Let f (x) = x^2.

A) which is greater: f(7) or f (-7)? Explain.

B) which is greater f(-10) or f(3)? Explain.

The formula for the volume of a rectangular prism is [tex]V = whl[/tex], where [tex]V[/tex] is the volume, [tex]w[/tex] is the width, [tex]h[/tex] is the height, and [tex]l[/tex] is the length. We can calculate the volume by substituting our values into this formula and solving.

[tex]V = 12 \cdot 2 \cdot 3\\V = 72[/tex]

So, our answer is [tex]\boxed{72 \text{ ft}^2}[/tex].

If the question is asking you for the number of cubes that we can fit, we replace each length with cubes that are [tex]1 \cdot 1 \cdot 1 \text{ ft}^3[/tex], which are the largest cubes you can fit without overlap, you fit 72 cubes in the prism, each of length [tex]1 \text{ ft}[/tex].

According to the information we can infer that Jim is currently 42 years old.

To calculate how old is Joyce now let's start by assigning variables to the unknown ages:

Using the information given in the problem, we can create two equations:

This means that Jim's age when Joyce was K years old is equal to J - K. According to the statement, J is now twice this age. So we can write:

This means that when Joyce is J years old, their ages will add up to 63. So we can write:

Now we have two equations with two variables. We can use substitution to solve for one of the variables:

We can substitute this expression for J in equation 2: 2K + K = 63, which simplifies to 3K = 63. Therefore, K = 21.

So Joyce is currently 21 years old. To find Jim's age, we can use equation 1 and substitute K = 21:

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Becky is correct if x + y = 180° ,   indicating that BCDF is a cyclic quadrilateral. Teboho's claim would be valid if x +  y ≠ 180°.

A cyclic quadrilateral, also known as an inscribed quadrilateral in Euclidean  geometry, is a quadrilateral with all   of its vertices on a single circle.

To determine the size of angle C in terms of x and y, we can use the fact that tangent BC touches the circle ABDE at B.

This means that angle C is equal to the angle formed between the chord AD and the tangent BC at point B.

4.1.1

Since AB || EC, we can use the alternate interior angles theorem to determine the relationship between angles C and A₁.

Angle C is equal to angle A₁ because they are corresponding angles.

Therefore, the size of angle C is y.

4.1.2   - To determine if BCDF is a cyclic quadrilateral

 In order to check if BCDF is cyclic, we need to determine if the opposite angles in the quadrilateral add up to 180° .

Let's consider angle BCD and angle BFD:

Angle BCD is equal to angle B₁ (given) and is represented by x.

Angle BFD is equal to angle A₁ (since BCDF is a cyclic quadrilateral) and is represented by y.

If x + y = 180 degrees, then BCDF is a cyclic quadrilateral.

conclusively , Becky is correct if x + y = 180°, indicating that BCDF is a cyclic quadrilateral. Teboho's claim would be valid if x + y ≠ 180°.

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The angles have been calculated as shown below.

A pie chart for to represent this information is shown below.

For the total number of people in the last election, we have the following:

Total number of people = 345 + 480 + 60 + 15

Total number of people = 900.

Next, we would determine the angles as follows;

Labour

345/900 × 360 = 138°

Conservative

480/900 × 360 = 192°

Lib Democrat

60/900 × 360 = 24°

Other

15/900 × 360 = 6°

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Finding the smallest possible integer value of k requires analyzing the given equation and determining the conditions under which one root is less than 1 and the other is greater than 1.

The equation is:

2^(2x) - 2(k-1)^(2x) + k = 0

Let's break down the conditions step by step.

1. Square root less than 1:

To make the square root less than 1, we need to substitute x = 1 into the equation and get a positive value. So if x = 1, then

2^(2*1) - 2(k-1)^(2*1) + k > 0

4 - 2(k-1)^2 + k > 0

Extensions and simplifications:

4 - 2(k^2 - 2k + 1) + k > 0

4 - 2k^2 + 4k - 2 + k > 0

-2k^2 + 5k + 2 > 0

2k^2 - 5k - 2 < 0 xss=removed xss=removed xss=removed xss=removed > 0.

Now we can combine both conditions to find the smallest integer value of k.

2k^2 - 5k - 2 < 0 > 0 (Condition 2)

By solving these conditions simultaneously, we can find the range of values of k that satisfy both conditions and determine the smallest integer value of k. However, this process requires calculations and algebraic manipulations beyond the scope of simple text-based answers.

It is recommended to use an algebraic calculator or software to solve the equation and find the smallest integer value of k that satisfies the given conditions. 

