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bazaltina [42]
2 years ago
5

On a map,1 in. represents 12 mi. Two cities are 6 1/2 in. on a map. How far apart are the actual cities? A. 78 mi B. 72 1/2 mi C

.72 mi D. 18 1/2 mi
Mathematics
1 answer:
Dovator [93]2 years ago
3 0
1 inch= 12 miles


Multiply 6 1/2 inches by total number of miles per 1 inch (12).

= 6 1/2 * 12
convert to improper fraction

= 13/2 * 12
multiply numerators

= (13*12)/2
multiply in parentheses

= 156/2
divide

= 78 miles


ANSWER: (A) 78 miles

Hope this helps! :)
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How do you find the x intercepts of 3x^(5/3) - 4x^(7/3)
kaheart [24]
Set the whole expression = to 0 and solve for x.

3x^(5/3) - 4x^(7/3) = 0.  Factor out x^(5/3):     x^(5/3) [3 - 4x^(2/3)] = 0

Then either x^(5/3) = 0, or 3 - 4x^(2/3) = 0.

In the latter case, 4x^(2/3) = 3. 

To solve this:  mult. both sides by x^(-2/3).  Then we have

4x^(2/3)x^(-2/3) = 3x^(-2/3),            or 4 = 3x^(-2/3).  It'd be easier to work with this if we rewrote it as

4           3
---  = --------------------
1            x^(+2/3)

Then 

4
---  = x^(-2/3).  Then, x^(2/3) = (3/4), and x = (3/4)^(3/2).  According to my     3                      calculator, that comes out to x = 0.65 (approx.)

Check this result!  subst. 0.65 for x in the given equation.  Is the equation then true?

My method here was a bit roundabout, and longer than it should have been.  Can you think of a more elegant (and shorter) solution?
7 0
3 years ago
Read 2 more answers
(5in.)(8 in.) <br>-------------- <br> 2
DerKrebs [107]

Answer:

20

Step-by-step explanation:

(8 * 5) / 2

=> 40/2

=> 20

6 0
3 years ago
7) Halogen lightbulbs last an average of 4,500 hours. If a particular
castortr0y [4]

Answer:

450 days

Step-by-step explanation:

4500/10 = 450 days

7 0
2 years ago
Select True or False from each pull-down menu, depending on whether the corresponding statement is true or false.
Schach [20]

Answer:

1) FALSE

2) FALSE

3) TRUE

4) TRUE

Step-by-step explanation:

Previous concepts

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 Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".  

Part 1

The mean and standard deviation of a normally distributed random variable which has been standardized are one and zero, respectively.

The mean and the deviation for  the normal standard distribution are:

\mu=0, \sigma =1

So then that's FALSE.

Part 2

Using the standard normal curve, the z−score representing the 10th percentile is 1.28.

We are looking for a value a, that satisfy this:

P(X>a)=0.90   (a)

P(X   (b)  

We can find a z value that satisfy the condition with 0.10 of the area on the left and 0.90 of the area on the right it's z=-1.28. On this case P(Z<-1.28)=0.10 and P(Z>-1.28)=0.90

So that's FALSE.

Part 3

Let z1 be a z−score that is unknown but identifiable by position and area. If the symmetrical area between −z1 and +z1 is 0.9544, the value of z1 is 2.0

If we find this probability:

P(-2.0< Z

So on this case we can approximate to 0.9544. And that's TRUE.

Part 4

Using the standard normal curve, the z−score representing the 75th percentile is 0.67.

We are looking for a value a, that satisfy this:

P(X>a)=0.25   (a)

P(X   (b)  

We can find a z value that satisfy the condition with 0.75 of the area on the left and 0.25 of the area on the right it's z=0.67. On this case P(Z<0.67)=0.75 and P(Z>0.67)=0.25

So that's TRUE.

3 0
3 years ago
A triangle has base 2x+1 and height 6x-3. What value of x would give an area of 240m2?
GREYUIT [131]

Answer:

The values of x which would give an area of 240m² would be:

x=-\frac{\sqrt{161}}{2},\:x=\frac{\sqrt{161}}{2}

Step-by-step explanation:

Given

The base of triangle b = 2x+1

The height of triangle h = 6x-3

The Area of the triangle A = 240 m²

The Area of the triangle has the formula

A = 1/2 × b × h

substituting b = 2x+1, h = 6x-3 and A = 240

240\:=\:\frac{1}{2}\:\left(2x+1\right)\:\times \left(6x-3\right)

480=\left(2x+1\right)\left(6x-3\right)

480=12x^2-3

Subtract 480 from both sides

12x^2-3-480=480-480

12x^2-483=0

3\left(4x^2-161\right)=0

3\left(2x+\sqrt{161}\right)\left(2x-\sqrt{161}\right)=0

Using the zero factor principle

if ab=0, then a=0 or b=0 (or both a=0 and b=0)

2x+\sqrt{161}=0\quad \mathrm{or}\quad \:2x-\sqrt{161}=0

solving

2x+\sqrt{161}=0

2x=-\sqrt{161}

Divide both sides by 2

\frac{2x}{2}=\frac{-\sqrt{161}}{2}

x=-\frac{\sqrt{161}}{2}

also solving

2x-\sqrt{161}=0

2x=\sqrt{161}

Divide both sides by 2

\frac{2x}{2}=\frac{\sqrt{161}}{2}

x=\frac{\sqrt{161}}{2}

Therefore, the values of x which would give an area of 240m² would be:

x=-\frac{\sqrt{161}}{2},\:x=\frac{\sqrt{161}}{2}

3 0
2 years ago
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