Determine the missing dimension of the area is 112 in.²

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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The distributed form of the expression [tex]x(x - 3)[/tex] is [tex]x^2 - 3x.[/tex] "Distributing" an expression means multiplying each term inside the parentheses by the term outside of the parentheses.

In this case, we are asked to distribute the expression [tex]x(x - 3).[/tex]

To do this mentally, we can use the distributive property of multiplication over addition/subtraction:

[tex]a(b + c) = ab + ac[/tex]

We can apply this property to the given expression as follows:

[tex]x(x - 3) = x * x - x * 3[/tex]

Simplifying the right-hand side using the multiplication property of real numbers, we get:

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

So, the distributed form of the expression x(x - 3) is [tex]x^2 - 3x[/tex].

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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.

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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After following the steps of quadratic equation described below,

We can prove,

⇒ x =  -b±√(-4ac+  b²)/2a

Given that;

The quadratic equation is,

ax²+bx+c = 0,

As a result, the following steps must be taken to obtain the quadratic formula from the equation:

ax²+bx+c = 0

Take subtraction of c both sides.

ax²+bx+c-c = 0-c

ax²+bx = -c

Substitute a for both sides of the equation.

ax²/a + bx/a = -c/a

x² + bx/a = -c/a

Complete the square by adding  (b/2a)² times a squared to each sides.

x² + bx/a +  (b/2a)² = -c/a +  (b/2a)²

Square the quantity  b/2a on the right side of the equation

x² + bx/a +  (b/2a)² =  -c/a +  b²/4a²

Find the lowest common denominator on the right side of the equation. 4a²

x² + bx/a +  (b/2a)² =  -4ac/4a² +  b²/4a²

Add the fractions on the right side of the equation together.

x² + bx/a +  (b/2a)² =  (-4ac+  b²)/4a²

Because, as shown in the question, the fraction on the right-hand side of the equation is to be added together rather than multiplied.

As demonstrated, the equation on the left should be expressed as a perfect square.

(x+b/2a)² =  (-4ac+  b²)/4a²

Add the square roots of both sides together.

√(x+b/2a)² = √ (-4ac+  b²)/4a²

(x+b/2a) =  √(-4ac+  b²)/2a

Take b/2a off both sides.

x+b/2a - b/2a =  -b/2a + √(-4ac+  b²)/2a

x =  -b/2a + √(-4ac+  b²)/2a

Add the fractions on the right side together.

x =  -b±√(-4ac+  b²)/2a

Therefore, This gives the required equation.

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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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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 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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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 statements that best describe the bowling scores data are:

- The MAD best describes the variability (C)

- The IQR best describes the spread (D)

Based on the given data in the table, the following statements can be made:

- There are no outliers in the data set, as all the scores fall within a reasonable range.

- The mean can be calculated as:

Mean = [tex]\frac{121 + 159 + 146 + 132 + 149}{5}[/tex]

          = 141.4,

but it may not be the best measure of central tendency due to the small size of the data set and the presence of outliers in larger data sets.

- The MAD (Median Absolute Deviation) can be calculated as the median of the absolute deviations from the median, which are:

|121 - 146| = 25,

|159 - 146| = 13,

|146 - 146| = 0,

|132 - 146| = 14,

|149 - 146| = 3.

The median of these values is 13, so the MAD is 13.

This describes the variability of the data well, as it takes into account the distance of each score from the median.

- The IQR (Interquartile Range) can be calculated as the difference between the third quartile (Q3) and the first quartile (Q1) of the data set. To do this, we need to first find the median of the lower half of the data set (Q1) and the median of the upper half of the data set (Q3). Ordering the data set from lowest to highest, we have:

               121, 132, 146, 149, 159.

Q1 is the median of the lower half, which is:

Median = [tex]\frac{121 + 132}{2}[/tex]  = 126.5.

Q3 is the median of the upper half, which is

Median = [tex]\frac{149 + 159}{2}[/tex] = 154.

The IQR is then:

IQR = Q3 - Q1

       = 154 - 126.5

       = 27.5.

This describes the spread of the data well, as it captures the middle 50% of the data set.

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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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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 equation in slope intercept form to represent the equation is y = 2.5x

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

The graph

On the graph, we have the following points

(x, y) = (0, 0) and (10, 25)

A linear equation is represented as

y = mx + c

Where

c = y when x = 0

So, we have

y = mx + 0

y = mx

Next, we have

25 = 10m

This gives

m = 2.5

So, we have

y = 2.5x

Hence, the equation is 2.5x

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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

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 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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Answer:

Step-by-step explanation:

First find the diameter of the small pizza.

Area = π r²

We have the area 201 in².

Let's subsitute into the formaula to find diameter of the small pizza.

201 in² = (3.14)π²

Divide both sides by π.

64.013 = r²

√64.013 = √r

8 = r (approximately) diameter is 2 times the radius.

So if the diameter of the small pizza is 8 × 2 = 16.

And the diameter of the large pizza is 16 × 2 = 32

Area of large pizza = π r²

radius would be half the diameter or 16

Area = 3.14 × 16²

803.84 in²

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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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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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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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. 

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 measure of the angle F is 33.69° to the nearest hundredth using the trigonometric ratio of tangent.

The trigonometric ratios is concerned with the relationship of an angle of a right-angled triangle to ratios of two side lengths.

The basic trigonometric ratios includes;

sine, cosine and tangent.

tan x° = 4/ {opposite/adjacent}

tan x° = 2/3

x° = tan⁻¹(2/3) {cross multiplication}

x° = 33.6901°

Therefore, the measure of the angle F is 33.69° to the nearest hundredth using the trigonometric ratio of tangent.

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The trigonometric identity, (sec(x) ÷ cos(x)) - (tan(x) ÷ cot(x)) is equivalent to the Pythagorean identity sec²(x) - tan²(x) = 1, therefore;

(sec(x) ÷ cos(x)) - (tan(x) ÷ cot(x)) = sec²(x) - tan²(x) = 1

A trigonometric identity is an equation involving trigonometric ratio which is correct for possible values of the input variables.

The specified trigonometric identities can be presented as follows;

sec(x) ÷ cos(x) - tan(x) ÷ cot(x) = 1

cos(x) = 1/sec(x)

tan(x) = 1/cot(x)

cot(x) = 1/tan(x)

Therefore; sec(x) ÷ cos(x) - tan(x) ÷ cot(x) = sec(x) ÷ (1/sec(x)) - tan(x) ÷ (1/tan(x)) = 1

Therefore;

sec(x) ÷ cos(x) - tan(x) ÷ cot(x) = sec²(x) - tan²(x)

The Pythagorean identities, indicates that we get;

sec²(x) - tan²(x) = 1

Therefore; sec(x) ÷ cos(x) - tan(x) ÷ cot(x) = sec²(x) - tan²(x) = 1

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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 correct answer among the choices provided is A. 11.48.

Given that side XY of triangle XYZ corresponds to side JK of triangle JKL, we can set up the following proportion:

XY/JK = YZ/LJ

Substituting the given values:

8.7 / 12.18 = 7.8 / LJ

We solve this for LJ:

LJ = (7.8 * 12.18) / 8.7

Calculating that gives us:

LJ ≈ 11.48

So, the correct answer among the choices provided is A. 11.48.

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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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