Mya has a raised garden bed in the shape of a rectangular prism. The bed is 8 feet long, 3 2/3 feet wide, and 2 feet high. Part A: Belinda wants to make a raised garden bed that covers the same area as Mya’s, but the space she has is only 3 feet wide. How long should her garden bed be? Part B: Find the volume of Mya’s gardening bed. Suppose Belinda’s garden bed is the same height as Mya’s. Will Belinda’s bed have the same volume? Explain. Part C: A small bag of soil contains 2 cubic feet. How many bags of soil should Mya buy if she wants to fill her garden bed completely? Show your work. Part D: Belinda already has 22 bags of soil. Use your answer to Part C to find the depth to which she can fill her garden bed

The common difference of the arithmetic sequence is:

                                       4

We kn ow that if the first term of an arithmetic sequence is a and d is the common difference of the sequence then the nth term of the sequence is given by the formula:

[tex]a_n=a+(n-1)d[/tex]

Here we are given:

[tex]a=-3[/tex]

and

[tex]a_15=53\\\\i.e.\\\\a+(15-1)d=53\\\\i.e.\\\\a+14d=53[/tex]

Now using the value of a we have:

[tex]-3+14d=53\\\\i.e.\\\\14d=56\\\\i.e.\\\\d=4[/tex]

To reach an 8-foot ceiling, you would need to stack approximately 1600 pennies. This is calculated by dividing the ceiling height in inches (96 inches) by the thickness of a penny, which is around 0.06 inches, and rounding to the nearest whole number.

To solve this problem, we need to understand that a penny is approximately 0.0598 inches thick. Since there are 12 inches in a foot, an 8-foot ceiling would be 96 inches tall. Therefore, to stack pennies from the floor to an 8-foot ceiling, you would divide 96 (the total inches of the ceiling height) by 0.0598 (the thickness of one penny).

Let's round 0.0598 inches to 0.06 inches for ease of computation. When we divide 96 by 0.06, we get approximately 1600 pennies. So, it would take roughly 1600 pennies to stack from the floor to an 8-foot ceiling.

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Answer:

First Part: 0.9769

Second Part: Some Americans may have traveled by other means

Step-by-step explanation:

First Part: You add 9.6 to 88.09 and put it in decimal form.

Second Part: Some Americans may have traveled by other means.

1 cup of fruit juice is equivalent to 1 cup of fresh fruit.​

Option B is the correct answer.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

1 cup of fresh juice.

Fresh juice and 1 cup of fresh fruit are the same.

So,

Fresh juice = 1 cup

Thus,

1 cup of fruit juice is equivalent to 1 cup of fresh fruit.​

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The minimum number of dots and/or dashes needed to represent any letter in the English alphabet in Morse code is one. The letters 'E' and 'T' each use one symbol, dot and dash respectively.

In International Morse code, each letter in the English alphabet is represented by a unique combination of dots and dashes. In regards to your question - the minimum number of dots and/or dashes needed to represent any letter in the English alphabet is one. The English letters 'E' and 'T' are represented by the single symbols "." (dot for 'E') and "-" (dash for 'T') respectively. Hence, this is the minimum for symbolizing any letter.

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To raise the average height by 1 inch, the 22nd person would have to be 88 inches tall.

To find how tall the 22nd person would have to be in order to raise the average height by 1 inch, we can use the concept of average. Currently, there are 21 people with an average height of 5 feet 6 inches. This means that the total height of all 21 people combined is 5 feet 6 inches multiplied by 21.

If we want to raise the average height by 1 inch, we need to add a certain amount of height to the total height of all the people in the room. Let's call this additional height 'x'. So the new total height would be the previous total height plus 'x'.

Since the total number of people in the room will become 22, the new average height will be the new total height divided by 22. We can set up an equation to solve for 'x':

5 feet 6 inches multiplied by 21 plus 'x' divided by 22 equals 5 feet 6 inches plus 1 inch.

To solve this equation, we can first convert the heights to inches: 5 feet 6 inches is equivalent to 66 inches. Now we can solve the equation:

66 multiplied by 21 plus 'x' divided by 22 equals 67.

Now we can simplify and solve for 'x':

1386 plus 'x' divided by 22 equals 67.

1386 plus 'x' equals 67 multiplied by 22.

1386 plus 'x' equals 1474.

Subtracting 1386 from both sides, we get 'x' equals 1474 minus 1386, which is 88 inches. Therefore, the 22nd person would have to be 88 inches tall to raise the average height by 1 inch.

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Answer: 1554

It is correct from the math answer keys

Tonya run 1,554 meters.

"Distance is the total path travelled by an object without considering the direction. "

Value used

1kilometer = 1000meters

According to the question,

Let x represents distance run by Tonya

Natasha ran = 3.1 kilometers

                    = 3100 meters

Therefore,

    x = (3100 / 2) + 4

⇒  x = 1554 meters  

Hence, Tonya run 1,554 meters.

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The angle θ = 133π/72 radians is equivalent to  332.5° degrees.

Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.

To convert radians to degrees, use the following formula:

Angle in degrees = angle in radians × 180°/π

Here's how to apply this formula to the given angle:

θ= 133π/72 radians

θ in degrees = (133π/72) × 180°/π

θ in degrees = (133/72) × 180

θ in degrees = 332.5°

Therefore, the angle θ = 133π/72 radians is equivalent to  332.5° degrees.

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Final answer:

Lucy will need to ride around the block 3 times today to cover 3/4 of a mile, as each lap around the block is 0.25 miles long.

Explanation:

Lucy rode her bike around the block and covered a total distance of 1 mile by doing so 4 times. Each lap around the block is therefore 0.25 miles long (1 mile ÷ 4 laps = 0.25 miles per lap). To cover 3/4 of a mile, Lucy needs to complete three laps (3/4 of a mile ÷ 0.25 miles per lap = 3 laps). This is because 3/4 divided by 1/4 (which is the distance of one lap) equals 3. Hence, Lucy will need to ride around the block 3 times today to cover 3/4 of a mile.

Answer:

the answer is -1/4

Step-by-step explanation:

Final answer:

The actual root of the polynomial f(x) = 60x²– 57x – 18 among the given options is -6/5.

Explanation:

According to the Rational Root Theorem, possible roots of the polynomial equation f(x) = 60x² − 57x − 18 are the factors of the constant term (−18) divided by the factors of the leading coefficient (60). The roots could be ±1/60, ±1/30, ±1/20, ±1/15, ±1/12, ±1/10, ±1/6, ±1/5, ±1/4, ±1/3, ±1/2, ±1, ±2/5, ±3/5, ±6/5, ±9/5, ±18/5, ±2, ±3, ±6, ±9, ±18.

To determine which of the given options are actual roots of the polynomial, we substitute each value into the polynomial and check if it returns a value of zero:

Substituting x = 3 into f(x) gives 60(3)² − 57(3) − 18 = 540 − 171 − 18 = 351, which is not zero.

Substituting x = 6 into f(x) gives 60(6)² − 57(6) − 18 = 2160 − 342 − 18 = 1800, which is not zero.

Substituting x = −1/4 into f(x) gives 60(−1/4)² − 57(−1/4) − 18 = 15 − −14.25 − 18 = 11.25, which is not zero.

Substituting x = −6/5 into f(x) gives 60(−6/5)² − 57(−6/5) − 18 = 86.4 − −68.4 − 18 = 0, which is zero. Therefore, −6/5 is an actual root of the equation.

Thus, the actual root among the given options is −6/5.

180 - 90 -18 = 72

Answer is D 72 degrees

The required solution is 8.

It is required to find the least common denominator.

The smallest common multiple of two or more numbers and the common multiple of lowest degree of two or more polynomials.

Given:

Multiply 4 times 2 to get 8, then multiply 1 times 4 for the numerator of the first fraction .

1/4=1*2/4*2=4/8

5/8=5*1/8*1=5/8

The least common denominator of 1/4 and 5/8 is 8.

Therefore, the required solution is 8.

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Final answer:

The flabby expression is found in the sentence 'In the future, we should be more careful about scheduling calls,' which can be more concisely stated as 'In the future, we should schedule calls more carefully.'

Explanation:

The sentence that contains a flabby expression is: "In the future, we should be more careful about scheduling calls."

Flabby expressions are phrases or sentences that are wordy and can be expressed more concisely without losing their meaning. The sentence could be more directly stated as "In the future, we should schedule calls more carefully." By removing unnecessary words, the sentence becomes clearer and more to the point. Flabby expressions are usually considered poor writing style because they can make sentences needlessly long and obscure the main point.

The 24 feet high up the ladder will reach to the wall if the ladder height is 25 feet and is placed 7 feet from the wall.

Trigonometry is a branch of mathematics that deals with the relationship between sides and angles of a right-angle triangle.

We have:

Length of the ladder = 7 feet

The distance between the wall bottom end to ladder bottom end = 7 feet

As we can see in the diagram the ladder and wall making a right angle triangle ABC in which

AC = 25 feet

BC = 7 feet

Let's suppose the length of the wall is h feet

AB = h feet

From the Pythagoras theorem:

AC² = AB² + BC²

Put the values of AC and BC, we get

25² = h² + 7²

625 = h² + 49

625 - 49 =  h²    (subtract by 49 on both sides)

576 = h²

h = 24 feet         (taking square root on both sides)

Thus, the 24 feet high up the ladder will reach to the wall.

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