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aivan3 [116]
2 years ago
4

Andy runs and eats breakfast every morning before work. When he runs, he bums 160 calories per mile for the first 3 miles. When

he runs more than 3 miles, he burns 98 calories per additional mile. On Tuesday morning. Andy runs an additional x miles over 3 miles and then consumes y calories for breakfast. Which of the following functions, f , models the net number of calories Andy has lost after running and eating breakfast on Tuesday morning? A)f(x, y) = 98x – yB)f(x, y) = 160x + 98x – y C)f(x, y) = 480 + 98x + yD)f(x, y) = 480 + 98x – y
Image of page 25
Mathematics
1 answer:
Likurg_2 [28]2 years ago
6 0

Answer:

C

Step-by-step explanation:

So you already know you do 480 calories for the first 3 miles so it doesnt need to be multiplied by the X amount of extra miles

Now you burn 98 calories per extra mile so for instance (if you did say 2 miles you would want to multiply 98 calories by 2 cause you burn 98 calories per mile)

Lastly, you just ate Y amount of calories so you need to subtract that from the burned calories cause you just now consumed Y amount of calories

So in conclusion, the answer would be C. f(x, y) = 480 + 98x + y

You might be interested in
Adrian Beltre hit 48 home runs during the 2004 Major League Baseball season, but only hit 19 home runs in the 2005 season. By wh
aliya0001 [1]

Answer:

60.42%

Step-by-step explanation:

Number of home runs hit by Adrian Beltre in 2004 = 48

Number of home runs hit by Adrian Beltre in 2005 = 19

To find:

Percentage decrease in home run production from 2004 to 2005.

Solution:

To find the percentage decrease, first of all we need to find the decrease in the number of home runs and then we will divide with the number of home runs in 2004 and then finally will multiply the result with 100 to get the percentage decrease.

Decrease in the number of home runs = Number of home runs in 2004 - Number of home runs in 2005 = 48 - 19 = 29

\text{Percentage of decrease in Home runs} = \dfrac{\text{Decrease in home runs}}{\text{Number of home runs in 2004}}\times 100\\\Rightarrow \text{Percentage of decrease in Home runs} = \dfrac{29}{48}\times 100 \approx \bold{60.42\%}

Therefore, by 60.42% Beltre's home run production has decreased from 2004 to 2005.

4 0
2 years ago
The most popular mathematician in the world is throwing aparty for all of his friends. As a way to kick things off, they decidet
ratelena [41]

Answer:

The no. of possible handshakes takes place are 45.

Step-by-step explanation:

Given : There are 10 people in the party .

To Find: Assuming all 10 people at the party each shake hands with every other person (but not themselves, obviously) exactly once, how many handshakes take place?

Solution:

We are given that there are 10 people in the party

No. of people involved in one handshake = 2

To find the no. of possible handshakes between 10 people we will use combination over here

Formula : ^nC_r=\frac{n!}{r!(n-r)!}

n = 10

r= 2

Substitute the values in the formula

^{10}C_{2}=\frac{10!}{2!(10-2)!}

^{10}C_{2}=\frac{10!}{2!(8)!}

^{10}C_{2}=\frac{10 \times 9 \times 8!}{2!(8)!}

^{10}C_{2}=\frac{10 \times 9 }{2 \times 1}

^{10}C_{2}=45

No. of possible handshakes are 45

Hence The no. of possible handshakes takes place are 45.

4 0
2 years ago
Miyoko's goal is to earn more than \$950$950dollar sign, 950 this week. She earns \$250$250dollar sign, 250 for every day she wo
GrogVix [38]

$250 c+ $ 180 g > $ 950

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

As a cryptographer (c), Miyoko earns per day = $ 250

As a geologist (g) , Miyoko earns per day = $ 180

So the equation comes to be $250 c+ $ 180 g = $ 950

The equation can be rewritten to find c as, (950-180 g) / 250

The equation can be rewritten to find g as, (950 - 250 c) / 180

Plugin different values of c and g in the above 2 equations, we can find that ,

To achieve the goal, Miyoko requires to be a geologist for 3 days and crpytographist for 2 days.

5 0
2 years ago
The quotient of 9.2 x 10 6 and 2.3 x 10 2 expressed in scientific notation is
Virty [35]
What we know:
quotient 9.2 x 10^6/ 2.3 x 10²
in quotients exponents are subtracted of they have the same base, for example 10^6 and 10² have the same base of 10

What we need to find: quotient 9.2 x 10^6/ 2.3 x 10²
9.2 x 10^6        
--------------  =    4 x 10^4    
 2.3 x 10²

Here in this problem I divided 9.2 by 2.3 and got 4, since the solution was simple and clean meaning no repeated decimals I went ahead and divided the 10^6 by 10^2 and got 10^4.


Another method would be to expand both numbers then divide and do scientific notation again.
Remember to change to normal notation you move the decimal to the right using the number of the exponent.

9.2 x 10^6= 9200000
2.3 x 10²= 230

920000/230=40000

40000= 4 x 10^4 scientific notation

Use the method that is best for you or just know you can use either method to check your work.

4 0
2 years ago
If a hurricane was headed your way, would you evacuate? The headline of a press release states, "Thirty-four Percent of People o
IgorC [24]

Answer:

The 98% confidence interval would be given by (0.326;0.354)

Step-by-step explanation:

1) Notation and definitions

X=63 number of people who live within 20 miles of the coast in high hurricane risk counties of eight southern states

n=6138 random sample taken

\hat p=0.34 estimated proportion of people who live within 20 miles of the coast in high hurricane risk counties of eight southern states

p true population proportion of people who live within 20 miles of the coast in high hurricane risk counties of eight southern states

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".  

The margin of error is the range of values below and above the sample statistic in a confidence interval.  

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".  

The population proportion have the following distribution

p \sim N(p,\sqrt{\frac{p(1-p)}{n}})

2) Confidence interval

In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 98% of confidence, our significance level would be given by \alpha=1-0.98=0.02 and \alpha/2 =0.01. And the critical value would be given by:

z_{\alpha/2}=-2.33, z_{1-\alpha/2}=2.33

The confidence interval for the mean is given by the following formula:  

\hat p \pm z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}

If we replace the values obtained we got:

0.34 - 2.33\sqrt{\frac{0.34(1-0.34)}{6138}}=0.326

0.34 + 2.33\sqrt{\frac{0.34(1-0.34)}{6138}}=0.354

The 98% confidence interval would be given by (0.326;0.354)

8 0
2 years ago
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