The short sides of a rectangle are 2 inches. The long sides of the same rectangle are three less than an unknown number of inches.

Two students are told that the perimeter of this rectangle is at least 30 inches. The first student says, "The length of the long side must be at least 13 inches". The second student says, "The unknown number must be at least 10 inches". Which of the following statements is true?

A. The first student is correct.

B. The second student is correct.

C. Both students are correct.

D. Neither student is correct.

Answer:

[tex] 664 \frac{47}{50}  [/tex]

Step-by-step explanation:

Let's first add 16/25 with 3/10. To do that, we look for the least common multiple between 25 and 10, which is 50 and we put it in the denominator. Then, we have to compute (50/25)*16, which is equal to 32, and add it to (50/10)*3, which is equal to 15  

[tex] \frac{16}{25} + \frac{3}{10} = \frac{32 + 15}{50} = \frac{47}{50} [/tex]

On the other hand, to the non-fraction terms, we just add them. So, 632 + 32 = 664

Finally, the result  is 664 47/50

Part 1: Pizza and tacos will be served on the same day again in 11 school days.

Part 2: No, pizza and tacos will not be served on the same day in 21 school days because 21 is not divisible by the LCM of 4 and 3, which is 12.

Part 1: To find the number of school days until pizza and tacos are served on the same day again, we need to find the least common multiple (LCM) of 4 and 3, which represents the cycle length for both pizza and tacos.

Find the least common multiple (LCM) of 4 and 3.

LCM(4, 3) = 12

Subtract 1 from the LCM to find the number of school days until pizza and tacos are served on the same day again.

Number of school days = LCM(4, 3) - 1

Number of school days = 12 - 1

Number of school days = 11

Therefore, pizza and tacos will be served on the same day again in 11 school days.

Part 2: To determine if pizza and tacos will be served on the same day in 21 school days, we need to check if 21 is divisible by the LCM of 4 and 3, which is 12.

Divide 21 by the LCM of 4 and 3.

21 ÷ 12 = 1, with a remainder of 9

Since the remainder is not 0, pizza and tacos will not be served on the same day in 21 school days.

Explanation: The cycle of pizza and tacos being served on the same day repeats every 12 school days (LCM of 4 and 3). If the number of school days is divisible by 12, then pizza and tacos will be served on the same day. However, since 21 is not divisible by 12 (it has a remainder of 9), pizza and tacos will not be served on the same day in 21 school days.

Complete question:

Part 1: Pizza is served in the school cafeteria every fourth school day. Tacos are served every third school day. Both pizzas and tacos are served today. In how many school days will pizza and tacos be served on the same day again? Part 2: If the pattern continues, will pizza and tacos be served on the same day in 21 school days? Explain why or why not.

The annual interest rate is 6% and this can be determined by using the formula of simple interest and also by using the given data.

Given :

The formula of the simple interest can be used in order to determine the annual interest rate.

The formula of the simple interest is given by:

A = P(1 + rt)

where A is the final amount, P is the principal amount, r is the rate of interest, and t is the time in years.

Now, substitute the values of the known terms in the above formula.

520 + 156 = 520(1 + 5r)

Simplify the above expression in order to determine the value of 'r'.

676 = 520(1 + 5r)

1.3 = (1 + 5r)

0.3 = 5r

r = 0.06

Now, multiply by 100 in order to determine the percentage.

r = 0.06 [tex]\times[/tex] 100

r = 6%

So, the annual interest rate is 6%.

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The  Statement 3: "There are exactly 30 more girls than boys". is absolutely true.

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.

The ratio of the number of boys to the number of girls at Liam's school is 4:5 and there are 270 students at his school.

4x + 5x = 270

9x = 270

x= 30

Then, Total boys = 4(30) = 120

Total girls = 5(30) = 150

We can see that Clearly, (Number of girls) > (Number of boys)

Difference =  (Total girls) - (Total boys)

= 150-120

= 30

Hence, The  Statement 3: "There are exactly 30 more girls than boys". is absolutely true.

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The number in question is 8. Multiplying it by 7, subtracting 2, and dividing the result by 6 gives you 9.

To find the number that, when multiplied by 7, subtracted by 2, and then divided by 6, results in 9, we can set up the equation to solve for the unknown number (let's call it x):

7x - 2 = 54 (since 6 times 9 equals 54)

7x = 54 + 2

7x = 56

x = 56 / 7

x = 8

So the number you're looking for is 8 because when you multiply 8 by 7, subtract 2, and then divide by 6, you indeed get 9.

Answer:

Numbers from least to greatest is   -85 , -1.4 , -0.9 , 0.6 , 14 .

Step-by-step explanation:

Given : Numbers −1.4,−85, 0.6,−0.9, 14.

To find : Order the numbers from least to greatest ?

Solution :

According to number system,

In left side there are negative numbers before zero and after on right side there are positive numbers.

In left side, number written from larger to smallest with negative sign.

