Suppose that the dollar cost of producing x radios is c(x) = 400 + 20x - 0.2x
2. Find the marginal cost when 30
radios are produced.

Answer:

Temperature in celcius scale to the nearest degree = 64

Step-by-step explanation:

Temperature in celcius scale = 18° C

We have the formula

[tex]C=\frac{5}{9}(F-32)[/tex]

Substituting value in celcius scale.

[tex]18=\frac{5}{9}(F-32)\\\\F=64.4^OC[/tex]

Temperature in celcius scale to the nearest degree = 64

which means the other asymptote is the line .

Answer: all real numbers

Step-by-step explanation:

The given function is : [tex]g(x) = 52x[/tex], which is polynomial function with degree one.

We know that the domain of a polynomial is the entire set of real numbers because for any real number r the polynomial function exists.

Therefore, the domain of the given function [tex]g(x) = 52x[/tex] is the set of real numbers.

Answer:

Supplementary angles are two angles whose sum is 180 degrees while complementary angles are two angles whose sum is 90 degrees. Supplementary and complementary angles do not have to be adjacent

Step-by-step explanation:

The inequality 5 + 7l ≤ 60 represents the scenario where a student has a 60-minute free trial of a game that requires 5 minutes to set up and 7 minutes to play each level, where 'l' denotes the number of levels the student can play.

The subject of this question is about setting up an inequality to represent a scenario. The student has a 60-minute free trial of a game and it takes 5 minutes to set up the game and another 7 minutes to play each level. Let's denote 'l' as the number of levels the student can play. The total time spent both setting and playing the game cannot exceed 60 minutes. Therefore, the inequality to determine the maximum number of levels the student can play would be: 5 + 7l ≤ 60.

To explain this further, the '5' is the time spent setting up the game and '7l' is the total time spent playing the levels. As we want to find out the maximum number of levels that can be played within a constraint of 60 minutes, thus we use the less than or equal to symbol ('≤').

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The first error Emi made was dividing by N - 1 instead of N when computing the population variance.

The first error in computing the variance is Emi divided by N - 1 instead of N. In Emi's calculations for the data set, which includes the numbers 87, 46, 90, 78, and 89, the correct method should be to divide by N, because she is dealing with a population data set, not a sample.

For the population variance, we divide the sum of squared differences from the mean by the total number of data points in the population, which is N. However, Emi incorrectly divided by N - 1, which would only be correct if she were calculating the sample variance to estimate the population variance based on a subset of the population data.

There are 6 ways the bags can be arranged.

The number of ways the bags can be arranged is equal to the number of permutations of the bags. In this case, Julia has 3 handbags in her closet, so we need to find the number of permutations of 3 objects taken from a set of 3. The formula for permutations is nPr = n! / (n-r)!, where n is the total number of objects and r is the number of objects being selected.

Plugging in the values, we get 3P3 = 3! / (3-3)! = 3! / 0! = 3 x 2 x 1 / 1 = 6.

Therefore, there are 6 ways the bags can be arranged.

The number of ways to arrange 3 handbags is 6.

The arrangement of objects where the order matters is a permutation problem. To find the number of permutations of n distinct objects, one uses the factorial of n, denoted as n!. The factorial of a non-negative integer n is the product of all positive integers less than or equal to n.

In this case, Julia has 3 handbags, so n = 3. We want to find the number of permutations of these 3 handbags, which is given by 3!.

Calculating 3!:

3! = 3 × 2 × 1 = 6

Therefore, there are 6 different ways to arrange the 3 handbags in Julia's closet.

To compare the maximum values of function, which is a discrete function with given values, we find that C ) It is 3 units lower for f ( x ) than g ( x )

To compare the maximum values of functions f(x) and g(x), we first analyze each function separately. The quadratic function f(x) = -4x2 + 5x has a vertex form which reveals its maximum value at x = 1/3, and since g(x) is a discrete function defined by its values at certain points, we look directly at the given values to find its maximum.