Answer:

[tex]x^2+\left(b^3-3bc\right)x+c^3=0[/tex]

[tex]\alpha = 1 \quad \textsf{and} \quad \beta=2[/tex]

[tex]b=-3[/tex]

Step-by-step explanation:

If α and β are roots of x² + bx + c = 0 then the equation must be:

[tex](x -\alpha)(x - \beta) = 0[/tex]

Expanding we get:

[tex]x^2-\beta x - \alpha x + \alpha \beta = 0[/tex]

[tex]x^2-(\alpha +\beta ) x + \alpha \beta = 0[/tex]

Equating the coefficients we get:

[tex]\alpha + \beta=-b[/tex]

[tex]\alpha \cdot \beta=c[/tex]

For an equation with the roots α³ and β³, the sum of the roots can be rewritten in terms of (α + β) and (α·β) using the Sum of Cubes formula, and the Square of Binomials formula:

[tex]\begin{aligned}\alpha^3+\beta^3&=(\alpha + \beta)(\alpha^2-\alpha\beta+\beta^2)\\&=(\alpha + \beta)(\alpha^2+2\alpha\beta+\beta^2-3\alpha\beta)\\&=(\alpha + \beta)((\alpha+\beta)^2-3\alpha\beta))\end{aligned}[/tex]

Substitute in the expressions for (α + β) and αβ to find the sum of the roots α³ and β³ in terms of b and c:

[tex]\begin{aligned}\alpha^3+\beta^3&=(\alpha + \beta)((\alpha+\beta)^2-3\alpha\beta))\\&=(-b)((-b)^2-3c))\\&=-b(b^2-3c)\\&=-b^3+3bc\end{aligned}[/tex]

The product of the roots α³ and β³ in terms of c is:

[tex]\alpha \cdot \beta = c[/tex]

[tex](\alpha \cdot \beta)^3 = c^3[/tex]

[tex]\alpha^3 \cdot \beta^3=c^3[/tex]

For a quadratic equation in the form x² + bx + c = 0:

So for x² + bx + c = 0 with roots α³ and β³:

[tex]x^2-(\alpha^3 + \beta^3)x+(\alpha^3 \cdot \beta^3)=0[/tex]

[tex]x^2-\left(-b^3-3bc\right)x+c^3=0[/tex]

[tex]x^2+\left(b^3-3bc\right)x+c^3=0[/tex]

Therefore, the equation with the roots α³ and β³ is:

[tex]\boxed{x^2+\left(b^3-3bc\right)x+c^3=0}[/tex]

Substitute the given value of c = 2:

[tex]x^2+\left(b^3-3b(2)\right)x+2^3=0[/tex]

[tex]x^2+\left(b^3-6b\right)x+8=0[/tex]

If b³ - 6b + 9 = 0, then (b³ - 6b) = -9.

Substitute this into the equation:

[tex]x^2-9x+8=0[/tex]

Factor:

[tex](x-1)(x-8)=0[/tex]

Therefore, the roots of the equation with the roots α³ and β³ are 1 and 8, so the values of α and β are:

[tex]\alpha^3 =1 \implies \alpha = 1[/tex]

[tex]\beta^3=8 \implies \beta=2[/tex]

To find the real roots of b³ - 6b + 9 = 0, substitute the found values of α and β into the expression for b:

[tex]b=-(\alpha + \beta)[/tex]

[tex]b=-(1+2)[/tex]

[tex]b=-3[/tex]

Therefore, the real root of b³ - 6b + 9 = 0 is b = -3.

We can confirm this by substituting b = -3 into the equation:

[tex]\begin{aligned}(-3)^3-6(-3)+9&=-27+18+9\\&=-9+9\\&=0\end{aligned}[/tex]

The amount in the account after 6 years of continuous compounding at an interest rate of 3.3% per year is $121.820.

To find the amount in the account for continuous compounding, we can use the formula:

A = Pe^(rt)

where:

A = the amount in the account

P = the principal (starting amount)

e is a mathematical constant that is roughly equivalent to 2.71828.

r denotes the yearly interest rate

t = the time (in years)

Plugging in the given values, we get:

A = $100 x [tex]e^{0.033 * 6}[/tex]

A = $100 x [tex]e^{(0.198)}[/tex]

A = $100 x [tex]2.71828^{(0.198)}[/tex]

A = $100 x 1.2182

A = $121.820

Therefore, the amount in the account after 6 years of continuous compounding at an interest rate of 3.3% per year is $121.820.

