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Troyanec [42]
3 years ago
10

Please helppp with this math question <333

Mathematics
1 answer:
Naya [18.7K]3 years ago
5 0

Answer:

The average rate of change of the function g(x)=x^2+10x+18 over the interval -11 \leq x\leq -1 is -1

Step-by-step explanation:

We are given the function g(x)=x^2+10x+18 over the interval -11 \leq x\leq -1

We need to find average rate of change.

The formula used to find average rate of change is : Average \ rate \ of \ change=\frac{g(b)-g(a)}{b-a}

We have b=-1 and a=-11

Finding g(b) = g(-1)

g(x)=x^2+10x+18\\Putting \ x=-1\\g(-1)=(-1)^2+10(-1)+18\\g(-1)=1-10+18\\g(-1)=9

Finding g(a) = g(-11)

g(x)=x^2+10x+18\\Putting \ x=-11\\g(-11)=(-11)^2+10(-11)+18\\g(-1)=121-110+18\\g(-1)=29

Finding average rate of change

Average \ rate \ of \ change=\frac{g(b)-g(a)}{b-a}\\Average \ rate \ of \ change=\frac{9-29}{-1-(-11)}\\Average \ rate \ of \ change=\frac{-10}{-1+11}\\Average \ rate \ of \ change=\frac{-10}{10}\\Average \ rate \ of \ change=-1

So, the average rate of change of the function g(x)=x^2+10x+18 over the interval -11 \leq x\leq -1 is -1

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Find the percent of area under a normal curve between the mean and the given number of standard deviations from the mean.​ (Note
coldgirl [10]

Answer:

15.86%

Step-by-step explanation:

When the distribution is normal, we use 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.

Percent of area between the mean and 0.20 standard deviations from the mean:

pvalue of Z = 0.2 subtracted by the pvalue of Z = -0.2

Z = 0.2 has a pvalue of 0.5793

Z = -0.2 has a pvalue of 0.4207

0.5793 - 0.4207 = 0.1586

So this percentage is 15.86%

8 0
3 years ago
Help me please thank youu
prohojiy [21]

Answer:

A

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This means the situation given represents a function → A

3 0
3 years ago
The y-intercept of the line whose equation is 7x - 4y = 8 is what
Anni [7]
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6 0
3 years ago
If y=e5t is a solution to the differential equation
a_sh-v [17]

Answer:

k = 30, y(t) = C_1e^{5t}+C_2e^{6t}

Step-by-step explanation:

Since y=e^{5t} is a solution, then it must satisfy the differential equation. So, we calculate the derivatives and replace the value in the equation. We have that

\frac{d^2y}{dt^2} = 25 e^{5t},\frac{dy}{dt} = 5e^{5t}

Then, replacing the derivatives in the equation we have:

25e^{5t}-11(5)e^{5t}+ke^{5t}=0 e^{5t}(25-55+k) =0

Since e^{5t} is a positive function, we have that

25-55+k = 0 \rightarrow k = 30.

Now, consider a general solution y(t) = Ae^{rt}, A \in \mathbb{R}, then, by calculating the derivatives and replacing them in the equation, we get

Ae^{rt}(r^2-11r+30)=0

We already know that r=5 is a solution of the equation, then we can divide the polynomial by the factor (r-5) to the get the other solution. If we do so, we get that (r-6)=0. So the other solution is r=6.

Therefore, the general solution is

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8 0
3 years ago
Cual es el valor de x? -5x+3=2×(x-1)
AVprozaik [17]
X=11+1=12 hope I helped you
5 0
2 years ago
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