Function g(x) reaches its maximum at g(2) = 8. Comparing this to f(x), whose vertex form shows that its maximum is f(1/3), we need to compute f(1/3) = -4(1/3)2 + 5(1/3) to find its specific value. After calculation, f(1/3) is found to be higher than 8, which is the maximum of g(x).

Thus,

g ( x ) maximum value = 8

f ( x ) maximum value = 5

g ( x ) max - f ( x ) max = 8 - 5 = 3

Complete Question:

Functions f(x) and g(x) are described as follows:

f(x) = -4x2 + 5

x g(x)

0 0

1 4

2 8

3 4

4 0

Which statement best compares the maximum value of the two functions? A. It is equal for both functions. B. It is 3 units higher for f(x) than g(x). C. It is 3 units lower for f(x) than g(x). D. It is 4 units lower for f(x) than g(x).

Answer:

Option D [tex]\$50+\$31.5x[/tex]

Step-by-step explanation:

Let

x------> the number of days

y----> the cost of renting a car

we know that

For [tex]x<7\ days[/tex]

[tex]y=\$50+\$35x[/tex]

For [tex]x\geq 7\ days[/tex]

The rate is equal to

[tex]0.90*\$35=\$31.5[/tex]

so

[tex]y=\$50+\$31.5x[/tex]

In this problem. the car has been rented for more than a week

therefore

[tex]x> 7\ days[/tex]

The cost of renting a car is equal to

[tex]y=\$50+\$31.5x[/tex]

Answer:

Option C. [tex]7.\frac{\sqrt{74}}{74}[/tex]

Step-by-step explanation:

At the end of one swipe the tip of one blade is at (-5, 7). We have to find sine value of this function.

As shown in the figure coordinates of the tip of the wiper blade are (-5, 7)

So [tex]sin a = \frac{Height}{Hypotenuse}[/tex]

Here Height of the triangle = 7

and Hypotenuse = x = [tex]\sqrt{(-5)^{2}+7^{2}}=\sqrt{25+49}=\sqrt{74}[/tex]

By putting these values in the expression

[tex]sina=\frac{7}{x}=\frac{7}{\sqrt{74}}=7.\frac{\sqrt{74}}{74}[/tex]

Answer is option C.[tex]7.\frac{\sqrt{74}}{74}[/tex]

In a mathematical proof, missing statements and reasons are usually concluded from the given statements and the relevant geometric postulates or theorems. They could include establishing the congruency of angles or declaring the parallelism of lines.

Without the concrete steps of the proof or the reasoning proposed, it is difficult to provide the exact missing statements and reasons. However, in a general mathematical proof, common reasons used include 'definition of congruent angles', 'definition of parallel lines', 'alternate interior angles theorem', etc.

For instance, if we have a proof that involves stating two angles are congruent, the missing statement might be 'Angle A is congruent to Angle B', and the missing reason could be 'Definition of Congruent Angles' or 'Angle Bisector Theorem', if an angle bisector comes into the picture.

Another missing statement might be 'Segment AB is parallel to Segment CD', with the reason being 'Corresponding Angles Postulate', or 'Alternate Interior Angles Theorem', if the proof involves parallel lines.

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The probability that the student answers the question on the first or second try is 0.60.

Given

P(A) = 0.2

[tex]\rm P(B|A^c)=0.5[/tex].

The conditional probability of an event is when the probability of one event depends on the probability of occurrence of the other event.

When two events are mutually exclusive.

Then,

[tex]\rm P(A\cap B)=0[/tex]

The first probability is;

[tex]\rm P(A^C)=1-0.2=0.8[/tex]

Therefore,

The probability that the student answers the question on the first or second try is;

[tex]\rm P(A\cup B)= P(A) +P(B)-P(A \cap B)\\\\ P(A\cup B)= P(A) +P(B|A^C) \times P(A^C)-P(A \cap B)\\\\ P(A\cup B)= 0.2+0.5 \times 0.8 -0\\\\P(A\cup B)=0.2+0.40\\\\ P(A\cup B)=0.60[/tex]

Hence, the probability that the student answers the question on the first or second try is 0.60.

