Debra will rent a car for the weekend. She can choose one of two plans. The first plan has an initial fee of $47.96 and costs an additional $0.19 per mile driven. The second plan has an initial fee of $53.96 and costs an additional $0.15 per mile driven. How many miles would Debra need to drive for the two plans to cost the same?

The length of the third side is 9.

A right-angled triangle is a triangle in which one of its angles is a right angle, meaning it measures exactly 90 degrees (π/2 radians). The other two angles are acute angles, meaning they measure less than 90 degrees.

In a right-angled triangle, the side opposite the right angle is called the hypotenuse. The other two sides are called the legs. The leg opposite to an acute angle is called the opposite side, and the leg adjacent to that angle is called the adjacent side.

The Pythagorean theorem is a fundamental concept in right-angled triangles. It states that the sum of the squares of the lengths of the legs of a right-angled triangle is equal to the square of the length of its hypotenuse. This theorem is often used to calculate the length of one side of a right-angled triangle when the lengths of the other two sides are known.

Let's call the missing side of the right triangle "x". We can use the Pythagorean theorem to solve for x, which states that in a right triangle, the sum of the squares of the two shorter sides (legs) is equal to the square of the length of the longest side (hypotenuse).

So, we have:

x² + 7² = (√130)²

Simplifying:

x² + 49 = 130

x² = 81

Taking the square root of both sides, we get:

x = 9

Therefore, the length of the third side is 9.

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Answer:

The length of the third side of the given right triangle is 9 units.

Step-by-step explanation:

We can use Pythagoras Theorem to find the length of the third side of the given right triangle.

[tex]\boxed{\begin{minipage}{9 cm}\underline{Pythagoras Theorem} \\\\$a^2+b^2=c^2$\\\\where:\\ \phantom{ww}$\bullet$ $a$ and $b$ are the legs of the right triangle. \\ \phantom{ww}$\bullet$ $c$ is the hypotenuse (longest side) of the right triangle.\\\end{minipage}}[/tex]

From inspection of the given right triangle:

Substitute these values into the formula and solve for the third side, b:

[tex]\implies 7^2+b^2=\left(\sqrt{130}\right)^2[/tex]

[tex]\implies 49+b^2=130[/tex]

[tex]\implies 49+b^2-49=130-49[/tex]

[tex]\implies b^2=81[/tex]

[tex]\implies \sqrt{b^2}=\sqrt{81}[/tex]

[tex]\implies b=9[/tex]

Therefore, the length of the third side of the given right triangle is 9 units.

According to the information, it can be inferred that the region and grade that the sales director should target to offer a new reading product based on low reading scores is West region, 4th grade.

To select the correct conclusion we must carefully look at the graphs and identify in which regions and grades the reading score rates are low. Based on this information, we can infer that the region and grade with the lowest rates in this area is West region, 4th grade.

Due to the above, the sales manager should focus his sales strategy on new products in this population because there is a high probability that they will buy the products to improve the rates they have.

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Answer:

Step-by-step explanation:

The formula for the circumference of a circle is C = πd, where C is the circumference and d is the diameter.

Given that the circumference is 132ft and π is 22/7, we can write:

132 = (22/7)d

To solve for d, we can multiply both sides by 7/22:

132 × 7/22 = d

Simplifying the left side:

42 = d

Therefore, the diameter of the circle is 42 feet.

Answer:

D = 42

Step-by-step explanation:

Formula to find Diameter = [tex]\frac{C}{\pi }[/tex]

D = 132 ÷ [tex]\frac{22}{7}[/tex]

[tex]D = \frac{132}{1}[/tex] × [tex]\frac{7}{22}[/tex]

132 divide 22 = 6

D = 6 × 7

D = 42

The tangent of angle Z is given as follows:

tan(Z) = length of opposite side/length of adjacent side.

The three trigonometric ratios are defined as follows:

Hence the tangent for angle Z is given by the ratio between the length of the opposite side to angle Z and the length of the adjacent side to angle Z.

The problem is incomplete, hence the general procedure to obtain the tangent of angle Z is presented.

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The retaining wall will need to have at least 32 rows of bricks to reach a height of at least 60 inches, not counting the initial 12-inch piece of stone.

Two or more expressions with an Equal sign is called as Equation.

The wall needs to be at least 60 inches tall, and we already have a 12-inch piece of stone, so we need to stack enough rows of bricks to reach a height of:

60 inches - 12 inches = 48 inches

Each row of bricks adds 1.5 inches to the height

we can divide the remaining height of 48 inches by the height of each row:

48/1.5 = 32 rows

Therefore, the retaining wall will need to have at least 32 rows of bricks to reach a height of at least 60 inches, not counting the initial 12-inch piece of stone.

