Evaluate the expression without using a calculator.<br> In1/e^7

vitfil [10]

Hello,
To solve this function for f(4) we need to plug 4 into f(x) and the result will be our answer. We know that f(x) is $3x^2-7$ . Plugging in 4 we get $3(4)^2-7=41$ . Therefore, f(4)=41. Hope this helps!

6 0

3 years ago

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A convenience store pays a farmer $1.25 per pineapple. If it costs the farmer $0.15 in seeds, $0.25 in fertilizer, and $0.25 in

maw [93]

Answer:

$0.60

Step-by-step explanation:

The costs are:

$0.15 + $0.25 = $0.40

He sells it for $1.25.

The value added is:

$1.25 - $0.40 = $0.85

6 0

3 years ago

Let X denote the number of flaws along a 100-m reel of magnetic tape (an integer-valued variable). Suppose Zdenote the number of

Lemur [1.5K]

Answer:

a) $P(20 \leq X \leq 30) = P(20-0.5 \leq X \leq 30+0.5)$

$P(19.5 \leq X \leq 30.5) = P(\frac{19.5-25}{5} \leq Z \leq \frac{30.5 -25}{5})=P(-1.1 \leq Z \leq 1.1)$

And we can find this probability like this:

$P(-1.1 \leq Z \leq 1.1)= P(Z\leq 1.1) -P(Z\leq -1.1) = 0.864-0.136= 0.728$

b) $P(X \leq 30)= P(X$

And using the z score we got:

$P(X$

c) $P(X$

And if we use the continuity correction we got:

$P(X$

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".

Continuity correction means that we need to add and subtract 0.5 before standardizing the value specified.

Part a

Let X the random variable that represent the variable of interest of a population, and for this case we know the distribution for X is given by:

$X \sim N(25,5)$

Where $\mu=25$ and $\sigma=5$

Part a

For this case we want to find this probability:

$P(20 \leq X \leq 30) = P(20-0.5 \leq X \leq 30+0.5)$

And if we use the z score given by:

$z =\frac{x-\mu}{\sigma}$

We got this:

$P(19.5 \leq X \leq 30.5) = P(\frac{19.5-25}{5} \leq Z \leq \frac{30.5 -25}{5})=P(-1.1 \leq Z \leq 1.1)$

And we can find this probability like this:

$P(-1.1 \leq Z \leq 1.1)= P(Z\leq 1.1) -P(Z\leq -1.1) = 0.864-0.136= 0.728$

Part b

For this case we want this probability:

$P(X \leq 30)$

And if we use the continuity correction we got:

$P(X \leq 30)= P(X$

And using the z score we got:

$P(X$

Part c

For this case we want this probability:

$P(X$

And if we use the continuity correction we got:

$P(X$

3 0

3 years ago

Let the following sample of 8 observations be drawn from a normal population with unknown mean and standard deviation: 22, 18, 1

BigorU [14]

Answer:

a: Sample mean: 20, Sample standard deviation: 1.732

b: 19.13 <µ < 20.87

c: 18.84< µ < 21.16

d: as the confidence level increases, the interval becomes wider

Step-by-step explanation:

a: Sample mean is found by adding up all the individual values of the sample, then dividing by the total number of values in the sample.

Sample standard deviation is the square root of the variance

See the first attached photo for the calculations of these values.

We need to create a 80% confidence interval for the population. Since n < 30, we will use a t-value with degree of freedom of 7 (the degree of freedom is always one less than the sample size.

Look for the column on the t-distribution chart that has "area in two tails" of 0.20 (80%), and row 7 (degree of freedom)

The t-value is 1.415

See the second attached photo for the construction of the confidence interval

We need to create a 90% confidence interval for the population. Since n < 30, we will use a t-value with degree of freedom of 7 (the degree of freedom is always one less than the sample size.

Look for the column on the t-distribution chart that has "area in two tails" of 0.10 (90%), and row 7 (degree of freedom)

The t-value is 1.895

See the third attached photo for the construction of the confidence interval

3 0

3 years ago

An exam worth 145 points contains 50 questions. The number of two-point questions is equal to 50 minus the number of five-point

abruzzese [7]

Answer:

Therefore there are 35 number of 2-point questions and 15 number of 5-point questions.

Step-by-step explanation:

i) let the number of 2 point question is x.

ii) let the number of 5 point questions be y

iii) total number of questions is 50

iv) therefore x + y = 50

v) it is also given that 2x + 5y = 145

vi) solving for the two equations found in iv) and v). Multiplying iv) by 2 we get

2x + 2y = 100

vii) subtracting equation vi) from equation v) we get 3y = 45.

viii) Therefore y = 15.

ix) using the value in viii) and substituting in iv) we get x + 15 = 50.

Therefore x = 50 - 15 = 35

x) Therefore there are 35 number of 2-point questions and 15 number of 5-point questions.

3 0

3 years ago

Read 2 more answers

Evaluate the expression without using a calculator. In1/e^7