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SSSSS [86.1K]
2 years ago
7

Audrey was given a gift card for a coffee shop. Each morning, Audrey uses the card to buy one cup of coffee. Each cup of coffee

costs $2.50 and after buying 2 cups of coffee, the card had a $45 remaining balance. Write an equation for A,A, in terms of x,and x representing the amount money remaining on the card after buying x cups of coffee.
Mathematics
1 answer:
Lunna [17]2 years ago
4 0

Answer:

<h2>The expression is y-2.50x=45</h2><h2>The gift card is worth $50</h2>

Step-by-step explanation:

step one:

let y be the amount of the gift card

and let x be the number of cups of coffee bought

given that Audrey bought 2 cups x=2

y-2.50x=45

step two:

substitute x= 2 in the expression we have

y-2.5(2)=45

y-5=45

solving for y

y=45+5

y=$50

the expression is y-2.50x=45

the gift card is worth $50

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Kevin says that lines p and m will eventually intersect. Lines A and B intersect. Plane A contains lines p, m, and n. Line n is
ANTONII [103]

Answer:

No, because they are parallel.

Step-by-step explanation:

The lines p and m will not intersect, so Kevin is not correct.

It is given that planes A and B intersects. The plane A contains the line p, m and n on its plane. The lines p and m are parallel to each other. They are identical and move in the same direction.

Since the line p and m are parallel, they will not meet each other at any point because parallel lines does not intersect or meet at a point, they run parallelly along each other.

So, line p and m will not intersect.

Thus the answer is " No, because they are parallel."

8 0
2 years ago
. Given f(x) = e 2x e 2x + 3e x + 2 : (a) Make the substitution u = e x to convert Z f(x) dx into an integral in u (HINT: The ea
MrRa [10]

Answer:

Step-by-step explanation:

Given;

f(x)=\frac{e^{2x}}{e^{2x}+3e^x+2}

a)

substitute u=e^x\\du=e^x dx\\\\\int\frac{e^{2x}}{e^{2x}+3e^x+2}dx=\int\frac{e^x\dot e^x}{e^x^{2x}+3e^x+2}dx\\\\=\int\frac{udu}{u^2+3u+2}

b)

Apply partial fraction in (a), we get;

\frac{u}{u^2+3u+2}=\frac{2}{u+2}-\frac{1}{u+1}\\\\\therefore u^2+3u+2\\=u^2+2u+u+2\\=u(u+2)+1(u+1)\\=(u+2)(u+1)\\\\Now\,\int\frac{u}{u^2+3u+2}\,du=\int\frac{2}{u+2}du-\int\frac{1}{u+1}du\\\\=2ln|u+2|-ln|u+1|+c\\=2ln|e^x+2|-lm|e^x+1|+c

where C is an arbitrary constant

8 0
2 years ago
Joanna set a goal to drink more water daily. The number of ounces of water she drank each of the last seven days is shown below.
butalik [34]
(a) Data with the eight day's measurement.
Raw data:      [60,58,64,64,68,50,57,82], 
Sorted data:  [50,57,58,60,64,64,68,82]
Sample size = 8 (even)
mean            = 62.875
median         = (60+64)/2 = 62
1st quartile   = (57+58)/2 = 57.5
3rd quartile  = (64+68)/2 =  66
IQR = 66 - 57.5 = 8.5

(b) Data without the eight day's measurement.
Raw data:      [60,58,64,64,68,50,57]
Sorted data:  [50,57,58,60,64,64,68]
Sample size = 7 (odd)
mean            = 60.143
median         = 60
1st quartile   = 57
3rd quartile = 64
IQR = 64 -57 = 7

Answers:
1. The average is the same with or without the 8th day's data.  FALSE
2. The median is the same with or without the 8th day's data.  FALSE
3. The IQR decreases when the 8th day is included.                  FALSE
4. The IQR increases when the 8th day is included.                   TRUE
5. The median is higher when the 8th day is included.              TRUE

8 0
2 years ago
Read 2 more answers
The probabilities of the orphaned pets in six cities' animal shelters being different types of animals are given in the table. I
olga2289 [7]
Given the table below showing t<span>he probabilities of the orphaned pets in six cities' animal shelters being different types of animals.

</span>
   City          Cat          Dog        Dog        Dog       <span>Dog                                      
                         −Lhasa Apso −Mastiff −Chihuahua −Collie
Austin       24.5%      2.76%    2.86%     3.44%    2.65%
Baltimore 19.9%      3.37%    3.22%     3.31%    2.85%
Charlotte  33.7%     3.25%     3.17%     2.89%    3.33%
St. Louis  43.8%     2.65%     2.46%     3.67%    2.91%
Salt Lake
City          28.9%     2.85%     2.78%     2.96%    2.46%
Orlando   37.6%     3.33%     3.41%     3.45%    2.78%
Total        22.9%     2.91%     2.68%     3.09%    2.58%</span><span>

Condtional probability </span><span>is a measure of the probability of an event given that another event has occurred. If the event of interest is A and the event B is known or assumed to have occurred, "the conditional probability of A given B", or "the probability of A under the condition B", is usually written as P(A|B).

The probability of A given B, is given by
P(A|B)= \frac{P(A\cap B)}{P(B)}

From the table, the probability that an </span>orphaned pet in a St. Louis animal shelter is a mastiff dog is 2.46% and the probability that <span>an <span>orphaned pet in a St. Louis animal shelter is a dog is 2.91% + 2.68% + 3.09% + 2.58% = 11.26%</span>

The probability that a randomly selected orphaned pet in a St. Louis animal shelter is a mastiff given that it is a dog, is given by
\frac{P(St. \, Louis\, and\, dog-mastiff)}{P(dog)} = \frac{2.46}{11.26} \times100\%=21.85\%</span>
5 0
2 years ago
Read 2 more answers
A semicircular flower bed has a diameter of 3 metres. What is the area of the flower bed?
Yuri [45]

The area of circle is

A_{\text{circle}}=\pi r^2.

Then the area of semicircular region is

A_{\text{semicircular region}}=\dfrac{1}{2} \pi r^2.

If r=3 m, you have

A_{\text{semicircular region}}=\dfrac{1}{2} \pi \cdot 3^2=\dfrac{9\pi}{2}=4.5\pi \approx 14.13 sq. m.

Answer: A_{\text{semicircular region}}=4.5\pi \approx 14.13 sq. m.

3 0
2 years ago
Read 2 more answers
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