Micah's gym is moving into a bigger space, where he can have more stationary bicycles and treadmills. Micah needs both stationary bicycles and treadmills in his gym. Let x be the number of bicycles and y be the number of treadmills. The number of new bicycles must be more than 13 times the number of new treadmills. Each bicycle costs $340 and each treadmill costs $670. He must spend less than $5,650. Select all of the constraints for this situation.

There are Four special line segments of a triangle.

SPECIAL LINE SEGMENTS OF TRIANGLES

The four special line segment of a triangle are ,

Let's see about mentioned segment in detail,

1.) Angle Bisector :

The angle bisector divides an angle into two equal parts. 

2.) Perpendicular bisector :

A line that cuts through the middle of a side and is also perpendicular to that side is known as a triangle's perpendicular bisector.

3.) Median :

A line segment connecting a vertex to the middle of the other side is the median of a triangle.

4.) Altitude :

A triangle's altitude is defined as a line segment passing through its apex and parallel to (or at a right angle to) the side that is deemed to be its base.

For more clarity see the image given below.

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According to the sum of n terms in geometric progression, the total time she took to complete her first five homework assignments is 219 minutes.

The time taken to complete first assignment is 70 minutes.

She takes 0.8 times as long to complete each homework assignment as she took to complete the preceding assignment.

This shows that the given series is in geometric progression, where

a = first term = 70

r = common ratio = 0.8

The sum of first n terms in geometric progression is given by,

Sₙ = a (rⁿ - 1) / r - 1

S₅ = 70 (0.8⁵ - 1) / 0.8 - 1

S₅ = 219

Therefore, the total time she took to complete her first five homework assignments is 219 minutes.

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Remove the parentheses before performing the reverse operations of addition and subtraction, Remove the parentheses before reversing the process of division and multiplication, Flip The Inequality Sign When Adding, Subtracting, or Multiplying By A Negative Number.

Hence, Remove the parentheses before performing the reverse operations of addition and subtraction, Remove the parentheses before reversing the process of division and multiplication, Flip The Inequality Sign When Adding, Subtracting, or Multiplying By A Negative Number.

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Fraction [tex]3 \frac{3}{4}[/tex] teaspoons of cinnamon are needed to make 60 oatmeal cookies.    

Given that,

A recipe calls for [tex]1\frac{1}{2}[/tex] teaspoons of cinnamon to make 2 dozen oatmeal cookies.

A fraction is numerical value that is a part of a whole. It is evaluated by dividing a whole into number of parts. For example, ½ represents half of a whole number or a thing.

Then,

We will find number of teaspoons needed to make one oatmeal cookies.

1 dozen = 12

2 dozens = 24

So,

We can write,

[tex]1\frac{1}{2}[/tex] divide by 24,

Convert mixed fraction into improper fraction:

[tex]\frac{3}{2}[/tex] divide by 24

Convert to division problem by flipping the second fraction as:

= [tex]\frac{3}{2}[/tex] * [tex]\frac{24}{1}[/tex]

= [tex]\frac{3}{48}[/tex]

= [tex]\frac{1}{16}[/tex]

Now, we will multiply amount needed for one cookie by 60 to find amount needed to make 60 cookies as:

= [tex]\frac{1}{16}[/tex] * 60

= [tex]\frac{15*4}{4*4}[/tex]

= [tex]\frac{15}{4}[/tex]

= [tex]3 \frac{3}{4}[/tex]

Therefore,  

Fraction [tex]3 \frac{3}{4}[/tex] teaspoons of cinnamon are needed to make 60 oatmeal cookies.

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Vasco da Gama has invented India

An invention is a brand-new or original product, process, composition, idea, or tool. A device, item, or method can be improved using an invention to boost functionality or cut costs. It could also be a brand-new idea. An concept can be patented if it is distinctive enough, either as a stand-alone innovation or as a major improvement over the work of others. 

