Graph the image of W(10,1) after a rotation 90° counterclockwise around the origin.

Answer:

5xy = - 13645

Step-by-step explanation:

Note that

(x - y)² = x² + y² - 2xy

Given

2x² + 2y² = 36 ( divide through by 2 )

x² + y² = 18

Then

(x- y)² = 74² = 5746 ← expand left side

x² + y² - 2xy = 5746 ← substitute x² + y² = 18

18 - 2xy = 5746 ( subtract 18 from both sides )

- 2xy = 5458 ( divide both sides by - 2 )

xy = - 2729

Thus

5xy = 5 × - 2729 = - 13645

Step-by-step explanation:

y = 5^x -9

5^x = y + 9

x = ^5 log (y+9)

f~'(x) = ^5 log (x+9)

To answer the research question, "Is there a relationship between the number of sodas consumed each year and the number of cavities formed?" a correlation analysis would be appropriate.

This type of statistical analysis examines the relationship between two variables to determine if there is a linear association between them.

In this case, the two variables are the number of sodas consumed each year and the number of cavities formed.

Correlation analysis measures the strength and direction of the relationship between two variables. The strength of the relationship is determined by the correlation coefficient, which ranges from -1 to +1.

A correlation coefficient of -1 indicates a perfect negative relationship, while a correlation coefficient of +1 indicates a perfect positive relationship. A correlation coefficient of 0 indicates no relationship between the two variables.

In this case, if the correlation coefficient is positive, it would indicate that there is a positive relationship between the number of sodas consumed each year and the number of cavities formed. This means that as the number of sodas consumed increases, the number of cavities formed also increases.

On the other hand, if the correlation coefficient is negative, it would indicate a negative relationship between the two variables, meaning that as the number of sodas consumed increases, the number of cavities formed decreases.

In conclusion, to determine if there is a relationship between the number of sodas consumed each year and the number of cavities formed, a correlation analysis would be appropriate.

This type of analysis would measure the strength and direction of the relationship between the two variables, providing valuable insights into the impact of soda consumption on dental health.

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Answer: C

Step-by-step explanation:

The Wilsons' monthly mortgage payment will be approximately $9,485.16.

To calculate the monthly payments for the Wilsons' mortgage, we need to follow these steps:

Convert the annual interest rate to a monthly interest rate using the formula APR(P) = P + 0.02.

Plug the monthly interest rate into the formula m(r) = 128,000 * (r / (1 - (1 + r)⁽⁻³⁶⁰⁾)).

Let's perform the calculations:

Step 1: Convert the annual interest rate to a monthly interest rate

Let's assume the prime interest rate (P) published by the Federal Reserve is 4.5% (0.045 as a decimal).

APR(P) = P + 0.02

APR(0.045) = 0.045 + 0.02

APR(0.045) = 0.065 (monthly interest rate as a decimal)

Step 2: Calculate the monthly payments (m(r)) for a loan of $128,000 with the monthly interest rate (r) obtained from Step 1.

m(r) = 128,000 * (r / (1 - (1 + r)⁽⁻³⁶⁰⁾))

m(0.065) = 128,000 * (0.065 / (1 - (1 + 0.065)⁽⁻³⁶⁰⁾))

Now, let's calculate the monthly payments (m(r)):

m(0.065) = 128,000 * (0.065 / (1 - (1 + 0.065)⁽⁻³⁶⁰⁾))

m(0.065) = 128,000 * (0.065 / (1 - (1.065)⁽⁻³⁶⁰⁾))

m(0.065) = 128,000 * (0.065 / (1 - 0.124823)) (Approximately, (1.065)⁽⁻³⁶⁰⁾ ≈ 0.124823)

m(0.065) = 128,000 * (0.065 / 0.875177)

m(0.065) = 128,000 * 0.074285 (Approximately, 0.065 / 0.875177 ≈ 0.074285)

m(0.065) = 9,485.16

The Wilsons' monthly mortgage payment will be approximately $9,485.16.

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For the inference in part b to be valid, the conditions required are reasonable satisfaction.

To determine if the conditions for the inference in part b are reasonably satisfied, we need to consider the specific details of the inference.

However, in general, the conditions for a valid inference typically include logical reasoning, accurate data, reliable sources, and relevant contextual information.

These conditions ensure that the conclusion drawn from the inference is supported by evidence and does not contain logical fallacies or biases. It is important to evaluate the quality and reliability of the information used in the inference to determine if the conditions are reasonably satisfied.

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To calculate how much Brianne needs to save each month, we'll subtract her current savings and her monthly income from her total expenses.

1. Total expenses:

  - Airfare: $1500

  - Backpack: $150

  - Spending money: $1000

  Total expenses: $1500 + $150 + $1000 = $2650

2. Current savings: $40

3. Monthly income:

  - Job at Porto's: $50/week * 4 weeks = $200/month

  - Extra chores: $1200/month

  Total monthly income: $200 + $1200 = $1400

4. Amount needed to save each month:

  Total expenses - Current savings - Monthly income = $2650 - $40 - $1400 = $1210

Therefore, Brianne needs to save $1210 each month to reach her total expenses for the European trip leaving in 5 months.

If she wanted to leave in 3 months instead, she would have less time to save. In that case, the calculation would be as follows:

1. Total expenses: $2650

2. Current savings: $40

3. Monthly income: $1400

4. Number of months: 3

5. Amount needed to save each month:

  (Total expenses - Current savings) / Number of months

  = ($2650 - $40) / 3

  ≈ $870 / 3

  ≈ $290

Therefore, if Brianne wanted to leave in 3 months, she would need to save approximately $290 each month to reach her total expenses for the European trip.

Answer:

£ 210  &  £ 270

Step-by-step explanation:

Amount =  £480

Ratio = 7 : 9

Total parts = 7+9 = 16

\(\dfrac{7}{16}*480=7 * 30\) =  £ 210

\(\dfrac{9}{16}*480=9*30= 270\)

Answer: First option

Step-by-step explanation:

Answer:

The correct answer is A. 8 feet by 4 feet by 3 feet & E. 3 feet by 5 feet by 7 feet

Step-by-step explanation:

Hope this helps! Have a great rest of your day/night! :)))

Answer:

A=h(b)b/2

Step-by-step explanation:

Answer:

Q5) 6.5833 (rounded to nearest 4 d.p.)

Q6) \(\frac{3}{10}\)

Step-by-step explanation:

Q5) \(\sqrt{2.38 + 6.4^{2} }\) = \(\sqrt{2.38 + 40.96}\)

                           = \(\sqrt{43.34}\)

                           ≈ 6.5833 (rounded to nearest 4 d.p.)

Q6) When working with mixed numbers, I would change them to improper fractions first for easier calculations.

1\(\frac{3}{4}\) × \(\frac{6}{35}\) = \(\frac{7}{4}\) × \(\frac{6}{35}\)

          = \(\frac{42}{140}\) (Simplify by dividing by 2)

          = \(\frac{21}{70}\) (Simplify by dividing by 7)

          = \(\frac{3}{10}\)

The correct statement is: b. The uncertainty will be larger in Study 1 than in Study 2.

This is because Study 2 used a larger random sample (100 cigarettes) compared to Study 1 (10 cigarettes), resulting in a more accurate estimate of the mean nicotine content and reduced uncertainty.

The uncertainty will be larger in study 1 than in study 2. This is because the sample size in study 1 is smaller than in study 2, which means there is more variability in the estimates due to the smaller sample size. In general, larger sample sizes lead to more precise estimates with less uncertainty.

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Answer:

i am not sure but i think it is 280

Answer: for the first one i would think $6,200 and the second $450

Step-by-step explanation:

i did 12x350=4,200+the deposit(2,000).

on the second one i did 8000-2600=5400   5400/12=$450

The meaning of the slope of the linear model is,

A.) There are 30 additional grams of sugar for every additional calorie in a menu item.

We have,

Katie uses the equation y= 30x + 70 to model the data.

Here, In graph,

x - axis represent sugar in grams and y - axis represent calories.

Here, The equation is,

y = 30x + 70

Slope = 30

Which represent 30 additional grams of sugar for every additional calorie in a menu item.

