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2 years ago

Which shapes have the same volume as the given rectangular prism?base area = 50 cm^2

Mathematics

1 answer:

icang [17]2 years ago

5 0

Answer:The first one

Step-by-step explanation:

V rectangular prism = Area of the base *5

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You mix soda water, fruit punch concentrate, and ginger ale in the ratio of 1 : 2 : 5 to make fruit punch. How many pints of eac

EastWind [94]

So the ratio is 1 to 2 to 5
so basically 1 unit of soda water to 2 units of fruit punch to 5 units of ginger ale

total is 1+2+5=8 units

so 4 gallons=8 units
divide by 8
1/2 gallon=1 unit

soda water=1 unit=1/2 gallon
fruit punch=2 unit=1/2 times 2=1 gallon
ginger ale=5 unit=5 times 1/2=5/2=2 and 1/2 gallon

soda water=1/2 gallon
fruit punch concentrate=1 gallon
ginger ale=5/2 gallon or 2 and 1/2 gallon

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2 years ago

If p is a polynomial show that lim x→ap(x)=p(a

Lostsunrise [7]

Let p(x) be a polynomial, and suppose that a is any real number. Prove that

lim x→a p(x) = p(a) .

Solution. Notice that

2(−1)4 − 3(−1)3 − 4(−1)2 − (−1) − 1 = 1 .

So x − (−1) must divide 2x^4 − 3x^3 − 4x^2 − x − 2. Do polynomial long division to get 2x^4 − 3x^3 − 4x^2 – x – 2 / (x − (−1)) = 2x^3 − 5x^2 + x – 2.

Let ε > 0. Set δ = min{ ε/40 , 1}. Let x be a real number such that 0 < |x−(−1)| < δ. Then |x + 1| < ε/40 . Also, |x + 1| < 1, so −2 < x < 0. In particular |x| < 2. So

|2x^3 − 5x^2 + x − 2| ≤ |2x^3 | + | − 5x^2 | + |x| + | − 2|

= 2|x|^3 + 5|x|^2 + |x| + 2

< 2(2)^3 + 5(2)^2 + (2) + 2

= 40

Thus, |2x^4 − 3x^3 − 4x^2 − x − 2| = |x + 1| · |2x^3 − 5x^2 + x − 2| < ε/40 · 40 = ε.

3 0

2 years ago

Mikela claims that the sum of any two numbers is greater than the larger of the two numbers. Jim claims that the sum of any two

qaws [65]

<u>ANSWER: </u>

The statement of Jim is correct

<u>SOLUTION: </u>

Given statements are

Mikela claims that sum of any two numbers is greater than the larger of the two numbers.

Jim claims that the sum of any two natural numbers is greater than the larger of the two numbers.

Let a,b be the two numbers and a is the greatest of a and b

According to the mikela statement = a + b > a

b > a – a

b > 0

Here, we got an condition that b > 0, but it may not be true always.

Above condition fails when b is either 0 or negative number.

Jim - sum of any two natural numbers is greater than the larger of the two numbers.

Let a,b be the two natural numbers. And a is the greatest of a and b

According to the jim statement = a + b > a

b > a – a

b > 0

Here, we got an condition that b > 0,

And this statement will always be true because b is an natural number, so it will be greater than 0.

Hence jim’s statement is true.

8 0

2 years ago

A professor is examining a new strain of bacteria. The amount of bacteria can be modeled by function s(n) = 20 · bn, where n is

user100 [1]

For this case we have a function of the form:
$y = A * (b) ^ n
$
Where,
A: initial amount
b: growth rate (if b> 1)
n: time in hours
Substituting values we have:
$s (n) = 20 * b ^ n
$
We have then that the initial amount is:
$A = 20
$
If b = 1.85 then the growth percentage is:
$(1.85-1) * (100) = 85%
$
Answer:
here were initially 20 bacteria.
The hourly percent growth rate of the bacteria would be 85%

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2 years ago

On your last credit card statement, you had a previous balance of $98.14, payments of $10, a periodic rate of 1.34 percent, and

Valentin [98]

The correct answer is D

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2 years ago

Which shapes have the same volume as the given rectangular prism?base area = 50 cm^2​

Which shapes have the same volume as the given rectangular prism?base area = 50 cm^2