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3 years ago

Jacob is training for a marathon. His plan is to run the same distance for 3 days a week, then increase that distance

Mathematics

1 answer:

Maurinko [17]3 years ago

6 0

Answer:

f(t) = 1.5t + 5

Step-by-step explanation:

each week he will run an extra 1.5 miles and one the first week he started off running 5 miles. 1.5 is your slope and 5 is the y-intercept.

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What is the equation of the circle?<br> Also no links please

Mnenie [13.5K]

Answer:

(x - 3)^2 + (y + 2)^2 = 2^2.

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3 years ago

A type is typically makes an error on one out of every 21 documents they complete if the typist can complete 120 documents an ho

motikmotik

<span>Answer: 21 document= 1 error 120 document= 1 hour in three and a half hours= 21 mistakes</span>

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3 years ago

Ryan Reynolds saw a coat was marked down 40 percent during a sale. If the original price was $150, what was the sale price of th

drek231 [11]

Hello!

To calculate the sale price of the coat, we can simply multiply 150 by .40, then subtract the product from 150.

150 × .40 = 60
150 - 60 = 90

The sale price of the coat is $90.

4 0

3 years ago

Read 2 more answers

Let f be a differentiable function such that f(0) = -5 and f'(x) is less than or equal to 3 for all x. Of the following, which i

stepladder [879]

E) 2
Remember that the first derivative of a function is the slope of the function at any specified point. We've been told that f(0) = -5 and that f'(x) is always less than or equal to 3. So let's look at the available options and see what the average slope would have to be in order to get the specified value of f(2).
A) -10: (-10 - -5)/(2 - 0) = -5/2 = -2.5
B) -5: (-5 - -5)/(2 - 0) = 0/2 = 0
C) 0: (0 - -5)/(2 - 0) = 5/2 = 2.5
D) 1: (1 - -5)/(2 - 0) = 6/2 = 3
E) 2: (2 - -5)/(2 - 0) = 7/2 = 3.5
Now taking into consideration the mean value theorem, the value of the function f'(x) has to have the value equal to the average slope between the two points at at least one point between the two given values. For options A, B, C, and D it's possible for f'(x) to return values that make that slope possible. However, for option E, the mean value theorem indicates that f'(x) has to have the value of 3.5 for at least 1 point between x=0 and x=2. And since we've been told that f'(x) is less than or equal to 3 for all possible values of x, that is in conflict and f(2) can not have the value of 2.

3 0

3 years ago

The town of Hayward (CA) has about 50,000 registered voters. A political research firm takes a simple random sample of 500 of th

Ilia_Sergeevich [38]

Answer:

(0.0757;0.1403)

Step-by-step explanation:

1) Data given and notation

Republicans =115

Democrats=331

Independents=54

Total= n= 115+331+54=500

$\hat p_{ind}=\frac{54}{500}=0.108$

Confidence=0.98=98%

2) Formula to use

The population proportion have the following distribution

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

The confidence interval for the population proportion is given by this formula

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

We have the proportion of independents calculated

$\hat p_{ind}=\frac{54}{500}=0.108$

We can calculate $\alpha=1-conf=1-0.98=0.02$

And we can find $\alpha/2 =0.02/2=0.01$ , with this value we can find the critical value $z_{\alpha/2}$ using the normal distribution table, excel or a calculator.

On this case $z_{\alpha/2}=2.326$

3) Calculating the interval

And now we can calculate the interval:

$0.108 - 2.326\sqrt{\frac{0.108(1-0.108)}{500}}=0.0757$

$0.108 + 2.326\sqrt{\frac{0.108(1-0.108)}{500}}=0.1403$

So the 98% confidence interval for this case would be:

(0.0757;0.1403)

7 0

3 years ago