Explain if Todd’s Conclusion is logical.How did you decide? If it is not logical,what can you do to improve his reasoning?

The image point of (2, −6) after the transformation R270° is (4,3).

Given:

(2,-6) and  R270° and (1,2)

Let (x,y) be the point

First translation (1,2)

(x,y) → (x+1,y+2)

Translation of  R270° for translated coordinates

(x+1,y+2) → (-(y+2),x+1)

substitute (2,-6)

= (-(-6+2),2+1)

= (-(-4),3)

= (4,3)

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If a value of 80.4° is added to the data, the range does not change.

The range is 48.

If a value of 60° is added to the data, the median change.

The median was 79.5.

The change median is 77.

It is the average value of the set given.

It is calculated as:

Mean = Sum of all the values of the set given / Number of values in the set

We have,

58, 61, 71, 77, 91, 100, 105, 102, 95, 82, 66, 57

The range formula = Highest value - Lowest value

Now,

Highest value = 105

Lowest value = 57

Range = 105 - 57 = 48.

Now,

If the value of 80.4 is added the range remains the same because the range is dependent only on the value of the highest and the lowest value.

We have,

58, 61, 71, 77, 91, 100, 105, 102, 95, 82, 66, 57

The median is the mid value of the given set of data after arranging in ascending order.

Arranging the set in ascending order.

57, 58, 61, 66, 71, 77, 82, 91, 95, 100, 102, 105

There are 12 elements in the set.

Median = (77 + 82) / 2 = 79.5

If 60 is added we get 13 elements in the set.

The arrangement becomes,

57, 58, 60, 61, 66, 71, 77, 82, 91, 95, 100, 102, 105

Median = 77

Thus,

If a value of 80.4° is added to the data, the range does not change.

The range is 48.

If a value of 60° is added to the data, the median change.

The median was 79.5.

The change median is 77.

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Since the discriminant of the quadratic equation Δ is equals to 0, the given quadratic equation has one solution. Thus, the fourth option is correct.

We know that for a quadratic equation [tex]ax^{2} +bx+c =0[/tex], there exists a discriminant, Δ = [tex]b^{2}-4ac[/tex]. This discriminant gives us the nature of roots that a quadratic equation can have.

Here, we have the given quadratic equation as -

[tex]x^{2} -16x+64=0[/tex]

Comparing this to the general expression of a quadratic equation, we have

a = 1

b = -16

c = 64

So, now we have to find the discriminant of the given quadratic equation.

Δ = [tex]b^{2}-4ac[/tex]

[tex]= (-16)^{2} -4*1*64\\= 256-256 = 0[/tex]

We see that the discriminant, Δ = 0. This implies that the given quadratic equation has one solution. Thus, the fourth option is correct.

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x= 11.

[tex]\sqrt{2x+3}=5[/tex]

[tex]\sqrt{2x+3} ^{2} =5^{2} \\ \\2x+3=25[/tex]

[tex]2x+3-3=25-3\\ \\2x=22[/tex]

[tex]\frac{2x}{2} =\frac{22}{2} \\ \\x=11[/tex]

[tex]\sqrt{2(11)+3}=5\\ \\\sqrt{22+3}=5\\ \\\sqrt{25}=5\\ \\5=5.[/tex]

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The bank discount is $93.33 and the proceeds are $5,906.67.

What is the discount?

Discount causes the product's selling price to drop, which increases its allure for the consumer. A price reduction has a psychological effect on the buyer, influencing them to make the purchase. The two types of discounts offered are trade discounts and cash discounts.

We have,

Amount Due at Maturity = $6,000

Discount rate = 3.5%

Time = 160 days

Bank Discount = $6,000*3.5%*160/360=$93.33

Proceeds = Maturity value - Bank Discount

= $6,000 - $93.33

= $5,906.67

Therefore, the bank discount is $93.33 and the proceeds are $5,906.67.

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Answer:

m∠C = 50 degrees

Step-by-step explanation:

∠CAQ is a straight angle (180) so ∠CAB is supplementary to ∠QAB

∠CAQ = ∠QAB + ∠CAB

180 = 110 + ∠CAB

180 - 110 = ∠CAB

70 = ∠CAB

The total angle measurement in all triangles is 180 degrees, knowing this, we can set up the equation:

180 = ∠CBA + ∠BCA + ∠CAB

180 = 2 + 29x + 24x + 2 + 70

180 = 74 + 53x

180 - 74 = 53x

106 = 53x

2 = x

Knowing x = 2, we can solve for m∠C

24(2) + 2 = ∠C

48 + 2 = ∠C

50 = ∠C

The probability that the mean of the sample is between 120 and 126 gallons is 0.4176

The normal distribution describes a symmetrical plot of data around its mean value, where the width of the curve is defined by the standard deviation

Given: population mean (µ) = 123, standard deviation(σ) =21 and number of sample (n) = 15

Let X represent the gallons of water: We want to find:

P(120 ≤ X ≤ 126)

Z-score(Z) = (X-µ) / (σ/√n)

Z₁ = (120-123)/ (21/√15) = -0.55

Z₂ = 126-123/ (21/√15)= 0.55

P(-0.55≤ Z ≤ 0.55) = = 0.7088 - 0.2912 = 0.4176

(Check the image of the table attached)

Therefore, the probability that the mean of a randomly selected sample of 15 people will be between 120 and 126 gallons is 0.4176

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If you have a 2 foot piece of string and cut off and use a piece 4 3/4 inches long and a piece 2 3/8 inches long, Then 16.875 is the remaining string.

A fraction represents a part of a whole.

1 foot =12 inches

2 foot=24 inches.

Given,

if you have a 2 foot piece of string and cut off and use a piece 4 3/4 inches long and a piece 2 3/8 inches long.

Then  how much string do you still have

We have to subtract the used strings from 24 inches string.

4 3/4 inches=19/4

2 3/8 inches=19/8

Now we have to subtract 19/4 and 19/8 from 24 inches.

24-19/4-19/8

24-4.75-2.375

16.875

Hence 16.875 is the string left with us.

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The exact values of the trigonometric functions of the ordered pair are listed below:

In this problem we find an ordered pair in rectangular form (x, y) that the represents the terminal side of angle θ and from which we must determine the exact values of the sine, secant and cotangent. The definitions for each of the three functions are:

sin θ = y / √(x² + y²)

sec θ = √(x² + y²) / x

cot θ = x / y

If we know that x = 7 and y = - 4, then the exact values of the trigonometric functions are, respectively:

sin θ = (- 4) / √[7² + (- 4)²]

sin θ = - 4√65 / 65

sec θ = √[7² + (- 4)²] / 7

sec θ = √65 / 7

cot θ = 7 / (- 4)

cot θ = - 7 / 4

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The discriminant of the quadratic equation -2x²-5x+7=0 is 81 units when formula of discriminant is (b²-4ac).

Keeping in mind that a, b, and c are the coefficients of your quadratic in standard form, the discriminant is calculated using the formula b squared minus 4ac. It reveals how many possible answers there are to a quadratic equation. There are two solutions if the discriminant is greater than zero. The square root's argument (i.e., its contents), which is the expression b²-4ac, is known as the "discriminant" because using its value, you can "discriminate" between (i.e., be able to distinguish between) the different solution types.

Here,

-2x²-5x+7=0

discriminant=(b²-4ac)

=(-5)²-(4*-2*7)

=25+56

=81 units

When the discriminant formula is (b²-4ac), the discriminant of the quadratic equation (-2x²-5x+7=0) is 81 units.

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If a window in the model is 1.5 in. wide, then the actual window is  7.5 feet wide.

A two-term ratio expressed with a second term of one is referred to as a unit ratio. A unit ratio can be created from any ratio. Example. An illustration of a set of marbles is shown below. The set has eight blue marbles and two red marbles.

Having a denominator of 1, a unit rate is a ratio between two separate units. Divide the numerator by the denominator to obtain the unit rate. The unit rate is the decimal number that results. The price of a good or service is the numerator of a ratio called the unit price, and the quantity is the denominator.

Given,

The scale of the Model =5 in: 25 ft.

Dividing both sides by 5 we get,

[tex]\frac{5in}{5}[/tex] :[tex]\frac{25ft}{5}[/tex]

1 inch:5 feet

If a window on the model is 1.5 inch wide, then from the unit ratio we get,

1 inch × 1.5 : 5 feet × 1.5 feet

1.5 Inch : 7.5 feet

As a result, a window that is 1.5 inches wide in the model will actually be 7.5 feet wide.

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The formula to model the given situation is   13 + p = 21   .

In the question ,

it is given that ,

Alisha and Emily are making T- Shirts for the Math's team .

total number of T- Shirts required = 21 shirts .

number of shirts made by Alisha = 13 shirts

number of shirts made by Emily = p shirts

So , the equation that represents the given situation is

13 + p = 21

Solving further , we get

p = 21 - 13

p = 8

So , Emily made 8 T - Shirts .