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The mean of the data is 1097.5

A mean in math is the average of a data set, found by adding all numbers together and then dividing the sum of the numbers by the number of numbers. For example, with the data set: 8, 9, 5, 6, 7, the mean is 7, as 8 + 9 + 5 + 6 + 7 = 35, 35/5 = 7.

Mean = summation of item /number of items

summation of item = 4390

number of items = 4

therefore mean = 4390/4

= 1,097.5

therefore the mean if the data is 1,097.5

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Answer:

n < 11

Step-by-step explanation:

We must solve for n, first we will rearrange the inequality

n - 2 < 9

n < 9 + 2

n < 11

Answer:

n < 11

Step-by-step explanation:

The arc length of a single section on a dartboard rounded to the nearest millimeter is 53 mm.

In mathematics, an equation is a statement that two expressions are equal. It typically involves one or more variables that can take on different values, and the goal is often to solve for the value(s) of the variable(s) that make the equation true.

The total circumference of the dartboard is given by:

C = 2πr

where r is the radius of the dartboard.

Substituting the given values, we get:

C = 2π(170 mm)

C = 1068.18 mm

Dividing the circumference by the number of sections, we get the arc length of a single section:

Arc length = C/20

Arc length = 1068.18 mm/20

Arc length ≈ 53.41 mm

Rounding this to the nearest millimeter, we get:

Arc length ≈ 53 mm

Therefore, the arc length of a single section on a dartboard rounded to the nearest millimeter is 53 mm.

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The solution to the system of linear equations,

2x - y = - 22 and - 7x + y = 67 is x = - 9 and y = 4.

If a system of equations only contains two linear equations with two variables, the system's equation can be graphed, the graph will have two straight lines, and the intersection point(s) of those lines will be the system's solution.

Given, Two linear equations 2x - y = 22 and y = 7x + 67 in two variable 'x' and 'y'.

Arranging the equation in a similar pattern we have,

2x - y = - 22 and - 7x + y = 67.

Now, Adding these two equations +y and -y will cancel out,

So, We have - 5x = 45.

x = - 9, and 2(-9) - y = - 22 ⇒ y = 4.

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Answer:

onomatopoeia

Step-by-step explanation:

Answer:

12:8

Step-by-step explanation:

3:2

12:x

12÷3=4

2×4=8

12:8

Answer:

The decoded message is: "Steve Jobs".

Step-by-step explanation:

The given code is a sequence of binary digits, which represents the ASCII code of a message in binary form. To decode the message, we need to convert each 8-bit binary sequence into its corresponding ASCII character.

1010011 1110100 1100101 1110110 1100101 0100000 1001010 1101111 1100010 1110011

To decode this message, we split it into 8-bit sequences:

01010011 --> 'S'

01110100 --> 't'

01100101 --> 'e'

01110110 --> 'v'

01100101 --> 'e'

00100000 --> ' '

01001010 --> 'J'

01101111 --> 'o'

01100010 --> 'b'

01110011 --> 's'

Therefore, the decoded message is: "Steve Jobs".

Answer:

The decoded message is: "Steve Jobs"

Step-by-step explanation:

Converting the binary code to ASCII, we get:

01010011 = S

1110100 = t

1100101 = e

1110110 = v

1100101 = e

0100000 = (space)

1001010 = J

1101111 = o

1100010 = b

1110011 = s

So the decoded message is: "Steve Jobs"

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

Here are the steps to decode the given binary code:

Break the binary code into groups of 8 digits, as each group represents a single ASCII character.

Convert each group of 8 digits into its corresponding ASCII character using a binary-to-text converter or an ASCII code chart.

Write down the decoded ASCII characters in the order in which they appear in the original binary code.

Let's follow these steps to decode the given binary code:

The given binary code is: 1010011 1110100 1100101 1110110 1100101 0100000 1001010 1101111 1100010 1110011

We break this binary code into groups of 8 digits:

1010011 = 53

1110100 = 74

1100101 = 65

1110110 = 76

1100101 = 65

0100000 = 32

1001010 = 74

1101111 = 111

1100010 = 98

1110011 = 115

We convert each group of 8 digits into its corresponding ASCII character using an ASCII code chart:

53 = S

74 = t

65 = e

76 = v

65 = e

32 = (space)

74 = J

111 = o

98 = b

115 = s

We write down the decoded ASCII characters in the order in which they appear in the original binary code:

Decoded message: "Steve Jobs"

ASCII mean?

