Please Answer in ( a + bi ) form

For converting fractions to decimals, we need to divide numerator with denominator,

So, the value of 51/16 as a decimal is equal to 3.1875.

In mathematics, the ratio of two integers is how a fraction is defined in mathematics.

The fraction indicates that it is the numerator value to denominator value ratio.

A decimal number is one in which the decimal point separates the whole number component from the decimal component.

From the question,

As we need to convert the given fractional value to decimal.

So, for determining the equivalent decimal value, we will simply divide the value given in the numerator to the value given in the denominator.

So, dividing 51 by 16

We will get it as:

51/16: 51 16 = 3.1875

As a result, 51/16 is equivalent to 3.1875 in decimal form.

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The correct answer will be V =8×6×3 & V= 48×3. The volume of a rectangular prism = Length x Width x Height.

Volume is the quantity of space a thing occupies, whereas capacity is a measure of the substance it can store, such as a solid, a liquid, or a gas. Although capacity can be measured in virtually any other unit, such as litres, gallons, pounds, etc., volume is determined in cubic units.

Capacity. The total volume of space an object occupies in three dimensions is indicated by its volume. The term "capacity" describes something's ability to contain, absorb, or absorb by an object (such as a solid substance, gas, or liquid).

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The conversion of 52 degree F into Celsius is 11.11 Degree Celsius.

The same attribute is expressed using a unit conversion, but in a different unit of measurement. For instance, time can be expressed in minutes rather than hours, and distance can be expressed in kilometres, feet, or any other measurement unit instead of miles.

Given:

C= 5/9 (F- 32)

and, F = 9/5C + 32

We have F= 52 F put the value to Celsius Formula

C = 5/9 (52- 32)

C = 5/9 (20)

C = 100/ 9

C= 11.11

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The square that must be cut from each corner of the cardboard to form a box with a volume of 189 cubic inches is 3 inches on each.

Four equal sides and four right angles make up the two-dimensional shape known as the square. It is one of the most prevalent geometric shapes. There are a variety of useful applications for squares, including constructing tiling, patterns, and grids.

Given:

Length = 15 - 2x

Width = 13 - 2x

So, volume = lwh

189 = (15- 2x) (13 -2x) x

189 = (195 - 30x - 26x + 4x²)x

195x -56x² + 4x³ = 189

4x³ - 56x² + 195x - 189 = 0

On solving the cubic equation we get

x= 1.69, 3 and 9.3

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Answer: 40.6

Step-by-step explanation:

first you write the formula (a= a+b divided by 2 times h)

11+3 divided by 2 times 5.8

14 divided by 2 = 7 times 5.8

The correct answer is 40.6

Now that we know the value of x, we can find the values of DP, PH, and HD:

DP = 17x = 17(0.295) = 5.015

PH = 6x + 5 = 6(0.295) + 5 = 6.77

HD = 20x - 3 = 20(0.295) - 3 = 2.9

Therefore, DP ≈ 5.015, PH ≈ 6.77, and HD ≈ 2.9.

The perimeter of a form is its edge's radius. Learn how to multiply the lengths of a shape's sides to determine its perimeter.

To solve this problem, we need to use the fact that the perimeter of ADPH is 23.5. We know that AD = DP + HD, and we also know the values of DP, PH, and HD in terms of x. So, we can set up an equation using these values and solve for x.

AD = DP + HD

AD = 17x + (20x - 3)

AD = 37x - 3

Perimeter of ADPH = AD + DP + PH + HD

23.5 = (37x - 3) + 17x + (6x + 5) + (20x - 3)

Simplifying the above equation, we get:

23.5 = 80x - 1

Solving for x, we get:

x = 0.295

Now that we know the value of x, we can find the values of DP, PH, and HD:

DP = 17x = 17(0.295) = 5.015

PH = 6x + 5 = 6(0.295) + 5 = 6.77

HD = 20x - 3 = 20(0.295) - 3 = 2.9

Therefore, DP ≈ 5.015, PH ≈ 6.77, and HD ≈ 2.9.

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The height of the silo is approximately 81 meters to the nearest meter.

One of the most basic areas of mathematics, trigonometry has a wide range of applications. The study of the relationship between the sides and angles of the right-angle triangle is essentially the focus of the field of mathematics known as "trigonometry."

Let's draw a diagram to visualize the situation. We have a right triangle with the transit (T), the silo (S), and a point on the ground (G) where the surveyor is standing. The angle of elevation of the silo from the surveyor's position is 52º, and we know the distance TG = 65 m and the height of the transit HT = 1.7 m. We want to find the height of the silo, which is HS.

