The price of a pencil is 1½. What is the cost of 10 such pencils? What about 20 such
pencils? Is the price directly proportional to the number of pencils?

The linear equation on the graph can be written as:

y = (3/4)*x - 1

Here we have the graph of a linear equation, these are written as:

y = mx + c

Where m is the slope and c is the y-intercept.

On the graph we can see that the line intercepts the y-axis at y = -1, then we can write:

c = -1

So the linear equation is:

y = mx - 1

Looking at the graph we can see that the line also passes through the point (4, 2).

Replacing that in the linear equation we will get:

2 = m*4 - 1

2 + 1 = m*4

3 = m*4

3/4 = m

Then the linear equation on the graph is:

y = (3/4)*x - 1

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The sum of the series is approximately -2.977069 x 10³⁷.

The sum of the series is calculated by applying the following methods as shown below.

We can write the sum as:

∑k=252(3)k = 3^252 + 3^253 + 3^254 + ...

Notice that this is an infinite geometric series with first term a = 3^252 and common ratio r = 3.

To find the sum of an infinite geometric series, we use the formula:

S = a/(1-r)

Applying this formula, we get:

S = 3^252/(1-3) = 3^252/(-2)

So the sum of the series is -0.5 times 3 raised to the power of 252, which is a very large negative number.

Specifically, it is approximately equal to: -2.977069 x 10³⁷.

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Answer:

Blaise Pascal is known for inventing the mechanical calculator, also called Pascaline, in 1642. The Pascaline was a type of mechanical calculator that could perform addition and subtraction by using a series of gears and wheels. It was one of the first machines capable of performing arithmetic operations automatically and quickly, without the need for manual calculations. The invention of the Pascaline was a significant contribution to the field of mathematics and engineering, and it paved the way for the development of more advanced calculating machines in the future.

Step-by-step explanation:

H o: [tex]\mu_{post[/tex] - [tex]\mu_{pre[/tex] = 0 This is the null hypothesis, which states that there is no difference in the mean depression symptoms before and after therapy.

A hypothesis is a proposed explanation for a phenomenon. It is a testable statement about the relationship between two or more variables that can be used to generate further investigation and research. Hypotheses are developed from research questions and provide a basis for predicting outcomes and testing theories. Hypotheses are not guesses or hunches; rather, they are educated statements that are backed up by evidence.

Ha: [tex]\mu_{post[/tex] - [tex]\mu_{pre[/tex] ≠ 0 This is the alternative hypothesis, which states that there is a difference in the mean depression symptoms before and after therapy.

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Answer:

We can use the simple interest formula to find the rate of interest that the town savings bank pays:

Simple Interest = Principal x Rate x Time

where Principal is the initial deposit, Rate is the interest rate, and Time is the time period.

We know that the Principal is $5000, the Simple Interest earned over the first 10 years is $2950, and the Time is 10 years. Substituting these values into the formula, we get:

$2950 = $5000 x Rate x 10

Simplifying the equation, we get:

Rate = $2950 / ($5000 x 10)

Rate = 0.059 or 5.9%

Therefore, the town savings bank pays an interest rate of 5.9% on its savings accounts.

Given:-

Solution:-

p³+10+m-m

put the value of p nd m in eqⁿ :

━━━━━━━━━━━

hope it helps⸙

The value of expression at m = 8 and p = 3 is,

⇒ 37

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;

The expression is,

⇒ p³ + 10 + m - m

Now,

Put m = 8 and p = 3 in above expression, we get;

⇒ p³ + 10 + m - m

⇒ 3³ + 10 + 8 - 8

⇒ 27 + 10

⇒ 37

Thus, The value of expression at m = 8 and p = 3 is,

⇒ 37

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The sigma notations when evaluated are Σ(3X - 1) = 33 and Σ(2X)² = 248

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

3, 7, 2

The notation Σ(3X - 1) can be represented as

Σ(3X - 1) = (3(3) - 1) + (3(7) - 1) + (3(2) - 1)

Evaluate

Σ(3X - 1) = 33

Using the above as a guide, we have the following operation

Σ(2X)² = (2 *(3))² + (2 * (7))² + (2 * (2))²

Evaluate

Σ(2X)² = 248

Hence, the value of Σ(2X)² is 248

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The percentage decrease in total principal and interest paid between a 30-year term mortgage and a 15-year mortgage with an APR of 6.5% and a principal balance of $242,300.00 is about 31.1%

An APR is an acronym for the Annual Percentage Rate, which is the interest on al loan amount expressed as a percentage of the amount on loan annually.

