What will be the class interval of a data set with 30 elements

Answers

Answer 1

The class interval of a data set with 30 elements is 5.

The range of a data set is the difference between the largest and smallest values in the set. Once the range is calculated, the class interval can then be calculated by dividing the range by the number of elements in the set.

In the case of a data set with 30 elements, the class interval can be calculated by dividing the range of the data set by 30. This will tell us the size of the intervals that the data is divided into.

If the range of the data is 150, the class interval would be 150/30, which is equal to 5. Therefore, the class interval of the data set would be 5.

It is important to note that the class interval should be chosen so that it is not too small or too large. If the class interval is too small, the data may become too granular, making it difficult to interpret. If the class interval is too large, important details about the data may be lost

To know more about interval here

https://brainly.com/question/30486507

#SPJ4


Related Questions

what is 36 cube root?

Answers

The cube root of 36 is a number between 3 and 3.5, and can be represented mathematically as ∛36.

Square roots are simply the opposite operation of squaring a number. For example, the square root of 9 is 3 because 3 x 3 = 9.

Similarly, the cube root is the opposite operation of cubing a number. The cube root of a number is the value that, when cubed, gives the original number. For instance, the cube root of 27 is 3 because 3 x 3 x 3 = 27.

Now, to answer your question, "What is 36 cube root?" - this can be written as ∛36 or as the cube root of 36. To find the cube root of 36, we need to find a number that, when cubed, gives 36.

We can start by using trial and error. We know that 2 x 2 x 2 = 8, which is less than 36. We also know that

=> 3 x 3 x 3 = 27, which is less than 36.

So, we can try a number between 3 and 4. Let's try 3.5.

If we cube 3.5, we get 42.875, which is greater than 36.

If we try a number lower than 3.5, we will get an even greater value. Therefore, the cube root of 36 is between 3 and 3.5.

We can use more precise methods to find the cube root of 36, such as using a calculator or estimating with decimal approximations. However, using trial and error is a simple and effective way to find an approximate answer.

To know more about cube root here

https://brainly.com/question/30038389

#SPJ4

A certain automotive dealer sells only cars and trucks, and the ratio of cars to trucks on the lot is 1 to 3. If there are currently 51 trucks for sale, how many cars does the dealer have for sale?(A) 17(B) 34(C) 68(D) 153(E) 204Spoiler: OA

Answers

The ratio of cars to trucks is 1 to 3, which means that for every three trucks, there is one car. Since there are 51 trucks, this means that there is 17 cars (51/3 = 17). Therefore, the dealer has 17 cars for sale.

The automotive dealer sells both cars and trucks and the ratio of cars to trucks on the lot is 1 to 3. This means that for every three trucks, there is one car. Therefore, if there are 51 trucks currently for sale, then the number of cars can be determined by dividing this number by 3. This equals 17 cars. Thus, the dealer has 17 cars for sale.

The ratio of cars to trucks is 1 to 3, which means that for every three trucks, there is one car. Since there are 51 trucks, this means that there is 17 cars (51/3 = 17). Therefore, the dealer has 17 cars for sale.

Learn more about ratio here

https://brainly.com/question/13419413

#SPJ4

PLEASE HELP ME
What is the value of x in this triangle?

Answers

Answer:

x = 39

Step-by-step explanation:

We need to solve for the interior angle measure. The sum of a triangle's interior angle measures are 180, so we just have to create an equation and solve for x.

[tex]x+102+39=180[/tex]

Add like terms

[tex]x+141=180[/tex]

Subtract 141 on both sides

[tex]x=39[/tex]

To check our work, we can add the angle measures together to see if they add up to 180.

[tex]39+102+39 = 180[/tex]

What is the value of R in an appropriate degree of accuracy

Answers

Answer:

Finished

Step-by-step explanation:

-Multiple the exponents together

-keep ×10 the same so you can apply the second law of exponents

-Then divide and subtract the exponents of ×10

-Let the 14.44 and 5.9 divide each other

-Leave it like that because it's standard form

Sam does a weekly exercise program consisting of cardiovascular work and weight training. Each week, he exercises for at least 10 hours. He spends at most 7 hours doing cardiovascular work. He spends at most 6 hours on weight training. Let × denote the time (in hours) that Sam spends doing cardiovascular work.
Let y denote the time (in hours) that he spends on weight training. Shade the region corresponding to all values of x and y that satisfy these requirements.

Answers

So, in response to the above question, we can state that We obtain the inequality following system of inequalities by combining these three constraints:

[tex]x + y \geq 10\\x \leq 7\\y \leq 6[/tex]

What is inequality?

An inequality in mathematics is a relationship between two expressions or values that is not equal. Thus, imbalance leads to inequality. An inequality creates the link between two values that are not equal in mathematics. Egality is distinct from inequality. When two values are not equal, most commonly use the not equal sign (). Different inequalities are used to contrast values, no matter how little or large. Many simple inequalities may be resolved by modifying the two sides until the variables are all that remain. But a number of things contribute to inequality: Negative values on both sides are divided or added. Trade off the left and right.

[tex]x + y \geq 10[/tex]

Next, we know that Sam works out his cardiovascular system for no more than 7 hours. Thus, x must be less than or equal to 7. This restriction can be shown by the inequality:

[tex]x \leq 7[/tex]

Finally, we are aware that Sam only devotes a maximum of 6 hours to weight training. This implies that y should be between -6 and -6. This restriction can be shown by the inequality:

[tex]y \leq 6[/tex]

We obtain the following system of inequalities by combining these three constraints:

[tex]x + y \geq 10\\x \leq 7\\y \leq 6[/tex]

To know more about inequality visit:

brainly.com/question/29914203

#SPJ1

1.you buy a car for $10,000. every year, the car loses 25% of its value. how would the function rule change if the car lost 10% of its value each year? and why does the function rule include 0.75 instead of 0.25?

2. You start a job making $10 per hour. at the end of each year, you earn a 10% raise. how will the function rule change if the annual raise is 8%?

Answers

The automobile is currently worth Rs 52,488. four years ago, it was worth 80,000.

What is Depreciation rate?The depreciation rate is the total amount depreciated each year, expressed as a percentage. For instance, if a business depreciated an asset at a rate of $15,000 per year for ten years, the total depreciation would be $100,000. This indicates that the rate would be 15% annually. To calculate depreciation using the straight-line method, the asset's salvage value, or what you expect it to be worth at the end of its useful life, must be deducted from the asset's cost.Depreciable basis, or the amount that may be written off, is the outcome. By how many years the asset will be useful, divide this sum.

Present Value A = Rs. 52,488

Depreciation rate r = 10 % per annum

Time t = 4 years

Let initial value be P

We know the formula, A =[tex]$\mathrm{P}\left(1-\frac{\mathrm{r}}{100}\right)^t$[/tex]

We obtain by substituting the supplied values.

52,488 =[tex]$\mathrm{P}\left[1-\frac{10}{100}\right]^4 \\[/tex]

52,488 = [tex]$\mathrm{P}(0.9)^4 \\[/tex]

[tex]$\mathrm{P}=\frac{52488}{0.6561} \\[/tex]

P = 80,000

The complete question is:

The value of a car depreciates every year at the rate of 10% on its value at the beginning of the year. If the present value of the car is Rs 52,488 its worth four years ago was

To learn more about Depreciation rate, refer to:

https://brainly.com/question/28201276

#SPJ1

You need to pay 8% tax on a car that costs $12,000. What will you end up paying in total? Show your reasoning

Answers

$12,960 is the answer I believe

1% of 12,000 is 120

120 times 8 is 960

12,000 plus the tax (960) = 12,960

Work out the number of sides of a regular polygon with interior angle 177

Answers

[tex]\underset{in~degrees}{\textit{sum of all interior angles}}\\\\ n\theta = 180(n-2) ~~ \begin{cases} n=\stackrel{number~of}{sides}\\ \theta = \stackrel{degrees}{angle}\\[-0.5em] \hrulefill\\ \theta =177 \end{cases}\implies n(177)=180n-360 \\\\\\ 177n=180n-360\implies 0=3n-360\implies 360=3n \\\\\\ \cfrac{360}{3}=n\implies 120=n[/tex]

Ellie is going to see a movie and is taking her 2 kids each movie ticket costs $13

Answers

Answer:

3x13=39

Step-by-step explanation:

ellie=13

kid 1=13

kid 2 =13

Which of the following is not an equivalent fraction of 1830?


610


25


35


1220

Answers

Which of the following is not an equivalent fraction of 1830, the correct answer is (option A)

What does equivalent fraction mean?

Fractions that represent the same value

Equivalent fractions are fractions that represent the same value, even though they look different. For example, if you have a cake, cut it into two equal pieces, and eat one of them, you will have eaten half the cake.

To find equivalent fractions, you just need to multiply the numerator and denominator of that reduced fraction (35) by the same natural number, ie, multiply by 2, 3, 4, 5, 6... Important: 1830 looks like a fraction, but it is actually an improper fraction. 610 is equivalent to 1830 because 3 × 25 × 2 = 610.

Hence, Which of the following is not an equivalent fraction of 1830, the correct answer is (option A)

Learn more about equivalent fraction here:

https://brainly.com/question/13023052

#SPJ3

Dawn took a picture of five airplanes at a local airshow. Each
airplane left a vapor trail behind them.
Airplane 1
Airplane 2
Airplane 3
4000
Airplane 4
Kood
Airplane 5.
4000
719
105
Which two planes created parallel trails?
110°
104

Answers

The two planes that have created the parallel traits would be airplane 3 and airplane 5

How to get the parallel lines

To get the parallel lines, we would have to check the angles that are formed

for angle 3 angles on a line is 180

x + 110 = 180

x = 70 degrees

For angle 5

we can see that the position of x in 3 is the same position in 5

hence we can see that in plane 5, x = 70

hence these two would be parallel

Read more on parallel lines here:https://brainly.com/question/24607467

#SPJ1

can someone help me with the first one please!!!!

Answers

The perimeter of the trapezoid ABFE and the prove that the triangle ΔABC is an isosceles are as follows;

First question;

The perimeter of the trapezoid ABFE is 100 units

Second question;

The sides AB and BC in the triangle ΔABC are congruent, therefore, triangle ΔABC is an isosceles triangle

What is an isosceles triangle?

An isosceles triangle is a triangle that has two sides that have the same lengths.

The specified parameters are;

The segment joining the midpoints of the side [tex]\overline{AC}[/tex] and [tex]\overline{BC}[/tex] of the equilateral triangle ΔABC = EF

EF = 2·x + 8 and AB = 7·x - 2

The midsegment theorem applied to the triangle ΔABC indicates that we get;

EF = (1/2) × AB

Therefore; 2·x + 8 = (1/2) × (7·x - 2)

(1/2) × (7·x - 2) = 2·x + 8

7·x - 2 = 2 × (2·x + 8)

7·x - 2 = 4·x + 16

7·x - 4·x = 16 + 2 = 18

3·x = 18

x = 18/3 = 6

x = 6

EF = 2·x + 8

Therefore; EF = 2 × 6 + 8 = 20

EF = 20

AB = 7·x - 2

Therefore; AB = 7 × 6 - 2 = 40

AB = 40

AB = AC = BC (Definition of an equilateral triangle)

Therefore;

AC = BC = AB = 40 (symmetric property)

The midpoints E and F, indicates that we get;

AE = CE and BF = CF

AC = AE + CE and BC = BF + CF (segment addition property)

Therefore; AC = AE + AE = 2 × AE

40 = 2 × AE

AE = 40/2 = 20

BC = 2 × BF

40 = 2 × BF

BF = 40/2 = 20

The perimeter of the trapezoid ABFE, P = AB + BF + EF + AE

P = 40 + 20 + 20 + 20 = 100

The perimeter of the trapezoid ABFE = 100 units

Second question

The coordinates of the vertices of the triangle are;

A(1, 2), B(-5, 3), and C(-6, -3)

The lengths of the sides of the triangle found using the distance formula are;

AB = √((-5 - 1)² + (3 - 2)²) = √(37)

BC = √((-6 - (-5))² + (-3 - 3)²) = √(37)

AC = √((-6 - 1)² + (-3 - 2)²) = √(74)

The lengths of the sides AB and BC in the triangle ΔABC are the same, therefore, the triangle ΔABC is an isosceles triangle.

Learn more on isosceles triangles here: https://brainly.com/question/2263856

#SPJ1

Which group shows all the numbers that are common factors of 24 and 30?
OA) 1, 2, 3, 4, 6
OB) 1, 2, 3, 6
OC) 1, 2, 3, 4
D) 1, 2, 3, 5, 6

Answers

Answer:

It should be OB, process of elimination helps a lot in questions like these

Seshni wants to cover six cushions, each measuring 36 cm x 36 cm, with fabric. She adds 1.5 cm extra for each seam. The fabric she wants to buy is 90 cm wide and costs R59,99/m excluding VAT. How much fabric must be bought to cover all six cushions? How much will the fabric cost, including VAT?​

Answers

If Seshni wants to cover six cushions, each measuring 36 cm x 36 cm, with fabric.  

a. Seshni needs to buy 0.84375 square meters of fabric.

b. It will cost R64.66 including VAT.

How to find the fabric cost ?

a. The dimensions of each cushion are 36 cm x 36 cm, and with the added 1.5 cm seam allowance, each cushion will require fabric with dimensions of (36 + 1.5) cm x (36 + 1.5) cm = 37.5 cm x 37.5 cm.

The total area of fabric required to cover all six cushions is:

6 cushions x (37.5 cm x 37.5 cm) = 8437.5 square centimeters

To convert to square meters, we need to divide by 10000:

8437.5 square centimeters / 10000 = 0.84375 square meters

So, Seshni needs to buy 0.84375 square meters of fabric.

b. Next, we can calculate the cost of the fabric.

0.84375 square meters / 0.9 meters = 0.9375 meters

The cost per meter is R59.99 excluding VAT, so the cost of the fabric is:

0.9375 meters x R59.99/meter = R56.23

To calculate the cost including VAT, we need to add the VAT amount. Assuming the VAT rate is 15%, the VAT amount is:

0.15 x R56.23 = R8.43

So the total cost including VAT is:

R56.23 + R8.43 = R64.66

Therefore, Seshni needs to buy 0.84375 square meters of fabric, and it will cost R64.66 including VAT.

Learn more about cost here:https://brainly.com/question/25109150

#SPJ1

A boy is older than his sister by 3years,find the percentage ages​

Answers

The present ages are the Boy is 17 years old and his sister's age is 14 years old.

Finding ages:  

Since the ratio of ages is 4: 3 take them as 4x and 3x and form an equation as given in the problem. Solve the resultant equation for the values of 'x'. And calculate the ages 5 years ago and add 5 to get the present ages.

Here we have

A boy is older than his sister by 3 years  

Then the difference is both ages = 3

Given that five years ago the ratio of ages = 4: 3  

Let 4x and 3x be the age of a boy and his sister five years

As we know the difference between them = 3 years

=> 4x - 3x = 3

=> x = 3 years

=> 4x = 4(3) = 12

Boy's age after '5' years = 12 + 5 = 17 years

His sister's age = 17 - 3 = 14 years

Therefore,

The present ages the Boy is 17 years old and his sister's age is 14 years old.

Learn more about Age problems at  

https://brainly.com/question/30375338

#SPJ1

Complete Question:

A boy is older than his sister by 3 years, five years ago the ratio was 4:3. Find his present age.

The population of Medway, Ohio, was 4,007 in 2000. It is expected to decrease by about 0.36% per year. Write an exponential decay function and use it to approximate the population in 2020.

Answers

The population of Medway, Ohio, is expected to be approximately 3728 in the year 2020.

How to determine the exponential decay function

From the question, we have the following parameters that can be used in our computation:

Initial, a = 4007

Rate = 0.36% per year

The decay function is represented as

y = a(1 - rate)^x

So, we have

y = 4007 * (1 - 0.36%)^x

This gives

y = 4007 * (0.9964)^x

The year 2020 is 20 years from 2000

So, we have

x = 20

Substitute the known values in the above equation, so, we have the following representation

y = 4007 * (0.9964)^20

Evaluate

y = 3728

Hence, the approximate solution is 3728

Read more about exponential function at

https://brainly.com/question/11464095

#SPJ1

The whole number n is such that n * (n+28) is a prime number. Find the prime number.

Answers

If the whole number n is such that n * (n+28) is a prime number.  the prime number is 29.

How to find the prime number?

We can start by expanding the expression n × (n+28) to get n^2 + 28n. Notice that n^2 + 28n is a quadratic expression that can be factored as n(n+28). Therefore, if n × (n+28) is a prime number, then n and n+28 must be either 1 and the prime number or the prime number and 1 (since a prime number has only two positive factors, 1 and itself).

If n = 1, then n+28 = 29, and n × (n+28) = 1 × 29 = 29, which is a prime number.

If n+28 = 1, then n = -27, which is not a whole number.

Therefore, the prime number in question is n × (n+28) = 29.

Learn more about prime number here:https://brainly.com/question/665631

#SPJ1

You pass through a particular stoplight on the way to school each morning. You have a 35% chance of catching the light red on any given day. In a three-day period:

a. What is the probability that you will catch the light red twice?
b. What is the probability that you catch the light red all three days?
c. what is the probability that you don’t catch the light red any of the three days?

Answers

To solve this problem, we can use the binomial distribution, which is a probability distribution that describes the number of successes in a fixed number of independent trials.

For each day, we have two possible outcomes: catching the light red (success) or not catching the light red (failure). The probability of success is 0.35 and the probability of failure is 0.65.

a. The probability of catching the light red twice in a three-day period can be calculated as follows:

P(catching red light twice) = (3 choose 2) * (0.35)^2 * (0.65)^1

where (3 choose 2) = 3! / (2! * (3 - 2)!) = 3 is the number of ways to choose 2 out of 3 days.

P(catching red light twice) = 0.44175

Therefore, the probability of catching the light red twice in a three-day period is 0.44175 or approximately 0.44.

b. The probability of catching the light red all three days can be calculated as follows:

P(catching red light all three days) = (0.35)^3

P(catching red light all three days) = 0.042875

Therefore, the probability of catching the light red all three days is 0.042875 or approximately 0.04.

c. The probability of not catching the light red any of the three days can be calculated as follows:

P(not catching red light any of the three days) = (0.65)^3

P(not catching red light any of the three days) = 0.274625

Therefore, the probability of not catching the light red any of the three days is 0.274625 or approximately 0.27.

What is the actual width, W, of the island if the width in the drawing is 2.5 inches? When given the length of a scale drawing and the length of the actual object, how can you find the scale factor?​

Answers

The width W of the island will be 3.75 ft by given scaling factor.

What exactly is scaling factor?

The Scale Factor is used to scale shapes in various dimensions. Geometry teaches us about various geometrical shapes in both two and three dimensions. The scale factor is a statistic for figures that seem similar but have different scales or measures. Imagine two circles have the same appearance but different radii.

The scale factor specifies how much larger or smaller a figure is than the original figure. With the use of a scale factor, you may design an expanded or smaller version of any original form.

Now,

Here given that 1 inch=1.5 ft

and as w=2.5 inches then the actual width W will be =2.5*1.5

=3.75 ft

and we can find scaling factor by  length of the actual object divided by length of scale drawing i.e.

S=length of object/length of drawing

hence,

          The width W of the island will be 3.75 ft.

To know more about scaling factor visit the link

https://brainly.com/question/30215119?referrer=searchResults

#SPJ1

How would the expression 2³ +64 be rewritten using Sum of Cubes?
OA. (2+4) (x² - 4x - 16)
OB. (x-4) (x² - 4x + 16)
O c. (x+4) (x² - 4x + 16)
OD. (x+4) (x² + 4x - 16)

Answers

Step-by-step explanation:

hence proved...

The answer mentioned in above pdf.

missing part is (. OC is correct option of cubic formula)...

what is unit circle calculator?

Answers

Answer:  In trigonometry, the unit circle has a radius of 1 and is centered at the origin. It’s useful for learning ratios like sine and cosine. It also illustrates the relationship between angles in degrees and radians.

Step-by-step explanation:

What is 2.3 as a fraction?

Answers

Answer:23/10

Step-by-step explanation:

you move the comma and  how many times you have to move it is how many zeros in the denominator

how to convert 178cm to inches?

Answers

The value after converting the length 178 cm  to inches , is 178 cm is equivalent to 70 inches .

The Centimeters (cm) and inches are both the units of measurement that  are used to measure length .

They both belong to different systems of measurement. Centimeters are used in the International System of Units (SI), whereas  inches are used in the Imperial and US Customary systems.

We know that 1 centimeter is = 0.3937 inches .

that means that conversion factor is 0.3937 ,

So , we can write ; 178 cm = 178 × 0.3937 inches ;

⇒ 178 cm = 70.0786 inches ≈ 70 inches .

Therefore , 178 cm is approximately equal to 70 inches .

Learn more about Conversion Factor here

https://brainly.com/question/16814684

#SPJ4

what is teh numpy matrix inverse?

Answers

The NumPy matrix inverse is a function that calculates the inverse of a given square matrix.

The NumPy matrix inverse function is a strategy that works out the opposite of a square grid involving the NumPy library in Python. The inverse of a matrix is a matrix that, when duplicated by the first grid, creates the identity matrix.

In NumPy, the matrix inverse function is executed as the linalg.inv() technique, which takes a NumPy cluster as information and returns its converse as an exhibit. The matrix should be square and invertible, the importance of its determinant isn't equivalent to nothing. The matrix inverse is utilized in different fields of math, designing, and science to solve systems of linear equations, track down the eigenvalues and eigenvectors of a network, and perform different procedure on matrices.

Learn more about numpy:

https://brainly.com/question/14105602

#SPJ4

Write an equation that describes the relationship between the number of square yards (x) of ground to be covered and the number of scoops (y) of bean seed needed. Your equation should be in the form y=kx.

The equation is:

Answers

Since we want the equation in the form y = kx, we need to find the value of k that will make this equation fellow to the bone we just wrote.

We can rewrite the equation as

y = ( m/ x) x b

Now, we can see that if we set k = m/ x, the equation will be in the form y = kx.

So, the equation that describes the relationship between the number of square yards( x) of ground to be covered and the number of scoops( y) of bean seed demanded is y = kx

where k = m/ x, and m and b are constants that depend on the specific situation.

To further about equation https//brainly.com/question/24169758

#SPJ1

What is the probability of at least one head in two coin tosses?

Answers

When tossing a fair coin, the possible outcomes are a head (H) or a tail (T), each with a probability of 1/2.

To find the probability of getting at least one head in two coin tosses, we can first find the probability of getting no heads (i.e., two tails) and then subtract that from 1 to get the probability of getting at least one head.

The probability of getting two tails is (1/2) * (1/2) = 1/4, since the probability of getting a tail on the first toss is 1/2 and the probability of getting a tail on the second toss is also 1/2, and we multiply these probabilities together to get the joint probability.

Therefore, the probability of getting at least one head in two coin tosses is:

1 - 1/4 = 3/4

So the probability of at least one head in two coin tosses is 3/4 or 0.75.

Learn more about probability here brainly.com/question/30034780

#SPJ4

how to find interior angles of a hexagon

Answers

The total of a hexagon's internal angles is 720 degrees.

The internal angles of a hexagon may be calculated using the formula "180 - (360/n)," where n is the number of sides. When you enter 6 for a hexagon, the response is 120 degrees.

We might begin by imagining a hexagon to better comprehend the notion. It is a basic design made up of six distinct straight lines that join to form a closed shape. The internal angles are the angles on the inside of the form.

The above-mentioned formula may be used to compute the internal angles of a hexagon. For each inner angle of a hexagon, the computation yields a value of 120 degrees. Hence the total of a hexagon's internal angles is 720 degrees.

