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1 year ago

find the length of the radius if the circumference is 13.2 round to one decimal place. use 3.14 for π

Mathematics

1 answer:

Helen [10]1 year ago

6 0

Given

$\begin{gathered} \text{Circumference of Circle = 13.2 unit} \\ \pi\text{ = 3.14} \end{gathered}$

Required :

$\text{length of radius (r) = ?}$

The formula for the circumference of a circle:

$\text{Circumference of circle = 2}\pi r$

When we substitute and simplify:

$\begin{gathered} 13.2\text{ = 2 }\times\text{ }\pi\text{ }\times\text{ r} \\ \text{making r the subject of formula} \\ r\text{ = }\frac{13.2}{2\text{ }\times\text{ 3.14}} \\ r\text{ = 2.1019} \\ \approx\text{ 2.1 unit (1.d.p)} \end{gathered}$

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Several years ago, 39% of parents who had children in grades K-12 were satisfied with the quality of education the students r

BaLLatris [955]

<h2>Answer with explanation:</h2>

Let p be the population proportion of parents who had children in grades K-12 were satisfied with the quality of education the students receive.

Given : Several years ago, 39% of parents who had children in grades K-12 were satisfied with the quality of education the students receive.

Set hypothesis to test :

$H_0: p=0.39\\\\H_a :p\neq0.39$

Sample size : n= 1055

Sample proportion : $\hat{p}=\dfrac{466}{1055}=0.441706161137\approx0.44$

Critical value for 95% confidence : $z_{\alpha/2}=1.96$

Confidence interval : $\hat{p}\pm z_{\alpha/2}\sqrt{\dfrac{p(1-p)}{n}}$

$0.44\pm (1.96)\sqrt{\dfrac{0.39(1-0.39)}{1055}}\\\\0.44\pm0.0299536805135\\\\0.44\pm0.03\\\\=(0.44-0.03, 0.44+0.03)\\\\=(0.41,\ 0.47)$

Since , Confidence interval does not contain 0.39.

It means we reject the null hypothesis.

We conclude that 95% confidence interval represents evidence that parents' attitudes toward the quality of education have changed.

8 0

3 years ago

What is x in 2x − 3 + 4x = 21

Serggg [28]

Answer: x = 4

Step-by-step explanation:

2x - 3 + 4x = 21

6x - 3 = 21

6x - 3 (+3) = 21 (+3)

6x = 24

24/6

x = 4

7 0

2 years ago

Read 2 more answers

Help me put this in order please help thanks

KATRIN_1 [288]

1. 8
2. 15
3. 2
4. 1/2
5. 3
those are the answers in order, hope this helps!

5 0

3 years ago

Please help me there are 2 answers Thank you

yaroslaw [1]

Answer:

m = 7, m = -15

Step-by-step explanation:

The absolute value makes it so we can make two equations:

m + 4 = 11 and m + 4 = -11.

solve the equations:

m + 4 = 11

m = 7

and

m + 4 = -11

m = -15.

6 0

3 years ago

2ᵃ = 5ᵇ = 10ⁿ.<br> Show that n = <img src="https://tex.z-dn.net/?f=%20%5Cfrac%7Bab%7D%7Ba%20%2B%20b%7D%20" id="TexFormula1" titl

11Alexandr11 [23.1K]

There are two ways you can go about this: I'll explain both ways.
<span>
</span><span>Solution 1: Using logarithmic properties
</span>The first way is to use logarithmic properties.

We can take the natural logarithm to all three terms to utilise our exponents.

Hence, ln2ᵃ = ln5ᵇ = ln10ⁿ becomes:
aln2 = bln5 = nln10.

What's so neat about ln10 is that it's ln(5·2).
Using our logarithmic rule (log(ab) = log(a) + log(b),
we can rewrite it as aln2 = bln5 = n(ln2 + ln5)

Since it's equal (given to us), we can let it all equal to another variable "c".

So, c = aln2 = bln5 = n(ln2 + ln5) and the reason why we do this, is so that we may find ln2 and ln5 respectively.

c = aln2; ln2 = $\frac{c}{a}$
c = bln5; ln5 = $\frac{c}{b}$

Hence, c = n(ln2 + ln5) = n( $\frac{c}{a}$ + $\frac{c}{b}$ )
Factorise c outside on the right hand side.

c = cn( $\frac{1}{a}$ + $\frac{1}{b}$ )
1 = n( $\frac{1}{a}$ + $\frac{1}{b}$ )
$\frac{1}{n}$ = $\frac{1}{a}$ + $\frac{1}{b}$

$\frac{1}{n}$ = $\frac{a + b}{ab}$
and thus, n = $\frac{ab}{a + b}$

<span>Solution 2: Using exponent rules
</span>In this solution, we'll be taking advantage of exponents.

So, let c = 2ᵃ = 5ᵇ = 10ⁿ
Since c = 2ᵃ, 2 = $\sqrt[a]{c}$ = $c^{\frac{1}{a}}$

Then, 5 = $c^{\frac{1}{b}}$
and 10 = $c^{\frac{1}{n}}$

But, 10 = 5·2, so 10 = $c^{\frac{1}{b}}$ · $c^{\frac{1}{a}}$
∴ $c^{\frac{1}{n}}$ = $c^{\frac{1}{b}}$ · $c^{\frac{1}{a}}$

$\frac{1}{n}$ = $\frac{1}{a}$ + $\frac{1}{b}$
and n = $\frac{ab}{a + b}$

4 0

3 years ago