The loan amount, the annual percentage rate, and the term of the loan are presented as follows;

Loan amount, P = $242,300.00

Term of the loan, t = 30 years and 15 years

Annual Percentage Rate (APR), r = 6.5%

The amount of the loan after the period can be obtained by using the formula;

A = P·(1 + r)^t

The amount of each loan can therefore be calculated as follows;

The monthly payment is; M = P·(r·(1 + r)^t)/((1 + r)^t - 1)

M = 242,300×((0.065/12) × (1 + (0.065/12))^(30×12))/((1 + ((0.065/12)))^(30×12) - 1) ≈ 1531.5

The total payment on the 30-year loan ≈ 360 × 1531.5 = 551,340

The monthly payment for the 15-year loan is therefore;

M = 242,300×((0.065/12) × (1 + (0.065/12))^(15×12))/((1 + ((0.065/12)))^(15×12) - 1) ≈ 2110.7

The total payment on the 15-year loan ≈ 360 × 2110.7 = 379962

551,340

The percentage change is therefore;

((551,340 - 379962)/551,340) × 100 ≈ 31.1%

The percentage decrease in the total principal and interest paid between the 30-year term mortgage and a 15-year mortgage is about 31.1%

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The height of the tower (h) is approximately 186.4 feet.

A ratio is simply the relation between two amounts showing how many times a value is contained within another value.

Given the data in the quesion;

We can set up a proportion to solve for the height of the tower:

Aidan's height / length of Aidan's shadow = height of the tower / length of the tower's shadow

Plugging in the values we know, we get:

5.5 / 9 = h / 305

To solve for h, we can cross-multiply and simplify:

9h = 5.5 × 305

9h = 1667.5

h = 1667.5 / 9

h = 186.4 ft

Therefore, the value of h is 186.4 feet.

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Answer:

Step-by-step explanation:

324-68=256

256-60=196

196-52=144

144-44=100

Yep...you were correct!

Answer:

a. aₙ=(aₙ₋₁ x 0.98) + 1150

After answering the presented question, we can conclude that The answer for the following expression will be as follows  [tex]4.4 X 10^3 = 4400[/tex]

In mathematics, you can double, divide, add, or subtract something. The following is an expression: Expression, numerical value, and math operator A mathematical expression is made up of numbers, parameters, and functions. Opposing sentences and expressions are possible. An expression, often known as an algebraic expression, is any mathematical statement that contains variables, numbers, and a mathematical action between them. For example, the phrase 4m + 5 is made up of the phrases 4m and 5, as well as the variable m from the above equation, which are all separated by the mathematical sign +.

The answer for the following expression will be as follows

[tex]4.4 X 10^3 = 4400[/tex]

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Answer:

72 cm^2

Step-by-step explanation:

2(3 x 2) + 2(6 x 3) + 2(6 x 2) = 2(6) + 2(18) + 2(12)

= 12 + 36 + 24 = 72 cm^2

The area of the shaded region of the composite shape is: 21.03  cm²

The formula for the area of a triangle is:

Area = ¹/₂ * base * height

Thus:

Area of given triangle = ¹/₂ * 14 * 14 = 98 cm²

Area of sector is given by the formula:

θ/360 * πr²

Area of sector = 45/360 * π * 14 * 14

= 76.97 cm²

Thus:

Area of shaded portion = 98 cm² - 76.97 cm² = 21.03  cm²

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The length of line JC is 20 miles.

What is Pythagorean theorem?

The Pythagorean theorem is a fundamental concept in geometry that states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of sides of triangle.

To find the length of line JC, which is the hypotenuse of the right triangle JSC, we can use the Pythagorean theorem, which states that in a right triangle, the sum of the squares of the two shorter sides (the legs) is equal to the square of the length of the longest side (the hypotenuse).

In this case, we have:

JS² + SC² = JC²

Substituting the given values, we get:

12² + 16² = JC²

144 + 256 = JC²

400 = JC²

Taking square root both sides, we get:

JC = √400

JC = 20

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Answer:

The value of sin^-1(-3√2) is an angle whose sine is -3√2.