ASCII stands for American Standard Code for Information Interchange. It is a character encoding standard that assigns unique numeric codes to represent text characters. The ASCII standard includes codes for uppercase and lowercase letters, digits, punctuation marks, and various other symbols. Each ASCII character is represented by a unique 7-bit binary code, allowing computers and other devices to communicate and display text in a consistent manner. The ASCII standard was first published in 1963 and has since been expanded and updated to include additional characters and support for different languages.

(a) One patient did not receive the medication.

(b) One patient did not get either the medicine or the placebo.

(c) None of the patients took the drug or experienced migraines (or both).

(d) One patient who received a placebo experienced no migraines.

A variable in algebra is an alphabet that is used to symbolize the unknowable integer. It stands in for the value. An amount that can fluctuate depending on the mathematical issue is referred to as a variable. The generic letters x, y, and z are frequently employed in mathematical expressions and equations. A variable, then, is a symbol denoting a number whose value is unknown.

from the question:

(a)

Logical expression: ∀x D(x)

Negation: ¬(∀x D(x))

Applying De Morgan's law: ∃x ¬D(x)

One patient did not receive the medication.

(b)

Logical expression: ∀x (D(x) ∨ P(x))

Negation: ¬(∀x (D(x) ∨ P(x)))

Applying De Morgan's law: ∃x ¬(D(x) ∨ P(x))

Applying De Morgan's law: ∃x (¬D(x) ∧ ¬P(x))

One patient did not get either the medicine or the placebo.

(c)

Logical expression: ∃x (D(x) ∧ M(x))

Negation: ¬∃x (D(x) ∧ M(x))

Applying De Morgan's law: ∀x ¬(D(x) ∧ M(x))

Applying De Morgan's law: ∀x (¬D(x) ∨ ¬M(x))

None of the patients took the drug or experienced migraines (or both)

(d)

Logical expression: ∀x (P(x) → M(x))

Using the conditional identity: ∀x (¬P(x) ∨ M(x))

Negation: ¬∀x (¬P(x) ∨ M(x))

Applying De Morgan's law: ∃x ¬(¬P(x) ∨ M(x))

Applying De Morgan's law: ∃x (P(x) ∧ ¬M(x))

One patient who received a placebo experienced no migraines.

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complete question;

In the following question, the domain of discourse is a set of male patients in a clinical study. Define the following predicates:

P(x): x was given the placebo

D(x): x was given the medication

M(x): x had migraines

Translate each statement into a logical expression. Then negate the expression by adding a negation operation to the beginning of the expression. Apply De Morgan's law until each negation operation applies directly to a predicate and then translate the logical expression back into English.

Sample question: Some patient was given the placebo and the medication.

∃x (P(x) ∧ D(x))

Negation: ¬∃x (P(x) ∧ D(x))

Applying De Morgan's law: ∀x (¬P(x) ∨ ¬D(x))

English: Every patient was either not given the placebo or not given the medication (or both).

(a)Every patient was given the medication.

(b)Every patient was given the medication or the placebo or both.

(c)There is a patient who took the medication and had migraines.

(d)Every patient who took the placebo had migraines. (Hint: you will need to apply the conditional identity, p → q ≡ ¬p ∨ q.)

In a right triangle, the tangent of an acute angle is the ratio of the length of the opposite side to the length of the adjacent side, the sine of an acute angle is the ratio of the length of the opposite side to the length of the hypotenuse, and the cosine of an acute angle is the ratio of the length of the adjacent side to the length of the hypotenuse.

Using the side lengths given in the problem, we can identify that angle B is the acute angle opposite the side with length 5.

So, we have:

tanB = opposite/adjacent = 12/5

sinB = opposite/hypotenuse = 12/13

cosB = adjacent/hypotenuse = 5/13

Therefore, the values of the trigonometric functions for angle B in this right triangle are:

tanB = 12/5

sinB = 12/13

cosB = 5/13

The x-coordinate at which F(x) = G(x) is 0.667. By graphing the functions, the answer has been discovered.

Making a graph of the pertinent function is the first step in graphing a function. The function equation will be satisfied by a curve if it reflects the function at that location.

We are given two functions as f(x) = log (2x) and g(x) = 3x - 2

The graph of the given functions has been plotted and attached below.

In the graph, the red line represents the log function i.e. f(x) and the blue line represents the linear function i.e. g(x).

From the graph, we can observe that the two functions meet at two points which are (0.667, 0) and (0, -2).

Hence, the x value where F(x) = G(x) is 0.667.

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There will be 21 computer workstations that may be arranged side by side along the wall.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.

The number of computer desks that can be placed side-by-side along the wall is calculated as,

⇒ (15 x 100) / 70

⇒ 1500 / 70

⇒ 21.42

There will be 21 computer workstations that may be arranged side by side along the wall.

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In response to the query, we have that The Pythagorean identity for theta = 30° is therefore confirmed since sin(30°) + cos(30°) = 1.

The fundamental Euclidean geometry relationship between the three sides of a right triangle is the Pythagorean Theorem, sometimes referred to as the Pythagorean Theorem. This rule states that the areas of squares with the other two sides added together equal the area of the square with the hypotenuse side. According to the Pythagorean Theorem, the square that spans the hypotenuse (the side that is opposite the right angle) of a right triangle equals the sum of the squares that span its sides. It may also be expressed using the standard algebraic notation, a2 + b2 = c2.

This trigonometric identity is valid for all theta values. Because it is connected to the geometry-related Pythagorean theorem, it is known as the Pythagorean identity.

According to Pythagorean theory,

[tex]Cos(theta)^2 + Sin(theta^)2 = 1[/tex]

So, you can easily include that value into the equation and simplify it if you need to assess sin(theta) + cos(theta) for a certain value of theta:

[tex]Cos(theta)2 + Sin(theta)2 = 1\\Sin(2) + Cos(30)\\If theta = 30, then 2(30) = 1.\\(1/2)\\c^2 + (√3/2)\\c^2 = 1 \s1/4 + 3/4 = 1 \s1 = 1[/tex]

The Pythagorean identity for theta = 30° is therefore confirmed since sin(30°) + cos(30°) = 1.

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Answer:

Before Tax Price: $40.00

Sale Tax: 5.00% or $2.00

After Tax Price: $42.00

Step-by-step explanation:

Answer:

42 dollars

Step-by-step explanation:

When doing tax problems, we need to memorize the formula of:

price + tax • price = price with sales tax.

This formula works because you have the initial percentage of the cost, with the added tax, which gives the extra value--then added together it gives the sales cost price.

So let's plug our numbers in

40 + (0.05 or 5%) • 40 = price with sales tax

40 + 2 = price with sales tax

42 = price with sales tax

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Answer:

x=3

Step-by-step explanation:

Let's assume that the customer ordered x burrito bowls.

The cost of x burrito bowls at $6.50 each is 6.50x.

The cost of the plate of corn tacos is $12.96.

The total cost of the order is $32.46.

So we can set up the equation:

6.50x + 12.96 = 32.46

Subtracting 12.96 from both sides, we get:

6.50x = 19.50

Dividing both sides by 6.50, we get:

x = 3

Therefore, the customer ordered 3 burrito bowls.

We need a retirement fund balance of  $714,285.71 in 25 years to generate an annual income of $50,000 at a constant APR of 7%.

percentage, a relative value indicating hundredth parts of any quantity.

To generate an income of $50,000 per year forever, we need to create a retirement fund that can generate this income through interest and not deplete the principal amount.

We can use the following formula to calculate the required balance in the retirement fund:

Balance = Annual income / Annual interest rate

The annual income we need is $50,000, and the annual interest rate is 7%, so we can calculate the required balance as:

Balance = $50,000 / 0.07

= $714,285.71

Therefore, we need a retirement fund balance of  $714,285.71 in 25 years to generate an annual income of $50,000 at a constant APR of 7%.

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Therefore , the solution of the given problem of angle comes out to be x = 15° option d is correct.

In Euclidean geometry, an angle is a shape made up of two rays, or circular sides, that split at the wall's apex and the wall's apex, which is located at the centre. Two rays can combine at their points to create an angle. Another result of two things interacting is an angle. Dihedral angles are what they are called. Two line beams can be arranged at their edges in a number of ways to form a curve through two dimensions.

Here,

Given :

It is an right angle or we can say 90° angle.

So,

In order to find the value of x :

We can,

=> x + 75 = 90

=> x =90 -75

=> x = 15°

Therefore , the solution of the given problem of angle comes out to be  x = 15° option d is correct.

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The surface area of the triangular prism is 72 ft squared.

The surface area of a triangular prism can be found as follows:

Therefore,

surface area of a triangular prism = bh + l(s₁ + s₂ + s₃)

Hence,

b = 4 ft

h = 3 ft

l = 5 ft

s₁ = 4 ft

s₂ = 3 ft

s₃ = 5 ft

Therefore,

surface area of a triangular prism = 4 × 3 + 5(4 + 3 + 5)

surface area of a triangular prism = 12 + 5(12)

surface area of a triangular prism = 12 + 60

surface area of a triangular prism = 72 ft²

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Given- The rectangle that represents the base of right rectangular prism

To find - The volume of the prism.

Explanation- we know that the volume of the right rectangular prism is product of area of rectangle and the height

Area of rectangle is [tex](lb)[/tex]

length (l) = 4.2

breadth = 3

area = 4.2×3=12.6

Volume of prism = 12.6 × height =12.6×6=75.6

Hence the volume of the prism is 75.6 in^3

Final answer - The correct option is D.

Answer:

g(2) = 20

Step-by-step explanation:

g(x) = 7x + 6                              g(2)

g(2) = 7(2) + 6

g(2) = 14 + 6

g(2) = 20

So, the answer is g(2) = 20

We can state that the polynomial [tex]x^3 + 10x^2 + 13x + 36[/tex] is

factored by (x + 9).

the remainder is 0, and the quotient is [tex]x^2 + 9x + 4[/tex]. The outcome can be expressed as

[tex]x^3 + 10x^2 + 13x + 36 = (x^2 + 9x + 4)(x + 9)[/tex]

Algebraic expressions called polynomials include coefficients and variables. Indeterminates are another name for variables. For polynomial expressions, we can do mathematical operations like addition, subtraction, multiplication, and positive integer exponents but not division by variables.

Poly (which means "many") and Nominal (which means "terms") are the two terms that make up polynomials. An expression that consists of variables, constants, and exponents that are combined using mathematical operations like addition, subtraction, multiplication, and division is referred to as a polynomial (No division operation by a variable)

From the question:

We use the long division method to divide polynomials.

[tex]x^2 + 9x + 4[/tex]

_____________________________

[tex]x + 9 | x^3 + 10x^2 + 13x + 36 - (x^3 + 9x^2)[/tex]

   _________________

        [tex]x^2 + 13x - (x^2 + 9x)[/tex]

           ___________

             [tex]4x + 36 - (4x + 36)[/tex]

                  __________

                          0

the remainder is 0, and the quotient is [tex]x^2 + 9x + 4[/tex]. The outcome can be expressed as

[tex]x^3 + 10x^2 + 13x + 36 = (x^2 + 9x + 4)(x + 9)[/tex]

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Answer:

The scale of measurement used by the researcher is interval scale as the data is continuous and there are equal intervals between the values.

Mean = (1+2+4+5+7+11)/6 = 5

Median = (4+5)/2 = 4.5

Mode = There is no mode in the data set as none of the numbers are repeated.

Range = maximum value - minimum value = 11 - 1 = 10

Sample Variance = ((1-5)^2 + (2-5)^2 + (4-5)^2 + (5-5)^2 + (7-5)^2 + (11-5)^2)/(6-1) = 14.67

Standard Deviation = sqrt(sample variance) = sqrt(14.67) = 3.83

Mean + 2SD = 5 + 2*3.83 = 12.66, rounded to the nearest integer = 13.

According to the Empirical Rule, 68% of the sample lies within 1 standard deviation of the mean. Therefore, we need to find the values that are 1 standard deviation away from the mean:

Lower limit = Mean - SD = 5 - 3.83 = 1.17, rounded to the nearest integer = 1.

Upper limit = Mean + SD = 5 + 3.83 = 8.83, rounded to the nearest integer = 9.

So the number of leaves associated with 68% of the sample is between 1 and 9.

Step-by-step explanation:

Answer: Provide the picture if you have one or write out the whole problem

Step-by-step explanation:

The clerk did not give Mary any change, so that is the correct response.

A price decrease from the normal or list amount or a proportional deduction from such a debt account, typically applied in exchange for on-time or cash payments.

The total cost of the shirt and three skirts before the coupon is:

$22.65 + 3($33.31) = $122.58

With the 10% discount, the total cost becomes:

$122.58 - 0.1($122.58) = $110.32

To find out how much change the cashier gave back to Mary, we need to subtract the total cost from the amount of money Mary's mom gave her:

$100.00 - $110.32 = -$10.32

Since the result is negative, it means Mary did not have enough money to pay for her purchases and would have to give the cashier an additional $10.32 to cover the full cost of her shopping.

Therefore, the answer is that Mary did not receive any change from the cashier.

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Answer:

36 Units

Step-by-step explanation:

The circumference (C) of a circle is related to its diameter (d) by the formula:

C = πd

We can rearrange this formula to solve for the diameter:

d = C / π

In this case, the circumference of the circle is C = 113.04 units and π is approximately 3.14. Substituting these values into the formula, we get:

d = 113.04 units / 3.14

d ≈ 36 units (rounded to the nearest unit)

Therefore, the diameter of the circle is approximately 36 units.

Answer:36 units

Step-by-step explanation: