What is (f- g)(x)?
f(x)= x¹ - x² +9
g(x) = x³ + 3x² + 12
Enter your answer in standard form in the box.
(f-g)(x) =

Answer:

92.3%

Step-by-step explanation:

If a continuous random variable X is normally distributed with mean μ and variance σ², it is written as:

[tex]\boxed{X \sim\text{N}(\mu,\sigma^2)}[/tex]

Given:

Therefore, if the speeds that people drive down the Pat Bay Highway are normally distributed:

[tex]\boxed{X \sim\text{N}(90,7^2)}[/tex]

where X is the speed in km/h.

f we want to find what proportion of drivers travel between 80 and 120 km/h, we need to find P(80 ≤ X ≤ 120).

[tex]\implies \sf P(80 \leq X \leq 120)=P(X \leq 120)-P(X \leq 80)[/tex]

Converting to the Z distribution:

[tex]\boxed{\textsf{If }\: X \sim\textsf{N}(\mu,\sigma^2)\:\textsf{ then }\: \dfrac{X-\mu}{\sigma}=Z, \quad \textsf{where }\: Z \sim \textsf{N}(0,1)}[/tex]

Transform X to Z:

[tex]\sf P(X \leq 120)=P\left(Z \leq \dfrac{120-90}{7}\right)=P\left(Z \leq \dfrac{30}{7}\right)[/tex]

[tex]\sf P(X \leq 80)=P\left(Z \leq \dfrac{80-90}{7}\right)=P\left(Z \leq -\dfrac{10}{7}\right)[/tex]

Therefore:

[tex]\begin{aligned}\implies \sf P(80 \leq X \leq 120)&=\sf P\left( -\dfrac{10}{7} \leq Z \leq \dfrac{30}{7}\right)\\\\&=\sf P\left(Z \leq \dfrac{30}{7}\right)-P\left(Z \leq -\dfrac{10}{7}\right)\\\\&=\sf 0.999990892...-0.0765637255...\\\\&= \sf 0.9234271...\\\\&=\sf 92.34271...\%\end{aligned}[/tex]

Therefore, the proportion of drivers travelling between 80 and 120 km/h is 92.3% (nearest tenth).

The data is qualitative, discrete, and at the nominal level of measurement.

The data is qualitative, as it describes the type of pizza ordered, which cannot be measured numerically.

The data is discrete, because there are only a finite number of possible values that the variable can take on, which in this case is one of the three types of pizza: Pepperoni, "Mushroom, or Black Olive.

The highest level of measurement for this data is nominal, because the numbers used to record the type of pizza do not imply any order or ranking between the categories. The numbers are simply a code to identify which type of pizza was ordered, and do not have any intrinsic numerical value or relationship between them. Therefore, the data falls into the nominal level of measurement, which is the lowest level of measurement that data can have.

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The required angle is 35 degrees whose supplementary angle is 35 degrees more than twice its complementary angle.

The definition of a supplementary angle is that it adds up to 180 degrees.

Let's represent the required angle as "x".

We know that the supplementary angle to "x" is 180 - "x".

Similarly, the definition of a complementary angle is that it adds up to 90 degrees, so we know that the complementary angle to "x" is 90 - "x".

Given that the supplementary angle to "x" is 35 degrees more than twice its complementary angle, so we can write this as an equation:

180 - x = 2(90 - x) + 35

Simplifying this equation, we get:

180 - x = 180 - 2x + 35

Adding x to both sides, we get:

x = 35

Therefore, the required angle is 35 degrees.

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The proportion that could be used is (a) 2/5=13/2x

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

Scale = 1 inch: 2 1/2 feet

The proportion that can be used is:

actual length / length on the floor plan = scale factor

So, we can set up the proportion as follows:

actual length / 6 1/2 inches = 2 1/2 feet / 1 inch

Solving for actual length (x), we get:

x/(13/2) = 5/2

So, we have

2x/13 = 5/2

Rewrite as

13/2x = 2/5

Hence, the proporton is (a) 2/5=13/2x

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The null hypothesis H0 to for mice to complete the maze is equal to 18 seconds and alternative hypothesis Ha for mice to complete the maze is less than 18 seconds.