Portuguese explorer Vasco de Gama becomes the first European to reach India via the Atlantic Ocean when he arrives at Calicut on the Malabar Coast.

Da Gama sailed from Lisbon, Portugal, in July 1497, rounded the Cape of Good Hope, and anchored at Malindi on the east coast of Africa. With the aid of an Indian merchant he met there, he then set off across the Indian Ocean. The Portuguese explorer was not greeted warmly by the Muslim merchants of Calicut, and in 1499 he had to fight his way out of the harbor on his return trip home. In 1502, he led a squadron of ships to Calicut to avenge the massacre of Portuguese explorers there and succeeded in subduing the inhabitants. In 1524, he was sent as viceroy to India, but he fell ill and died in Cochin.

hence Vasco da Gama has invented India

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Vasco da Gama has invented India

In July 1497, Vasco da Gama set sail from Lisbon, Portugal, crossed the Cape of Good Hope, and stopped at Malindi on the continent's east coast. He then embarked on a journey across the Indian Ocean with the help of an Indian merchant he met there. The Muslim traders of Calicut did not welcome the Portuguese explorer with open arms, and on his way back to Portugal in 1499, he had to fight his way out of the harbor. He successfully subdued the locals in 1502 after leading a fleet of ships to Calicut to revenge the massacre of Portuguese explorers there. He was appointed viceroy of India in 1524 but passed away in Cochin after becoming unwell.

Answer:

Step-by-step explanation:

Part A: you can just restate parts of the text to make a vaild argument or you can make you own

Part B: he should measure N, O, P and Qas

Triangles MNO and QPO are congruent. To find the width of the creek, Andre should find the measurement of NP

When two triangles are congruent, their corresponding three sides and their three angles match precisely.

Given that

O is the midpoint of NP,

NP is perpendicular to MN, and

NP is perpendicular to PQ.

When two lines intersect at a specific point, the opposite angles formed in this situation are equal.

a) Then ∠MNP =∠QPO=90°

∠MON=∠QOP

Also, NO = OP (by the definition of midpoints)

Therefore, Triangles MNO and QPO are congruent by ASA rule

And,

b) To find the width of the creek, Andre should find the measurement of NP, because according to the figure the width is represented by NP. He should find NO and OP and then add it.

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Answer:

  5 units

Step-by-step explanation:

You want to know the side length of the rhombus with vertices (2, 0), (7, 0), (5, 4), and (10, 4).

You can find the length of the horizontal edges by counting the grid squares, or by subtracting the x-coordinates:

  7 -2 = 5

  10 -5 = 5

The slanted sides are each the hypotenuse of a 3-4-5 right triangle, so are also 5 units long. (You expect all of the sides of the rhombus to be the same length.)

Each side is 5 units long.

The answer is 5, 4.47, 5, and 8.94.

                The distance formula is d = √(x2-x1)^2 + (y2-y1)^2

                                    d = √(7-2)^2 + (0-0)^2

                                    d = √(5)^2 + (0)^2                

                                    d = √(25) + (0)

                                    d = 5

                                     d = √(5 - 7)^2 + (4 - 0)^2

                                      d = √(-2)^2 + (4)^2

                                      d = √4 + 16

                                      d = √20

                                      d = 4.47

                                      d = √(10 - 5)^2 + (4 - 4)^2      

                                      d = √25 + 0

                                      d = 5

                                       d = √(2 - 10)^2 + (0- 4)^2

                                       d = √(-8)^2 + (-4)^2

                                       d = √64 + 16

                                       d = √80

                                       d = 8.94

Therefore, each side of the rhombus has a length of 5, 4.47, 5, and 8.94.

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Answer:

1 5/6

Step-by-step explanation:

Take 11 divided by 6; we can have 1 number 6 and 5/6 left. So, the answer is  1 5/6

Let's test:

1 5/6 = 11/6

So, my answer is correct!

The size of the angle C is θ = 56°, given that BC and DE are tangents to the circle.

The tangent to a circle theorem states that a line is tangent to a circle if and only if the line is perpendicular to the radius drawn to the point of tangency

Considering the Isosceles triangle ∆AOB and its exterior angle ∠BOD;

∠BOD = 180° - 2(48) {exterior angle of a triangle equals 2 opposite interior angles}

∠BOD = 96°

If the line DE is extended to line BC at E' we will have a quadrilateral BODE' and a triangle ∆CE'D, hence;

∠B = ∠D = 90° (angles between radius and lines tangent to the circle)

so;

∠BOD + ∠OBD + ∠ODE' + ∠BE'D = 360° {sum of interior angles of a quadrilateral}

96° + 90° + 90° + ∠BE'D = 360°

276° + ∠BE'D = 360°

∠BE'D = 360° - 276° {subtract 276° from both sides}

∠BE'D = 84°

Considering triangle ∆CE'D;

∠DE'C = 180° - 84° {sum of angles on a straight line}

∠DE'C = 96°

We thus derive θ using the triangle ∆CE'D;

θ = 180° - (28 + 96)° {sum of interior angles of a triangle}

θ = 180° - 124°

θ = 56°

In conclusion, we have derived the size of the angel θ as 56° by proper application of the tangent to a circle theorem.

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3 pyramids can fit inside a rectangular prism if both figures have the same measures of bases.

A three-dimensional figure is a pyramid. Its base is a flat polygon. The remaining faces are all triangles and are referred to as lateral faces. The number of sides on its base is equal to the number of lateral faces. The line segments that two faces intersect to form its edges.

The ratio of volume of pyramid and a prism is 1:3 when they have the same base and height.

A cylinder with the same radius and height is precisely filled with the contents of three conical cups. A prism with the same base and height as three rectangular-base pyramids is exactly filled with their contents.

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The number of terms that the expression 4xy  +5 has is 2 terms.

What is an algebraic expression?

An algebraic expression is a set of numbers and letters that make up an expression that has a meaning, the letters are variables and the numbers are coefficients or independent terms, algebraic expressions can be part of an equation and model mathematical processes.

How to determine terms?

To determine the number of terms in an algebraic expression, we only have to count the spaces (addition and/or subtraction symbols) and add the unit, in this way we will have the number of terms.

4xy +5 has 2 spaces

1 + 1 = 2 terms.

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By Dilation, if the scale factor is greater than 1 image gets enlarged.

Resizing an item uses a transition called dilation. Dilation is used to enlarge or contract the items. The result of this transformation is an image with the same shape as the original. However, there is a variation in the shape's size. The initial shape should be stretched or contracted during a dilatation. The phrase "scale factor" describes this transition.

Enlargement is the term used when a dilatation results in a larger image.

Reduction occurs when a dilatation results in a smaller picture.

As the scale factor of given question is greater than 1 it is Enlargement.

By Dilation, if the scale factor is greater than 1 image gets enlarged.

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The linear equation y = 3x + 5 has an infinitely many solutions.

We looked for as many solutions as possible to the given equation.

y = 3x + 5 is a linear equation with two variables as of ax + by + c = 0.

Thus,

A linear equation with two variables hence has an endless number of solutions.

y = 3x + 5 thus has an endless number of solutions.

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The correct question is-

What is the solution of y =  3x + 5?

Yes, it is hard but with a lot of practice and putting effort one cam also find it easy.

Physics requires the ability to solve problems, which can only be acquired via practice. In addition to these difficult ideas, there are theoretical concepts, mathematical calculations, and laboratory experiments.

It is better to comprehend the derivations than to memorize the formulas. Making a mess of several formulas will just increase your anxiety over the topic. Instead, if you strive to comprehend where they originate, you will begin to appreciate physics and its applications.

Physics is a difficult topic since it combines science and arithmetic, which may be challenging for the best of us. Nevertheless, despite how difficult it is, you can achieve if you follow a few simple guidelines and put yourself through some practice.

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The correct answer is A) -12t.

To evaluate this expression, we need to use the order of operations. The order of operations is a set of rules that specifies the sequence in which operations should be performed in a math expression to get the correct result. The order of operations is typically abbreviated as PEMDAS, which stands for Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right).

Following the order of operations, we first need to evaluate the expression inside the parentheses, which is 2+(-4t). This gives us 2-4t. Next, we need to perform the multiplication, which gives us 3(2-4t) = 6-12t. Finally, we need to perform the addition, which gives us -6+6-12t = -12t. Therefore, the expression -6+3(2+(-4t)) is equivalent to -12t.

Option B) 12t-12 is incorrect because the multiplication and addition operations are not performed in the correct order.

Option C) none of the above is incorrect because the correct answer is A) -12t.

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The number of beads if A bag contains n beads. 6 of the beads are red, and the rest are blue. Ravi is going to take random 2 beads, is 18.

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a value between 0 and 1.

Given:

A bag contains n beads. 6 of the beads are red, and the rest are blue. Ravi is going to take random 2 beads,

The probability of same color beads = 9 / 17

Calculate the probability as shown below,

ⁿ⁻⁶C₂ / ⁿC₂ + ⁶C² / ⁿC₂ = 9 / 17

(n - 6) (n - 7) / 2 / n(n - 1) / 2 + 15 / n(n - 1) / 2  =  9 / 17

8n² - 212n + 1224 = 0

Solve for the value of x as shown below,

x = 18

Thus, the number of beads is 18.

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Step-by-step explanation:

angle3 is the supplementary angle to angle2.

that means together they are 180°.

180 = 117 + angle3

angle3 = 180 - 117 = 63°

The system of linear equations are said to have no solution if they are parallel to each other or have infinitely many solutions if they are coincident.

Considering two system of equations:

y1 = mx +c and  y2 = px+ q.

The lines are said to be parallel if their slopes m and p are equal but the y intercepts c and q are not equal. Which further concludes that the system of equations has no solution.

The lines are said to be coincident if their slopes m and p are equal along with the y intercepts c and q being equal. And hence we conclude that the system of equations have infinitely many solutions.

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800 ways meal be ordered.

There are 5 main courses to choose from, so there are 5 ways to choose a main course. There are 4 vegetables to choose from, so there are 4 ways to choose a vegetable. There are 5 beverages to choose from, so there are 5 ways to choose a beverage. And there are 4 desserts to choose from, so there are 4 ways to choose a dessert.

The total number of ways to order a meal is the product of the number of choices for each category.

So there are 5 * 4 * 5 * 4 = 800 ways to order a meal.

Hence, 800 ways meal be ordered.

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Answer:

34 m

Step-by-step explanation:

s=side of square

A=Area of square

P = Perimeter of square

s*s = A

s*s = 289

s^2 = 289

s = [tex]\sqrt{289}[/tex]

s = 17 m

P = s + s + s + s

P = 4s

P = 4(17)

P = 68 m

68/2 = 34 m

The population of the region is 1300 people.

It should be noted that population simply means the number of people on a particular region or area. Population density is the number of people per unit of area.

Since the population density of a certain region is 50 people per square kilometer and the region covers 26 square kilometer, the population will be:

= Number of square kilometers × Number of region

= 50 × 26

= 1300

The population is 1300 people.

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The set of rational numbers is closed under addition, subtraction, multiplication, and division (division by zero is not defined) because if you complete any of these operations on rational numbers, the solution is always a rational number. -1 and 1.

What is a closed set ?

A Closed Set Math has a way of explaining a lot of things, and one of those explanations is called a closed set.

Closure property holds for addition and multiplication of whole numbers. The sum of any two whole numbers will always be a whole number, i.e. if a and b are any two whole numbers, a + b will be a whole number. The difference between any two whole numbers may or may not be a whole number. Hence, the whole numbers are not closed under subtraction.

According to the given question:

A set is closed under addition if you can add any two numbers in the set and still have a number in the set as a result. A set is closed under (scalar) multiplication if you can multiply any two elements, and the result is still a number in the set.

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The given statement "the value in the middle of a confidence interval is always the point estimate for the population parameter" is TRUE.

In statistics, a confidence interval describes the likelihood that a population parameter would fall between a set of values for a given percentage of the time.

Confidence ranges that include 95% or 99% of anticipated observations are frequently used by analysts.

The point estimate for the population parameter is always the value at the center of a confidence range.

You have a 5% probability of being incorrect with a 95% confidence interval.

We have a 10% probability of being incorrect with a 90% confidence interval.

A 95% confidence interval is narrower than a 99% confidence interval (for example, plus or minus 4.5 percent instead of 3.5 percent).

Therefore, the given statement "the value in the middle of a confidence interval is always the point estimate for the population parameter" is TRUE.

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Answer:

Step-by-step explanation:

To convert from liters per day to gallons per week, we need to use the conversion factors for these units. One gallon is equivalent to 3.785 liters, and one week is equivalent to 7 days.

We can use these conversion factors to write the following conversion equation:

1 gallon/week = (3.785 liters/gallon) / (7 days/week)

We can then use this equation to convert 400 liters per day to gallons per week by multiplying the number of liters per day by the conversion factor. This gives us:

400 liters/day * (1 gallon/week) / (3.785 liters/gallon) / (7 days/week)

We can simplify this expression by canceling out the units that appear on both the numerator and denominator. This gives us:

400 / 3.785 / 7 = 105.66

Therefore, 400 liters per day is equivalent to 105.66 gallons per week

Answer:

40 tickets

Step-by-step explanation:

2800 = 70x

x is the number of tickets. You have to solve for x

Divide each side by 70

2800/70 = 70x/70

40 = x

The equation in slope-intercept form of the line that crossed the x-axis at 36 and is perpendicular to the line represented by y = -4/9x + 5​ is y = 9/4 ( x ) + 36

Given :

line equation is y = -4/9 x + 5

We have to find the line equation which is perpendicular to the given line in slope intercept form.

y = mx + c where m is slope and c is intercept.

slope m = -4/9

perpendicular slope = -1/m

= -1 / -4 / 9

= 9 / 4

x - intercept of x - axis = 36

so the equation is y = 9/4 ( x ) + 36 .

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The most common occurrence of a number or the one that does so most frequently is known as the mode of the data.

A set of data values' mode is the value that appears the most frequently.

The value of X at which the probability mass function reaches its highest value is known as the mode if X is a discrete random variable.

In other words, it is the value that will be sampled most frequently.

The number that appears the most frequently, or the one that does so most frequently.

Example: Since the number 2 appears three times, more than any other number, it is the mode of the numbers  {4, 2, 4, 3, 2, 2}.

Therefore, the most common occurrence of a number or the one that does so most frequently is known as the mode of the data.

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The second coordinate are ( 7 , 2 )

Given data :

Formula of slope, m = (y2 - y1)/(x2 - x1)

y2 - ( -12 ) / x2 - 2 = -19 / 1

To get -19 / 1

we have to apply suitable no to y2 & x2

7 - (-12) / 3 - 2 = -19 / 1

so, the second coordinate are ( 7 , 2 )

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The value of x+y is 289

An expression in math is a sentence with a minimum of two numbers or variables and at least one math operation. This math operation can be addition, subtraction, multiplication, or division.

Given is an expression, x²+74x+2021=y²

On solving, we get

x²+2×37x + 37² = y²-652

(x+37)²= y²-652

(x+37)²- y² = -652

(x+y+37) (x-y+37) = 289 × -2

Thus, x+y+37 = 289......(i)

x-y+37  = -2.......(ii)

Solving the equations, we get

x = 125 & y=164

Therefore,

x+y = 125+164

= 289

Hence, The correct answer is x+y = 125+164 = 289

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