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2 years ago

10

Rita's family is moving to Grand Junction to Dallas. The moving van averages 60 miles each hour. About how many hours does the v

an take to reach Dallas? Explain your work

1 answer:

Eddi Din [679]2 years ago

5 0

Answer:

16 hours and 20 minutes.

Step-by-step explanation:

Please consider the complete question.

Rita's family is moving to Grand Junction to Dallas, which is 980 miles. The moving van averages 60 miles each hour. About how many hours does the van take to reach Dallas?

To find the time taken by van to reach Dallas, we will divide total distance by speed.

$\text{Time}=\frac{\text{Distance}}{\text{Speed}}$

$\text{Time taken to reach Dallas}=\frac{980\text{ Miles}}{60\frac{\text{ Miles}}{\text{Hour}}}$

$\text{Time taken to reach Dallas}=\frac{980\text{ Miles}}{60}\times \frac{\text{ Hour}}{\text{Miles}}$

$\text{Time taken to reach Dallas}=\frac{98}{6}\text{ Hour}$

$\text{Time taken to reach Dallas}=16.3333\text{ Hour}$

Let us convert 0.3333 hours into minutes by multiplying 0.3333 by 60.

$0.3333\times 60=19.998\approx 20$

Therefore, it will take 16 hours and 20 minutes for the van to reach Dallas.

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If x% of four-digit numbers have a repeated digit (the repeated digits do not need to be adjacent), then what is x? Express your

joja [24]

Answer

It is a 4 digit number but 1 digit (exactly one digit) is repeated just once.

So 3 digits out of 10 have to be chosen.

There are 10C3 = 120 ways to do this.

say the digits chose are 5,6 and 9, they can be in any order and there are 3! possible orders =6 orders.

So so far that is 120*6=720 ways to get a 3 digit number where the digits are all different.

But we want a 4 digit number.

One digit has to be repeated there are 3 possibilities so that is 720*3 = 2160 posibilities.

But there are 4 postions that extra number can be put in. So that is 2160*4=8640 numbers

But I have double counted because 1434 is the same if I swap the 4s around so I have to halve this answer

8640/2 = 4320

So the number of favourable outcomes is 4320.

Altogether there are 10*10*10*10 = 10000 4 digit numbers (if they are allowed to start with 0)

so the prob of getting just one digit repeated once is 4320/10000 = 0.4320 = 43.2%

Do you understand now?

You will need to write your query on this thread but also send me a private message with the address of this thread attached. Otherwise I will not see it.

If you do have a query try to ask a specific question.

Anyway I hope that you understand

8 0

2 years ago

The blue whale is the largest animal living on the earth. The average blue whale measures 100 feet long (30 meters) and weighs 3

mamaluj [8]

The average blue whale measures 100 feet(30 meters) long and weighs 300,000 pounds(136,000 kilograms).

A whale’s head is $\frac{1}{3}$ of the length of its body. So, the length of a whale's head $=(\frac{1}{3}*100)feet = 33.33 feet$ or $(\frac{1}{3}*30)meter= 10 meter$

A new baby whale is $\frac{1}{4}$ length of a grown whale. So, the length of a new baby whale $=(\frac{1}{4}*100)feet = 25 feet$ or $(\frac{1}{4}*30)meter = 7.5 meter$

The average man is $\frac{1}{17}$ the length of a blue whale. So, the height of the average man $=(\frac{1}{17}*100)feet = 5.88 feet$ or $(\frac{1}{17}*30)meter =1.76 meter$

The average man is $\frac{1}{1818}$ the weight of a blue whale. So, the average man weighs $= (\frac{1}{1818}*300000)pounds= 165.02 pounds$ or $= (\frac{1}{1818}*136000)kilograms= 74.81 kilograms$

A human baby measures $\frac{1}{4}$ of the length of an adult. So, the height of the average human baby $= (\frac{1}{4}*5.88)feet = 1.47 feet$ or $= (\frac{1}{4}*1.76)meter = 0.44 meter$

5 0

2 years ago

T= 300 (d−15) 2 +20space, T, equals, start fraction, left parenthesis, d, minus, 15, right parenthesis, start superscript, 2,

stealth61 [152]

As can be read from your statement written "T, equals, start fraction, left parenthesis, d, minus, 15, right parenthesis, strt superscript, 2, end superscript, divided by, 300, end fraction, plus, 20", I hope your model equation is this :

$T = \frac{(d-15)^{2}}{300} + 20$

Hope this is your question, if not I think you will, still be able to find an answer of your question based on this solution

As we have to find lowest average temperature, So for minimum of a function its derivative is equal to 0 there.