          S

          |\

          | \

    HS |  \  TG = 65 m

          |   \

          |    \

          |     \

          |      \

          |       \

          |        \

          T--------G

             HT = 1.7 m

Using trigonometry, we have the following equation:

tan(52º) = HS / TG + HT

Solving for HS, we get:

HS = (TG + HT) * tan(52º)

= (65 + 1.7) * tan(52º)

≈ 81.1 m

Therefore, the height of the silo is approximately 81 meters to the nearest meter.

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The relationship between quart to ml is that 1 quart is equal to 946.6 mililitres.

Quart and ml both are the unit of volume. ml is abbreviated form of mililitres and the two units are related together. Here is how they are related -

1 quart is equal to 946.6 mililitres.

Thus, in this method we can simply relate and calculate the quart amount of liquid in mililitres. Let us interpret the above mentioned statement through example. For instance, we need to know the mililitres in 0.25 quart. Here is how we will solve this.

Quantity in mililitres = quantity in quart × amount of mililitres in one quart

Quantity of mentioned liquid in mililitres = 0.25 × 946.4

Performing multiplication on Right Hand Side of the equation

Quantity of mentioned liquid in mililitres = 236.6 mililitres

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The value which is converted from Celsius to Fahrenheit is given by 38 Celsius is equal to 89.6 Fahrenheit.

Units which represents the measurement of the temperature in standard form Celsius and Fahrenheit .

Formula which relates the Celsius and Fahrenheit are given by

(°C × 9/5) + 32 =°F

Now Substitute the value 32 Celsius which needs to convert  into Fahrenheit we get,

(32°C × 9/5) + 32

= ( 288 / 5 ) + 32

= ( 57.6 ) + 32

= 89.6°F

Therefore, the converted value from Celsius to Fahrenheit for the given 32 Celsius is given by 89.6 Fahrenheit.

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The above question is incomplete , the complete question is:

What is the conversion of 32°C to °F ?

The formula for a solid sphere is V = 4/3πr³

A sphere is a geometrical entity with three dimensions that resembles a two-dimensional circle. It is a group of points in three dimensions that are all situated at the same r-distance from one another. The supplied point is the sphere's centre, while the letter r stands for the sphere's radius. It has a spherical, symmetrical shape.

It is a three-dimensional solid with equal distances between each surface point and the centre. On the basis of its radius, it has a surface area and a volume. There are no faces, corners, or edges on this geometrical figure. The formula for a solid sphere is V = 4/3πr³. Here V is the volume of the shape and r is the radius of the shape.

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The area of the teacher workroom is 64 feet squared

The range of the number of miles Maria jogged is 1 to 7.99

C. 1 to 7.99

What is the histogram?

A histogram is a graph used to represent the frequency distribution of a few data Set of one variable.

Let's recall that for calculating the range of a data set, we have to find out the lowest and the highest values of the data set.

As we can see in the graph below, the lowest value in the histogram is 1 and the highest is 7.99, therefore the correct answer is:

Hence, the range of the number of miles Maria jogged is 1 to 7.99

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Randomization in an experiment is important because it ensures that the results achieved are accurate .

Randomization in an experiment refers to a random assignment of participants to the treatment in an experiment .

Randomizing the experiments can help you get the best cause-effect relationships among the variables. It helps in controlling the lurking variables . These variables can affect the results to be different from what they are supposed to be . Randomization prevents biases and makes the results fair.

For ensuring that the information obtained from the experiment is correct, A randomized experiment is perfect to help us .

Researchers control values of the explanatory variable with a randomization procedure. So, if we see a relationship between the explanatory variable and response variables, we can say that it is a causal one.

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Answer:

Here is how to write and graph an inequality for the budget problem:

Let x be the number of large boxes and y be the number of small boxes. The total cost of the boxes must be less than or equal to the budget of $500. So, we can write the inequality as:

65x + 35y ≤ 500

To graph this inequality, we need to find the boundary line and the shaded region. The boundary line is the equation that we get when we replace the inequality sign with an equal sign, which is:

65x + 35y = 500

To graph this line, we need to find two points on it. We can do this by plugging in some values for x or y and solving for the other variable. For example, if x = 0, then y = 500/35 = 14.29. If y = 0, then x = 500/65 = 7.69. So, two points on the line are (0, 14.29) and (7.69, 0). We can plot these points on a coordinate plane and draw a solid line through them, since the inequality includes the equal sign.

To find the shaded region, we need to test a point that is not on the line and see if it satisfies the inequality. For example, we can test the point (0, 0), which is the origin. Plugging in x = 0 and y = 0 into the inequality, we get:

65(0) + 35(0) ≤ 500

0 ≤ 500

This is true, so the point (0, 0) is a solution to the inequality. This means that the shaded region is the area that includes the point (0, 0) and is below the line.

