A group of people were asked if they had run a red light in the last year. 386 responded "yes", and 137 responded "no". Find the probability that if a person is chosen at random, they have run a red light in the last year.

The property you are referring to is called the associative property of multiplication. According to this property, when multiplying three numbers, the grouping of the numbers does not affect the result. In other words, you can change the grouping of the factors without changing the product.

In the equation you provided: 3x(5x7) = (3x5)7

The associative property allows us to group the factors in different ways without changing the result. So, whether we multiply 5 and 7 first, or multiply 3 and 5 first, the final product will be the same.

The equivalent exponential equations are given as follows:

\(2^{4x} = 2^{3(x - 3)}\)

The exponential expression for this problem is defined as follows:

\(2^{4x} = 8^{x - 3}\)

The number eight is the third power of 3, that is:

8 = 2³.

The power of a power rule is used when a single base is elevated to multiple exponents.

Then the simplified expression is obtained keeping the base, while the exponents are multiplied.

Meaning that the equivalent expression on the right side of the equality in this problem is given as follows:

\(8^{x - 3} = (2^3)^{x - 3} = 2^{3(x - 3)}\)

Meaning that the correct option is given by the fourth option.

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Answer:

The line has no slope. I hope this helps

You would need to save approximately $56.62 each month to achieve your savings goal of $3,000.00 over four years.

To calculate the monthly savings required to reach a savings goal of $3,000.00 over four years with a 10% annual interest rate,  we can use the PMT (Payment) function.

The PMT function helps us determine the fixed payment amount needed to achieve a specific future value within a given time frame.

Let's break down the given information:

Present Value (PV): $0.00 (initial account balance)

Future Value (FV): $3,000.00 (savings goal)

Interest Rate (rate): 10% per year (annual interest rate)

Number of Periods (nper): 4 years (48 months)

Using the PMT function, we need to plug in the values and solve for the monthly payment (savings amount).

The formula for the PMT function is:

PMT(rate, nper, pv, [fv], [type])

Where:

rate = Interest rate per period

nper = Total number of periods

pv = Present value (initial account balance)

fv = Future value (savings goal)

type = (Optional) Indicates whether the payment is made at the beginning (1) or end (0) of the period.

We'll assume 0 for monthly savings.

Let's calculate the monthly savings using the PMT function:

PMT(10%/12, 4*12, 0, -3000, 0)

Here, we divide the annual interest rate by 12 to get the monthly interest rate (10%/12), multiply the number of years by 12 to get the total number of months (4*12), set the initial account balance (pv) as $0, set the future value (fv) as -$3,000 (negative because it's an outgoing payment), and assume the savings are made at the end of each month (type = 0).

Using a financial calculator or spreadsheet software, the monthly savings required to reach the goal of $3,000.00 over four years with a 10% annual interest rate is approximately $56.62.

Therefore, you would need to save approximately $56.62 each month to achieve your savings goal of $3,000.00 over four year.

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Question : you want to reach $3,000.00 in savings over four years. Your account will earn 10% interest per yea Initially your account has a zero balance. How much must you save each month to achieve this goal? Use the PMT() function. Look it up in the e-book if you do not know how to use it. TIP: This is monthly so do not forget to adjust the interest rate and number of payment.

Using the given profit function, it is found that he earns $650 more selling 15 items than 5 items.

The profit in dollars earned selling x items is given by:

\(P(x) = 0.2x^3 - 10\)

Hence, selling 5 items, the profit in dollars is:

\(P(5) = 0.2(5)^3 - 10 = 15\)

Selling 15 items, the profit is:

\(P(15) = 0.2(15)^3 - 10 = 665\)

The difference is:

665 - 15 = 650.

He earns $650 more selling 15 items than 5 items.

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Answer:

B. xy(y - x) (y + x)

Step-by-step explanation:

"Let x be any vector in \(C^n\), let q = \(x^T\)Ax, and let A be an n-by-n real matrix with the characteristic that \(A^T\) = A. By confirming that q = q, the equalities below demonstrate that q is a real number.

Let A be n x n real matrix with the property that. \(A^T = A\).

if Ax = λx.

(Ax) = λx

\(xA^T=\) λx

xA = λx( and therefore dλ are real, A =\(A^{T}\) = and dλ = λ).

x(A-λL) = 0

Therefore, A-λL is a real matrix.

