Solve for x
E
12
c
А
D
3 B
9

X=pi/2 only in the interval 0 to 4 . We have the maximum value of f(x) = sinx = 1

What is  function interval ?

If the value of the function f (x) grows with an increase in the value of x, the function interval is said to be positive.

                         The function interval, on the other hand, is said to be negative if the value of the function f (x) decreases as the value of x increases.

First of all to apply the extreme value theorem function must be countions at the interval 0 to 4.

F(x)=(x^2-16)/(x^2+x-20) is countinious int the given interval .

Now we find

F'(x)= d(F(x))/dx=1/(x+5)^2 so here we don't have in critical point therefore this choice is incorrect

Similarly if we take

F(x)= sinx

F'(x) = cosx

For critical point ,

Cosx =0

X=pi/2 only in the interval 0 to 4

And this point we have the maximum value of f(x) = sinx = 1

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The first quartile is always equal to one of the values in the sample when the sample size is a multiple of 4.

This is because the first quartile is the median of the lower half of the data set, and when the sample size is a multiple of 4, there is anThe first quartile is always equal to one of the  valuesin the sample when the sample size is a multiple of 4. This is because the first quartile is the median of the lower half of the data set, and when the sample size is a multiple of 4, there is an even number of values in the lower half of the data set. Therefore, the first quartile will be one of the values in the sample. For example, if the sample size is 8, the first quartile will be the median of the first 4 values, which will be one of the values in the sample.

In summary, the first quartile is always equal to one of the values in the sample when the sample size is a multiple of 4. of values in the lower half of the data set. Therefore, the first quartile will be one of the values in the sample. For example, if the sample size is 8, the first quartile will be the median of the first 4 values, which will be one of the values in the sample.
In summary, the first quartile is always equal to one of the values in the sample when the sample size is a multiple of 4.

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Hence, the answer is 9.

Hoped this helped.

\(BrainiacUser1357\)

Answer:

-2

Step-by-step explanation: has to be -2 postive it has to be but /////////////////////////////////////

a) The probability of randomly selecting 4 males out of 7 spectators, given that 70% of the spectators are males, can be calculated using the binomial probability formula.

b) To find the probability that at most 5 of the randomly selected spectators are females, we need to calculate the cumulative probability of selecting 0, 1, 2, 3, 4, and 5 females from the total number of selected spectators.

a) To calculate the probability of selecting 4 males out of 7 spectators, we can use the binomial probability formula:

P(X = k) = C(n, k) * p^k * (1 - p)^(n - k)

Where:

- n is the total number of trials (number of people selected)

- k is the number of successful trials (number of males selected)

- p is the probability of success in a single trial (probability of selecting a male)

- C(n, k) is the binomial coefficient, calculated as C(n, k) = n! / (k! * (n - k)!)

In this case, n = 7, k = 4, and p = 0.70 (probability of selecting a male). Therefore, the probability of selecting 4 males out of 7 spectators is:

P(X = 4) = C(7, 4) * (0.70)^4 * (1 - 0.70)^(7 - 4)

b) To find the probability that at most 5 of the selected spectators are females, we need to calculate the cumulative probability of selecting 0, 1, 2, 3, 4, and 5 females. This can be done by summing the individual probabilities for each case.

P(X ≤ 5 females) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5)

To calculate each individual probability, we use the same binomial probability formula as in part a), with p = 0.30 (probability of selecting a female).

Finally, we sum up the probabilities for each case to find the probability that at most 5 of the selected spectators are females.

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Macmon fue un obispo cristiano del siglo IV que desempeñó un papel importante en la cristianización del Imperio Romano.

Nacido en una familia pagana, Macmon se convirtió al cristianismo después de una visión que tuvo durante una enfermedad. Fue ordenado obispo de la ciudad de Cesarea en Capadocia y se convirtió en un defensor de la ortodoxia cristiana frente a las herejías que surgían en esa época.

Macmon también desempeñó un papel importante en el Concilio de Nicea en el año 325 d.C., donde luchó contra la herejía de Arrio y contribuyó a la redacción del Credo Niceno.

En resumen, la biografía de Macmon es importante porque representa un ejemplo de conversión y defensa de la ortodoxia cristiana en una época crucial para la cristianización del Imperio Romano. Su papel en el Concilio de Nicea también fue fundamental para la redacción del Credo Niceno, uno de los textos fundamentales del cristianismo.

