Which of the following is a correct way to name this angle? B, 2 ACB А, САВ D. BCA C. Z CBA

Laura is paying 1.07x including tax for a sweater that costs x before tax. Write this expression in another way to show the amou

ludmilkaskok [199]

Laura is paying 7% as tax.

1.07 is equal to 107%. To get the total price of something with tax you multiply it by 100% plus the tax. Simplify the percent to 1.07,

1.07x = x + 0.07x

8 0

3 years ago

4> Solve by using Laplace transform: y'+5y'+4y=0; y(0)=3 y'(o)=o

harina [27]

Answer:

$y=3e^{-4t}$

Step-by-step explanation:

$y''+5y'+4y=0$

Applying the Laplace transform:

$\mathcal{L}[y'']+5\mathcal{L}[y']+4\mathcal{L}[y']=0$

With the formulas:

$\mathcal{L}[y'']=s^2\mathcal{L}[y]-y(0)s-y'(0)$

$\mathcal{L}[y']=s\mathcal{L}[y]-y(0)$

$\mathcal{L}[x]=L$

$s^2L-3s+5sL-3+4L=0$

Solving for $L$

$L(s^2+5s+4)=3s+3$

$L=\frac{3s+3}{s^2+5s+4}$

$L=\frac{3(s+1)}{(s+1)(s+4)}$

$L=\frac3{s+4}$

Apply the inverse Laplace transform with this formula:

$\mathcal{L}^{-1}[\frac1{s-a}]=e^{at}$

$y=3\mathcal{L}^{-1}[\frac1{s+4}]=3e^{-4t}$

7 0

3 years ago

About 16 % of the population of a large country is allergic to pollen. If two people are randomly selected, what is the probabil

Vinvika [58]

Answer:

(a) 0.0256

(b) 0.2944

Step-by-step explanation:

For solving this exercise we can apply the binomial distribution. The equation that give as the probability is:

$P(x,n,p)=(nCx)*p^{x} *(1-p)^{n-x}$

Where n is the number of identical events, p is the probability that the event has a success and x is the number of success in the n identical events.

Additionally, nCx is calculated as:

$nCx=\frac{n!}{x!(n-x)!}$

So, in this case we have 2 identical events because we are going to select two people randomly and the probability p of success is the probability that the person is allergic to pollen and this probability is 16%.

Then, for the first case, x is 2 because their are asking for the probability that both are allergic to pollen. Replacing the values of x, n and p we get:

$P(2,2,0.16)=(2C2)*0.16^{2} *(1-0.16)^{2-2}$

P(2,2,0.16)=0.0256

For the second case, their are asking for the probability that at least one is allergic to pollen, that means that we need to sum the probability that both are allergic to pollen with the probability that just one is allergic to pollen.

Using the same equation to calculate P(1,2,0.16) we get:

$P(1,2,0.16)=(2C1)*0.16^{1} *(1-0.16)^{2-1}$

P(1,2,0.16)=0.2688

So, the probability that at least one person is allergic to pollen is 0.2944 and it is calculated as:

0.0256 + 0.2688 = 0.2944

7 0

3 years ago

Pleaseeeeee hellopppppppp!!

Nastasia [14]

Answer:

A. 29

B. 11

C. 10

D. 12

Step-by-step explanation:

A. 180 - 122 = 58

58 divided by 2 = 29

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B. 180 - 37 = 143

x = 11

5 x 11 = 55

8 x 11 = 88

55 + 88 = 143 + 37 - 180

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C. the small box in a triangle means right angle = 90

90 - 68 = 22

(2x - 2) we subtract before finding out what x is

22 - 2 = 20

2x = 20 divide by 2 = 10

x is equal to 10

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D. to find the total, you must figure out what each equation is to add them up to make 180.

(8x + 3) + (2x + 9) + 4x = 180

add up the numbers with x and the numbers without them

14x + 12 = 180

subtract 180 - 12 = 168

168 divided by 14 = 12

x = 12

Hope this helped !!

6 0

3 years ago

A building is 20 feet tall and casts a 12 foot shadow. and a person who is standing right next to the building casts 1 3 foot sh

Nesterboy [21]

I need help in this one too

5 0

3 years ago