So lets find derivative of T function first

So first expand $(d-15)^{2}$ as (d-15)(d-15)

we will use FOIL to multiply these

so $(d-15)(d-15) = d^{2} -15d -15d +225$

$= d^{2} -30d +225$

so we have $T = \frac{d^{2} -30d +225}{300} +20$

Now we will derivate each term here,300 in denominator is constant so that will come as it in in denominator.

To derivate terms in $dx^{2} -30d +225$ we will use power rule formula:

$(x^{n} )'= nx^{n-1}$

so derivative of $(d^{2} )'= 2d^{2-1} = 2d^{1} = 2d$

Then derivative of d will be 1

so that of -30d will be -30

then derivate of constant -225 will be 0

so we will have derivative as $\frac{2d-30}{300}$ for the fraction part and then derivative of +20 is again 0 as its constant term

$T' = \frac{2d-30}{300}$

For minimum we will put this derivative =0

$0 = \frac{2d-30}{300}$

Now solve for d

times both sides by 300

$0 \times 300 = \frac{2d-30}{300} \times 300$

$0 = 2d-30$

$0 +30 = 2d -30 +30$

$30 = 2d$

$\frac{30}{2} = \frac{2d}{2}$

$15 = d$

So now we have to find value of lowest temperature.

For that simply plug 15 in d place in original T function equation

$T = \frac{(d-15)^{2}}{300} + 20$

$T = \frac{(15-15)^{2}}{300} + 20$

$T = 20$

So T = 20 °C is the lowest average temperature and the answer.

6 0

2 years ago

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Pam bought 50 kg of sugar. She used 10 kg of sugar. What percentage of sugar was left? (step by step answer would be appreciated

galben [10]

Answer:

80%

Step-by-step explanation:

50 x 50 would be 100 and 50kg=100% and 10 x 2 = 20 so you used 20% therefore you have 80% left.

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2 years ago

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Study the steps used to solve the equation. Given: StartFraction c Over 2 EndFraction minus 5 equals 7 Step 1: StartFraction c O

Bas_tet [7]

Answer:

addition property of equality
integers are closed to addition
identity element
multiplication property of equality
commutative property of multiplication; reals are closed to multiplication; identity element

Step-by-step explanation:

<u>Given</u>:

c/2 -5 = 7

Step 1: c/2 -5 +5 = 7 +5

Step 2: c/2 +0 = 12

Step 3: c/2 = 12

Step 4: 2(c/2) = 12(2)

Step 5: c = 24

<u>Find</u>:

The property that justifies each step of the solution.

<u>Solution</u>:

Step 1: addition property of equality (lets you add the same to both sides)

Step 2: integers are closed to addition

Step 3: identity property of addition (adding 0 changes nothing)

Step 4: multiplication property of equality

Step 5: closure of real numbers to multiplication; identity property of multiplication

_____

It is hard to say what "property" you want to claim when you simplify an arithmetic expression. Above, we have used the property that the sets of integers and real numbers are closed to addition and multiplication. That is, adding or multiplying real numbers gives a real number.

In Step 5, we can rearrange 2(c/2) to c(2/2) using the commutative property of multiplication. 2/2=1, and c×1 = c. The latter is due to the identity element for multiplication: multiplying by 1 changes nothing.

Apart from the arithmetic, the other properties used are properties of equality. Those let you perform any operation on an equation, as long as you do it to both sides of the equation. The operations we have performed in this fashion are adding 5 and multiplying by 2.

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2 years ago

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