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4 years ago

The sum of a number w and 3 is less than or equal to ten.

Mathematics

1 answer:

Zinaida [17]4 years ago

8 0

<h2>Answer:</h2>

In this problem we must translate English words into Algebraic Expressions. So we have the following English words:

<em>The sum of a number w and 3 is less than or equal to ten</em>

<em />

So let's do that using two steps:

<h3>1. The sum of a number w and 3:</h3>

Here we have two numbers w and 3. So we must makes the sum these numbers, therefore:

$w+3$

<h3>2. The sum of a number w and 3 is less than or equal to ten:</h3>

The symbol for the English words less than or equal to is ≤ hence we can write these words as:

$\boxed{w+3\leq 10}$

As you can see, the algebraic expression is an inequality.

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Maze phrase for fractions

ICE Princess25 [194]

I dont know what your asking but i would like to have the points thanks.

6 0

3 years ago

Trapezoid DEFG is dilated by scale factor of 2\3 to form trapezoid D'E'FG. Side E'F' measures 32. What is the measure of side EF

Mamont248 [21]

Answer: 48

Step-by-step explanation:

Given

Trapezoid DEFG is dilated by a scale factor of $\frac{2}{3}$

$E'F'=32$

Suppose the length of EF is $x$

Multiply the side length of DEFG by $\frac{2}{3}$ to form E'F'

$\Rightarrow E'F'=x\times \dfrac{2}{3}\\\\\Rightarrow 32=x\times \dfrac{2}{3}\\\\\Rightarrow x=16\times 3\\\Rightarrow x=48$

$\therefore EF=48$

6 0

3 years ago

Bob bought a megahunk chocolate bar that weighed 9/10 lb he has already eaten 1/3 lb how much chocolate dose he have left

torisob [31]

Hi there! :)

<u>Answer:</u>

The answer is B) 17/30

Step-by-step explanation:

In order to find your answer you need to subtract 1/3 from 9/10:

9/10 - 1/3 = chocolate left

Since theses fractions do not have the same denominators (bottom number), the key here is to rewrite both of the fractions so that they have the same denominator:

The denominator is going to be a common multiple of "10" and "3". Ideally it's going to be the <u>least common multiple</u> of "10" and "3".

Let's start with the larger of the two denominators, which is "10". You have to go through its multiples and and see when we get to one that's divisible perfectly by 3.

So 10 is not divisible perfectly by 3, neither is 20. 30 on the other hand is divisible perfectly by 3. 30 is three times 10.

So you can rewrite both of these fractions as something over 30.

1/3 = ?/30

To get from 3 to 30, we have to multiply by 10. So if you multiply the denominator by 10, if you don't want to change the value of the fraction, you have to multiply the numerator (top number) by 10 also.

1/3 = <u>10/30</u>

Same thing with the other fraction:

9/10 = ?/30 → 3 × 10 = 30 / SO, you need to multiply the numerator by three also → 9 × 3 = 27

9/10 = <u>27/30</u>

Now that your fractions both have the same denominator, you can subtract the numerators together and put the answer on 30.

27/30 - 10/30 = ?

27 - 10 = 17 → <u>17/30</u>

Since the fraction is simplified, you are now done.

There you go! I really hope this helped, if there's anything just let me know! :)

8 0

4 years ago

The area of shaded region.

Korvikt [17]

Answer:

160π cm²

Step-by-step explanation:

The area of the shaded region is

area of outer circle - area of inner circle

A = πr₁² - πr₂²

r₁ is the radius of the outer circle = 10 + 3 = 13 cm

r₂ is the radius of the inner circle = 3 cm

A = π × 13² - π × 3²

= π(169 - 9) = 160π cm² ≈ 502.65 cm² ( to 2 dec. places )

5 0

3 years ago

Read 2 more answers

A bag contains 10 marbles,7 of which are black and 3 are red.three marbles are drawn at one after the other.find the probability

S_A_V [24]

<h3>Answer: 17/24</h3>

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Explanation:

We have these four cases or possible outcomes

Case 1) We select 0 black marbles and 3 red marbles.
Case 2) We select 1 black marble and 2 red marbles.
Case 3) We select 2 black marbles and 1 red marble.
Case 4) We select 3 black marbles and 0 red marbles.

Let's calculate the probability for case 4.

There are 7 black marbles out of 10 total. The probability of picking black is 7/10. If no replacement is made, then 6/9 is the probability of picking black again (subtract 1 from the numerator and denominator separately). Finally, 5/8 is the probability of getting black a third time.

The probability of getting 3 black marbles in a row is

(7/10)*(6/9)*(5/8) = (7*6*5)/(10*9*8) = 210/720 = 7/24.

That fraction 7/24 means that if you had 24 chances, then you expect about 7 of them will lead to getting three black marbles in a row (aka case 4). Therefore, 24-7 = 17 occurrences are expected where we get cases 1 through 3 occur in some fashion (pick one case only).

Notice how cases 1 through 3 encapsulate the phrasing "at most 2 black marbles" which is another way of saying "2 black marbles is the highest we can go".

So that's why the answer is 17/24.

8 0

3 years ago