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Maurinko [17]
3 years ago
10

Solve log(2)(4x+8)=5

Mathematics
1 answer:
marysya [2.9K]3 years ago
6 0
4x+8 = 32, 4x = 24, x = 6
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Karen is typing a 4,000 word essay. She can type at about 30 words per minute. If she types for 45 minutes on Monday and 55 minu
horrorfan [7]

Answer:The number of words that she would still have to type to finish her essay is 1000

Step-by-step explanation:

Karen is typing a 4,000 word essay. She can type at about 30 words per minute. This means that if her rate remains constant, the total number of minutes that it will take her to finish would be

4000/30 = 133.33 minutes.

If she types for 45 minutes on Monday, it means that the total number of words that she typed on Monday would be

45 × 30 = 1350 words

If she types for 55 minutes on Tuesday, it means that the total number of words that she typed on Tuesday would be

55 × 30 = 1650 words

Total number of words typed on Monday and Tuesday would be

1350 + 1650 = 3000 words

The number of words that she would still have to type to finish her essay would be

4000 - 3000 = 1000 words

8 0
3 years ago
To avoid detection at customs, a traveler places 6 narcotic tablets in a bottle containing 9 vitamin tablets that are similar in
Olenka [21]
The probability is 0.3, or 30%.

These are not independent events; one pill being chosen will affect the probability after that, as the pill will not be replaced before selecting the next one.

The probability of getting exactly 1 narcotic pill is given by:
(6/15)(9/14)(8/13) = 432/2730.  It does not matter what order the narcotic pill is in, the overall product will be the same.

The probability of getting exactly 2 narcotic pills is given by:
(6/15)(5/14)(9/13) = 270/2730.  Again, the order these are found in does not matter, as it is multiplication and will not change the product.

The probability of all 3 pills being narcotics is given by:
(6/15)(5/14)(4/13) = 120/2730.

Adding these three possibilities together, we have 822/2730 = 0.30.
8 0
3 years ago
Read 2 more answers
−5y+8x=−18<br> 5y+2x=58 <br> Solve the system of equations.<br> ​
kvasek [131]

Answer:

1:   −5y+8x=−18  

Slope = 3.200/2.000 = 1.600

 x-intercept = -18/8 = -9/4 = -2.25000

 y-intercept = 18/5 = 3.60000

2:   Slope = -0.800/2.000 = -0.400

 x-intercept = 58/2 = 29

 y-intercept = 58/5 = 11.60000

Step-by-step explanation:

1: Step  1  :

Equation of a Straight Line

1.1     Solve   -5y+8x+18  = 0

Tiger recognizes that we have here an equation of a straight line. Such an equation is usually written y=mx+b ("y=mx+c" in the UK).

"y=mx+b" is the formula of a straight line drawn on Cartesian coordinate system in which "y" is the vertical axis and "x" the horizontal axis.

In this formula :

y tells us how far up the line goes

x tells us how far along

m is the Slope or Gradient i.e. how steep the line is

b is the Y-intercept i.e. where the line crosses the Y axis

The X and Y intercepts and the Slope are called the line properties. We shall now graph the line  -5y+8x+18  = 0 and calculate its properties

Graph of a Straight Line :

 

 

Calculate the Y-Intercept :

Notice that when x = 0 the value of y is 18/5 so this line "cuts" the y axis at y= 3.60000

 y-intercept = 18/5  =  3.60000  

Calculate the X-Intercept :

When y = 0 the value of x is -9/4 Our line therefore "cuts" the x axis at x=-2.25000

 x-intercept = -18/8 = -9/4  = -2.25000  

Calculate the Slope :

Slope is defined as the change in y divided by the change in x. We note that for x=0, the value of y is 3.600 and for x=2.000, the value of y is 6.800. So, for a change of 2.000 in x (The change in x is sometimes referred to as "RUN") we get a change of 6.800 - 3.600 = 3.200 in y. (The change in y is sometimes referred to as "RISE" and the Slope is m = RISE / RUN)

2: Same thing

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Which statements are true regarding the diagram?
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x=18 the angles are 36 and 54


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