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3 years ago

9

Verify the given linear approximation at a = 0. Then determine the values of x for which the linear approximation is accurate to

within 0.1. (Enter your answer using interval notation. Round your answers to three decimal places).
ln(1 + x) ≈ x

1 answer:

Darya [45]3 years ago

3 0

We are asked to evaluate the equation ln (1+x) = x.In this case, we can raise both sides exponentially to 1 + x = e^x. In this case, the obvious answer would be zero. That is 1 = 1 which is a valid statement. The answer therefore to this problem is equal to zero

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What is 4855/200 simplified

EleoNora [17]

Answer:

The answer is 2427.5

Step-by-step explanation:

The fraction consists of two numbers and a fraction bar: 4,855/200

The number above the bar is called numerator: 4,855

The number below the bar is called denominator: 200

The fraction bar means that the two numbers are dividing themselves.

To get fraction's value divide the numerator by the denominator:

Value = 4,855 ÷ 200

To calculate the greatest common factor, GCF:

1. Build the prime factorizations of the numerator and denominator.

2. Multiply all the common prime factors, by the lowest exponents.

Factor both the numerator and denominator, break them down to prime factors:

Prime Factorization of a number: finding the prime numbers that multiply together to make that number.

4,855 = 5 × 971;

4,855 is a composite number;

In exponential notation:

200 = 2 × 2 × 2 × 5 × 5 = 23 × 52;

200 is a composite number;

3 0

3 years ago

Cooper is measuring ingredients for his special dessert. He needs a total of 70.4 mL of milk and melted butter. The recipe calls

SVETLANKA909090 [29]

21.5m

i think that may be the answer!!
hopefully this helped some?!!!

8 0

3 years ago

Read 2 more answers

Which of the expressions below could be factored quickly using the "difference of squares"? Select all that apply.

boyakko [2]

Answer:

Difference of squares method is a method that is used to evaluate the difference between two perfect squares.

For example, given an algebraic expression in the form:

can be factored as follows:

From the given expressions, the only expression containing two perfect squares with the minus sign in the middle is the expression in option A.

i.e.

which can be factored as follows:

.

3 0

3 years ago

Read 2 more answers

The amount of money spent on textbooks per year for students is approximately normal.

Ostrovityanka [42]

Answer:a

a

$336.04 < \mu < 443.96$

b

The margin of error will increase

c

The margin of error will decreases

d

The 99% confidence interval is $0.4107 < p < 0.4293$

Step-by-step explanation:

From the question we are told that

The sample size $n = 19$

The sample mean is $\= x = \$\ 390$

The standard deviation is $\sigma = \$ \ 120$

Given that the confidence level is 95% then the level of significance is mathematically represented as

$\alpha = 100 - 95$

$\alpha = 5 \%$

$\alpha = 0.05$

Next we obtain the critical value of $\frac{\alpha }{2}$ from the normal distribution table

So

$Z_{\frac{\alpha }{2} } = 1.96$

The margin of error is mathematically represented as

$E = Z_{\frac{\alpha }{2} } * \frac{\sigma}{\sqrt{n} }$

=> $E = 1.96 * \frac{120}{\sqrt{19} }$

=> $E = 53.96$

The 95% confidence interval is

$\= x - E < \mu < \= x + E$

=> $390 - 53.96 < \mu < 390 - 53.96$

=> $336.04 < \mu < 443.96$

When the confidence level increases the $Z_{\frac{\alpha }{2} }$ also increases which increases the margin of error hence the confidence level becomes wider

Generally the sample size mathematically varies with margin of error as follows

$n \ \ \alpha \ \ \frac{1}{E^2 }$

So if the sample size increases the margin of error decrease

The sample proportion is mathematically represented as

$\r p = \frac{210}{500}$

$\r p = 0.42$

Given that the confidence level is 0.99 the level of significance is $\alpha = 0.01$

The critical value of $\frac{\alpha }{2}$ from the normal distribution table is

$Z_{\frac{\alpha }{2} } = 2.58$

Generally the margin of error is mathematically represented as

$E = Z_{\frac{\alpha }{2} }* \sqrt{ \frac{\r p (1- \r p )}{n} }$

=> $E = 0.42 * \sqrt{ \frac{0.42 (1- 0.42 )}{ 500} }$

=> $E = 0.0093$

The 99% confidence interval is

$\r p - E < p < \r p + E$

$0.42 - 0.0093 < p < 0.42 + 0.0093$

$0.4107 < p < 0.4293$

4 0

3 years ago

Point S is on line segment RT. Given RT=4x, ST = 5x-10, and RS = 6 determine the numerical length of ST.

Art [367]

Answer:

ST=10

Step-by-step explanation:

8 0

3 years ago