7 ft
12 ft
6 ft...
Find the area of the figure above.
[?] square feet

The truth values of the composite propositions are listed below:

Case 7: T, Case 9: T, Case 11: F, Case 13: T, Case 15: F, Case 17: F

Propositions are constructions that contain itself a truth value. This exercise presents a proposition p is false and proposition q is true. Then, we proceed to find the truth value of each composite proposition, that is, a combination of propositions and operators.

Case 7

Case 9

Case 11

Case 13

Case 15

Case 17

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Answer:

(-6, 26),( -4, 8,) (0, -4), (2,2), (8,68)

Step-by-step explanation:

Answer:

(-6, 26),( -4, 8,) (0, -4), (2,2), (8,68)

Step-by-step explanation:

do you have a picture of your work?

and if you have 9.9 in your graph and you get a point it can be valid otherwise it would not help you at all

(a) The scale of the drawing is in centimeters.

(b) The scale factor of the drawing is 5 mm.

(c) The size of the spider's mate drawing should be 4 cm.

Given scale drawing of a spider is 5 cm long.

The actual spider is 10 mm long

(a) The scale of the drawing is in centimeters because the scale drawing of a spider given is in 5 centimeters,

(b) Scale factor:

The scale factor shows by how much the original model has been multiplied or divided by to get the measurements of the drawing.

In this case, the spider is 10 mm long but the drawing length is 5 cm.

Let’s convert both into the same units

5 cm - 50 mm

Original - 10 mm

Painting -50 mm

X - scale factor

50 = X * 10

X = 50/10 = 5 mm

The spider has been multiplied/ enlarged by a scale factor of 5 mm to draw the painting.

(c) Given the spider's mate is 8mm long.

Now for the drawing, we need to choose the scale factor as above to get the perfect measurement.

So, the 8 mm spider has been enlarged by a scale factor of 5 mm to get the size for drawing.

= 8 * 5

= 40 mm

= 4 cm

The size of the drawing should be 4 cm.

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Answer:

x = r ,r is a whole number

y = 5(.5)^r

y=5(.5)

Step-by-step explanation:

The equation of the exponential function represented by the table given is f(x)=(5)[tex](0.5^{x} )[/tex].

Function:

In mathematics, a function is a unique arrangement of the inputs (also referred to as the domain) and their outputs (sometimes referred to as the codomain), where each input has exactly one output and the output can be linked to its input.

For x=0 for  f(0)=(5)[tex](0.5^{0} )[/tex]=5

⇒ x=1 for  f(1)=(5)[tex](0.5^{1} )[/tex]=2.5

⇒ x=2 for  f(2)=(5)[tex](0.5^{2} )[/tex]=1.25

⇒ x=3 for  f(3)=(5)[tex](0.5^{3} )[/tex]= 0.625

Therefore,The equation of the exponential function represented by the table given is f(x)=(5)[tex](0.5^{x} )[/tex].

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The total purchase price is $28496 if a total of 52 microphones are to be purchased. Each microphone costs $548.

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

It is given that:

A total of 52 microphones are to be purchased. Each microphone costs $548.

Let x be the total purchase price

x = 52x548

x = $28496

Thus, the total purchase price is $28496 if a total of 52 microphones are to be purchased. Each microphone costs $548.

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The average price per square foot in 2002 was approximately $85.86.

A mathematical expression of one or more algebraic terms each of which consists of a constant multiplied by one or more variables raised to a nonnegative integral power.

Example: a + bx + cx²

We have,

P(t) = 0.019t³ - 0.287t² + 3.073t + 55.130

Where t = number of years.

From 1992 to 2002 we have,

2002 - 1992 = 10 years

Now,

P(10) = 0.019(10)³ - 0.287(10)² + 3.073(10) + 55.130

P(10) = 19 - 28.7 + 30.73 + 55.130

P(10) = 85.86

Thus the average price per square foot in 2002 was approximately $85.86.

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Answer: A quadrilateral is a four-sided figure.

EX: a square, a rectangle, a trapezoid, or a rhombus.

A closed plane figure or figure formed by four nonintersecting line segments which are not on the same line and connected end to end is called quadrilateral.

The geometric probability which represents the chances of having the waste material hit the car as described in the task content is; 3/20,000.

It follows from the task content that the probability which is to be evaluated is the chance of having the waste material hit the car.

First, since the dimension of the parking lot is; 500 by 800 feet. It follows that;

Area of parking lot = 500 × 800 = 400,000.

Also, since the dimension of the rectangular car is approximately 6 by 10. It follows that;

Area occupied by car = 6 ×10 = 60.

Consequently, the chances of the waste material hitting the car is the ratio of desired outcome to the possible outcome and hence is;

P = 60/400,000

P = 3/20,000.

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The amount of time he spent on the bicycle is; 2.5 hours

The formula that shows the relationship between distance, speed and time is;

distance = velocity * time  

Let W = walking time

B = bicycling time

Thus, from the given data we have;

86 = 4W + 32B      

W + B = 4    

W = 4 - B  substitute 6-B for W in 86 = 4W + 32B to get;

86 = 4(4 - B) + 32B

86 = 16 - 4B + 32B

86 = 16 + 28B

70 = 28B

B = 70/28

B = 2.5 hours on the bicycle

W = 4 - 2.5= 1.5 hours walking

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Answer:

Step-by-step explanation:

x^2 - 14x = -48

x^2 +48 -14 x

x^2 - 14x - 48 = 0

a = 1

b = -14

c = 48

x=8, x=6

The area of the shape with parallel sides is 35 unit² of trapezoid .

Describe the trapezoid shape?

A = (1/2) * (a + b)h

Where a, b is the length of the parallel sides and h is the height of the trapezoid.

Given that a = 8, b = 6 and h = 5, hence:

A = (1/2) * (8 + 6) * 5 = 35 unit²

The area of the shape with parallel sides is 35 unit².

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The absolute and relative errors are 0. 8 and 0. 01 respectively.

Absolute error can be defined as the difference between the inferred or measured value and the actual value of a given quantity.

The formula for absolute error is expressed as;

Absolute error = | VA - VE |

Where;

Substitute the values into the formula

Absolute error = | 60. 8 - 60. 0|

Find the difference

Absolute error = | 0. 8|

Absolute error = 0. 8

Relative error = Absolute error/ actual value

Relative error = 0. 8/ 60. 0

Relative error = 0. 01

Thus, the absolute and relative errors are 0. 8 and 0. 01 respectively.

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1) The soccer team can make 48 pizzas using 12 one-pound packages of cheese.

2) The total cost Dan paid for the mulch was $87.50.

3) The number of acres that Mr. Hamilton will own after the planned purchase is 3¹³/₁₂.

The above values are determined using mathematical operations of addition, division, and multiplication.

For instance, Mr. Hamilton's land increased to 3¹³/₁₂ through the addition of 2¾ and 1¹/₃ acres.

The total cost that Dan paid for the mulch was a multiplication operation.

The number of pizzas the soccer team could make resulted from a division operation.

1) Quantity of cheese on each pizza = 1/4 lb

The total quantity of cheese = 12 lb

The number of pizzas to make = 48 (12/1/4) or (12/0.25)

2) The number of yards of mulch purchased = 3¹/₂ yards

Cost of mulch per yard = $25

The total cost for the mulch = $87.50 ($25 x 3¹/₂)

3) Measurement of land owned = 2¾ acres

The planned purchase of additional land = 1¹/₃

The total acres Mr. Hamilton will own = 3¹³/₁₂ (2¾ + 1¹/₃)

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Answer: draw a parallelogram like figure A and make it the same area of the unlabeled rectangle.

Answer:

1.296623028 grams

Step-by-step explanation:

your answer is 1.296623028 grams because you multiply the given number of moles which was 0.0564 by the molar mass to get the grams

Answer: -1/8 is the answer

The numeric values of the function are given and explained as follows:

To find the numeric value of a function, we replace each instance of the variable by the desired value.

For this problem, the function is given by:

f(x) = 10000 + 1000x.

In which:

When x = -2, we have that:

f(-2) = 10000 + 1000(-2) = 8000.

Hence:

f(-2) = 8000, meaning a qualifying applicant with -2 siblings would receive a financial aid of $8,000. This interpretation does not make sense in the context of the problem.

When x = 4, we have that:

f(4) = 10000 + 1000(4) = 14,000.

Hence:

f(4) = 14,000, meaning a qualifying applicant with 4 siblings would receive a financial aid of $14,000. This interpretation makes sense in the context of the problem.

The number of siblings is a discrete number, and has to be of at least 0, hence:

The domain is: {x is a whole number and x ≥ 0}.