The null hypothesis is the default assumption that there is no effect of the noise stimulus on the time it takes for mice to complete the maze. The alternative hypothesis is the hypothesis that the noise stimulus does have an effect and causes the mice to complete the maze faster. The researcher will conduct a statistical test to determine if there is sufficient evidence to reject the null hypothesis and support the alternative hypothesis.

The researcher is hypothesizing that the true population mean time taken by mice to complete the maze with a loud noise stimulus is less than 18 seconds, Ha< 18seconds. The mean time for mice to complete the maze with the noise stimulus is equal to 18 seconds. Ha: 18 seconds

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The circumference of a circular garden is 51.5 feet.

The area of a circle is the space occupied by the circle in a two-dimensional plane. Alternatively, the space occupied within the boundary/circumference of a circle is called the area of the circle. The formula for the area of a circle is A = πr², where r is the radius of the circle.

Given that, the area of a circular garden is 210 square feet.

Here, 210=3.14×r²

r²=210/3.14

r²=66.87

r=8.2 feet

Now, circumference =2πr

= 2×3.14×8.2

= 51.5 feet

Therefore, the circumference of a circular garden is 51.5 feet.

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The numerator is 4 and the denominator is 7. It is a proper fraction.

A fraction represents the part of a set of objects. It has two parts separated by a dividing line, generally written

a/b

Where

There are 3 types of fraction. They are

1. Proper fraction

A proper fraction is a fraction whose numerator is less than the denominator. It makes the value is less than 1.

Example: 3/4, 2/5.

2. Improper fraction

An improper fraction is a fraction whose numerator is more than the denominator. The value is more than 1.

Example: 9/8, 7/5.

3. Mixed fraction

A mixed fraction is a combination of a whole number and a proper fraction. It is the quotient and the remainder of improper fraction.

Example:

From the explanation above, the fraction of 4/7 has the numerator of 4 and the denominator of 7. The numerator 4 is less than the denominator 7, so the fraction is a proper fraction.

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There are 60 students who chose spaghetti and pizza over corn dogs, tacos, and cheeseburgers, as their favorite lunch.

A circular graph is also known as a pie chart. It is used to display a set of data. The data can be in percentages or degrees or radians.

The given data are as follows:

Pizza: 45%

Corn dogs: 10%

Cheeseburger: 8%

Tacos: 12%

Spaghetti: 25%

The total number of students is 150.

The total percentage of students who eat spaghetti and pizza is (25%+45%), that is, 70%.

The total percentage of students who eat corn dogs, tacos, and cheeseburgers is (10%+12%+8%), that is, 30%.

The percentage difference is (70%-30%), that is, 40%.

Now, calculate 40% of the total students, that is, 150.

150×40% = 150×40/100

= 60

Therefore, the obtained answer is 60.

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The complete question is given in the following chart.

An equation is a part of every formula. A formula is not always an equation. In order to be solved for a variable, equations must be given. Evaluation of formulas

Given,

[tex]$\left(6 x^4 y^2-3 x y^3-4 x y\right)+\left(4 x^4 y^2-x y^3+4 x y\right)[/tex]

[tex]$=6 x^4 y^2-3 x y^3-4 x y+4 x^4 y^2-x y^3+4 x y[/tex]

Group like terms

[tex]$=6 x^4 y^2+4 x^4 y^2-3 x y^3-x y^3-4 x y+4 x y[/tex]

Simplifying the above equation,

[tex]$=10 x^4 y^2-3 x y^3-x y^3-4 x y+4 x y[/tex]

Simplify,

[tex]$=10 x^4 y^2-4 x y^3-4 x y+4 x y[/tex]

Then we get,

[tex]$=10 x^4 y^2-4 x y^3[/tex]

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The given two ratios are not form a proportion.

Ratio is defined as the comparison of two quantities of the same kind by the method of division.

Proportion is an equation it is formed when two ratios are equivalent to each other.

The given two ratios are 4/8 and 1/7.

i.e., 4:8 and 1:7

By simplifying this ratio 4:8 we get 1:2

That is these two ratios are not equal.

proportion is formed only when the two ratios are equal.

Hence, the given two ratios are not form a proportion.

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Answer:

1743.46[tex]\frac{meters}{min}[/tex]

Step-by-step explanation:

Two unit multipliers will be used here:

1 mile (mi)  = 1,609.344 meters

1 hour (hr) = 60 minutes (min)

65 [tex]\frac{mi}{hr}[/tex] = (65[tex]\frac{mil}{hr}[/tex])×([tex]\frac{1609.344 meters}{1 mile}[/tex])×([tex]\frac{1 hour}{60 minutes}[/tex])

The miles unit in the numerator and denominator will cannel each other out completely. In addition, the hour unit in the numerator and denominator will also cancel each other out completely:

         = 1743.46 [tex]\frac{meters}{min}[/tex]

Answer: We can find the value of x by solving the equation 2x + 1/3x = 4.

Combining the terms on the left side, we get:

(6/3)x = 4

Dividing both sides by 6/3, we get:

x = 2

Substituting the value of x back into the expression 27x³ + 1/8x³, we get:

27 * 2³ + 1/8 * 2³ = 27 * 8 + 1/8 * 8 = 216 + 1 = 217

So the value of the expression 27x³ + 1/8x³ is 217.

Step-by-step explanation:

The camera must turn at a rate of about 53.67 degrees/s to follow the ball at an angle of 15 degrees.

In this issue, we are given the underlying speed of the football and the distance of the television camera from the way of the football. We really want to find the rate at which the camera should go to follow the ball at a specific point theta=15 degrees. We can utilize geometry to take care of this issue. The point between the way of the ball and the line associating the camera and the ball is given by 90 - 15 = 75 degrees. Utilizing the cosine capability, we can find the part of the speed of the football opposite to the camera, which is 56*cos(15) = 53.17 ft/s. Presently, utilizing the digression capability, we can find the rate at which the camera should go to follow the ball, which is (53.17/92)*tan(75) = 0.937 radians/s or roughly 53.67 degrees/s. In this manner, the camera should turn at a pace of around 53.67 degrees/s to follow the ball at a point of 15 degrees.

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The complete question is:

A football is thrown horizontally (very little arc) at 56 ft./s parallel to the sideline. A TV camera is 92 ft. from the path of the football. Find de/dt, the rate at which the camera must turn to follow the ball when θ = 15°. football TV camerao 92 ft.

For given triangle, x is 4√5 using Pythagorean theorem.

What is Pythagorean Theorem?

Pythagoras Theorem (also known as Pythagorean Theorem) is a mathematical concept that explains the relationship between the sides of a right-angled triangle. The sides of a right triangle are also referred to as Pythagorean triples. This theorem's formula and proof are discussed with examples here.

The Pythagorean theorem is used to calculate the length of an unknown side and the angle of a triangle. We can deduce the base, perpendicular, and hypotenuse formulae from this theorem.

The Pythagoras Theorem formula is presented in the definition as:

Perpendicular² + Base² = Hypotenuse²

c² = a² + b²

Now,

Given that perpendicular =19

Hypotenuse=21

then Base²=21²-19²  using Pythagoras theorem

Base=√441-361

=√80

=4√5

Hence,

          x is 4√5

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The probability of digits 0 to 9 represent the medicine being not effective.

It is a branch of mathematics that deals with the occurrence of a random event.

As the digit 9 is not effective

So the number of not effective is 2+1+2+2+1+3

=11

The probability=effective numbers/all numbers

=30-11/30

=19/30

Hence, the probability of digits 0 to 9 represent the medicine being not effective.

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Correct expression is,

Table A represents an additive relationship because y is 5.5 more than x.

Table B represents a multiplicative relationship because , y, is 4.5 times x.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

These tables represent the relationships between x and y for two different sets of data.

Hence, The equation for table A is,

Two points from the table A are, (1, 6.5) and (2, 7.5)..

Thus, The equation fop table is,

y - 6.5 = (7.5 - 6.5) / (2 - 1) (x - 1)

y - 6.5 = 1 (x - 1)

y - 6.5 = x - 1

y = x - 1 + 6.5

y = x + 5.5

Thus, Table A represents an additive relationship because y is 5.5 more than x.

Hence, The equation for table B is,

Two points from the table A are, (1, 4.5) and (2, 9)..

Thus, The equation fop table is,

y - 4.5 = (9 - 4.5) / (2 - 1) (x - 1)

y - 4.5 = 4.5 (x - 1)

y - 4.5 = 4.5x - 4.5

y = 4.5x

Thus, Table B represents a multiplicative relationship because , y, is 4.5 times , x,.

Therefore, We get;

Correct expression is,

Table A represents an additive relationship because y is 5.5 more than x.

Table B represents a multiplicative relationship because , y, is 4.5 times x.

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The best describes reason the proof is not correct is c. The proof violates the parity property.

The reason the attempted proof of the statement "The difference between any odd integer and any even integer is odd" is not correct is "The proof violates the parity property."

The student incorrectly subtracted an even integer from an odd integer and concluded that the result is odd. However, the difference between an odd integer and an even integer is always odd, which can be proven directly as follows:

Let n be any odd integer and m be any even integer. Then, by definition, n = 2k + 1 and m = 2j for some integers k and j. The difference between n and m is:

n - m = (2k + 1) - 2j

= 2k - 2j + 1

= 2(k - j) + 1

Since k and j are integers, k - j is also an integer. Therefore, the difference between any odd integer and any even integer is of the form 2x + 1, where x is an integer, which is an odd integer.

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Answer:

-5+6a-8-3a

=6a-3a-5-8

=3a-13

The process by which the various phase of matter affect its properties is mentioned below.

Given is to find how does the phase of matter affect its properties.

Therefore, the process by which the various phase of matter affect its properties is mentioned above.

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Answer:

  (a)  6a³ +22a² +14a -10

Step-by-step explanation:

You want the product of (3a +5) and (2a² +4a -2).

The distributive property is used to eliminate the parentheses when simplifying the product.

  (3a +5)(2a² +4a -2) = 3a(2a² +4a -2) +5(2a² +4a -2)

  = 6a³ +12a² -6a +10a² +20a -10

  = 6a³ +(12+10)a² +(-6+20)a -10

  = 6a³ +22a² +14a -10

__

Additional comment

The leading coefficient of the product is the product of the leading coefficients: 3·2 = 6. This eliminates the last two answer choices.

The first two answer choices differ only in the "a" term, so you only need to find that one. It will be the sum of terms (3a)(-2) and (5)(4a), so is -6a+20a = 14a.

You can also "guess" that the "a" term will be 14a, because that appears the most often among the answer choices.

The first answer choice is the correct one.

Using the values provided on the sketch of the triangular trellis, the values for x, y, and z are 13.33 ft, 6.75 ft, and 17.37 ft, respectively.

From the provided sketch of the trellis, we can use the similar triangles and similar trapezoids to solve the values of x, y, and z.

Consider similar trapezoids at the bottom of the trellis.

10/(10 + 6) = x/(8 + x)

80 + 10x = 16x

6x = 80

x = 40/3 = 13.33

Consider the similar triangles at the top of the trellis.

9/(9 + x) = 7/z

9/(9 + 40/3) = 7/z

z = 469/27 = 17.37

y/(y + 10) = 9/(9 + x)

y/(y + 10) = 9/(9 + 40/3)

(67/3)y = 9y + 90

(40/3)y = 90

y = 27/4 = 6.75

Hence, the length of x, y, and z is 13.33 ft, 6.75 ft, and 17.37 ft, respectively.

The problem seems incomplete, it must have been...

"Jack and Diane are designing a trellis for some special plants they are planning to put in their backyard garden. Use the values provided on the sketch of the trellis to find the missing values for x, y, and z. (Round your answers to the nearest hundredth.)

See attached copy of the complete question."

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Answer:

50+6.3= 56.3

Step-by-step explanation:

The length of the altitude drawn to the hypotenuse is √105 units

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

The triangle

Represent the required length

so, we have the following representation

x/7 = 15/x

Cross multiply the equation

x^2 = 7 * 15

So, we have

x^2 = 105

Take the square roots

x = √105

Hence, the length is √105 units

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Answer:

the two integers are 11 and -8

Step-by-step explanation:

Let's call the two integers we're trying to find "x" and "y".

From the problem statement, we know two things:

x + y = 3 (the sum of the two integers is three)

x^2 + y^2 = 185 (the sum of the squares is 185)

We can use the first equation to solve for one of the variables in terms of the other. For example, we can solve for "y" in terms of "x" by subtracting "x" from both sides:

y = 3 - x

Now we can substitute this expression for "y" into the second equation:

x^2 + (3 - x)^2 = 185

Expanding the square on the left-hand side, we get:

x^2 + 9 - 6x + x^2 = 185

Combining like terms, we get:

2x^2 - 6x - 176 = 0

We can simplify this equation by dividing both sides by 2:

x^2 - 3x - 88 = 0

Now we can solve for "x" using the quadratic formula:

x = (3 ± sqrt(3^2 - 4(1)(-88))) / 2(1)

Simplifying, we get:

x = (3 ± sqrt(361)) / 2

We can ignore the negative root, since it would give us a negative value for "y". So, taking the positive root, we get:

x = (3 + 19) / 2 = 11

Now we can use the first equation to solve for "y":

y = 3 - x = 3 - 11 = -8

The probability of selecting a junior who usually drinks bottled water is 0.0156. This is calculated by finding the probability of each separate event (being a junior and drinking bottled water) and multiplying them together.

To find the probability of selecting a junior who usually drinks bottled water, first calculate the probability of being a junior. There are 12 juniors out of a total of 30 students, so the probability of being a junior is 0.4. Then, calculate the probability of usually drinking bottled water. There are 10 students who usually drink bottled water out of a total of 30, so the probability of usually drinking bottled water is 0.3333. Finally, multiply the probabilities together to get the overall probability of 0.0156. This can be rounded to four decimal places to get the final answer of 0.0156.

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Answer:

A

Step-by-step explanation:

There probably is a good explanation but I don't have it.

Answer:

Step-by-step explanation:

To find the result of increasing 24,312 by 22,211, you would simply add the two numbers:

24,312 + 22,211 = 46,523

So, the result of increasing 24,312 by 22,211 is 46,523.

Answer: 46,523

Step-by-step explanation:

Line up the two numbers by their number places (making sure to put the larger number on top). The add the digits that are on top of each other until you get your answer.

For any given positive real number x and natural number n, there exists a unique positive real number r such that [tex]x = r^n[/tex].

Let x be a positive real number and n be a natural number. We want to show that there exists a unique positive real number r such that [tex]x = r^n[/tex]. This can be expressed mathematically as [tex]x^(1/n) = r[/tex], where r is the unique positive real number we are looking for.

To solve for r, we can take the nth root of both sides of the equation. This gives us [tex]r = x^(1/n)[/tex]. Since x is a positive real number and n is a natural number, it follows that r is also a positive real number.

Furthermore, since x is a fixed value and n is a fixed value, we can conclude that the positive real number r is unique. In other words, for any given x and n, there is only one r that satisfies the equation [tex]x = r^n[/tex].

Therefore, for any given positive real number x and natural number n, there exists a unique positive real number r such that [tex]x = r^n[/tex].

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Answer:

Step-by-step explanation: