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3 years ago

14

Harold randomly selected one square tile and one round tile from the sets shown below. What is the probability that Harold selec

ted a pink square tile, and either a red or a blue round tile ?
A. 3/5
B. 14/60
C. 1/9
D. 4/45

1 answer:

Rus_ich [418]3 years ago

4 0

Answer:

C. 1/9

Step-by-step explanation:

Assuming the selections are independent, their joint probability is the product of the probabilities of the individual events.

P(pink square) = (# pink squares)/(# squares) = 16/60 = 4/15

P(red or blue round) = (#red or blue rounds)/(# rounds) = 15/36

Then the joint probability is ...

P(defined event) = (4/15)(15/36) = 4/36 = 1/9

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mihalych1998 [28]

To solve this we are going to use the future value of annuity due formula: $FV=(1+ \frac{r}{n} )*P[ \frac{(1+ \frac{r}{n} )^{kt} -1}{ \frac{r}{n} } ]$
where
$FV$ is the future value $P$ is the periodic payment $r$ is the interest rate in decimal form $n$ is the number of times the interest is compounded per year $k$ is the number of payments per year $t$ is the number of years

We know for our problem that $P=295$ and $t=6$ . To convert the interest rate to decimal for, we are going to divide the rate by 100%:
$r= \frac{10}{100}$
$r=0.1$
Since the payment is made quarterly, it is made 4 times per year; therefore, $k=4$ .
Since the type of the annuity is due, payments are made at the beginning of each period, and we know that we have 4 periods, so $n=4$ .
Lets replace those values in our formula:

$FV=(1+ \frac{r}{n} )*P[ \frac{(1+ \frac{r}{n} )^{kt} -1}{ \frac{r}{n} } ]$
$FV=(1+ \frac{0.1}{4} )*295[ \frac{(1+ \frac{0.1}{4} )^{(4)(6)} -1}{ \frac{0.1}{4} } ]$
$FV=9781.54$

We can conclude that the amount of the annuity after 10 years is $9,781.54

6 0

3 years ago

Rewrite the equation by completing the square.<br> x^2 - 4x + 3 = 0

Degger [83]

Answer:

the answer would be x=3,1

4 0

3 years ago

Read 2 more answers

Brad bought 70.030 m of chain to make necklaces. He used 0.667 m of the chain to make one necklace.

Margaret [11]

Brad bought 70.030m of this chain to make a necklace, then he used 0.667m of it to make one, and how much he had left, the key word ''used'' and have left'' means subtract so all we have to do is subtract 70.030m minus 0.667m and we get the answer.

Answer: 69.363m of his chain is left.

6 0

3 years ago

Reinhardt Furniture Company has 40,000 shares of cumulative preferred 2% stock, $150 par and 100,000 shares of $5 par common sto

Ann [662]

Answer:

for year 1

common stock = $1.75 per share

preferred stock = Zero

for year 2

common stock = $4.25 per share

preferred stock = $0.3 per share

for year 3

common stock = $3 per share

preferred stock = $2 per share

Step-by-step explanation:

step 1

preferred stock value = (40000 shares * $150) = $6000000

common stock value = (100000 shares * $5) = $500000

step 2

For year 1:

Dividend on preferred stock;

$\frac{6000000 * 2}{100}$ = $120000

But total dividend in the question was $70000 therefore total amount of dividend on cumulative preferred stock is $70000.

hence, dividend per share

$= \frac{70000}{40000 shares}$ = $1.75 per share

Dividend on common stock;

70,000 - 70,000 = Zero

as total dividend distributed in year 1 is insufficient for cumulative preferred stock therefore no dividend will be paid on common stock.

For year 2:

Dividend on cumulative preferred stock;

$\frac{6000000 * 2}{100}$ = $120000

extra dividend of year 1 ($120000 - $70000) = $50000

Thus total dividend on cumulative preferred stock

($120000 + $50000) = $170000

So dividend per share

$\frac{170000}{40000\ shares}$ = $4.25 per share

Dividend on common stock;

($200000 – $170000) = $30000

dividend per share

$\frac{30000}{100000\ shares}$ = $0.3 per share

For year 3:

Dividend on cumulative preferred stock;

$\frac{6000000 * 2}{100}$ = $120000

total dividend on cumulative preferred stock $120000

dividend per share

$\frac{120000}{40000 shares}$ = $3 per share

No dividend was extra in the year 2 therefore only available dividend of this year will be paid.

Dividend on common stock;

($320000 – $120000) = $200000

dividend per share

$\frac{200000}{100000\ shares}$ = $2 per share

3 0

3 years ago

In the pulley system shown in this figure, MQ = 30 mm, NP = 10 mm, and QP = 21 mm. Find MN.

ankoles [38]

<h2>Answer:</h2>

$\boxed{\overline{MN}=37.96}$

<h2>Step-by-step explanation:</h2>

For a better understanding of this problem, see the figure below. Our goal is to find $\overline{MN}$ . Since:

$\angle MRS=\angle MQP=90^{\circ} \\ \\ \overline{MQ}=\overline{MR}=30mm$

and $\overline{MN}$ is a common side both for ΔMRN and ΔMQN, then by SAS postulate, these two triangles are congruent and:

$\overline{RN}=\overline{QN}$

By Pythagorean theorem, for triangle NQP:

$\overline{QN}=\sqrt{\overline{NP}^2+\overline{QP}^2} \\ \\ \overline{QN}=\sqrt{10^2+21^2} \\ \\ \overline{QN}=\sqrt{541}$

Applying Pythagorean theorem again, but for triangle MQN:

$\overline{MN}=\sqrt{\overline{MQ}^2+\overline{QN}^2} \\ \\ \overline{MN}=\sqrt{30^2+(\sqrt{541})^2} \\ \\ \boxed{\overline{MN}=37.96}$

3 0

3 years ago