In right side, number written from smallest to larger with positive sign.

Numbers from least to greatest is   -85 , -1.4 , -0.9 , 0.6 , 14 .

C 2 years at 6.5 percent

Step-by-step explanation:

On my quiz it said c was correct.

Answer:

D. 11,200

Step-by-step explanation:

I said that because it has been a lot of cat fishing

The possible number of rows that Brooke could set up are 2, 5, 7, 10, and 14.

Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.

Let x be the number of rows. There is not room for more than 20 rows:

x ≤ 20

Since all rows must be equal, when we divide 70 by x, we must get a whole number. So, we must find all divisors of 70 smaller or equal to 20 and they are: 2, 5, 7, 10, and 14.

So, the possibilities are:

2 rows with 35 chairs in each row

5 rows with 14 chairs in each row

7 rows with 10 chairs in each row

10 rows with 7 chairs in each row

14 rows with 5 chairs in each row

Therefore, the possible number of rows that Brooke could set up are 2, 5, 7, 10, and 14.

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"Your question is incomplete, probably the complete question/missing part is:"

Brooke has to set up 70 chairs in equal rows for the class talent show. but, there is not room for more than 20 rows. what are the possible number of rows that Brooke could set up.

Final answer:

As per the given case, there are 301 watermelons.

Explanation:

To calculate the number of watermelons at the farmer's market, we need to subtract the percentages of apples, oranges, and honeydew melons from the total percentage (100%) and then apply that percentage to the total number of fruits available. The calculations are as follows:

Total percentage of these three fruits: 39% + 28% + 13% = 80%

Percentage of watermelons = 100% - 80% = 20%

So, if 20% of the fruits are watermelons, and there are 1505 fruits in total, we calculate the number of watermelons as follows:

Number of watermelons = 20% of 1505 = 0.20 × 1505 = 301 watermelons

Therefore, there are 301 watermelons for sale at the farmer's market.

To write an equation in slope-intercept form, we can use the given points to find the slope and y-intercept of the line. The equation that represents the amount of water in the can after x seconds is y = -2x + 68.

To write an equation in slope-intercept form, we need to find the equation of a line in the form y = mx + b, where m is the slope and b is the y-intercept.

Given that the watering can contains 58 ounces of water after 5 seconds and 28 ounces of water after 20 seconds, we can use these two points to find the slope (m).

m = (28 - 58) / (20 - 5) = -30 / 15 = -2

Next, we can substitute one of the points and the slope into the equation and solve for b:

58 = -2(5) + b

b = 68

Therefore, the equation that represents the amount of water in the can after x seconds is

y = -2x + 68

Therefore, the equation in slope-intercept form that represents the amount y (in ounces) of water in the can after x seconds is y = -2x + 68.

To write the equation in slope-intercept form that represents the amount y (in ounces) of water in the can after x seconds, we need to determine the rate at which the water level decreases over time.

Given data:

- After 5 seconds, the can contains 58 ounces of water.

- After 20 seconds (5 seconds + 15 seconds), the can contains 28 ounces of water.

Let's define our points based on this data:

- First point: (5, 58) (5 seconds, 58 ounces)

- Second point: (20, 28) (20 seconds, 28 ounces)

Now, let's find the slope m of the line passing through these two points. The slope m is calculated as:

[tex]\[ m = \frac{y_2 - y_1}{x_2 - x_1} \][/tex]

[tex]\[ m = \frac{28 - 58}{20 - 5} \][/tex]

[tex]\[ m = \frac{-30}{15} \][/tex]

[tex]\[ m = -2 \][/tex]

Now that we have the slope m, we can use the point-slope form of the equation of a line, [tex]\( y - y_1 = m(x - x_1) \)[/tex], where [tex]\( (x_1, y_1) \)[/tex] is one of our points. Let's use the point (5, 58):

[tex]\[ y - 58 = -2(x - 5) \][/tex]

Now, simplify and solve for y to get the equation in slope-intercept form (y-intercept form), y = mx + b:

[tex]\[ y - 58 = -2x + 10 \][/tex]

[tex]\[ y = -2x + 10 + 58 \][/tex]

[tex]\[ y = -2x + 68 \][/tex]

Answer:

The answer is 20%

Step-by-step explanation:

The percent error is 20%

The percentage is defined as a ratio expressed as a fraction of 100.

Arithmetic operations can also be specified by subtracting, dividing, and multiplying built-in functions.

+ Addition operation: Adds values on either side of the operator.

For example 4 + 2 = 6

- Subtraction operation: Subtracts the right-hand operand from the left-hand operand.

for example 4 -2 = 2

We have been given that Jessie estimated the weight of his cat to be 12 pounds. The actual weight of the cat is 15 pounds.

We have to determine the percent error.

Here the percent error is the percentage of the difference between the estimated weight and actual weight of the cat.

So the percent error is

⇒ the percentage of (15 - 12)/15 = (3/15) = 20 %

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