Learn more about hexagons at

https://brainly.com/question/3295271

#SPJ4

Please, Help me with this question

Answers

Answer:

The quadratic equation [tex]2x^2-10x\:+\:27\:=\:-10[/tex] has no real roots

The two complex roots are:

[tex]x = 2.5 + 3.5 \, i\\\\and\\\\x = 2.5 - 3.5 \, i[/tex]

Step-by-step explanation:

There are no real root solutions to this quadratic equation

The quadratic formula for solving an equation of the standard form

[tex]ax^2 + bx + c = 0[/tex]

is given by


[tex]x = \dfrac{ -b \pm \sqrt{b^2 - 4ac}}{ 2a }[/tex]

The term under the square root is called the discriminant and determines the type number of roots(solutions) to the quadratic

When [tex]b^2 - 4ac=0[/tex] there is one real root.When [tex]b^2 - 4ac > 0[/tex]  there are two real roots.When [tex]b^2 - 4ac < 0[/tex] there are no real roots - roots are complex

The given quadratic equation is
[tex]2x^2-10x\:+\:27\:=\:-10[/tex]

Add 10 to both sides:
[tex]2x^2-10x\:+\:37\:=0[/tex]

Comparing to the standard form we see
a = 2, b = -10, c = 37

The discriminant is
[tex]b^2 - 4ac = (-10)^2 - 4\cdot2\cdot 37\\= 100 - 296\\= -196[/tex]

Since the discriminant is negative both roots will be comples
[tex]x = \dfrac{ -b \pm \sqrt{b^2 - 4ac}}{ 2a }\\\\x = \dfrac{ -(-10) \pm \sqrt{(-10)^2 - 4(2)(37)}}{ 2(2) }\\\\x = \dfrac{ 10 \pm \sqrt{100 - 296}}{ 4 }\\\\x = \dfrac{ 10 \pm \sqrt{-196}}{ 4 }[/tex]

[tex]\text {To find $\sqrt{-196}$}[/tex]

[tex]\sqrt{-196} = \sqrt{196}\sqrt{-1} =\sqrt{196}\;i[/tex]

where i = [tex]\sqrt{-1}[/tex]

We have

[tex]\sqrt{196} = 14\\\\So\\\\\sqrt{-196} = 14i[/tex]

The solutions are

[tex]x = \dfrac{ 10 \pm 14\, i}{ 4 }[/tex]

[tex]x = \dfrac{ 10 }{ 4 } \pm \dfrac{14\, i}{ 4 }[/tex]

[tex]x = \dfrac{ 5}{ 2 } \pm \dfrac{ 7\, i}{ 2 }[/tex]

[tex]x = 2.5 \pm 3.5i[/tex]

The two complex solutions are:

[tex]x = 2.5 + 3.5 \, i\\\\and\\\\x = 2.5 - 3.5 \, i[/tex]

At Luehrs Middle School, 112 sixth-grade students have a dog as a pet; this represents 35% of the sixth-grade students. How many sixth-grade students are at Luehrs Middle School? Responses

Answers

Answer:

its 320

Step-by-step explanation:

The total number of many sixth-grade students at Luehrs Middle School found using the percentage is 320.

What is meant by percentage?

A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100. The proportion, therefore, refers to a component per hundred. Per 100 is what the word percent means. There is no dimension to percentages. As a result, it is known as a dimensionless number.

Given,

Number of students in sixth grade who has a pet dog = 112

The percentage of sixth grade students who has a pet dog = 35%

Let the number of total sixth grade students be x.

Percentage

= (Number of students with pet dog/Total number of sixth grade students *    100

35 = (112/x) * 100

35/100 = 112/x

x = (100/35) * 112 = 320

Therefore the total number of many sixth-grade students at Luehrs Middle School found using the percentage is 320.

To learn more about percentages, follow the link.

https://brainly.com/question/24877689

#SPJ1

Describe the relationship between x and y in the equation y=x+6.
Choose the correct answer from each drop-down menu to complete the statement.

The relationship is
because the value of y is
the value of x.

