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polet [3.4K]
3 years ago
12

Evaluate the expressions (2/7)^0= (9)^0=

Mathematics
1 answer:
zysi [14]3 years ago
4 0
(2/7)^0= 1
(9)^0=1
i think that's what your asking if not let me know
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Sam chose a number. He then multiplied his number by 2 and added 7. His result was 23. What was his original number?
hichkok12 [17]
the original number was 8
8 0
3 years ago
Solve the following equation with the initial conditions. x¨ + 4 ˙x + 53x = 15 , x(0) = 8, x˙ = −19
Katen [24]

x''+4x'+53x=15

has characteristic equation

r^2+4r+53=0

with roots at r=-2\pm7i. Then the characteristic solution is

x_c=C_1e^{(-2+7i)t}+C_2e^{(-2-7i)t}=e^{-2t}\left(C_1\cos(7t)+C_2\sin(7t)\right)

For the particular solution, consider the ansatz x_p=a_0, whose first and second derivatives vanish. Substitute x_p and its derivatives into the equation:

53a_0=15\implies a_0=\dfrac{15}{53}

Then the general solution to the equation is

x=e^{-2t}\left(C_1\cos(7t)+C_2\sin(7t)\right)+\dfrac{15}{53}

With x(0)=8, we have

8=C_1+\dfrac{15}{53}\implies C_1=\dfrac{409}{53}

and with x'(0)=-19,

-19=-2C_1+7C_2\implies C_2=-\dfrac{27}{53}

Then the particular solution to the equation is

\boxed{x(t)=\dfrac1{53}e^{-2t}(409cos(7t)-27\sin(7t)+15)}

8 0
3 years ago
Suppose Z has a standard normal distribution with a mean of 0 and standard deviation of 1. The probability that Z is less than 1
solmaris [256]

Answer:

0.8749

Step-by-step explanation:

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the zscore of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

\mu = 0, \sigma = 1

The probability that Z is less than 1.15 is:

This is the pvalue of Z = 1.15, which is 0.8749.

8 0
3 years ago
40% of 50 is what number
nikitadnepr [17]

20

Step-by-step explanation:

Step 1:

Let the number be 50 and to find 40% of  50 is given interms of expression as follows

To express the percentage the following strategy is used

Eg: 40% = 40/100

∴ To express 40% of 50 is

(40/100)*50

Step 2:

On simplification the above expression we could get

0.4*50

= 20

4 0
3 years ago
Read 2 more answers
What is the resulting equation?
nadezda [96]
The answer for this question is B.
3 0
3 years ago
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