If the sum of a number and six is doubled, the result is three less than the number. Find the number.

Answer:

20x -64

Step-by-step explanation:

(−2)5x(−2)-3 2×2​

2x5x x2-32x2

20x-32 x 2

20x -64

Answer:

The statement is false. Vertical angles are the left and right angles of the four angles formed by two intersecting lines.

The sum of the numbers they wrote on the piece of paper is 2,305,843,009,213,693,954

What is Pythagoras's theorem?

The Pythagorean Theorem states that the squares on the hypotenuse (the side across from the right angle) of a right triangle or in standard algebraic notation, a² + b² = c², is equal to the squares on the legs.

What is the sum of numbers?

The outcome or conclusion we arrive at when we add two or more integers is known as the sum. Addends are the numbers that are added.

Here, we calculate the sum of the given numbers

= (1³)^²⁰  +  (1³)²⁰  +  (2³)²⁰  +  (-2³)²⁰

= 2,305,843,009,213,693,954

Hence, the sum of the numbers they wrote on the piece of paper is 2,305,843,009,213,693,954.

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a. The probability for each day is 1/2 and we expect him to seat for 10 days.

b The probability is 1/2 for each day and we expect her to seat for 50 days.

c. Jill will have a value closer to the expected value than Jack.

A. To know how many times Jack will get to ride in the front seat in the first 20 days, we can use the concept of probability of him seating there each day for the 20 days.

When the die is even, he get's to seat in the front seat.

The probability of each day will be 3/6 = 1/2

The probability for 20 days = 1/2 * 20 = 10 days.

b. Using similar concept, we can determine how many times Jill will seat in the front seat for 100 days.

Probability for each day = 1/2

For 100 days = 1/2 * 100 = 50 days.

C. From the probabilities of both events, over a longer period of trials, we expect Jill to have a value closer to the expected value than Jack.

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To find the total area of all three gardens, we need to calculate the area of one garden and then multiply it by three.

Each garden is in the shape of a square with a 3-foot by 3-foot section removed from each of the four corners. This means the side length of each garden's square portion is (16 ft - 3 ft) = 13 ft. Therefore, the area of one garden is (13 ft)^2 = 169 sq ft.

To find the total area of all three gardens, we multiply the area of one garden (169 sq ft) by three:

Total area = 169 sq ft/garden × 3 gardens = 507 sq ft.

Therefore, the total area of all three gardens is 507 square feet.

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Answer:

so then it to be 25000

Step-by-step explanation:

Answer:

He is right

Step-by-step explanation:

10/25 times 4/4 = 40/100

10 x 4 = 40

25 x 4 = 100

Answer:

Step-by-step explanation:

10/25  

simplest form is2/5

For 40/100

=8/20

=2/5 is the simplest form  

so he is right

Kyle's speed in feet per minute. That has to be what it is; if it's not, I am sorry. I hope this is the correct answer. Good luck.

Answer:

The Median is 75

Step-by-step explanation:

median is the middle number in a set of given numbers

arranging in order will be

30,64,70,80,90,110

the middle numbers are 70 and 80

Median=80+70/2

=150/2

Median=75

The median is the middle value when an odd number of data values are arranged in order.

The median is an important concept in statistics that helps to describe the central tendency of a dataset. When dealing with an odd number of data values, finding the median is straightforward. First, you need to arrange the values in either ascending or descending order. Once the data is ordered, the middle value is the median. For example, if you have the following dataset: 1, 3, 5, 7, 9. The median is the middle value, which in this case is 5. It is important to note that the median is not affected by extreme values or outliers. It is a reliable measure that represents the central value in a dataset.

In summary, when an odd number of data values are arranged in order, the middle value is known as the median. It is a measure of central tendency that helps to describe the middle value in a dataset.

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A cylindrical object is 3.13 cm in diameter and 8.94 cm long and weighs 60.0 g. The density of the cylindrical object is 0.849 g/cm^3.

To calculate the density, we first need to find the volume of the cylindrical object. The volume of a cylinder can be calculated using the formula V = πr^2h, where r is the radius (half of the diameter) and h is the height (length) of the cylinder.

Given that the diameter is 3.13 cm, the radius is half of that, which is 3.13/2 = 1.565 cm. The length of the cylinder is 8.94 cm.

Using the values obtained, we can calculate the volume: V = π * (1.565 cm)^2 * 8.94 cm = 70.672 cm^3.

The density is calculated by dividing the weight (mass) of the object by its volume. In this case, the weight is given as 60.0 g. Therefore, the density is: Density = 60.0 g / 70.672 cm^3 = 0.849 g/cm^3.

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The solution of the system of equations using Cramer's rule is x = 37/39 and y = 9/39.