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Answer:

80

Step-by-step explanation:

80 is the only number that is a multiple of ALL 2, 8 and 10

Answer:

the only answer that is a multiple of 2,8 and 10 between 49 and 95, is 80.

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

3 1/6

Step-by-step explanation:

First, we turn 11/12 and 3/4 to have the same denominator  

3/4 x 3 is 9/12

11/12- 9/12 is 2/12

Now we add the extra 3 to 2/12 which is 3 2/12

3 2/12 can be simplified to 3 1/6

The correction option is B, It is out of control as one of these data points is more than 3 standard deviations from the mean.

The normal distribution, also known as the Gaussian distribution, is a symmetric probability distribution about the mean, indicating that data near the mean occur more frequently than data distant from the mean. The normal distribution will show as a bell curve on a graph.

Given that the candy produced by a company has a sugar level that is normally distributed with a mean of 16.1 grams and a standard deviation of 0.9 grams. Therefore, the maximum and the minimum weight of the candy can be,

Maximum weight = Mean + 3(Standard deviation)

                             = μ + 3σ

                             = 16.1 + 3(0.9)

                             = 16.1 + 2.7

                             = 18.8

Minimum weight = Mean - 3(Standard deviation)

                            = μ - 3σ

                            = 16.1 - 3(0.9)

                            = 16.1 - 2.7

                            = 13.4

Since one of the reading point, 19.4 is more than 3 standard deviations from the mean, therefore, it can be concluded that the process is out of control.

Hence, It is out of control as one of these data points is more than 3 standard deviations from the mean.

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Answer: ok?

Step-by-step explanation:

The sequence that can be modeled by the expression is T(n+1) = Tn + 8x - 5 where n >= 1

The expression of the first difference is given as

8x - 5

Rewrite properly as

d = 8x - 5

Where the common difference is represented by d

The common difference of an arithmetic sequence is calculated as

d = T2 - T1

So, we have

T2 - T1 = 8x - 5

Add T1 to both sides of the equation

So, we have

T2 = T1 + 8x - 5

Express 2 as 1 + 1

So, we have

T(1+1) = T1 + 8x - 5

Express 1 as n

So, we have

T(n+1) = Tn + 8x - 5 where n >= 1

Hence, the sequence that can be modeled by the expression is T(n+1) = Tn + 8x - 5 where n >= 1

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3y = -8x -27

Solution :

A line equation is an algebraic way of expressing the collection of points that make up a line in a coordinate system. The many points that collectively make up a line on the coordinate axis are represented as a group of variables (x, y) to create an algebraic equation, also known as an equation of a line.

Given line: 3x - 8y = -7

-8y = -7 -3x

y=- (-7 -3x)/8

y= 7+3x/8

So, the slope (m1) = 3/8

Let’s consider the slope of the line perpendicular to the given line as m2

Then, m1 x m2 = -1

3/8 x m2 = -1

m2 = -8/3

Now,

The equation of the line perpendicular to the given line and passing through the point (-3, -3) will be

y – y1 = m (x – x1)

y – (-3) = -(8/3) (x – (-3))

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

3y + 3 = - 8x - 24

3y = -8x -24-3

3y = -8x -27

Thus, the equation of the required line is 3y = -8x -27

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Answer:

Step-by-step explanation:

8806

The function is a continuous function. Then the value of variables a and b will be 2.5 and 3.5, respectively.

A statement, principle, or policy that creates the link between two variables is known as a function. Functions are found all across mathematics and are required for the creation of complex relationships.

The piecewise function is given below.

[tex]f\left ( \rm x \right ) = \left\{\begin{matrix} \rm \dfrac{x^2 - 4}{x-2} \ or \ x + 2,& \rm x < 2\\ \rm ax^2 - bx + 1, & \rm 2\leq x < 3\\ \rm 4x - a + b, & \rm x \geq 3\end{matrix}\right.[/tex]

At x = 2, the function is continuous, then we have

2 + 2 = a(2²) - 2b + 1

4a - 2b = 3          ...1

At x = 3, the function is continuous, then we have

a(3²) - 3b + 1 = 4(3) - a + b

10a - 4b = 11        ...2

From equations 1 and 2, we have

8a - 10a = 6 - 11

2a = 5

a = 2.5

Then the value of b will be

10(2.5) - 4b = 11

25 - 4b = 11

4b = 14

b = 3.5

The value of the variable a and b will be 2.5 and 3.5, respectively.

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