Knowledge Check Divide. (x+6)/(3x+9)-:(7)/(9x)+42 Simplify your answer as much as possible.

B

-6

...................

The length of the top surface in standard form is [tex]H(x) = (60x^2 + 16x + 1)/(6x + 1)[/tex]

Algebraic expressions are mathematical phrases that involve numbers, variables, and arithmetic operations such as addition, subtraction, multiplication, and division. They can also involve exponents, roots, and other mathematical symbols.

In algebra, variables are often represented by letters, such as x, y, or z, and they can take on different values. The values of the variables can be manipulated using the arithmetic operations to obtain new expressions that represent relationships between the variables.

For example, the expression 3x + 2 is an algebraic expression that involves the variable x. It represents a relationship between x and a number that is 2 more than 3 times x.

Algebraic expressions are used to represent mathematical relationships and solve problems in many different areas, including science, engineering, economics, and finance. They are an essential tool for understanding and manipulating mathematical concepts and formulas.

The area of a rectangle can be found by multiplying its length and width. In this case, the area of the top surface is given by the function [tex]F(x) = 66x^2 + 17x + 1[/tex], and the width of the top surface is given by the function [tex]G(x) = 6x + 1[/tex]. Therefore, the length of the top surface can be expressed as:

Length x Width = Area

[tex]Length x (6x + 1) = 66x^2 + 17x + 1[/tex]

Expanding the left side of the equation, we get:

[tex]6x^2 + x Length = 66x^2 + 17x + 1[/tex]

Bringing all the terms to one side, we get:

[tex]60x^2 + 16x + 1 - Length x = 0[/tex]

Rearranging the terms, we get:

[tex]Length x = 60x^2 + 16x + 1[/tex]

Finally, dividing both sides by the width function G(x), we get the expression for the length of the top surface in standard form:

[tex]H(x) = (60x^2 + 16x + 1)/(6x + 1)[/tex]

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P(X = 1) = (50 choose 1) * (0.06)^1 * (0.94)^49 ≈ 0.198

And so on for the other values of X.

An example of independent random variables X and Y such that P(X < Y) = 1 is X = 0 and Y = 1. Since X is always less than Y, the probability that X is less than Y is 1.

The probability of a person ordering both a Quarter Pounder and a Diet Coke is p1*p2 = 0.2*0.3 = 0.06. Since each person orders independently of all others, the number of people ordering both a Quarter Pounder and a Diet Coke follows a binomial distribution with parameters n = 50 and p = 0.06. Therefore, the PMF of X is:

P(X = x) = (50 choose x) * (0.06)^x * (0.94)^(50-x)

for x = 0, 1, ..., 50.

Using the above formula, we can calculate the probability of X taking on any value between 0 and 50. For example, the probability of X = 0 is:

P(X = 0) = (50 choose 0) * (0.06)^0 * (0.94)^50 = 0.94^50 ≈ 0.076

The probability of X = 1 is:

P(X = 1) = (50 choose 1) * (0.06)^1 * (0.94)^49 ≈ 0.198

And so on for the other values of X.

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Subtracting -15/18 from -12/18, the answer is -3/18 in simplest form.

Subtracting two fractions with different denominators involves finding a common denominator and then subtracting the fractions.

The common denominator for (-5)/(6) and (-2)/(3) is 6*3=18.

To make the fractions have the same denominator, the numerators need to be multiplied by the denominators and then divided by the denominator.

(-5)/(6) can be rewritten as -(5*3)/(6*3)=-15/18
(-2)/(3) can be rewritten as -(2*6)/(3*6)=-12/18

Subtracting -15/18 from -12/18, the answer is -3/18 in simplest form.

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Answer: Here are three specific examples of public health problems that epidemiologists may investigate:

Obesity: Epidemiologists may investigate the causes and risk factors for obesity, as well as the prevalence and trends in obesity rates over time. They may also evaluate the effectiveness of interventions to prevent or treat obesity, such as diet and exercise programs, policy changes, or medical treatments.

Environmental exposures: Epidemiologists may investigate the health effects of exposure to environmental toxins, such as air pollution, lead, or pesticides. They may evaluate the risks associated with exposure to these toxins, identify populations that are particularly vulnerable, and assess the effectiveness of interventions to reduce exposure or mitigate health effects.

Injury prevention: Epidemiologists may investigate the causes and risk factors for injuries, such as motor vehicle crashes, falls, or firearm injuries. They may identify populations that are at higher risk for injuries, evaluate the effectiveness of injury prevention programs or policies, and develop strategies to reduce the incidence or severity of injuries.

Step-by-step explanation:

The total surface area of the two hemispherical domes is 6.16m^2

To find the TSA (total surface area) of two hemispherical domes, we need to first find the surface area of one hemispherical dome, and then multiply it by 2.

The surface area of one hemispherical dome can be found using the formula:

SA = 2πr^2

where r is the radius of the base of the hemisphere.

Given that the base radius of each hemisphere is 0.7m, the total diameter of each hemisphere is 1.4m (since the diameter is twice the radius), and therefore the radius is 0.7m.

So the surface area of one hemisphere is:

SA = 2π(0.7m)^2

= 3.08m^2

Therefore, the TSA of two hemispherical domes is:

TSA = 2 × SA

= 2 × 3.08m^2

= 6.16m^2

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The original price of the given pair of shoes is; £59.4

It is known the original price is:

OP=(100+DP)/100X.... (i), where,

OP = Original Price

CP = Cost Price = £54,

DP = Discount percentage = 10%.

Substituting the values in equation (i), we get:

OP = (100+10)/100X54 ,

Or, OP = 110/100x54 = 59.4.

Therefore the Original Price of the Pair of Shoes is £59.4.

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The velocity of the car is 80m/s

v= u + at²

The parameters given are:

velocity= ?

initial velocity(u)= 0

acceleration(a)= 5

time(t)= 4

The velocity can be calculated as follows

v= 0 + 5(4²)

v= 0 + 5(16)

v= 0 + 80

v = 80

Hence the velocity of the car is 80m/s

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The number of pounds of durian needed to produce 216 pounds of durian-flavored chocolate bars is 50 pounds.

We have,

To determine the amount of durian needed to produce 216 pounds of durian-flavored chocolate bars, we need to calculate the cost and compare it to the budget constraint.

Let's assume x represents the number of pounds of durian needed.

The cost of plain chocolate per pound is $3.50, so the cost of x pounds of plain chocolate is 3.50x dollars.

The cost of durian per pound is $15.75, so the cost of x pounds of durian is 15.75x dollars.

To ensure the cost does not exceed $4.50 per pound, we set up the inequality:

3.50x + 15.75x ≤ 4.50 x 216.

Combining like terms:

19.25x ≤ 972.

Dividing both sides by 19.25:

x ≤ 50.45.

Since we cannot have a fraction of a pound, we round down to the nearest whole number.

Therefore,

The number of pounds of durian needed to produce 216 pounds of durian-flavored chocolate bars is 50 pounds.

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The Euclidean algorithm can be applied to Gaussian integers in the same way it is applied to ordinary integers. In this case, we are given x = 3+2i and y = 2-5i and we need to find q and r such that x = qy + r and d(r) < d(y).

First, we divide x by y to get a quotient and remainder:
x/y = (3+2i)/(2-5i) = (3+2i)(2+5i)/(2-5i)(2+5i) = (16+7i)/29 = 0.551724 + 0.241379i

Since q and r must be Gaussian integers, we round the real and imaginary parts of the quotient to the nearest integer to get q = 1 + 0i = 1.

Next, we multiply q by y and subtract from x to get the remainder:
r = x - qy = (3+2i) - (1)(2-5i) = 1+7i

Finally, we check that d(r) < d(y):
d(r) = 1^2 + 7^2 = 50
d(y) = 2^2 + (-5)^2 = 29

Since d(r) > d(y), we need to adjust our quotient and remainder. We can do this by subtracting 1 from the real part of q and adding y to the remainder:
q = 0 + 0i = 0
r = (1+7i) + (2-5i) = 3+2i

Now, d(r) = 3^2 + 2^2 = 13 < 29 = d(y), so our final answer is q = 0 and r = 3+2i.

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A frequency table is a type of statistic used to organize and display data.

A data set is a collection of related data records or observations, usually containing information about a particular subject or area of study. Data sets can be used to analyze trends, make predictions, and provide insights into various phenomena. Data sets can be collected from a variety of sources, such as surveys, experiments, simulations, or other research methods. They are typically organized into tables and can include both quantitative and qualitative data.

It is a chart that shows how often something occurs within a given set of data. The categories in a frequency table are the different values or categories of data, and the frequencies are the number of times each category occurs.

Relative frequency is the ratio of the number of times a category occurs in the data set to the total number of values in the data set. It is usually expressed as a percentage or decimal. For example, if the data set contains 20 values and the category "A" occurs 5 times, the relative frequency of "A" is 25%.

Cumulative frequency is the sum of the frequencies up to a given point in the data set. It is used to show how many values are below or above a certain category. For example, if the data set contains 20 values and the category "A" occurs 5 times, the cumulative frequency of "A" is 5. This means that there are 5 values that are below or equal to "A" in the data set.

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Answer:

A frequency table is a type of statistic used to organize and display data.

What is data set?

A data set is a collection of related data records or observations, usually containing information about a particular subject or area of study. Data sets can be used to analyze trends, make predictions, and provide insights into various phenomena. Data sets can be collected from a variety of sources, such as surveys, experiments, simulations, or other research methods. They are typically organized into tables and can include both quantitative and qualitative data.

It is a chart that shows how often something occurs within a given set of data. The categories in a frequency table are the different values or categories of data, and the frequencies are the number of times each category occurs.

Relative frequency is the ratio of the number of times a category occurs in the data set to the total number of values in the data set. It is usually expressed as a percentage or decimal. For example, if the data set contains 20 values and the category "A" occurs 5 times, the relative frequency of "A" is 25%.

Cumulative frequency is the sum of the frequencies up to a given point in the data set. It is used to show how many values are below or above a certain category. For example, if the data set contains 20 values and the category "A" occurs 5 times, the cumulative frequency of "A" is 5. This means that there are 5 values that are below or equal to "A" in the data set.

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Therefore , the solution of the given problem of triangle comes out to be  the shape is 55 square miles.

Because a triangular has two or more extra sections, it is a polygon. It's shape is a simple rectangle. A triangular shape can only be distinguished from a parallelogram by its sides A, B, and C. A singular plane rather than a cube is produced by Euclidean geometry when the edges are not perfectly collinear. A shape is referred to as triangular if it has three sides and three angles. An angle is the point where a quadrilateral's three sides meet. A triangle's sides add up to 180 degrees.

Here.

Two triangles with a base of 10 miles and heights of 7 miles and 4 miles can be formed from the composite design.

The following method can be used to determine a triangle's area:

A = (1/2)bh

where A represents area, B represents foundation, and H represents height.

We can calculate each triangle's area using the following formula:

=> Area of 1st triangle

=>  (1/2)(10)(7) = 35 square miles

=> Area of 2nd triangle

=>  (1/2)(10)(4) = 20 square miles

The two triangles' combined regions make up the composite shape's surface area.

55 square miles is the combined shape's area

=>  (35 + 20).

Consequently, the combined size of the two triangles in the shape is 55 square miles.

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The amount of time each would require working alone is 6 hours for Bill and 4 hours for his father.

To find the time each person would require working alone, we can use the combined work rate formula: 1/t₁ + 1/t₂ = 1/t, where t₁ is the time for Bill's father, t₂ is the time for Bill, and t is the time they take working together.

We are given that t = 2 hours and 24 minutes, or 2.4 hours. We are also told that Bill's father can paint a room in 2 hours less than Bill, so t₁ = t₂ - 2.

Substituting these values into the formula, we get:

1/(t₂ - 2) + 1/t₂ = 1/2.4

Multiplying both sides by 2.4t₂(t₂ - 2) to clear the denominators gives us:

2.4t₂ + 2.4(t₂ - 2) = t₂(t₂ - 2)

Simplifying and rearranging gives us:

2.4t₂ + 2.4t₂ - 4.8 = t₂² - 2t₂

t₂² - 6.8t₂ + 4.8 = 0

Multiply the whole equation by 5 and factor.

5t₂² - 34t₂ + 24 = 0

(5t₂ - 4)(t₂ - 6) = 0

t₂ = -4/5 or t₂ = 6

Since t₂ cannot be less than 2 (because Bill's father takes 2 hours less than Bill), the only valid solution is t₂ = 6. Therefore, Bill would take approximately 6 hours to paint the room alone, and Bill's father would take approximately 4 hours (6 - 2) to paint the room alone.

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Answer:

go to the y and go all the way down to two i think

Answer:

Step-by-step explanation:

4 - 2(1) = 2

i'm pretty sure, sorry if its wrong, pls do not report.

how i got it

4 - 2 = 2

2 x 1 = 2

                        4 - 2y = 2

                       4 - 2(1) = 2

Type the second one exactly how i did, don't put a symbol or space, just copy and paste it.

The evaluated expressions are 2, -7, -2, -12, -8, and 7.

To evaluate the expressions without using a calculator, we need to substitute the given values of the variables into the expressions and simplify.

a. Substitutex=4into the expressionx−2

=4-2

=2

b. SubstituteB=−5into the expressionB−2

=-5-2

=-7

c. Substitutew=−2into the expression−w−4

=-(-2)-4

=2-4

=-2

d. Substitutey=−3into the expression(y)4

=(-3)4

=-12

e. Substitutet=4into the expression−t2

=-(4)2

=-8

f. SubstituteR=−10into the expression−R−3

=-(-10)-3

=10-3

=7

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In the three-month period, the water level was 6.5 inches, 6.3 inches, and 6.7 inches, respectively. This is lower than the yearly average of 7.2 inches

Water level is a term used to describe the height of a body of water, usually in reference to an ocean, lake, river, or other body of water. It can also refer to the height of the water above sea level or other reference points.

The table indicates that the water level of the reservoir for the three-month period is lower than the yearly average. This can be seen by comparing the data in the table.

This could be due to a number of factors, including decreased precipitation and increased evaporation during the three-month period.

Ultimately, the data shows that the water level of the reservoir for the three-month period is lower than the yearly average. This could be a cause for concern in the long-term, as the water level of the reservoir could become too low to sustain local populations and ecosystems in the area.

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Answer:

A. The number of actual outcomes is 6 (since there are 6 sides to the block).

B. The number of all possible outcomes would be the number of ways the block could land on the table, which is also 6 (since each of the 6 sides is equally likely to face up).

C. The probability that the block will land with either the T, C or R facing up is the probability of landing on any one of those 3 sides. Since there are 3 such sides, and each side is equally likely to face up, the probability is 3/6 or 1/2.

Answer:

1st one: (x-7)

2nd: (-x+7)

3rd: (5x+3)

Step-by-step explanation:

1: you subtract like terms so first you do 3x-2x which is x and do -2-5 and get -7 so its (x-7)

2: do 2x-3x and get (-x) and then do 5-(-2) and get 7 so the answer is (-x+7)

3: first do 2x+3x and get 5x and then do 5+(-2) and get 3 so the answer is (5x+3)

Answer:

Step-by-step explanation:

( 3x - 2 ) - ( 2x + 5 ) = 3x - 2 - 2x - 5  = x - 7

( 2x + 5 ) - ( 3x - 2 ) = 2x + 5 - 3x + 2 = - x + 7

( 2x + 5 ) + ( 3x - 2 ) = 2x + 5 + 3x - 2 = 5x + 3

The factored form of the expression [tex]3x^2 - 3x - 18[/tex] is B) 3(x-3)(x+2).

To factor a quadratic expression like this, we want to find two numbers that multiply to the constant term (-18) and add up to the coefficient of the x term (-3). In this case, those numbers are -3 and 6, because (-3) * 6 = -18 and (-3) + 6 = 3.

Then, we can use those numbers to split the middle term into two terms:

[tex]3x^2 - 3x - 18 = 3x^2 - 9x + 6x - 18[/tex]

[tex]= 3x(x-3) + 6(x-3)[/tex]

[tex]= (x-3)(3x+6)[/tex]

[tex]= 3(x-3)(x+2)[/tex]

So the factored form of the expression is 3(x-3)(x+2), which is equivalent to choice B.

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The length of QS to 3 significant figures is 26.9 cm. QS is the side of the triangle that is adjacent to the angle of 27°.

An adjacent angle is an angle that shares a common side and a common vertex with another angle. Adjacent angles are commonly seen when two lines intersect, forming four angles.

QS is the side of the triangle that is adjacent to the angle of 27°. To calculate the length of this side, we can use the Law of Sines. The Law of Sines states that for any triangle with sides a, b and c and angles A, B and C respectively, the following equation holds true:

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

Therefore, for our triangle, we can use the equation as follows:

11/sin 27° = QS/sin 90°

Rearranging this equation, we can solve for QS:

QS = (11/sin 27°) x sin 90°

QS = 26.9 cm

Therefore, the length of QS to 3 significant figures is 26.9 cm.

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Answer: its D

i suck at explaining but ik its D

Answer:

Step-by-step explanation:

(1) The percentage of males that drive sports cars is 46.43 %.

(2) The percentage of all drivers that are male is 25 %.

(3) The percentage of sports car drivers that are male is 46.43 %.

(4) Yes, question 1 and question 3 are the same.

The percentage of males that drive sports cars is calculated as follows;

= 39 / 84  x 100%

= 46.43 %

The percentage of all drivers that are male is calculated as follows;

= 60 / 240  x 100%

= 25%

The percentage of sports car drivers that are male is calculated as;

= 39 / 84  x  100%

= 46.43 %

Thus, question 1 and question 3 are the same.

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Calculate acceleration using this equation: acceleration = delta v / time. expressions  To solve for acceleration, enter the values you calculated for delta v and the amount of time it took the object to change directions.

Multiplying, dividing, adding, and subtracting are all mathematical operations. As an example, consider the following expression: Expression, mathematics, and a numeric value Numbers, parameters, and functions are the components of an expression in mathematics. Using opposing words and phrases is possible. An expression, sometimes referred to as an algebraic expression, is any mathematical statement that includes variables, numbers, and a mathematical action between them. For instance, the expression 4m + 5 is made up of the expressions 4m and 5, as well as the variable m from the previous equation, all of which are separated by the mathematical symbol +.

An object's acceleration adjusts together with its direction. You may use the next several stages to get the object's acceleration at this point:

Calculate the object's initial and ultimate velocities before and after a direction change.

Subtract the end velocity from the beginning velocity to determine the change in velocity (delta v). This will reveal how much the velocity has changed.

Establish the time difference. This is the amount of time it takes for the velocity to switch from one direction to the other.

Calculate acceleration using this equation: acceleration = delta v / time. To solve for acceleration, enter the values you calculated for delta v and the amount of time it took the object to change directions.

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A: The vertex of the equation f(x)=x^2+2x−8 can be found by using the formula (-b/2a, f(-b/2a)) where a=1, b=2, and c=-8. Plugging in the values gives us the vertex (-1, -9).

B: The line of symmetry can be found by using the formula x=-b/2a. Plugging in the values gives us the equation x=-1.

C: The x-intercepts can be found by setting f(x)=0 and solving for x. This gives us the equation x^2+2x-8=0. Using the quadratic formula, we get x=(-2±√(2^2-4(1)(-8)))/(2(1)). Simplifying gives us x=(-2±√36)/2, which gives us the x-intercepts (-5.24, 1.24). The y-intercept can be found by setting x=0 and solving for y. This gives us the equation y=-8.

D: The domain of the function is all real numbers, or (-∞,∞).

E: The range of the function is all real numbers greater than or equal to -9, or [-9,∞).

F: The increasing interval of the function is (-1,∞).

G: The decreasing interval of the function is (-∞,-1).

H: The end behavior of the function is as x→+∞,y→∞ and as x→-∞,y→∞.

I: To graph the function, first plot the vertex (-1, -9) and the x-intercepts (-5.24, 0) and (1.24, 0). Then, plot two additional points on either side of the vertex, such as (-2, -6) and (0, -8). Connect the points with a smooth curve to complete the graph.

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Substituting in the given values for a and b, we can solve for d and find that it is approximately 9.48 inches.

Pythagorean Theorem is a mathematical formula that states that the square of the hypotenuse (the side opposite the right angle) of a right triangle is equal to the sum of the squares of the other two sides. It is expressed as a2 + b2 = c2, where c is the length of the hypotenuse and a and b are the lengths of the other two sides.

The given diagram is a right triangle with two of its sides labeled in inches. To find the length of the third side (d), one must use the Pythagorean Theorem. The Pythagorean Theorem states that in a right triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides. In this case, d is the hypotenuse, so d2 = a2 + b2. Therefore, substituting in the given values for a and b, we can solve for d and find that it is approximately 9.48 inches.

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step 1: convert to improper fraction

57/7 - 26/7

step 2: subtract numerators

31/7

step 3: change to a mixed number

4 3/7

Answer:

Both of the shapes correspond with one another.

(For explanation, look to the second image. Brainly would not let me submit that for an unknown reason)

(It is my explanation)

Good luck!

Answer: D

Step-by-step explanation: Disregard the $ and solve algebraically.

[tex]4x+36\leq 52[/tex]

[tex]4x\leq 52-36[/tex]

[tex]4x\leq 16[/tex]

[tex]x\leq 4[/tex]

Answer: Choice D is the correct answer :)

Step-by-step explanation: