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2 years ago

10

Item 17 The cities Portland, Oregon; Tacoma, Washington; and Seattle, Washington, in respective order, lie approximately in a st

raight line. The distance from Portland to Tacoma is 120 miles. The distance from Portland to Seattle is 145 miles. Find the distance from Tacoma to Seattle.

1 answer:

muminat2 years ago

3 0

Answer:

Distance: 25 miles

Step-by-step explanation:

we have distances between cities as follows:

From Portland to Tacoma: 120 miles

from Portland to Seattle: 145 miles

120+x=145 ⇒ x = 145 - 120 = 25 miles

from Tacoma to Seattle : 25 miles (according graph)

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A cube with a side 1 m long has been cut into cubes of a side 1 dm each. all small cubes have been put one on top of the other,

Ivenika [448]

First, we have to find how many small cubes formed by the large cube.
To find the number of small cubes, we should calculate the volume of each large cube and small cube. Equalize the volume units to dm³

Dimension of large cube
s = 1 m
s = 10 dm

Volume of large cube
v = s³
v = 10³
v = 1,000 dm³

Dimension of small cube
s = 1 dm

Volume of small cube
v = s³
v = 1³
v = 1 dm³

Second, calculate the number of small cubes formed
n = volume of large cube / volume of small cube
n = 1,000 dm³ / 1 dm³
n = 1,000
There are 1,000 small cubes.

Third, calculate the height of the structure.
The structure is formed by 1,000 cubes. Each of them is 1 dm high.
The height of the structure is
h = 1 dm × 1,000
h = 1,000 dm
h = 100 m
The height of the structure is 1,000 dm or 100 m

8 0

2 years ago

Budget planners in two towns, Alphaville and Betaville, developed models to determine the budget surplus (in dollars) for a year

kramer

Answer:

(a) $-3x^2+150x-10000$

(b) $-\$16,863,760,000$

Step-by-step explanation:

Alphaville's Budget Surplus Model is $-2x^2+ 500x$

Betaville's Budget Surplus Model is $x^2- 100x + 10000.$

We want to determine the expression that shows how much greater Alphaville’s annual budget surplus is than Betaville’s for a particular amount of tax revenue.

To do this, we subtract Betaville's Model from Alphaville's model.

$-2x^2+ 500x-(x^2- 100x + 10000)\\$

Opening the brackets

$-2x^2+ 500x-x^2+100x - 10000\\$

Collect like terms and simplify

$-2x^2-x^2+100x + 500x- 10000\\=-3x^2+150x-10000$

The expression that shows how much greater Alphaville's Budget is:

$-3x^2+150x-10000$

(b) If the tax revenue that year in each town is $75,000

We want to evaluate the expression derived above when the tax revenue that year in each town is $75,000 i.e.at x=75000

$-3x^2+150x-10000\\=-3(75000)^2+150(75000)-10000\\=-\$16,863,760,000$

3 0

2 years ago

If r is the midpoint of qs rs=2x-4, st= 4x-1 and rt = 8x-43 find qs

sammy [17]

Answer:

$QS=68\ units$

Step-by-step explanation:

step 1

Find the value of x

we know that

r is the midpoint of qs

so

QR=RS

QS=QR+RS------> QS=2RS -----> equation A

RT=RS+ST ----> equation B

see the attached figure to better understand the problem

Substitute the given values in the equation B and solve for x

$8x-43=(2x-4)+(4x-1)$

$8x-43=6x-5$

$8x-6x=43-5$

$2x=38$

$x=19$

step 2

Find the value of RS

$RS=2x-4$

substitute the value of x

$RS=2(19)-4$

$RS=34\ units$

step 3

Find the value of QS

Remember equation A

QS=2RS

so

$QS=2(34)=68\ units$

6 0

2 years ago

Casey ran out of time while taking a multiple-choice test and plans to guess on the last 101010 questions. Each question has 555

Soloha48 [4]

Answer:

There is a 40.96% probability that he answers exactly 1 question correctly in the last 4 questions.

Step-by-step explanation:

For each question, there are only two possible outcomes. Either it is correct, or it is not. This means that we use the binomial probability distribution to solve this problem.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

In which is the number of different combinatios of x objects from a set of n elements, given by the following formula.

And p is the probability of X happening.

In this problem we have that:

There are four questions, so n = 4.

Each question has 5 options, one of which is correct. So

What is the probability that he answers exactly 1 question correctly in the last 4 questions?

This is

There is a 40.96% probability that he answers exactly 1 question correctly in the last 4 questions.

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2 years ago

Read 2 more answers

A transportation engineer uses the formula, R = 1600/15+127e, to determine the minimum radius of curvature (R) in meters, for a

Mashcka [7]

Answer:

The value is $e = 1.92$

Step-by-step explanation:

From the question we are told that

The formula for radius of curvature is $R = \frac{1600}{15} +127e$

The design speed of the roadway is $v = 40 \ km/hr$

The value of radius of curvature considered R = 350 m

From the equation given e is the superelevation rate

Now making the subject of the formula

$e = \frac{R}{127} - \frac{1600}{1905}$

At R= 350

$e = \frac{350 }{127} - \frac{1600}{1905}$

$e = 1.92$

5 0

2 years ago