Molly knows that 30% of the students at her school are boys and that there are 600 boys at her school. She wants to find the total number of students at the school, because she needs to order t-shirts for all the students.
What is the total number of students at Molly's school?

The unit rate is the cost of the certain brand of nuts per ounce, which is $0.20. This is the same as 20 cents per ounce.

The unit rate is a measure of a quantity, such as the cost of a product, in relation to a single unit of that quantity. In this case, the cost of the nuts is measured in dollars and the quantity is measured in ounces.

To find the unit rate, we need to divide the total cost by the total quantity. In this problem, the total cost of the nuts is given as $3.20 and the total quantity is given as 16 ounces. Dividing these two numbers, we get:

Unit rate = Total cost / Total quantity

= $3.20 / 16 ounces

= $0.20 per ounce

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The answer of the given question based on the linear equalities is the system of linear inequalities that represents the constraints is:

6x + 3y ≤ 600 , 3x + 6y ≤ 60 , x ≥ 0, y ≥ 0 .

constraints refer to a set of limitations or restrictions on the variables in a problem. These constraints can be in the form of equations or inequalities, and they define the feasible region of the problem.

The goal of solving a system of linear equations subject to constraints is to find a solution that satisfies all of the constraints while also solving the system of equations. The constraints limit the possible solutions to a subset of the full solution space, and finding a feasible solution that satisfies all of the constraints can be more challenging than finding a solution to the system of equations alone.

Let's first identify the variables in the problem:

x: number of Type 1 TV stands produced

y: number of Type 2 TV stands produced

Next, let's identify the constraints:

Labor constraint: the total labor hours used for producing the TV stands cannot exceed 600 hours.

6x + 3y ≤ 600

Single drawer pull constraint: the total number of single drawer pulls used for producing the TV stands cannot exceed 60 pulls.

3x + 6y ≤ 60

Non-negative constraint: the number of TV stands produced cannot be negative.

x ≥ 0, y ≥ 0

Therefore, the system of linear inequalities that represents the constraints is:

6x + 3y ≤ 600

3x + 6y ≤ 60

x ≥ 0, y ≥ 0

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Where the objective function is: Profit = 200x + 150y.

What is inequalities?

In mathematics, an inequality is a mathematical statement that indicates that two expressions are not equal. It is a statement that compares two values, usually using one of the following symbols: "<" (less than), ">" (greater than), "≤" (less than or equal to), or "≥" (greater than or equal to).

Let x represent the number of Type 1 TV stands produced and y represent the number of Type 2 TV stands produced. Then, the constraints for the available labor and single drawer pulls can be represented as follows:

Labor constraint:

3x + 2y ≤ 600

Single-drawer pulls constraint:

3x + 6y ≤ 60

Non-negative constraint:

x, y ≥ 0

We also need to consider the practical constraint that we cannot produce a negative number of TV stands. Therefore, we must add the non-negative constraint as shown above.

Note that the coefficients 3, 2, 3, and 6 in the above inequalities are based on the information given in the problem statement.

Finally, to represent the objective function for maximizing profit, we use the following expression:

Profit = 200x + 150y

Thus, the system of linear inequalities that represents the given problem is:

3x + 2y ≤ 600

3x + 6y ≤ 60

x, y ≥ 0

Therefore, where the objective function is: Profit = 200x + 150y.

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The area of the triangle is  5√11 cm².

A point where two lines meet produces an angle.

The breadth of the "opening" between these two rays is referred to as a "angle". It is depicted by the figure.

Radians, a unit of circularity or rotation, and degrees are two common units used to describe angles.

By connecting two rays at their ends, one can make an angle in geometry. The sides or limbs of the angle are what are meant by these rays.

The limbs and the vertex are the two main parts of an angle.

The common terminal of the two beams is the shared vertex.

According to our question-

b = base of the triangle = 2(√6² - 5²) = 2(√36 - 25) = 2√11 cm

h = height of the triangle = 5 cm

area of the triangle = 1 / 2 × 2√11 × 5

area of the triangle = 5√11

area of the triangle =  5√11 cm²

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Mr. Paquette has 2 pencils and 6 pens after simplification.

An equation is a mathematical statement that asserts that two expressions are equal. It is a representation of a relationship between two or more variables, which can be solved to find the values of those variables that satisfy the equation. An equation typically consists of two sides separated by an equal sign (=), with expressions containing variables and constants on each side.

