A table measures 3.6 feet long. How long does the table measure in inches and in yards?

147 is 3/2 of an original amount. What is the original amount

Dovator [93]

Answer:

98

Step-by-step explanation:

147/3=49x2=98

8 0

3 years ago

PLEASE HELP PICTURE IS SHOWN

marshall27 [118]

AAS, HA
Hope this helps!

3 0

3 years ago

Write the equation of the quadratic function that passes through the points (-1, 1), (1, 5), and (2,10).

Serjik [45]

Answer:

$\displaystyle f(x)=x^2+2x+2$

Step-by-step explanation:

System Of Linear Equations

In this problem, we'll need to solve a 3x3 system of linear equations because we have three unknowns and three conditions.

We are required to find the equation of the quadratic function that passes through the points (-1, 1), (1, 5), and (2,10)

The general quadratic function can be written as

$\displaystyle f(x)=ax^2+bx+c$

We need to find the values of a,b, and c. Let's use the first condition, i.e. f(-1)=1

$\displaystyle f(-1)=a(-1)^2+b(-1)+c$

$\displaystyle f(-1)=a-b+c$

$\displaystyle a-b+c=1.....[eq\ 1]$

Now we use the second condition f(1)=5

$\displaystyle f(1)=a(1)^2+b(1)+c$

$\displaystyle f(1)=a+b+c$

$\displaystyle a+b+c=5.......[eq\ 2]$

Finally, we use the third condition f(2)=10

$\displaystyle f(2)=a(2)^2+b(2)+c$

$\displaystyle f(2)=4a+2b+c$

$\displaystyle 4a+2b+c=10....[eq\ 3]$

We put together eq 1, eq 2, and eq 3 to form the system

$\displaystyle \left\{\begin{matrix}a-b+c=1\\ a+b+c=5\\ 4a+2b+c=10\end{matrix}\right.$

Adding the first two equations we have

$\displaystyle 2a+2c=6$

$\displaystyle a+c=3$

And also

$\displaystyle b=2$

Using the above equation and the value of b in the third equation, we have

$\displaystyle \left\{\begin{matrix}a+c=3\\ 4a+c=6\end{matrix}\right.$

Subtracting the first equation from the second

$\displaystyle 3a=3$

$\displaystyle a=1$

And therefore

$\displaystyle c=2$

Now we have all the values, the quadratic function is

$\displaystyle \boxed{f(x)=x^2+2x+2}$

6 0

3 years ago

A spray irrigation system waters a section of a farmer’s field. If the water shoots a distance of 85 feet, what is the area that

gtnhenbr [62]

Answer:

3,781

Step-by-step explanation:

To solve this problem, we will find the area of the whole circle and use that to find teh area of the 60º section.

First, recognize the formula for the area of a circle:

A = 3.14 $r^{2}$

In this scenario, the radius (r) is 85 feet:

A = 3.14(85 $)^{2}$

A circle is 360º and we only require the area of 60º. 360º / 60º = 6 so we will divide by 6:

A = $\frac{3.14(85)^{2} }{6}$

Finally, we will simplify and round:

A = 3,781

7 0

2 years ago

An optical inspection system is used to distinguish among different part types. The probability of a correct classification of a

dsp73

Answer:

P(X=0)=0.000008

P(X=1)=0.00176

P(X=2)=0.057624

P(X=3)=0.941192

Step-by-step explanation:

Probability of correct classification = p = 0.98

Probability of incorrect classification = q = 1 - p = 0.02

The probability of success and failure is the same for all the trials. The trials are independent of each other and the number of trials is fixed i.e. n = 3.

This satisfies all the conditions of a Binomial Experiment. So we can use Binomial experiment to model the probability mass function.

The general formula of a binomial probability is:

$P(X=x)=^{n}C_{x}(p)^{x}q^{n-x}$

Here x denote the number of successes, which can be {0, 1, 2, 3}. So we need to evaluate the above equation for each value of x to determine the probability Mass function of X, as shown below:

$P(X=0)=^{3}C_{0}(0.98)^{0}(0.02)^{3-0}=0.000008\\\\ P(X=1)=^{3}C_{1}(0.98)^{1}(0.02)^{3-1}=0.001176\\\\ P(X=2)=^{3}C_{2}(0.98)^{2}(0.02)^{3-2}=0.057624\\\\ P(X=3)=^{3}C_{3}(0.98)^{3}(0.02)^{3-3}=0.941192$

7 0

2 years ago