Answers

Answer:

The relationship is additive because the value of y is 6 more than the value of x

Step-by-step explanation:

did the test and there's a plus sign in the equation so y would be 6 more than the value of x

The relationship between x and y in the equation y = x + 6, is Linear relationship, because the value of y can be represented in a straight line.

What is an equation?

An equation consists of numbers and variables linked together by mathematical operations to form an expression.

A linear equation is in the form:

y = mx + b

Where m is the rate of change and b is the initial value

Given the equation:

y = x + 6

This is a linear equation.

The slope is 1 and the initial value (y intercept) is 6

Hence, the relationship between x and y in the equation y = x + 6, is Linear relationship.

Learn more on equation at: brainly.com/question/2972832

#SPJ7

Other Questions
a real estate broker who acts as a dual agent and represent both the buyer and the seller in the same transaction must make sure that both parties What word best describes the writer's TONE in the poem, "Sympath" how was gregorian chant transferred between communities before printing machines were used in 1473 to publish complete music pages?' refer to the above table. if the price of a hamburger falls from $5 to $4, then the weekly market quantity of hamburgers supplied will What is the ICD code for cervical radiculopathy? _____ holds that individuals must decide what is ethical based on their own feelings about what is right and wrong. which condition is the most common symptom of chronic salicxylate intoxication in adults How to convert 64kg to pounds? the idea of a criminal justice nonsystem, in which different criminal justice agencies are more self-serving and focus more on performance measures than on justice, is the basis of the ________. 2.3 Discuss TWO reasons why each of the sustaining positive relationship a. Understanding others b. Communicating feelings, beliefs c. Attitudes d. Acceptance of responsibility eat of the following (3x2) (6) are important in initiating and FATHER Each task in MS Project has a unique identifier called Task ID, a sequential number and is not affected by:A. Inserting TasksO B. Moving TasksOC. Deleting TasksOD. Indenting Tasks This person wrote proudly of black people in books, poems, and plays.answer choices.A.Lil Uzi Vert.B.Langston Hughes.C.Frederick Douglas.D.Louis Armstrong. Which of these companies is taking advantage of the globalization of production?a.ABC Fabrics, an American textile manufacturer, buys fabric from France and exports it to India for garment production.b. DEF Group, a U.S.-based fashion designer, is planning to open a flagship store in China to serve the Asian market.c. GH Waters, a U.K. facial products company, serves customers worldwide through its local franchises.d. IJK Inc. uses sales personnel from the respective host country to sell its products and services.e. LMNO Pie, an Italian pizza chain, customizes its pizzas and pastas to suit the tastes of its American and Australian customers. Question content area topPart 1The intensity of a sound is given by II0100.1L, where L is the loudness of the sound as measured in decibels and I0 is the minimum intensity detectable by the human ear.a) Find I, in terms of I0, for the loudness of a small engine, which is decibels.b) Find I, in terms of I0, for the loudness of a quiet sound, which is decibels.c) Compare your answers to parts (a) and (b).d) Find the rate of change dI/dL.e) Interpret the meaning of dI/dL On March 17, Advanced Technologies purchased a patent related to laser surgery techniques. The purchase price of the patent is $1,250,000. The patent is expected to benefit the company for the next five years. The company had the following additional costs: $25,000 in legal fees associated with the purchase and filing of the patent, $40,000 to advertise its new laser surgery techniques, and $50,000 to train employees. None of these additional costs were included in the purchase price or paid to the seller. Now assume that instead of purchasing the patent, Advanced Technologies spent $1,250,000 to develop the patent internally, consisting of personnel ($825,000), equipment ($315,000), and materials ($110,000). All additional costs were incurred for the same amount.What is the recorded cost of the patent? How do you cite in APA a website with no author? How do you write an APA citation page? The pure expectations theory assumes that a one-year bond purchased today will have the same return as a one-Year bond purchased five years from now.a. Falseb. True what name is given to the following reaction? disaccharide water monosaccharide monosaccharide What happens to interest earned if the annuitant dies before the payout start date?A. It is taxableB. It is taxable only if no beneficiary is namedC. It is not taxableD. It is only taxable if contract has been in force under one year