones.
Let’s start from 1 = 1 x 10 = 10
That would be 10 X 10 = 100
then 100 X 10 = 1000

Notice that their value increase base on its place value if we multiply the given number by 10. 

Another one is

912.98 in where 9 is hundreds, 1 is tens, 2 is ones and after the decimal points, in where  9 is tenths and 8 is hundredths.

Notice each place value next to each other. Each value is ten times in difference.

The volume of the cake pan Hilary wants to use is calculated using the formula for the volume of a rectangular prism. With dimensions of 4.0 inches by 9.0 inches by 2.2 inches, the volume is 79.2 cubic inches.

To find the volume of the cake pan that Hilary wants to use for making a mini cake for Phillip's party, we need to use the formula for the volume of a rectangular prism, which is Volume = length × width ×height. Given the dimensions of the cake pan are 4.0 inches long, 9.0 inches wide, and 2.2 inches deep, we can calculate the volume as follows:

Volume = length × width × height

Volume = 4.0 in×  9.0 in  × 2.2 in

Volume = 79.2 in³

Therefore, the volume of the cake pan is 79.2 cubic inches.

a) To find k for parallel lines, equate slopes to get k = -10/3. b) For perpendicular lines, use negative reciprocal slopes to find k = 3/10.

To determine the conditions for parallelism and perpendicularity, we need the slope of each line. The slope-intercept form of a line is y = mx + b where m is the slope.

To find the slope of the first line, we rearrange 3x-5y=9 to the form of y = mx + b, resulting in y = (3/5)x - (9/5). Therefore, the slope is 3/5. For the second line, rearranging 2x+ky=11 gives us y = (-2/k)x + (11/k). The slope of the second line is -2/k.

For the lines to be parallel, their slopes must be equal, so 3/5 = -2/k. Solving for k, we get k = -10/3. For the lines to be perpendicular, the product of their slopes must be -1 (since perpendicular lines have negative reciprocal slopes). This gives us (3/5)(-2/k) = -1, and solving for k yields k = 3/10.

Compare prices, consider discounts, and watch for additional costs like shipping. Choose the option with the lowest total expense for buying the $100 item.

To determine the most cost-effective choice for buying the $100 item, you should consider any available discounts, promotions, or deals offered by different sellers or platforms. Here are a few strategies you could consider:

1. **Comparison Shopping**: Check multiple retailers or online platforms to see if the item is available at a lower price elsewhere. Websites and apps dedicated to comparison shopping can help streamline this process.

2. **Discounts and Coupons**: Look for any available discounts or coupons that you can apply to your purchase. Many retailers offer promotional codes or special deals that can help reduce the cost of the item.

3. **Cashback and Rewards**: Some credit cards or loyalty programs offer cashback or rewards points for purchases. If you have a card or program like this, see if you can earn rewards or cashback by buying the item through a specific retailer.

4. **Timing**: Consider timing your purchase to coincide with sales events or promotions, such as Black Friday, Cyber Monday, or seasonal sales. Buying during these periods can often result in significant savings.

5. **Shipping and Handling Costs**: Be mindful of any additional costs associated with shipping and handling. Sometimes, even if the base price of the item seems lower from one seller, the shipping costs may make the overall purchase more expensive.

By comparing prices, looking for discounts, and considering additional costs, you can find the most cost-effective option for purchasing the $100 item.

Complete Question:

Which of these is the most cost effective choice for buying the item using a paid membership card to buy it at a 10 percent discount buying it on line at a 10 percent discount without sales tax?

1st character = 26 possibilities ( 26 letters in the alphabet)

2nd character = 26 possibilities

3rd character = 26 possibilities

4th character = 10 ( 10 special characters)

26 x 26 x 26 x 10 = 175,760 combinations