A nationwide survey of seniors by the University of Michigan reveals that almost 18.0% disapprove of daily pot smoking. If 8 seniors are selected at random, what is the probability that at least 2 disapprove of daily pot smoking.

Answer: 1e-16

Step-by-step explanation:

Steps

(x)n =  (10)-16

=  

1

10 x 10 x .... x 10

=  

1

10000000000000000

=  1e-16

Answer:

the first graph

y=-2/3x-1

Step-by-step explanation:

y-3=-2/3(x+6) .        

y-3=-2/3x+4

y=-2/3x-4+3

y=-2/3x-1

Answer:  $1.40

Work Shown:

x = cost before markup

1.45x = cost after the 45% markup

1.45x = 2.03

x = (2.03)/(1.45)

x = 1.40

Answer:

19

Step-by-step explanation:

top = bottom so 4x-4y = 3x+5y so x = 9y

left = right so 2-2y = x-3y so x= y+2

so 9y = y+2

8y = 2

y= 0.25

x=2.25

so just add them all up

2*(4x-4y) + 2*(2-2y )

= 8*(x-y)+4*(1-y)

=16+4*0.75

=19

The area of the trapezoid is 1.56 square units

The area of trapezoid is calculated using the formula

= 1/2 (sum of bases) * height

= 1/2 (a + b) * height

In the problem the dimensions made available are

height =

base (a) = 1

base (b) = 1 3/5

substituting the values into the formula

= 0.5 (1 + 1 3/5) * 1 1/5

= 0.5 * 13/5 * 1 1/5

= 1.56 square units

The area of the trapezoid is 1.56 square units

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The probability that the system can decode the correct message is approximately 0.9477.

The random variable N denotes the number of error-free transmissions for a single meter upon receiving the wake-up call.

Since each transmission is error-free with probability p=0.9 and the transmissions are independent, the number of error-free transmissions follows a binomial distribution with parameters n=4 (number of trials) and p=0.9 (probability of success in each trial).

The probability mass function (PMF) of N is given by:

P(N=k) = (4 choose k) × \(0.9^k\) × \(0.1^{(4-k)}\), for k = 0, 1, 2, 3, 4

where (4 choose k) is the binomial coefficient, which represents the number of ways to choose k successes out of 4 trials.

The error correction scheme can decode the correct message if at least 3 out of 4 transmissions are error-free. Let X be the number of error-free transmissions for a single meter.

Then the probability that the system can decode the correct message is:

P(X >= 3) = P(X = 3) + P(X = 4)

To find these probabilities, we use the PMF of N from part 1:

P(X = 3) = P(N = 3) + P(N = 4) = (4 choose 3) × \(0.9^3\) × 0.1 + (4 choose 4) × \(0.9^4\) × \(0.1^0\) = 0.2916

P(X = 4) = P(N = 4) = (4 choose 4) × \(0.9^4\) × \(0.1^0\) = 0.6561

Therefore, the probability that the system can decode the correct message is:

P(X >= 3) = P(X = 3) + P(X = 4) = 0.2916 + 0.6561 = 0.9477.

So the probability that the system can decode the correct message is approximately 0.9477.

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The teacher can thus use social sciences as a vehicle to develop mathematical skills by facilitating the development of skills such as data interpretation and analysis.

As an instructor, I would use social sciences to develop mathematical skills in the following manner:Consider a social science topic like demography. In this case, a teacher could use mathematics to assist students in interpreting population statistics.

Teachers might guide students to gather information about population size, growth rate, and geographical distribution from various countries and then use statistics to analyze the data.

For example, a teacher could give students graphs or charts to help them understand population growth rates. They can be asked to make comparisons and identify trends.

In this way, students' understanding of the population is improved, as is their mathematical reasoning.Aside from using mathematics to interpret population statistics,

the teacher can also incorporate mathematical skills development in social sciences by using methods that involve understanding and analysis of data. In other words, students learn how to use data to reach conclusions and make decisions.

They learn how to interpret data and how to extract information from it.This method of teaching creates opportunities for the use of the same skills in different contexts and areas of learning.

It enables students to see connections between subjects and fosters an integrated approach to learning.

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Answer: 6

Step-by-step explanation: Division use a calculator 12/2

Answer:

6

Step-by-step explanation:

From question:

Dan has put his coins into 2 stacks

2 stacks in total

Each stack has the same number of coins

Number of coins in stack 1 = number of coins in stack 2

x = x

There are 12 coins total

Total number of coins in 2 stacks = 12

2x = 12

x = 6

There are six coins in one stack.

Answer:The solution is in the attached file

Step-by-step explanation:

a. The chart is prepared below.

b. At the end of 4 years, Ross still owes his parents $1,576.92.

To solve this problem, we need to calculate the balance of Ross's loan at the end of each year.

The balance for each year can be calculated by subtracting the yearly payment from the balance at the beginning of the year and adding the interest earned for the year.

The interest for each year is calculated by multiplying the balance at the beginning of the year by the annual interest rate of 3.2%.

Here are the steps for calculating the balance for each year:

Year 1:

Beginning balance = $2,500.00

Interest for the year = $2,500.00 x 0.032 = $80.00

Ending balance = $2,500.00 + $80.00 - $300.00 = $2,280.00

Year 2:

Beginning balance = $2,280.00

Interest for the year = $2,280.00 x 0.032 = $72.96

Ending balance = $2,280.00 + $72.96 - $300.00 = $2,052.96

Year 3:

Beginning balance = $2,052.96

Interest for the year = $2,052.96 x 0.032 = $65.76

Ending balance = $2,052.96 + $65.76 - $300.00 = $1,818.72

Year 4:

Beginning balance = $1,818.72

Interest for the year = $1,818.72 x 0.032 = $58.20

Ending balance = $1,818.72 + $58.20 - $300.00 = $1,576.92

Here's a table that shows the details:

Year ,principal ,Interest rate, interest, Payment ,annual owing

1 $2,500.00 $80.00 $300.00              $2,280.00

2 $2,280.00 $72.96 $300.00              $2,052.96

3 $2,052.96 $65.76 $300.00               $1,818.72

4 $1,818.72         $58.20  $300.00       $1,576.92

b. At the end of 4 years, Ross still owes his parents $1,576.92.

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Answer:

Total distance: 600 + 345 = 945 meters

Total time: 120 + 150 = 270 seconds

Average speed for trip:

945 meters / 270 seconds = 3.5 m/s

Answer:

-15.5 cannot be simplified further more.

Step-by-step explanation:

But if you want me to simplify 15.5/5

then here it is

\( \frac{15.5}{5} = \frac{3.1}{1} = 3.1\)

Answer:

b

Step-by-step explanation:

they both have 5 so we divide 5/5 and we get one.

Answer:

B. 1

Step-by-step explanation:

Answer:

x = 7

Step-by-step explanation:

7x + 1 = 130 = 180

7x = 180 - 130 - 1

7x = 49

x = 7

Answer:

\(16x^6y^3\)

Step-by-step explanation:

Given the expression, \((16x^8y^4)^{3/4}\\\\\), we are to simplify the expression

\((16x^8y^4)^{3/4}\\\\= 16x^{8*3/4}y^{4*3/4}\\\\= 16x^{24/4}y^{12/4}\\\\= 16x^6y^3\)

Hence the simplified form of the expression is \(16x^6y^3\)

Answer:

a^6

Step-by-step explanation:

(a^2)^3 =

you multiply the exponents

a^6

To find all points on the x-axis that are 16 units away from the point (5, -8), we can use the distance formula. The distance between two points (x₁, y₁) and (x₂, y₂) is given by the formula:

d = √((x₂ - x₁)² + (y₂ - y₁)²)

In this case, the y-coordinate of the point (5, -8) is -8, which lies on the x-axis. So, any point on the x-axis will have a y-coordinate of 0. Let's substitute the given values and solve for the x-coordinate.

d = √((x - 5)² + (0 - (-8))²)

Simplifying:

d = √((x - 5)² + 64)

Now, we want the distance d to be equal to 16 units. So, we set up the equation:

16 = √((x - 5)² + 64)

Squaring both sides of the equation to eliminate the square root:

16² = (x - 5)² + 64

256 = (x - 5)² + 64

Subtracting 64 from both sides:

192 = (x - 5)²

Taking the square root of both sides

√192 = x - 5

±√192 = x - 5

x = 5 ± √192

Therefore, the two points on the x-axis that are 16 units away from the point (5, -8) are:

Point 1: (5 + √192, 0)

Point 2: (5 - √192, 0)

In summary, the points on the x-axis that are 16 units away from the point (5, -8) are (5 + √192, 0) and (5 - √192, 0).

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The graph of linear function y – 2x = 3 is attached. The equation transformed 2 units up and 3 units down are y = 2x + 5 and y = 2x respectively.

In order to graph a linear function, determine the value of y substituting different values of x and plot the resulting coordinates on a graph and connect them with a line. The graph is plotted for the linear function: y – 2x = 3. The slope-intercept form of a linear equation is where one side contains just y and is given in general form: y = mx + b where m is the slope and b is the y-intercept. The slope intercept forms the linear equation is y = 2x + 3.

Function transformation takes a function (and its graph) and, by adding and subtraction, moves the graph around the plane without changing its shape. In order to transform the linear function 2 units up, the graph will move up by 2 units. Hence, the slope-intercept form of transformed equation is y = 2x + 3 + 2, hence y = 2x + 5. In order to transform the linear function 3 units down, the graph will move down by 3 units. Hence, the slope-intercept form of transformed equation is y = 2x + 3 - 3, hence y = 2x.

