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Lisa invests $4,000 in two types of bonds, bond A and bond B. Bond A offers a 10% return, and bond B offers a 6% return. Lisa in

ss7ja [257]

X+y=4000....(1)
10x+6y=340*100⇒5x+3y=17000......(2)

(2)- 3*(1)⇒ 2x=5000⇒x=2500,y=4000-2500=1500

7 0

2 years ago

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chong earns an annual salary of 29,500. how much is his biweekly paycheck? $1,134.62 $1,135.62 $1,234.62 none of the above

oee [108]

To figure this out, divide the annual salary by the months in a year.
29,500/12=2458.33
Now divide that by half of the amount of weeks in month
2458.33/1.5=1638.88
So the answer is none of the above.

6 0

2 years ago

What is the domain of validity for csctheta =start fraction 1 over sine theta end fraction? (1 point) all real numbers all real

dem82 [27]

We know the following relationship:

$csc(\theta)=\frac{1}{sin(\theta)}$

The domain of a function are the inputs of the function, that is, a function $f$ is a relation that assigns to each element $x$ in the set A exactly one element in the set B. The set A is the domain (or set of inputs) of the function and the set B contains the range (or set of outputs).Then applying this concept to our function $csc(\theta)$ we can write its domain as follows:

1. Domain of validity for $csc(\theta)$ :

$D: \{\theta \in R/ sin(\theta) \neq 0 \} \\ In words: All \ \theta \ that \ are \ real \ values \ except \ those \ that \ makes \ sin(\theta)=0$

When:

$sin(\theta)=0$ ?

when:

$\theta=..., -2\pi,-\pi,0,\pi,\2pi,3pi,...,k\pi$

where k is an integer either positive or negative. That is:

$sin(k\theta)=0 \ for \ k=...,-2,-1,0,1,2,3,...$

To match this with the choices above, the answer is:

"All real numbers except multiples of $\pi$ "


2. which identity is not used in the proof of the identity $1+cot^{2}(\theta)=csc^{2}(\theta)$ :

This identity can proved as follows:

$sin^2{\theta}+cos^{2}(\theta)=1 \ Dividing \ by \ sin^{2}(\theta) \\ \\ \therefore \frac{sin^2{\theta}}{sin^{2}(\theta)}+\frac{cos^{2}(\theta)}{sin^{2}(\theta)}=\frac{1}{sin^{2}(\theta)} \\ \\ \therefore 1+cot^{2}(\theta)=csc^{2}(\theta)$

The identity that is not used is as established in the statement above:

"1 +cos squared theta over sin squared theta= csc2theta"

Written in mathematical language as follows:

 $\frac{1+cos^{2}(\theta)}{sin^{2}(\theta)}=csc^{2}(\theta)$

4 0

2 years ago

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The Great Lakes differ in both their areas (measured in square miles) and their depths. However these two dimensions do not keep

Masteriza [31]

Answer:

The order of Great Lakes according to depth is (descending order): 1. Lake Superior 2. Lake Michigan 3. Lake Ontario 4. Lake Huron 5. Lake Erie

Step-by-step explanation:

Lake Superior is by far the largest and deepest of the great Lakes. Lake Michigan is exceeded in depth only by Lake Superior, but it is exceeded in area by both Lakes Superior and Huron. Lake Ontario, which is the smallest in area, is deeper than both Lakes Huron and Erie. Lake Erie is larger than Lake Ontario but it is not only shallower than Huron; it is also shallower than Ontario. So, the order of Great Lakes according to depth is (descending order): 1. Lake Superior 2. Lake Michigan 3. Lake Ontario 4. Lake Huron 5. Lake Erie

3 0

2 years ago

The radius of circle G is 4 cm. What is the tangent

qaws [65]

The tangent of a given circle is perpendicular to the radius a the point called point if tangency. The radius of the circle is perpendicular to the tangent at the point of tangency. This property is especially useful in cases where the radius that connects to the point of tangency forms a part of right angle because the pythagorean theorem and trigonometry apply to right angles.

4 0

2 years ago