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Answer:

2X+1 = 2 [ (1X/2)-1]

Solve the equation and represent the solution on the number line and on the Cartesian plane?

Given equation is 2X+1 = 2 [ (1X/2)-1]

=> 2X+1 = 2[(1X-2)/2]

=> 2X+1 = 2(X-2)/2

=> 2X+1 = X-2

=> 2X-X = -2-1

=> X = -3

Therefore, X = -3

The graph is parallel to Y-axis

The coordinates are (-3,0),(-3,1),(-3,2),...

On X - axis 1 cm = 1 unit

On Y - axis 1 cm = 1 unit

The solution for the given equation is -3.

Answer:

Step-by-step explanation:

Answer: Answer is 9

Step-by-step explanation:

Answer:

the answer to this question is C. 9

Step-by-step explanation:

To the nearest percent, the probability that an earthquake will occur while you are at work is approximately 23%.

The probability that an earthquake will occur while you are at work can be calculated by dividing the number of hours you are at work by the total number of hours in a year.
Step 1: Calculate the total number of hours in a year:
There are 24 hours in a day, so multiplying 24 by 365 (the number of days in a year) gives us 8,760 hours in a year.
Step 2: Calculate the number of hours you are at work in a year:
Since you work 8 hours per day, multiply 8 by 250 (the number of days you work in a year) to get 2,000 hours.
Step 3: Calculate the probability:
Divide the number of hours you are at work (2,000) by the total number of hours in a year (8,760) and multiply by 100 to convert to a percentage.
Probability = (2,000 / 8,760) * 100 = 22.83%
Therefore, to the nearest percent, the probability that an earthquake will occur while you are at work is approximately 23%.

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The approximate area between y=3x^(2)+1 and the x-axis on the interval -1 to 5 is 136.6875.

We can approximate the area between y=3x^(2)+1 and the x-axis on the interval -1 to 5 using a Riemann sum with 4 rectangles of equal width. The left-hand endpoint of each subinterval will be used.

The width of each rectangle is the length of the interval (5-(-1)) divided by the number of rectangles (4). Therefore, the width of each rectangle is

(5-(-1))/4 = 6/4 = 1.5.

Since we are using the left-hand endpoint of each subinterval, the x-values of the left-hand endpoints of the rectangles are

-1, -1+1.5

-1+1.5+1.5

-1+1.5+1.5+1.5 = -1+4.5=3.5

The height of each rectangle is determined by the value of y at the corresponding x-value.

Therefore, the heights of the rectangles are

3(-1)^2+1=2

3(-1+1.5)^2+1=7.125

3(3.5)^2+1=35.125

3(3.5+1.5)^2+1=46.875

The area of each rectangle is the product of its width and height, so the areas of the rectangles are

2*1.5=3

7.125*1.5=10.6875

35.125*1.5=52.6875

46.875*1.5=70.3125.

Therefore, the approximate area between y=3x^(2)+1 and the x-axis on the interval -1 to 5 is 136.6875.

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Answer: \(-2x^{2}+x+10\)

Step-by-step explanation:

Answer:

Answers below

Step-by-step explanation:

Radius = 3m

Diameter:

d = 2r

d = 2(3m)

d = 6m

Circumference:

c = 2πr

c = 2π(3m)

c = 6π m

c = 18.85 m

Area:

A = 2πr^2

A = 2π(3m)^2

A = 18π m^2

A = 56.55 m^2

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a) Common ratio R is 1/2.

b) Sum P0 + P1 + ... + P11 is 8190/4096.

a. To find the common ratio R, we need to divide any term by its previous term. Let's use P1 and P0:

R = P1 / P0 = 2 / 4 = 1/2

So, the common ratio R is 1/2.

b. To find the sum P0 + P1 + ... + P11, we will use the geometric sum formula, which is:

Sum = P0 * (1 - \(R^{n+1\)) / (1 - R), where n is the number of terms minus 1.

Here, P0 = 4, R = 1/2, and we have 12 terms (P0 to P11), so n = 11.

Now let's put the values into the formula:
Sum = 4 * (1 - (1/2)¹¹⁺¹) / (1 - 1/2)
Sum = 4 * (1 - (1/2)¹²) / (1/2)
Sum = 4 * (1 - 1/4096) / (1/2)
Sum = 4 * (4095/4096) / (1/2)
Sum = (4 * 4095/4096) * 2
Sum = 8190/4096

Thus, the sum P0 + P1 + ... + P11 is 8190/4096.