The solution of the system of equations using Cramer's rule is calculated as follows;

The given equations are as follows;

9x - 2y = -9

-3x - 8y = 1

The determinant of the coefficient matrix is calculated as;

D = [9      -2]

      [-3     -8]

D = -8(9) - (-3 x - 2)

D = -72 - 6 = -78

The x coefficient is calculated as;

Dx = [-2      -9]

       [ -8       1]

Dx = -2(1) - (-8 x -9)

Dx = -2 - 72 = -74

The y coefficient is calculated as;

Dy = [9      -9]

       [ -3       1]

Dy = 9(1) - (-3 x -9)

Dy = 9 - 27 = -18

The x and y values is calculated as;

x = Dx/D  = -74/-78 = 74/78 = 37/39

y = Dy/D = -18/-78 = 18/78 = 9/39

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Answer:

15x^2-24x+9

Step-by-step explanation:

Answer:

198

Step-by-step explanation:

Make use of the multiples that can divide both of them until their remainders are both 1

Answer:

rational

Step-by-step explanation:

Answer:

Rational

Step-by-step explanation:

Rational numbers are numbers you can use in a ratio, basically things like negative/regular numbers, and fractions, decimals! Since you have a decimal negative number, it would be rational. It can't be Irrational because only numbers that are complicated

{ π, √10, and 1,271971910...)

The length of the longer leg of a 30-60-90 special right triangle is option 3) 17√3 yd.


In a 30-60-90 special right triangle, the ratio of the side lengths is 1 : √3 : 2, where the shortest leg is opposite the 30-degree angle, the longer leg is opposite the 60-degree angle, and the hypotenuse is opposite the 90-degree angle.

Given that the shorter leg is 17 yd, we can determine the length of the longer leg using the ratio. The longer leg is √3 times the length of the shorter leg. Therefore, the longer leg is 17√3 yd.

The answer options are:

17 yd (incorrect, this is the length of the given shorter leg)
17√2 yd (incorrect, this does not follow the ratio for a 30-60-90 triangle)
17√3 yd (correct, matches the ratio and is the length of the longer leg)
34 yd (incorrect, this is double the length of the shorter leg and does not follow the ratio).

Hence, the correct answer is option 3) 17√3 yd.

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The major methods of recording unstructured observational data are Narrative Description, Field Notes, Audio or Video Recording, Photography, Diagrams or Maps.

The major methods of recording unstructured observational data are:

1. Narrative Description: This method involves writing a detailed, chronological account of the observed events or behaviors, capturing the context and interactions as they occur naturally.

2. Field Notes: In this method, the observer takes brief, concise notes during the observation, focusing on key events, behaviors, or interactions. These notes can be expanded and organized later for further analysis.

3. Audio or Video Recording: Using audio or video equipment, the observer captures the events and interactions in their entirety. This allows for a more accurate record and the ability to review and analyze the data multiple times.

4. Photography: Taking photographs during the observation can provide a visual record of the events and behaviors. These images can supplement other data collection methods and help to illustrate specific aspects of the observation.

5. Diagrams or Maps: Drawing diagrams or maps of the observation setting can help capture the spatial relationships between individuals and objects, as well as the overall layout of the environment.

These methods can be used individually or in combination, depending on the research question and the specific needs of the study. Remember to always respect participants' privacy and obtain informed consent when necessary.

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The average value of a necklace at Julie's shop is $4.90. For further explanation;-

Julie the jeweler has two gold necklaces worth $105, seven silver necklaces valued at $100, twenty-seven plated necklaces valued at $55, and twenty-two beaded necklaces worth $25. The average value of a necklace at Julie's shop can be calculated by finding the sum of the values of all the necklaces and dividing it by the total number of necklaces.

The total value of all the necklaces is $105 + $100 + $55 + $25 = $285. The total number of necklaces is 2 + 7 + 27 + 22 = 58.

Therefore, the average value of a necklace is $285 / 58 = $4.90. This answer should be rounded to the nearest cent, giving an average value of $4.90 per necklace at Julie's shop.

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Answer:y=128.8 +25x

Step-by-step explanation:

Insurance plus the fee means that he has to pay $25 per day(x). 644•$0.2 is 128.8, so that represents how much driving 644 miles costs him.

Answer:

Each card will have a value of $15 when they equal after 600 days which also is 20 30-day periods.

Step-by-step explanation:

Card1: \(85 - \frac{3.50}{30} x\)

Card2: \(75 - \frac{3}{30} x\)

x is number of days

\(85 - \frac{3.50}{30} x = 75 - \frac{3}{30} x\)

2550 - 3.50x = 2250 - 3x

2550 - 0.50x = 2250

-0.50x = -300

x = 600 days

Card1: \(85 - \frac{3.50}{30} (600)\)

         85 - 70 = 15 dollars

Card2: \(75 - \frac{3}{30} (600)\)

         75 - 60 = 15 dollars

The value of each card will be when they have equal value is $15.

In mathematics, an equation is a formula that expresses the equality of two expressions by connecting them with the equal sign = .

Now, Let x be the number of time periods for which the gift card is not used, then

For the gift card $ 85 if it is not used for x periods, then the amount that will be lost is

85 - 3.50 x---------------------(1)

For the gift card $ 75 if it is not used for x periods, then the amount that will be lost is

75 - 3x---------------------- (2)

Now when both the amount lost is equal

85 - 3.50 x = 75 - 3x

solving the equation, we get

or, 3.50 x - 3x = 85 -75

or, 0.50 x = 10

or,  x = 20

Thus the value of gift cards will be equal for 20 ,30 day periods.

Now,the value of each card be when they have equal​ value

The two cards  will have equal value after 20, 30 day periods, this denotes that at this time, the value of each card will be equal.

Then

85 - 3.50 x = 75 - 3x

substituting  x = 20, we get

85 - 3.50*20 = 75 - 3*20

85 - 70  = 75 - 60

15  = 15

So, when they have equal​ value, the value of each card will be $15.

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Answer:

92 units^2

Explanation:

Assuming both sides are congruent.

Answer:

The gradient of the line segment between the points (1,-1) and (3,-13) is -6

Step-by-step explanation:

We need to find the gradient of the line segment between the points (1,-1) and (3,-13)

The gradient is basically the slope of line.

The formula used to calculate slope\gradient is: \(Slope=\frac{y_2-y_1}{x_2-x_1}\\\)

We have \(x_1=1, y_1=-1, x_2=3, y_2=-13\)

Putting values and finding slope

\(Slope=\frac{y_2-y_1}{x_2-x_1}\\\\Slope=\frac{-13-(-1)}{3-1} \\Slope=\frac{-13+1}{2} \\Slope=\frac{-12}{2}\\Slope=-6\)

So, gradient of the line segment between the points (1,-1) and (3,-13) is -6

The distance between the two planes after 4 hours is approximately 150 km.

to find out how far apart the planes are after 4 hours, we can use the concept of vectors.

Let's start by finding the positions of the two planes after 4 hours.

The first plane flies at a speed of 110 km/h in a direction of 280°. To find its position after 4 hours, we can use the formula: distance = speed × time. So, the distance traveled by the first plane is 110 km/h × 4 hours = 440 km.

To determine the position of the first plane, we need to convert the direction (280°) into components. The x-component is given by: cos(280°) × distance = cos(280°) × 440 km. The y-component is given by: sin(280°) × distance = sin(280°) × 440 km.

Similarly, for the second plane, which flies at a speed of 250 km/h in a direction of 200°, the distance traveled after 4 hours is 250 km/h × 4 hours = 1000 km. To determine its position, we need to convert the direction (200°) into components. The x-component is given by: cos(200°) × distance = cos(200°) × 1000 km. The y-component is given by: sin(200°) × distance = sin(200°) × 1000 km.

Now, let's calculate the x and y components for both planes:

For the first plane:
x-component = cos(280°) × 440 km
y-component = sin(280°) × 440 km

For the second plane:
x-component = cos(200°) × 1000 km
y-component = sin(200°) × 1000 km

the distance between the two planes, we can use the distance formula, which is given by: distance = √((x2 - x1)^2 + (y2 - y1)^2), where (x1, y1) and (x2, y2) are the positions of the first and second planes respectively.

Now, substitute the values we calculated into the distance formula:

distance = √((x2 - x1)^2 + (y2 - y1)^2)
distance = √((cos(200°) × 1000 km - cos(280°) × 440 km)^2 + (sin(200°) × 1000 km - sin(280°) × 440 km)^2)

After evaluating the above expression, the distance between the two planes after 4 hours is approximately 150 km.

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Answer:

n=3 x=225,000km

Step-by-step explanation:

1hour=60mins

20:60

1:3

n=3

1/25000=9/x

x=9×25000

x=225,000km

hope it helps:)

Using proportions, some equivalent measurements are given as follows:

A proportion is a fraction of a total amount, and equations can be built to find the desired measures in the problem using a rule of three, that can be either direct(cross multiplication) or inverse(line multiplication), deriving from proportional relationships. One example of application of proportions is for unit conversion problems, as unit conversion involve rates between the variables.

Each meter has 100 centimeters, hence:

1 centimeter - 0.01 meters.

Each hour has 60 minutes, hence:

Each feet has 12 inches, hence:

3 and 1/3 feet - 40 inches.

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The simplified expression is given by (x² - 3x - 3) / ((x + 3)(x - 2)(x - 4)).

To simplify this expression, we need to find a common denominator for the two fractions and then combine them. To do this, we need to factor the denominators of both fractions.

Let's start with the first fraction's denominator:

x² + x - 6

We need to find two numbers that multiply to -6 and add to +1. These numbers are +3 and -2. Therefore, we can write:

x² + x - 6 = (x + 3)(x - 2)

Now let's factor the second fraction's denominator:

x² - 6x + 8

We need to find two numbers that multiply to 8 and add to -6. These numbers are -2 and -4. Therefore, we can write:

x² - 6x + 8 = (x - 2)(x - 4)

Now we can rewrite the original expression with a common denominator:

(x(x - 2) - (1)(x + 3)) / ((x + 3)(x - 2)(x - 4))

Next, we can simplify the numerator:

(x² - 2x - x - 3) / ((x + 3)(x - 2)(x - 4))

(x² - 3x - 3) / ((x + 3)(x - 2)(x - 4))

Finally, we can't simplify this expression any further. Therefore, the simplified expression is:

(x² - 3x - 3) / ((x + 3)(x - 2)(x - 4))

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