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What is the value of x? 2.5x=35 Answer ASAP

Bumek [7]

Answer:

14

Step-by-step explanation:

x=35÷2.5 will devide 35 by 2.5 to get x

6 0

3 years ago

Read 2 more answers

A car traveled at a constant speed. The graph shows how far the car traveled, in miles, during a given amount of time, in hours.

snow_tiger [21]

Answer:

Step-by-step explanation:

A car traveled at a constant speed as shown in the graph.

Distance traveled is on the y-axis and duration of travel on the x-axis.

Point A(3.5, 210) shows,

Distance traveled = 210 miles

Time to travel = 3.5 hours

So the point (3.5, 210) shows the distance traveled by the car in 3.5 hours is 210 miles.

Slope of the line = speed of the car = $\frac{\text{Distance traveled}}{\text{Time}}$

= $\frac{210}{3.5}$

= 60 mph

Now we will find the speed of the car at another point B(1, 60).

If the speed of car is same as the point B as of point A, point B will lie on the graph.

Speed of the car at B(1, 60) = $\frac{\text{Distance traveled}}{\text{Time}}$

= $\frac{60}{1}$

= 60 mph

Hence, we can say that point B(1, 60) lies on the graph.

8 0

3 years ago

The line parellel to 2x+y=5 and passing through (5,4) has equation

mrs_skeptik [129]

Answer:

y=-2x+14

Step-by-step explanation:

If we are looking for a line parallel to 2x+y=5.

Then we are looking for an equation with the same slope as the equation 2x+y=5.

To obtain the slope of equaiton 2x+y=5 I will put it in slope-intercept form.

Luckily there is only one step which is to subtract 2x on both sides.

y=-2x+5

The slope of this line is -2

The slope of parallel line will also be -2.

So we know our equation is in the form y=-2x+b

To find b we will just use the point (x,y)=(5,4) we know is on the line.

Plug in and solve for b.

4=-2(5)+b

4=-10+b

14=b

So the equation that is parallel to 2x+y=5 and goes through (5,4) is y=-2x+14

4 0

3 years ago

New York City is the most expensive city in the United States for lodging. The room rate is $204 per night (USA Today, April 30,

Sever21 [200]

Answer:

a. 0.35197 or 35.20%; b. 0.1230 or 12.30%; c. 0.48784 or 48.78%; d. $250.20 or more.

Step-by-step explanation:

In general, we can solve this question using the <em>standard normal distribution</em>, whose values are valid for any <em>normally distributed data</em>, provided that they are previously transformed to <em>z-scores</em>. After having these z-scores, we can consult the table to finally obtain the probability associated with that value. Likewise, for a given probability, we can find, using the same table, the z-score associated to solve the value <em>x</em> of the equation for the formula of z-scores.

We know that the room rates are <em>normally distributed</em> with a <em>population mean</em> and a <em>population standard deviation</em> of (according to the cited source in the question):

$\\ \mu = \$204$ <em>(population mean)</em>

$\\ \sigma = \$55$ <em>(population standard deviation)</em>

A <em>z-score</em> is the needed value to consult the <em>standard normal table. </em>It is a transformation of the data so that we can consult this standard normal table to obtain the probabilities associated. The standard normal table has a mean of 0 and a standard deviation of 1.

$\\ z_{score}=\frac{x-\mu}{\sigma}$

After having all this information, we can proceed as follows:

<h3>What is the probability that a hotel room costs $225 or more per night? </h3>

1. We need to calculate the z-score associated with x = $225.

$\\ z_{score}=\frac{225-204}{55}$

$\\ z_{score}=0.381818$

$\\ z_{score}=0.38$

We rounded the value to two decimals since the <em>cumulative standard normal table </em>(values for cumulative probabilities from negative infinity to the value x) to consult only have until two decimals for z values.

Then

2. For a z = 0.38, the corresponding probability is P(z<0.38) = 0.64803. But the question is asking for values greater than this value, then:

$\\ P(z>038) = 1 - P(z$ (that is, the complement of the area)

$\\ P(z>038) = 1 - 0.64803$

$\\ P(z>038) = 0.35197$

So, the probability that a hotel room costs $225 or more per night is P(x>$225) = 0.35197 or 35.20%, approximately.

<h3>What is the probability that a hotel room costs less than $140 per night?</h3>

We follow a similar procedure as before, so:

$\\ z_{score}=\frac{x-\mu}{\sigma}$

$\\ z_{score}=\frac{140-204}{55}$

$\\ z_{score}= -1.163636 \approx -1.16$

This value is below the mean (it has a negative sign). The standard normal tables does not have these values. However, we can find them subtracting the value of the probability obtained for z = 1.16 from 1, since the symmetry for normal distribution permits it. Then, the probability associated with z = -1.16 is:

$\\ P(z$

Then, the probability that a hotel room costs less than $140 per night is P(x<$140) = 0.1230 or 12.30%.

<h3>What is the probability that a hotel room costs between $200 and $300 per night?</h3>

$\\ z_{score}=\frac{x-\mu}{\sigma}$

<em>The z-score and probability for x = $200:</em>

$\\ z_{score}=\frac{200-204}{55}$

$\\ z_{score}= -0.072727 \approx -0.07$

$\\ P(z$

<em>The z-score and probability for x = $300:</em>

$\\ z_{score}=\frac{300-204}{55}$

$\\ z_{score}=1.745454$

$\\ P(z$

Then, the probability that a hotel room costs between $200 and $300 per night is 0.48784 or 48.78%.

<h3>What is the cost of the most expensive 20% of hotel rooms in New York City?</h3>

A way to solve this is as follows: we need to consult, using the cumulative standard normal table, the value for z such as the probability is 80%. This value is, approximately, z = 0.84. Then, solving the next equation for <em>x:</em>

$\\ z_{score}=\frac{x-\mu}{\sigma}$

$\\ 0.84=\frac{x-204}{55}$