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3 years ago

What percent of 29.5 is 10.03

1 answer:

7 0

So if we take 29.5 to be the 100%, what is 10.03 in percentage?

$\bf \begin{array}{ccll}
amount&\%\\
\text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\
29.5&100\\
10.03&p
\end{array}\implies \cfrac{29.5}{10.03}=\cfrac{100}{p}\implies p=\cfrac{10.03\cdot 100}{29.5}$

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1) Given: circle k(O), ED= diameter ,m∠OEF=32°, m(arc)EF=(2x+10)° Find: x

qaws [65]

1. The major arc ED has measure 180 degrees since ED is a diameter of the circle. The measure of arc EF is $(2x+10)^\circ$ , so the measure of arc DF is

$m\widehat{DF}=360^\circ-180^\circ-(2x+10)^\circ=(170-2x)^\circ$

The inscribed angle theorem tells us that the central angle subtended by arc DF, $\angle DOF$ , has a measure of twice the measure of the inscribed angle DEF (which is the same angle OEF) so

$m\angle DOF=2m\angle OEF=64^\circ$

so the measure of arc DF is also 64 degrees. So we have

$170-2x=64\implies106=2x\implies\boxed{x=53}$

###

2. Arc FE and angle EOF have the same measure, 56 degrees. By the inscribed angle theorem,

$m\angle EOF=2m\angle EDF\implies56^\circ=2m\angle EDF\implies m\angle EDF=28^\circ$

Triangle DEF is isosceles because FD and ED have the same length, so angles EFD and DEF are congruent. Also, the sum of the interior angles of any triangle is 180 degrees. It follows that

$m\angle EFD+m\angle EDF+m\angle DEF=180^\circ\implies\boxed{m\angle EFD=76^\circ}$

Triangle OFE is also isosceles, so angles EFO and FEO are congruent. So we have

$m\angle EFO+m\angle FEO+m\angle EOF=180^\circ\implies\boxed{m\angle EFO=62^\circ}$

7 0

3 years ago

Belle borrowed $18.275 to buy a new car. The interest rate she agreed to pay is 5%. If she takes 5 years to pay back the loan, h

mamaluj [8]

Answer:

$22843.75

Step-by-step explanation:

I'm assuming that $18.275 is $18,275

First, converting R percent to r a decimal

r = R/100 = 5%/100 = 0.05 per year,

then, solving our equation

I = 18275 × 0.05 × 5 = 4568.75

I = $ 4,568.75

The simple interest accumulated

on a principal of $ 18,275.00

at a rate of 5% per year

for 5 years is $ 4,568.75.

4 0

3 years ago

Read 2 more answers

Samir is an expert marksman. When he takes aim at a particular target on the shooting range, there is a 0.950.950, point, 95 pro

Vinvika [58]

Answer:

40.1% probability that he will miss at least one of them

Step-by-step explanation:

For each target, there are only two possible outcomes. Either he hits it, or he does not. The probability of hitting a target is independent of other targets. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

0.95 probaiblity of hitting a target

This means that $p = 0.95$

10 targets

This means that $n = 10$

What is the probability that he will miss at least one of them?

Either he hits all the targets, or he misses at least one of them. The sum of the probabilities of these events is decimal 1. So

$P(X = 10) + P(X < 10) = 1$

We want P(X < 10). So

$P(X < 10) = 1 - P(X = 10)$

In which

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 10) = C_{10,10}.(0.95)^{10}.(0.05)^{0} = 0.5987$

$P(X < 10) = 1 - P(X = 10) = 1 - 0.5987 = 0.401$

40.1% probability that he will miss at least one of them

7 0

3 years ago

Applying Rate of change

olga nikolaevna [1]

$\bf \begin{array}{ccllll}
minutes(x)&Mbs\ left(y)\\
-----&-----\\
2&38.4\\
8&9.6
\end{array}\\\\
-----------------------------\\\\
slope = {{ m}}= \cfrac{rise}{run} \implies 
\cfrac{{{ y_2}}-{{ y_1}}}{{{ x_2}}-{{ x_1}}}\impliedby \textit{rate of change}
\\\\\\
m=\cfrac{9.6-38.4}{8-2}\implies m=-\cfrac{24}{5}\iff m= -4.8$

now, notice, the rate of change for downloading is negative, because, "y" is decreasing, namely the Mbs to be downloaded, are less and less and less as the minutes go by, because the file is almost fully downloaded

so is -4.8

now... at 8minutes, there are 9.6Mbs to download
bear in mind that 9.6 is just 4.8 * 2
that simply means, another minute, another 4.8 Mbs, and another minute and another 4.8 Mbs and the file is done

so, the file downloaded really in 10minutes

now, we know the rate is -4.8 or -24/5, let us nevermind the sign for now

since we know the file is downloading at 24Mbs in 5minutes, a rate of 24/5

how much is it for 10 minutes? well 10 is really just 5 * 2

so if it downloads at a rate of 24Mbs per 5mins, in 10 minutes it downloaded 24*2 or 48Mbs

7 0

3 years ago

Do you know the answer to this question

kozerog [31]

The correct answer is: [C]: " f(x) = log₃ (x - 3) " .
_______________________________________________________

3 0

4 years ago