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il63 [147K]
3 years ago
13

Kayla is blowing up balloons for her sister’s birthday party. She tries to blow up each balloon to a maximum diameter of 5 inche

s. At that diameter, the volume of each balloon is about 26 cubic inches. Find the independent and dependent variable in words for examples like Height in inches or something similar.
Mathematics
1 answer:
ale4655 [162]3 years ago
8 0

Answer: Independent variable = diameter of balloon

Dependent variable = Volume

Step-by-step explanation:

Definitions:

  • Independent variable : Variable that can be manipulated to see the effect in the response variable in a study.
  • Dependent variable : Response variable which depends on the independent variable.

Here, diameter of balloon = Independent variable

and Volume = Dependent variable

Because volume can change with the change of diameter of the balloon.

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I had 8 tampons this morning but 2/3 of the girls in my class got their period and now I’m out of tampons
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4 years ago
In the expansion of (1/ax +2ax^2)^5 the coefficient of x is five. Find the value of the constant a.
DedPeter [7]

Answer:

80x⁴

Step-by-step explanation:

(\frac{1}{ax} + 2ax^2)^5 = 5C_0(\frac{1}{ax})^5(2ax^2)^0 + 5C_1(\frac{1}{ax})^4(2ax^2)^1 + 5C_2(\frac{1}{ax})^3 (2ax^2)^2

                           + 5C_3 (\frac{1}{ax})^2(2ax^2)^3 + 5C_4(\frac{1}{ax})^1(2ax^2)^4 + 5C_5(\frac{1}{ax})^0(2ax^2)^5

5C_0(\frac{1}{ax})^5(2ax^2)^0  =1 \times (\frac{1}{ax})^5 \times 1 = \frac{1}{a^5x^5}\\\\5C_1(\frac{1}{ax})^4(2ax^2)^1  = 5 \times (\frac{1}{ax})^4 \times (2ax^2)^1 = 10 ax^2 \times \frac{1}{a^4x^4} = \frac{10}{a^3x^2}\\\\5C_2 (\frac{1}{ax})^3 (2ax^2)^2= 10 \times (\frac{1}{ax})^3 \times (2ax^2)^2 = 10 \times \frac{1}{a^3x^3} \times 4a^2x^4 = \frac{40x}{a}\\\\5C_3 (\frac{1}{ax})^2 (2ax^2)^3 = 10 \times (\frac{1}{ax})^2 \times (2ax^2)^3 = 10 \times \frac{1}{a^2x^2} \times 8a^3 x^6 = 80ax^4\\\\

5C_4(\frac{1}{ax})^1(2ax^2)^4 = 5 \times \frac{1}{ax} \times 16a^4x^8 = 80a^3x^7\\\\5C_5(\frac{1}{ax})^0(2ax^2)^5 = 1 \times 1 \times 32a^5x^{10}

The fourth term of the expansion has the constant a,

the coefficient of a is 80x⁴

6 0
3 years ago
A karaoke marked at ₽3,750 was sold for ₽3,225. What was the rate of discount?
ikadub [295]

Answer:

Step-by-step explanation:

14%  increase

4 0
3 years ago
The poll found that 38% of a random sample of 1012 American adults said they believe in ghosts. What is the lower bound for a 90
Brrunno [24]

Answer:

The lower bound for a 90% confidence interval for the percentage of all American adults who believe in ghosts is 0.3549

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of \pi, and a confidence level of 1-\alpha, we have the following confidence interval of proportions.

\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}

In which

z is the zscore that has a pvalue of 1 - \frac{\alpha}{2}.

For this problem, we have that:

n = 1012, \pi = 0.38

90% confidence level

So \alpha = 0.1, z is the value of Z that has a pvalue of 1 - \frac{0.1}{2} = 0.95, so Z = 1.645.

The lower limit of this interval is:

\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.38 - 1.645\sqrt{\frac{0.38*0.62}{1012}} = 0.3549

The lower bound for a 90% confidence interval for the percentage of all American adults who believe in ghosts is 0.3549

6 0
4 years ago
What is the stem-and-leaf plot for
Verdich [7]

The stem-and-leaf plot for 29,22,21,6,13,6,17,29,26,9,16,10,25,3,2,23,13,10,7,16,29,30,4,11,7,28,27,22,10 is shown in the image attached below (see attachment).

<h3>What is a Stem-and-leaf Plot?</h3>

A stem-and-leaf plot is a table which is used to display a set of data in such a way that, on the left we have the "stem" which displays the first digit or digits of a data value.

On the right, we have the 'leaf' which displays the last digit of the data value.

For example, if we are to represent "25" and "26" on a stem-and-leaf plot, we would have: 2 | 5, 6.

Therefore, the stem-and-leaf plot for 29,22,21,6,13,6,17,29,26,9,16,10,25,3,2,23,13,10,7,16,29,30,4,11,7,28,27,22,10 is shown in the image attached below (see attachment).

Learn more about the stem-and-leaf plot on:

brainly.com/question/8649311

8 0
2 years ago
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