Find the surface of the triangular prism

The price of a sweater was reduced from $20 to $12. By what percentage was the price of the sweater reduced

kirill [66]

Answer:

The price was decreased by 40%

Step-by-step explanation:

Take the original price and subtract the new price

20-12 = 8

Divide by the original price

8/20 = .4

Change to a percent

40 %

The price was decreased by 40%

4 0

3 years ago

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Evaluate 17 + 70/x when x = 14.

kipiarov [429]

Answer:

34.5

Step-by-step explanation:

17 + 70/x when x = 14.

substitute x for 14

17 + 70/4

17 + 17.5

34.5

5 0

3 years ago

3. The curve C with equation y=f(x) is such that, dy/dx = 3x^2 + 4x +k

Andreas93 [3]

a. Given that y = f(x) and f(0) = -2, by the fundamental theorem of calculus we have

$\displaystyle \frac{dy}{dx} = 3x^2 + 4x + k \implies y = f(0) + \int_0^x (3t^2+4t+k) \, dt$

Evaluate the integral to solve for y :

$\displaystyle y = -2 + \int_0^x (3t^2+4t+k) \, dt$

$\displaystyle y = -2 + (t^3+2t^2+kt)\bigg|_0^x$

$\displaystyle y = x^3+2x^2+kx - 2$

Use the other known value, f(2) = 18, to solve for k :

$18 = 2^3 + 2\times2^2+2k - 2 \implies \boxed{k = 2}$

Then the curve C has equation

$\boxed{y = x^3 + 2x^2 + 2x - 2}$

b. Any tangent to the curve C at a point (a, f(a)) has slope equal to the derivative of y at that point:

$\dfrac{dy}{dx}\bigg|_{x=a} = 3a^2 + 4a + 2$

The slope of the given tangent line $y=x-2$ is 1. Solve for a :

$3a^2 + 4a + 2 = 1 \implies 3a^2 + 4a + 1 = (3a+1)(a+1)=0 \implies a = -\dfrac13 \text{ or }a = -1$

so we know there exists a tangent to C with slope 1. When x = -1/3, we have y = f(-1/3) = -67/27; when x = -1, we have y = f(-1) = -3. This means the tangent line must meet C at either (-1/3, -67/27) or (-1, -3).

Decide which of these points is correct:

$x - 2 = x^3 + 2x^2 + 2x - 2 \implies x^3 + 2x^2 + x = x(x+1)^2=0 \implies x=0 \text{ or } x = -1$

So, the point of contact between the tangent line and C is (-1, -3).

7 0

2 years ago

Excel computes a two‑sample confidence interval for the difference in proportions just as well and as easily as Minitab and othe

True [87]

Answer:

See ecplanation below

Step-by-step explanation:

False.

On the Data analysis tool from excel we can conduct the following procedures:

Anova: Single Factor

Anova: Two factor with replication

Anova: Two factor without replication

Correlation

Covariance

Descriptive statistics

Exponential smoothing

F-test Two sample for Variances

Fourier analysis

Histogram

Moving Average

Random number generation

Rank and percentile

Regression

Sampling

t test: Paired two sample for means

t tes: Two sample assuming equal variances

t test: Two sample Assuming Unequal Variances

z test: Two sample for means

And as we can see we don't have an specific procedure just to obtain confidence interval for the difference of proportions. We need to remember that if we select a z test in excel, for example the output will contain the confidence associated to the parameter, but for this case is not too easy obtain a confidence interval for the difference of proportion like on a statistical software as (Minitab, R, SAS, etc) since all of these statistical softwares are elaborated in order to conduct all the possible statistical tests and confidence intervals for parameters of interest.

5 0

3 years ago

Montrell went to the store to purchase a bag of flamin' hot Cheetos. One bag of chips was $3.39 for 9 oz. What is the unit rate?

castortr0y [4]

Answer:

$0.37 per oz

Step-by-step explanation:

Unit rate

<u>9 oz costs $3.39 and 1 oz of chips cost: </u>

$3.39/9 = $0.37 per oz of chips

5 0

3 years ago

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