How many terms are there in the following sequence?
19, 21, 23, ..., 53

The equation relating to the total cost and number of students attending the park is $22.5x = y

According to the question we have been given that

Total money paid by Mrs. Jameson = $202.50

Total number of the students = 9

Let the amount of one student to visit the amusement park be X

Thus first we have to find the value of X by following equation,

          9X = $202.50

Solving for X we get,

           X = 202.50/9

           X = $22.5

That is amount for one student is = $22.5

Now we will solve the second part

Let the total cost be represented as y

Let the number of students attending the park be represented as x

Then the equation related to total cost and number of students is given as

                  $22.5x = y

Hence the equation is given above

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The general term for the sequences 2, 2/3, 2/9, 2/27, and 2/81 .. is Tₙ = 2/3ⁿ⁻¹.

Given sequence is 2, 2/3, 2/9, 2/27, 2/81 .....

Geometric Progression is also known as a geometric sequence in which each term after the first term is obtained by multiplying the previous one by a constant, non-zero number called the common ratio.

We know that a given sequence is a Geometric progression. So we need to find the common ratio

Here the first term is a = 2

common ratio r = 2/3/2 = 1/3

Now the formula for a geometric sequence for n terms is

Tₙ = a * rⁿ⁻¹

Tₙ = 2 * (1/3)ⁿ⁻¹

Tₙ = 2/3ⁿ⁻¹

Therefore the general term for the sequences 2, 2/3, 2/9, 2/27, and 2/81 .. is Tₙ = 2/3ⁿ⁻¹.

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The numbers are 77 , 177 and 308 .

Numbers are the building blocks in mathematics. It is an arithmetic value that is used to represent a quantity. Real numbers , integers , natural numbers, whole numbers , irrational numbers are are various types of numbers.

Let us consider the first number to be x . Then the second number is 4x+100 , and the third number is 100 more than the first number. Therefore the the sum of the three numbers will be:

x+4x+(x+100)=6x+100

Now the sum of all the numbers is 562.

Therefore we can write a linear equation in x to find the values of x.

∴ 6x+100=562

or, 6x = 562 - 100

or, 6x = 462

or, x = 462 ÷ 6

or, x = 77

Therefore the second number is 4x = 4 × 77 = 308 and the third number is x + 100 = 77 + 100 = 177 .

So the numbers are 77 , 177 and 308 .

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The product will be 332 / 15 .

Given : - 5[tex]\frac{1}{3}[/tex] , - 4[tex]\frac{15}{100}[/tex]

To find : the product of two given nos.

We are given mixed fractions .

Multiplying both the nos . we get ,

( - 5[tex]\frac{1}{3}[/tex] ) * ( - 4[tex]\frac{15}{100}[/tex] )

On converting mixed fractions we get ,

= ( - 16 / 3 ) * ( - 83 / 20 )         ( multiplication of a fraction with a fraction )

= ( 4 * 83 ) / 15

= 332 / 15

Hence , the product will be 332 / 15 .

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The number doesn't share the same pattern 12,24,9,3,300,39 is 39.

A pattern is a series or sequence that generally repeats itself. Color, exertion, shape, number, and other patterns that we see in our diurnal lives are exemplifications of patterns.

They might be finite or horizonless and can be tied to any event or object. In mathematics, a pattern is a sequence of integers that are related to each other according to a specified rule. These rules specify how to cipher or break issues. In a sequence of,,, for illustration, each number increases by 3. So, following the pattern, the final number will be 12 3 = 15.

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Scale Factor is defined as the ratio of the size of the new image to the size of the old image. The center of dilation is a fixed point in the plane. Based on the scale factor and the center of dilation, the dilation transformation is defined. If the scale factor is more than 1, then the image stretches.

For example, if a square is dilated and the side of the smaller (original) square is 4 units and the side of the dilated square (enlarged) is 12 units, then, in this case, the scale factor will be: 12 ÷ 4 = 3.

Perform a Dilation of 4 on point A (2, 3) which you can see in the picture below. Multiply the coordinates of the original point (2, 3), called the image, by 4. Image's coordinates = (2 * 4, 3 * 4) to get the coordinates of the image (8, 12).

And so if you dilate it with a factor of three, then you're going to want to go three times as far down. So minus three, and three times as far to the left, so you'll go minus six.

The basic formula to find the scale factor of a dilated figure is: Scale factor = Dimension of the new shape ÷ Dimension of the original shape.

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The statement that explains why this is true is (d) dividing both sides of Equation A by -3 gives x + 7 = − 8 .

The equations are given as

In equation A, we have

-3(x + 7) = 24

Divide both sides of this equation by -3

So, we have

-3(x + 7)/-3 = 24/-3

Evaluate the quotient

So, we have

x + 7 = -8

The above equation is the same as equation B

Hence, the statement that explains why this is true is (d) dividing both sides of Equation A by -3 gives x + 7 = − 8 .

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An equation for the line for walnut street is: y = 2x + 1.

The slope intercept form for line is given by;

y = mx + c

where

m = slope

c = y-intercept

As, the two streets chestnut street and walnut street are parallel in a map, their slopes are also equal.

The equation of chestnut is y = 2x-6; comparing with general form;

m = 2.

The coordinates of walnut street is (1, 3) = (x₁, y₁)

Thus, equation is;

(y - y₁) = m(x - x₁)

Put the values.

(y - 3) = 2( x - 1)

simplify,

y - 3 = 2x - 1

y = 2x + 1

Thus, the equation for the walnut street is found as; y = 2x + 1.

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Answer:

There are many formations a group of 5 can make. Examples could be STS (Shoulder To Shoulder), single file, and double column with one leader. There are many more formations that could be made but these three would be the most acceptable line formations in a school environment.

Answer:

Yes.

Step-by-step explanation:

4.635 is larger that 4.6135.

The mean score is 18.5833 , Mode is 21 and Range is 39 of the given scores.

Mean is the average value of all the given numbers

To calculate the mean we have to add all the values and divide the sum by the numbers of values.

Total of all value = 21+18+3+12+15+21+42+24+31+3+12+21 = 223

No of values = 12

Mean = [tex]\frac{223}{12} =18.58333[/tex]

Mode is the value which comes frequently in data set

In the given data 21 is come three times which is most frequently so Mode is 21.

Range is the difference between the largest number and the smallest number of the given data set.

Largest number of the data set is 42 and smallest number is 3 so the range is 42-3 = 39.

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The equation of a line perpendicular to y = -10 + 3x that passes through the point (9,2) is y = -1/3x + 1

The equation of the line is given as

y = -10 + 3x

Rewrite the equation as

y = 3x - 10

A linear equation is represented as

y = mx + c

Where

Slope = m

So, we have

m = 3

The slopes of perpendicular lines are opposite reciprocals

This means that

m2 = -1/m1

So, we have

m = -1/3

Evaluate

m = -1/3

The equation of the perpendicular line is then calculated as

y = m(x - x1) + y1

Where

(x1, y1) = (9, -2)

This gives

y = -1/3(x - 9) - 2

Evaluate

y = -1/3x + 3 - 2

Evaluate the sum and the difference

y = -1/3x + 1

So, the equation of a line perpendicular to y = -10 + 3x that passes through the point (9,2) is y = -1/3x + 1

Hence, the required equation of a line perpendicular to y = -10 + 3x that passes through the point (9,2) is y = -1/3x + 1

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The digits of 7,444,000 can be only be arranged in 140 ways

Combinations are used to determine the number of selections of an item within another

The arrangements of the digits is an illustration of factorials

The number is given as: 7,444,000

From the given number, we have the following parameters:

Total (n) = 7 i.e. number of digits

n(4) = 3 i.e. number of digit-4

n(0) = 3 i.e. number of digit-0

So, the number (N) of arrangements is:

N = n!/(n(4)! * n(0)!)

Substitute known values in the above equation

So, we have

N = 7!/(3! * 3!)

Evaluate the factorials in the above equation

So, we have

N = 5040/(6 * 6)

Evaluate the quotients in the above equation

N = 140

Hence, the digits of 7,444,000 can be arranged in 140 ways

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The equation of the linear function in slope intercept form is f(x) = -2x + 1

The table can be used to write linear equation in slope intercept form.

Therefore, the equation of the linear function in slope intercept form is as follows:

y = mx + b

where

Therefore,

m = 3 - 5 / -1 + 2

m = - 2 / 1

m = -2

Therefore, the y-intercept can be solved as follows;

using (0, 1)

y = -2x + b

1 = -2x + b

1 = -2(0) + b

b = 1

Hence, the the equation of the linear function in slope intercept form is f(x) = -2x + 1

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An account into which someone deposits an equal amount of money at equal periods or equal intervals of time is an annuity.

A predetermined sum of money that you will receive annually for the rest of your life is called an annuity. An annuity is a contract that you have with an insurance provider that calls for regular payments to be made by the insurer to you, either now or in the future.

Certain annuities have payments that are made for a set (limited) amount of time known as the annuity's term. A 30-year mortgage payment is one illustration. With a contingent annuity, payments are made up to a specific occurrence.

As, the deposits have an equal amount with equal intervals.

Hence, An account into which someone deposits an equal amount of money at equal periods or equal intervals of time is an annuity.

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The value of sin(t) in fourth quadrant is  -120/169.

Given that cos(t)= 17

t is in fourth quadrant, so sint<0 and cost>0

So sint = -sqrt(1-cos^2(t))= -sqrt(1-25/169)= - sqrt((169-25)/169)= -12/13

Sin(2t) = 2sin(t)cos(t)= 2*-12/13* 5/13 = -120/169

The region enclosed by such an arc and two sketched radii, one at each extremity. a component of a machine that has a quarter-circle form.

Each of the four divisions of the coordinate plane is referred to as a quadrant. Additionally, when we refer to the sections, we mean the sections as they are divided by the coordinate axes. The x-axis is located here, and the y-axis is located on this up-down axis. As you can see, it creates four portions on a coordinate plane.

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Answer:4

Step-by-step explanation:

im pretty sure its right

The probability of a random student being male or between the ages of 18 and 20 will be 0.07.

From the information, 55% of its students were male (M), 33% of its students were between the ages of 18 and 20 (A), and that 26% were both male and between the ages of 18 and 20.

Therefore, the probability of a random student being male or between the ages of 18 and 20 will be:

= 33% - 26%

= 7%

Therefore, the probability of a random student being male or between the ages of 18 and 20 will be 7%.

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The place value of the digit "6" in the given number 760,000 is Ten thousand's i.e., sixty thousand.

Definition of place value

The numerical value of the digit in the given number is based on its position in the number.

The place values are:

Hundred thousands(Hth) - 100,000

Ten thousands(Tth) - 10,000

Thousands(Th) - 1,000

Hundreds(H) - 100

Tens(T) - 10

Ones(O) - 1

Given number is 760,000

The place values for the given number are:

Hth  Tth  Th  H  T  O

7       6     0    0  0  0

So, the digit '6' is in the ten thousand's place. So, its place value is "ten thousand" i.e., "sixty thousand".

In math, every digit in more than a few has an area cost. place value can be described as the value represented by a digit in quite a number on the premise of its position within the number.

for instance, the region value of seven in 3,743 is 7 loads or seven-hundred. but, the place value of seven in 7,432 is 7 thousands or 7,000. here, we will see that despite the fact that the digits are identical in both the numbers, it’s region cost adjustments with the exchange in it’s position.

area value Chart is a completely beneficial table format that helps us in finding the place value of each digit primarily based on it’s function in various.

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we get that option (d) 2 x + 3 is a factor of the quadratic function g (x)= a x² - 7 x - 15.

We are given a quadratic function:

g (x)= a x² - 7 x - 15

We also know that 5 is a root for it.

So, we get that:

a (5)² - 7 (5) - 15 = 0

25 a - 35 - 15 = 0

25 a - 50 = 0

25 a = 50

a = 50 / 25

a = 2

So, the function becomes:

g (x)= 2 x² - 7 x - 15

Now factorizing the function:

2 x² - 7 x - 15

2 x² - 10 x + 3 x - 15

2 x ( x - 5 ) + 3 ( x - 5 )

( 2 x + 3 ) ( x - 5 )

Therefore, we get that option (d) 2 x + 3 is a factor of the quadratic function g (x)= a x² - 7 x - 15.

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Answer:

4 units

5 units

6.4 units

Step-by-step explanation:

we have two catheti, one measures 4 units and one measures 5 units, with Pythagoras we find the hypotenuse

hypotenuse = √(4²+5²)

hypotenuse = √(16 + 25)

hypotenuse = √41

hypotenuse = 6.4 units

Answer:The answer is -2 over 3

Step-by-step explanation:

The measures of the angles are <1 = 85, <2 = 105, <3 = 85 and <4 = 105

The diagram that completes the question is added as an attachment

From the diagram, we have

<1 + <2 = 180 degrees --- supplementary angles

Given that

<2 - <1 = 30 degrees

Add the above equations

So, we have

2<2 = 210

Divide both sides by 2

<2 = 105

Substitute <2 = 105 in <2 - <1 = 30

So, we have

105 - <1 = 30

Evaluate

<1 = 85

Also, we have

<3 = <1

<4 = <2

This means that

<3 = 85

<4 = 105

Hence, the measures of the angles are <1 = 85, <2 = 105, <3 = 85 and <4 = 105

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Answer:

6.7 ≈ 7

Step-by-step explanation:

Rounding rule x is supposed to be the decimal for this example

I hope that example helps you understand. If you have any concerns, ask me, but otherwise, have a great day!

The value of function R+Q is 14x+45.

A mathematical expression, rule, or law that establishes the relationship between an independent variable and a dependent variable (the dependent variable). In mathematics, functions are everywhere, and they are crucial for constructing physical relationships in the sciences.

Four broad categories can be used to classify different types of functions. dependent upon element Function is a one-to-one relationship, a many-to-one relationship, onto function, one-to-one and into function.

An output variable and one or more input variables are the minimum number of variables in a function. An equation can have any number of variables and declares that two expressions are equal (none, one, or more).

Disclaimer:

If the value of R = 2x+21, Q= 12 x + 24, P​ =2x-9, then find the value of R+Q ,where R and Q are functions.

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Answer: 1) slope of 2/3.

2) slope of -1/2

3) slope of 3

4) slope of -2/3

5) slope of undefined

6) slope of -1 1/2

7) slope of 1

8) slope of 0

Step-by-step explanation:

Answer:

4

Step-by-step explanation: