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If BC=6x-2 and DE=2x+2, then the length of BC is 16.

DE is a midsegment of the triangle.

As we know that;

A midsegment is a line segment that joins two of the midpoints of a triangle's sides.

The midsegment linking the midpoints of two sides of a triangle is parallel to the third side of the triangle, and its length is half that of the third side, according to the midsegment theorem.

So according to Midpoint Theorem

DE = BC/2

Now putting the value

2x+2 = (6x-2)/2

Multiply by 2 on both side, we get

4x + 4 = 6x-2

Add 2 on both side, we get

6x = 4x + 6

Subtract 4x on both side, we get

2x = 6

Divide by 2 on both side, we get

x = 3

Now putting the value of x in BC=6x-2

BC = 6(3) - 2

BC = 18 - 2

BC = 16

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The possible amounts of time for which they could rent the meeting room is 1.71 hours

The question states that

This implies that

35x + 5.80x ≤69.80

Solving the inequality to have

40.8x ≤69.80

Making x the subject of the relation we have

x≤1.71

In conclusion it takes the college 1.71 of time for them to rent the meeting room

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The thirty-fifth term in an arithmetic sequence is 1.

The formula for the nth term of an arithmetic sequence is:  

[tex]t_{n}[/tex]  =  a + (n - 1)d

The twenty-third term in an arithmetic sequence is [tex]$\frac{2}{3}[/tex].

a + 22d = [tex]$\frac{2}{3}[/tex] ...... (1)

The fifty-third term in an arithmetic sequence is  [tex]$\frac{3}{2}[/tex].

a + 52d = [tex]$\frac{3}{2}[/tex]........(2)

Subtracting both the equations.

Subtract equation (1) from equation (2):

a + 52d - (a + 22d) = [tex]$\frac{3}{2} - \frac{2}{3}[/tex]

a + 52d - a - 22d = [tex]$\frac{9-4}{6}[/tex]

30d = [tex]$\frac{5}{6}[/tex]

d = [tex]$\frac{1}{36}[/tex]

Substitute the value of d in equation (1).

We get:

a + 22[tex]$(\frac{1}{36})[/tex] = [tex]$\frac{2}{3}[/tex]

a + [tex]$\frac{11}{18}[/tex] = [tex]$\frac{2}{3}[/tex]

a = [tex]$\frac{2}{3}[/tex] - [tex]$\frac{11}{18}[/tex]

a = [tex]$\frac{12}{18} - \frac{11}{18}[/tex]

a = [tex]$\frac{1}{18}[/tex]

To find the 35th term substitute the values of a and d in the nth term equation.

The thirty-fifth term in an arithmetic sequence is:

=  [tex]$\frac{1}{18}[/tex] + (35 - 1) [tex]$\frac{1}{36}[/tex]

=  [tex]$\frac{1}{18}[/tex] +  [tex]$\frac{34}{36}[/tex]

=  [tex]$\frac{1}{18}[/tex] +  [tex]$\frac{17}{18}[/tex]

= [tex]$\frac{18}{18}[/tex]

= 1

Therefore the thirty-fifth term is 1.

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Answer: y,x = -2,3 is your answer. I hope this helps!

Step-by-step explanation:

The equivalent of the expression -(-0.1p+4) is 0.1p-4

Equivalent expressions are expressions that work the same even though they look different. If two algebraic expressions are equivalent, then the two expressions have the same value.

For example: 3(x + 2) and 3x + 6 are equivalent expressions because the value of both the expressions remains the same for any value of x. 3x + 6 = 3 × 4 + 6 = 18. and can also be written as 6(x² + 2y + 1) = 6x² + 12y + 6.

Similarly -( - 0.1p + 4) can be written in another for by multiplying the negative sign with every term in the parentheses.

therefore -1× -0.1p + -1×4 = 0.1p -4

This means -(-0.1p+4) and 0.1p -4 are equivalent

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Answer:

1,942,364

Step-by-step explanation:

   1 8 4 9 0 3 2

+        9 3 3 3 2

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

   1 9 4 2 3 6 4

Joseph now has 1,942,364 apples.

No. of apples Joseph had in the beginning = 93332

No. of apples he gets more = 1849032

Total no. of apples he has now = 93332 + 1849032

= 1,942,364

The number of hours that the rented the boat, if the total cost was $33 would be represented by the equation: 33 = 2h + 15

To write the equation on the number of hours that the boat would have been rented for to get a total cost of $ 33, use the formula :
Total cost = Deposit fee + ( Cost per hour x Number of hours boat was used)

Total cost = $ 33

Cost per hour = $ 2

Number of hours boat was in use = h

The equation therefore is:

33 = 2 h + 15

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The full question is:

Speedy Boat Rental charges a $15 deposit fee plus $2 for each hour of use to rent a paddleboat.  Write an equation to find out for how many hours, h, they rented the Boat if the total cost was $33.

Answer:

Solid Sounds

Step-by-step explanation:

As a test, let's say the dance-a-thon lasted 10 hours.  Plug in 10 hours to each:

Gabe's:  $60/hr x 10 hr = $600

Derek's:  $100 + ($40/hr x 10 hr) = $500

Solid Sounds:  $175 + ($30/hr x 10 hr) = $475

This shows that Solid Sounds is the cheapest (no matter how many hours the dance lasts)

Answer:

Step-by-step explanation:

To calculate a percentage decrease, first calculate the difference (decrease) between the two numbers you are comparing. Next, divide the decrease by the original number and multiply the answer by 100.

In this case, our difference is 32-28=4

4 divided by 32= 4/32, and multiplying by 100 gives us 400/32=12.5

Therefore, the percent decrease is 12.5%

The inequality says that the cost of each song is less than 4 dollars.

We want to see which situation can be represented by the inequality below.

8 + 4x < 12 + 3x

Where we know that each song costs x dollars.

The situation represented by that inequality can be:

"8 dollars plus 4 songs has less value than 12 dollars plus 3 songs"

We can also simplify the inequality to get:

8 + 4x < 12 + 3x

4x  -3x < 12  - 4

x < 4

We also can see that the cost of each song is less than $4.

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With a negative leading coefficient, quadratic polynomials, and the horizontal offset for a scaled 1/x function.

Section 1's wiggles might be attributed to a variety of distinct purposes. A fourth-degree polynomial is maybe the simplest. It would have to have a negative leading coefficient in order to have downward-trending end behavior.

The curve in section 2 appears to represent either an exponential function or a scaled and translated version of 1/x. We prefer a version of 1/x because the latter is anticipated to approach the horizontal asymptote more quickly than is depicted above.

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Answer:

Step-by-step explanation:

To find out how many batches of bread you can make with 2 cups of flour, you need to divide the amount of flour you have by the amount of flour each batch requires.We know that a batch of bread requires 3 cups of flour. To find out how many batches you can make with 2 cups of flour, you can divide 2 by 3:2 / 3 = 0.67Therefore, you can make 0.67 batches of bread with 2 cups of flour. However, since you can't bake a fraction of a batch, you can't make any batches of bread with 2 cups of flour, as it is not enough. You will need at least 3 cups of flour to make a batch of bread.

Answer: (x+1)^2 + (y-0)^2 = 8pi^2

Step-by-step explanation:

An equation to represent the total amount she has saved each month is 350x + 1200.

We have to write an equation to represent the total amount she has saved each month.

Brynn has $1,200 in her savings account and plans to save an additional $350 each month in order to purchase a car.

To write an expression we have to read the statement very carefully and also write the expression after reading the statement.

Let she save the money in x months.

If she save $350 each month, then the total saving in x months = 350x

She has $1200 in saving account. Now the expression is

= 350x + 1200

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The equations which represents the given graph is 3x-y=2 and

4x+9y=36 .

What is Linear equation ?

Linear equation can be defined as the equation in which the highest degree is one

Given ,

The graphs of lines k1 and k2 are shown on the grid.

From the given graph ,

The Two lines are intersecting at a point x = 49/31 and y=85/31

So, lets put the values of and y in the given linear equations

so we get,

3x-y=2

4x+9y=36

put values x = 49/31 and y=85/31

so ,

3*(49/31) - 85/31  = 2

= 62/31

= RHS

which is equals to RHS

4*(49/31)+9*(85/31) = 36

=36* 31  / 31

= RHS

Which equals to RHS

Hence, The equations which represents the given graph is 3x-y=2

4x+9y=36 .

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Answer: Yes it's 15

Step-by-step explanation:

20/100 x 75 = 15

Using the arithmetic operation of division -

a) 3 people can be fed by 1 pizza.

b) Maria would need 11 pizzas for 33 people.

What is arithmetic operation?

A subject of mathematics known as arithmetic operations deals with the study and use of numbers in all other branches of mathematics. Basic operations including addition, subtraction, multiplication, and division are included.

The number of pizzas ordered = 8

The number of people are = 24.

Number of people that can be fed if 1 pizza was there =

Number of people = Number of people that came/ Number of pizza

Use the arithmetic operation of division -

Number of people = 24/8

Number of people = 3

Therefore, 3 people can be fed.

Now, the number of people = 33

Number of pizzas required for 33 people can be obtained as -

Use the arithmetic operation of division -

Number of pizzas = Number of people/ Number of people fed by 1 pizza

Number of pizzas = 33/3

Number of pizzas = 11

Therefore, Maria will require 11 pizzas.

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The length of the line segment is given by the distance equation

D = 7.2 units

The distance of a line between 2 points is always positive and given by the formula

Let the first point be A ( x₁ , y₁ ) and the second point be B ( x₂ , y₂ )

The distance between A and B is D , and the distance D is

Distance D = √ ( x₂ - x₁ )² + ( y₂ - y₁ )²

Given data ,

Let the distance of the line segment between two points be D

Now , the equation will be

Let the first point be represented as P ( 1 , 6 )

Let the second point be represented as Q ( 7 , 2 )

Now , distance between P and Q is D , and the distance D is

Distance D = √ ( x₂ - x₁ )² + ( y₂ - y₁ )²

D = √ ( 1 - 7 )² + ( 6 - 2 )²

On simplifying the equation , we get

D = √ ( -6 )² + ( 4 )²

D = √ ( 36 + 16 )

D = √ 52

D = 7.2 units

Hence , the distance is 7.2 units

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The least amount of time spent per week on meetings for the sample of 25 CEOs is 12 hours.

The least amount of time spent per week on meetings for the sample of 25 CEOs can be found by looking at the lowest value in the data set. The data set provided above lists the time spent per week on meetings for a sample of 25 CEOs, and the least amount of time spent is 12 hours per week.

This is the smallest value in the data set, and it represents the minimum amount of time spent on meetings among the CEOs in the sample.

Note that this data is a sample of 25 CEOs and not the entire population of CEOs, so it is not representative of all CEOs. Additionally, the time spent per week on meetings is a quantitative variable, and it is continuous. Therefore, it is recommended to use measures of central tendency (mean or median) and measures of dispersion (standard deviation, range) to make inferences about the population.

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This is because a survey of healthy high school students who were chosen at random revealed that stress is more likely to produce muscle cramps.

(a) What kind of research is this?

"Observational study" is the study's type.

Reason: This is because a survey of healthy high school students who were chosen at random revealed that stress is more likely to produce muscle cramps.

Can this data be used to draw a causal conclusion about the link between elevated stress levels and muscle cramps?

No, an observational study was unable to draw any conclusions about the link between elevated stress levels and muscle cramps. The Chi-square test can be used to determine the relationship between increasing stress and cramps.

(c) Describe any potential confounding factors that could account for the correlation between greater stress and muscle cramps.

Muscle cramps may be impacted by the increased stress.

In this case, the factors under consideration are qualitative variables. Count the number of times that high school students have visited a doctor with a muscular ailment.

Confounding factors for stress may include anxiety over taking the exam, less sleep, spending more time studying, eating less, drinking more coffee, and other factors.

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Answer: Using the formula for similar triangles, you can find the value of h by multiplying b by the ratio of corresponding sides. If a = 6 and b = 24, then the ratio of corresponding sides is 6/24 = 1/4. Therefore, h = b * (1/4) = 24 * (1/4) = 6

To find the area of Leo's actual bedroom in square meters, you can use the scale factor of 1 cm : 1.5 m and multiply the dimensions of the scaled plan by this factor. If the dimensions of the scaled plan are 2 cm by 3 cm, then the actual dimensions of the bedroom are 2 cm x 1.5 m/cm x 3 cm x 1.5 m/cm = 3 m x 4.5 m = 13.5 square meters

To find how long it will take to jog 3.2 miles at the same rate, you can use the formula distance = rate x time. If you jogged 2.4 miles in 30 minutes, then you can find the rate by dividing distance by time, which is 2.4 miles / 30 minutes = 0.08 miles/minute. Therefore, time = distance / rate = 3.2 miles / 0.08 miles/minute = 40 minutes

To find how far an airplane can fly in 1 1/4 hours, you can use the formula distance = rate x time. If the airplane flies 100 miles in half an hour, then the rate is 100 miles / 0.5 hours = 200 miles/hour. Therefore, distance = rate x time = 200 miles/hour x 1.25 hours = 250 miles

To find how much money in Somoni you would get with ₱500, you can use the exchange rate of 0.17 Somoni = 1 Philippine peso. Therefore, 0.17 Somoni x ₱500 = ₱85 Somoni

To find how many liters of gasoline you would need to drive from the first town to the second, you can use the map scale and

Step-by-step explanation:

The area of the octagon is 0.875 units square.

Two unit squares share the same center. The overlapping region of the two squares is an octagon with perimeter 3.5.

Area of a triangle:

We need to know how to calculate the area of a triangle, in order to solve this question. The area of a triangle with base b and height h is [tex]\frac{hb}{2}[/tex]. An octagon is a 2D figure with 8 sides.

Let A, B, C, D, E, F, G, and H be eight consecutive vertices of the octagon. Let 0 be the common center of the square units.

Draw the segments OA, OB, OC, OD, OE, OF, OG and OH, connecting the vertices with the common center O of the squares.

The segments divide the octagon into 8 concurrent triangles.

In these triangles, AB, BC, CD, DE,EF, FG, GH, and HA are the bases; the height is 12 of a unit in all the triangles.

Thus, the area of the octagon=[tex]\frac{1}{2}[/tex]×[tex]\frac{1}{2}[/tex]×(AB+BC+CD+DE+EF+FG+GH+HA)

        =[tex]\frac{1}{4}[/tex]×(Perimeter of the hexagon)=14×3.5=3.54=0.875

Therefore, the area of the octagon is 0.875 units square.

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The Volume or liters required to fill a 12.0 - gal gas tank is 45.42 liters.

Gallon to liter conversion factors are:

[tex]1 \ Gallon = 3.785 \ Liter[/tex]

Assuming that the gallon measurement for the gas tank is 12.0 gal.

We now need to calculate the gas tank's liter capacity.

As, 1 gallon = 3.785 liter

[tex]So \ 12\ gallon = 12*3.785[/tex]

[tex]=45.42\ gallons.[/tex]

Therefore, 45.42 liters of liquid are needed to fill the gas tank.

Meaning of gasoline:

Petroleum is the source of gasoline, which is a mixture of flammable, volatile liquid hydrocarbons used as a fuel for internal combustion engines and as a solvent for oils and fats.

It is a by-product of the petroleum industry and is used as fuel for cars because it burns with a high degree of energy and mixes easily with air in a carburetor.

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By  using the unit circle , we found that the value of Sec(0°) is (b) Sec(0°) = 1  .

The Unit Circle is defined as a circle that have a radius of 1 which is centered at the origin of a coordinate plane.

The angle in the unit circle are measured in radians.

The Secant function, denoted by Sec(x), is defined as 1/Cos(x)  ;

we have to find the value of Sec(0°) ;

So , at 0 degrees, the point (1,0) lies on the unit circle and

the x-coordinate of this point is 1 which is the cos(0) and

the value of Sec(0) = 1/cos(0) = 1/1 = 1

Therefore , the value of Sec(0°) is = 1  .

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The probability that a randomly selected battery of this kind lasts longer than 70 months is approximately 0.104(rounded off to the second decimal place).

The cumulative distribution function of an exponential distribution with a mean of 60 months is given by:

F(x) = 1 - e^(-x/60)

The probability that a randomly selected battery lasts longer than 70 months is given by:

P(X > 70) = 1 - F(70) = 1 - (1 - e^(-70/60)) = e^(-70/60) = 0.104

So, the probability that a randomly selected battery of this kind lasts longer than 70 months is approximately 0.104 (rounded off to the second decimal place).

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The median of the given set of numbers is 82.

Median is the middle element when the data set is arranged in an increasing or decreasing order.

Given is a stem and leaf plot.

We have to write each of the corresponding number in stem attached with each of the corresponding number in leaf plot.

So the numbers in the first row will be 71, 75, 77 and 78.

Numbers in the second row will be 80, 80, 81, 82, 84, 85, 86, 86, 87, 89.

Number in the third row will be 95.

Writing the numbers from the plot, we will get the values as,

71, 75, 77, 78, 80, 80, 81, 82, 84, 85, 86, 86, 87, 89, 95.

The numbers are already in the increasing order.

There are 15 number of data in the set.

Median is the middle element, that is 8th element, which is 82.

Hence the median of the data is 82.

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Above 95% confidence interval for population mean =(6.7149 to 9.2051)

Given that,

3.3.8 One of the writers asked her students how many hours a week they anticipated studying statistics outside of class in a pre-course, anonymous survey for her introductory statistics course. The average response time was 8.2 hours, with a standard deviation of 3.79 hours, from 49 students. Data were not significantly skewed.

To find : a) specify the study's observational unit. b) Determine if the variable is categorical or quantitative and the variable of interest. c) compute and present the 95% confidence interval for the parameter of interest using the theory-based inference applet. d) Was it appropriate to determine a confidence interval using the theory-based (t-distribution) technique in the setting of this study?

sample mean x= 7.960

sample size   n= 36.00

sample std deviation s= 3.68

std error sx=s/√n= 0.6133

for 95% CI; and 35 df, value of t= 2.030

margin of error E=t*std error    = 1.245

lower bound=sample mean-E = 6.7149

Upper bound=sample mean+E = 9.2051

from above 95% confidence interval for population mean =(6.7149 to 9.2051)

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To obtain 80 number of gallons of a mixture that contains 70% pure antifreeze, you must use 56 gallons of the 60% pure antifreeze and 24 gallons of the 85% pure antifreeze.

1. Calculate the total amount of antifreeze needed to make 80 gallons of the 70% mixture.

80 gallons x 0.7 = 56 gallons of antifreeze

2. Calculate the amount of 60% pure antifreeze needed.

56 gallons x 0.6 = 33.6 gallons of 60% pure antifreeze

3. Calculate the amount of 85% pure antifreeze needed.

56 gallons x 0.85 = 47.6 gallons of 85% pure antifreeze

4. Subtract the amount of 60% antifreeze from the total amount of antifreeze needed to determine the amount of 85% antifreeze needed.

56 gallons - 33.6 gallons = 22.4 gallons of 85% pure antifreeze

5. Round the amounts to the nearest whole number.

33.6 gallons of 60% pure antifreeze and 24 number of gallons of 85% pure antifreeze.

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If the rectangle is 9 cm longer than it's width , and the width is 1/7th of perimeter , then the length of rectangle is 15 cm and width of rectangle is  6 cm.

let the rectangle's length be  = l cm ;

and let the width of rectangle is  = w cm ;

the length is 9 cm longer than its width , that means ;

⇒ l = w + 9  ...equation(1)

and the width is 1/7 of perimeter , then

⇒ w = (1/7)(2l + 2w)

⇒ w = 2/7(l  + w)  .....equation(2) ;

substituting value of equation(1) in equation(2) ;

we get ;

⇒ w = (2/7) × ( w + 9 + w ) ;

on simplifying ,

we get ;

⇒ w = 6 .

from equation(1) ⇒ l = 6 + 9 = 15 .

Therefore , the length is 15 cm and width is 6 cm .

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