Since the sine function is an odd function, sin(-θ) = -sin(θ), we can find the reference angle by taking the inverse sine of the positive value 3√2, which gives:

sin^-1(3√2) ≈ 80.06°

The sine function is also negative in the third and fourth quadrants of the unit circle. Since the given value is negative, the angle must lie in either the third or fourth quadrant.

To determine in which quadrant the angle lies, we can use the fact that sine is negative in the third and fourth quadrants. Since sin^-1(-3√2) gives a positive value, the angle must lie in the third quadrant where the sine is negative.

Therefore, sin^-1(-3√2) = -80.06° (rounded to two decimal places).

Step-by-step explanation:

Answer:

a)  Area of inner square = 58 cm²

b)  Area of inner square = (2x² - 2xy + y²) cm²

Step-by-step explanation:

To calculate the area of a square, multiply the length of one of its sides by itself. This can be expressed as A = s², where A is the area and s is the side length of the square.

To calculate the area of a triangle, halve the product of its base and height. This can be expressed as A = (1/2)bh, where A is the area, b is the base and h is the height of the triangle.

The easiest way to calculate the area of the inner square is to subtract the areas of the 4 congruent triangles from the area of the outer square.

[tex]\hrulefill[/tex]

The outer square has a side length of 10 cm. Therefore its area is:

[tex]\implies \sf A_{outer\;square} = 10^2 = 100 \; cm^2[/tex]

Each corner triangle has a height of 3 cm and a length of (10 - 3) cm.

Therefore, the area of one triangle is:

[tex]\implies \sf A_{triangle}=\dfrac{1}{2} \cdot 7 \cdot 3=10.5\;cm^2[/tex]

Therefore, the area of the inner square is:

[tex]\begin{aligned} \implies \sf Area\;of\;inner\;square&=\sf 100-(4 \cdot 10.5)\\&=\sf 100-42\\&=\sf 58\; cm^2\end{aligned}[/tex]

[tex]\hrulefill[/tex]

The outer square has a side length of y cm. Therefore its area is:

[tex]\implies \textsf{A$_{\sf outer\;square}$} = y^2 \; \sf cm^2[/tex]

Each corner triangle has a height of x cm and a length of (y - x) cm.

Therefore, the area of one triangle is:

[tex]\begin{aligned}\implies \sf A_{triangle}&=\dfrac{1}{2} \cdot (y-x) \cdot x\\\\&=\dfrac{1}{2}x(y-x)\;\sf cm^2\end{aligned}[/tex]

Therefore, the area of the inner square is:

[tex]\begin{aligned} \implies \sf Area\;of\;inner\;square&=y^2-4\left(\dfrac{1}{2}x(y-x)\right)\\\\&=y^2-2x(y-x)\\\\&=y^2-2xy+2x^2\\\\&=(2x^2-2xy+y^2)\; \sf cm^2\end{aligned}[/tex]

Answer:

y=2 x=-13

Step-by-step explanation:

Answer:

Step-by-step explanation:

Me personally, I think buffets are the best because you can take as music food as you much, without being charged for much! But thats only for some buffets. If you go to a chinese buffet, they might lower the price allowing you to get as much food as you please!

Answer:

[tex]\huge\boxed{\sf x = -2}[/tex]

Step-by-step explanation:

2(3x - 3) = -18

6x - 6 = -18

6x = -18 + 6

6x = -12

x = -12/6

[tex]\rule[225]{225}{2}[/tex]

Answer: x=-2

Step-by-step explanation:

Step 1. Multiply the 2×3x and 2×3 which would make the problem 6x-6=-18

Step 2. Add the -6 to the -18 and multiply that answer of -12 by 6 to get your final answer of x=-2

The slope of the function is -29 and the y-intercept is the point (0, 2).

What is function ?

In mathematics, a function is a relation between a set of inputs and a set of possible outputs with the property that each input is related to exactly one output. It is a rule that assigns to each element of a set (called the domain) exactly one element of another set (called the range).

To find the slope and y-intercept of the function p(x) = 2 - 29x, we can write it in the slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept.

So, by comparing p(x) = 2 - 29x with y = mx + b, we can see that:

m = -29 (the coefficient of x)

b = 2 (the constant term)

Therefore, the slope of the function is -29 and the y-intercept is the point (0, 2).

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Answer:

The probability that a randomly selected member of the labor force is Asian given that he or she is unemployed is 4.98%

Step-by-step explanation:

We want to find the probability that a randomly selected member of the labor force is Asian given that he or she is unemployed, which can be written as P(A|U). Using Bayes' theorem, we have:

P(A|U) = P(U|A) * P(A) / P(U)

We are given P(A) = 0.06 (6% of the labor force is Asian), P(U|A) = 0.05 (among Asians in the labor force, 5% are unemployed), and P(U|not A) = 0.06 (among non-Asians in the labor force, 6% are unemployed).

To find P(U), we can use the law of total probability:

P(U) = P(U|A) * P(A) + P(U|not A) * P(not A)

We know P(A) = 0.06, so P(not A) = 1 - P(A) = 0.94.

Therefore,

P(U) = 0.05 * 0.06 + 0.06 * 0.94 = 0.0602

Now we can substitute all the values into Bayes' theorem:

P(A|U) = 0.05 * 0.06 / 0.0602 = 0.0498

So the probability that a randomly selected member of the labor force is Asian given that he or she is unemployed is 4.98% (rounded to the nearest percentage with no decimal places).

The height of the trapezoid with an area of 21 square centimeters is equal to 3 cm.

area of a trapezoid is calculated using the formula: 1/2 × (A + B) × height where A is and B are the parallel bases.

we shall represent the height of the trapezoid with the letter h so that:

21 cm² = 1/2 × (5 + 9) cm × h

21 cm² = 1/2 × 14 cm × h

21 cm² = 7 cm × h

divide through by 7 cm

h = 21 cm²/7 cm

h = 3 cm

Therefore, the height of the trapezoid with an area of 21 square centimeters is equal to 3 cm.

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The set representing the domain of the relation is given as follows:

{-4,-2,0,3,5}.

For the relation in this problem, the x-coordinates of each point are given as follows:

Hence the set representing the domain of the relation is given as follows:

{-4,-2,0,3,5}.

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Answer: I took the test and got it right

Tthe matrix representing this system of equations is:

[6 11 | -4]

[5 -9 | 1]

The equations in the image can be expressed as a matrix as follows:

[6 11] [x] [-4]

[5 -9] * [y] = [1]

The constants on the right-hand side of each equation are represented by the matrix on the right, while the coefficients of the variables x and y are represented by the matrix on the left. We use square brackets to surround the coefficients matrix and vertical bars to demarcate the variables and constants in order to represent this in matrix form. As a result, the matrix used to describe this set of equations is:

[6 11 | -4]

[5 -9 | 1]

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The value of the fraction x/y is 3/25 and option b is the correct answer.

An expression for a portion of a whole is a fraction. In general, the whole can be any particular object or value, and the fraction might be a piece of any quantity out of it.

The top and bottom numbers of a fraction are explained by the fundamentals of fractions. The bottom number reflects the entire number of components, while the top number represents the number of chosen or coloured portions of the whole.

The given equation is:

5x + y / y = 8/5

Divide the terms individually at the left side of the equation:

5x/y + y/y = 8/5

5 (x/y) + 1 = 8/5

5 (x/y) = 8/5 - 1

5 (x/y) = 3/5

x/y = 3/25

Hence, the value of the fraction x/y is 3/25 and option b is the correct answer.

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Answer: The journal entry to record the addition of $500 to the Allowance for Doubtful Accounts account would be:

Debit Allowance for Doubtful Accounts account: $500

Credit Bad Debt Expense account: $500

The resulting balance in the Allowance for Doubtful Accounts account would be $2,500.

Step-by-step explanation:

Yes, the previous balance in the Allowance for Doubtful Accounts account does come into play when you add $500 to the account. The Allowance for Doubtful Accounts account is a contra asset account that is used to offset the Accounts Receivable account. It represents an estimate of the amount of accounts receivable that are expected to be uncollectible.

The balance in the Allowance for Doubtful Accounts account is based on the estimated amount of uncollectible accounts, which is typically a percentage of the total accounts receivable balance. When you add $500 to the account, you are increasing the estimated amount of uncollectible accounts.

To record this journal entry, you would debit the Allowance for Doubtful Accounts account for $500 and credit an expense account (such as Bad Debt Expense) for the same amount. The previous balance of $2,000 would also be included in the account balance and would be reflected in the new balance of $2,500.

The journal entry to record the addition of $500 to the Allowance for Doubtful Accounts account would be:

Debit Allowance for Doubtful Accounts account: $500

Credit Bad Debt Expense account: $500

The resulting balance in the Allowance for Doubtful Accounts account would be $2,500.