Simplification refers to the process of making something simpler or easier to understand. It involves breaking down complex or complicated information into smaller, more manageable parts, and eliminating unnecessary or redundant details.

Let's assume that Mr. Paquette has x pencils. Since he has a combined total of 8 pencils and pens, he must have (8 - x) pens.

We know that for each pencil he has, he has 3 pens. Therefore, the total number of pens he has is 3 times the number of pencils:

Total number of pens = 3x

We also know that the total number of pencils and pens is 8. Therefore, we can write an equation:

x + 3x = 8

Simplifying and solving for x, we get:

4x = 8

x = 2

So Mr. Paquette has 2 pencils and 6 pens (since he has 3 pens for each pencil).

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The mathematical expression that would make "h" the subject of the equation is h= k-1/3

To begin an equation is a mathematical expression that relates variables by using the = symbol. Due to this, the letters of variables involved can be changed to create equivalent equations.

The equation given is written is k= 3h - 1. To make h the subject of formula 3h= k - 1 Divide both sides by the coefficient of h which in this case is 33h/3= k-1/3h= k - 1/3.

Hence the value of h in the equation is k - 1/3

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The number of rectangles in Josh's drawing should be 6.

A three-dimensional solid shape that has six rectangular faces is a rectangular prism. It has eight vertices, or corners, and 12 edges connecting the vertices.

To draw a net of a rectangular prism, Josh needs to represent the three-dimensional object on a two-dimensional surface by drawing each face of the prism separately. A rectangular prism has six faces, and every face is a rectangle.

Josh needs to draw all six rectangles that make up the six faces of the prism. The six faces consist of a pair of congruent rectangles for the top and bottom faces, and four rectangles for the sides. Josh can arrange the six rectangles in different ways to create a net that will fold into a rectangular prism.

It is important that Josh draws the rectangles accurately and with correct dimensions to ensure that the net can be assembled into a rectangular prism.

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10%.

Identified are:StatisticSignificance LevelTest StatisticP-valueStep 1: State the null and alternative hypothesis for the claimThe null hypothesis H0: P≥0.1 (or P=0.1)The alternative hypothesis H1: P<0.1Step 2: Determine the significance levelα= 0.05Step 3: Compute the test statistic, P-value, and critical value.Test statistic is given as z= (x- μ) / (σ/√n)Where x= 21 (number of patients who experienced nausea)μ= nP = 0.1(300)= 30σ= √(n*P*(1-P)) = √(300*0.1*0.9) = 4.74z= (21-30)/(4.74/√300)= -5.87P-value= P(z<-5.87)≈0Critical value= zα= z0.05= -1.64Step 4: Make a decisionReject H0 if z≤zα else do not reject H0z= -5.87 < zα= -1.64Hence, reject the null hypothesis, which means there is evidence that the proportion of patients who experience nausea from taking the drug is less than 10%.

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The best predictor of y when r is not significantly different from 0 is the mean of the data values of y, which can be calculated using the formula (∑y)/n.

The best predictor of y when r is not significantly different from 0 is the mean of the data values of y. This can be calculated using the formula:

mean = (∑y)/n

Where ∑y is the sum of all the y values in the data set and n is the number of y values in the data set.

For example, if the data set is comprised of five y values of -2, -1, 0, 1, and 2, we would have ∑y = -2 + -1 + 0 + 1 + 2 = 0. The number of y values, n, is 5. Therefore, the mean of the data would be 0/5 = 0.

The mean of the data is a useful predictor of y when r is not significantly different from 0 because it is an average of all the values in the data set. This means that it takes into account all the data points and can give a reliable prediction of what the value of y is likely to be. Since r is not significantly different from 0, this means that there is no strong relationship between the two variables, and so the mean of the data can be used to provide an accurate prediction of y.

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the probability of selecting a clown is 1/3, which is the answer to the problem.

The probability of an event happening is defined as the number of favorable outcomes divided by the total number of possible outcomes.

In this case, the total number of performers is 15, and the number of clowns is 5. Therefore, the probability of selecting a clown is:

P(clown) = number of clowns / total number of performers

= 5 / 15

= 1/3

Probability is a branch of mathematics that deals with the study of random events and their likelihood of occurrence. It is defined as the measure of the likelihood or chance of an event occurring.

The probability of an event is expressed as a number between 0 and 1, where 0 means that the event is impossible, and 1 means that the event is certain to happen. An event with a probability of 0.5 (or 50%) is considered to be equally likely to happen or not happen.

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Answer:

D. 9/4

Step-by-step explanation:

Answer: D

Step-by-step explanation:

-1 1/4 + -3 2/4

Cross out the negative sign because we're working with negatives in this equation. Due to taking away the negative sign, we would subtract.

3 2/4 - 1 1/4 = 9/4

Have a good day :D

Answer: The board is 54 inches wide

The width of a whiteboard, in inches, is 54.

Multiplication is a type of mathematical operation. The repetition of the same expression types is another aspect of the practice.

For instance, the expression 2 x 3 indicates that 3 has been multiplied by two.

We know that the width of the whiteboard is 4.5 feet.

However, if we need to express this width in inches, we have to convert feet to inches, as the two units are not directly comparable.

There are 12 inches in a foot.

Therefore, to convert a value in feet to inches, we can simply multiply the value by 12. In other words, 1 foot is equal to 12 inches.

So, to convert the width of the whiteboard from feet to inches, we can simply multiply the width (4.5 feet) by the conversion factor of 12 inches/foot as follows:

4.5 feet × 12 inches/foot = 54 inches

Therefore, the whiteboard is 54 inches wide.

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0.4103

Answer:GivenA fair die is rolled six times.The probability that it comes up 4 at least once is to be determined.We have to find the probability that it comes up 4 atleast once which means that it can come up more than once as well.Therefore we have to consider all the cases i.e 1,2,3,4,5,6Case 1 : Number of times that it comes up 4 is 1The remaining number of times can be any of the remaining 5 numbersTherefore the probability of the event is(1/6) * (5/6)^5Case 2 : Number of times that it comes up 4 is 2The remaining number of times can be any of the remaining 5 numbersTherefore the probability of the event is(5C2 * (1/6)^2 * (5/6)^4)Case 3 : Number of times that it comes up 4 is 3The remaining number of times can be any of the remaining 5 numbersTherefore the probability of the event is(5C3 * (1/6)^3 * (5/6)^3)Case 4 : Number of times that it comes up 4 is 4The remaining number of times can be any of the remaining 5 numbersTherefore the probability of the event is(5C4 * (1/6)^4 * (5/6)^2)Case 5 : Number of times that it comes up 4 is 5The remaining number of times can be any of the remaining 5 numbersTherefore the probability of the event is(5C5 * (1/6)^5 * (5/6)^1)Now we will add all the cases to get the probability that it comes up 4 atleast once.P(A) = (1/6) * (5/6)^5 + (5C2 * (1/6)^2 * (5/6)^4) + (5C3 * (1/6)^3 * (5/6)^3) + (5C4 * (1/6)^4 * (5/6)^2) + (5C5 * (1/6)^5 * (5/6)^1)On solving we get P(A) = 0.4103Therefore the required probability is 0.4103 or 41.03% (approximately)Answer : 0.4103

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Answer:

Independent events and their probability

The steps he can use in solving the quadratic equations are [tex]x = \frac{-12 \± \sqrt{12\² - 4 \cdot 2 \cdot -3}}{4}[/tex], (x + 3)² = 21/2 and 2(x² + 6x + 9) = 3 + 18

The equation is given as

2x² + 12x - 3 = 0

Assuming he uses the quadratic formula method, which is represented as

[tex]x = \frac{-b \± \sqrt{b\² - 4ac}}{2a}[/tex]

So, we have

[tex]x = \frac{-12 \± \sqrt{12\² - 4 \cdot 2 \cdot -3}}{2 \cdot 2}[/tex]

[tex]x = \frac{-12 \± \sqrt{12\² - 4 \cdot 2 \cdot -3}}{4}[/tex]

If he uses completing the square, then we have

2x² + 12x = 3

So, we have

x² + 6x = 3/2

x² + 6x + 9 = 3/2 + 9

So, we have

(x + 3)² = 21/2

If he factorizes, then the expression is

2(x² + 6x + 9) = 3 + 18

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The amount of simple interest after 17 months is $72.21.

To calculate the amount of simple interest after 17 months, given that Joanne has $4408 in an account earning 3.7% simple interest per annum, the following steps are involved:

Calculation of simple interest

Simple interest can be calculated using the formula;

Simple interest = P × R × T

where, P = principal amount, R = rate of interest, and T = time in years.To calculate the amount of simple interest for Joanne, we have;

P = $4408R = 3.7% per annum

T = 17 months ÷ 12 months/year

T = 1.4167 years

Substituting the values into the formula for simple interest;

Simple interest = P × R × T= $4408 × 3.7% × 1.4167= $72.21.

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Answer:

18

Step-by-step explanation:

The range of the data set is 18, which is calculated by subtracting the smallest value (10) from the largest value (28).

Answer: <

It is "<" because 8 1/2 as a decimal is 8.50 and the other decimal is 8.375. 8.50 is greater than 8.375.

Your welcome!

=^..^=

Answer:<

Step-by-step explanation:

8.375= [tex]8\frac{375}{1000} =8\frac{3}{80} \\[/tex]

1/2=40/80

40/80>3/80

so,

If x and y have a proportional relationship, we may write: y = kx where k is the proportionality constant. To calculate k, we may utilise the supplied data point (x=29, y=275.5) and plug .

The following values into the equation: 275.5 = k(29) (29) When we solve for k, we get: k = 275.5/29 ≈ 9.5 As a result, the proportionality constant is 9.5. We can utilise this constant to obtain x for y=408.5 by plugging y=408.5 and k=9.5 into the equation and solving for x: 408.5 = 9.5x x = 408.5/9.5 ≈ 43 As a result, when y equals 408.5, x is around 43. By charting the data and seeing if the points fall on a straight line flowing through the origin, we may determine if a connection is proportional (0,0). If the points are lost.

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The diameter of the middle layer is 18 cm and the height is 9 cm. The diameter of the top layer is 12 cm and the height is 5 cm.

The ratios of the diameters and the heights are 5:3:2. Therefore, to calculate the diameters and heights of the other two layers, we need to take the bottom layer's diameter and height as our reference values.

The diameter of the bottom layer is 30 cm and the height is 10 cm.

To find the diameter and height of the middle layer, we multiply the bottom layer's values by 3/5 and then 3/2 respectively. So, the diameter of the middle layer is (30 x 3/5) cm = 18 cm and the height is (10 x 3/2) cm = 9 cm.

To find the diameter and height of the top layer, we multiply the bottom layer's values by 2/5 and then 1/2 respectively. So, the diameter of the top layer is (30 x 2/5) cm = 12 cm and the height is (10 x 1/2) cm = 5 cm.

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The graph has x-intercepts at 1/2, 3, and 4/3, a y-intercept at (0, 12), and is symmetric about x = 1.833. The left end goes up, and the right end goes down.

What is the function?

A function is a relation between a set of inputs (called the domain) and a set of possible outputs (called the range) such that each input is associated with exactly one output. In other words, a function takes an input value, performs a specific operation on it, and produces a unique output value.

To graph the function, we can start by finding its intercepts, symmetry, and behavior at infinity.

The x-intercepts occur when the function is equal to zero, so we have already found them to be 1/2, 3, and 4/3.

The y-intercept occurs when x is zero, so we have:

f(0) = (2(0)-1)(-0+3)(3(0)-4) = 12

So the y-intercept is (0, 12).

To find the axis of symmetry, we can use the fact that the function is symmetric about the vertical line x = (1/2 + 3 + 4/3) / 3 = 1.833.

To determine the end behavior, we can look at the leading term of the function, which is -6x³. As x goes to negative infinity, the leading term becomes very negative, so the graph goes down to negative infinity on the left side. As x goes to positive infinity, the leading term becomes very positive, so the graph goes up to positive infinity on the right side.

The graph has x-intercepts at 1/2, 3, and 4/3, a y-intercept at (0, 12), and is symmetric about x = 1.833. The left end goes up, and the right end goes down.

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The time it takes to empty the tank is given as follows:

1.85 minutes.

The volume of a cylinder of radius r and height h is given by the equation presented as follows, which the square of the radius is multiplied by π and the height.

V = πr²h.

The parameters for this problem are given as follows:

Hence the volume of the cylinder in ft³ is given as follows:

V = π x 0.7² x 3

V = 4.62 ft³.

Oil is drained at a rate of 2.5 ft³ per minute, hence the time it takes to drain the oil is given as follows:

4.62/2.5 = 1.85 minutes.

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We can say that after answering the offered question Hence, p > 8 is the equation inequality expressing the range of feasible values for p.

An equation is a mathematical statement that proves the equality of two expressions connected by an equal sign '='. For instance, 2x – 5 = 13. Expressions include 2x-5 and 13. '=' is the character that links the two expressions. A mathematical formula that has two algebraic expressions on either side of an equal sign (=) is known as an equation. It depicts the equivalency relationship between the left and right formulas. L.H.S. = R.H.S. (left side = right side) in any formula.

Let's use the letter "p" to indicate how many pounds Carmen will spend.

Candy is $7 for every pound.

Carmen's sweets expenditure is expressed as follows:

Cost per pound times the weight of the candy purchased is 7p.

Carmen will undoubtedly spend more than $56 on sweets, therefore we may say:

More than $56 was spent on candy

Using the following equation in place of the amount spent on candy:

7p > $56

When we multiply both sides by 7, we get:

p > 8

So, any figure more than 8 is a possibility for the amount of pounds Carmen will purchase. We can express this as follows:

p > 8

Hence, p > 8 is the inequality expressing the range of feasible values for p.

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Answer:

x + y > 30

3x + 0.5y > 40.00

Step-by-step explanation:

Let x be the number of xylophones and y be the number of yo-yos sold.

The total number of toys sold must be greater than 30, so we have:

x + y > 30

The total amount earned must be greater than $40.00 to earn a profit, so we have:

3x + 0.5y > 40.00

Therefore, the system of inequalities is:

x + y > 30

3x + 0.5y > 40.00

The probability of selecting a soprano is 0.125 or 12.5%.

The percentage of times you anticipate seeing a certain occurrence across many trials is the chance that it will happen. Probabilities are always in the 0 to 1 range. The probability of an event happening divided by the likelihood that it won't happen is how odds are calculated.

Probability 0 is equivalent to chances 0. Odds less than 1.0 are represented by probabilities between 0 and 0.5. The chances of 1.0 are the same as a probability of 0.5. Consider it like this: 50% of the time, a coin will land on its head. The chances are "50:50," which translates to 1.0.

The total number of singers are:

5 + 22 + 8 + 5 = 40

Now, the probability of selecting a soprano is:

P(soprano) = 5 / 40

P(soprano) = 1/8 or 0.125

Therefore, the probability of selecting a soprano is 0.125 or 12.5%.

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The bottom cutoff for receiving an A grade is 88.16.

A statistical concept known as the empirical rule, often called the 68-95-99.7 rule, asserts that for a normal distribution: Around 68% of the data falls within one standard deviation of the mean.

The data is within two standard deviations of the mean for around 95% of the time. The data is within three standard deviations of the mean for about 99.7% of the time.

To find the bottom cutoff we need to find 5% of the students that score higher.

Using the z-score for 5% distribution we have:

z = 1.645

Formula for converting a z-score to a raw score:

z = (x - μ) / σ

x = z * σ + μ

x = 1.645 * 8 + 75

x = 88.16

Hence, the bottom cutoff for receiving an A grade is 88.16.

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The equation of the line passing through (-2,-4) and (4,4) is y = (4/3)x - 4/3.

The slope intercept formula, y = mx + b, is used when the slope of the line under study is known and the specified point is also the y intercept (0, b). In the equation, the term b stands in for the y value of the y intercept point.

Using the point-slope form of the equation, we can determine the equation of the line across two points:

y - y1 = m(x - x1)

where m is the slope of the line, and (x1, y1) is one of the provided locations.

Let's start by determining the line's slope:

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

where (x1, Y1) equals (-2, -4), and (x2, Y2) equals (4, 4)

m = (4 - (-4)) / (4 - (-2)) = 8 / 6 = 4 / 3

The equation of the line can now be determined using any of the supplied points:

Making use of (x1, y1) = (-2, -4)

y - (-4) = (4/3)(x - (-2))

y + 4 = (4/3)(x + 2)

y = (4/3)x + (8/3) - 4

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

Hence, y = (4/3)x - 4/3 is the equation for the line through (-2,-4) and (4,4).

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Libby requires an additional 8 blue beads to make a bracelet combing white beads and blue beads in a ratio of 1:3.

The ratio refers to the relative size of one value or quantity compared to another.

Ratios are expressed in percentages, fractions, or decimals and can also be expressed in the standard ratio forms (:) to show the comparative relationship one value bears to another.

The ratio of white beads to blue beads = 1:3

The sum of ratios = 4 (1 + 3)

The number of white beads = 6

The total number of beads = 24 (6 ÷ ¹/₄)

The number of blue beads required = 18 (24 - 6)

The number of blue beads Libby has = 10

The additional number of blue beads required = 8 (18 - 10)

Thus, based on the ratio of white beads to blue beads, Libby requires additional 8 blue beads to make a bracelet.

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How many more blue beads does Libby require?

To convert a quadratic expression [tex]ax^2 + bx + c[/tex] to the form [tex](x+p)^2 + q[/tex], where p=b/2a and [tex]q=(b^2-4ac)/4a[/tex], complete the square by adding and subtracting [tex](b/2)^2[/tex] and simplify the resulting expression.

To express the quadratic expression [tex]x^2 + 12x + 11[/tex] in the form [tex](x+p)^2 + q[/tex], we need to complete the square by adding and subtracting a suitable constant term.

First, we take half of the coefficient of x (which is 12) and square it, giving [tex](12/2)^2 = 36[/tex]. We then add and subtract this value inside the bracket:

[tex]x^2 + 12x + 11 = x^2 + 12x + 36 - 36 + 11[/tex]

Now we can group the first three terms and write them as a square of a binomial:

[tex]x^2 + 12x + 36 = (x + 6)^2[/tex]

Simplifying the remaining terms, we have:

[tex]x^2 + 12x + 11 = (x + 6)^2 - 25[/tex]

Therefore, we have expressed the quadratic expression [tex]x^2 + 12x + 11[/tex] in the form [tex](x+p)^2 + q[/tex], where p = 6 and q = -25.

In general, to express a quadratic expression of the form [tex]ax^2 + bx + c[/tex] in the form [tex](x+p)^2 + q[/tex], where a, b, and c are constants and p and q are to be determined, we can follow these steps:

Take half of the coefficient of x (which is b/2) and square it, giving [tex](b/2)^2[/tex].

Calculate this value inside the bracket:

[tex]ax^2 + bx + c = ax^2 + bx + (b/2)^2 - (b/2)^2 + c[/tex]

Group the first three terms and write them as a square of a binomial:

[tex]ax^2 + bx + (b/2)^2 = a(x + b/2a)^2[/tex]

Simplify the remaining terms:

[tex]ax^2 + bx + (b/2)^2 + c - (b/2)^2 = a(x + b/2a)^2 + (4ac-b^2)/4a[/tex]

We can simplify the expression (4ac-b^2)/4a by recognizing that it is the discriminant of the quadratic equation [tex]ax^2 + bx + c = 0[/tex], which is [tex]b^2 - 4ac[/tex]. Therefore, we have:

[tex]ax^2 + bx + c = a(x + b/2a)^2 + (b^2 - 4ac)/4a[/tex]

We can rewrite this in the form [tex](x+p)^2 + q[/tex] by identifying p and q:

p = b/2a, and [tex]q = (b^2 - 4ac)/4a[/tex].

Therefore, the quadratic expression [tex]ax^2 + bx + c[/tex] can be expressed in the form [tex](x+p)^2 + q[/tex], where p = b/2a and [tex]q = (b^2 - 4ac)/4a[/tex].

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Tan has a value of 3/4. Trigonometric theory has been used to arrive at this value.

This is due to the fact that trigonometry is still regarded as a relatively challenging and abstract branch of mathematics in comparison to other branches. When learning trigonometry, students frequently run across mistakes, misunderstandings, and barriers.

Calculus is the most difficult math topic, and very few students, whether in junior high or elsewhere, succeed in it. In vector space, linear algebra is a subset of abstract algebra. Matrix technology makes things less abstract & easier to understand because it is more concrete.

tan α [tex]= \frac{15}{20}[/tex]

⇒tan α [tex]=\frac{3}{4}[/tex]

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Answer:

900

Step-by-step explanation:

because 14132.77/14.5%