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Eva8 [605]
3 years ago
14

Last autumn, julia noticed something interesting as she blew up spherical balloons for harris's birthday party. she calculated t

he volume of a balloon with a radius of 4 cm and then the volume of a balloon with a radius of 8cm. did she discover that the volume is twice as big when the radius is doubled?
Mathematics
2 answers:
zmey [24]3 years ago
8 0

She would not find out that the volume is twice as big when the radius is doubled.

Vikki [24]3 years ago
4 0
To find whether the volume would be doubled when the radius is,we can find the volume of the two balloons.

The formula of a sphere is:
\frac{4}{3} \pi \: {r}^{3}
Let's take 丌 as 3.14

The volume of the balloon with 4cm radius:
\frac{4}{3}(3.14)  \times  {4}^{3}  \\  = 4.18667 \times 64 \\  = 267.94688

The volume of the balloon with 8cm radius:
\frac{4}{3}(3.14)  \times  {8}^{3}  \\  = 4.18667 \times 512 \\  = 2143.57504
As we can see,
267.94668 × 2 = 535.89 ≠2145.56

Thus,she wouldn't discover that the volume is twice as big when the radius is doubled.

Hope it helps!
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densk [106]

9514 1404 393

Answer:

  (a)  15/17

Step-by-step explanation:

The mnemonic SOH CAH TOA reminds you of the cosine relation:

  Cos = Adjacent/Hypotenuse

  cos(P) = PQ/PR

  cos(P) = 15/17

8 0
3 years ago
5. A researcher creates a scatter plot that displays the relationship between the number of years in business, , and the percent
Black_prince [1.1K]

Based on the information given, it should be noted that the residual for the two points will be 0.087 and -0.033 respectively.

<h3>How to find the residual.</h3>

From the complete information, the predicted value for the point (3, 0.42) will be:

= (0.091 × 3) + 0.060

= 0.0273 + 0.060

= 0.333

Therefore, the residual will be:

= 0.42 - 0.333 = 0.087

The predicted value for the point (3, 0.3) will be:

y = 0.091x + 0.060.

= (0.091 × 3) + 0.060.

= 0.333

Therefore, the residual will be:

= 0.3 - 0.333 = -0.033

Therefore, the residual for the two points will be 0.087 and -0.333 respectively.

Learn more about residuals on:

brainly.com/question/26255019

8 0
2 years ago
One condition for performing a hypothesis test is that the observations are independent. Marta is going to take a sample from a
AleksandrR [38]

Answer:

The correct answer to the following question will be "60 students".

Step-by-step explanation:

Marta will be taking a sampling frame from some kind of 600 student group.

Mean,

N = 60  

Although the sampling method could perhaps consist of the following components 10% of the population,

⇒  600\times 10 \ percent

⇒  60

In order to view these findings as autonomous, 60 students would then have to analyze Marta lacking replacements.

6 0
3 years ago
Help please solve<br> <img src="https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7B6x%5E5%2B11x%5E4-11x-6%7D%7B%282x%5E2-3x%2B1
Shkiper50 [21]

Answer:

\displaystyle  -\frac{1}{2} \leq x < 1

Step-by-step explanation:

<u>Inequalities</u>

They relate one or more variables with comparison operators other than the equality.

We must find the set of values for x that make the expression stand

\displaystyle \frac{6x^5+11x^4-11x-6}{(2x^2-3x+1)^2} \leq 0

The roots of numerator can be found by trial and error. The only real roots are x=1 and x=-1/2.

The roots of the denominator are easy to find since it's a second-degree polynomial: x=1, x=1/2. Hence, the given expression can be factored as

\displaystyle \frac{(x-1)(x+\frac{1}{2})(6x^3+14x^2+10x+12)}{(x-1)^2(x-\frac{1}{2})^2} \leq 0

Simplifying by x-1 and taking x=1 out of the possible solutions:

\displaystyle \frac{(x+\frac{1}{2})(6x^3+14x^2+10x+12)}{(x-1)(x-\frac{1}{2})^2} \leq 0

We need to find the values of x that make the expression less or equal to 0, i.e. negative or zero. The expressions

(6x^3+14x^2+10x+12)

is always positive and doesn't affect the result. It can be neglected. The expression

(x-\frac{1}{2})^2

can be 0 or positive. We exclude the value x=1/2 from the solution and neglect the expression as being always positive. This leads to analyze the remaining expression

\displaystyle \frac{(x+\frac{1}{2})}{(x-1)} \leq 0

For the expression to be negative, both signs must be opposite, that is

(x+\frac{1}{2})\geq 0, (x-1)

Or

(x+\frac{1}{2})\leq 0, (x-1)>0

Note we have excluded x=1 from the solution.

The first inequality gives us the solution

\displaystyle  -\frac{1}{2} \leq x < 1

The second inequality gives no solution because it's impossible to comply with both conditions.

Thus, the solution for the given inequality is

\boxed{\displaystyle  -\frac{1}{2} \leq x < 1 }

7 0
3 years ago
A bakery uses 10 1/5 ounces of icing for every 1/4 of a cake. What is the unit rate in ounces of icing per cake
Marrrta [24]

Answer:   40\dfrac{4}{5}\text{ ounces}

Step-by-step explanation:

Given : The amount of icing used for every \dfrac{1}{4} of a cake = 10\dfrac{1}{5}\text{ ounces}

=\dfrac{51}{5}\text{ ounces}

To find the unit rate in ounces of icing per cake, we need to divide \dfrac{51}{5} by  \dfrac{1}{4} , we get

The unit rate in ounces of icing per cake = \dfrac{51}{5}\div\dfrac{1}{4}

\dfrac{51}{5}\times4=\dfrac{204}{5}=40\dfrac{4}{5}

Hence, the unit rate in ounces of icing per cake = 40\dfrac{4}{5}\text{ ounces}

4 0
3 years ago
Read 2 more answers
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