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3 years ago

Write the difference as a mixed number.3- 1 1/3

Mathematics

1 answer:

BigorU [14]3 years ago

6 0

Answer:

11/3 as a mixed number would be 3 2/3

Step-by-step explanation:

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Malia is planting tomato and pepper plants in her garden each tomato plant t requires 6 square feet and each pepper plant p requ

MAVERICK [17]

Answer:

6 t + 4 p ≤ 150 is the required inequality.

Step-by-step explanation:

Here, the area required for 1 tomato plant = 6 sq ft

So, the area required to plant t tomato plants

= t x ( Area required by 1 tomato plant) = t x ( 6 sq ft) = 6 t

the area required for 1 pepper plant = 4 sq ft

So, the area required to plant p pepper plants

= p x ( Area required by 1 pepper plant) = p x ( 4 sq ft) = 4 p

Now, total area of the garden = 150 Sq ft.

Also, area of p pepper pants + t tomato plants = (6 t + 4 p) sq ft

So, now according to the question:

Total area of both plants ≤ Total area of the garden

⇒ (6 t + 4 p) sq ft ≤ 150 sq ft

or, 6 t + 4 p ≤ 150 is the required inequality.

5 0

3 years ago

Type the missing numbers in this sequence:<br> -101, -105,<br> -109,<br> -117

PIT_PIT [208]

Answer:

The answer is - 113 that is the correct answer skipping in three's and the first one is - 97

6 0

3 years ago

Read 2 more answers

Prove or disprove (from i=0 to n) sum([2i]^4) <= (4n)^4. If true use induction, else give the smallest value of n that it doe

ddd [48]

Answer:

The statement is true for every n between 0 and 77 and it is false for $n\geq 78$

Step-by-step explanation:

First, observe that, for n=0 and n=1 the statement is true:

For n=0: $\sum^{n}_{i=0} (2i)^4=0 \leq 0=(4n)^4$

For n=1: $\sum^{n}_{i=0} (2i)^4=16 \leq 256=(4n)^4$

From this point we will assume that $n\geq 2$

As we can see, $\sum^{n}_{i=0} (2i)^4=\sum^{n}_{i=0} 16i^4=16\sum^{n}_{i=0} i^4$ and $(4n)^4=256n^4$ . Then,

$\sum^{n}_{i=0} (2i)^4 \leq(4n)^4 \iff \sum^{n}_{i=0} i^4 \leq 16n^4$

Now, we will use the formula for the sum of the first 4th powers:

$\sum^{n}_{i=0} i^4=\frac{n^5}{5} +\frac{n^4}{2} +\frac{n^3}{3}-\frac{n}{30}=\frac{6n^5+15n^4+10n^3-n}{30}$

Therefore:

$\sum^{n}_{i=0} i^4 \leq 16n^4 \iff \frac{6n^5+15n^4+10n^3-n}{30} \leq 16n^4 \\\\ \iff 6n^5+10n^3-n \leq 465n^4 \iff 465n^4-6n^5-10n^3+n\geq 0$

and, because $n \geq 0$ ,

$465n^4-6n^5-10n^3+n\geq 0 \iff n(465n^3-6n^4-10n^2+1)\geq 0 \\\iff 465n^3-6n^4-10n^2+1\geq 0 \iff 465n^3-6n^4-10n^2\geq -1\\\iff n^2(465n-6n^2-10)\geq -1$

Observe that, because $n \geq 2$ and is an integer,

$n^2(465n-6n^2-10)\geq -1 \iff 465n-6n^2-10 \geq 0 \iff n(465-6n) \geq 10\\\iff 465-6n \geq 0 \iff n \leq \frac{465}{6}=\frac{155}{2}=77.5$

In concusion, the statement is true if and only if n is a non negative integer such that $n\leq 77$

So, 78 is the smallest value of n that does not satisfy the inequality.

Note: If you compute $(4n)^4- \sum^{n}_{i=0} (2i)^4$ for 77 and 78 you will obtain:

$(4n)^4- \sum^{n}_{i=0} (2i)^4=53810064$

$(4n)^4- \sum^{n}_{i=0} (2i)^4=-61754992$

7 0

4 years ago

Solve the equation: 3 (x + 4) = 2x -- 8

kotegsom [21]

Answer:

x = -20

Step-by-step explanation:

Let me know if you need the work.

5 0

3 years ago

PLEASE HELP SCHOOLS ALMOST OVER AND I NEED THIS

jekas [21]

Answer: A (10)

Step-by-step explanation:

4 0

3 years ago

Read 2 more answers

Write the difference as a mixed number.3- 1 1/3​

Write the difference as a mixed number.3- 1 1/3