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2 years ago

A fan is marked up 40% on the original price. The original price was $20. What is the new price of the fan before sales tax?

Mathematics

1 answer:

JulsSmile [24]2 years ago

8 0

Answer:

$28

Step-by-step explanation:

40% of 20 is 8

20 + 8 = 28

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Evaluate the Riemann sum for f(x) = 3 - 1/2 times x between 2 and 14 where the endpoints are included with six subintervals taki

Digiron [165]

Answer:

-6

Step-by-step explanation:

Given that :

we are to evaluate the Riemann sum for $f(x) = 3 - \dfrac{1}{2}x$ from 2 ≤ x ≤ 14

where the endpoints are included with six subintervals, taking the sample points to be the left endpoints.

The Riemann sum can be computed as follows:

$L_6 = \int ^{14}_{2}3- \dfrac{1}{2}x \dx = \lim_{n \to \infty} \sum \limits ^6 _{i=1} \ f (x_i -1) \Delta x$

where:

$\Delta x = \dfrac{b-a}{a}$

a = 2

b =14

n = 6

∴

$\Delta x = \dfrac{14-2}{6}$

$\Delta x = \dfrac{12}{6}$

$\Delta x =2$

Hence;

$x_0 = 2 \\ \\ x_1 = 2+2 =4\\ \\ x_2 = 2 + 2(2) \\ \\ x_i = 2 + 2i$

Here, we are using left end-points, then:

$x_i-1 = 2+ 2(i-1)$

Replacing it into Riemann equation;

$L_6 = \lim_{n \to \infty} \sum \imits ^{6}_{i=1} \begin {pmatrix}3 - \dfrac{1}{2} \begin {pmatrix} 2+2 (i-1) \end {pmatrix} \end {pmatrix}2$

$L_6 = \lim_{n \to \infty} \sum \imits ^{6}_{i=1} 6 - (2+2(i-1))$

$L_6 = \lim_{n \to \infty} \sum \imits ^{6}_{i=1} 6 - (2+2i-2)$

$L_6 = \lim_{n \to \infty} \sum \imits ^{6}_{i=1} 6 -2i$

$L_6 = \lim_{n \to \infty} \sum \imits ^{6}_{i=1} 6 - \lim_{n \to \infty} \sum \imits ^{6}_{i=1} 2i$

$L_6 = \lim_{n \to \infty} \sum \imits ^{6}_{i=1} 6 - 2 \lim_{n \to \infty} \sum \imits ^{6}_{i=1} i$

Estimating the integrals, we have :

$= 6n - 2 ( \dfrac{n(n-1)}{2})$

= 6n - n(n+1)

replacing thevalue of n = 6 (i.e the sub interval number), we have:

= 6(6) - 6(6+1)

= 36 - 36 -6

= -6

5 0

2 years ago

What is the probability that Ryan is not chosen today

Orlov [11]

Where is the pic...?

8 0

2 years ago

Enlarge the triangle by scale factor of -1/3

Bess [88]

The attached image represents the triangle after it has been enlarged

<h3>How to enlarge the triangle?</h3>

The given parameters are:

Scale factor, k = -1/3
Center, (a,b) = (-1,2)

From the graph, the coordinates of the triangle are:

A = (-4,2)

B = (-4,-4)

C = (-1,-4)

The rule of dilation is calculated using:

$(x,y) \to (k(x - a) + a, k(y - b) + b)$

So, we have:

$A' = (-\frac 13(-4 +1) - 1, -\frac 13(2 - 2) + 2)$

A' = (0, 2)

$B' = (-\frac 13(-4 +1) - 1, -\frac 13(-4 - 2) + 2)$

B' = (0, 4)

$C' = (-\frac 13(-1 +1) - 1, -\frac 13(-4 - 2) + 2)$

C' = (-1, 4)

See attachment for the image of the triangle, after it has been enlarged