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Answer:

2/1

Step-by-step explanation:

8/4 which is also 2/1

Answer:

3.14 would be answer !

Step-by-step explanation:

Josh should mix 1.2 gallons of dark pink paint and 1.8 gallons of light pink paint to achieve the desired medium pink color.

To find out how much of each leftover paint Josh should mix to achieve a medium pink color (50% red), we can set up a system of equations based on the percentages of red in the paints.

Let's assume that Josh needs x gallons of dark pink paint and y gallons of light pink paint to achieve the desired color.

The total amount of paint needed is 3 gallons, so we have the equation:

x + y = 3

The percentage of red in the dark pink paint is 80%, which means 80% of x gallons is red. Similarly, the percentage of red in the light pink paint is 30%, which means 30% of y gallons is red. Since Josh wants a 50% red mixture, we have the equation:

(80/100)x + (30/100)y = (50/100)(x + y)

Simplifying this equation, we get:

0.8x + 0.3y = 0.5(x + y)

Now, we can solve this system of equations to find the values of x and y.

Let's multiply both sides of the first equation by 0.3 to eliminate decimals:

0.3x + 0.3y = 0.3(3)

0.3x + 0.3y = 0.9

Now we can subtract the second equation from this equation:

(0.3x + 0.3y) - (0.8x + 0.3y) = 0.9 - 0.5(x + y)

-0.5x = 0.9 - 0.5x - 0.5y

Simplifying further, we have:

-0.5x = 0.9 - 0.5x - 0.5y

Now, rearrange the equation to isolate y:

0.5x - 0.5y = 0.9 - 0.5x

Next, divide through by -0.5:

x - y = -1.8 + x

Canceling out the x terms, we get:

-y = -1.8

Finally, solve for y:

y = 1.8

Substitute this value of y back into the first equation to solve for x:

x + 1.8 = 3

x = 3 - 1.8

x = 1.2

Therefore, Josh should mix 1.2 gallons of dark pink paint and 1.8 gallons of light pink paint to achieve the desired medium pink color.

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The z-score would be most useful if you want to know how many standard deviations from the mean a single score in a data set falls. So, the answer to the given question is option B) Az score.

The z-score is a standard score that indicates how many standard deviations an observation is from the mean. A z-score expresses the difference between a measurement and the mean in units of standard deviation. It is calculated as follows: Z-score= (score – mean) / standard deviation

The z-score is frequently utilized in statistics as an index of the likelihood that a result will occur. It is often utilized to determine whether a value is significantly different from the average. It is also known as a standard score or a normal deviate.

The z-score indicates how many standard deviations an observation is from the mean. A positive z-score indicates that the measurement is above the mean, whereas a negative z-score indicates that the measurement is below the mean. A z-score of zero indicates that the score is equal to the mean.

Hence, the answer to the given question is option B) Az score.

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The standard form of the equation of a line perpendicular to the line (3x + 6y = 5) and passing through the point (1, 3) is (2x - y = -1)

To determine the equation of a line perpendicular to the line (3x + 6y = 5) and passing through the point (1, 3), we can follow these steps:

1. Obtain the slope of the provided line.

To do this, we rearrange the equation (3x + 6y = 5) into slope-intercept form (y = mx + b):

6y = -3x + 5

y =\(-\frac{1}{2}x + \frac{5}{6}\)

The slope of the line is the coefficient of x, which is \(\(-\frac{1}{2}\)\).

2. Determine the slope of the line perpendicular to the provided line.

The slope of a line perpendicular to another line is the negative reciprocal of the slope of the provided line.

So, the slope of the perpendicular line is \(\(\frac{2}{1}\)\) or simply 2.

3. Use the slope and the provided point to obtain the equation of the perpendicular line.

We can use the point-slope form of a line to determine the equation:

y - y1 = m(x - x1)

where x1, y1 is the provided point and m is the slope.

Substituting the provided point (1, 3) and the slope 2 into the equation, we have:

y - 3 = 2(x - 1)

4. Convert the equation to standard form.

To convert the equation to standard form, we expand the expression:

y - 3 = 2x - 2

2x - y = -1

Rearranging the equation in the form (Ax + By = C), where A, B, and C are constants, we obtain the standard form:

2x - y = -1

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Let's go through the process of finding the inverse of the function in more detail.

Given the function f(x) = 3/x - 2, we want to find its inverse, denoted as f^(-1)(x).

Step 1 : Replace f(x) with y:

y = 3/x - 2

Step 2 : Swap x and y:

x = 3/y - 2

Step 3 : Solve for y:

To find the inverse function, we want to isolate y on one side of the equation.

Let's manipulate the equation to achieve that:

x = 3/y - 2

Add 2 to both sides of the equation:

x + 2 = 3/y

Now, let's take the reciprocal of both sides:

1/(x + 2) = y/3

We can also write this as:

y = 3/(x + 2)

So, the inverse function of f(x) = 3/x - 2 is given by:

f^(-1)(x) = 3/(x + 2)

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Answer:

The equation can become 4x − 12 − 5x − 5 = 3 by applying the distributive property.

Step-by-step explanation:

4(x − 3) − 5(x + 1) = 3

The first thing would be distribute the 4 and the 5 respectively

4x-12 -5x-5 =3

Answer:

2.1 m

Step-by-step explanation:

The gutter is in the shape of a cylinder.

Its volume is 20 liters and its diameter is 11 cm (0.11 m).

Its radius is half of its diameter => r = 0.055 m.

The volume in cubic metres:

1 litre = 0.001 cubic metres

20 litres = 20 * 0.001 = 0.02 cubic metres

The volume of a section of guttering is given as:

\(V = \pi r^2h\)

where h = length of the guttering

Therefore:

\(0.02 = \pi * 0.055^2 * h\\\\0.02 = 0.009503h\\\\h = 0.02 / 0.009503\\\\h = 2.10 m\)

The length of the section of guttering is 2.1 m long.

The composite result function of ( f ° g )(x) in the given functions f( x ) = x² + 9 and g( x ) = x² - 9 is x⁴ - 18x² + 90.

A function is simply a relationship that maps one input to one output.

Given the data in the question;

First, we set up the composite result function f(g(x)).

f( x ) = x² + 9

f( g(x) ) = f( x² - 9 ) = ( x² - 9  )² + 9

f( g(x) ) = ( x² - 9  )² + 9

Expand the parenthesis

f( g(x) ) = ( x² - 9 )( x² - 9 )  + 9

f( g(x) ) = ( x²( x² - 9 ) -9( x² - 9 ) + 9

f( g(x) ) = x⁴ - 9x² - 9x² + 81 + 9

Collect and add like terms

f( g(x) ) = x⁴ - 18x² + 81 + 9

f( g(x) ) = x⁴ - 18x² + 90

Therefore,  ( f ° g )(x) in the given functions is x⁴ - 18x² + 90.

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Answer:

To compare the proportion of children in the audience for both films, we can calculate the percentage of children in each audience.

For Film A, the ratio of children to adults is 11:19, which means that the total number of parts is 11 + 19 = 30.

The percentage of children in Film A audience is:

(11/30) x 100% = 36.67%

For Film B, the ratio of children to adults is 5:7, which means that the total number of parts is 5 + 7 = 12.

The percentage of children in Film B audience is:

(5/12) x 100% = 41.67%

Since the percentage of children in Film B audience is greater than that of Film A, we can conclude that Film B has a greater proportion of children in the audience. Therefore, the answer is Film B.

The number of weeks that Jenny can withdraw from her account is 14 weeks.

Given the inequality, 600-20w>300 , in order to determine the value of w, take the following steps:

Combine similar terms together:

600 - 300 > 20w

Add similar terms together

300 > 20w

Divide both sides of the equation by 20

300 / 20 > 20w / 20

15 > w

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Answer:

0.04% difference

Step-by-step explanation:

If you're talking about subtraction, you have to turn 0.4 into 0.40 (same thing as 0.4) and subtract that from 0.44, giving you 0.04.

I was not sure which type of difference you were talking about, so I gave the subtraction type of difference.

Answer: He has 4 apples left.

Step-by-step explanation:

5-1=4

(hope this helps)

Answer:4

Step-by-step explanation: James had 5 apples which later he gave one to aliya so 5-1 is 4

Answer: If every quadrilateral has at least two congruent sides, then an obtuse angle is an quadrilateral.

Step-by-step explanation:

A counterexample is basically the opposite of a conditional statement. So the Hypothesis is true but the conclusion is false. An obtuse triangle has different size sides and congruent sides means same size sides. Hope this helps!!!! Let me know if you need further explanation.

The rationing function of prices refers to ability of competitive forces of supply and demand to establish a price at which scarce goods or resources are allocated among different users or consumers.