Therefore , The formula to model the given situation is   13 + p = 21   .

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Answer: The equation that represents this situation is y = -15x + 135

A linear equation is given by:

y = mx + b;

where y, x are variables, m is the rate of change and b is the y intercept.

Let y represent the amount of boxes remaining after x days.

She starts with 135 boxes, hence b = 135. She sells at a constant rate of 15 boxes each day, hence m = -15. The equation becomes:

y = -15x + 135

The first point should be plotted at (9,0) then the next at (0,135). Just plot multiples of 15 on the chart until you get to the 9th multiple

Step-by-step explanation:

Answer:

answer in image

Step-by-step explanation:

The subtraction of matrices B and A cannot be computed, as the matrices have different dimensions, hence we cannot calculate the matrix B - A.

Matrices are subtracted subtracting the terms at the same position in each matrix.

Hence, two matrices can only be subtracted if they have the same dimensions.

Matrix A in this problem is defined as follows:

A = [-5 4]

      [-8 -2]

Hence it's dimensions are 2 x 2, as it has 2 rows and 2 columns.

Matrix B in this problem is defined as follows:

B = [-2 7 -3]

      [1 -6 0]

Hence it's dimensions are 2 x 3, as it has 2 rows and 3 columns.

The matrices A and B have different dimensions, a different number of columns in this case, and hence their subtraction cannot be computed.

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The time until the water is drained from the basement is 24.67 hours.

From the information, it was stated that the burst pipe fills a basement with 37 in. of water and a pump empties the water at a rate of 1.5 in./hr.

Also, the water level h, in inches, after t hours is represented by h = 37 - 1.5t. In this case, for the water to be drained, it'll be at zero. This will be illustrated as:

37 - 1.5t = 0

1.5t = -37

Divide.

t = 37 / 1.5

t = 24.67 hours.

The time is 24.67 hours.

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The numbers from least to greatest is arranged as 5 2/9 < 21/4 < 5.96 < 5.961

To solve this problem, we have to arrange the numbers in an ascending order from the least to the greatest. To do this, we can convert all numbers to whole numbers or fractions to decimal form to make it easier.

convert 5 2/9 to decimal = 5.222

convert 21/4 = 5.25

Let's arrange the number in ascending order

5.22 < 5. 25 < 5.96 < 5.961

The numbers can be arranged from least to greatest using a number line.

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Answer: x > -7, see attached

Step-by-step explanation:

    Given:

x + 6 > -1

   Subtract 6 from both sides of the equation:

x > -7

    Graph, see attached. We will graph x = -7, and shade to the right.

Answer:

Half as big as little drop?

Step-by-step explanation:

The complete statements for solving the equation in the steps are:

1. Distribute -2 to 5x and 8

2. Subtract both sides by 6x

3. Add both sides by 16

4. Divide both sides by -16

Solving an equation involves finding the value of the variable in the equation that would make the it true. This is done by isolating the variable to one side of the expression to determine its value.

Given the equation, -2(5x + 8) = 14 + 6x, the following steps are taken to find the value of x in the expression:

Step 1: Distribute -2 to 5x and 8

10x + 16 = 14 + 6x

Step 2: Subtract both sides by 6x

-16x + 16 = 14

Step 3: Add both sides by 16

-16x = 30

Step 4: Divide both sides by -16

x = 30/-16

Simplify

x = -15/8

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The value of  differential dy when x = 4 and dx = 0.2 is 0.68   .

In the question ,

it is given that ,

the equation is y = tan(3x + 8) ,

we need to find the differential dy , when x = 4 and dx = 0.2

So , differentiating  y = tan(3x + 8) with respect to "x" ,

we get

dy/dx = sec²(3x + 8) *3

dy/dx = 3*sec²(3x + 8)

Substituting the values of x = 4 and dx = 0.2 ,

we get ,

dy/(0.2) = 3*sec²(3(4) + 8)

dy/0.2 = 3*sec²(20)

dy/0.2 = 3*1.1324

dy/0.2 = 3.3972

dy = 0.2 * 3.3972

dy = 0.67944

dy ≈ 0.68

Therefore , The value of differential dy when x = 4 and dx = 0.2 is 0.68   .

The given question is incomplete , the complete question is

Let y = tan(3x + 8). Find the differential dy when x = 4 and dx = 0.2  ?

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Answer:

no solution

Step-by-step explanation:

The distributive property allows the expression 18 + 24 to be expressed as 6(3 + 4).

Most algebraic structures that include two operations, addition and multiplication, such as complex numbers, polynomials, matrices, rings, and fields, are defined in terms of this fundamental feature of numbers. The distributive property of binary operations generalizes the equality-proclaiming distributive law in mathematics. One of the axioms for rings and fields is that of the distributive laws. Boolean algebras like the algebra of sets or the switching algebra are examples of structures with two operations that are each distributive over the other.

We do the following to express using the distributive property:

Find the biggest common factor between the numbers 18 and 24.

18 = 1, 2, 3, 6, 9, 18

24 = 1, 2, 3, 4, 6, 8, 12, 24

6 is the most common value between the numbers 18 and 24, making it the most common factor

The values should be divided by 6 and expressed in the form a(b + c):

b = 18 /6 = 3

c = 24 / 6 = 4

6(3 + 4)

Consequently, the necessary expression is 6(3 + 4).

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if M > N then the inequality M/N > N/M will be always true

What is Linear Inequality?

The mathematical expression with unequal sides is known as an inequality in mathematics. Inequality is referred to in mathematics when a relationship results in a non-equal comparison between two expressions or two numbers. In this instance, any of the inequality symbols, such as greater than symbol (>), less than symbol (), greater than or equal to symbol (), less than or equal to symbol (), or not equal to symbol (), is used in place of the equal sign "=" in the expression. Polynomial inequality, rational inequality, and absolute value inequality are the various types of inequalities that can exist in mathematics.

The symbols "" and ">" signify tight inequalities, while "" and "" signify slack inequalities. A linear inequality looks precisely like a linear equation, but the symbol connecting two expressions is different.

As in the question M is always greater N

So, is M is divided by a number that is less than M the answer will always be greater than 1

but on the other hand, if N is divided by a number greater than N then the answer will always be less than 1

Therefore, M/N > N/M will always be True

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Answer: 15,070

Step-by-step explanation: subtraction 16200-1130=15,070

Starting with the provided assertions, a flow proof arranges statements in a logical order.

A mathematically formatted proof known as a "flow proof" uses logic to back up a truth assertion.

Thus, opening with the provided assertions, a flow proof arranges statements in a logical order. Arrows are being used to show the sequence of the assertions, and each assertion has its justification stated beneath it.

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The price of the pair of shoes in the department store is $7.

The wholesale price for a pair of shoes is $4.50. A certain department store marks up the wholesale price by 50%.

To find out the price of the pair of shoes in the department store:

The price of the pair of shoes in the department store: $7

Given the wholesale price of pair of shoes is $4.50

Department store of wholesale price is 50%

Than whole sale = 1.5 times the whole sale

Price in department store = 1.5*4.5

= $6.75

Rounded to the nearest cent = $7

Hence the answer is the price of the pair of shoes in the department store is $7.

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The value of one sixth times quantity x plus 24 end quantity equals negative 6 is -180.

Expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both. Addition, subtraction, multiplication, and division are all possible mathematical operations.

In this case, the expression given will be illustrated as:

1/6x + 24 = -6

Collect like terms

x / 6 = -6 - 24

x/6 = -30

Cross multiply

x = -30 × 6

x = -180

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Answer:

Answer: (D) x= 12

Step-by-step explanation:

First you would distribute 1/6 into everything. 1/6 is equal to .16, so you can do that if you would like. you would get .16x + 4

Next, divide .16 on both sides. It should look like this

.16x/.16 + 4/.16.

Your answer should be x+ 25 = -6, or x = 12.

I hope this helps, as I could be wrong. Good luck!

P.S. The guy above me just put the question into AI and just copy pasted it. Not worrying if it was right or not.

Answer:

I think the answer is 144

The value of w to the nearest whole number is 16°

If a polygon has equal sides and angles, it is said to be regular. As a result, an equilateral triangle is a regular triangle, and a square is a regular quadrilateral.

Given:

Decagon has 10 sides.

As, sum of interior angles of a polygon = ( n - 2) x 180

where n = number of sides of polygon

Here n = 10

sum of interior angle = ( 10 - 2) x 180 which is 1440°

If a regular polygon has equal angles and each angle is (8w + 17)

10( 8w + 17) = 1440

8w + 17 = 144

8w = 144 - 17

8w = 127

w = 127/8

w = 15.875

Thus, the value of w = 16°

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