Using PEMDAS (Order of Operations), what is the value of the expression 4+3^2+(4−12)? A. 15. B. 17. C. 13. D. 10.

Answers

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Lin rode a bike 20 miles in 150 minutes. If she rode at a constant speed, how far did she ride in 15 minutes? How long did it take her to ride 6 miles? How fast did she ride in miles per hour?

Answers

Hey there! :)

Answer:

First part: 2 miles.

Second part: 45 minutes

Third part: 8 mph.

Step-by-step explanation:

We can divide this question into 3 parts.

Begin by solving for the distance traveled after 15 minutes by creating a ratio:

$(20 mi)/(150min) = (x)/(15 min)$

Cross multiply:

20 · 15 = 150 · x

300 = 150x

300/150 = 150x/150

x = 2 miles.

2nd part: How long it took her to ride 6 miles.

Set up another ratio similar to the one used before:

$(20 mi)/(150min) = (6mi)/(x min)$

Cross multiply:

20 · x = 6 · 150

20x = 900

20x/20 = 900/20

x = 45 minutes.

3rd part:

For this part, we will need to convert from minutes to hours.

$(20 mi)/(150 min)* (60 min)/(1 hr) = (1200mi)/(150hr) = 8 mi/h$

Therefore, her speed is 8 mph.

What is the quotient (x^3+8)/(x+2)

Answers

Answer:

Step-by-step explanation:

The easiest way to do this is by using synthetic division (I really hope you know what I'm talking about!)

If the factor is x + 2 = 0, then the solution or the root is x = -2. We will put -2 outside the "box" and the coefficients from the terms of the polynomial inside the "box":

-2| 1 0 0 8

Bring down the first number and multiply it by the -2. Put the product up under the first 0 and add:

-2| 1 0 0 8

-2

1 -2

Now multiply the -2 by the -2, put the product up under the next 0 and add:

-2| 1 0 0 8

-2 4

1 -2 4

Now multiply the 4 by the -2, put the product up under the 8 and add:

-2| 1 0 0 8

-2 4 -8

1 -2 4 0

Those bold numbers are the coefficients to the quotient, which is another polynomial, but is one degree less than the one you started with:

x² - 2x + 4 = 0

Since there is no remainder, then x = -2 is a zero of x³ + 8, and (x + 2) is a factor.

There is a whole world of stuff to learn about quadratics!!

Simplify the expression
49 $(1)/(2)$

Answers

To convert a mixed fraction into an improper fraction:

$a(b)/(c) =((a\cdot c)+b)/(c)$

$49 (1)/(2) = ((49\cdot 2)+1)/(2) = (98 +1)/(2) = \boxed{\bf{(99)/(2)}}$

Ebony walked at a rate of 3 1/2 miles per hour for 1 1/3 hours. how far did she walk?

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Answer:

She walked $4(2)/(3)$ miles

Step-by-step explanation:

Speed of ebony = $3(1)/(2)$ miles/hour

= $(7)/(2)$ miles/hour

Time Taken = $1(1)/(3)$ hours.

= $(4)/(3)$ hours.

We are supposed to find how far did she walk i.e. Distance

Formula : $Distance = Speed * Time$

$Distance = (7)/(2) * (4)/(3)$

$Distance = (14)/(3)$

$Distance = 4(2)/(3)$

Hence she walked $4(2)/(3)$ miles

im wondering the same thing i have this question to

What is the y-intercept of the quadratic function f(x) = (x – 6)(x – 2)? (0,–6) (0,12) (–8,0) (2,0)

Answers

Answer:

(0,12)

Step-by-step explanation:

$f(x) = (x - 6)(x - 2)$

To find out y intercept , plug in 0 for x and find out f(0)

y intercept are the value where the graph crosses y axis

$f(x) = (x - 6)(x - 2)$

$f(0)= (0-6)(0 - 2)=12$

When x is 0 the value of y is 12

Write y intercept as (0,y) that is (0,12)

Answer:

(0,12)

Step-by-step explanation:

Just plug in 0 for x so (0-6)(0-2) = 12 so that's the y value.

Also, a y intercept has to be of the form (0,y) where y is some number. The x value has to be 0, so that eliminates the last two options automatically, but if we put the x and y value we got together we get (0,12)

Suppose 5% of the population have a certain disease. A laboratory blood test gives a positive reading for 95% of people who have the disease. What is the probability of testing positive and having the disease?

Answers

Answer:

The probability of testing positive and having the disease is 4.75%.

Step-by-step explanation:

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