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Answer:

x = 106°

Step-by-step explanation:

180 - 74 = 106°

hope this helps, good luck :)

Answer:

x = 106

Step-by-step explanation:

The hypotenuse of the right triangle is y = x+6 and the value of x is y-6 which is one of the side adjacent to the right angle.

It is a type of triangle where one of the angles is 90 degrees and two of the sides are perpendicular to each other.

In a right triangle, the sides adjacent to the right angle are called legs and the longest side opposite the right angle is called the hypotenuse.

We can use the Pythagorean theorem to solve for x:

y² = x² + (6√2)²

y² = x² + 36

y² - 36 = x²

√(y² - 36) = x

y-6 = x

Therefore, the value of x is y-6.

Since we are given that the hypotenuse of the right triangle is y, we can substitute y for the value of x.

y² = x² + 36

y = √(x² + 36)

y = x+6

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The right triangle's hypotenuse is y = x+6, and the value of x is y-6, which is one of the sides close to the right angle.

The hypotenuse of a right-angled triangle is the longest edge in comparison to the length of the base and perpendicular. The hypotenuse side is the side opposing the right angle, which is the largest of all three perspectives in a right triangle. The hypotenuse is essentially a feature of only the right triangle and not any other triangle.

Pythagoras' theorem defines the hypotenuse theorem. According to this theorem, the square of a right-angled triangle's hypotenuse side is equivalent to the sum of the squares of its base and perpendicular, such that;

\(Base^2 + Perpendicular^2 = Hypotenuse^2\)

We can solve for x using the Pythagorean theorem:

y² = x² + (6√2)²

Simplify the above equation

y² = x² + 36

Substitute 'x' value

y² - 36 = x²

√(y² - 36) = x

y-6 = x

The value of x is y-6.

We can swap y for the value of x because we know the hypotenuse of the right triangle is y.

y² = x² + 36

y = √(x² + 36)

Simplify the above equation

y = x+6

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Let's assume the amount invested at the higher interest rate (16%) is x dollars.

The amount invested at the lower interest rate (6%) would then be ($80,000 - x) dollars, as the total investment is $80,000.

The interest earned from the investment at 16% is calculated as (x * 16%) = 0.16x dollars.

The interest earned from the investment at 6% is calculated as (($80,000 - x) * 6%) = 0.06(80,000 - x) dollars.

According to the given information, the retiree receives a total interest of $8,900 per year. So we can set up the equation:

0.16x + 0.06(80,000 - x) = 8,900

Now, let's solve the equation to find the value of x:

0.16x + 0.06(80,000 - x) = 8,900

0.16x + 4,800 - 0.06x = 8,900

0.1x + 4,800 = 8,900

0.1x = 8,900 - 4,800

0.1x = 4,100

x = 4,100 / 0.1

x = 41,000

Therefore, $41,000 is being invested at the higher interest rate (16%).

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The given expression is a series of fractions: 14/15, 13/15, -12/15, 11/15, -10/15, -4/15, 3/15, -2/15, 1/15. Simplifying this expression, we find that the sum reduces to -1/3.

1. To simplify the expression, we can combine the fractions with the same denominators. The denominators are all 15, so we can add the numerators to find the numerator of the simplified fraction.

2. Adding the numerators: 14 + 13 - 12 + 11 - 10 - 4 + 3 - 2 + 1 = 14 - 12 - 10 - 4 + 13 + 11 + 3 - 2 + 1 = 15 - 15 = 0.

3. The numerator is 0, and the denominator remains 15. Therefore, the simplified fraction is 0/15. However, we can further simplify this fraction by dividing both the numerator and denominator by their greatest common divisor (GCD), which is 15.

4. Dividing 0 by 15 gives 0, and dividing 15 by 15 gives 1. So, the simplified fraction is 0/15 = 0/1 = 0.

5. Thus, the sum of the given expression simplifies to -1/3 or 0, depending on how you interpret the fractions (as negative fractions or zero).

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Step-by-step explanation:

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Answer:

185 dimes and 73 quarters

Step-by-step explanation:

q + d = 258

25(q) + 10(d) = 3675

Answer:

1.25x + 1.5y=25

Step-by-step explanation:

let the number of lip balms that can be bought be x and the notebooks be y then their total cost is 1.25x + 1.5y. The total $25 there for the equation becomes 1.25x + 1.5y=25.

The required linear equation can be used to determine how many of each prize she can buy is 1.2x + 1.50y = 25.

Given that,
Jung-Soon has $25 to spend on prizes for a game at the school fair. Lip balm costs $1.25 each, and mini-notebooks cost $1.50 each. Write a linear equation that can be used to determine how many of each prize she can buy is ot be determined.

The equation is the relationship between variables and represented as y = ax + b is an example of a polynomial equation.

Here,
Let the number of lip balm that can be purchased be x,  and the number of mini notebooks purchased be y,
according to the question,
1.2x + 1.50y = 25

Thus, the required linear equation can be used to determine how many of each prize she can buy is 1.2x + 1.50y = 25.

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The exact value of cscθ is (35 * √(1190)) / 1190.

To find the value of cscθ (cosecant θ) given that cosθ = 1/√35 and sinθ < 0, we can use the reciprocal relationship between sine and cosecant.

Recall that cscθ is the reciprocal of sinθ. Since sinθ is negative, we can determine its value based on the quadrant in which θ lies.

In the unit circle, the cosine is positive in the first and fourth quadrants, while the sine is negative in the third and fourth quadrants.

Given that cosθ = 1/√35 and sinθ < 0, we can conclude that θ lies in the fourth quadrant.

Using the Pythagorean identity, sinθ = √(1 - cos^2θ), we can calculate the value of sinθ:

sinθ = √(1 - (1/√35)^2)

     = √(1 - 1/35)

     = √(34/35)

     = √34 / √35

     = (√34 / √35) * (√35 / √35)     [Multiplying numerator and denominator by √35 to rationalize the denominator]

     = √(34 * 35) / 35

     = √(1190) / 35

Now, since cscθ is the reciprocal of sinθ, we have:

cscθ = 1 / sinθ

     = 1 / (√(1190) / 35)

     = 35 / √(1190)

     = (35 * √(1190)) / 1190.

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Answer:

77 years old

Step-by-step explanation:

The length of arc BC is 8/3 feet.

To find the length of arc BC, we first need to find the measure of angle BOC, where O is the center of the circle. Since angle BAC is 1/3 of one radian, and the central angle BOC intercepts the same arc BC, we know that angle BOC is three times angle BAC, or one radian.

Since the radius of the circle is 8 feet, the circumference is 2πr, or 16π feet. Since angle BOC is one radian, it subtends an arc on the circumference that is 1/2 of the total circumference, or 8π feet.

Therefore, the length of arc BC is 1/3 of arc BOC, or 8π/3 feet.

To find the length of arc BC, we will follow these steps:

1. Identify the given information: The radius of the circle is 8 feet, and the angle BAC is 1/3 of a radian.

2. Determine the central angle in radians: Since angle BAC is 1/3 of a radian, the central angle (θ) of the circle that corresponds to arc BC is also 1/3 of a radian.

3. Calculate the length of arc BC using the formula: Arc length (L) = radius (r) × central angle (θ).

In this case, r = 8 feet and θ = 1/3 radian.

L = 8 × (1/3)
L = 8/3

4. Simplify the expression: L = 8/3 feet.

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Answer:

angle R = 23.5°

Step-by-step explanation:

we should know the total interior angle of a triangle is 180°

angle R + 47.5° + 109° = 180°

angle R = 180° - 47.5° - 109°

angle R = 23.5°

Answer:

x<-2

Step-by-step explanation:

17+4x<9

4x<-8

x<-2

The solution is:

Work/explanation:

Recall that the process for solving an inequality is the same as the process for solving an equation (a linear equation in one variable).

Make sure that all constants are on the right:

\(\bf{4x < 9-17}\)

\(\bf{4x < -8}\)

Divide each side by 4:

\(\bf{x < -2}\)

The rectangle. Since we're rotating it 90° clockwise about the origin, we can assume that the rectangle's sides are parallel to the x- and y-axes. Let's say the rectangle has vertices at (-2,1), (-2,-3), (4,-3), and (4,1).

