Given that f (x )is continuous. f (3 )equals 1, f (1 )equals 6, f (6 )equals negative 2, and f (negative 2 )equals 3. Determine limit as x rightwards arrow 6 to the power of plus of f (x ), and limit as x rightwards arrow negative 2 to the power of minus of f (x ).

Answer:

7x ( - x + 5 )

Step-by-step explanation:

- 7x² = 7x × - x

35x = 7x × 5

- 7x² + 35x = 7x ( - x + 5 )

The rational expression that is equivalent to the expression f(x) = 4/(x - 3) is {x + 2/x - 3} • {4/x + 2}.

Given is the expression as follows -

f(x) = 4/(x - 3)

[A] -

{x - 3/x + 2} • {x + 2/4} = {x - 3/4}

[B] -

{x - 3}/{x + 2} / {4/x + 2} = {x - 3}/{x + 2} × {x + 2/4} = {x - 3/4}

[C] -

{x + 2/x - 3} • {4/x + 2} = {4/x - 3}

[D] -

{x + 2/x - 3} / {4/x + 2} = {(x + 2)²/ 4x - 3}

Therefore, the rational expression that is equivalent to the expression f(x) = 4/(x - 3) is {x + 2/x - 3} • {4/x + 2}.

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The probability of getting heads on the a coin and a number less than 3 on cube is given as 1/6.

In order to find the probability take the ratio of the favorable outcome to the total possible outcome.

The set of total possible outcomes is known as sample space.

The number of elements in the sample space is given as,

Possible outcomes for coin × Possible outcomes for cube

= 2 × 6 = 12

The given two events flipping of coin and rolling of cube are mutually independent.

Which implies it is not the case of conditional probability.

The favorable number of outcomes are as below,

Number of head × Number of numbers less than 3

= 1 × 2 = 2

Now, the probability is given as,

P(getting head on coin and less than 3 on cube) = 2/12 = 1/6

Hence, the probability of getting the required outcome is given as 1/6.

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The values of x, y and z are 24, 10 and 17 using the similar triangles properties and triangles sum properties.

A triangle in geometry is a three-sided polygon with three edges and three vertices. The fact that a triangle's internal angles add up to 180 degrees is its most crucial characteristic. This characteristic is known as the triangle's angle sum property.

Given that ΔHPS≅ΔCNF.

We can see that angle H in triangle HPS is obtuse whereas angle N in triangle CNF is obtuse so comparing this we get,

6x - 29 = 115

6x = 144

x = 24

Comparing angle C and angle P we get

4z - 32 = 36

4z = 68

z = 17

Now the remaining angle in trinagle CNF is angle F which is 3y - 1 as we know that sum of angles in a triangle is 180 and the angle C and N are 36 and 115 we can say that F  is  29

Now to find y we equalise it to 29

3y - 1 = 29

3y = 30

y = 10.

The values of x, y and z are 24, 10 and 17 using the similar triangles properties and triangles sum properties.

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Answer:

304

Step-by-step explanation:

To find the surface area of a rectangular prism with length 4, width 10, and height 8, you can use the formula 2 * (length * width + width * height + height * length).

Plugging in the given values, the surface area is equal to 2 * (4 * 10 + 10 * 8 + 8 * 4) = 2 * (40 + 80 + 32) = 2 * 152 = 304.

Answer: 304

Step-by-step explanation:

By the Application of Prime factorization method the value of x is 48

what is Prime factorization method?

Writing all numbers as the product of primes is a procedure known as prime factorization. Consider the case of the number 20, for instance. We can divide that into two elements. Well, that's four times five, we can say. Furthermore, 5 is a prime number.

Solution:

HCF = ( X, 54 ) = 6

LCM = ( X, 54 ) = 432

a = x  b = 54

using property

a * b = LCM * HCF

54a = 6 * 432

   a  = (6 * 432) / 54

   a = 48

Hence the value of x is 48.

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The area of the shape as shown in the diagram is 11.25 cm².

Area is the region occuppied by a plane shape.

To calculate the area of the shape, we use the formula below.

Formula:

Where:

From the diagram,

Given:

Substitute these question into equation 1

Hence, the area of the shape is 11.25 cm².

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Answer:

x = 6 ans y=4

Step-by-step explanation:

The number of free throws made = x

The number of three points shots made = y

We can make an equation

x+y= total shots made

x+y= 10

So if we want "x",

x=10-y (First equation)

x is one point

y is three point

We can make another equation on how much points gained

(1)x + 3(y) = total points gained

x + 3y =18

If we want "x" ,

x =18-3y (second equation).

Now that we got two equation solve the question with simultaneous equations

x=10-y

x=18-3y

Substitute "x=18-3y" into equation 1

18-3y=10-y

10-y=18-3y

3y-y=18-10

2y=8

y=4 (Three points shots)

x=10-y

x=10-4

x=6 (Free throws made)

Therefore , x=6 and y=4

The quadratic equations, or the equations that are quadratic in form, for this problem is given as follows:

The degree of a function is given by the highest exponent that appears in the definition of the function.

A quadratic function is a function that has a degree of 2.

The standard format of a quadratic function is given as follows:

y = ax² + bx + c.

(in which the coefficient a must assume a value different of zero).

The quadratic function in this problem is given as follows:

6(2x + 4)² = 2x + 4 + 2.

As (2x + 4)² = 4x² + 16x + 16, meaning that the highest exponent would be of 2.

However, equations of the fourth degree can also be quadratic in form, as long as the exponents go as follows: 4, 2 and 0.

Hence these following equations are also quadratic in form:

They are classified as quadratic in form because a transformation such as y = x² can make them quadratic.

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The distances that represent the percentages are given as follows:

A proportion is a fraction of a total amount, used along with the unit measures and basic arithmetic operations to obtain the desired measures in the context of a problem.

28m is 80% of the distance, hence 100% of the distance is obtained applying the proportion as follows:

0.8x = 28

x = 28/0.8

x = 35.

Then the distance that represents 20% of a rotation is calculated as follows:

0.2 x 35 = 7 meters.

The complete problem is given by the image shown at the end of the answer.

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bro this is middle school work not college

Step-by-step explanation:

always remember that 100% is the whole.

so, 15% means 15/100 of the whole.

1/5 = 0.2 = 20/100 of the whole.

so, Target is taking 15/100 off the price.

Walmart is taking 20/100 off the price.

20/100 is bigger than 15/100, so Walmart deducts more off the price, and has therefore the lower and therefore better sale price.

Target sale price :

100/100 - 15/100 = 85/100 × 80 = $68

in short

80 × (1 - 0.15) = 80 × 0.85 = $68

Walmart sale price :

100/100 - 20/100 = 80/100 × 80 = $64

in short

80 × (1 - 0.20) = 80 × 0.80 = $64

The probability that there were at most three successes in a trial is approximately 0.9.

It looks like the histogram shows the probability mass function (PMF) for the number of successes in a trial. The PMF for a random variable gives the probability of each possible value of the random variable.

To find the probability that there were at most three successes in a trial, we need to add up the probabilities of 0, 1, 2, and 3 successes. From the histogram, it looks like the probabilities of these values are approximately 0.2, 0.4, 0.2, and 0.1, respectively. Adding these up, we get an approximate probability of 0.2 + 0.4 + 0.2 + 0.1 = 0.9.

Therefore, the probability that there were at most three successes in a trial is approximate $\boxed{0.9}$.

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67 books will fit on the shell.

One foot has 12 inches (in) (ft). In the US customary and imperial measurement systems, both feet and inches are units of length. The foot has had many different definitions throughout history, but since 1959, it has been defined as exactly 0.3048 meters, and the inch as 2.52 centimeters. The meter is the International System of Units' base unit of length (SI).

In the given question,

Then the number of books

= 42 / (5/8)

= 42 (8/5)

= 336/5

= 67 1/5

Finally, we round 67.2 to the nearest LESSER integer number and obtain

67.

Hence, 67 books will fit on the shell.

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The interval containing the rational zero of f(x) = 3x³ - 5x² + 5x + 7 is given as follows:

-1 < x < 0.

To obtain the possible rational zeros of the function, we use the Rational Zero Theroem.

The rational zero theorem states that all the possible rational zeros of a function are given by plus/minus the factors of the constant by the factors of the leading coefficient.

The parameters for this function are given as follows:

The factors are given as follows:

Hence the possible zeros are given as follows:

±1/3, ±1, ±7/3, ±7.

The numeric values for the function are these points are of:

This means that there is a zero between -7/3 and -1/3, as the function changes from negative to positive, hence the interval is given as follows:

-1 < x < 0.

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The difference between the number of miles travelled on train and car is 110 miles

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

The difference between the distance covered can be calculated as

Distance difference = The difference of the product of speed and time

Substitute the known values in the above equation, so, we have the following representation

Distance difference = 70 * 3 - 50 * 2

Evaluate the products

This gives

Distance difference = 210 - 100

Evaluate the

Distance difference = 110 miles

Hence, the distance difference is 110 miles

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Answer:

coach seats is 310 and first class seats are 77

Step-by-step explanation:

x+4x+2=387

5x+2=387

5x=385

x=77

4x+2

4(77)+2=310

Answer:

There are 77 first-class seats. We can use this information to now define the number of seats in coach. And there are 310 seats in coach.

Step-by-step explanation:

A. By decreasing the base number the graph was affected vertically. A lower base number caused the graph to rise at a slower rate.

What is a logarithm function?

The logarithm is exponentiation's opposite function in mathematics. This indicates that the exponent to which b must be raised in order to obtain a number x is the logarithm of x to the base b. For instance, because 1000 = 10³, its logarithm in base 10 is 3, or log₁₀ 10³= 3.

Given function are

f(x) = log x and g(x) = log₃ x.

The rate of raise of the graph g(x) is more than that of the graph f(x).

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An example of a function that is discontinuous at one and only one point in its domain but is continuous at every other point is the function

This function is continuous at every point in its domain, which is the set of all real numbers (-infinity < x < infinity). However, at the point x = 0, the function is discontinuous.

At x = 0, the function f(x) = x^2 is equal to 0, but if we approach the point x = 0 from the left (x = -0.1, -0.01, etc.), the function is equal to a negative value (-0.01, -0.0001, etc.), and if we approach the point x = 0 from the right (x = 0.1, 0.01, etc.), the function is equal to a positive value (0.01, 0.0001, etc.). This means that the function is not continuous at the point x = 0, and is therefore discontinuous at this point.

The point of discontinuity in this example is an essential discontinuity, which means that it cannot be removed by redefining the function at that point. This is because the function f(x) = x^2 is defined differently for x < 0 and x > 0, and there is no way to redefine the function at x = 0 to make it continuous.

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Therefore, In  Optimistic Criterion  decision of cases : 300 and in Pessimistic Criterion decision of cases : 200

Probabilities can be written as percentages with a 0%–100% range or proportions with a 0–1 range. An event's probability is measured from 0 to 1, with 0 being the most unlikely scenario and 1 being the most likely. When an event's probability is 0.45 (45%), there are 45 percent (100) odds that it will happen.

Here,

a) Optimistic Criterion

Demand/#of  No. of cases

cases

100      $1,000 $900 $800

200     $800 $2,000 $1,900

300     $600 $1,800 $3,000

Maximum of

Column    $1,000 $2,000  $3,000

Maximum

Decision: 300 cases

b) Pessimistic Criterion

Demand/#of   No. of cases

cases

100      $1,000 $900 $800

200     $800 $2,000 $1,900

300     $600 $1,800 $3,000

Minimum Of

Column    $600  $900  $800

Maximin

Decision: 200 cases

Therefore in  Optimistic Criterion  decision of cases : 300 and in Pessimistic Criterion decision of cases : 200

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All the given three conditions are true for conducting a two proportion significance test.

To check the significance of two proportions, following conditions should be met

Hence, all the three conditions must be met to conduct a two-proportion significance test.

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Answer:

the mean (i.e. the average)

Step-by-step explanation:

There's no clear outlier or inconsistency therefore the mean should be used.

Answer:

Step-by-step explanation:

40k

You can quickly calculate the radius of a cylinder using an online calculator.

What is the radius of a cylinder with a capacity of 100 cubic units and a height of 5 units?

Solution:

The radius of a cylinder (r) is equal to (V / h).

= √(100 / π × 5)

= 2.523 units

As a result, a cylinder's radius is 2.523 units.

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Answer:

Step-by-step explanation:

its a

Answer:

To solve a problem involving a whole number and a fraction, you can first convert the whole number to a fraction by writing it as a fraction with a denominator of 1. For example, if the whole number is 4, you can write it as the fraction 4/1.

Then, you can add or subtract the fractions as you would normally, making sure to find a common denominator if necessary. For example, suppose you want to add the whole number 4 and the fraction 3/5. You can first write 4 as the fraction 4/1, giving you:

4/1 + 3/5

To add these fractions, you need to find a common denominator. A common denominator for 1 and 5 is 5, so you can rewrite the fractions with denominators of 5:

4/1 = 20/5

3/5 = 3/5

Now you can add the fractions:

20/5 + 3/5 = 23/5

So the solution to the problem is 23/5.

If you need to multiply or divide the whole number and fraction, you can treat the whole number as a fraction with a denominator of 1 and then perform the multiplication or division as you would normally with fractions.

Step-by-step explanation:

Step-by-step explanation:

the slope-intercept form is

y = ax + b

a being the slope, b being the y-intercept (the y-value when x = 0), which we get from (0, 3) : 3.

the slope is the ratio (y coordinate difference / x coordinate difference) when going from one point on the line to another.

we got 2 points, so, let's use them :

(-4, 0) and (0, 3)

x changes by +4 (from -4 to 0).

y charges by +3 (from 0 to +3).

so, the slope is +3/+4 = 3/4.

therefore, our equation is

y = f(x) = (3/4)x + 3

Answer:

--------------------------------

If the amount of sales for current week is x, Jamie's earning is:

Solve it for x:

The equation for the relationship between the number of cans of paint, x, and the total weight of the cans, y, in slope-intercept form is y = 6x + 0. This equation can be derived from the formula for the slope-intercept form of a line, y = mx + b, where m is the slope of the line and b is the y-intercept. In this case, since the weight of each can of paint is 6 pounds and there is no y-intercept (the line passes through the origin), the slope of the line is 6 and the y-intercept is 0.

A table of possible values for the number of cans of paint, x, and the total weight of the cans, y, based on this equation is shown below:

x (number of cans of paint) y (total weight of cans)

1 6

2 12

3 18

4 24

5 30

As the table shows, for each additional can of paint, the total weight of the cans increases by 6 pounds. This is because each can of paint weighs 6 pounds, and the weight of the cans is equal to the number of cans multiplied by the weight of each can.

Answer: y = 6x

Step-by-step explanation:

       For each can of paint (x) 6 pounds is added. This is represented as;

         y = 6x

       For the table of possible values, we will plug a value in for x, and then evaluate the function for y. See attached.

y = 6(1) = 6

y = 6(2) = 12

y = 6(3) = 18

The critical value is -2.70

What is a null hypothesis?

Two alternatives being the same is the null hypothesis. The underlying assumption is that the observed difference is just the result of chance. It is feasible to estimate the probability that the null hypothesis is correct using statistical testing.

Here, we have

The objective of this experiment is to compare two compounds, designed to reduce braking distance, used in tire manufacturing to prove if the braking distance of SUVs equipped with tires made with compound 1 is shorter than the braking distance of SUVs equipped with tires made with compound 2.

So you have 2 independent populations, SUV's equipped with tires made using compound 1 and SUVs equipped with tires made using compound 2.

Two samples of 66 braking tests are made and the braking distance was measured each time, the study variables are determined as:

X₁: Braking distance of an SUV equipped with tires made with compound one.

Its sample mean is X[bar]₁= 41 feet

And the Standard deviation S₁= 12.1 feet

X₂: Braking distance of an SUV equipped with tires made with compound two.

Its sample mean is X[bar]₂= 46 feet

And the Standard deviation S₂= 9.0 feet

We don't have any information on the distribution of the study variables, nor the sample data to test it, but since both sample sizes are large enough n₁ and n₂ ≥ 30 we can apply the central limit theorem and approximate the distribution of both variables sample means to normal.

The researcher's hypothesis, as mentioned before, is that the braking distance using compound one is less than the distance obtained using compound 2, symbolically: μ₁ < μ₂

The statistical hypotheses are:

H₀: μ₁ ≥ μ₂

H₁: μ₁ < μ₂

α: 0.05

The statistic to use to compare these two populations is a pooled Z test

Z= {(X[bar]₁-X[bar]₂) - (μ₁ - μ₂)}/√S₁²/n₁+S₂²/n₂ ≈ N(0;1)

Z = {(41-46)-0}/√146.41/66+81/66

Z = -5/1.85

Z = -2.70

The rejection region of this hypothesis test is one-tailed to the right, so you'll reject the null hypothesis to small values of the statistic. The critical value for this test is:

Z(α) = Z(0.05) = -1.645

Decision rule:

If Z(H₀) ≥  -1.645, then you do not reject the null hypothesis.

If Z(H₀) < -1.645, then you reject the null hypothesis.

Since the statistic value is greater than the critical value, the decision is to not reject the null hypothesis.

At a 5% significance level, you can conclude that the average braking distance of SUVs equipped with tires manufactured used compound 1 is greater than the average braking distance of SUVs equipped with tires manufactured used compound 2.

Hence, the critical value is -2.70.

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Answer:

10°

Step-by-step explanation:

The sum of the measures of the exterior angles of any polygon, one per vertex, is 360°.

x + 3x + 4x + 5x + 6x + 8x + 9x = 360

36x = 360

x = 10

In a polygon, an exterior angle is supplementary to its adjacent interior angle.

The smallest exterior angle is x, and x = 10.

Answer: 10°