MATHEMATICS HIGH SCHOOL

Johnathan ran 5 days this week. The most he ran in one day was 3.5 miles. Write an inequality that shows the distance johnathan could of ran any day this week

Answers

Answer 1

Answer:

An inequality that shows the distance Johnathan could of ran any day this week is:

$x\leq 3.5$

Solution:

Let "x" be the distance Johnathan can run any day of this week

Given that,

Johnathan ran 5 days this week. The most he ran in one day was 3.5 miles

Therefore,

Number of days ran = 5

The most he ran in 1 day = 3.5 miles

Thus, the maximum distance he ran in a week is given as:

$distance = 5 * 3.5 = 17.5$

The maximum distance he ran in a week is 17.5 miles

If we let x be the distance he can run any day of this week then, we get a inequality as:

$x\leq 3.5$

If we let y be the total distance he can travel in a week then, we may express it as,

$y\leq 17.5$

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If x=2+√3,then find the value of x-1/x

Answers

A :-) x = 2+_/3
x-1/x = 1/2+_/3
( rationalize the denominator )
x-1/x = 1/2+_/3 x 2 -_/3/2 - _/3
[ ( a + b ) ( a - b ) = a^2 -b^2 ]
x-1/x = 2 - _/3/( 2 )^2 - ( _/3 )^2
x-1/x = 2 - _/3/4 - 3
x-1/x = 2 - _/3/1
x-1/x = 2 - _/3
x-1/x = ( 2+_/3 ) ( 2 - _/3 )
x -1/x = ( 2 )^2 - ( _/3 )^2
( x = 2+_/3 )
x-1/x = 4 - 3
x-1/x = 1

.:. The value of x-1/x is 1 .

50% of all the cakes Lucy bakes that week were party cakes: one fifth were fruit cakes and the remainder were sponge cakes. What percentage of cakes were sponge cakes ?

Answers

50%=5/10 1/5=2/10 5/10+2/10=7/10 10/10-7/10=3/10 so 3/10 were sponge cakes

A person leaves home at 8.00 a.m. and drives to a destination at a rate of 40 mph. The person returns at a rate of 25 mph and arrives at 2:30 p.m. If x represents how far it is to the destination, then which of the following expressions represents the amount of time to make the return trip?25x
6.5-x
x/25

Answers

time = distance / speed

distance= x
speed = 25 mph

time = x/25

A conditional relative frequency table is generated by row from a set of data. The conditional relative frequencies of the two categorical variables are then compared.If the relative frequencies are 0.48 and 0.52, which conclusion is most likely supported by the data?

A.) There is likely an association between the categorical variables because the relative frequencies are similar in value.

B.) An association cannot be determined between the categorical variables because the relative frequencies are similar in value.

C.) An association cannot be determined between the categorical variables because the relative frequencies are not similar in value.

D.) There is likely an association between the categorical variables because the relative frequencies are both close to 0.50.

Answers

If the relative frequencies are 0.48 and 0.52, we conclude that: A. There is an association between the categorical variables because they are similar in value.

What is a two-way frequency table?

A two-way frequency table can be defined as a type of table that is used for the graphical representation of frequencies (relative frequencies) that are associated with two (2) categorical variables.

This ultimately implies that, a two-way frequency table can be used to show, analyze, and examine the relationships that exists between two (2) categorical variables.

In conclusion, we can conclude that there is an association between the categorical variables because the relative frequencies have the same (similar) value, especially if theyare 0.48 and 0.52.

Read more on frequency here: brainly.com/question/20744563

Answer: A

Step-by-step explanation:

Did it on edge

Casey is reading a book for a book report. At 3:30 P.M., he started reading where he had left off the day before. At 5:30 P.M. he was on page 160. At 8:00 P.M. he was on page 280. If reading the book is modeled by a linear function, what page did Casey start on at 3:30 P.M.?

Answers

To find the time Casey read today, 5:30 from 8:00.
8:00 - 5:30 = 2:30
Casey

To find the number of pages Casey read today subtract the page number he started reading on to the page he stopped on.
280 - 160 = 120
Casey read 120 pages today.

Now you need to find how many pages Casey read in one hour.

If Casey read 120 pages in 2.5 hours, you can find how many pages he read in one hour by dividing 120 by 2.5.
120 ÷ 2.5 = 48.
Casey read 48 pages in one hour.

Casey was on page 160 at 5:30, and you need to find what page he was on at 3:30. Since Casey read for 2 hours before he reached page 160, you need to subtract 2 hours worth of reading from that number.

160 - (2×48)
160 - 96
64

Casey was on page 64 at 3:30 pm today.

if he started reading from where he left off, and it's 5:30 and he is at page 160, and then he got to page 280 by 8:00, that is 2 hours and 30 minutes. so bring the reading time down into easier numbers so that 5-> 30 minute terms, then find out how many pages he read in 30 minutes. The difference between 160 pages and 280 pages is 120 pages. 120 divided by 30 equals 4. the amount of time between 3:30 and 5:30 is 2 hours which is 4-> 30 minute terms. So if it takes 30 minutes to read 4 pages then multiply 4 with 4 which equals 16, and finally subtract 16 from 160 and that's going to equal 144 pages.

(Sorry about the paragraph but i figured ide give you my reasoning and work just in case if i was wrong, ide like to know what i did if i am wrong. And if I'm right then that's how you show your work!)

the Kelly family bought a new pet rabbit. They want to build an enclosure outside so it has lots of room to roam. They have 30 feet of leftover lumber to use. Find the length and width of the enclosure if the length is to be 4fteet longer than twice the width.

Answers

assume that since this is a simple math problem and they only mentioned legnth and witdth,
assume a perfect rectangle

so assuming they use all the lumber
30=perimiter
perimiter=legnth around=legnth+legnth+with+width

30=2legnth+2width
undistribute
30=2(legnth+width)
divide by 2
15=legnth+width
legnth is 4 more than 2width
legnth=4+2width
subsitute
15=legnth+width
15=4+2width+width
subtract 4
11=2width+width
divide by 3
11/3=width

legnth=4+2width
legnth=4+2 times (11/3)
lefnth=4+22/3
4=12/3
legnth=12/3+22/3
legnth=34/3 feet=11 and 1/3 foot

width=11/3=3 and 2/3

legnth=11 and 1/3 foot
width=3 and 2/3 foot

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