If Renaldo buys 6 small gift boxes, then y = 6. To find how many large gift boxes he can afford, we need to plug in y = 6 into the inequality and solve for x. We get:

65x + 35(6) ≤ 500

65x + 210 ≤ 500

65x ≤ 290

x ≤ 290/65

x ≤ 4.46

This means that Renaldo can buy at most 4 large gift boxes if he buys 6 small gift boxes. However, since x has to be a whole number, the largest possible value for x is 4. So, Renaldo can buy 4 large gift boxes and 6 small gift boxes and still stay within his budget.

I hope this helps!

Step-by-step explanation:

The conversied value of 152 centimetres in feet is equals to the 4.98 feet.

Unit conversion, by definition, is the conversion between different units and measurements of the same quantity done in the process of multiplication or division. In mathematics, conversion is the process of changing a value from one form to another, such as converting a value from inches to millimeters, for time minutes to hours, or other units.

How to convert centimeters to feet : 1 meter is a measure of length and equals approximately 3.28 feet.

152 meters = 152×3.28 feet = 498.56 feet --(1)

But we need to convert 152 centimeters to feet. So change meters to centimeters. As you know, 1 meter is 100 centimeters, so 152 meters = 15200 centimeters --(2). Now from equations (1) and (2),

15200 centimeters = 498.56 feet,

Divide both parts by 100,

=> 152 centimetres = 498.56/100 feet

= 4.98 feet

Hence required value is 4.98 feet.

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Answer:

Step-by-step explanation:

(90 +100) / 2 = 190/2 = 95

Answer:

The correct answer is B. 60 and 64. When y is directly proportional to x, it means that the ratio of y to x remains constant. In this case, when x=6, y=36, which means that the ratio of y to x is 36/6. Since the ratio is constant, we can use that ratio to find the values of y when x=8 and x=10. When x=8, y = (36/6)x8 = 60 and when x=10, y = (36/6)x10 = 64.

1. Option B. A correlation exists between two variables when higher values of one variable consistently go with higher or lower values of another variable

2. Option C. Amount of smoking and lung cancer, height and weight of people, price of a good and demand of the good

Examples of pairs of variables that are correlated:

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An equation describing r as a function of A and π is r = √(A/π).

Mathematically, the area of a circle can be calculated by using this formula:

A = πr²

Where:

In this exercise, you are required to make "r" the subject of the formula in the given mathematical expression by using the following steps.

By dividing both sides of the mathematical expression by π, we have the following:

r² = A/π

By taking the square root, we have:

r = √(A/π)

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Complete Question:

Make r the subject: A = πr²

The equation tan(30°) = 5/b can be used to solve for b. The solution has been obtained by using trigonometry.

What is trigonometry?

The study of the sides, angles, and connections of the right-angle triangle falls under the purview of the branch of mathematics known as trigonometry.

We are given a right angled triangle, with angle BCA = 90° and angle CAB = 30°. Also, the length of side BC is 5 centimeters, the length of BA is 10 centimeters, and the length of CA is b.

Using trigonometry,

We know that tan theta = opposite side/ adjacent side

So,

⇒tan θ = 5/b

Here, θ = 30°

So,

⇒tan 30° = 5/b

Hence, the equation tan(30°) = 5/b can be used to solve for b.

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The explicit formula for the nth term of the sequence 14,16,18,... is aₙ = 2n + 12.

What is an explicit formula?

The explicit equations for L-functions are the relationships that Riemann introduced for the Riemann zeta function between sums over an L-complex function's number zeroes and sums over prime powers.

Here, we have

Given:  the sequence 14,16,18,….

First term a₁ = 14

Common difference d = 16 - 14 = 2

Now, plug the values into the above formula and simplify.

aₙ = a₁ + d( n - 1 )

aₙ = 14 + 2( n - 1 )

aₙ = 14 + 2n - 2

aₙ = 14 - 2 + 2n

aₙ = 2n + 12

Hence,  the explicit formula is aₙ = 2n + 12.

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The possibility of any other range other than 13-6 through 17-10 with several recurring values (mode) is not possible because mean 12 is the median. Hence, I went with 16 and 9.

The mean of a dataset, sometimes referred to as the arithmetic mean, is the sum of all results multiplied by the number of values . This is the most popular way to measure central tendency and is sometimes refereed to as the "mean." This is obtained by dividing the total total of values within the dataset by the sum of the values. Calculations may be performed using both raw data and information that has been compiled into frequency tables. The average of a number is referred to as average. Calculating the following is easy: After adding all the digits, divide by the number of digits. the sum split by the count.

The query is not complete. It would still be 9 and 16 if the question asked for the two numbers that may represent the lowest and highest scores.

9 numbers in total. List them in descending order. Your Median is the middle number. The gap between the greatest and the lowest number called the range. The probabilities are therefore 8-1, 9-2, 10-3, 11-4, 12-5, 13-6, 14-7, 15-8, 16-9, 17-10, 18-11, and 19-12. The possibility of any other range other than 13-6 through 17-10 with several recurring values (mode) is not possible because 12 is the median. Hence, I went with 16 and 9.

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The conventional conversion rates state that 1.72 is equivalent to 5.504 feet.

We use the unit of the meter to measure the distance between any two objects, but we may also use the unit of the foot for short distances because these two units are interchangeable.

One meter is equivalent to 3.2 feet using common conversion factors used in the US.

The measurement of 1.72 metres into feet may be determined using the same conversion factor.

We shall thus write 1 m = 3.2 ft.

1.72m is 1.78 x 3.2 feet, or 5.504 feet.

The result is that 1.78 meters is equivalent to 5.696 feet.

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The volume of each soup can is approximately 785.4 cubic centimeters.

The volume of a cylinder can be calculated using the formula:

Volume =[tex]\pi[/tex] ×[tex]radius^2[/tex]× height

where π (pi) is a mathematical constant approximately equal to 3.14159, the radius is the distance from the center of the circular base of the cylinder to its edge, and height is the vertical distance between the circular bases.

In other words, the volume of a cylinder is the amount of space occupied by the cylinder, and it depends on the size of the circular base and the height of the cylinder.

In this case, the radius of the can is given as centimeters and the height is also given as centimeters. So, we can substitute these values in the formula and calculate the volume:

Volume = π × [tex]radius^2[/tex] × height

Volume = π ×[tex]5^2[/tex] × 10

Substituting radius = 5 cm and height = 10 cm

Volume = 250π cubic centimeters

Volume ≈ 785.4 cubic centimeters (rounded to one decimal place)

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Answer:

52.75

i hope it helps

The value of the residual for Shawna's weight and height is 12.4 and option 2 is the correct answer.

A linear equation is one that has the form Ax+By=C. This definition comes from mathematics. It consists of two variables combined with a constant value that exists in each of them.

The collection of all values that, when substituted for unknowns, cause an equation to hold true is known as the solution. Two fundamental algebraic rules using the additive property and the multiplicative property are utilised to determine the solutions for equations needing a single unknown raised to a power of one.

The equation given to predict the weight from height is:

ŷ = -260 + 6.6x

Given that, Shawna’s height was 64 inches.

Substituting the value in x we have:

ŷ = -260 + 6.6x

ŷ = -260 + 6.6(64)

ŷ = 162.4

The actual weight is given as 150 pounds.

The residual value of the weight from the predicted formula is:

r = 162.4 - 150

r = 12.4

Hence, the value of the residual for Shawna's weight and height is 12.4 and option 2 is the correct answer.

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Answer:

-12.4

Step-by-step explanation:

Answer: 1.65831239518

Step-by-step explanation:

The square root of 2.75 is defined as the only positive real number such that, multiplied by itself, it is equal to 2.75.The square root of 2.75 can be written as

(2.75)1/2. So,(2.75)1/2 = (1.6583123951777 × 1.6583123951777)1/2(2.75)1/2 = [(1.6583123951777)2]1/2(2.75)1/2 = (1.6583123951777)2/2(2.75)1/2 = (1.6583123951777)1Thus,√2.75 = 1.6583123951777

Answer:

x = 14°

z = 74°

Step-by-step explanation:

10x - 34° = 106° ( A.I.A )

x = 72°

106° + z = 180° ( linear pair axiom )

z = 74°

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Answer:

x=14°

z= 74°

Step-by-step explanation:

Here

(10x-34)°= 106°

since the Vertically Opposite Angle are equal.

so solving for it.

First, we can add 34° to both sides of the equation to get:

10x° - 34°+ 34° = 106° + 34°

Simplifying the left side gives:

10x° = 140°

Then we can divide both sides of the equation by 10 to get:

x = 14°

Again

z+106°=180°

since the sum of angle in the linear pair is equal to 180°

solving for it

we can subtract 106° from both sides of the equation to get:

z + 106° - 106° = 180° - 106°

Simplifying the left side gives:

z = 74°

MaryAnn can order a total of 213 prints for cost $35, including shipping.

Each print costs $0.15, so MaryAnn can order $35/$0.15 = 233.33 prints, but since she can only order whole prints, she can order a maximum of 233 prints.

The shipping charge is a flat fee of $3.00 per order, regardless of how many prints MaryAnn orders.

Let's say MaryAnn orders x prints, then her total cost would be:

Cost = $0.15 x + $3.00

Since her total cost can't exceed her budget of $35, we can set up the following inequality:

$0.15 x + $3.00 ≤ $35.00

Subtracting $3.00 from both sides, we get:

$0.15 x ≤ $32.00

Dividing both sides by $0.15, we get:

x ≤ 213.33

Since MaryAnn can only order whole prints, she can order a maximum of 213 prints.

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