Which numbers are 4 units from -2 on this number line?

Compare and contrast a square and parallelogram using a Venn diagram

Eva8 [605]

A square and a parallelogram both have 2 sets of parallel lines. A square has equal lengths for all four sides while a parallelogram doesn't. A parallelogram is a more broad idea because a parallelogram involves trapezoids, rectangles, and squares too.But a square is more specific.

8 0

3 years ago

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A guitar string is plucked at a distance of 0.6 centimeters above its resting position and then released, causing vibration. The

liubo4ka [24]

Answer:

The equation that represents the motion of the string is given by:

$y =Ae^{-kt}\cos(2\pi ft)$ .....[1] where t represents the time in second.

Given that: A = 0.6 cm (distance above its resting position) , k = 1.8(damping constant) and frequency(f) = 105 cycles per second.

Substitute the given values in [1] we get;

$y =0.6e^{-1.8t}\cos(2\pi 105t)$

or

$y =0.6e^{-1.8t}\cos(210\pi t)$

(a)

The trigonometric function that models the motion of the string is given by:

$y =0.6e^{-1.8t}\cos(210\pi t)$

(b)

Determine the amount of time t that it takes the string to be damped so that $-0.24\leq y \leq0.24$

Using graphing calculator for the equation

$y =0.6e^{-1.8x}\cos(210\pi x)$

let x = t (time in sec)

Graph as shown below in the attachment:

we get:

the amount of time t that it takes the string to be damped so that $-0.24\leq y \leq0.24$ is, 0.5 sec

4 0

3 years ago

Among 46- to 51-year-olds, 28% say they have called a talk show while under the influence of peer pressurepeer pressure. Supp

sasho [114]

Answer:

0.8997, 0.9999

Step-by-step explanation:

Given that among 46- to 51-year-olds, 28% say they have called a talk show while under the influence of peer pressure.

i.e. X no of people who say they have called a talk show while under the influence of peer pressure is binomial with p = 0.28

Each person is independent of the other and there are only two outcomes

n =7

a) the probability that at least one has not called a talk showcalled a talk show while under the influence of peer pressure

= $P(Y\geq 1)$ where Y is binomial with p = 0.72

= $1-(1-0.72)^7\\=0.9999$

b) the probability that at least one has called a talk showcalled a talk show while under the influence of peer pressurepeer pressurethe probability that at least one has not called a talk showcalled a talk show while under the influence of peer pressure

= $P(x\geq 1) =1-P(0)\\= 1-(1-0.28)^7\\=0.8997$

3 0

3 years ago

Solve the equation by graphing. If exact roots cannot be found, state the consecutive integers between which the roots are locat

eimsori [14]

Answer:

There are NO real roots for this equation. The only roots have imaginary parts and therefore cannot be represented on the real x-axis.

Step-by-step explanation:

We notice that the expression on the left of the equation is a quadratic with leading term $2x^2$ , which means that its graph is that of a parabola with branches going up.

Therefore, there can be three different situations:

1) if its vertex is ON the x axis, there would be one unique real solution (root) to the equation.

2) if its vertex is below the x-axis, the parabola's branches are forced to cross it at two locations, giving then two real solutions (roots) to the equation.

3) if its vertex is above the x-axis, it will have NO real solutions (roots) but only non-real ones.

So we proceed to examine the vertex's location, which is also a great way to decide on which set of points to use in order to plot its graph efficiently.

We recall that the x-position of the vertex for a quadratic function of the form $f(x)=ax^2+bx+c$ is given by the expression:

$x_v=\frac{-b}{2a}$

Since in our case $a=2$ and $b=-3$ , we get that the x-position of the vertex is:

$x_v=\frac{-b}{2a}\\x_v=\frac{-(-3)}{2(2)}\\x_v=\frac{3}{4}$

Now we can find the y-value of the vertex by evaluating this quadratic expression for x = 3/4:

$y_v=f(\frac{3}{4})=2( \frac{3}{4})^2-3(\frac{3}{4})+4\\f(\frac{3}{4})=2( \frac{9}{16})-\frac{9}{4}+4\\f(\frac{3}{4})=\frac{9}{8}-\frac{9}{4}+4\\f(\frac{3}{4})=\frac{9}{8}-\frac{18}{8}+\frac{32}{8}\\f(\frac{3}{4})=\frac{23}{8}$

This is a positive value for y, therefore we are in the situation where there is NO x-axis crossing of the parabola's graph, and therefore no real roots.

We can though estimate a few more points of the parabola's graph in order to complete the graph as requested in the problem. For such we select a couple of x-values to the right of the vertex, and a couple to the right so we can draw the branches. For example: x = 1, and x = 2 to the right; and x = 0 and x = -1 to the left of the vertex:

$f(-1) = 2(-1)^2-3(-1)+4= 2+3+4=9\\f(0)=2(0)^2-3(0)+4=0+0+4=4\\f(1)=2(1)^2-3(-1)+4=2-3+4=3\\f(2)=2(2)^2-3(2)+4=8-6+4=6$

See the graph produced in the attached image.

4 0

3 years ago

A study of class attendance and grades among first-year students at a state university showed that, in general, students who mis

ratelena [41]

Answer:

the numerical value of the correlation between percent of classes attended and grade index is r = 0.4

Step-by-step explanation:

Given the data in the question;

we know that;

the coefficient of determination is r²

while the correlation coefficient is defined as r = √(r²)

The coefficient of determination tells us the percentage of the variation in y by the corresponding variation in x.

Now, given that class attendance explained 16% of the variation in grade index among the students.

so

coefficient of determination is r² = 16%

The correlation coefficient between percent of classes attended and grade index will be;

r = √(r²)

r = √( 16% )

r = √( 0.16 )

r = 0.4

Therefore, the numerical value of the correlation between percent of classes attended and grade index is r = 0.4

3 0

3 years ago