To know more about Conditional probability click the link given below.

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Julie studied for 3 1 3 hours during the 4 days before her last math test. If she studied for the same amount of time each day, how much time did she spend studying each day?

Solution:

Julie studied for 3 [tex]\frac{1}{3}[/tex] hrs in 4 days

Let us first find how many minutes Julie studied in 4 days

In 1 hour, there are 60 minutes

Julie studied for 3 complete hours and one-third of the hour.

So, Number of minutes in 3 hours is 3*60=180hrs

and, Number of minutes in one-third of an hour=[tex]\frac{1}{3} *60[/tex]

=[tex]\frac{60}{3}[/tex]=20minutes

So, time spent by Julie in studying in 4 days is 3[tex]\frac{1}{3}[/tex] hours

or, Julie studied for 180+20 minutes in 4 days

Adding 180 and 20

Julie studied for 200 minutes during the 4 days

To find time she spend studying each day, we must divide total time spent in studies by number of days

Time she spend studying each day= [tex]\frac{200}{4}[/tex] minutes

Dividing 200 by 4, we get

Time she spend studying each day=50 minutes

Answer:

time she spend studying each day=50 minutes

To find the sum of the geometric series, we use the formula: Sn = a1 * (r^n - 1) / (r - 1). Substituting the given values and solving, we find that the sum is 16,383.

To find the sum of a geometric series, we can use the formula Sn = a1 * (r^n - 1) / (r - 1), where Sn is the sum of the series, a1 is the first term, r is the common ratio, and n is the number of terms.

In this case, a1 = 3, r = 4, and an = 49,152. We can use the formula to find n, which is the exponent.

49,152 = 3 * (4^n - 1) / (4 - 1)

49,152 = 3 * (4^n - 1) / 3

16,384 = 4^n - 1

4^n = 16,385

n = log4(16,385)

n ≈ 7

Now, we can substitute the values into the formula for Sn.

Sn = 3 * (4^7 - 1) / (4 - 1)

Sn = 3 * (16,384 - 1) / 3

Sn = 3 * 16,383 / 3

Sn = 16,383

Therefore, the sum of the geometric series is 16,383. So the correct answer is Sn = 16,383.

The correct answer is [tex]\( S_n = 65,535 \)[/tex].

To find the sum of a geometric series, you can use the formula:

[tex]\[ S_n = a_1 \frac{(r^n - 1)}{r - 1} \][/tex]

Where:

- [tex]\( S_n \)[/tex] is the sum of the series,

- [tex]\( a_1 \)[/tex] is the first term,

- [tex]\( r \)[/tex] is the common ratio,

- [tex]\( n \)[/tex] is the number of terms.

Given [tex]\( a_1 = 3 \), \( r = 4 \), and \( a_n = 49,152 \)[/tex], we need to find [tex]\( n \)[/tex]. The formula for the [tex]\( n^{th} \)[/tex] term in a geometric series is [tex]\( a_n = a_1 \times r^{(n-1)} \)[/tex]. In this case, [tex]\( 49,152 = 3 \times 4^{(n-1)} \)[/tex]

Let's solve for n:

[tex]\[ 4^{(n-1)} = \frac{49,152}{3} \][/tex]

[tex]\[ 4^{(n-1)} = 16,384 \][/tex]

[tex]\[ n-1 = \log_4(16,384) \][/tex]

[tex]\[ n-1 = 7 \][/tex]

[tex]\[ n = 8 \][/tex]

Now that we have [tex]\( n = 8 \)[/tex], we can use it in the sum formula:

[tex]\[ S_n = 3 \frac{(4^8 - 1)}{4 - 1} \][/tex]

[tex]\[ S_n = 3 \frac{(65,536 - 1)}{3} \][/tex]

[tex]\[ S_n = 3 \frac{65,535}{3} \][/tex]

[tex]\[ S_n = 65,535 \][/tex]

Therefore, the correct answer is [tex]\( S_n = 65,535 \)[/tex].