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Scilla [17]
1 year ago
6

Estimates show that there are 1.4x10^8 pet fish and 9.4x10^6 pet reptiles in the United States. How many pet fish and reptile pe

ts are in the United States. Answer in scientific notation.
Mathematics
1 answer:
azamat1 year ago
8 0

Answer:

There are total number of pet fish and reptile pets are 1.49\times 10^8.

Step-by-step explanation:

Number of pet fish are 1.4\times 10^8 and the number of pet reptiles are 9.4\times 10^6.

It is required to find the total number of pet fish and reptile pets in the United States. It can be done by simply adding the above numbers such that total numbers are given by :

T=1.4\times10^{8}+9.4\times10^{6}\\\\T=149400000\\\\T=1.49\times 10^8

So, there are total number of pet fish and reptile pets are 1.49\times 10^8.

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EXAMPLE 5 If F(x, y, z) = 4y2i + (8xy + 4e4z)j + 16ye4zk, find a function f such that ∇f = F. SOLUTION If there is such a functi
Valentin [98]

If there is such a scalar function <em>f</em>, then

\dfrac{\partial f}{\partial x}=4y^2

\dfrac{\partial f}{\partial y}=8xy+4e^{4z}

\dfrac{\partial f}{\partial z}=16ye^{4z}

Integrate both sides of the first equation with respect to <em>x</em> :

f(x,y,z)=4xy^2+g(y,z)

Differentiate both sides with respect to <em>y</em> :

\dfrac{\partial f}{\partial y}=8xy+4e^{4z}=8xy+\dfrac{\partial g}{\partial y}

\implies\dfrac{\partial g}{\partial y}=4e^{4z}

Integrate both sides with respect to <em>y</em> :

g(y,z)=4ye^{4z}+h(z)

Plug this into the equation above with <em>f</em> , then differentiate both sides with respect to <em>z</em> :

f(x,y,z)=4xy^2+4ye^{4z}+h(z)

\dfrac{\partial f}{\partial z}=16ye^{4z}=16ye^{4z}+\dfrac{\mathrm dh}{\mathrm dz}

\implies\dfrac{\mathrm dh}{\mathrm dz}=0

Integrate both sides with respect to <em>z</em> :

h(z)=C

So we end up with

\boxed{f(x,y,z)=4xy^2+4ye^{4z}+C}

7 0
1 year ago
Part A
Ber [7]

Answer:learn your self

Step-by-step explanation:

Lol

7 0
1 year ago
Mark and Sofia walk together down a long, straight road. They walk without stopping for 4 miles. At this point Sofia says their
Marina CMI [18]

Answer:

Sofia is correct.

Step-by-step explanation:

Mark's statement depends on the starting point. He can be correct if they started at the 0 mile, but in this case we don't know where they started. They could had started at the 12 mile and their current position after the walking would be 16 miles.

On the other hand, Sofia's statement doesn't depend on where they started. She refers to how much they walked, not to where they are after the walking. Since they stopped after 4 non-stopping miles, their displacement was exactly 4 miles. So Sofia is correct.

5 0
1 year ago
A psychologist is collecting data on the time it takes to learn a certain task. For 50 randomly selected adult subjects, the sam
tatuchka [14]

Answer: (15.263,\ 17.537)

Step-by-step explanation:

According to the given information, we have

Sample size : n= 50

\overline{x}=16.40

s=4.00

Since population standard deviation is unknown, so we use t-test.

Critical value for  95 percent confidence interval  :

t_{n-1,\alpha/2}=t_{49, 0.025}= 2.009575\approx2.010

Confidence interval : \overline{x}\pm t_{n-1, \alpha/2}\dfrac{s}{\sqrt{n}}

16.40\pm (2.010)\dfrac{4}{\sqrt{50}}\\\\=16.40\pm1.13702770415\\\\=16.40\pm1.1370\\\\=(16.40-1.1370,\ 16.40+1.1370)\\\\=(15.263,\ 17.537)

Required 95% confidence interval :  (15.263,\ 17.537)

8 0
1 year ago
Which shows the correct substitution of the values a, b, and c from the equation 0 = – 3x2 – 2x + 6 into the quadratic formula?
Gemiola [76]
Hello : 
the discriminat of each quadratic equation : ax²+bx+c=0 ....(a <span>≠ 0) is :
</span><span>Δ = b² -4ac
1 )  </span>Δ > 0  the equation has two reals solutions : x =  (-b±√Δ)/2a
2 ) Δ = 0 : one solution : x = -b/2a
3 ) Δ <span>< 0 : no reals solutions
in this exercice : -3x²-2x+6 =0.....a = -3   b = -2     c =6
calculate : </span>Δ............................
7 0
1 year ago
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