The price serves as a mechanism,

To determine who gets access to a limited quantity of goods or resources when the demand exceeds the available supply.

When the demand for a particular good or resource is high and the supply is limited, the price tends to increase.

This increase in price acts as a signal to both consumers and producers.

On the consumer side, the higher price encourages individuals to reduce their demand or seek alternative substitutes.

As the higher price may make the good less affordable or desirable.

On the producer side, the higher price provides an incentive to produce more of the scarce good, as it becomes more profitable.

Through this interplay of supply and demand, the price helps to allocate the limited resources efficiently.

Those who value the good or resource the most and are willing to pay the higher price will be able to obtain it.

While others who are not willing or able to pay the higher price may choose to forgo the purchase.

In this way, the rationing function of prices helps to allocate resources based on individuals' willingness.

And ability to pay, ensuring that resources are distributed among those who value them the most.

Therefore, rationing function of prices refers to ability of supply and demand to establish a price at which scarce goods or resources are allocated among consumers based on their willingness and ability to pay.

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The rationing function of prices refers to the ability of supply and demand to establish prices which leads to an equilibrium where shortage or surplus is minimized, ensuring an efficient allocation of resources in a perfectly competitive market.

The rationing function of prices refers to the ability of the competitive forces of supply and demand to establish a price at which selling and buying occurs in a way that gross imbalance does not occur. This characteristic of a market is called allocative efficiency. In a perfectly competitive market, prices tend to be established where marginal cost crosses the demand curve. This point is sometimes regulated to ensure the firm produces the output at where marginal cost equals the price, which then benefits both consumers and the broader social interest. This situation assures consumers a higher quantity and lower price, and it results in the most efficient allocation of resources.

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Answer:

11/3

Step-by-step explanation:

Answer:

Part A). 25 feet

Part B). 16.25 feet

Step-by-step explanation:

Part A). By applying Pythagoras theorem in ΔABC,

            AC² = AB² + BC²

            AC² = (24)² + 7²

            AC² = 576 + 49

            AC = √625

                  = 25 feet

Part B). By applying Pythagoras theorem in ΔABC,

            AC² = AB² + BC²

           (25)² = (19)² + x²

           625 = 361 + x²

           x² = 625 - 361

           x = √264

           x = 16.25 feet

Answer:

line of best fit: y = -2.9114x + 46.569

Step-by-step explanation:

Plugging in your table into Excel, it turns out that y = -2.9114x + 46.569  provides a better fit of the data points into the line.  Please see the attached image for details.

Hope this helps.

Answer:

Step-by-step explanation:

2.

u would use probability for that which gives them the answer

4.

looking at the chart it may be a 14% chance

5.

i would use 3 coins so that the number of coins is equivalent to the amount of pets they have. so that they can see what pets they may have (cats or dogs)

The probability of getting between three and seven heads, inclusively, when flipping a coin 10 times is approximately 0.377 or 37.7%.

The probability of getting between three and seven heads, inclusively, when flipping a coin 10 times can be calculated using the binomial probability distribution.

The probability of getting x successes in n trials, where the probability of success in a single trial is p, is given by the formula P(x) = nCx * p^x * (1-p)^(n-x), where nCx is the number of combinations of n things taken x at a time.

In this case, the probability of getting a head on a single coin flip is 0.5, and we are flipping the coin 10 times. So the probability of getting between three and seven heads, inclusively, is:

P(3) + P(4) + P(5) + P(6) + P(7)

= (10C3 * 0.5³ * 0.5⁷) + (10C4 * 0.5⁴ * 0.5⁶) + (10C5 * 0.5⁵ * 0.5⁵) + (10C6 * 0.5⁶ * 0.5⁴) + (10C7 * 0.5⁷ * 0.5³)

= 0.376953125

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Your grandmother originally invested R 2950.00, which grew at 5% interest for 18 years to become R 6649.93.

To determine how much your grandmother originally invested, we need to use the formula for the future value of a lump sum, which is:

FV = PV x (1 + r)^n

Where:

FV is the future value of the investment

PV is the present value or the initial investment

r is the interest rate

n is the number of compounding periods

We know that the investment was made 18 years ago, and the interest rate was 5%. We also know the future value of the investment, which is R 6649,93. Therefore, we can rearrange the formula to solve for PV:

PV = FV / (1 + r)^n

Plugging in the values, we get:

PV = 6649.93 / (1 + 0.05)^18 ≈ R 2950.00

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