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The interquartile range for the museum is 280

The interquartile range for the farm is 200

The interquartile range for the museum is greater than the interquartile range for the farm.

This suggests that the numbers of visitors to the museum are less consistent.

The interquartile range is solved using the formula

= top quartile - bottom quartile

Where

the bottom quartile is at the box's edge, the top side.

the top quartile is towards the box's edge the downside.

the museum

The interquartile range is

= top quartile - bottom quartile

= 500  -  220

= 280

the farm

The interquartile range is

= top quartile - bottom quartile

= 460  -  260

= 200

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Answer:

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

Consider the properties of absolute value:

Since x is negative, 2x will also be negative.

To remove the absolute value symbol and keep the expression equivalent, multiply by -1:

The value of absolute value symbol is,

⇒ - 2x

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

We have to given that;

⇒ |2x|

If x < 0

Hence, Number write in without the absolute value symbol as;

⇒ |2x|

⇒ - 2x

Thus, The value of absolute value symbol is,

⇒ - 2x

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The volume of solids, to the nearest tenth are calculated as: 7. 103.7 km³; 18. 5575.3 cubic cm; 19. 2144.7 mi³

The first shape is a cone while the other two solids are spheres, therefore:

The volume of a sphere (V) = 4/3 * πr³

Volume of cone (V) = 1/3 * πr²h

17. radius (r) = 6/2 = 3 km

height (h) = 11 km

Volume = 1/3 * π * 3² * 11 ≈ 103.7 km³

18. The solid is a sphere with a diameter of 22 cm. Therefore, we have:

radius (r) = 22/2 = 11 cm

Volume of the sphere = 4/3 * π(11)³

Volume of the sphere ≈ 5575.3 cubic cm

19. r = 16/2 = 8 mi

Volume = 4/3 * π * 8³ ≈ 2144.7 mi³

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Question:

Find the Volume of each solid. Round to the nearest tenth is necessary.

Answer: The digit in the following number is the one that determines its precision is 1.

Step-by-step explanation:

Precision is the ability to consistently produce outcomes with a high degree of accuracy. In general, precision can be thought of as the opposite of randomness or imprecision. It is also important for creating and maintaining machines, such as those in manufacturing, and for ensuring that the parts involved in a process fit together exactly as they should.

34.81 is a number with decimal digits up two places behind the decimal.

Since this number is 34.81, the precision is determined by the value at the 2nd decimal place which is 1 since it determines the how the value is performing at the second decimal place after the first decimal place. Hope this helps!

The function that provides the height of the stack of cups based on any number of cups is height(n) = 7.5 + 1.5(n-1)

Let's assume that the height of one cup is 7.5 inches.

When we add the second cup, the bottom of the second cup rests on the top of the first cup, including the 1.5" lip.

Therefore, the height of the second cup is 7.5 inches plus 1.5 inches, or 9 inches.

When we add the third cup, the bottom of the third cup rests on the top of the second cup, including the 1.5" lip.

Therefore, the height of the third cup is the height of the first two cups plus 1.5 inches, or 16.5 inches.

The function we get by continuing this pattern for any number of cups n by using the formula:

height(n) = 7.5 + 1.5(n-1)

Therefore, the function that provides the height of the stack of cups based on any number of cups is height(n) = 7.5 + 1.5(n-1)

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The value of n is -77/24.

To solve this expression,

Start with the expression: 3/5 × (-6 + 2 2/3) ÷ 1 1/2 - 1 1/8 - 5/2 + (1 4/5 ÷ 9/10).

Simplify the addition and subtraction within parentheses first:

-6 + 2 2/3 = -6 + 8/3 = -18/3 + 8/3 = -10/3

1 4/5 ÷ 9/10 = 9/5 ÷ 9/10 = 9/5 × 10/9 = 90/45 = 2

Now the expression becomes: 3/5 × (-10/3) ÷ 1 1/2 - 1 1/8 - 5/2 + 2.

Next, let's simplify the division:

-10/3 ÷ 1 1/2 = -10/3 ÷ 3/2 = -10/3 × 2/3 = -20/9

The expression now becomes: 3/5 × (-20/9) - 1 1/8 - 5/2 + 2.

Now let's simplify the subtraction:

1 1/8 = 8/8 + 1/8 = 9/8

The expression becomes: 3/5 × (-20/9) - 9/8 - 5/2 + 2.

Convert all fractions to a common denominator:

The common denominator for 5, 9, 8, and 2 is 360.

The expression becomes: (3/5) × (-160/72) - (9/8) × (45/45) - (5/2) × (180/180) + (2/1) × (180/180).

