f(x) = 3x² + 4x - 6
g(x) = 6x³5x² - 2

Find (f - g)(x).

O A. (f-g)(x) = 6x³ - 2x² + 4x - 8
O B. (f-g)(x) = -6x³ - 2x² + 4x - 8
O c. (f - g)(x) = 6x³ - 8x² - 4x + 4
O D. (f - g)(x) = -6x³ + 8x² + 4x - 4

Answer: A

Step-by-step explanation: when 18/20 is turned into a decimal it comes out as even and is the best one you can choose from

The sections of the function that are decreasing, defined by the ordered pairs are;

Section 2; (-1, 4) to (1, 0)

Section 4; (3, 2), to (5, -2)

The part of the second function that is decreasing is; (2, -2) to (3, -5)

A function is a definition of the mapping of the set of input variables unto the set of the output variables.

The points in the specified functions are;

Section 1 line ; (-3, 4) to (-1, 4)

Section 2 line ; (-1, 4) to (1, 0)

Section 3 line ; (1, 0) to (3, 2)

Section 4 line ; (3, 2) to (5, -2)

The points through which the function goes through are; (-4, -2.5), (3, -5), (-2, -2), (0, 5), (2, -2), (3, -5), (4, 2.5) and (5, -2)

A function is decreasing when the positive increase in the x-value of the function is accompanied by a decrease in the y-value.

The sections of the functions that are decreasing are;

Section 2 line ; (-1, 4) to (1, 0),

Section 4; (3, 2) to (5, -2)

Parts of the function that is decreasing is; (2, -2), (3, -5)

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Answer: B

Step-by-step explanation:

Answer:

The equation of the line passing through the point (6,-2) that is parallel to the line y=4x-11 is y = 4x - 26

The equation of the linear passes through the point (6, -2) and is parallel to the line y = 4x - 11

Parallel lines have the same slope.

Therefore,

y = 4x - 11

using

y = mx + b

where

m = slope

b= y-intercept

Therefore, the slope of y = 4x - 11 is 4.

And the slope of the other line will be 4 because they are parallel.

Therefore,

y = mx + b

y = 4x + b

it passes through (6, -2)

-2 = 6(4) + b

-2 - 24 = b

b = -26

The equation will be y = 4x - 26

Answer: $1,184,537.217

Step-by-step explanation:

You just multiply the number by 1.22 every year.

For example: year 1 (60,000 * 1.22)= 73,200

Year 2: (73,200 *1.22) =89,304

and so on until year 15 is reached.

Answer:

1

Step-by-step explanation:

The missing part of the triangle are x = 7.5 units, y = (7.5√3)/2 units, y = (7.5√3)/2 units, z = (15√3)/2 units, a = 3.75 units and b = 11.25 units

Given: c = a+b = 15, X = 30°, Z = 60°, C = 90° for the triangles

Using the sine rule

x/sin X = z/sin Z = c/sin C

x/sin X =  c/sin C

x/sin30 = 15/sin90

x/0.5 = 15/1

x = 0.5 × 15 = 7.5 units

Using trigonometrical ratio:

sin 60 = y/x

(√3)/2 = y/7.5

y = (7.5√3)/2 units

sin 30 = y/z

1/2 = (7.5√3)/2/z

z = [(7.5√3)/2] / (1/2)

z = (15√3)/2 units

cos 30 =  b/z

(√3)/2 = b/(15√3)/2

b = [(√3)/2] × [(15√3)/2]

b = 45/4 = 11.25 units

a+b = 15

11.25 + b = 15

a = 15 - 11.25

a = 3.75 units

b = 45/4 = 11.25 units

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We observe that there are p² polynomials of the form x² + ax + b in Zp.

Since there are p choices for each of a and b.

Now a polynomial which is reducible over Zp may be rewritten in the form

(x - c)(x - d)

where c and d are roots.  

So there are p choices if c = d

and if c ≠ d then there are [tex]\frac{p(p-1)}{2}[/tex] choices, the division of 2 eliminates repeated pairs.

Therefore there are p² - ( p + [tex]\frac{p(p-1)}{2}[/tex]) polynomials irreducible over Zp.

A polynomial is said to be irreducible if it cannot be factored into nontrivial polynomials over the same field. The property of irreducibly depends on the field or ring to which the coefficients are considered to belong. Irreducible polynomials appear naturally in polynomial factorization and algebraic field extension.

A polynomial expressible as the product of two or more polynomials of lower degree is known as Reducible polynomial.

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Therefore the  the time todd needed to complete one full rotation around the Ferris wheel is 0.785min

There are numerous ways to define an equation in mathematics. In algebra, an equation is a mathematical statement that establishes the equality of two mathematical expressions. In the equation 2x + 4 = 14, for example, the two expressions 2x + 4 and 14 are separated by the symbol "equal." Mathematical variables are used in even the simplest and most basic mathematical equations.

Here,

the ferris wheel  radius = 10 meters

and he is 14 meters above the ground.

So we can build an equation with given data to find the time todd needed to complete one full rotation around the Ferris wheel

thus time is represented as t

Therefore ,the Ferris wheel rotates at a constant rate so that the angle sweeps out & radians per minute

so speed =8 rad/min

t=distance/speed

t=2[tex]\pi[/tex]/8 min

t=0.785min

Therefore the  the time todd needed to complete one full rotation around the Ferris wheel is 0.785min

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The sixth term of the sequence 9, 16,23,30,37 is 44

An arithmetic sequence is a sequence of numbers such that the difference between the consecutive terms is constant. For instance, the sequence 2, 4, 6, 8, 10, 12.. . is an arithmetic progression with a common difference of 2.

The nth term of an arithmetic sequence is given as a+(n-1)d. Where d is the common difference and a is the first term.

fourth term = 30

second term = 16

third term = (30+16)/2 = 46/2 = 23

therefore d= 30-23 = 7

a = 16-7 = 9

therefore the sixth term = 9+(6-1)7= 9+5×7 = 9+35= 44.

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Answer:

In this problem, we are looking for an equation in the form of y = mx + b that describes the situation where a bank puts $50 into a savings account when it is opened and 12 weeks later, the account has a total of $275.

To find the equation, we need to find the slope (m) and the y-intercept (b). The y-intercept is the point at which the line crosses the y-axis, which in this case is the initial amount of money in the account ($50). The slope is the rate at which the amount of money in the account is changing over time.

To find the slope, we can use the following formula:

slope = (y2 - y1) / (x2 - x1)

In this case, y2 is the total amount of money in the account after 12 weeks ($275), y1 is the initial amount of money in the account ($50), x2 is the number of weeks after the account is opened (12 weeks), and x1 is the number of weeks before the account is opened (0 weeks).

Plugging these values into the formula, we get:

slope = (275 - 50) / (12 - 0) = 225 / 12 = 18.75

Now that we have the slope, we can plug it into the equation y = mx + b, along with the y-intercept (b = 50), to get the final equation:

y = 18.75x + 50

This equation represents the situation described in the problem, where the bank puts $50 into a savings account when it is opened and 12 weeks later, the account has a total of $275.

The velocity at which the diver hits the water is 45.96 feet/s.

The velocity of an object is in feet per sec after it has fallen a distance of d feet is approximated by the function v(d) = √64.4d

Given that, height of olympic diving platform d = 10 m = 32.8 feet

We know that, v(d) = √64.4d and d = 32.8

So, substituting in the above function, we have

v(d) = √64.4d

⇒ √64.4 * 32.8

⇒ √ 2112.32

⇒ 45.96 feet/s

Thus, the velocity at which the diver hits the water is 45.96 feet/s.

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Congruent triangles are triangles having corresponding sides and angles to be equal.

Congruent triangles are triangles that have both the same size and the same shape and they have the same perimeter and the same area. Congruence is denoted by “≅”.  For example, we can write ABC ≅ DEF. They have the same area and the same perimeter.

Congruent triangles have the same angle measures and the same side lengths.

On the other hand, the similar triangle is the term used for triangles that have the same shape, but not necessarily the same size.

Two triangles are considered to be congruent if they meet one of the following criteria.

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The given equation can be written in standard form as x + 6y + 11 = 0.

A linear equation can be solved by equating the LHS and RHS of the equation following some basic rules such as by adding or subtracting the same numbers on both sides and similarly, doing division and multiplication with the same numbers.

The given equation is 2y + 3 = −1/3 (x − 2).

It can be written in the standard form of ax + by + c = 0 as follows,

2y + 3 = −1/3 (x − 2)

=> 3(2y + 3) = -1(x − 2)

=> 6y + 9 = 2 - x

=> 6y + x + 9 + 2 = 0

=> x + 6y + 11 = 0

Hence, the standard form of the given equation is x + 6y + 11 = 0.

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The volume of the rind is growing at the rate 681.097 cubic centimeters per week at the end of the fifth week.

In the given question, the radius of a spherical watermelon is growing at a constant rate of 2 centimeters per week.

The thickness of the rind is always one tenth of the radius.

We have to find the volume of the rind is growing at the rate cubic centimeters per week at the end of the fifth week.

Assume that the radius is initially zero.

Let r be the radius of watermelon.

dr/dt = 2 cm/week

Radius after 5 week = 10 cm

Thickness of the rind = r/10 cm = 0.1r cm

Now the volume of rind

V = 4/3 π[r^3-(0.9r)^3]

dV/dt = 4/3 π[3r^2-3r^2(0.9)^3]dr/dt

dV/dt = 4/3 π[1-(0.9)^3](3r^3)(2)

dV/dt = 8(3.14)(0.271)(10)^3

dV/dt = 8(3.14)(0.271)(1000)

dV/dt = 681.097 cm^3/ week.

Hence, the volume of the rind is growing at the rate 681.097 cubic centimeters per week at the end of the fifth week.

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Fraction which are equivalent to the given fractions are as follow:

a. 4 /6 is equivalent to 2/3, 8/12, 12/18 ,...

b. 4/8 is equivalent to 1/2 , 8/16, 12/24,.....

c. 2/6 is equivalent to 1/3 , 4/12, 6/18,....

d. 2/4 is equivalent to 1/2, 4/8, 6/12,...

e. 3/4 is equivalent to 6/8, 9/12, 12/16,...

As given in the question,

Equivalent fraction are the fractions which when reduced have the same numerator and denominator.

Multiply or divide by 2/2, 3/3, 4/4, 5/5,...so on to all numerator and denominators of the given fractions to get equivalent fraction.

a. 4/6 divide by 2 both numerator and denominator we get

4/6 = 2/3

Now multiply by both numerator and denominator by 2/2, 3/3,...so on.

4/6 is equivalent to 2/3 , 8/12, 12/18,...

Multiply and divide by same numbers in the numerator and denominator of all the fractions to get equivalent

b. b. 4/8 is equivalent to 1/2 , 8/16, 12/24,.....

c. 2/6 is equivalent to 1/3 , 4/12, 6/18,....

d. 2/4 is equivalent to 1/2, 4/8, 6/12,...

e. 3/4 is equivalent to 6/8, 9/12, 12/16,...

Therefore, equivalent fractions of the given fractions are :

a. 4 /6 is equivalent to 2/3, 8/12, 12/18 ,...

b. b. 4/8 is equivalent to 1/2 , 8/16, 12/24,.....

c. 2/6 is equivalent to 1/3 , 4/12, 6/18,....

d. 2/4 is equivalent to 1/2, 4/8, 6/12,...

e. 3/4 is equivalent to 6/8, 9/12, 12/16,...

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The shape of the population can be disregarded when working with sampling distribution of sample mean.

The correct option is Option D)

What is central limit theorem?

The central limit theorem in probability theory proves that, even if independent random variables are not normally distributed in themselves, in many cases, when they are added together, their correctly normalized sum tends toward a normal distribution.

As in the central limit theorem mean and standard deviation is given but there is not mention of shape of the distribution.

Hence shape of the distribution is not taken into considerations.

Therefore, The shape of the population can be disregarded when working with sampling distribution of sample mean.

The correct option is Option D)

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A game that has an equal probability of winning or losing is said to be fair.

The foundational elements of fair play can be observed and learned both on and off the field, and include honesty, solidarity, tolerance, care, excellence, and joy. Fair competition, respect, camaraderie, team spirit, equality, and sport without doping are also examples.

A simple game of chance is deemed fair if there is an equal chance of winning for each player. If there is an equal chance of selecting each alternative, the decision is fair. Your understanding of probability can help you evaluate the fairness of games and make just decisions.

Children love playing together more when everyone is being fair. Additionally, it plays a significant role in getting along with people.

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As per the 98% confidence interval for the proportion of all American adults who would report having earned money by selling something online in the previous year is (0.1859,0.2133).

Confidence interval:

In statistics, confidence interval is an estimate of an interval in statistics that may contain a population parameter.

Given,

According to a recent pew research center report, many American adults have made money by selling something online. in a random sample of 4579 American adults, 914 reported that they earned money by selling something online in the previous year. assume the conditions for inference are met.

Here we need to construct a 98% confidence interval for the proportion of all American adults who would report having earned money by selling something online in the previous year.

As per the given question, the value of

Confidence interval = 98%

Number of samples = 4579

Reported numbers = 914

Therefore, the number of failure is calculated as,

=> 4579 - 914

=> 3665

Here the sample proportion is the number of successes divided by the sample size:

=> 941/4579

=> 0.1996

Here for confidence level 1 − α = 0.98,

We have to determine zα / 2 ​= z0.01​ using the normal probability table in the appendix, we get

zα/2 ​= 2.33

Then the margin of error is calculated as,

E = 2.33 x √[0.1996 x (1 - 0.1996)]/4579

E = 0.0137

Then the boundaries of the confidence interval are then:

p⁻ˣ = 0.1996−0.0137 = 0.1859

p⁺ˣ = 0.1996+0.0137 = 0.2133

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If the decision of enrolling in the course in independent events, the probability of not enroll in chemistry is 0.55

The chances of enroll in physics = 10%

The chances of the not enroll in physics but enroll in chemistry = 45%

The probability is the ratio of the number of favorable outcomes to the total number of outcomes

The probability = Number of favorable outcomes / Total number of outcomes

Given that her decision of enrolling in a course is independent of enrolling in other courses

The probability of not enroll in chemistry = 1 - The probability of enroll in chemistry

Substitute the value in the equation

The probability of not enroll in chemistry = 1 - 0.45

= 0.55

Therefore, the probability of not enroll in chemistry is 0.55

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Answer:

yes

Step-by-step explanation:

Answer: 44.55

Step-by-step explanation:

[tex]\stackrel{\textit{\LARGE P~E~M~D~A~S}}{3^2 + 3[ ~~ 2^3 (\sqrt{49}-2^2)(3^2-2^3) -2^2 ~~ ]}\implies 3^2 + 3[ ~~ 2^3 (\sqrt{49}-4)(9-8) -2^2 ~~ ] \\\\\\ 3^2 + 3[ ~~ 2^3 (7-4)(9-8) -2^2 ~~ ]\implies 3^2 + 3[ ~~ 2^3 (3)(1) -2^2 ~~ ] \\\\\\ 3^2 + 3[ ~~ 8 (3)(1) -4 ~~ ]\implies 3^2 + 3[ ~~ 24 -4 ~~ ]\implies 3^2 + 3[ ~~ 20 ~~ ] \\\\\\ 9+3[20]\implies 9+60\implies \text{\LARGE 69}[/tex]

The maximum number of automobile registrations that the police may have to check is 72 license.

Concept Introduction:-

Mathematics defines time as an ongoing and continuous series of events that take place in order, from the past to the present to the future.

Given Information:-

We have been given that a witness to a hit-and-run accident told the police that the license number contained the letters RLH followed by  3 digits, the first of which was a 5 . If the witness cannot recall the last  2 digits, but is certain that all 3 digits are different.

We have to find that the maximum number of automobile registrations that the police may have to check

According to the problem

Since digits are different, available digits are 0,1,2,3,4,6,7,8,9  ( as 5 is already used)

Number of available digits = 9

2nd digit can be any of the above 9 digits

3rd digit can be any of the remaining 8 digits

Police have to check 9*8 = 72 registrations.

Hence , The maximum number of automobile registrations that the police may have to check is 72 license.

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Simple linear regression is a model that assesses the relationship between a dependent variable and an independent variable. The simple linear model is expressed using the following equation:

Where:

1. Y– Dependent variable

2. X– Independent (explanatory) variable

3. a– Intercept

4. b– Slope

Statistical Analysis Regression uses the statistics methods such as mean, median, normal distributions to figure out the relationships between the dependent and independent variables, to access the relationship strength between the variables and for modelling the new relationship among them, as it involves various variations such as simple linear, multilinear and non-linear where the non-linear regression is mainly used for complicated datasets in which the independent and dependent variables shows the nonlinear relationship.

Answer:

1/14

Step-by-step explanation:

all together the probability would be 1/21 because we're adding all the color eyes together. After that, it narrows to only blue and hazel which is 14 so the new probability is 1/14, so the answer is 1/14.

The force exerted by her biceps to allow her hold the tray is 282 N.

Force is the product of mass and acceleration.

To calculate the force the biceps must exert to allow her hold the tray, we use the formula below.

Formula:

Where:

From the question,

Given:

Substitute these values into equation 1 and solve for F'

Hence, the force exerted by her biceps is 282 N.

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Answer:To find the mean of the heights of the 17 students, we need to add up all of the heights and divide the sum by the number of students. The sum of the heights is 1777 cm, and when we divide this by 17, we get a mean height of 104 cm.

To find the median of the heights of the 17 students, we first need to put the heights in order from least to greatest. The heights in order are 101,102,106,109,110,110,112,115,115,115,115,115,117,120,120,123,125. There are 17 students, so the median is the height of the 9th student, which is 115 cm.

Step-by-step explanation:

Answer:

Step-by-step explanation: