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3 years ago

Determine whether the statement is true or false, and explain why.

Mathematics

1 answer:

Zielflug [23.3K]3 years ago

4 0

Answer:

False

Step-by-step explanation:

In this case, i woudnt reccomend to use integration by parts, becuase you are not simplifying the expression by doing an integration and a derivation. It is not easy to integrate 1/x³+1, and if you derivate it, then a natural logarithm would appear, and the integral wont be easier after this parts step.

It is a better idea to use integration by substitution. Note that if you replace x³+1 by a variable y, we have that dy = 3x² dx. We can easily make a 3xdx appear in the integral by multiplying and dividing by 3, solving the integral easily:

$\int\limits_0^1 x^2/x^3+1 \, dx = 1/3 * \int\limits_1^2 du/u = (ln(2) - ln(1) )/3$

(Note that, if x ranges from 0 to 1, then u = x³+1 ranges from 0³+1 = 1 to 1³+1 = 2)

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The selling price of an item is $720. It is marked down by 30%, but this sale price is still marked up from the cost of $420.

Anna35 [415]

The markup cost is $84 if the selling price of an item is $720. It is marked down by 30%, but this sale price is still marked up from the cost of $420.

<h3>What is markup price?</h3>

Markup pricing is the practice in which the price of products or commodity is determined by taking all the goods together and adds a fraction as a markup.

We have:

The selling price of an item is $720. It is marked down by 30%

$\rm = 720\times \dfrac{30}{100}$

Markdown = 216

Now subtract it from the selling price:

= 720-216

Sale price = 504

Now,

= 504-420

Markup cost = $84

Thus, the markup cost is $84 if the selling price of an item is $720. It is marked down by 30%, but this sale price is still marked up from the cost of $420.

Learn more about the markup price here:

brainly.com/question/1099507

#SPJ1

6 0

2 years ago

A 95 percent confidence interval for the mean of a population is to be constructedand must be accurate within 0.3 unit. A prelim

jarptica [38.1K]

Answer:

B. 359

Step-by-step explanation:

Given that:

The margin of error (e) must be within 0.3 unit, The standard deviation (σ) = 2.9 and the the confidence level = 95% = 0.95

α = 1 =0.95 = 0.05

$\frac{\alpha}{2}=\frac{0.05}{2}=0.025$

The z score of 0.025 corresponds to the z score of 0.0475 (0.5 - 0.025) which can be gotten from the normal probability table.

Therefore: $z_\frac{\alpha}{2}= z_{0.025}=1.96$

The formula for the margin of error is given by:

$e=z_{0.025}\frac{\sigma}{\sqrt{n} } \\Substituting:\\0.3=1.96*\frac{2.9}{\sqrt{n} } \\\sqrt{n}=\frac{1.96*2.9}{0.3}\\\sqrt{n} =18.95\\ n=18.95^2=359$

Therefore the smallest sample size (n) is 359

5 0

3 years ago

The probability of picking a quarter from a jar of coins is 0.125. If Cindy has 280 coins in the jar, how many quarters are in t

shusha [124]

Answer:

Step-by-step explanation:

8 0

3 years ago

Find the rate of change, or slope, in the following equation:

Elena-2011 [213]

The answer is -4.

Step-by-step explanation:

the number before the x is how u can tell

3 0

3 years ago

Read 2 more answers

Use the graph of f at the right to complete each of the parts (a) through (h)

Maru [420]

Answers:

a. The domain of f is ]-∞ , ∞[

b. The range of f is [-4 , ∞[

c. f(1) = 5

d. The vales of x for which f(x) is -3 are 7 and 9

e. The points at which the graph crosses the x-axis are (6,0) and (10,0)

f. The point where the graph of f crosses the y-axis is (0,5)

g. The values of x for which f(x) < 0 are ]6 , 10[

h. f(-7) is positive

Explanation:

Part a:

The domain of the function refers to all the possible x-values that can be used as an input for this function.

Taking a look at the graph, we can see that the graph extends endlessly from both ends of the x-axis. This means that all x-values can be used as a domain for the function. In other words, the domain of the function is all the real numbers.

In interval notation, this is written as:

Domain = ]-∞ , ∞[

Part b:

The range of the function refers to all the possible y-values that can be used as an output for the function.

From the graph, we can note that the function extends endlessly in the direction of the positive y-axis while it stops at a value of -4 in the direction of the negative y-axis.

This means that the range of the function starts from -4 (included) and extends to positive infinity.

In interval notation, this is written as:

R = [-4 , ∞[

Part c:

f(1) means that we are looking for the output (the value of y) for which the input (the value of x) is 1.

From the graph, we start by searching for x=1 (first square edge after the origin) and then move vertically till we intersect the graph.

Doing this, we will find that the value of y at x=1 is 5

Therefore:

f(1) = 5

Part d:

f(x) = -3 means that the output value (the value of the y) for the certain input (value of x) is -3

To get the value of x, we go y=-3 and move horizontally till we intersect the graph.

Doing this, we will find that the value of y is -3 at x = 7 and x = 9

Part e:

The points where the graph crosses the x-axis are the points that have y-value equal to 0

Checking the graph, we can note that the function crosses the x-axis at two points which are (6,0) and (10,0)

Part f:

The point where the graph crosses the y-axis is the point that has x-value equal to 0

Checking the graph, we can note that the function crosses the y-axis at only one point which is (0,5)

Part g:

f(x) < 0 means that the output of the function (the y-value) is less than 0 (0 is not included)

Taking a look at the graph, we can note that the function has negative output on the interval from 6 (excluded) to 10 (excluded)

In interval notation, this is written as ]6 , 10[

Part h:

f(-7) means the output of the function (the y-value) at input (x-vale) equal to -7

From the graph, we can note that the function has a constant value of 5 starting from x=5 till -∞

This means that, at x=-7, the value of y is 5 which is a positive value

Hope this helps :)

6 0

4 years ago

Read 2 more answers