Perform the multiplications:

(3/5) × (-160/72) = -480/360 = -4/3

(9/8) × (45/45) = 405/360 = 9/8

(5/2) × (180/180) = 900/360 = 5/2

(2/1) × (180/180) = 360/360 = 1

The expression becomes: (-4/3) - (9/8) - (5/2) + 1.

Simplify the expression:

-4/3 - 9/8 - 5/2 + 1 = (-128/96) - (27/24) - (60/48) + (48/48) = -128/96 - 108/96 - 120/96 + 48/48

= (-128 - 108 - 120 + 48)/96 = -308/96 = -77/24.

Therefore, the value of n is -77/24.

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An equation, in slope-intercept form, for the line of best fit for the table  above is y = 0.05x + 0.7.

In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical equation (formula):

y - y₁ = m(x - x₁)

Where:

First of all, we would determine the slope of this line;

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Slope (m) = (1.3 - 1.1)/(4 - 8)

Slope (m) = -0.2/4

Slope (m) = 0.05

At data point (8, 1.1) and a slope of 0.05, a linear equation for this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - 1.1 = 0.05(x - 8)  

y = 0.05x - 0.4 + 1.1

y = 0.05x + 0.7

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The simplified expression in this problem has the result given as follows:

40.

The expression for this problem is defined as follows:

[tex]\frac{(8^4)^3 \times 5^2 \times 5^3}{8^7 \times (8 \times 5)^4}[/tex]

Applying the power of power rule, which states that we keep the bases and multiply the exponents we, have that:

Hence:

[tex]\frac{8^{12} \times 5^2 \times 5^3}{8^7 \times 8^4 \times 5^4}[/tex]

When two terms with the same base and different exponents are multiplied, we keep the bases and add the exponents, hence:

[tex]\frac{8^{12} \times 5^5}{8^{11} \times 5^4}[/tex]

When two terms with the same base and different exponents are divided, we keep the bases and add the exponents, hence:

8 x 5 = 40.

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The chance of drawing a red ball has the value P (red ball) = 1/4.

We have to given that;

There are 2 red balls,

And,  2 blue balls

And, 4 green balls in a pail.

Since, We know that;

The possibility of an event happening is referred to as probability. Probability is the ability to happen. The subject of this area of mathematics is the occurrence of random events. From 0 to 1 is used to express the value

Hence, Total number of balls is,

= 2 + 2 + 4

= 8

So, the probability of pulling out a red ball is,

⇒ P = 2 / 8

⇒ P = 1/4

Therefore, We can formulate;

The chance of drawing a red ball has the value P (red ball) = 1/4.

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1. 6/10 2. 6/15 3. 7/20

Step-by-step explanation:

because when your converted the numbers into a decimal fraction,it gives you this percents

The answer is True. In the Venn Diagram for an EIO - 2 Categorical Syllogism, X represents the area of the diagram where the subject of the conclusion statement (the term in the predicate of the minor premise) overlaps with the complement of the predicate of the major premise.

In a EIO syllogism, the conclusion statement is negative and particular, meaning that it denies the existence of some members of the subject class. This area of the diagram is represented by number 6. Therefore, there should be an X in number 6 of the Venn Diagram for an EIO - 2 Categorical Syllogism.

In the Venn Diagram for an EIO-2 Categorical Syllogism, there is an X in number 6. The statement is true. An EIO-2 Categorical Syllogism consists of a negative major premise, a negative minor premise, and a negative conclusion. In a Venn Diagram, an "X" represents an instance where the two categories overlap, and number 6 is the area where the two categories overlap negatively. So, in this case, the presence of an X in number 6 indicates the truth of the EIO-2 Categorical Syllogism.

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Therefore, in a 2x2 table, the pattern of cell frequencies that would indicate independence is d. All cell frequencies are exactly the same.

In a 2x2 contingency table, the expected cell frequencies under the null hypothesis of independence are equal for all cells. If the observed cell frequencies in the table are approximately equal to the expected cell frequencies, then we can conclude that there is no significant association between the two variables being studied. In other words, the pattern of observed cell frequencies is consistent with the null hypothesis of independence. Therefore, if all cell frequencies are exactly the same, it suggests that the variables are independent, as each cell has an equal chance of being filled by any observation regardless of the value of the other variable.

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Answer:

Shown below.

Step-by-step explanation:

The commutative property is a property of binary operations that states that the order of the operands does not affect the result of the operation. In other words, if you swap the order of the operands, you will still get the same result. This property holds true for addition and multiplication but not for subtraction and division.

Therefore, the equivalent expressions in order are 7 × 5, 24 + 10, 1 × 3 and 5 × 7.

The complete table:

                                      Unlikely    |       Equally   |    Likely

P(4)                                    _                        0                0

P(greater than 1)                _                        _                0

P(even)                              _                        0                0

Matching the outcomes to each event:

P(4): Equally likely. Each face of the cube has an equal chance of landing face up, so the probability of rolling a 4 is the same as the probability of rolling any other single number.

Therefore, P(4) is equally likely.

P(greater than 1): Likely. There are five faces that have a number greater than 1 (2, 3, 4, 5, and 6) and only one face that has a 1.

Therefore, the probability of rolling a number greater than 1 is much higher than the probability of rolling a 1, making it a likely outcome.

P(even): Equally likely. There are three even numbers (2, 4, and 6) and three odd numbers (1, 3, and 5) on the cube, so the probability of rolling an even number is the same as the probability of rolling an odd number. Therefore, P(even) is equally likely.

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The number 24, 22, 34, 28, 29, 24, 25, 29, a and b have a median of 27 and a mode of 29 then a is 26 and b is 29

We need to arrange the numbers in order to find the median

22, 24, 24, 25, 28, 29, 29, 34, a, b

The middle number when the numbers are arranged in order is the median

Since we have 10 numbers, the median is the average of the 5th and 6th numbers:

Median = (28 + 29)/2 = 27

The mode is the most occuring number.

Here, the number 29 appears twice, which is more than any other number.

Since a < b, we know that a must be one of the numbers that appears earlier in the list.

Since the mode is 29, we know that b must be 29.

Looking at the list, the only number earlier than 28 that is not 24, 25, or 22 is 26.

Hence, the value of a is 26 and b is 29

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Yes, there are two possible shapes that fit this description.

Lilly is describing a parallelogram, which is a quadrilateral with two pairs of parallel opposite sides.

A parallelogram has opposite sides that are congruent and parallel, and opposite angles that are congruent. Therefore, it has two pairs of equal opposite sides.

There are two types of parallelograms: a rectangle and a rhombus. A rectangle is a parallelogram with four right angles, while a rhombus is a parallelogram with four congruent sides.

Both shapes have two pairs of equal opposite sides and opposite sides that are parallel.

Therefore, Robin is correct that there are two possible shapes. Depending on whether all four angles are right angles or all four sides are congruent, the shape could be a rectangle or a rhombus. It is also possible for a shape to be both a rectangle and a rhombus, in which case it would be called a square.

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Answer:

A and C

Step-by-step explanation:

A. 52 mph and C. 48 mph represent the same level of accuracy compared to the speed limit sign since they are within the range of -5 mph to +5 mph from the limit of 55 mph. Therefore, the correct answers are A and C.

The absolute guessing errors for all 10 guesses are:

45, 5, 20, 12, 22, 15, 3, 55, 25, 30

To calculate the absolute guessing error, we need to find the absolute difference between each guess and the actual number of marbles (145).

Absolute guessing error for each guess:

|190 - 145| = 45

|150 - 145| = 5

|125 - 145| = 20

|133 - 145| = 12

|167 - 145| = 22

|160 - 145| = 15

|148 - 145| = 3

|200 - 145| = 55

|170 - 145| = 25

|115 - 145| = 30

Therefore, the absolute guessing errors for all 10 guesses are:

45, 5, 20, 12, 22, 15, 3, 55, 25, 30

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In the given diagram, given that the shapes have the same area, the value of y is 3.

From the question, we are to determine the value of y in the given diagram.

From the given information,

The yellow shapes have the same area.

The area of the shape is

Area = 8 × (3y + 1)

Area = 24y + 8

For the second shape,

Area = (15 × (y + 5)) - (4 × (7y - 11))

Area = (15y + 75) - (28y - 44)

Area = 15y + 75 - 28y + 44

Area = 119 - 13y

Since the shapes have the same area, we can write that

24y + 8 = 119 - 13y

24y + 13y = 119 - 8

37y = 111

y = 111/37

y = 3

Hence, the value of y is 3

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Answer:

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

Using the formula for the union of two sets:

where

We are given that:

Plugging in the values, we get:

Therefore, set B contains 42 elements.

Answer:

12.3cm

Step-by-step explanation:

length

= 65.9

- 9.2

- 4.7

- 4.7

- 2.2

- 9.2

- 2.2

- 12

- 4.7

- 4.7

= 12.3 cm