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marta [7]
3 years ago
13

Convert 4 3/4 to an improper fraction:

Mathematics
1 answer:
RoseWind [281]3 years ago
4 0

4 3/4= 19/4=4.75 its a terminating decimal

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GE = 3x + 12 and GH = 72. Find the value of x.
Furkat [3]

Answer: x=20

Step-by-step explanation:

5 0
3 years ago
16 - x = -2 solve for x
poizon [28]

Answer:

16 - x = -2

16 + 2 = x

x = 18

hope it helps!

4 0
2 years ago
The circumference of a sphere was measured to be 80 cm with a possible error of 0.5 cm. A) Use differentials to estimate the max
siniylev [52]

Answer:

A) The maximum error in the calculated surface area: 25cm^2

Relative error: 0.013

B) The maximum error in the calculated volume: 162cm^2

Relative error: 0.019

Step-by-step explanation:

A) The formula for the surface area is:

A=4\pi r^2

The measured value is the circumference which is equal to:

C=2\pi r

then the radius is:

r=\frac{C}{2\pi}

Substituting in the formula of the surface:

A=4\pi(\frac{C}{2\pi})^2\\A=4\pi(\frac{C^2}{4\pi^2})\\A=\frac{C^2}{\pi}

Using the formula to calculate the error:

dy=f'(x)dx

Where x is the variable measured and y is a function of x(y=f(x)).

dA=f'(C)dC\\dA=\frac{2C^{(2-1)}}{\pi}dC\\dA=\frac{2C}{\pi}dC

We have C=80cm and dC=0.5cm

dA=\frac{2C}{\pi}dC\\dA=\frac{2(80)}{\pi}(0.5)\\dA=\frac{160}{\pi}(0.5)\\dA=50.9296(0.5)\\dA=25.4648\approx25cm^2

The relative error is the maximum error divide by the total area. The total area is: A=\frac{C^2}{\pi}=\frac{(80)^2}{\pi}=\frac{6400}{\pi}=2037.1833cm^2

\frac{dA}{A}=\frac{25.4648}{2037.1833} =0.0125\approx0.013

B) The formula for the volume is:

V=\frac{4}{3} \pi r^3

Using r=\frac{C}{2\pi}

V=\frac{4}{3} \pi r^3\\V=\frac{4}{3} \pi (\frac{C}{2\pi})^3\\V=\frac{4}{3} \pi (\frac{C^3}{8\pi^3})\\V=\frac{1}{3}(\frac{C^3}{2\pi^2})\\V=\frac{C^3}{6\pi^2}

The maximum error is:

dV=\frac{3C^{3-1}}{6\pi^2}dC\\dV=\frac{C^{2}}{2\pi^2}dC\\dV=\frac{(80)^{2}}{2\pi^2}(0.5)\\dV=\frac{6400}{2\pi^2}(0.5)\\dV=\frac{6400}{2\pi^2}(0.5)\\dV=(324.2278)(0.5)\\dV=162.1139\approx162cm^2

The calculated volume is:

V=\frac{C^3}{6\pi^2}\\V=\frac{(80)^3}{6\pi^2}\\V=\frac{512000}{6\pi^2}\\V=8646.0743

The relative error is:

\frac{dV}{V}=\frac{162.1139}{8646.0743}=0.0188\approx0.019

3 0
3 years ago
Insect Weights Consider a dataset giving the adult weight of species of insects. Most species of insects weigh less than 5 grams
Ann [662]

Answer:

Step-by-step explanation:

71 grams would definitely be an outlier on the high side, whereas "most" species would weigh much less.  Thus, the graph of this distribution of weights would be skewed towards the lower side, that is, to the left.

8 0
3 years ago
Which parent function is represented by the graph?
sattari [20]

Answer:

D. The linear parent function

Step-by-step explanation:

Linear functions are always characterized by a straight line graph with or without an intercept on the vertical or horizontal axis. A linear function usually has an independent variable and a dependent variable. The independent variable is commonly depicted as x while the dependent variable is y.

Thus a linear equation is an equation of the type y=ax where a is a constant term. The equation of a straight line graph his y=mx +c, where;

m= gradient of the straight line graph

x= the independent variable

y= the dependent variable

c= the vertical intercept

3 0
3 years ago
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