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2 years ago

13

The Canadian labor force as of 2019 was 32.7 million. There were 30.9 million employed What the unemployment rate would be?

1 answer:

Afina-wow [57]2 years ago

8 0

Answer:

The unemployment rate would be 5.5%.

Step-by-step explanation:

It is given that,

The Canadian labor force as of 2019 was 32.7 million.

There were 30.9 million employed

We need to find the unemployment rate.

Unemployed = labor force - employed

= 32.7 - 30.9

= 1.8 million

$\text{unemployment rate}=\dfrac{\text{unemployed}}{\text{labor force}}\times 100\\\\=\dfrac{1.8}{32.7}\times 100\\\\=5.5\%$

So, the unemployment rate would be 5.5%.

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Find a homogeneous linear differential equation with constant coefficients whose general solution is given by

frez [133]

Answer:

$y" + 2y' + 2y = 0$

Step-by-step explanation:

Given

$y=c_1e^{-x}cosx+c_2e^{-x}sinx$

Required

Determine a homogeneous linear differential equation

Rewrite the expression as:

$y=c_1e^{\alpha x}cos(\beta x)+c_2e^{\alpha x}sin(\beta x)$

Where

$\alpha = -1$ and $\beta = 1$

For a homogeneous linear differential equation, the repeated value m is given as:

$m = \alpha \± \beta i$

Substitute values for $\alpha$ and $\beta$

$m = -1 \± 1*i$

$m = -1 \± i$

Add 1 to both sides

$m +1= 1 -1 \± i$

$m +1= \± i$

Square both sides

$(m +1)^2= (\± i)^2$

$m^2 + m + m + 1 = i^2$

$m^2 + 2m + 1 = i^2$

In complex numbers:

$i^2 = -1$

So, the expression becomes:

$m^2 + 2m + 1 = -1$

Add 1 to both sides

$m^2 + 2m + 1 +1= -1+1$

$m^2 + 2m + 2= 0$

This corresponds to the homogeneous linear differential equation

$y" + 2y' + 2y = 0$

6 0

3 years ago

210 is how many tens? an also what does 240 equals how many tens

qwelly [4]

210 is 21 groups of ten. 240 is 24 tens

6 0

2 years ago

Complete the generic rectangle (PLEASE HELP)

navik [9.2K]

I believe the area of the blank rectangle, the biggest one, is 2800. The whole rectangle all together is 3225.

Explanation:

Since the length of one of the rectangles is 70, the rectangle with an area of 210 will have a side length of 3. This means the rectangle with an area of 15 has a side length of 5. <em>That</em> means the rectangle with an area of 200 has a side length of 40. Therefore, the blank rectangle has an area of 2800, as it's 2 side lengths are 70 and 40.

4 0

3 years ago

Fine length of BC on the following photo.

MrMuchimi

Answer:

$BC=4\sqrt{5}\ units$

Step-by-step explanation:

see the attached figure with letters to better understand the problem

step 1

In the right triangle ACD

Find the length side AC

Applying the Pythagorean Theorem

$AC^2=AD^2+DC^2$

substitute the given values

$AC^2=16^2+8^2$

$AC^2=320$

$AC=\sqrt{320}\ units$

simplify

$AC=8\sqrt{5}\ units$

step 2

In the right triangle ACD

Find the cosine of angle CAD

$cos(\angle CAD)=\frac{AD}{AC}$

substitute the given values

$cos(\angle CAD)=\frac{16}{8\sqrt{5}}$

$cos(\angle CAD)=\frac{2}{\sqrt{5}}$ ----> equation A

step 3

In the right triangle ABC

Find the cosine of angle BAC

$cos(\angle BAC)=\frac{AC}{AB}$

substitute the given values

$cos(\angle BAC)=\frac{8\sqrt{5}}{16+x}$ ----> equation B

step 4

Find the value of x

In this problem

$\angle CAD=\angle BAC$ ----> is the same angle

so

equate equation A and equation B

$\frac{8\sqrt{5}}{16+x}=\frac{2}{\sqrt{5}}$

solve for x

Multiply in cross

$(8\sqrt{5})(\sqrt{5})=(16+x)(2)\\\\40=32+2x\\\\2x=40-32\\\\2x=8\\\\x=4\ units$

$DB=4\ units$

step 5

Find the length of BC

In the right triangle BCD

Applying the Pythagorean Theorem

$BC^2=DC^2+DB^2$

substitute the given values

$BC^2=8^2+4^2$

$BC^2=80$

$BC=\sqrt{80}\ units$

simplify

$BC=4\sqrt{5}\ units$

7 0

2 years ago

19. A girl has four skirts and six blouses. How many different skirt-blouse combiNtions can she wear?

cupoosta [38]

4 combinations of skirt blouses

7 0

2 years ago