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4 years ago

How to calculate the volume of the prism

Mathematics

1 answer:

Elena L [17]4 years ago

6 0

The volume of a prism is found by : the area of the base which in this exercise is a rectangle • (times) the height.
Area of the base :
3•10=30 m^
The volume of the prism is :
30m^ • 7m = 210 in cubic metres

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Can someone help me with this

Andru [333]

Answer:

87, I'm pretty sure it's just 95-8. I might be wrong.

7 0

3 years ago

How many feet long is the fence ?

grandymaker [24]

Answer:

50 feet long

Step-by-step explanation:

Use the Pythagorean theorem to find the value of the missing side. The pythagoreon theorem only works with right triangles such as this one.

a²+b²=c²

Where a and b are length of legs (sides) of a triangle. And c is the length of the hypotenuse. The hypotenuse is the side across from the right angle.

We know by looking at the image posted in the question, that one leg of the triangle is 14 feet. And another leg is 48 feet. (Length of picnic area) (length of campground)

14²+48²=c²

Simplify

196+2304=2500

Find square root of 2500

√(2500)=50

So 14²+48²=50²

The missing side is 50 feet long. The fence is 50 feet long.

Attached is another example.

7 0

3 years ago

A store has been selling 100 Blu-ray disc players a week at $600 each. A market survey indicates that for each $40 rebate offere

Sav [38]

Answer:

The rebate should be $220

Step-by-step explanation:

Demand Curve

It's the relationship between price (P) and quantity (Q) demanded a certain product or service.

(a) We need to find the function that relates both magnitudes assuming a linear equation. The equation of a line can be found with the point-point formula:

$\displaystyle Q-Q_1=\frac{Q_2-Q_1}{P_2-P_1}(P-P_1)$

Two sets of data are given: 100 Blu-ray disc players are sold a week at $600 each. The ordered pair for this condition is (P,Q)=(600,100).

The other point comes from the market survey: The number of units sold will increase by 80 (100+80=180) when the price goes down $40 (600-40=560). The new point is (P,Q)=(560,180)

We set up the equation of the demand

$\displaystyle Q-100=\frac{180-100}{560-600}(P-560)$

Rearranging

$-40Q+4000=80P-44800$

$80P+40Q=48800$

Simplifying

$2P+Q=1120$

(b) The revenue function is Q times the price

$R=Q.P$

Solving the equation of the demand for P

$\displaystyle P=\frac{1120-Q}{2}$

Thus, the revenue is

$\displaystyle R=Q\cdot \frac{1120-Q}{2}$

$\displaystyle R=\frac{1120Q-Q^2}{2}$

$\displaystyle R'=\frac{1120-2Q}{2}=560-Q=0$

Solving

Q=560 units a week

For which the revenue is

$\displaystyle R=\frac{1120(560)-560^2}{2}$

$R=\$156,800$

And the price is

$\displaystyle P=\frac{1120-560}{2}=280$

$P=\$280$

The rebate should be $600-$280=$220

4 0

3 years ago

Consider this scenario: The population of a city increased steadily over a ten-year span. The following ordered pairs show the p

vova2212 [387]

Answer:

Regression function: $y=1986.406+0.0059x$

The function predicts that population will reach 14,000 in year 2068.

Step-by-step explanation:

We have to determine a function $y=b_0+b_1x_1$ by applying linear regression. The data we have is 5 pair of points which relates population to year.

According to the simple regression model (one independent variable), if we minimize the error between the model (the linear function) and the points given, the parameters are:

$b_0=\bar{y}+b_1\bar{x}\\\\b_1=\frac{\sum\limits^5_{i=1} {(x_i-\bar x)(y_i-\bar y)}}{\sum\limits^5_{i=1} {(x_i-\bar x)^2}}$

We start calculating the average of x and y

$\bar x=\frac{2500+2650+3000+3500+4200}{5}=\frac{15850}{5}=3170\\\\ \bar y=\frac{2001+2002+2004+2007+2011}{5}=\frac{10025}{5}=2005$

The sample covariance can be calculated as

$\sum\limits^5_{i=1} {(x_i-\bar x)(y_i-\bar y)}=(2500-3170)(2001-2005)+(2650-3170)(2002-2005)+(3000-3170)(2004-2005)+(3500-3170)(2007-2005)+(4200-3170)(2011-2005)\\\\\sum\limits^5_{i=1} {(x_i-\bar x)(y_i-\bar y)}=2680+1560+170+660+6180\\\\ \sum\limits^5_{i=1} {(x_i-\bar x)(y_i-\bar y)}=11250$

The variance of x can be calculated as

$\sum\limits^5_{i=1} {(x_i-\bar x)^2}=(2500-3170)^2+(2650-3170)^2+(3000-3170)^2+(3500-3170)^2+(4200-3170)^2\\\\\sum\limits^5_{i=1} {(x_i-\bar x)^2}=448900+270400+28900+108900+1060900\\\\\sum\limits^5_{i=1} {(x_i-\bar x)^2}=1918000$

Now we can calculate the parameters of the regression model

$b_1=\frac{\sum\limits^5_{i=1} {(x_i-\bar x)(y_i-\bar y)}}{\sum\limits^5_{i=1} {(x_i-\bar x)^2}}=\frac{11250}{1918000}=0.005865485 \\\\ b_0=\bar{y}+b_1\bar{x}=2005-0.005865485*3170=1986.406413$