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Expand and simplify 2(x + 7) + 3(x + 1)

The expression to represent TJ's number is  1/3n - 3 and this can be determined by using the arithmetic operations and the given data.

What does a math equation mean?

An equation is a mathematical statement that proves two mathematical expressions are equal in algebra, and this is how it is most commonly used.

                             For instance, the equation 3x + 5 = 14 contains two expressions, 3x + 5 and 14, which are separated by the 'equal' sign. When two expressions are joined by an equal sign, a mathematical statement is called an equation.

The following steps can be used in order to determine the expression to represent TJ's number:

According to the given data, the number TJ's thinking about is 'n'.

Now, TJ's find 1/3 of the number 'n'. That is

               = 1/3n

Now, he subtracts that number obtained in the above step by 3.

      = 1/3n - 3

So, the expression to represent TJ's number is 1/3 n - 3.

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The complete question is -

TJ is thinking of a number which he calls n. he finds 1/3 of the number and then subtracts 5. write an expression to represent tj's number.​

The average age of the interviewees in the study investigating childhood asthma is 15.2 years.

To find the average age at the interview, you need to follow these steps. Here's how you can calculate it:

First, add up all the ages of the interviewees:18 + 16 + 16 + 17 + 14 + 13 + 15 + 16 + 19 + 12 + 16 + 13 + 13 + 18 + 13 = 228Next, count the total number of interviewees in the study:

15 interviewees

Finally, divide the sum of ages by the number of interviewees: 228 ÷ 15 = 15.2

Therefore, the average age calculated in the study while investigating childhood asthma is approximately 15.2 years.

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Step-by-step explanation:

From n=1, to n=4, plug this in the sigma notation

The first four terms of this series are

-4,-8/3,-16/9,-32/27

b. Since -1<r<1, the series diverge

c. The sum of an infinite geometric series is equal to

[tex] \frac{a}{1 - r} [/tex]

Where a is the initial value and r is the rate

a=-4

r =2/3

[tex] \frac{ - 4}{1 - \frac{2}{3} } = \frac{ - 4}{ \frac{1}{3} } = - 12[/tex]

Answer: 35

Step-by-step explanation:

Let's assume that Mr. Nelson took "x" students on the trip.

According to the problem, the observatory charges a trip fee of $100, which Mr. Nelson had to pay regardless of how many students he took.

In addition to that, he also had to pay $6.50 per student. So the total cost of the trip can be expressed as:

Total cost = $100 + ($6.50 * number of students)

We know from the problem that the total cost of the trip was $327.50. So we can set up an equation:

$327.50 = $100 + ($6.50 * x)

Now we can solve for "x" by first subtracting $100 from both sides:

$327.50 - $100 = $6.50x

$227.50 = $6.50x

Finally, we can solve for "x" by dividing both sides by $6.50:

x = $227.50 ÷ $6.50

x ≈ 35

Therefore, Mr. Nelson took approximately 35 students on the field trip.

Investment a grows faster than investment b, and thus investment b is the better choice.

We can calculate the worth of each investment after 1 year by applying the given rates of growth.

a. For investment a, the initial investment of $1000 grows by 10% per year. Therefore, the worth of the investment after 1 year is:

1000 + 0.1*1000 = $1100

b. For investment b, the initial investment of $3000 grows by $150 per year. Therefore, the worth of the investment after 1 year is:

3000 + 150 = $3150

Comparing the two worths, we see that investment b worth more after 1 year, since $3150 is greater than $1100. Therefore, investment b is the better choice.

Alternatively, we can also calculate the growth rates of each investment and compare them directly. For investment a, the growth rate is 10% = 0.1, whereas for investment b, the growth rate is 150/3000 = 0.05 or 5%. Since 0.1 > 0.05, we can again conclude that investment a grows faster than investment b, and thus investment b is the better choice.

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If a sample of 6-marbles is drawn with replacement, then probability that 1 is blue, 2 are white and 3 are red is 0.2597.

The different number and color of marbles that the box contains 4 white, 5 red and 2 blue marbles.

The total number of marbles are = 4+5+2 = 11 marbles,

We can choose 6 marbles in ¹¹C₆ ways,

The one blue marble can be chosen in ²C₁ ways, the two white marbles can be selected in ⁴C₂ ways and the three red marbles in ⁵C₃ ways.

⇒ The number of ways in which we can choose the marbles with the given color combinations is = ²C₁ × ⁴C₂ × ⁵C₃ ways.

So, Probability that one is blue, two are white and three are red

⇒ (²C₁ × ⁴C₂ × ⁵C₃)/¹¹C₆,

⇒ (2 × 6 × 10)/462,

⇒ 0.2597.

Therefore, the required probability is 0.2597.

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Answer: The height of the arrow shot into the air can be represented by the equation:

h = -16t² + vt + h0

where t is the time in seconds, h is the height in feet, v is the initial velocity in feet per second, and h0 is the initial height in feet.

In this problem, the arrow is shot into the air with an initial velocity of 112 feet per second, and the bow is held 5 feet off the ground. Therefore, we have:

v = 112

h0 = 5

To find the maximum height of the arrow, we need to find the vertex of the parabolic function given by the equation. The vertex of a parabola of the form y = ax² + bx + c is given by the point (-b/2a, c - b²/4a).

In our case, the equation of the parabola is h = -16t² + 112t + 5. So we have:

a = -16

b = 112

c = 5

The t-value of the vertex is given by -b/2a. Therefore, we have:

t = -b/2a = -112/(2*(-16)) = 3.5

To find the maximum height, we substitute t = 3.5 into the equation:

h = -16t² + 112t + 5 = -16(3.5)² + 112(3.5) + 5 = 196

Therefore, the maximum height of the arrow is 196 feet.

Step-by-step explanation:

The distance that Bucky walked is 25.908 meters

What is distance ?
Distance is a numerical measurement of how far apart two objects or points are in space. It is a scalar quantity, which means that it is defined only by its magnitude and not by its direction. Distance can be measured using various units, such as meters, feet, kilometers, miles, and so on, depending on the system of measurement being used.

Distance is an important concept in mathematics, physics, and other fields that deal with spatial relationships. It is often used to describe the length of a path traveled by an object or the separation between two objects in space.

According to the question:
To convert feet to meters, we can use the conversion factor 1 foot = 0.3048 meter.

The distance that Bucky walked is given as 85 feet. To find the distance in meters, we can multiply the number of feet by the conversion factor:

Distance in meters = 85 feet x 0.3048 meter/foot

Simplifying this expression, we get:

Distance in meters = 25.908 meters

Therefore, Bucky walked 25.908 meters.

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Answer:

Before we can simplify this expression, we need to first find a common denominator for all the fractions. The prime factorization of the denominators is:

2 × 5

3 × 7 × x

Therefore, a common denominator is:

2 × 5 × 3 × 7 × x = 210x

Using this common denominator, we can rewrite the expression as:

[(5 × 21) / (2 × 5 × x) - (16 × 42) / (5 × 2 × 21 × x)] - [(-35) / (3 × x × 7 × 21)]

Simplifying each fraction, we get:

[105 / (10x) - 672 / (210x)] - [-5 / (3 × 7 × x × 21)]

Combining the two fractions and simplifying, we get:

[105 - 672] / (10x) + [5 / (3 × 7 × x × 21)]

= -567 / (10x) + 1 / (3 × 7 × x)

= (-567 × 21 + 10) / (210x)

= -11897 / (210x)

Therefore, the simplified expression is:

-11897 / (210x)

Answer:

angle o = 2×angle D (central angle twice inscribed angle)

angle a= angle d = 65

So, the area of the composite figure is 96.57 square centimeters.

In geometry, area refers to the measure of the size of a two-dimensional surface or region. It is typically expressed in square units, such as square meters, square feet, or square centimeters.

To find the area of a shape, you need to measure the length and width of the shape and then multiply those measurements together. The formula for calculating the area of a rectangle, for example, is length x width. The formula for calculating the area of a circle is pi x radius squared, where pi is a mathematical constant, and the radius is the distance from the center of the circle to its edge.

by the question.

sure, I can help you with that!

To find the area of the composite figure, we need to find the area of each individual shape and then add them up.

First, let's find the area of the sector of the circle. We know that the radius of the circle is 6 cm, and the central angle of the sector is 82% of a full circle. Since a full circle has 360 degrees, we can find the central angle of the sector by multiplying 360 by 0.82:

[tex]Central angle of sector = 360 x 0.82 = 295.2 degrees[/tex]

The area of the sector can be found using the formula:

Area of sector = (central angle/360) x π x radius^2

Substituting the values, we know:

[tex]Area of sector = (295.2/360) x 3.14 x 6^2 = 56.57 cm^2[/tex]

Next, let's find the area of the triangle. We know that the base of the triangle is 8 cm, and the height is 10 cm. We can use the formula for the area of a triangle:

[tex]Area of triangle = 1/2 x base x height[/tex]

Substituting the values, we know:

[tex]Area of triangle = 1/2 x 8 x 10 = 40 cm^2[/tex]

Now, we can add the areas of the sector and the triangle to find the total area of the composite figure:

Total area = area of sector + area of triangle

[tex]Total area = 56.57 + 40 = 96.57 cm^2[/tex]

Rounding this to the nearest hundredth, we get:

[tex]Total area =96.57 cm^2[/tex]

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Answer:

1/4x

Step-by-step explanation:

1-1/3=3/3-1/3=2/3

3/8x(2/3)

6/24x

then simplify

1/4x

Answer:

The area of a parallelogram is given by the formula A = b × h, where b is the base length and h is the height. So, for each tile, the area is:A = 8.5 inches × 3.5 inches = 29.75 square inchesTherefore, the area of each tile is 29.75 square inches.

Step-by-step explanation:

Answer:

She can create 9 outfits

Step-by-step explanation:

Imagine it's like a 3x3 grid of what she can and can't do. You can't wear two shirts and two pants at the same time, so for each input you have one equal output.

Therefore, for the first blouse, she can choose to wear either the jeans, khakis, or grey pants (3 options)

For the second blouse, she can wear either the jeans, khakis, or grey pants (3 options)

And again for the third blouse, she can wear either the jeans, khakis, or grey pants (3 options).

3 + 3 + 3 = 9, therefore 9 outfit choices :)

So, the final equation for the sine function is:

[tex]y = 5 sin(2x - \pi /2) + 2[/tex].

The general form of a trigonometric equation can vary depending on which trigonometric function is being used (sine, cosine, tangent, etc.), but the most general form is:

[tex]f(x) = A sin(Bx + C) + D[/tex]

where f(x) is the trigonometric function, A is the amplitude, B is the frequency, C is the phase shift, and D is the vertical shift. The phase shift and vertical shift are optional components and may not always be present in a trigonometric equation.

If using cosine instead of sine, the equation would be:

[tex]f(x) = A cos(Bx + C) + D[/tex]

If using tangent, the equation would be:

[tex]f(x) = A tan(Bx + C) + D[/tex]

Other trigonometric functions, such as secant, cosecant, and cotangent, can also be used in trigonometric equations, but the general form would follow the same structure as above.

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We can conclude that the lines are perpendicular, the slopes are negative reciprocals of each other,

What are the slopes?

To determine if the lines are parallel or perpendicular, we need to put both equations in slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept.

y = 3x -x

-3y = -x + 4 (divide both sides by -3)

y = (1/3)x - (4/3)

Now we can see that the slope of the first equation is 3, and the slope of the second equation is (1/3). If two lines are perpendicular, their slopes are negative reciprocals of each other, meaning that one slope is the negative inverse of the other. The negative reciprocal of 3 is -1/3, and the negative reciprocal of 1/3 is -3. Since the slopes are negative reciprocals of each other, we can conclude that the lines are perpendicular.

The slope of a line can be positive, negative, zero or undefined. A positive slope indicates that the line is slanting upward from left to right, while a negative slope indicates that the line is slanting downward from left to right. A slope of zero indicates that the line is horizontal, while an undefined slope indicates that the line is vertical.

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The answer is either A or D, 0.045

The inequality to find the maximum number of t-shirts is:

32 + 7x <= 60

A type of inequality expression known as a compound inequality is made up of two or more simple inequalities.

Inequality with a "and" indicates that both disparities are real.

If there is a "Or" inequality, any of the statements is true.

Considering inequality,

Jospeh has at most $60 to spend

Then it will be <=60

Now she has to spend 32 dollars on jeans so 32 will be add to the initial amount for sure.

And

Let x be the number of t-shirts

Then the cost of x t-shirts will be 7x

Putting this in to inequality will be:

32 + 7x <= 60

The inequality to find the maximum number of t-shirts is:

32 + 7x <= 60

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Answer:

2/4=1/2

Step-by-step explanation:

Answer:

20 hours

Step-by-step explanation:

[tex]\text{x} = \text{number of hours}[/tex]

A yard cleanup service charges a $365 fee plus $14.75 per hour.

[tex]365 + 14.75x[/tex]

Another cleanup service charges a $250 fee plus $20.50 per hour.

[tex]250 + 20.50x[/tex]

How long is a job for which the two companies' costs are the same?

[tex]365 + 14.75x = 250 + 20.50x[/tex]

[tex]365 - 250 = 20.50x - 14.75x[/tex]

[tex]115 = 5.75x[/tex]

x = 20

a. The independent variable in this function is the amount of time a car is parked, measured in hours. The dependent variable is the cost of parking, measured in dollars.

b. "The cost of parking is a function of the amount of time a car is parked."

c. Here is a possible graph of the function:

           ^

           |

   $12     +--------/-----

           |      /      

           |    /        

           |  /          

   $3      o              

           |              

           |              

           |              

           +--------------->

                 Time

In this graph, the vertical axis represents the cost of parking in dollars, and the horizontal axis represents the amount of time a car is parked in hours. The graph shows a linear relationship between the two variables, with a slope of $3 per hour, up to a maximum cost of $12. This means that the cost of parking increases by $3 for each additional hour of parking, up to a maximum cost of $12.

In the word problem , Chris takes 40 ml of 20% alcohol and 160 ml of 60% alcohol.

What is percentage?

Divide the A value or ratio that may be stated as a fraction of 100 is referred to in mathematics as a number by the total and multiply by 100 to find the percent of a given number. Therefore, the percentage refers to a portion per hundred. Per 100 is what the word percentage signifies. The letter "%" stands for it.

Let the volume of 20% solution be x

Then volume of 60% solution is 200 - x

Alcohol in 20% solution = 0.2*x = 0.2x

Alcohol in 60% sol = 0.6(200-x) = 120 - 0.6 x

If the final solution is of 52% concentration, it means the volume of alcohol in it

= 200*0.52 = 104 ml

So we have the equation

=> 0.2x + 120 -0.6x = 104

=> 120-104 = 0.4x

=> 0.4x = 16

=> x = 40 ml

So he takes 40 ml of 20% alcohol and 160 ml of 60% alcohol.

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changes in the base pairs can alter the overall shape of the DNA molecule, disrupt specific interactions between different regions of the DNA, and potentially affect the normal functioning of the DNA.

The structure of DNA is determined by the sequence of its base pairs. There are four types of base pairs in DNA: adenine (A), thymine (T), guanine (G), and cytosine (C). The base pairs form the rungs of the DNA ladder, with the backbone consisting of sugar and phosphate groups.

The sequence of base pairs determines the overall shape of the DNA molecule. The base pairs are held together by hydrogen bonds, which are relatively weak but collectively provide enough stability to maintain the double helix structure of DNA. The sequence of base pairs also determines the specific interactions between different regions of the DNA molecule, such as the interaction between the two complementary strands.

Changes in the base pairs can have a significant impact on the structure of DNA. For example, a substitution of one base pair for another can result in a different hydrogen bonding pattern, which can affect the stability of the double helix. This can result in a change in the shape of the DNA molecule, and can also affect the specific interactions between different regions of the DNA.

Insertions or deletions of base pairs can also have a significant impact on the structure of DNA. These types of mutations can disrupt the regular spacing of base pairs along the DNA molecule, which can cause kinks or bends in the DNA. This can also affect the specific interactions between different regions of the DNA, and can potentially interfere with the normal functioning of the DNA molecule.

In general, changes in the base pairs can alter the overall shape of the DNA molecule, disrupt specific interactions between different regions of the DNA, and potentially affect the normal functioning of the DNA.
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If 1,000 points are selected randomly inside the square with all points equally likely to be selected, points to lie inside the circle is 785.4 points.

We can find the answer by finding the ratio of the areas of the regions and then multiplying by the total number of points.

The square has an area of 1 (since it has sides of length 1).

The circle has a radius of 1/2 and an area of pi/4.

So the ratio of the areas is:

(π/4) / 1 = π/4

Therefore, we would expect:

(π/4) * 1000 =  ( 3.14 / 4 ) 1000

(π/4) * 1000 = 1000 × ( 0.785 ) = 785 points

points to lie inside the circle. This is approximately 785 points.

Your question is incomplete but mos probably your full question was

If 1,000 points are selected randomly inside the square with all points equally likely to be selected, how many of those points are expected to lie inside the circle?

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Carmen is comparing two bike rental companies, A and B. Company A charges a flat rate fee of $30 and $2 per hour, while company B charges a flat rate fee of $10 and $4 per hour.

Carmen can use mathematical equations to compare the costs of the two companies and make an informed decision.

The equation for the cost of renting from Company A is y=2h+30, where y represents the total cost in dollars and h represents the number of hours rented. The equation for the cost of renting from Company B is y=4h+10, where y represents the total cost in dollars and h represents the number of hours rented.

To compare the cost of renting from Company A and Company B for a specific number of hours, Carmen can substitute the value of h into each equation and solve for y. For example, if Carmen plans to rent a bike for 5 hours, the cost of renting from Company A would be y=2(5)+30=$40, and the cost of renting from Company B would be y=4(5)+10=$30. In this case, renting from Company B would be the more cost-effective option.

Carmen can also use algebraic methods to determine the break-even point, or the point at which the cost of renting from Company A is the same as the cost of renting from Company B. To find the break-even point, Carmen can set the two equations equal to each other and solve for h:

2h+30=4h+10

2h=20

h=10

This means that if Carmen plans to rent a bike for 10 hours or less, it would be more cost-effective to rent from Company B. If she plans to rent a bike for more than 10 hours, it would be more cost-effective to rent from Company A.

Another method of comparing the two companies is to graph the two equations on the same coordinate plane. The x-axis can represent the number of hours rented (h), and the y-axis can represent the total cost in dollars (y). Carmen can plot the two equations and visually compare the graphs to determine which company is more cost-effective for a specific number of hours rented.

In summary, Carmen can use mathematical equations, algebraic methods, and graphing to compare the costs of renting from Company A and Company B based on the number of hours rented. By comparing the costs, she can make an informed decision about which company to rent from based on her budget and the duration of the rental period.

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The probability that he gets exactly one rose given that at least one of the flowers he gets is pink is 4/7.

To calculate the probability that he gets exactly one rose given that at least one of the flowers he gets is pink, we need to use conditional probability. Let R be the event that he gets a rose and P be the event that he gets a pink flower. Then, we want to find P(R=1 | P≥1).

Using Bayes' theorem, we have:

P(R=1 | P≥1) = P(R=1 and P≥1) / P(P≥1)

We can calculate the probability of getting at least one pink flower as:

P(P≥1) = 1 - P(P=0)

Assuming the probabilities of getting a rose and a pink flower are independent, we can calculate the probabilities of getting exactly one rose and at least one pink flower as:

P(R=1 and P≥1) = P(R=1) * P(P≥1) = (2/5) * (1 - 3/5) = 2/5 * 2/5 = 4/25

P(P=0) = 3/5, since there are 3 flowers that are not pink out of a total of 5.

Therefore, we have:

P(R=1 | P≥1) = (4/25) / (1 - 3/5) = 4/7

So the probability that he gets exactly one rose given that at least one of the flowers he gets is pink is 4/7.

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Answer: 324

Step-by-step explanation:

Ratio--> 1/0.15=x/48.6

Do the butterfly method of multiplying

0.15x=48.6

Divide by 0.15 on both sides

48.6/0.15=324

Answer:

Because the P-value of 0.0733 > , Lucy should fail to reject H0. There is not convincing evidence that the proportion of customers who will ask for a straw is less than 50%.

the area of the first sector piece is approximately 42.4115 square . and area of the second sector piece is approximately 149.03 cm².centimeters.

what is area of circle?

The area of a circle is given by the formula,where A is the area of the circle, r is the radius of the circle, and π (pi) is a mathematical constant that is approximately equal to 3.14159.In words, the area of a circle is equal to pi times the square of its radius.

In the given question,

The area of a sector of a circle is given by the formula:

A = (θ/360) * πr²

where:

θ is the angle at the center of the circle (in degrees)

r is the radius of the circle

π is the mathematical constant pi (approximately equal to 3.14)

In this case, the angle at the vertex of the sector piece is 60 degrees, and the radius is 9 cm. Therefore, the area of the sector piece is:

A = (60/360) * π * 9²

A = (1/6) * π * 81

A = 13.5π

A ≈ 42.4115 cm²

So the area of the sector piece is approximately 42.4115 square centimeters

A = π(8.4 cm)²

A = 221.76 cm²

Next, we need to find the fraction of the circle that corresponds to the given angle. The total angle of a circle is 360 degrees, so the fraction of the circle that corresponds to an angle θ in degrees is:

f = θ/360

Plugging in the given angle of 242 degrees, we have:

f = 242/360

f = 0.6722

So the area of the sector piece is:

A_sector = f * A

A_sector = 0.6722 * 221.76 cm²

A_sector = 149.03 cm²

Therefore, the area of the sector piece is approximately 149.03 cm².

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The area of the sector of for the given radius is 1. 42.4 cm² and 2. 152.9 cm².

A sector of a circle is an area that is bounded by two circle radii and the arc that runs between them. The length of the arc is proportional to the circumference of the circle, and the angle formed by the radii is known as the sector's central angle. The formula  A = (θ/360)πr² may be used to determine the area of a sector, where r denotes the radius of the circle, denotes the constant pi, and denotes the central angle in degrees.

The area of a sector can be calculated using the formula:

A = (θ/360)πr²

1. For r = 9 and theta = 60 we have:

A = (60/360)π(9)² ≈ 42.4 cm²

2. For r = 8.4 and theta = 242 we have:

A = (242/360)π(8.4)² ≈ 152.9 cm²

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