For an activity in class, the teacher gave each student a small card with a binomial on it. While music played for a few seconds students walked around the room. When the music stopped the students paired with the person nearest to them.

Elinor’s card had 3x + 4 on it. She paired first with Mike whose card showed −2x – 1. The teacher asked the students to add, subtract, and then multiply the binomials on their two cards together, and then to record the solutions on a white board. Which of the following could NOT be one of this pair of student’s answers?
5x + 3
x + 3
5x + 5
−6x2 – 11x – 4

Answer:

A. 63

Step-by-step explanation:

in triangle TRS, it is an isosceles triangle with TS congruent to RS. So, angle T congruent to angle r. So, the angle is 63.

The correct work done by the person walking up the spiral staircase is -3,325.89 ft-lb, indicating that the person did work against gravity while climbing up the stairs.

The force required to lift a person of weight 195 lb against gravity is F = mg,

where g is the acceleration due to gravity and

m is the mass of the person.

We can convert the weight in pounds to mass in pounds by dividing by the gravitational acceleration, g = 32.2 ft/s²:

m = 195 lb / 32.2 ft/s²= 6.05 slugs

The work done by a force F over a distance d is given by the dot product of the force and displacement vectors:

W = F · d

In this case, the force is the weight of the person, F = mg, and the displacement vector is the difference between the initial and final positions, d = r(1) - r(0),

where r(t) is the position vector parameterized by t.

We can compute the displacement vector as follows:

r(1) = ⟨4cos(2π), 4sin(2π), 18⟩ = ⟨4, 0, 18⟩

r(0) = ⟨4cos(0), 4sin(0), 0⟩ = ⟨4, 0, 0⟩

d = r(1) - r(0) = ⟨0, 0, 18⟩

The work done is therefore:

W = F · d = (6.05 slugs) · (32.2 ft/s^2) · ⟨0, 0, 18⟩

= 0 · 0 + 0 · 0 + (6.05 slugs) · (32.2 ft/s^2) · 18 ft

= 3,325.89 ft-lb

Therefore, the work done by the person walking one revolution up the spiral staircase is 3,325.89 ft-lb.

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Answer:

the answer is (A) 21-1/2.

Step-by-step explanation:

First, we need to calculate the rate of descent in feet per mile:

750 ft / 3 miles = 250 ft/mile

Next, we can set up a proportion to solve for the distance traveled:

(distance traveled) / (total altitude change) = (distance traveled) / (altitude change due to descent) + (altitude at which descent begins)

Let m be the distance traveled:

m / (32000 ft - 16000 ft) = m / (250 ft/mile * x miles) + 16000 ft

where x is the number of miles traveled when the pilot is 16000 ft above the ground.

Simplifying:

m / 16000 ft = m / (250 ft/mile * x miles) + 1

Multiplying both sides by 16000 ft:

m = m / (250 ft/mile * x miles) * 16000 ft + 16000 ft * 16000 ft

Multiplying both sides by (250 ft/mile * x miles):

m * (250 ft/mile * x miles) = m * 16000 ft + 16000 ft * (250 ft/mile * x miles)

Simplifying:

250 * x * m = 16000 * m + 4000 * x * m

Dividing both sides by m:

250 * x = 16000 + 4000 * x

Subtracting 4000 * x from both sides:

-3750 * x = -16000

Dividing both sides by -3750:

x = 4.266666... miles

Rounding to the nearest half mile gives us:

x ≈ 4.5 miles

Therefore, the answer is (A) 21-1/2.

Answer:

12x - 8x^2 - 8.

Step-by-step explanation:

To find the sum of the two expressions, we add the corresponding coefficients of each term:

(x - 5x^2 - 12) + (4 + 11x - 3x^2)

= x + 11x - 5x^2 - 3x^2 - 12 + 4

= 12x - 8x^2 - 8

Using the remainder theorem, the quotient of (x³ + 3x² + 5x + 3) divided by (x + 1) is Ox²+2x+3

What exactly is the remainder theorem?

The Remainder Theorem is an approach to Euclidean polynomial division. According to this theorem, dividing a polynomial P(x) by a factor (x - a), which is not an element of the polynomial, yields a smaller polynomial and a remainder.

Given Data

x³ +3x² +5x +3 / x+1 = x² +2x +3

x³ +x²

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

0   2x² +5x

  2x² +2x

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

    0      3x +3

            3x+3

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

            0    0  

The quotient of (x³ + 3x² + 5x + 3) divided by (x + 1) is x² +2x+3 using remainder theorem.

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Therefore , the solution of the given problem of probability comes out to be the likelihood of turning a six is 1/7, or roughly 0.143 or 14.3%.

The assessment of the probability that a claim is true or that a particular event will happen is the main objective of the schemes inside a practise known as criteria. Any number among both 0 and 1 is able to symbolise chance, with 0 typically denoting possibility and 1 typically denoting a degree of certainty. A probability diagram illustrates the likelihood that a particular occurrence will take place.

Here,

Only one of the wheel's seven equally sized regions, which there are a total of seven of, correlates to the number 6.

The likelihood of spinning a 6 on a single rotation is thus:

=> P(six) = 1/7

=>  P(six) = 0.143

Therefore, the likelihood of turning a six is 1/7, or roughly 0.143 or 14.3%.

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Answer:

Second option 168= 18.X + 12.2X

Step-by-step explanation:

Area of the shape is in two parts,

Are of the larger rectangle is Lenght x width

Lenght is 12cm and width is x +2x

Area = 12 x 3x = 36x cm²

Area of the smaller rectangle = 6 x X = 6xcm²

Total area 36x + 6x = 168cm²

Another method

Find the area of the big rectangle including the cut off area

Lenght x width = 18 x (2x + X)

Area =18 x 3x or 18.3x

Calculate the white area

Length x width = 6 x 2x = 12x

Deduct the white area from the larger area

168= 18.3x - 12x

Third method

Divide the rectangle from top down

First rectangle length x width = 18x X or 18x

Second rectangle length x width = 12 x 2x

168= 18. x + 12 . 2x

The correct equation which can be used to find the value of x is,

⇒ 168 = 18 × x + 12 × 2x

A rectangle is a two dimension figure with 4 sides, 4 corners and 4 right angles. The opposite sides of the rectangle are equal and parallel to each other.

Given that;

The figure shown has a total area of 168 cm².

Now, We can find as;

Area of rectangle = Length x width

Hence, We can formulate;

⇒ 18 × x + 12 × 2x = 168

Thus, The correct equation which can be used to find the value of x is,

⇒ 168 = 18 × x + 12 × 2x

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The height of the tower is 25.8 feet to the nearest foot, which can be calculated using trigonometry with the length of the laser beam and the angle to the top of the tower.

A. The length of each laser beam is 30 feet. Andrea uses a laser measuring device to find the distance to the top of the tower at an angle of about 35°, so the length of the laser beam is 30 feet. Then, when she moves forward so the angle is 45°, the length of the laser beam is reduced by 30 ft.

B. The height of the tower can be calculated using trigonometry. The height of the tower can be represented by h, and the angle to the top of the tower is represented by θ. The equation that can be used to calculate the height of the tower is h = x * sin(θ), where x is the length of the laser beam. Therefore, the height of the tower when the angle is 35° is (30 ft) * sin(35°) = 25.8 ft. The height of the tower when the angle is 45° is (30 ft) * sin(45°) = 21.2 ft. Therefore, the height of the tower is 25.8 ft to the nearest foot.

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The solution yn+1 is always less than or equal to yn, which means that the solution is stable for a < 0. Therefore the solution is of trapezoidal method.

The model problem (4.3) with a real constant a < 0 is given by:
[tex]y' = ay, y(0) = 1[/tex]
The trapezoidal method is given by:
[tex]yn+1 = yn + (h/2)(f(tn, yn) + f(tn+1, yn+1))[/tex]
where h is the step size, tn and yn are the current time and solution values, and  [tex]f(t, y) = ay[/tex]  is the right-hand side of the model problem.

To show that the solution of the trapezoidal method is stable for a < 0, we can substitute the right-hand side into the trapezoidal method and solve for yn+1:
[tex]yn+1 = yn + (h/2)(ayn + ayn+1)yn+1 - (h/2)ayn+1 = yn + (h/2)aynyn+1(1 - (h/2)a) = yn(1 + (h/2)a)yn+1 = yn(1 + (h/2)a)/(1 - (h/2)a)[/tex]

Since a < 0, the denominator [tex](1 - (h/2)a)[/tex] is always positive, and the numerator [tex](1 + (h/2)a)[/tex] is always less than or equal to 1. Therefore, the solution yn+1 is always less than or equal to yn, which means that the solution is stable for a < 0.

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According to simple interest, Patricio will have $537.50 in his savings account after 5 years.

To calculate the amount of money Patricio will have in his savings account after 5 years, we can use the formula for simple interest, which is I = prt. "I" stands for the amount of interest earned, "p" stands for the principal amount deposited, "r" stands for the interest rate per year (as a decimal), and "t" stands for the time period in years.

In this case, the principal amount (p) is $500, the interest rate (r) is 1.5% or 0.015 as a decimal, and the time period (t) is 5 years. Using the formula I = prt, we can calculate the amount of interest earned over 5 years:

I = prt

I = $500 x 0.015 x 5

I = $37.50

So, Patricio will earn $37.50 in simple interest over 5 years. To find out the total amount of money he will have in his savings account after 5 years, we simply add the interest earned to the principal amount:

Total amount = Principal amount + Interest earned

Total amount = $500 + $37.50

Total amount = $537.50

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Answer:

The fraction that looks the same even if you turn it upside down is 6/9 or six-ninths.

Step-by-step explanation:

Therefore , the solution of the given problem of equation comes out to be the first plant makes 5x + 22 more items per day.

Mathematical formulas frequently employ same variable word to guarantee agreement between two claims. Many academic numbers are shown to be equal using mathematical expression, also known as assertions. In this case, the normalise method adds b + 6 to employ the example of y + 6 rather than splitting 12 into two parts. It is possible to determine the length of the line and the quantity of connections between each sign's constituents. The significance of a symbol usually contradicts itself.

Here,

The first plant cranks out 8x + 15 items every day, while the second cranks out 3x - 7 items every day. By deducting the daily output of the second plant from the daily output of the first plant, we can determine how many more items the first plant creates than the second plant:

=> (8x + 15) - (3x - 7) (3x - 7)

If we condense this phrase, we get:

=> 8x + 15 - 3x + 7

Combining related words gives us:

=> 5x + 22

Therefore, compared to the second plant, the first plant makes 5x + 22 more items per day.

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Answer:The ratio of the area of the small circle to that of the bigger circle is 25:36.

Step-by-step explanation:

To find the derivative of the function, we can use the chain rule and the power rule of differentiation.

What is chain rule?

The chain rule is a formula used to find the derivative of a composite function. If y = f(g(x)), then as per chain rule the instantaneous rate of change of function ‘f’ relative to ‘g’ and ‘g’ relative to x  results in an instantaneous rate of change of ‘f’ with respect to ‘x’

Let u = x² - 3, then we can rewrite the function as:

f(x) = [tex](u^{7})^\frac{1}{2}[/tex]

Using the chain rule and the power rule, we have:

f'(x) = (1/2) x (u^7)^(-1/2) x 7u^6 x 2x

Simplifying this expression, we get:

f'(x) = 7x(u^6) / (2(u^7)^(1/2))

Now, we can substitute x = -2 into this expression to find f'(-2):

f'(-2) = 7(-2)((-2)^2 - 3)^6 / (2(((-2)^2 - 3)^7)^(1/2))

Simplifying this expression, we get:

f'(-2) = -168/(2sqrt(19)^7) = -12.77 (rounded to two decimal places)

Therefore, f'(-2) = -12.77.

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The survey questiοn is What is yοur favοrite brand οf sοda?

In mathematics, a survey is a technique fοr gathering data that invοlves pοsing a series οf questiοns tο participants in οrder tο learn mοre abοut their attitudes and behaviοrs. It is the mοst typical and affοrdable methοd οf data cοllectiοn. A sample size can change depending οn the situatiοn.

What dο yοu like and dοn’t like abοut the CEO? It is nοt a survey questiοn. In a survey questiοn, there shοuld be an οbject, nοt a  persοn.

Dο yοu οwn a car οr a truck? It is nοt a survey questiοn.  The survey is dοne οn a particular prοduct. But in the questiοn, nο band is mentiοned.

Hοw much credit card debt dο yοu οwe? It is nοt a survey questiοn. It is a persοnal questiοn.

What is yοur favοrite brand οf sοda? It is a survey questiοn. The survey is dοne οn a sοda brand.

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The surface area of building with the skyview is found as 331.625 sq. yd.

A solid shape having six square faces is called a cube. Because every square face shares a comparable side length, each face is the same size. A cube has 8 vertices and 12 edges. An intersection of three cube edges is referred to as a vertex.

Total area = TSA of cuboid + CSA of hemisphere - area of circle

Total area = 2(lb + bh + hl) + 2πr² - πr²

Total area = 2(6*10 + 10*6 + 6*6) + 2*3.14*2.5² - 3.14*2.5²

On simplification:

Total area = 331.625

Thus, surface area of the building with the skyview is found as 331.625 sq. yd.

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Therefore, the ladder touches the house at a height of 28 feet above the ground.

A triangle is a geometric shape that consists of three straight sides and three angles. It is a polygon with three sides. The sides of a triangle are connected by its vertices or corners. The triangle is one of the simplest and most fundamental shapes in geometry, and it has many important properties and applications. Triangles have many practical applications in everyday life and in various fields, such as architecture, engineering, and physics. The study of triangles and their properties is an important part of mathematics and geometry.

Here,

We can use the Pythagorean theorem to solve this problem. The Pythagorean theorem states that in a right triangle, the sum of the squares of the lengths of the legs (the two shorter sides) is equal to the square of the length of the hypotenuse (the longest side, which is opposite the right angle). In this problem, the ladder, the side of the house, and the ground form a right triangle. The ladder is the hypotenuse, the distance from the house to the ladder is one leg, and the height we want to find is the other leg.

Let x be the height above the ground where the ladder touches the house. Then, using the Pythagorean theorem, we have:

x² + 21² = 35²

Simplifying and solving for x, we get:

x² + 441 = 1225

x² = 784

x = 28

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The slope of the line is 2, which was calculated using the slope-intercept form of a linear equation and the given point (5,8) and y-intercept of -2.

To calculate the slope, we need to use the slope-intercept form of a linear equation:

y = mx + b

where m is the slope and b is the y-intercept.

We are given that the point (5, 8) lies on the line, so we can substitute x = 5 and y = 8 into the equation:

8 = 5m + b

We are also given that the y-intercept is -2, which means that when x = 0, y = -2. We can use this information to find b:

-2 = 0m + b

b = -2

Substituting this value into the equation above, we have:

8 = 5m - 2

Solving for m, we get:

5m = 10

m = 2

Therefore, the slope of the line is 2.

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There are 27 different ways to choose a lunch special combination.

To determine how many different ways there are to choose a lunch special combination:

At a pizza parlor, the lunch special comes with your choice of a pizza slice, a salad and a drink.

There are pizza slice options, salad options, and soda options.

Therefore, there are three options for each category, which are pizza slice, salad, and drink.

Then, we can use the multiplication principle to determine how many different ways there are to choose a lunch special combination:

3 options for pizza × 3 options for salad × 3 options for drink

= 27 different ways to choose a lunch special combination.

Therefore, there are 27 different ways to choose a lunch special combination.

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The standard error of the mean is smaller due to the better accuracy of the data.

Standard deviations are a measure of how spread out a dataset is. It is calculated by taking the square root of the variance of the data. The standard deviation is calculated by subtracting the mean of the dataset from each individual value, squaring the differences, and then adding them all together and dividing by the number of values in the dataset. The result is a measure of how much the individual values vary from the mean.

The average of means for a sample of size 10 is 5.0. Comparing the sample mean to the average of means, we can see that the sample mean for all sample sizes is close to the average of means for a sample of size 10. The sample standard deviation for the 50 sample size is the greatest, whereas the sample standard deviation for the 500 sample size is the least. Additionally, the standard error of the mean decreases as the sample size increases. This is an expected result, as the larger the sample size, the more accurate the data will be. Therefore, the standard error of the mean is smaller due to the better accuracy of the data.

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Answer:

We can substitute m = 2.5 and n = 5 into the expression:

m + (7*9)/n = 2.5 + (7*9)/5

We can simplify the second term:

(7*9)/5 = 63/5

Substituting back into the expression:

m + (7*9)/n = 2.5 + 63/5

We can find a common denominator and add the terms:

2.5 + 63/5 = 12.5/5 + 63/5 = 75/5 = 15

Therefore, the value of the expression is 15, which corresponds to option (b) as the correct answer.

The distance around the track along the inside edge of each lane is 614.44 yd for lane 1, 634.88 yd for lane 2, 655.32 yd for lane 3, 675.76 yd for lane 4, 696.20 yd for lane 5, 716.64 yd for lane 6, 737.08 yd for lane 7 and 757.52 yd for lane 8.

The distance around the track along the inside edge of each lane can be calculated using the following formula:

Distance = (2 × 44 yd) + (2 × π × radius)

where the radius is equal to 44 yd + (lane number × 10 yd).

For lane 1, the radius is equal to 44 yd + (1 × 10 yd) = 54 yd. Therefore, the distance around the track along the inside edge of lane 1 is (2 × 44 yd) + (2 × π × 54 yd) = 614.44 yd.

The same calculation can be done for the other lanes, with the radius increasing by 10 yd for each lane. The radius for lane 2 is 64 yd, for lane 3 is 74 yd, for lane 4 is 84 yd, for lane 5 is 94 yd, for lane 6 is 104 yd, for lane 7 is 114 yd and for lane 8 is 124 yd.

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According to the information, the graphics would remain as seen in the attached images. In them, graph A has a greater dispersion than graph B because it integrates a greater number of values.

A dot plot is a term for a type of graph used to display data by locating points on a number line. This graph is used to graphically represent certain trends or groupings of data.

According to the above, if we want to graph the information in the statement we must include at least 5 points in each graph. Additionally, we must put at least 7 points in the central value of the graph. Finally, we must have a greater dispersion of data in graph A than in graph B.

According to the above, the graphics would remain as shown in the image.

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The total weight of the 4 small jars of coffee is W = 400 grams

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

Substituting the values in the equation , we get

Let the weight of large jar be x

Let the weight of small jar be y

5 large jars of coffee have a total weight of 1250 grams.

So , 5x = 1250

Divide by 5 on both sides , we get

x = 250 grams

And , 2 large jars of coffee and 7 small jars of coffee have a total weight of 1200 grams.

So , 2x + 7y = 1200

2 ( 250 ) + 7y = 1200

Subtracting 500 on both sides , we get

7y = 1200 - 500

7y = 700

Divide by 7 on both sides , we get

y = 100 grams

On simplifying the equation , we get

So , the weight of 4 small jars is 4y = 400 grams

Hence , the weight of 4 small jars is y = 400 grams

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After addressing the issue at hand, we can state that As a result, decimal midfielders make up around 36.36% of the players on the pitch

The decimal number system is frequently used to express both integer and non-integer quantities. Non-integer values have been added to the Hindu-Arabic numeral system. The technique used to represent numbers in the decimal system is known as decimal notation. A decimal number consists of both a whole number and a fractional number. The numerical value of complete and partially whole amounts is expressed using decimal numbers, which are in between integers. The full number and the fractional part of a decimal number are separated by a decimal point. The decimal point is the little dot that appears between whole numbers and fractions. An example of a decimal number is 25.5. In this case, 25 is the total number, and 5 is the minimum.

The following formula can be used to determine the percentage of midfielders on the field:

Overall number of players on the field / Total number of midfielders

In this situation, the total number of midfielders is 4, and the total number of players on the pitch is 11.

As a result, the percentage of midfielders on the field is:

4 / 11

This can be expressed in decimal or percentage form as follows:

0.3636 (rounded to four decimal places) (rounded to four decimal places)

36.36% (rounded to two decimal places) (rounded to two decimal places)

As a result, midfielders make up around 36.36% of the players on the pitch.

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If Ahmed is given a 15% discount of the total price, discounted price that ahmed pays is $1134. 75, the price of the computer before the discount was $335.14.

To calculate the price of the computer before the discount, we need to use the information given in the problem and some algebraic manipulation.

Let's start by setting up an equation. We can let x be the price of the computer before the discount. We know that Ahmed received a 15% discount off the total price, so the total price would be:

Total price = x + 375 + 70

Then, we can use the fact that the discounted price that Ahmed paid was $1134.75 to set up an equation:

Discounted price = Total price - 15% of Total price

$1134.75 = (x + 375 + 70) - 0.15(x + 375 + 70)

Simplifying this equation by combining like terms, we get:

$1134.75 = 1.85x + 513.75

To solve for x, we can subtract 513.75 from both sides of the equation:

$621 = 1.85x

Finally, we can divide both sides of the equation by 1.85 to get the price of the computer before the discount:

x = $335.14

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Complete question is:

Ahmed buys a new monitor, keyboard and computer.

He is given a 15% discount off the total price.

The discounted price that Ahmed pays is $1134.75.

The price of the monitor before the discount was $375.

The price of the keyboard before the discount was $70.

Calculate the price of the computer before the discount?

The percentage value that represents what percent of 64 is 4? is (b) 6 1/4%

A percentage is a way to express a fraction or portion of a whole as a number out of 100.

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

What percent of 64 is 4?

Represent the percentage with x

So, we have

x percent of 64 is 4

Express as product expression

x% * 64 = 4

Multiply through by 100

x * 64 = 400

Divide by 64

x = 6.25 or 6 1/4

Hence, the percentage is 6 1/4%

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Answer:

Step-by-step explanation:

To find this answer you need to find the vertex of the parabola. Do this by using the formulas for h and k as follows:

[tex]h=\frac{-b}{a}[/tex]    and    [tex]k=c-\frac{b^2}{4a}[/tex], where a, b, and c come from the quadratic equation.

Filling in for h:

[tex]h=\frac{10}{2(.2)}=25[/tex]

Filling in for k:

[tex]k=650-\frac{100}{4(.2)} =525[/tex]

Thus, the coordinates for the vertex are (25, 525). The h value interprets the number of bowls that should be produced to minimize the cost of production (25) and the minimum production cost is the k value (525).

The average rate of change is the slope of the line between the points

     ( -4, f(-4) ) and ( 4, f(4) )

f(-4) = 16 + 40 + 5 = 61

f(4) = 16 - 40 + 5 = 19

The slope (AKA average rate of change) is then

    [tex]m =\dfrac{19-61}{4-(-4)}=\dfrac{-42}{8} = -\dfrac{21}{4}[/tex]