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2 years ago

If I have a candy bar divided into 6 equal parts, and I eat 2 of the parts, what fraction of the candy bar did I eat?

Mathematics

2 answers:

Afina-wow [57]2 years ago

6 0

Answer:

2/6 or 1/3

Step-by-step explanation:

Nothing it is just basic mathematics

SVEN [57.7K]2 years ago

3 0

Eaten part=2
Total parts=6

Fraction form

$\\ \tt\rightarrowtail \dfrac{2}{6}$

$\\ \tt\rightarrowtail \dfrac{1}{3}$

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Mel Needs to park his car for eight hours. Spikes parking place charges five dollars per hour for the first three hours and thre

Dima020 [189]

Answer:

Spike's Parking
$5 less

Step-by-step explanation:

After 3 hours, Spike charges 6 dollars per hour. For 3 hours, the charge is only $5×3 = $15 (which is $3 less than $6×3). So the rate after 3 hours can be modeled by ...

s(h) = 6h -3

For 8 hours, s(8) = 6·8 -3 = 45 . . . . dollars

After 4 hours, Main Deck charges 8 dollars per hour. For 4 hours, the charge is only $18 (which is $14 less than $8×4). So the rate after 4 hours can be modeled by ...

m(h) = 8h -14

For 8 hours, m(8) = 8·8 -14 = 50 . . . . dollars

For 8 hours, the $45 charge at Spike's is $5 less than the $50 charge at Main Deck.

6 0

2 years ago

Assume that adults have IQ scores that are normally distributed with a mean of 101.3 and a standard deviation 19.9. Find the fir

AnnyKZ [126]

Answer:

87.9

Step-by-step explanation:

Use a calculator or table to find the z-score that corresponds to 25%.

P(Z < z) = 0.25

z = -0.675

Now find the value that corresponds to that z score.

z = (x − μ) / σ

-0.675 = (x − 101.3) / 19.9

x = 87.9

4 0

2 years ago

the ratio of the sides of a certain triangle is 2:7:8 if the longest side of the triangle is 40cm how long are the other two sid

Zigmanuir [339]

The length of the other two sides is 10 and 35 respectively.

<h3>What is a ratio?</h3>

A ratio is a quantitative relation showing the comparison between two or more numbers. It can also be written in the fractional form where the first part is the numerator and the second part is called the denominator.

From the given information:

The sides of the triangle = 2:7:8
The total sides of the triangle = 2+7+8 = 17

We are being told that the longest side is the triangle is equal to 40.

i.e.

$\mathbf{\to\dfrac{8}{17}\times x = 40}$

$\mathbf{x = 40 \div \dfrac{8}{17}}$

$\mathbf{x = 40 \times \dfrac{17}{8}}$

x = 85

Now for the other two sides 2 and 7, their length is as follows.

$\mathbf{\dfrac{2}{17}\times 85 = 10}$

$\mathbf{\dfrac{7}{17}\times 85 = 35}$

Therefore, we can conclude that the length of the other two sides is 10 and 35 respectively.

Learn more about ratios here:

brainly.com/question/2328454

3 0

1 year ago

Solve only if you know the solution and show work.

SashulF [63]

$\displaystyle\int\frac{\cos x+3\sin x+7}{\cos x+\sin x+1}\,\mathrm dx=\int\mathrm dx+2\int\frac{\sin x+3}{\cos x+\sin x+1}\,\mathrm dx$

For the remaining integral, let $t=\tan\dfrac x2$ . Then

$\sin x=\sin\left(2\times\dfrac x2\right)=2\sin\dfrac x2\cos\dfrac x2=\dfrac{2t}{1+t^2}$
$\cos x=\cos\left(2\times\dfrac x2\right)=\cos^2\dfrac x2-\sin^2\dfrac x2=\dfrac{1-t^2}{1+t^2}$

and

$\mathrm dt=\dfrac12\sec^2\dfrac x2\,\mathrm dx\implies \mathrm dx=2\cos^2\dfrac x2\,\mathrm dt=\dfrac2{1+t^2}\,\mathrm dt$

Now the integral is

$\displaystyle\int\mathrm dx+2\int\frac{\dfrac{2t}{1+t^2}+3}{\dfrac{1-t^2}{1+t^2}+\dfrac{2t}{1+t^2}+1}\times\frac2{1+t^2}\,\mathrm dt$

The first integral is trivial, so we'll focus on the latter one. You have

$\displaystyle2\int\frac{2t+3(1+t^2)}{(1-t^2+2t+1+t^2)(1+t^2)}\,\mathrm dt=2\int\frac{3t^2+2t+3}{(1+t)(1+t^2)}\,\mathrm dt$

Decompose the integrand into partial fractions:

$\dfrac{3t^2+2t+3}{(1+t)(1+t^2)}=\dfrac2{1+t}+\dfrac{1+t}{1+t^2}$

so you have

$\displaystyle2\int\frac{3t^2+2t+3}{(1+t)(1+t^2)}\,\mathrm dt=4\int\frac{\mathrm dt}{1+t}+2\int\frac{\mathrm dt}{1+t^2}+\int\frac{2t}{1+t^2}\,\mathrm dt$

which are all standard integrals. You end up with

$\displaystyle\int\mathrm dx+4\int\frac{\mathrm dt}{1+t}+2\int\frac{\mathrm dt}{1+t^2}+\int\frac{2t}{1+t^2}\,\mathrm dt$
$=x+4\ln|1+t|+2\arctan t+\ln(1+t^2)+C$
$=x+4\ln\left|1+\tan\dfrac x2\right|+2\arctan\left(\arctan\dfrac x2\right)+\ln\left(1+\tan^2\dfrac x2\right)+C$
$=2x+4\ln\left|1+\tan\dfrac x2\right|+\ln\left(\sec^2\dfrac x2\right)+C$

To try to get the terms to match up with the available answers, let's add and subtract $\ln\left|1+\tan\dfrac x2\right|$ to get

$2x+5\ln\left|1+\tan\dfrac x2\right|+\ln\left(\sec^2\dfrac x2\right)-\ln\left|1+\tan\dfrac x2\right|+C$
$2x+5\ln\left|1+\tan\dfrac x2\right|+\ln\left|\dfrac{\sec^2\dfrac x2}{1+\tan\dfrac x2}\right|+C$

which suggests A may be the answer. To make sure this is the case, show that

$\dfrac{\sec^2\dfrac x2}{1+\tan\dfrac x2}=\sin x+\cos x+1$

You have

$\dfrac{\sec^2\dfrac x2}{1+\tan\dfrac x2}=\dfrac1{\cos^2\dfrac x2+\sin\dfrac x2\cos\dfrac x2}$
$\dfrac{\sec^2\dfrac x2}{1+\tan\dfrac x2}=\dfrac1{\dfrac{1+\cos x}2+\dfrac{\sin x}2}$
$\dfrac{\sec^2\dfrac x2}{1+\tan\dfrac x2}=\dfrac2{\cos x+\sin x+1}$

So in the corresponding term of the antiderivative, you get

$\ln\left|\dfrac{\sec^2\dfrac x2}{1+\tan\dfrac x2}\right|=\ln\left|\dfrac2{\cos x+\sin x+1}\right|$
$=\ln2-\ln|\cos x+\sin x+1|$

The $\ln2$ term gets absorbed into the general constant, and so the antiderivative is indeed given by A,

$\displaystyle\int\frac{\cos x+3\sin x+7}{\cos x+\sin x+1}\,\mathrm dx=2x+5\ln\left|1+\tan\dfrac x2\right|-\ln|\cos x+\sin x+1|+C$

5 0

2 years ago

What do we know about a system of linear equations when is has

Radda [10]

Linear systems that have infinite solutions have the same slope and they have the same line on the graph

4 0

2 years ago