Therefore, The meaning of the slope of the linear model is,

A.) There are 30 additional grams of sugar for every additional calorie in a menu item.

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Answer:

The height of the square pyramid is 9.8 in.

Step-by-step explanation:

Given;

area of the square pyramid, A = 96 in²

base length, a = 4 in

height of the pyramid, h = x in

The surface area of the pyramid is calculated as follows;

\(SA = a^2 + 2a \sqrt{\frac{a^2}{4} + h^2} \\\\96 = 4^2 + 2(4)\sqrt{\frac{4^2}{4}+ x^2} \\\\96 = 16 + 8\sqrt{4+ x^2} \\\\96-16 = 8\sqrt{4+ x^2}\\\\80 = 8\sqrt{4+ x^2}\\\\\frac{80}{8} = \sqrt{4+ x^2}\\\\10 =\sqrt{4+ x^2}\\\\ (10)^2 = 4+ x^2\\\\100 = 4 + x^2\\\\ x^2 = 100-4\\\\x^2 = 96\\\\x = \sqrt{96} \\\\x = 9.80 \ in\)

Therefore, the height of the square pyramid is 9.8 in.

The probability of selecting two purple shirts then a blue shirt is  28/323

Given, there are 12 blue shirts and 7 purple shirts in a drawer.

three shirts are randomly selected without replacement.

the probability of selecting two purple shirts then a blue shirt is,

(C(7 , 2) × C(12 , 1))/C(19 , 3) = ((7×6)/2 × 12)/(19×18×17)/6

= (7×6×6)/(19×3×17)

= 84/969

= 28/323

Hence, the probability of selecting two purple shirts then a blue shirt is  28/323

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Answer:

69.9°

Step-by-step explanation:

sin28/11 = sinx/22

22(sin28) = 11(sinx)

sinx = 22(sin28) / 11 = 0.9389

x = sin⁻¹(0.9389) = 69.9°

Compound interest is a very powerful way to save for your retirement. Saving a little and giving it time to grow is often more effective than saving a lot over a short period of time. To illustrate this, suppose your goal is to save 1 million by the age of 65.

This can be accomplished by socking away 5,010 per year starting at age 25 with a 7% annual interest rate. This goal can also be achieved by saving 24,393 per year starting at age 45.Let's check whether both of the saving plans will amount to 1 million by the age of 65. According to the first plan, you would invest 5,010 per year for 40 years (65 – 25) with a 7% annual interest rate, so that by the time you’re 65, you will have accumulated:

\(5,010 * ((1 + 0.07) ^ 40 - 1) / 0.07 = 1,006,299.17\)

Therefore, saving 5,010 per year starting at age 25 with a 7% annual interest rate would result in 1 million savings by the age of 65. According to the second plan, you would invest 24,393 per year for 20 years (65 – 45) with a 7% annual interest rate, so that by the time you’re 65, you will have accumulated:

\(24,393 * ((1 + 0.07) ^ 20 - 1) / 0.07 = 1,001,543.68\)

Therefore, saving 24,393 per year starting at age 45 with a 7% annual interest rate would also result in 1 million savings by the age of 65. Thus, it is shown that both of the plans will amount to 1 million by the age of 65.

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Answer:

v = b/0.75 - 0.95s/0.75

Or

v = (b - 0.95s) / 0.75

Step-by-step explanation:

Solve 0.75v + 0.95s = b for v

This means making v the subject of the formula

0.75v + 0.95s = b

Subtract 0.95s from both sides

0.75v + 0.95s - 0.95s = b - 0.95s

0.75v = b - 0.95s

Divide both sides by 0.75

v = (b - 0.95s) / 0.75

v = b/0.75 - 0.95s/0.75

The equation will be useful in determining the number of vegetarian

Answer:

Step-by-step explanation:

To find the missing side lengths in the given right triangles, use trigonometric ratios.