Assume that A is a n by n matrix with a characteristic polynomial defined by det(λI−A). The number of times an eigenvalue of A appears as a root of that distinctive polynomial is known as its multiplicity.

and x (λI-A) = 0

Therefore, x(λL-A) is also real.

X1 is real.

Therefore, since is one of A's eigenvalues, there exists a nonzero vector X\(C^n\) such that AX=X

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The market research department of a Company recommends that the Company to manufacture and market a new transistor radio after suitable test. The marginal cost of the company is 7000 - 2X  and marginal revenue is 10X - X/250.

Marginal cost is an extra cost per unit incurred when an extra unit of output produced or service rendered. Or in other words it can be said that marginal cost is an element of additional unit cost that incurred due to production of goods or services. Some time it is also considering as relevant cost or variable cost.

So in order to compute the transistor manufacturing company's marginal cost, marginal revenue and marginal profit of the company one shall equated the derivative function between them.

In micro economics technical relationship between the said marginal terms is written through derivative function:

Revenue = Price × Quantity Demanded,

Profit Maximize Point where Marginal cost is equal to marginal revenue;

MR = MC,

The marketing department also presents the following demand equation:

X = 5,000 - 500 P

P = 10 - (X ÷ 500), where P is Price and X is quantity demand.

Furthermore, the financial department provides the following cost equation:​

C(X) = 7, 000 + 2x

So the revenue function by the help of substitution method:

X = 5,000 - 500 P

Revenue = Price × Quantity Demanded,

Revenue =  10 - (X ÷ 500) × X

               =  10X - X^2 ÷ 500

Marginal Revenue! = 10X - !2X/500 = 10X - X/250

Marginal Cost =  7, 000 + 2 (5,000 - 500 P)

= 7000 + 10000 - 1000 P

= 17000 - 1000 ( 10 - (X ÷ 500))

= 17000 - 10000 - 2X

= 7000 - 2X

Therefore marginal revenue is revenue or additional earning made by a seller by selling an extra unit. Revenue is earned when extra unit is being sold.

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The statements that are true are:

Clayton could use the relationship (x, y) right-arrow (y, x) to find the points of the image.

Clayton could negate both the x and y values in the points to find the points of the image.

C’ will move because all points move in a reflection.

The image and the pre-image will be congruent triangles.

The image and pre-image will not have the same orientation because reflections flip figures.

Options A, B, D, E, and F.

There are two ways of reflection.

Along x-axis:

(x, y) – (x, -y)

Along y-axis:

(x, y) - (-x, y)

We have,

Clayton could use the relationship (x, y) → (y, x) to find the points of the image.

This is the y = x reflection rule.

This is true.

Clayton could negate both the x and y values in the points to find the points of the image.

Reflection of (x, y) along the x-axis and y-axis consecutively will give us

(-x, -y).

This is true.

C’ will remain in the same location as C because it is on the line of reflection.

This is not true.

C’ will move because all points move in a reflection.

This is true.

The image and the pre-image will be congruent triangles.

This is true.

The image and pre-image will not have the same orientation because reflections flip figures.

This is true.

Thus,

All statements are true except the statement:

C’ will remain in the same location as C because it is on the line of reflection.

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The length of a pendulum that makes one full swing in 1.9 seconds is 3 feet.

As per the given data, the given formula is:

\($T=2 \pi \sqrt{\left(\frac{L}{32}\right)}\) gives the time it takes in seconds.

Where,

T is the time it takes for a pendulum to make one full swing back and forth (in seconds).

L is the length of the pendulum, in feet.

Here we need to find the length of a pendulum that makes one full swing in 1.9 seconds to the nearest foot.

Substitute the given parameters into the formula will give;

\($1.9=2 \pi \sqrt{\left(\frac{L}{32}\right)}\)

Now divide both sides by 2π.

\($ \frac{1.9}{2 \pi}=\sqrt{\left(\frac{L}{32}\right)} \\\)

\($ 0.3024=\sqrt{\left(\frac{L}{32}\right)}\)

Then taking square on both sides.

\($ (0.3024)^2=\frac{L}{32} \\\)

0.09144576 = \($\frac{L}{32}\)

Later multiply both sides by 32.

2.9262 = L

The approximate value of the length of a pendulum:

L ≈ 3

Therefore, the length of a pendulum is about 3 feet.

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Answer:

Use prime factorizations to find the GCF of 18 and 33.