To graph the rectangle after the rotation, we need to determine the new coordinates of each vertex. To do this, we'll use the following formula for a 90° clockwise rotation about the origin:
(x', y') = (y, -x)
The original coordinates and (x', y') are the new coordinates.
The first vertex, (-2,1). To find its new coordinates after the rotation, we plug in the original coordinates into the formula:
(x', y') = (y, -x)
= (1, -(-2))
= (1, 2)
(-2,-3) -> (-3, -(-2)) -> (-3, 2)
(4,-3) -> (-3, -4) -> (3, 4)
(4,1) -> (1, -4) -> (-1, -1)

Now we have the new coordinates for each vertex, so we can graph the rectangle by connecting the points with line segments. Starting with the first vertex, (-2,1), we'll draw a line segment to the second vertex, (-3,2). Then we'll connect the second vertex to the third vertex, (3,4), and so on until we've drawn all four sides of the rectangle.
The final graph of the rectangle after a 90° clockwise rotation about the origin looks like this:

      (1,2)     (3,4)
       *---------*
       |         |
(-2,1)  |         |  (-1,-1)
       |         |
       *---------*
    (-3,2)    (3,-4)

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Answer:

Colin will have $1,265 after three years.

Step-by-step explanation:

First, we find the amount of interest Colin will have by using the following formula,

simple interest = principal * interest rate * time

now that we know the formula, we substitute the numbers in.

simple interest = $1,100 * 5% * 3

since the interest rate is obviously a percentage, we have to convert it into a decimal.

simple interest = $1,100 * 0.05 * 3

now that it is a decimal, we can solve this expression.

simple interest = $1,100 * 0.05 * 3

simple interest = $55 * 3 (here, we did $1,100 * 0.05 first so that it doesn't get confusing with all the numbers, it will be easier with two final numbers)

simple interest = $165

Colin has $165 simple interest but over here asks how much she will have AFTER 3 years. think about it, can you have $165 after having $1,100 in your bank AFTER 3 years? no, so we need to add the interest by the principal by using the following formula,

total amount = principal + simple interest

now, we substitute the numbers in.

total amount = principal + simple interest

total amount = $1,100 + $165

total amount = $1,265  

Therefore, Colin will have $1,265 after 3 years.

Answer:

y=6

Step-by-step explanation:

Answer:

x+y= -6

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Answer:

Hi,

6

Step-by-step explanation:

the number divided by 5 has a remainder of 1 , its last digit is 1 or 6.

the number is divisible by 2, its last digit is 0 or 2,or 4, or 6 or 8.

Both conditions give : the last digit must be 6.

Answer:

x(13−29) is equivalent to the 13x - 29x.

Step-by-step explanation:

Consider the given expression 13x - 29x

Distributive property of real numbers,

Let a, b, c be three real numbers then  holds.

Here, using inverse of distributive property stated above,

We can take x common from both the terms,

13x - 29x = x( 13 -29 )

soooo x(13−29)

Answer:

-16x

Step-by-step explanation:

One of the equivalent expression can be found by combining the like terms and solve.

13x - 29x = -16x

-16x is an equivalent expresion to 13x-29x

The long jump pit was recently rebuilt to make it level with the runway.  the amount of wood, in meters, is 12.29 meters.

Generally, To determine the amount of wood needed in meters, you will need to convert the length of each piece of wood from feet to meters. You can use the conversion factor that 1 foot is equal to approximately 0.3048 meters.

To convert the length of the wood from feet to meters, you can use the formula:

length in meters = length in feet * 0.3048

Using this formula, you can calculate that 2.75 meters is equal to approximately 9 feet, and 9.54 meters is equal to approximately 31.25 feet.

Therefore, the total amount of wood needed in meters is 2.75 meters + 9.54 meters = 12.29 meters.

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A.) The statistical methods of analysis of variance (ANOVA) assume that the populations are normally distributed.
Answer: True

B.) Data from a completely randomized design are shown in the following table.
Treatment Level
1 2 3
27 26 27
26 22 29
23 21 27
24 23 26
For a one-way ANOVA, the Between Sum of Squares (SSB) is 28.75.

C.) For the following ANOVA table, the MS Treatment value is 50.
Source of Variation SS df MS F
Treatment 150 2 75 3.49
Error 40 20 2 Total 190 22

D.) The head of the math department at a local community college is interested in conducting an experiment to determine effective teaching strategies for improving student math comprehension and math literacy. In particular, she is interested in a new pedagogical model called "flipped classroom," in which the typical lecture and homework elements of the course are reversed. Short video lectures are viewed by students at home before the class session, while in-class time is devoted to exercises, projects, or discussions. For this purpose, the math head will have half of the sections of Calculus II this coming semester be taught in the traditional setting, while the other half will use the flipped classroom model. In this experiment, the independent variable has 2 levels.

E.) Data from a completely randomized design are shown in the following table.
Treatment Level
1 2 3
27 26 27
26 22 29
23 21 27
24 23 26
For a one-way ANOVA, the Error Sum of Squares (SSE) is 64.92.

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