\(\boxed{\begin{minipage}{9.4 cm}\underline{Trigonometric ratios} \\\\$\sf \sin(\theta)=\dfrac{O}{H}\quad\cos(\theta)=\dfrac{A}{H}\quad\tan(\theta)=\dfrac{O}{A}$\\\\where:\\ \phantom{ww}$\bullet$ $\theta$ is the angle. \\ \phantom{ww}$\bullet$ $\sf O$ is the side opposite the angle. \\\phantom{ww}$\bullet$ $\sf A$ is the side adjacent the angle. \\\phantom{ww}$\bullet$ $\sf H$ is the hypotenuse (the side opposite the right angle). \\\end{minipage}}\)

From inspection of the first triangle ABC, we have been given the angle, the side opposite the angle and the side adjacent the angle.

Therefore, to calculate the length of the adjacent side, x, substitute the values into the tangent ratio:

\(\implies \tan 18^{\circ}=\dfrac{15}{x}\)

\(\implies x\tan 18^{\circ}=15\)

\(\implies x=\dfrac{15}{\tan 18^{\circ}}\)

\(\implies x=46.165253...\)

\(\implies x=46.2\;\;\sf(nearest\;tenth)\)

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

Triangle LMN is a right triangle. Interior angles of a triangle sum to 180°.

Therefore, as m∠M = 50° and m∠MLN = 90°, then m∠MNL = 40°.

As KN is perpendicular to NM and m∠MNL = 40° then m∠KNL = 50°.

As KL is parallel to NM, then m∠K = 90°.  Therefore, m∠KLN = 40°.

(Refer to the attached diagram).

For right triangle LMN, we have been given the angle (∠M) and the side adjacent to the angle (LM). To find an expression for the length of the side opposite the angle (LN), use the tangent ratio:

\(\implies \tan 50^{\circ}=\dfrac{LN}{45}\)

\(\implies LN=45\tan 50^{\circ}\)

LN is the hypotenuse of right triangle KLN.

If we use ∠KNL as θ, then side KN is adjacent to the angle.

Therefore, to find the KN use the cosine ratio:

\(\implies \cos 50^{\circ}=\dfrac{KN}{LN}\)

\(\implies \cos 50^{\circ}=\dfrac{KN}{45\tan 50^{\circ}}\)

\(\implies KN=45\tan 50^{\circ}\cos 50^{\circ}\)

\(\implies KN=34.471999...\)

\(\implies KN=34.5\;\; \sf (nearest\;tenth)\)

As KL is the side opposite ∠KNL, to find KL use the sine ratio:

\(\implies \sin 50^{\circ}=\dfrac{KL}{LN}\)

\(\implies \sin50^{\circ}=\dfrac{KL}{45\tan 50^{\circ}}\)

\(\implies KL=45\tan 50^{\circ}\sin50^{\circ}\)

\(\implies KL=41.0821297...\)

\(\implies KL=41.1\;\;\sf (nearest\;tenth)\)

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

From inspection of the second triangle ABC, we have been given the angle, the side adjacent the angle and the hypotenuse.

Therefore, to calculate the length of the adjacent side, x, substitute the values into the cosine ratio:

\(\implies \cos 70^{\circ}=\dfrac{x}{46}\)

\(\implies x=46\cos 70^{\circ}\)

\(\implies x=15.732926...\)

\(\implies x=15.7\;\;\sf(nearest\;tenth)\)

There are 720 different completed answer sheets possible, where no blanks are allowed.

In this problem, we have 6 questions and 6 different answers to match with each question. We need to determine how many different completed answer sheets are possible, where no blanks are allowed. To solve this, we'll use combinatorics and permutations.

To find the number of different completed answer sheets, we can consider each question as a distinct entity. Let's label the questions as Q1, Q2, Q3, Q4, Q5, and Q6. Similarly, let's label the answers as A1, A2, A3, A4, A5, and A6.

Since each question needs to be matched with a different answer, we can think of this as a one-to-one mapping between the questions and answers. In other words, we want to find the number of permutations of the answers that satisfy the matching condition.

The first question (Q1) can be matched with any of the 6 answers (A1, A2, A3, A4, A5, or A6). Once Q1 is matched, the second question (Q2) can be matched with any of the remaining 5 answers. Similarly, the third question (Q3) can be matched with any of the remaining 4 answers, and so on.

Using the fundamental principle of counting, we can multiply the number of choices available for each question.

The number of possible completed answer sheets is given by:

Number of completed answer sheets = 6 * 5 * 4 * 3 * 2 * 1 = 720.

So, there are 720 different completed answer sheets possible, where no blanks are allowed.

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Mate's car can travel approximately 5 more minutes per gallon of gas compared to Jenna's car.

To determine how many more minutes Mate's car can travel per gallon of gas compared to Jenna's car, we would need additional information about the fuel efficiency or miles per gallon (MPG) for each car.

Fuel efficiency is typically measured in terms of miles per gallon, indicating the number of miles a car can travel on a gallon of gas.

To calculate the difference in travel time, we would also need to know the average speed at which the cars are traveling.

Once we have the MPG values for Mate's car and Jenna's car, we can calculate the difference in travel time per gallon of gas by considering their respective fuel efficiencies and average speeds.

If Mate's car has a fuel efficiency of 30 MPG and Jenna's car has a fuel efficiency of 25 MPG, we can calculate the difference in travel time by comparing the distances they can travel on a gallon of gas.

Let's assume both cars are traveling at an average speed of 60 miles per hour.

For Mate's car:

Travel time = Distance / Speed

= (30 miles / 1 gallon) / 60 miles per hour

= 0.5 hours or 30 minutes.

For Jenna's car:

Travel time = Distance / Speed

= (25 miles / 1 gallon) / 60 miles per hour

= 0.4167 hours or approximately 25 minutes.

Without specific information about the MPG values and average speeds of the cars, it is not possible to provide an accurate answer regarding the difference in travel time per gallon of gas between Mate's car and Jenna's car.

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\({ \qquad\qquad\huge\underline{{\sf Answer}}} \)

In the first sequence,

let's take ratio of the next term with its preceding term, so we will get the common ratio ~

\(\qquad \sf  \dashrightarrow \: \cfrac{4}{16} = \dfrac{1}{4} \)

So, we can imply that The next term of the sequence is 1/4 times the previous term.

hence, the unknown term will be 1/4 times of previous term.

Therefore, the next term here is 1

In the second sequence,

Do the same procedure as above, we will get common ratio as :

\(\qquad \sf  \dashrightarrow \: \cfrac{18}{6} = 3\)

So, the next term is 3 times the preceding term, that is :

Therefore, the next term is 162

Answer:

\(m = \frac{17 - 7}{ - 15 + 16} = 10 \\ \\ m = \frac{6 - 15}{ - 11 + 11} = \frac{ - 9}{0} = und\)

The equation can be solved as below

What is an equation?

A mathematical equation is a formula that uses the equals sign to represent the equality of two expressions. The definitions of the word equation and its cognates in various languages might vary slightly. For instance, in French, an equation is defined as having one or more variables, but in English, an equation is any well-formed formula that consists of two expressions linked by the equals sign. Finding the values of the variables that result in the equality is the first step in solving an equation with variables. The unknown variables are also known as the variables for which the equation must be solved, and the unknown variable values that fulfill the equality are known as the equation's solutions. Equations come in two varieties: identities and conditional equations.

The equation can be solved as

x² + 16x + c = 0

or, c = - x² - 16x

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Answer:

c

Step-by-step explanation:

1/3 is actually the ratio between 1 and 3. So "ratio" is kind of equivalent to "divide by", which is why all fractions (of whole numbers) are rational numbers.

Answer:

120

Step-by-step explanation:

The options are:

flake view, screened-in balcony, upgraded landscaping, pool - 5 in total

Using the fundamental counting principle formula - n! where n is the number of elements = 5, we have

n! =5! = 5x 4 x 3 x 2 x 1 = 120.

There are 120 120 options for purchasing a house in the community.

Answer:

1/4

Explanation: 0.25 multiplied by 4 is 1. This shows that 0.25 is 1/4 of 1

Answer:

f(-3) = g(-3)

Step-by-step explanation:

Let's look at each option to which one is true with regard to the given functions on the graph.

The option that is correct is the option that shows where the graph of f(x) and g(x) intercepts or cut across each other.

Now, take a look at the graph, the line of both functions intercepts at x = -3. At this point, the value of f(-3) and g(-3) is equal to -4.

Therefore: f(-3) = g(-3)