Prime factorization of 18: 2 × 3 × 3

Prime factorization of 33: 3 x 11

The GCF of 18 and 33 is

Step-by-step explanation:

Use prime factorizations to find the GCF of 18 and 33.

Prime factorization of 18: 2 × 3 × 3

Prime factorization of 33: 3 x 11

The GCF of 18 and 33 is

Answer:

3 XD

Step-by-step explanation:

Answer:

Step-by-step explanation:

There are 540 men living in the mini city.

x + (x + 150) = 1230

Simplifying this equation, we get:

2x + 150 = 1230

Subtracting 150 from both sides, we get:

2x = 1080

Dividing both sides by 2, we get:

x = 540

Therefore, there are 540 men living in the mini city.

To check our answer, we can substitute x = 540 into our original equation:

540 + (540 + 150) = 1230

690 = 1230

This is false, so there must be an error in our calculation. We can double-check our work by trying a different approach.

We know that the number of women exceeds the number of men by 150, so we can represent the number of women as (x + 150). We also know that the total number of people is 1230, so we can set up an equation:

x + (x + 150) = 1230

Simplifying this equation, we get:

2x + 150 = 1230

Subtracting 150 from both sides, we get:

2x = 1080

Dividing both sides by 2, we get:

x = 540

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Using trigonometric identities, we found that sec Φ = -7/(2√10), sin Φ = 3/7, tan β = √11/5, and sin β = √11/6 for the given values of csc Φ, cot Φ, and sec β.

1. We can start by using the Pythagorean identity to find the values of sin Φ:

\(sin^2\) Φ + \(cos^2\) Φ = 1

Since csc Φ = 1/sin Φ, we can substitute and solve for sin Φ:

1/(7/3) = sin Φ

sin Φ = 3/7

Next, we can use the fact that cot Φ = cos Φ/sin Φ:

cot Φ = cos Φ/(3/7) = - (2√10)/(3)

Simplifying this expression, we get:

cos Φ = - (2√10)/(3) * (3/7) = - 2√10/7

Finally, we can use the fact that sec Φ = 1/cos Φ:

sec Φ = 1/(- 2√10/7) = -7/(2√10)

2. We can use the fact that sec β = 1/cos β to find the value of cos β:

sec β = 6/5

cos β = 5/6

Next, we can use the Pythagorean identity to find the value of sin β:

\(sin^2\) β + \(cos^2\) β = 1

sin β = √(1 - \(cos^2\) β) = √(1 - 25/36) = √(11/36) = √11/6

Finally, we can use the fact that tan β = sin β/cos β:

tan β = (√11/6)/(5/6) = √11/5

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Answer: x=3

Step-by-step explanation:

6*6=36

36*6=216

6*6*6=216

6*6*6=\(6^{2}\)

\(6^{x} =6^{3}\)

x=3

Answer:

Step-by-step explanation:

we need to find a base for 216 that is equal to 6.

216 / 6  = 36

36 / 6 = 6,

So 6 * 6 = 36 and 36 * 6 = 216.

From this we know that 216 = 6^3

6^x = 6^3

x=3

Answer:

\(y = 3x + 5 \\ y = ( 3 \times - 10 )+ 5 \\ y = - 30 + 5 \\ y = - 25\)

Answer:

\(y=-25\)

Step-by-step explanation:

Substitute x = -10 into the equation:

\(y=3(-10) + 5\)

Multiply:

\(y=-30+5\)

Add:

\(y=-25\)

The expression for the given word phrase is

46M + M² + 2 + 1/M²

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

Number = M

Reciprocal of M = 1/M

Now,

46 x (M + 1/M)²

Step 1:

46M + M² + 2 + 1/M²

Thus,

The expression is 46M + M² + 2 + 1/M²

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Step-by-Step Explanation:

n = 45

Therefore, 2 + 4(n - 1)

Putting n = 45, we have

2 + 4(45 - 1)

= 2 + 4 × 44

= 2 + 176

= 178

Answer:

B) 178

Hope it helps.

If you have any query, feel free to ask.

Answer:

The line y+2x=b is perpendicular to a line that passes through the origin. If the two lines intersect at the point (k+2,2k)

Step-by-step explanation:

that should be right

The value of k is 2/3.

We have,

To determine the value of k, we need to find the equation of the line passing through the origin that is perpendicular to the line y + 2x = b.

The given line, y + 2x = b, can be rewritten in slope-intercept form

(y = mx + c) by solving for y:

y = -2x + b

Since the line passing through the origin is perpendicular to this line, its slope will be the negative reciprocal of the slope of the given line.

The given line has a slope of -2, so the perpendicular line will have a slope of 1/2.

Using the point-slope form (y - y1 = m(x - x1)) with the point (k + 2, 2k), we can write the equation of the perpendicular line passing through the origin as:

y - 0 = (1/2)(x - 0)

y = (1/2)x

To find the value of k, we equate the y-values of the two lines at the point of intersection:

(1/2)x = 2k

x = 4k

Since the x-coordinate of the point of intersection is k + 2, we can set it equal to 4k and solve for k:

k + 2 = 4k

2 = 3k

k = 2/3

Therefore,

The value of k is 2/3.

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The probability is equal to 0.9788.

We have given that,

Sociologists say that 85% of married women claim that their husband's mother is the biggest bone of contention in their marriages (sex and money are lower-rated areas of contention). Suppose that six married women are having coffee together one morning.

We have to find the probability

Probability all dislike is

\(0.85^8= 0.27\)

Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and 1, where, roughly speaking, 0 indicates the impossibility of the event and 1 indicates certainty.

The probability that none dislike is,

\(0.15^8= 2.6 \times 10^{(-7)}\)

At least 5 dislike

5 dislike 8C5

\((0.85)^5(0.15)^3= 0.0839\)

6 dislike 8C6

\((0.85^6 0.15)^2= 0.2376\)

7 dislike

\(8*(0.85^7) (0.15)=0.3848\)

8 dislike

\(0.85^8= 0.2725\)

Therefore the probability is equal to 0.9788.

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Answer:

(1,3)

Step-by-step explanation:

\(\sf Answer\begin{cases} \sf \rightarrowtail \: - 2x + y = 1 \dots(1) \\ \sf \rightarrowtail \: - 4x + y = - 1 \dots(2) \\ \sf 2 \times (1) \implies - 4x + 2y = 2 \\ \sf 1 \times (2) \implies - 4x + y = - 1 \\ \bf \star \: substracting \: both \\ \sf \rightarrowtail \: y = 3 \\ \sf \rightarrowtail \: -2x+(3)=1 \\ \sf \rightarrowtail \: -2x=-2 \\ \sf \rightarrowtail \: x=1\end{cases}\)

The domain of the graph of the exponential function is (d) all real numbers

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

The graph of the exponential function

The rule of an exponential function is that

The domain is the set of all real numbers

This means that the input value can take all real values

However, the range is always greater than the constant term

From the graph, the constant term is 0

So, the range is y > 0

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Answer:

\(\huge\boxed{\sf 18^{-3}}\)

Step-by-step explanation:

\(\displaystyle \frac{18^4}{18^7}\)

So, the expression becomes:

= \(18 ^{4-7}\)

= \(18^{-3}\)

\(\rule[225]{225}{2}\)

There are 117 pieces in the puzzle.

What is area?

Area is a mathematical concept that expresses the size of a region on a planar or curved surface. Surface area refers to the area of an open surface or the boundary of a three-dimensional object, whereas the area of a plane region or plane area refers to the area of a form or planar lamina.

in the given question,

area of one puzzle piece = area of square

area of square = side*side

we are given that one side of the square to be 1/2 inch or 0.5 inch  

= 0.5*0.5

= 0.25 sq. inch

area of the entire puzzle = area of a rectangle

area of the rectangle = length * breadth

we are given the length of the rectangle 6 and a half inches

=\(6 \frac{1}{2}\) inches or \(\frac{13}{2}\) inches or in decimal 6.5inches

and the breadth of the rectangle to be 4 and a half inches

=\(4{\frac{1}{2\\ }{}\) inches or \(\frac{9}{2}\) inches or 4.5 inches.

area of the rectangle = 6.5*4.5

=29.25 sq. inch

Number of puzzle pieces in the puzzle:
area of the puzzle/area of one piece of the puzzle

= 29.25/0.25

=117

Therefore 117 pieces are in the puzzle.

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Answer:

Step-by-step explanation:

1.rational

2.irrational

3.rational

4.rational

5.rational

6.irrational

Answer:

V=280

Step-by-step explanation:

7·5=35

310\35 = 8.8

V=whl=5·8·7=280

Answer:

m=8,-10

Step-by-step explanation: