Bill has x pence.

Dora drove east at a constant rate of 75 kph. One hour later, Tim started driving on the same road at a constant rate of 90 kph.

PIT_PIT [208]

Ok so let T=time from when Tim starts
Distance Tim travels= T*90
Distance Dora travels=T*75 + 75 (<as already started)
for him to have caught up His distance must equal hers so:
90T=75T + 75 (now minus 75T)
15T=75 (now divide by 15)
T=5 :)
So five hourse, hope this helped :)

3 0

2 years ago

Read 2 more answers

The sum of the measures of the angles of a triangle is 180. The sum of the measures of the second and third angles is five times

rusak2 [61]

Answer:

$x=30\\y=68\\z=82$

Step-by-step explanation:

x = measure of the first angle

y = measure of the second angle

z = measure of the third angle

The sum of the measures of the second and third (y+z) is five times the measure of the first angle (=5x)

$y+z=5x$

The third angle is 14 more than the second

$z=y+14$

And remember that the sum of these three angles must be equal to 180.

$x+y+z=180$

Let's take these equations

$y+z=5x\\z=y+14\\x+y+z=180$

If you take a look at the first equation, we have y+z = 5x and we have y+z in the third equation as well, we can replace that....

$x+y+z=180\\x+(y+z)=180\\x+(5x)=180$

Distribute the + sign

$x+5x=180$

Combine like terms;

$6x=180$

Divide by 6.

$x=\frac{180}{6}\\ x=30$

We have now defined that the measure of the first angle is 30º.

Let's take another equation... for example $z=y+14$

I'm going to take this one because if I replace x and z in the third equation, all I'll have left will be y.

$x+y+z=180\\30+y+(y+14)=180$

Distribute the + sign and Combine like terms;

$30+y+y+14=180\\44+2y=180\\$

Subtract 44 to isolate 2y.

$2y=180-44\\2y=136$

Now divide by 2.

$y=\frac{136}{2}\\ y=68$

We already have the value of x and y. Once again, replacing this in the third equation will leave us with z to solve for.

$x+y+z=180\\30+68+z=180\\98+z=180\\z=180-98\\z=82$

5 0

2 years ago

The Wall Street Journal reports that 33% of taxpayers with adjusted gross incomes between $30,000 and $60,000 itemized deduction

Len [333]

Answer:

(a) n : 20 50 100 500

P (-200 < X - μ < 200) : 0.2886 0.4444 0.5954 0.9376

(b) The correct option is (b).

Step-by-step explanation:

Let the random variable X represent the amount of deductions for taxpayers with adjusted gross incomes between $30,000 and $60,000 itemized deductions on their federal income tax return.

The mean amount of deductions is, μ = $16,642 and standard deviation is, σ = $2,400.

Assuming that the random variable X follows a normal distribution.

(a)

Compute the probability that a sample of taxpayers from this income group who have itemized deductions will show a sample mean within $200 of the population mean as follows:

For a sample size of n = 20

$P(\mu-200$

$=P(-0.37$

For a sample size of n = 50

$P(\mu-200$

$=P(-0.59$

For a sample size of n = 100

$P(\mu-200$

$=P(-0.83$

For a sample size of n = 500

$P(\mu-200$

$=P(-1.86$

n : 20 50 100 500

P (-200 < X - μ < 200) : 0.2886 0.4444 0.5954 0.9376

(b)

The law of large numbers, in probability concept, states that as we increase the sample size, the mean of the sample ( $\bar x$ ) approaches the whole population mean ( $\mu_{x}$ ).

Consider the probabilities computed in part (a).

As the sample size increases from 20 to 500 the probability that the sample mean is within $200 of the population mean gets closer to 1.

So, a larger sample increases the probability that the sample mean will be within a specified distance of the population mean.

Thus, the correct option is (b).

8 0

2 years ago

the amount of gasoline at a gas station changes from 58,432.4 gallon to 56,475.2 gallon from 2:00 pm to 4:00 pm. what rational n

jarptica [38.1K]

Answer:

I take it you mean the average gallons lost an hour, in which case you would do 58,432.4 - 56,475.2 to get 1,597.2 to which you divide by 2 getting your final answer of 978.6

4 0

2 years ago

Stepping from the embrace, she smoothly extracts the broom from my grip. Which type of phrase is the underlined portion of the s

guajiro [1.7K]

Answer:

A). Participle phrase.

Step-by-step explanation:

'Participle phrases' are defined as the phrases that consist of a participle(present or past) followed by modifiers and their object plus any/or complements. These phrases primarily function as adjectives by providing information about a noun or pronoun in the sentence.

In the given sentence, the underlined portion('stepping from the embrace') is a participle phrase as it begins with a participle('present as it ends with 'ing') followed by the modifier prepositional phrase 'from the embrace'(as an adverb). It is functioning as an adjective as it modifies the pronoun 'she' in the sentence. Thus, option A is the correct answer.

5 0

2 years ago