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2 years ago

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A taxi charges a flat rate of $3.00 plus $1.50 per mile. If Xander has $45.00, which inequality represents m, the distances in m

iles he can travel in the taxi? m less-than-or-equal-to 10 m greater-than-or-equal-to 10 m less-than-or-equal-to 28 m greater-than-or-equal-to 28

2 answers:

son4ous [18]2 years ago

7 0

Answer:

m less-than-or-equal-to 28

Step-by-step explanation:

Xander's charge for m miles will be (3 +1.50m). He wants this to be no more than $45, so ...

3 +1.50m ≤ 45

1.50m ≤ 42 . . . . . . subtract 3

m ≤ 28 . . . . . . . . . .divide by 1.5

hammer [34]2 years ago

4 0

Answer: M is less than or equal to 28 or C

Step-by-step explanation:

GOT RIGHT ON E D G

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A financial advisor tells you that you can make your child a millionaire if you just start saving early. You decide to put an eq

Blababa [14]

Answer:

$12159 per year.

Step-by-step explanation:

If I invest $x each year at the simple interest of 7.5%, then the first $x will grow for 35 years, the second $x will grow for 34 years and so on.

So, the total amount that will grow after 35 years by investing $x at the start of each year at the rate of 7.5% simple interest will be given by

$x( 1 + \frac{35 \times 7.5}{100}) + x( 1 + \frac{34 \times 7.5}{100}) + x( 1 + \frac{33 \times 7.5}{100}) + ......... + x( 1 + \frac{1 \times 7.5}{100})$

= $35x + \frac{x \times 7.5}{100} [35 + 34 + 33 + ......... + 1]$

= $35x + \frac{x \times 7.5}{100} [\frac{1}{2} (35) (35 + 1)]$

{Since sum of n natural numbers is given by $\frac{1}{2} (n)(n + 1)$ }

= 35x + 47.25x

= 82.25x

Now, given that the final amount will be i million dollars = $1000000

So, 82.25x = 1000000

⇒ x = $12,158. 05 ≈ $12159

Therefore. I have to invest $12159 per year. (Answer)

5 0

2 years ago

Find the smallest relation containing the relation {(1, 2), (1, 4), (3, 3), (4, 1)} that is:

professor190 [17]

Answer:

Remember, if B is a set, R is a relation in B and a is related with b (aRb or (a,b))

1. R is reflexive if for each element a∈B, aRa.

2. R is symmetric if satisfies that if aRb then bRa.

3. R is transitive if satisfies that if aRb and bRc then aRc.

Then, our set B is $\{1,2,3,4\}$ .

a) We need to find a relation R reflexive and transitive that contain the relation $R1=\{(1, 2), (1, 4), (3, 3), (4, 1)\}$

Then, we need:

1. That 1R1, 2R2, 3R3, 4R4 to the relation be reflexive and,

2. Observe that

1R4 and 4R1, then 1 must be related with itself.
4R1 and 1R4, then 4 must be related with itself.
4R1 and 1R2, then 4 must be related with 2.

Therefore $\{(1,1),(2,2),(3,3),(4,4),(1,2),(1,4),(4,1),(4,2)\}$ is the smallest relation containing the relation R1.

b) We need a new relation symmetric and transitive, then

since 1R2, then 2 must be related with 1.
since 1R4, 4 must be related with 1.

and the analysis for be transitive is the same that we did in a).

Observe that

1R2 and 2R1, then 1 must be related with itself.
4R1 and 1R4, then 4 must be related with itself.
2R1 and 1R4, then 2 must be related with 4.
4R1 and 1R2, then 4 must be related with 2.
2R4 and 4R2, then 2 must be related with itself

Therefore, the smallest relation containing R1 that is symmetric and transitive is

$\{(1,1),(2,2),(3,3),(4,4),(1,2),(1,4),(2,1),(2,4),(3,3),(4,1),(4,2),(4,4)\}$

c) We need a new relation reflexive, symmetric and transitive containing R1.

For be reflexive

1 must be related with 1,

2 must be related with 2,

3 must be related with 3,

4 must be related with 4

For be symmetric

since 1R2, 2 must be related with 1,
since 1R4, 4 must be related with 1.

For be transitive

Since 4R1 and 1R2, 4 must be related with 2,
since 2R1 and 1R4, 2 must be related with 4.

Then, the smallest relation reflexive, symmetric and transitive containing R1 is

$\{(1,1),(2,2),(3,3),(4,4),(1,2),(1,4),(2,1),(2,4),(3,3),(4,1),(4,2),(4,4)\}$

5 0

1 year ago

A ramp with a constant incline is made to connect a driveway to a front door. At a point 4 feet from the driveway, the height of

katen-ka-za [31]

So, we're finding ratios first okay, for every 4ft:12in and 6ft:18in so for every one foot there is 3 inches which is your rate of incline 1:3 or every one foot there are 3 inches of incline hope this helped you have an amazing day

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2 years ago

Use Simpson's Rule with n = 10 to estimate the arc length of the curve. Compare your answer with the value of the integral produ

SOVA2 [1]

$y=\ln(6+x^3)\implies y'=\dfrac{3x^2}{6+x^3}$

The arc length of the curve is

$\displaystyle\int_0^5\sqrt{1+\frac{9x^4}{(6+x^3)^2}}\,\mathrm dx$

which has a value of about 5.99086.

Let $f(x)=\sqrt{1+\frac{9x^4}{(6+x^3)^2}}$ . Split up the interval of integration into 10 subintervals,

[0, 1/2], [1/2, 1], [1, 3/2], ..., [9/2, 5]

The left and right endpoints are given respectively by the sequences,

$\ell_i=\dfrac{i-1}2$

$r_i=\dfrac i2$

with $1\le i\le10$ .

These subintervals have midpoints given by

$m_i=\dfrac{\ell_i+r_i}2=\dfrac{2i-1}4$

Over each subinterval, we approximate $f(x)$ with the quadratic polynomial

$p_i(x)=f(\ell_i)\dfrac{(x-m_i)(x-r_i)}{(\ell_i-m_i)(\ell_i-r_i)}+f(m_i)\dfrac{(x-\ell_i)(x-r_i)}{(m_i-\ell_i)(m_i-r_i)}+f(r_i)\dfrac{(x-\ell_i)(x-m_i)}{(r_i-\ell_i)(r_i-m_i)}$

so that the integral we want to find can be estimated as

$\displaystyle\sum_{i=1}^{10}\int_{\ell_i}^{r_i}p_i(x)\,\mathrm dx$

It turns out that

$\displaystyle\int_{\ell_i}^{r_i}p_i(x)\,\mathrm dx=\frac{f(\ell_i)+4f(m_i)+f(r_i)}6$

so that the arc length is approximately

$\displaystyle\sum_{i=1}^{10}\frac{f(\ell_i)+4f(m_i)+f(r_i)}6\approx5.99086$

5 0

2 years ago

The equation y=−0.0088x2+0.79x+15 models the speed x (in miles per hour) and average gas mileage y (in miles per gallon) for a v

rewona [7]

Answer: 30.72 miles per gallon

To find <span>best approximate for the average gas mileage at a speed of 60 miles per hour you need to replace the variable x with 60. The calculation would be:

</span><span> y=−0.0088x2+0.79x+15
y= -31.68 +47.4 + 15
y= 30.72
</span>

5 0

2 years ago

Read 2 more answers