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Answer:3/4 * 1/5 = 3/20 = 0.15

Step-by-step explanation:Multiple: 3/

4 * 1/5 = 3 · 1/4 · 5 = 3/20

Multiply both numerators and denominators. The result fraction keep to the lowest possible denominator GCD(3, 20) = 1. In the following intermediate step, it cannot further simplify the fraction result by canceling.

In other words - three quarters multiplied by one-fifth is three twentieths.

The radius of the semicircle protractor is approximately 4.693 cm.

Given,Perimeter of a semicircle protractor = 14.8 cm.

To find:The radius of a semicircle protractor.Solution:We know that the perimeter of a semicircle protractor is the sum of the straight edge of a protractor and half of the circumference of the circle whose radius is the radius of the protractor.

Circumference of a circle = 2πrWhere, r is the radius of the circle.If the radius of the semicircle protractor is r, then Perimeter of a semicircle protractor = r + πr [∵ half of the circumference of a circle =\((1/2) × 2πr = πr]14.8 = r + πr14.8 = r(1 + π) r = 14.8 / (1 + π)r ≈ 4.693\) cm.

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Answer:

2/3

Step-by-step explanation:

divide by a fraction = multiply by reciprocal

1/4 * 8/3

2/3

Answer:

⅔

Step-by-step explanation:

= ¼ ÷ ⅜

= ¼ × ⁸/3

= ⅔

Have a great day !

The inverse of the conditional "If t<5, then t>6" is "If t≥5, then t≤6"  is not always true but true for some values of t.

An expression, rule, or law that defines a relationship between one variable and another variable.

Let's first consider the original statement: "If t<5, then t>6."

This statement is saying that if t is less than 5, then it must be greater than 6, which is impossible since no number can be less than 5 and greater than 6 at the same time.

So the original statement is always false, no matter what value of t we choose.

So, the inverse of "If t<5, then t>6" is "If t≥5, then t≤6".

This statement is saying that if t is greater than or equal to 5, then it must be less than or equal to 6.

This statement is true for any value of t that is greater than or equal to 5 and less than or equal to 6.

Hence, the inverse of the conditional "If t<5, then t>6" is "If t≥5, then t≤6"  is not always true but true for some values of t.

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we can change cos to sin by saying cosx=sin(90-x)

now we drop sin and make the angles equal (nothing needs to be added or subtracted since its in the first quadrant)

90-x=20+x+k.360.......kEZ (k is an element of set of integers) (we say k.360 if it's cos and sin and k.180 if it's tan)

-x-x=20-90+k.360........kEZ

-2x=-70+k.360.........kEZ

divide all terms by -2

x=35-k.180.......kEZ

Answer:

x=35°

Step-by-step explanation:

If cos x = sin(20 + x)° and 0° < x < 90°, the value of x is 35°.

Answer:

It doesn't form a right triangle

Step-by-step explanation:

According to the Pythagorean theorem, the area of the square whose side is the hypotenuse is equal to the sum of the areas of the squares on the other two sides.

a^2 + b^2 = c^2 by substituting the three values, 10, 15, and 20 you should get an equivalent value of the hypotenuse.

10^2 + 15^2 = 20^2

100 + 225 = 400

325 =/= 400

This is false.

Since this is not equivalent, it is NOT a right triangle.

Hope this helped :)

A) 0.06 ✔✔.............

Answer:

A. \( 0.0 \bar6\)

Step-by-step explanation:

\( \pink{ \huge \frac{1}{15}} = \orange{ 0.06666666....} \\ \\ \huge \purple{\frac{1}{15}} = \red{0.0 \bar6}\)

Answer:

\(108\ \text{m}^2\)

Step-by-step explanation:

The sides are rectangle is shown in the diagram

The perimeter of the fence will be

\(3x+2y=36\\\Rightarrow x=\dfrac{36-2y}{3}\)

Area of the smaller section of the garden

\(A=xy\\\Rightarrow A=\dfrac{36-2y}{3}y\\\Rightarrow A=\dfrac{36y-2y^2}{3}\)

Differentiating with respect to y we get

\(\dfrac{dA}{dy}=\dfrac{1}{3}(36-4y)\)

Equating with zero we get

\(\dfrac{1}{3}(36-4y)=0\\\Rightarrow 36-4y=0\\\Rightarrow y=\dfrac{36}{4}\\\Rightarrow y=9\)

Double derivative of area

\(\dfrac{d^2A}{dy^2}=-4<0\)

at y = 9 the area is maximum

\(x=\dfrac{36-2y}{3}=\dfrac{36-2\times 9}{3}\\\Rightarrow x=6\)

The sides of the entire garden are \(2y=2\times 9=18\ \text{m}\) and \(6\ \text{m}\)

The maximum area of the natural fertilizer garden is \(18\times 6=108\ \text{m}^2\)

Answer:

So if 14% are over 65, and 320 residents are over 65, then we can say that 14% of the town is 320. Then, we can divide by 14 to find 1%, which is 22.857142857 Now we can multiply this by 100 to get 2285.7142857.

Step-by-step explanation: