how many liters is 79.1 ml? calculate and type your answer with correct significant numbers. (show your work for full credit)

The Var (X) for the random variable X with probability density function

f ₓ(x) = Cx² for |x| ≤ 1 is equal to 3/5.

Probability density function (pdf) :

f ₓ(x) = Cx² for |x| ≤ 1

            0 other wise

[tex]\int\limits^a_b {f(x)} \, dx = 1[/tex]

⇒ [tex]\int_{-1}^{1}Cx^{2}[/tex] = 1

⇒ C (x³ /3) [tex]|_{-1}^{1}[/tex] = 1

⇒ C/3 (  1 - (-1 )) = 1

⇒(2/3) C = 1

⇒ C = 3/2

Now,

E(x) = [tex]\int_{-1}^{1}x (3/2)x^{2}dx[/tex]

      = (3/2)[tex]\int_{-1}^{1}x^{3}dx[/tex]

      = ( 3/2) ( x⁴ /4 ) [tex]|_{-1}^{1}[/tex]

      = 0

Var (X) = [tex]\int_{-1}^{1}x^{2} (3/2)x^{2}dx[/tex] - [E(x)]²

           = (3/2) [tex]\int_{-1}^{1} x^{4}dx[/tex]  -0

           = (3/2) ( x⁵ /5 )[tex]|_{-1}^{1}[/tex]

           = (3/2 ) ( 1/5 + 1/5)

           = 3/5

Therefore, the Var (X) of the probability density function for the random variable X is equal to 3/5.

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The volume in units of cubic inches is 101.63 cubic inches.

Unit conversion is a process with multiple steps involving multiplication or division by a numerical factor, particularly a conversion factor. The procedure may also demand the selection of the correct number of substantial digits and rounding. Different units of conversion are used to calculate different parameters.

We convert the units of any quantity to understand better. For example, the length of a table is measured in inches; on the other hand, the length of a garden is measured in yards to make it simple to comprehend. We cannot calculate the length of a finger in miles.

1 quart is equal to 57.75 cubic inches. So, to convert a volume of 1.75 quarts to cubic inches, we multiply by 57.75:

1.75 quarts × 57.75 cubic inches/quart = 101.63 cubic inches

Therefore, the volume of the box of ice cream in cubic inches is 101.63 cubic inches.

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The true statement is (c). The coefficients of x^n and y^n are both equal

From the question, we have the following parameters that can be used in our computation:

(x + y)^n

When the above expression is expanded, we have

(x + y)^n = x^n + ..... + y^n

See that the coefficients of x^n and y^n is 1

This means that they have equal coefficient of 1

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Answer:

196 grams of zinc

Step-by-step explanation:

[tex]\frac{4}{11}=\frac{z}{539}\\ \\(539)(4)=11z\\\\2156=11z\\\\196=z[/tex]

Thus, the jar of the chemical will contain 196 grams of zinc.

The nth value equals 1 more than twice the previous value.

This statement correctly describes the sequence {1, 3, 7, 15, ...}, as each value in the sequence is 1 more than twice the previous value.

The probability of the union of events a and b is 0.21. the sum of their individual probabilities : P(a ∪ b) = 0.01 + 0.2 = 0.21.  Events a and b are mutually exclusive, it means that they cannot both happen at the same time.

In the event that occasions an and b are totally unrelated, it implies that the two of them can't occur simultaneously. In this way, the likelihood of their association (that is, the likelihood that either occasion an or occasion b will happen) is the amount of their singular probabilities:

P(a ∪ b) = P(a) + P(b)

Considering that P(a) = 0.01 and P(b) = 0.2, we can ascertain the likelihood of their association:

P(a ∪ b) = 0.01 + 0.2 = 0.21

In this way, the likelihood of the association of occasions an and b is 0.21.

The likelihood of occasion An incident is 0.01 and the likelihood of occasion B happening is 0.2. Assuming that these occasions are fundamentally unrelated, it implies the two of them can't occur simultaneously. The complete opportunity of either occasion An or occasion B happening is found by including the singular probabilities. In this way, the likelihood of occasion An occurrence or occasion B happening is 0.01 + 0.2 = 0.21. In basic terms, the opportunity of either occasion happening is 0.21.

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Answer:f

Step-by-step explanation:

its not that hard

The function is concave up for  x < 1 and concave down for x > 1 because the second derivative is positive for x < 1 and negative for x > 1. As a result, the critical point at x  < 1 is a relative maximum.

A function is an equation with just one solution for y for every x. A function produces exactly one output for each input of a certain type. Instead of y, it is common to call a function f(x) or g(x). f(2) indicates that we should discover our function's value when x equals 2. A function is an equation that depicts the connection between an input x and an output y, with precisely one output for each input. Another name for input is domain, while another one for output is range.

Here,

The derivative of the function f(x) can be found by taking the derivative of the expression e^(-x) (x^2 + 2x) using the product rule:

f'(x) = -e^(-x) (x^2 + 2x) + e^(-x) (2x + 2) = 2e^(-x) - 2xe^(-x) (x + 1)

Setting f'(x) equal to zero and solving for x gives us the critical points:

0 = 2e^(-x) - 2xe^(-x).(x + 1)

2xe^(-x).(x + 1) = 2e^(-x)

x(x + 1) = e^x

x^2 + x - e^x = 0

Next, we determine the concavity of the function at the critical points by analyzing the second derivative of the function:

f''(x) = 2e^(-x) + 2xe^(-x) + 2xe^(-x).(x + 1) - 2e^(-x).(x + 1)

= 2e^(-x).(1 - x)

Since the second derivative is positive for x < 1 and negative for x > 1, the function is concave up for x < 1 and concave down for x > 1. Thus, the critical point at x < 1 corresponds to a relative maximum.

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Answer: Alan would have to sell less than 540 boxes.

Step-by-step explanation:

The Probability that a randomly selected student who performed in the spring play, but did not perform in the spring concert is chosen is 26/53.

Now let A be the event of the student performing in Spring play

Let B be the event of students performing i the spring concert

Now according to what we know,

n(A) = 68

n(B) = 54

n(A ∩ B) = 16

Now total no. of students will be n(A U B) = 68 + 54 - 16

= 106

We need to find the number of people who performed in the spring play and not in the concert

Hence we need to find the Probability

P(A ∩ not B)

Now we can say that (A ∩ not B) will clearly be

A - (A ∩ B) Hence we get it to be

68 - 16 = 52

Hence, P(A ∩ notB) = 52/106

= 26/53

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Answer:

(-41)/6 or -6 5/6 as a mixed fraction

Step-by-step explanation:

Simplify the following:

1 + 2/3 - (8 + 1/2)

Put 8 + 1/2 over the common denominator 2. 8 + 1/2 = (2×8)/2 + 1/2:

1 + 2/3 - ((2×8)/2 + 1/2)

2×8 = 16:

1 + 2/3 - (16/2 + 1/2)

16/2 + 1/2 = (16 + 1)/2:

1 + 2/3 - ((16 + 1)/2)

16 + 1 = 17:

1 + 2/3 - 17/2

Put 1 + 2/3 - 17/2 over the common denominator 6. 1 + 2/3 - 17/2 = 6/6 + (2×2)/6 + (3 (-17))/6:

6/6 + (2×2)/6 + (3 (-17))/6

2×2 = 4:

6/6 + 4/6 + (3 (-17))/6

3 (-17) = -51:

6/6 + 4/6 + (-51)/6

6/6 + 4/6 - 51/6 = (6 + 4 - 51)/6:

(6 + 4 - 51)/6

6 + 4 = 10:

(10 - 51)/6

10 - 51 = -(51 - 10):

(-(51 - 10))/6

| 5 | 1

- | 1 | 0

| 4 | 1:

Answer:  (-41)/6

The numerical form of the statement is 4n + 7 = 2.

A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.

Given, A statement the sum of 4 times a number and 7 is equal to 2.

Let, The number be 'n'.

The numerical form of the statement will be,

4n + 7 = 2.

4n = 2 - 7.

4n = - 5.

n = - 5/4.

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The probability that a bag of chip is lower than 9.07 oz of weight is 0.1587.

A continuous probability distribution for a real-valued random variable is called a normal distribution or a Gaussian distribution.

An example of a continuous probability distribution is the normal distribution, in which the majority of data points cluster in the middle of the range while the remaining ones taper off symmetrically toward either extreme. The distribution's mean is another name for the center of the range.

The normal distribution defines how a variable's values are distributed, just like any probability distribution does. Because it properly depicts the distribution of values for many natural occurrences, it is the most significant probability distribution in statistics.

the mean of the data = 9.12 oz

The SD = 0.05 oz

The probability of the bag to be less than 9.07 oz

x = 9.07

z = x - mean / SD = 9.07 - 9.12/0.05 = - 1

for z = -ve

Ф(z) = 1 - Ф(-z) = 1 - Ф(1) = 1 - 0.8413 = 0.1587

The probability that a bag of chip is lower than 9.07 oz of weight is 0.1587.

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The critical region for a hypothesis test consists of outcomes that have a very low probability if the null hypothesis is true. This means that if the null hypothesis is true, these outcomes should not occur. The critical region is used to decide when to reject the null hypothesis and accept the alternative hypothesis.

Hypothesis testing is a process used in statistics to determine whether a certain claim or hypothesis is valid. It involves collecting data, analyzing the data, and making decisions based on the analysis of the data. The goal of hypothesis testing is to either reject or accept a null hypothesis, which is an assumption that there is no relationship between two measured phenomena. Hypothesis testing can also be used to compare two groups or to determine the effectiveness of a treatment or intervention.

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Answer:

25 degree

Step-by-step explanation:

23 - 25 = -2 degree

So, the temperature change is 25 degrees.

Answer:

Step-by-step explanation:

what two numbers can you multiply that will equal to 30 when you multiply but 13 when you add them?

10+3=13     10*3=30  

so we can use 10 and 3

since the first symbol (x^2+13x) is positive than the bigger number you got earlier (10) will be positive

(x+10)

since the second symbol (13x+30) is positive than our next symbol will be positive as well

(x+3)

combine them so now they are (x+10)(x+3)

The ESE (estimated standard error) in the bottom of the independent-measure t statistic measures the variability in the sample data used to calculate the t statistic and provides information on the precision of the t statistic.

The t statistic is used to compare the difference between two means from independent groups to determine if the difference is significant or not.

The ESE reflects the degree of uncertainty in the difference between the two sample means and is calculated as the standard deviation of the sampling distribution of the difference between the two sample means. The ESE is an estimate of the standard deviation of the population difference and is used to calculate the t statistic.

The ESE is an important measure because it provides information on the precision of the t statistic, which is used to make inferences about the population difference. If the ESE is large, it means that the sample difference is less precise and the t statistic is less significant. If the ESE is small, it means that the sample difference is more precise and the t statistic is more significant.

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Domain: (-6, -1]

This is where the graph lines up with the x-axis.

Range: [-6, 4)

This is where the graph lines up with the y-axis.

See the two pictures for a visual reason why.

Answer:

The answer is C

Step-by-step explanation:

This is because the graph shifts to the right as the value correlated with x is 6, meaning the new zeros of the graph would be at (0,0) and (6,0)

Thus, the solution of the inequality is x > -4 or x < 0.

The graph of the solution is option B.

An inequality is a relationship that makes a non-equal comparison between two numbers or other mathematical expressions e.g. 2x > 4

Because of absolute sign | |, the inequality |x+2l <2 can be written as:

x+2 <2 or -(x+2) <2

For x+2 <2:

x+2 <2

x < 2-2

x < 0

For -(x+2) <2:

-(x+2) <2

-x - 2 < 2

-x < 2+2

-x < 4

x > -4

Thus, the solution is x > -4 or x < 0.

The graph of the solution is option B because x > -4 or x < 0 can be written as -4<x<0, which shows the value of x is between -4 and 0.

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The simplified dorm of the expression [tex]\frac{\sqrt{15}}{5\sqrt{48}}\times\frac{\sqrt{48}}{\sqrt{48}}[/tex] is √720/240.

We know there are two types of radicals one is surds when the number has been raised by such power that it is greater than zero and less than one,

The other type of radicals are indices where a number is raised to such power that is greater than one.

Given, A radical expression [tex]\frac{\sqrt{15}}{5\sqrt{48}}[/tex].

Therefore,

[tex]\frac{\sqrt{15}}{5\sqrt{48}}\times\frac{\sqrt{48}}{\sqrt{48}}[/tex].

= (√15×√48)/(5×48).

= √720/240 or √720×(1/240).

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Explanation:

Each term has an x attached to it. We add the numbers in front

4x+7x+x = 4x+7x+1x = (4+7+1)x = 12x

Think of it like saying

4 boxes + 7 boxes + 1 box = 12 boxes

Replace each "boxes" with the letter "x".

In a 10-player round-robin tennis tournament, each player must play 45 games, and a total of 90 games will be played in the tournament.

A round-robin tournament is a type of competition in which every participant plays against every other participant. In a 10-player tournament, the number of games needed can be calculated using the formula for combination.

The density of a tournament can be defined as the number of games each player must participate in to play against every other player.

To calculate the density of a 10-player round-robin tournament, we use the formula

=> n(n-1)/2,

where n is the number of players.

In this case, n = 10. So, the density of the tournament is

=> 10(10-1)/2 = 45.

This means that each player must play 45 games in total, and each game involves 2 players.

So, there will be a total of

=> 45*2 = 90

games played in the tournament.

To summarize, The density of the tournament, 45 games per player, is calculated using the formula n(n-1)/2.

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The remaining side is 16.9 and remaining angles are 83.1 and 34.9.

The cosine formula to find the side of the triangle is given by:

c = √[a² + b² – 2ab cos C] Where a,b and c are the sides of the triangle.

Given:

m∠B = 62°, a = 11, and c = 19

Now, b² = a² + c² - 2ac cos B.

b = √ a² + c² - 2ac cos B

b = √ 11² + 19² - 2x 11  x 19 cos 62

b= 16.9

Now. a/ sin A = b/ sin B= c/ sin C

So, <C = arc sin ( c sin B /b)

<C = arc sin ( 19 sin 62 /16.9)

<C = 83.1

and, <A = arc sin ( a sin B /b)

<A = arc sin ( 11 sin 62 /16.9)

<A = 34.9

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Yes, if function f(x) = 5, then f is defined for all x, including x = 1.

Yes, f is defined for every x, including x = 1, if f(x) = 5. And if f is defined at x = 1, then f(1) = 5. The equation f(x) = 5 means that the function f takes on the value 5 for all x, so if the function is defined at x = 1, its value at that point must be 5.

The term "function" refers to a relationship between a set of inputs and outputs. To put it simply, a function is a relationship between inputs where each input is associated to exactly one output.

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Answer:

3/4 of a lap

Step-by-step explanation:

You have to find the LCD (lowest common denominator)

That is 4, so your equation will be:

[tex]\frac{1}{4} + \frac{1}{2} = x\\\\\frac{1}{4} + \frac{2}{4} = x \\\\\frac{3}{4} = x[/tex]

The value of constant a is 2.45.

To find the value of the constant a, we need to make sure that the pdf (probability density function) is properly normalized. The pdf must satisfy the following property:

∫[a, ∞] f(x) dx = 1

In this case, we have pdf:

∫[a, ∞] (12/x^3) dx = 12∫[a, ∞] (1/x^3) dx

= 12 [-1/(2x^2)]ₐ∞

= 12 * (1/(2a^2))

= 6/ a²

Therefore, to ensure that the integral is equal to 1, we need:

6/ a² = 1

Solving for a:

a^2 = 6

a = ±√6

Since x is always positive, we have a = √6 ≈ 2.45.

So, the constant a is equal to 2.45.

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In the transformation ABC → A'B'C', the preimage of B' is B.

In Mathematics, a transformation can be defined as the movement of a point from its original (actual) position to a final (new) location. This ultimately implies that, when an object (pre-image) is transformed, all of its points would be transformed as well to form a new image.

Generally, there are four (4) major types of transformation and these include the following:

In this context, we can reasonably infer and logically deduce that corresponding vertices, points, or coordinates would be matched together in any type of transformation such as the following:

Point A → Point A'.

Point B → Point B'.

Point C → Point C'.

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The line of reflection would be x+y =4, Hence the correct option is C.

The equation of a line's standard form is given as follows:

[tex]y = mx+c[/tex]

Where m is the slope and c is the y-intercept of the line.

The slope can be determined by

[tex]m =\dfrac{(y_2 - y_1)}{(x_2 - x_1)}[/tex]

Now, Along its diagonals should be reflected in order to reflect it back to itself.

The diagonals will pass through the points [tex]A(3, 1)[/tex] and [tex]C( 1,3)[/tex]

Hence, The slope of the line is,

[tex]m =\dfrac{(y_2 - y_1)}{(x_2 - x_1)}[/tex]

[tex]m =\dfrac{(3 - 1)}{(1 - 3}[/tex]

[tex]m =\dfrac{(2)}{(- 2)}[/tex]

[tex]m = - 1[/tex]

Hence, The equation of the line AC,

[tex](y - y_1) = m(x-x_1)[/tex]

It passes through the point (1,3)

[tex](y - 3) = -1( x-1 )[/tex]

[tex]y - 3 = -x +1[/tex]

[tex]y +x =4[/tex]

Therefore, Option C is true.

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Answer:

(t + 3)(7t - 2)

Step-by-step explanation:

7t² - 19t - 6

consider the factors of the product of the coefficient of the t² term and the constant term which sum to give the coefficient of the t- term

product = 7 × - 6 = - 42 and sum = - 19

the factors are 21 and - 2

use these factors to split the t- term

7t² + 21t - 2t - 6 ( factor the first/second and third/fourth terms )

7t(t + 3) - 2(t + 3) ← factor out (t + 3) from each term

(t + 3)(7t - 2) ← in factored form